Ellen Kuhl

All Publications

Mechanical characterization of human brain tissue ACTA BIOMATERIALIA Budday, S., Sommer, G., Birkl, C., Langkammer, C., Haybaeck, J., Kohnert, J., Bauer, M., Paulsen, F., Steinmann, P., Kuhl, E., Holzapfel, G. A. 2017; 48: 319-340
Abstract

Mechanics are increasingly recognized to play an important role in modulating brain form and function. Computational simulations are a powerful tool to predict the mechanical behavior of the human brain in health and disease. The success of these simulations depends critically on the underlying constitutive model and on the reliable identification of its material parameters. Thus, there is an urgent need to thoroughly characterize the mechanical behavior of brain tissue and to identify mathematical models that capture the tissue response under arbitrary loading conditions. However, most constitutive models have only been calibrated for a single loading mode. Here, we perform a sequence of multiple loading modes on the same human brain specimen - simple shear in two orthogonal directions, compression, and tension - and characterize the loading-mode specific regional and directional behavior. We complement these three individual tests by combined multiaxial compression/tension-shear tests and discuss effects of conditioning and hysteresis. To explore to which extent the macrostructural response is a result of the underlying microstructural architecture, we supplement our biomechanical tests with diffusion tensor imaging and histology. We show that the heterogeneous microstructure leads to a regional but not directional dependence of the mechanical properties. Our experiments confirm that human brain tissue is nonlinear and viscoelastic, with a pronounced compression-tension asymmetry. Using our measurements, we compare the performance of five common constitutive models, neo-Hookean, Mooney-Rivlin, Demiray, Gent, and Ogden, and show that only the isotropic modified one-term Ogden model is capable of representing the hyperelastic behavior under combined shear, compression, and tension loadings: with a shear modulus of 0.4-1.4kPa and a negative nonlinearity parameter it captures the compression-tension asymmetry and the increase in shear stress under superimposed compression but not tension. Our results demonstrate that material parameters identified for a single loading mode fail to predict the response under arbitrary loading conditions. Our systematic characterization of human brain tissue will lead to more accurate computational simulations, which will allow us to determine criteria for injury, to develop smart protection systems, and to predict brain development and disease progression.There is a pressing need to characterize the mechanical behavior of human brain tissue under multiple loading conditions, and to identify constitutive models that are able to capture the tissue response under these conditions. We perform a sequence of experimental tests on the same brain specimen to characterize the regional and directional behavior, and we supplement our tests with DTI and histology to explore to which extent the macrostructural response is a result of the underlying microstructure. Results demonstrate that human brain tissue is nonlinear and viscoelastic, with a pronounced compression-tension asymmetry, and we show that the multiaxial data can best be captured by a modified version of the one-term Ogden model.

View details for DOI 10.1016/j.actbio.2016.10.036

View details for Web of Science ID 000393247000027

View details for PubMedID 27989920
Biophysics: Unfolding the brain Nature Physics Kuhl, E. 2016
View details for DOI 10.1038/nphys3641
Tau-ism: The Yin and Yang of Microtubule Sliding, Detachment, and Rupture BIOPHYSICAL JOURNAL van den Bedem, H., Kuhl, E. 2015; 109 (11): 2215-2217
View details for DOI 10.1016/j.bpj.2015.10.020

View details for Web of Science ID 000365929500001
Physical biology of human brain development FRONTIERS IN CELLULAR NEUROSCIENCE Budday, S., Steinmann, P., Kuhl, E. 2015; 9
Abstract

Neurodevelopment is a complex, dynamic process that involves a precisely orchestrated sequence of genetic, environmental, biochemical, and physical events. Developmental biology and genetics have shaped our understanding of the molecular and cellular mechanisms during neurodevelopment. Recent studies suggest that physical forces play a central role in translating these cellular mechanisms into the complex surface morphology of the human brain. However, the precise impact of neuronal differentiation, migration, and connection on the physical forces during cortical folding remains unknown. Here we review the cellular mechanisms of neurodevelopment with a view toward surface morphogenesis, pattern selection, and evolution of shape. We revisit cortical folding as the instability problem of constrained differential growth in a multi-layered system. To identify the contributing factors of differential growth, we map out the timeline of neurodevelopment in humans and highlight the cellular events associated with extreme radial and tangential expansion. We demonstrate how computational modeling of differential growth can bridge the scales-from phenomena on the cellular level toward form and function on the organ level-to make quantitative, personalized predictions. Physics-based models can quantify cortical stresses, identify critical folding conditions, rationalize pattern selection, and predict gyral wavelengths and gyrification indices. We illustrate that physical forces can explain cortical malformations as emergent properties of developmental disorders. Combining biology and physics holds promise to advance our understanding of human brain development and enable early diagnostics of cortical malformations with the ultimate goal to improve treatment of neurodevelopmental disorders including epilepsy, autism spectrum disorders, and schizophrenia.

View details for DOI 10.3389/fncel.2015.00257

View details for Web of Science ID 000357831600001

View details for PubMedID 26217183
Mechanical properties of gray and white matter brain tissue by indentation. Journal of the mechanical behavior of biomedical materials Budday, S., Nay, R., de Rooij, R., Steinmann, P., Wyrobek, T., Ovaert, T. C., Kuhl, E. 2015; 46: 318-330
View details for DOI 10.1016/j.jmbbm.2015.02.024

View details for PubMedID 25819199
The Living Heart Project: A robust and integrative simulator for human heart function EUROPEAN JOURNAL OF MECHANICS A-SOLIDS Baillargeon, B., Rebelo, N., Fox, D. D., Taylor, R. L., Kuhl, E. 2014; 48: 38-47
View details for DOI 10.1016/j.euromechsol.2014.04.001

View details for Web of Science ID 000342879100005
A mechanical model predicts morphological abnormalities in the developing human brain SCIENTIFIC REPORTS Budday, S., Raybaud, C., Kuhl, E. 2014; 4
Abstract

The developing human brain remains one of the few unsolved mysteries of science. Advancements in developmental biology, neuroscience, and medical imaging have brought us closer than ever to understand brain development in health and disease. However, the precise role of mechanics throughout this process remains underestimated and poorly understood. Here we show that mechanical stretch plays a crucial role in brain development. Using the nonlinear field theories of mechanics supplemented by the theory of finite growth, we model the human brain as a living system with a morphogenetically growing outer surface and a stretch-driven growing inner core. This approach seamlessly integrates the two popular but competing hypotheses for cortical folding: axonal tension and differential growth. We calibrate our model using magnetic resonance images from very preterm neonates. Our model predicts that deviations in cortical growth and thickness induce morphological abnormalities. Using the gyrification index, the ratio between the total and exposed surface area, we demonstrate that these abnormalities agree with the classical pathologies of lissencephaly and polymicrogyria. Understanding the mechanisms of cortical folding in the developing human brain has direct implications in the diagnostics and treatment of neurological disorders, including epilepsy, schizophrenia, and autism.

View details for DOI 10.1038/srep05644

View details for Web of Science ID 000338763700006

View details for PubMedID 25008163
Wrinkling instabilities in soft bilayered systems PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES Budday, S., Andres, S., Walter, B., Steinmann, P., Kuhl, E. 2017; 375 (2093)
Abstract

Wrinkling phenomena control the surface morphology of many technical and biological systems. While primary wrinkling has been extensively studied, experimentally, analytically and computationally, higher-order instabilities remain insufficiently understood, especially in systems with stiffness contrasts well below 100. Here, we use the model system of an elastomeric bilayer to experimentally characterize primary and secondary wrinkling at moderate stiffness contrasts. We systematically vary the film thickness and substrate prestretch to explore which parameters modulate the emergence of secondary instabilities, including period-doubling, period-tripling and wrinkle-to-fold transitions. Our experiments suggest that period-doubling is the favourable secondary instability mode and that period-tripling can emerge under disturbed boundary conditions. High substrate prestretch can suppress period-doubling and primary wrinkles immediately transform into folds. We combine analytical models with computational simulations to predict the onset of primary wrinkling, the post-buckling behaviour, secondary bifurcations and the wrinkle-to-fold transition. Understanding the mechanisms of pattern selection and identifying the critical control parameters of wrinkling will allow us to fabricate smart surfaces with tunable properties and to control undesired surface patterns like in the asthmatic airway.This article is part of the themed issue 'Patterning through instabilities in complex media: theory and applications.'

View details for DOI 10.1098/rsta.2016.0163

View details for Web of Science ID 000398215500009

View details for PubMedID 28373385
The mechanical importance of myelination in the central nervous system. Journal of the mechanical behavior of biomedical materials Weickenmeier, J., de Rooij, R., Budday, S., Ovaert, T. C., Kuhl, E. 2017
Abstract

Neurons in the central nervous system are surrounded and cross-linked by myelin, a fatty white substance that wraps around axons to create an electrically insulating layer. The electrical function of myelin is widely recognized; yet, its mechanical importance remains underestimated. Here we combined nanoindentation testing and histological staining to correlate brain stiffness to the degree of myelination in immature, pre-natal brains and mature, post-natal brains. We found that both gray and white matter tissue stiffened significantly (p≪0.001) upon maturation: the gray matter stiffness doubled from 0.31±0.20kPa pre-natally to 0.68±0.20kPa post-natally; the white matter stiffness tripled from 0.45±0.18kPa pre-natally to 1.33±0.64kPa post-natally. At the same time, the white matter myelin content increased significantly (p≪0.001) from 58±2% to 74±9%. White matter stiffness and myelin content were correlated with a Pearson correlation coefficient of ρ=0.92 (p≪0.001). Our study suggests that myelin is not only important to ensure smooth electrical signal propagation in neurons, but also to protect neurons against physical forces and provide a strong microstructural network that stiffens the white matter tissue as a whole. Our results suggest that brain tissue stiffness could serve as a biomarker for multiple sclerosis and other forms of demyelinating disorders. Understanding how tissue maturation translates into changes in mechanical properties and knowing the precise brain stiffness at different stages of life has important medical implications in development, aging, and neurodegeneration.

View details for DOI 10.1016/j.jmbbm.2017.04.017

View details for PubMedID 28462864
Quantification of Strain in a Porcine Model of Skin Expansion Using Multi-View Stereo and Isogeometric Kinematics JOVE-JOURNAL OF VISUALIZED EXPERIMENTS Tepole, A. B., Vaca, E. E., Purnell, C. A., Gart, M., McGrath, J., Kuhl, E., Gosain, A. K. 2017
Abstract

Tissue expansion is a popular technique in plastic and reconstructive surgery that grows skin in vivo for correction of large defects such as burns and giant congenital nevi. Despite its widespread use, planning and executing an expansion protocol is challenging due to the difficulty in measuring the deformation imposed at each inflation step and over the length of the procedure. Quantifying the deformation fields is crucial, as the distribution of stretch over time determines the rate and amount of skin grown at the end of the treatment. In this manuscript, we present a method to study tissue expansion in order to gain quantitative knowledge of the deformations induced during an expansion process. This experimental protocol incorporates multi-view stereo and isogeometric kinematic analysis in a porcine model of tissue expansion. Multi-view stereo allows three-dimensional geometric reconstruction from uncalibrated sequences of images. The isogeometric kinematic analysis uses splines to describe the regional deformations between smooth surfaces with few mesh points. Our protocol has the potential to bridge the gap between basic scientific inquiry regarding the mechanics of skin expansion and the clinical setting. Eventually, we expect that the knowledge gained with our methodology will enable treatment planning using computational simulations of skin deformation in a personalized manner.

View details for DOI 10.3791/55052

View details for Web of Science ID 000401077600013

View details for PubMedID 28448015
Modeling molecular mechanisms in the axon COMPUTATIONAL MECHANICS de Rooij, R., Miller, K. E., Kuhl, E. 2017; 59 (3): 523-537
View details for DOI 10.1007/s00466-016-1359-y

View details for Web of Science ID 000394999900009
A virtual sizing tool for mitral valve annuloplasty. International journal for numerical methods in biomedical engineering Rausch, M. K., Zöllner, A. M., Genet, M., Baillargeon, B., Bothe, W., Kuhl, E. 2017; 33 (2)
Abstract

Functional mitral regurgitation, a backward leakage of the mitral valve, is a result of left ventricular growth and mitral annular dilatation. Its gold standard treatment is mitral annuloplasty, the surgical reduction in mitral annular area through the implantation of annuloplasty rings. Recurrent regurgitation rates may, however, be as high as 30% and more. While the degree of annular downsizing has been linked to improved long-term outcomes, too aggressive downsizing increases the risk of ring dehiscences and significantly impairs repair durability. Here, we prototype a virtual sizing tool to quantify changes in annular dimensions, surgically induced tissue strains, mitral annular stretches, and suture forces in response to mitral annuloplasty. We create a computational model of dilated cardiomyopathy onto which we virtually implant annuloplasty rings of different sizes. Our simulations confirm the common intuition that smaller rings are more invasive to the surrounding tissue, induce higher strains, and require larger suture forces than larger rings: The total suture force was 2.2 N for a 24-mm ring, 1.9 N for a 28-mm ring, and 0.8 N for a 32-mm ring. Our model predicts the highest risk of dehiscence in the septal and postero-lateral annulus where suture forces are maximal. These regions co-localize with regional peaks in myocardial strain and annular stretch. Our study illustrates the potential of realistic predictive simulations in cardiac surgery to identify areas at risk for dehiscence, guide the selection of ring size and shape, rationalize the design of smart annuloplasty rings and, ultimately, improve long-term outcomes after surgical mitral annuloplasty. Copyright © 2016 John Wiley & Sons, Ltd.

View details for DOI 10.1002/cnm.2788

View details for PubMedID 27028496
The mechanics of decompressive craniectomy: Personalized simulations COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING Weickenmeier, J., Butler, C. A., Young, P. G., Goriely, A., Kuhl, E. 2017; 314: 180-195
View details for DOI 10.1016/j.cma.2016.08.011

View details for Web of Science ID 000392782900011
Instabilities of soft films on compliant substrates JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS Holland, M. A., Li, B., Feng, X. Q., Kuhl, E. 2017; 98: 350-365
View details for DOI 10.1016/j.jmps.2016.09.012

View details for Web of Science ID 000390972900019
The mechanics of decompressive craniectomy: Bulging in idealized geometries JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS Weickenmeier, J., Kuhl, E., Goriely, A. 2016; 96: 572-590
View details for DOI 10.1016/j.jmps.2016.08.009

View details for Web of Science ID 000386744600032
Stress Singularities in Swelling Soft Solids PHYSICAL REVIEW LETTERS Goriely, A., Weickenmeier, J., Kuhl, E. 2016; 117 (13)
Abstract

When a swelling soft solid is rigidly constrained on all sides except for a circular opening, it will bulge out to expand as observed during decompressive craniectomy, a surgical procedure used to reduce stresses in swollen brains. While the elastic energy of the solid decreases throughout this process, large stresses develop close to the opening. At the point of contact, the stresses exhibit a singularity similar to the ones found in the classic punch indentation problem. Here, we study the stresses generated by swelling and the evolution of the bulging shape associated with this process. We also consider the possibility of damage triggered by zones of either high shear stresses or high fiber stretches.

View details for DOI 10.1103/PhysRevLett.117.138001

View details for Web of Science ID 000383851000021

View details for PubMedID 27715096
Brain stiffness increases with myelin content. Acta biomaterialia Weickenmeier, J., de Rooij, R., Budday, S., Steinmann, P., Ovaert, T. C., Kuhl, E. 2016; 42: 265-272
Abstract

Brain stiffness plays an important role in neuronal development and disease, but reported stiffness values vary significantly for different species, for different brains, and even for different regions within the same brain. Despite extensive research throughout the past decade, the mechanistic origin of these stiffness variations remains elusive. Here we show that brain tissue stiffness is correlated to the underlying tissue microstructure and directly proportional to the local myelin content. In 116 indentation tests of six freshly harvested bovine brains, we found that the cerebral stiffnesses of 1.33±0.63kPa in white matter and 0.68±0.20kPa in gray matter were significantly different (p<0.01). Strikingly, while the inter-specimen variation was rather moderate, the minimum and maximum cerebral white matter stiffnesses of 0.59±0.19 kPa and 2.36±0.64kPa in each brain varied by a factor of four on average. To provide a mechanistic interpretation for this variation, we performed a histological characterization of the tested brain regions. We stained the samples with hematoxylin and eosin and luxol fast blue and quantified the local myelin content using image analysis. Interestingly, we found that the cerebral white matter stiffness increased with increasing myelin content, from 0.72kPa at a myelin content of 64-2.45kPa at a myelin content of 89%, with a Pearson correlation coefficient of ρ=0.91 (p<0.01). This direct correlation could have significant neurological implications. During development, our results could help explain why immature, incompletely myelinated brains are softer than mature, myelinated brains and more vulnerable to mechanical insult as evident, for example, in shaken baby syndrome. During demyelinating disease, our findings suggest to use stiffness alterations as clinical markers for demyelination to quantify the onset of disease progression, for example, in multiple sclerosis. Taken together, our study indicates that myelin might play a more important function than previously thought: It not only insulates signal propagation and improves electrical function of single axons, it also provides structural support and mechanical stiffness to the brain as a whole.Increasing evidence suggests that the mechanical environment of the brain plays an important role in neuronal development and disease. Reported stiffness values vary significantly, but the origin of these variations remains unknown. Here we show that stiffness of our brain is correlated to the underlying tissue microstructure and directly proportional to the local myelin content. Myelin has been discovered in 1854 as an insulating layer around nerve cells to improve electric signal propagation. Our study now shows that it also plays an important mechanical role: Using a combined mechanical characterization and histological characterization, we found that the white matter stiffness increases linearly with increasing myelin content, from 0.5kPa at a myelin content of 63-2.5kPa at 92%.

View details for DOI 10.1016/j.actbio.2016.07.040

View details for PubMedID 27475531
Elastosis during airway wall remodeling explains multiple co-existing instability patterns JOURNAL OF THEORETICAL BIOLOGY Eskandari, M., Javili, A., Kuhl, E. 2016; 403: 209-218
Abstract

Living structures can undergo morphological changes in response to growth and alterations in microstructural properties in response to remodeling. From a biological perspective, airway wall inflammation and airway elastosis are classical hallmarks of growth and remodeling during chronic lung disease. From a mechanical point of view, growth and remodeling trigger mechanical instabilities that result in inward folding and airway obstruction. While previous analytical and computational studies have focused on identifying the critical parameters at the onset of folding, few have considered the post-buckling behavior. All prior studies assume constant microstructural properties during the folding process; yet, clinical studies now reveal progressive airway elastosis, the degeneration of elastic fibers associated with a gradual stiffening of the inner layer. Here, we explore the influence of temporally evolving material properties on the post-bifurcation behavior of the airway wall. We show that a growing and stiffening inner layer triggers an additional subsequent bifurcation after the first instability occurs. Evolving material stiffnesses provoke failure modes with multiple co-existing wavelengths, associated with the superposition of larger folds evolving on top of the initial smaller folds. This phenomenon is exclusive to material stiffening and conceptually different from the phenomenon of period doubling observed in constant-stiffness growth. Our study suggests that the clinically observed multiple wavelengths in diseased airways are a result of gradual airway wall stiffening. While our evolving material properties are inspired by the clinical phenomenon of airway elastosis, the underlying concept is broadly applicable to other types of remodeling including aneurysm formation or brain folding.

View details for DOI 10.1016/j.jtbi.2016.05.022

View details for Web of Science ID 000378987100019

View details for PubMedID 27211101
Generating Purkinje networks in the human heart. Journal of biomechanics Sahli Costabal, F., Hurtado, D. E., Kuhl, E. 2016; 49 (12): 2455-2465
Abstract

The Purkinje network is an integral part of the excitation system in the human heart. Yet, to date, there is no in vivo imaging technique to accurately reconstruct its geometry and structure. Computational modeling of the Purkinje network is increasingly recognized as an alternative strategy to visualize, simulate, and understand the role of the Purkinje system. However, most computational models either have to be generated manually, or fail to smoothly cover the irregular surfaces inside the left and right ventricles. Here we present a new algorithm to reliably create robust Purkinje networks within the human heart. We made the source code of this algorithm freely available online. Using Monte Carlo simulations, we demonstrate that the fractal tree algorithm with our new projection method generates denser and more compact Purkinje networks than previous approaches on irregular surfaces. Under similar conditions, our algorithm generates a network with 1219±61 branches, three times more than a conventional algorithm with 419±107 branches. With a coverage of 11±3mm, the surface density of our new Purkije network is twice as dense as the conventional network with 22±7mm. To demonstrate the importance of a dense Purkinje network in cardiac electrophysiology, we simulated three cases of excitation: with our new Purkinje network, with left-sided Purkinje network, and without Purkinje network. Simulations with our new Purkinje network predicted more realistic activation sequences and activation times than simulations without. Six-lead electrocardiograms of the three case studies agreed with the clinical electrocardiograms under physiological conditions, under pathological conditions of right bundle branch block, and under pathological conditions of trifascicular block. Taken together, our results underpin the importance of the Purkinje network in realistic human heart simulations. Human heart modeling has the potential to support the design of personalized strategies for single- or bi-ventricular pacing, radiofrequency ablation, and cardiac defibrillation with the common goal to restore a normal heart rhythm.

View details for DOI 10.1016/j.jbiomech.2015.12.025

View details for PubMedID 26748729
Generating Purkinje networks in the human heart JOURNAL OF BIOMECHANICS Costabal, F. S., Hurtado, D. E., Kuhl, E. 2016; 49 (12): 2455-2465
View details for DOI 10.1016/j.jbiomech.2015.12.025

View details for Web of Science ID 000384857800018
Partial LVAD restores ventricular outputs and normalizes LV but not RV stress distributions in the acutely failing heart in silico INTERNATIONAL JOURNAL OF ARTIFICIAL ORGANS Sack, K. L., Baillargeon, B., Acevedo-Bolton, G., Genet, M., Rebelo, N., Kuhl, E., Klein, L., Weiselthaler, G. M., Burkhoff, D., Franz, T., Guccione, J. M. 2016; 39 (8): 421-430
Abstract

Heart failure is a worldwide epidemic that is unlikely to change as the population ages and life expectancy increases. We sought to detail significant recent improvements to the Dassault Systèmes Living Heart Model (LHM) and use the LHM to compute left ventricular (LV) and right ventricular (RV) myofiber stress distributions under the following 4 conditions: (1) normal cardiac function; (2) acute left heart failure (ALHF); (3) ALHF treated using an LV assist device (LVAD) flow rate of 2 L/min; and (4) ALHF treated using an LVAD flow rate of 4.5 L/min.Incorporating improved systolic myocardial material properties in the LHM resulted in its ability to simulate the Frank-Starling law of the heart. We decreased myocardial contractility in the LV myocardium so that LV ejection fraction decreased from 56% to 28%. This caused mean LV end diastolic (ED) stress to increase to 508% of normal, mean LV end systolic (ES) stress to increase to 113% of normal, mean RV ED stress to decrease to 94% of normal and RV ES to increase to 570% of normal. When ALHF in the model was treated with an LVAD flow rate of 4.5 L/min, most stress results normalized. Mean LV ED stress became 85% of normal, mean LV ES stress became 109% of normal and mean RV ED stress became 95% of normal. However, mean RV ES stress improved less dramatically (to 342% of normal values).These simulations strongly suggest that an LVAD is effective in normalizing LV stresses but not RV stresses that become elevated as a result of ALHF.

View details for DOI 10.5301/ijao.5000520

View details for Web of Science ID 000388286900004

View details for PubMedID 27646633
Computational modeling of acute myocardial infarction COMPUTER METHODS IN BIOMECHANICS AND BIOMEDICAL ENGINEERING Saez, P., Kuhl, E. 2016; 19 (10): 1107-1115
Abstract

Myocardial infarction, commonly known as heart attack, is caused by reduced blood supply and damages the heart muscle because of a lack of oxygen. Myocardial infarction initiates a cascade of biochemical and mechanical events. In the early stages, cardiomyocytes death, wall thinning, collagen degradation, and ventricular dilation are the immediate consequences of myocardial infarction. In the later stages, collagenous scar formation in the infarcted zone and hypertrophy of the non-infarcted zone are auto-regulatory mechanisms to partly correct for these events. Here we propose a computational model for the short-term adaptation after myocardial infarction using the continuum theory of multiplicative growth. Our model captures the effects of cell death initiating wall thinning, and collagen degradation initiating ventricular dilation. Our simulations agree well with clinical observations in early myocardial infarction. They represent a first step toward simulating the progression of myocardial infarction with the ultimate goal to predict the propensity toward heart failure as a function of infarct intensity, location, and size.

View details for DOI 10.1080/10255842.2015.1105965

View details for Web of Science ID 000373937700009

View details for PubMedID 26583449
Using 3D Printing to Create Personalized Brain Models for Neurosurgical Training and Preoperative Planning. World neurosurgery Ploch, C. C., Mansi, C. S., Jayamohan, J., Kuhl, E. 2016; 90: 668-674
Abstract

Three-dimensional (3D) printing holds promise for a wide variety of biomedical applications, from surgical planning, practicing, and teaching to creating implantable devices. The growth of this cheap and easy additive manufacturing technology in orthopedic, plastic, and vascular surgery has been explosive; however, its potential in the field of neurosurgery remains underexplored. A major limitation is that current technologies are unable to directly print ultrasoft materials like human brain tissue.In this technical note, the authors present a new technology to create deformable, personalized models of the human brain.The method combines 3D printing, molding, and casting to create a physiologically, anatomically, and tactilely realistic model based on magnetic resonance images. Created from soft gelatin, the model is easy to produce, cost-efficient, durable, and orders of magnitude softer than conventionally printed 3D models. The personalized brain model cost $50, and its fabrication took 24 hours.In mechanical tests, the model stiffness (E = 25.29 ± 2.68 kPa) was 5 orders of magnitude softer than common 3D printed materials, and less than an order of magnitude stiffer than mammalian brain tissue (E = 2.64 ± 0.40 kPa). In a multicenter surgical survey, model size (100.00%), visual appearance (83.33%), and surgical anatomy (81.25%) were perceived as very realistic. The model was perceived as very useful for patient illustration (85.00%), teaching (94.44%), learning (100.00%), surgical training (95.00%), and preoperative planning (95.00%).With minor refinements, personalized, deformable brain models created via 3D printing will improve surgical training and preoperative planning with the ultimate goal to provide accurate, customized, high-precision treatment.

View details for DOI 10.1016/j.wneu.2016.02.081

View details for PubMedID 26924117
The Incompatibility of Living Systems: Characterizing Growth-Induced Incompatibilities in Expanded Skin ANNALS OF BIOMEDICAL ENGINEERING Tepole, A. B., Gart, M., Purnell, C. A., Gosain, A. K., Kuhl, E. 2016; 44 (5): 1734-1752
Abstract

Skin expansion is a common surgical technique to correct large cutaneous defects. Selecting a successful expansion protocol is solely based on the experience and personal preference of the operating surgeon. Skin expansion could be improved by predictive computational simulations. Towards this goal, we model skin expansion using the continuum framework of finite growth. This approach crucially relies on the concept of incompatible configurations. However, aside from the classical opening angle experiment, our current understanding of growth-induced incompatibilities remains rather vague. Here we visualize and characterize incompatibilities in living systems using skin expansion in a porcine model: We implanted and inflated two expanders, crescent, and spherical, and filled them to 225 cc throughout a period of 21 days. To quantify the residual strains developed during this period, we excised the expanded skin patches and subdivided them into smaller pieces. Skin growth averaged 1.17 times the original area for the spherical and 1.10 for the crescent expander, and displayed significant regional variations. When subdivided into smaller pieces, the grown skin patches retracted heterogeneously and confirmed the existence of incompatibilities. Understanding skin growth through mechanical stretch will allow surgeons to improve-and ultimately personalize-preoperative treatment planning in plastic and reconstructive surgery.

View details for DOI 10.1007/s10439-015-1467-4

View details for Web of Science ID 000374665900032

View details for PubMedID 26416721
Computational modeling of chemo-bio-mechanical coupling: a systems-biology approach toward wound healing COMPUTER METHODS IN BIOMECHANICS AND BIOMEDICAL ENGINEERING Tepole, A. B., Kuhl, E. 2016; 19 (1): 13-30
View details for DOI 10.1080/10255842.2014.980821

View details for Web of Science ID 000363870900002

View details for PubMedID 25421487
Tri-layer wrinkling as a mechanism for anchoring center initiation in the developing cerebellum SOFT MATTER Lejeune, E., Javili, A., Weickenmeier, J., Kuhl, E., Linder, C. 2016; 12 (25): 5613-5620
Abstract

During cerebellar development, anchoring centers form at the base of each fissure and remain fixed in place while the rest of the cerebellum grows outward. Cerebellar foliation has been extensively studied; yet, the mechanisms that control anchoring center initiation and position remain insufficiently understood. Here we show that a tri-layer model can predict surface wrinkling as a potential mechanism to explain anchoring center initiation and position. Motivated by the cerebellar microstructure, we model the developing cerebellum as a tri-layer system with an external molecular layer and an internal granular layer of similar stiffness and a significantly softer intermediate Purkinje cell layer. Including a weak intermediate layer proves key to predicting surface morphogenesis, even at low stiffness contrasts between the top and bottom layers. The proposed tri-layer model provides insight into the hierarchical formation of anchoring centers and establishes an essential missing link between gene expression and evolution of shape.

View details for DOI 10.1039/c6sm00526h

View details for Web of Science ID 000378935000013

View details for PubMedID 27252048
Modeling Pathologies of Diastolic and Systolic Heart Failure ANNALS OF BIOMEDICAL ENGINEERING Genet, M., Lee, L. C., BAILLARGEON, B., Guccione, J. M., Kuhl, E. 2016; 44 (1): 112-127
View details for DOI 10.1007/s10439-015-1351-2

View details for Web of Science ID 000367330800010
Constitutive Modeling of Brain Tissue: Current Perspectives APPLIED MECHANICS REVIEWS de Rooij, R., Kuhl, E. 2016; 68 (1)
View details for DOI 10.1115/1.4032436

View details for Web of Science ID 000388740800001
Computational modeling of chemo-bio-mechanical coupling: a systems-biology approach toward wound healing. Computer methods in biomechanics and biomedical engineering Buganza Tepole, A., Kuhl, E. 2016; 19 (1): 13-30
Abstract

Wound healing is a synchronized cascade of chemical, biological, and mechanical phenomena, which act in concert to restore the damaged tissue. An imbalance between these events can induce painful scarring. Despite intense efforts to decipher the mechanisms of wound healing, the role of mechanics remains poorly understood. Here, we establish a computational systems biology model to identify the chemical, biological, and mechanical mechanisms of scar formation. First, we introduce the generic problem of coupled chemo-bio-mechanics. Then, we introduce the model problem of wound healing in terms of a particular chemical signal, inflammation, a particular biological cell type, fibroblasts, and a particular mechanical model, isotropic hyperelasticity. We explore the cross-talk between chemical, biological, and mechanical signals and show that all three fields have a significant impact on scar formation. Our model is the first step toward rigorous multiscale, multifield modeling in wound healing. Our formulation has the potential to improve effective wound management and optimize treatment on an individualized patient-specific basis.

View details for DOI 10.1080/10255842.2014.980821

View details for PubMedID 25421487
Systems biology and mechanics of growth WILEY INTERDISCIPLINARY REVIEWS-SYSTEMS BIOLOGY AND MEDICINE Eskandari, M., Kuhl, E. 2015; 7 (6): 401-412
View details for DOI 10.1002/wsbm.1312

View details for Web of Science ID 000362732500004

View details for PubMedID 26352286
Secondary instabilities modulate cortical complexity in the mammalian brain PHILOSOPHICAL MAGAZINE Budday, S., Steinmann, P., Kuhl, E. 2015; 95 (28-30): 3244-3256
View details for DOI 10.1080/14786435.2015.1024184

View details for Web of Science ID 000364157500011
Period-doubling and period-tripling in growing bilayered systems PHILOSOPHICAL MAGAZINE Budday, S., Kuhl, E., Hutchinson, J. W. 2015; 95 (28-30): 3208-3224
View details for DOI 10.1080/14786435.2015.1014443

View details for Web of Science ID 000364157500009
Multi-view stereo analysis reveals anisotropy of prestrain, deformation, and growth in living skin. Biomechanics and modeling in mechanobiology Buganza Tepole, A., Gart, M., Purnell, C. A., Gosain, A. K., Kuhl, E. 2015; 14 (5): 1007-1019
Abstract

Skin expansion delivers newly grown skin that maintains histological and mechanical features of the original tissue. Although it is the gold standard for cutaneous defect correction today, the underlying mechanisms remain poorly understood. Here we present a novel technique to quantify anisotropic prestrain, deformation, and growth in a porcine skin expansion model. Building on our recently proposed method, we combine two novel technologies, multi-view stereo and isogeometric analysis, to characterize skin kinematics: Upon explantation, a unit square retracts ex vivo to a square of average dimensions of [Formula: see text]. Upon expansion, the unit square deforms in vivo into a rectangle of average dimensions of [Formula: see text]. Deformations are larger parallel than perpendicular to the dorsal midline suggesting that skin responds anisotropically with smaller deformations along the skin tension lines. Upon expansion, the patch grows in vivo by [Formula: see text] with respect to the explanted, unexpanded state. Growth is larger parallel than perpendicular to the midline, suggesting that elevated stretch activates mechanotransduction pathways to stimulate tissue growth. The proposed method provides a powerful tool to characterize the kinematics of living skin. Our results shed light on the mechanobiology of skin and help us to better understand and optimize clinically relevant procedures in plastic and reconstructive surgery.

View details for DOI 10.1007/s10237-015-0650-8

View details for PubMedID 25634600
Mechanics of the brain: perspectives, challenges, and opportunities BIOMECHANICS AND MODELING IN MECHANOBIOLOGY Goriely, A., Geers, M. G., Holzapfel, G. A., Jayamohan, J., Jerusalem, A., Sivaloganathan, S., Squier, W., Van Dommelen, J. A., Waters, S., Kuhl, E. 2015; 14 (5): 931-965
View details for DOI 10.1007/s10237-015-0662-4

View details for Web of Science ID 000360862600001

View details for PubMedID 25716305
Patient-Specific Airway Wall Remodeling in Chronic Lung Disease. Annals of biomedical engineering Eskandari, M., Kuschner, W. G., Kuhl, E. 2015; 43 (10): 2538-2551
Abstract

Chronic lung disease affects more than a quarter of the adult population; yet, the mechanics of the airways are poorly understood. The pathophysiology of chronic lung disease is commonly characterized by mucosal growth and smooth muscle contraction of the airways, which initiate an inward folding of the mucosal layer and progressive airflow obstruction. Since the degree of obstruction is closely correlated with the number of folds, mucosal folding has been extensively studied in idealized circular cross sections. However, airflow obstruction has never been studied in real airway geometries; the behavior of imperfect, non-cylindrical, continuously branching airways remains unknown. Here we model the effects of chronic lung disease using the nonlinear field theories of mechanics supplemented by the theory of finite growth. We perform finite element analysis of patient-specific Y-branch segments created from magnetic resonance images. We demonstrate that the mucosal folding pattern is insensitive to the specific airway geometry, but that it critically depends on the mucosal and submucosal stiffness, thickness, and loading mechanism. Our results suggests that patient-specific airway models with inherent geometric imperfections are more sensitive to obstruction than idealized circular models. Our models help to explain the pathophysiology of airway obstruction in chronic lung disease and hold promise to improve the diagnostics and treatment of asthma, bronchitis, chronic obstructive pulmonary disease, and respiratory failure.

View details for DOI 10.1007/s10439-015-1306-7

View details for PubMedID 25821112
Computational aspects of growth-induced instabilities through eigenvalue analysis COMPUTATIONAL MECHANICS Javili, A., Dortdivanlioglu, B., Kuhl, E., Linder, C. 2015; 56 (3): 405-420
View details for DOI 10.1007/s00466-015-1178-6

View details for Web of Science ID 000359381500002
Isogeometric Kirchhoff-Love shell formulations for biological membranes COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING Tepole, A. B., Kabaria, H., Bletzinger, K., Kuhl, E. 2015; 293: 328-347
View details for DOI 10.1016/j.cma.2015.05.006

View details for Web of Science ID 000361475900016
Heterogeneous growth-induced prestrain in the heart JOURNAL OF BIOMECHANICS Genet, M., Rausch, M. K., Lee, L. C., Choy, S., Zhao, X., Kassab, G. S., Kozerke, S., Guccione, J. M., Kuhl, E. 2015; 48 (10): 2080-2089
View details for DOI 10.1016/j.jbiomech.2015.03.012

View details for Web of Science ID 000358459800055
Heterogeneous growth-induced prestrain in the heart. Journal of biomechanics Genet, M., Rausch, M. K., Lee, L. C., Choy, S., Zhao, X., Kassab, G. S., Kozerke, S., Guccione, J. M., Kuhl, E. 2015; 48 (10): 2080-2089
Abstract

Even when entirely unloaded, biological structures are not stress-free, as shown by Y.C. Fung׳s seminal opening angle experiment on arteries and the left ventricle. As a result of this prestrain, subject-specific geometries extracted from medical imaging do not represent an unloaded reference configuration necessary for mechanical analysis, even if the structure is externally unloaded. Here we propose a new computational method to create physiological residual stress fields in subject-specific left ventricular geometries using the continuum theory of fictitious configurations combined with a fixed-point iteration. We also reproduced the opening angle experiment on four swine models, to characterize the range of normal opening angle values. The proposed method generates residual stress fields which can reliably reproduce the range of opening angles between 8.7±1.8 and 16.6±13.7 as measured experimentally. We demonstrate that including the effects of prestrain reduces the left ventricular stiffness by up to 40%, thus facilitating the ventricular filling, which has a significant impact on cardiac function. This method can improve the fidelity of subject-specific models to improve our understanding of cardiac diseases and to optimize treatment options.

View details for DOI 10.1016/j.jbiomech.2015.03.012

View details for PubMedID 25913241
Emerging Brain Morphologies from Axonal Elongation ANNALS OF BIOMEDICAL ENGINEERING Holland, M. A., Miller, K. E., Kuhl, E. 2015; 43 (7): 1640-1653
Abstract

Understanding the characteristic morphology of our brain remains a challenging, yet important task in human evolution, developmental biology, and neurosciences. Mathematical modeling shapes our understanding of cortical folding and provides functional relations between cortical wavelength, thickness, and stiffness. Yet, current mathematical models are phenomenologically isotropic and typically predict non-physiological, periodic folding patterns. Here we establish a mechanistic model for cortical folding, in which macroscopic changes in white matter volume are a natural consequence of microscopic axonal growth. To calibrate our model, we consult axon elongation experiments in chick sensory neurons. We demonstrate that a single parameter, the axonal growth rate, explains a wide variety of in vitro conditions including immediate axonal thinning and gradual thickness restoration. We embed our axonal growth model into a continuum model for brain development using axonal orientation distributions motivated by diffusion spectrum imaging. Our simulations suggest that white matter anisotropy-as an emergent property from directional axonal growth-intrinsically induces symmetry breaking, and predicts more physiological, less regular morphologies with regionally varying gyral wavelengths and sulcal depths. Mechanistic modeling of brain development could establish valuable relationships between brain connectivity, brain anatomy, and brain function.

View details for DOI 10.1007/s10439-015-1312-9

View details for Web of Science ID 000358258200014
A new sparse matrix vector multiplication graphics processing unit algorithm designed for finite element problems INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING Wong, J., Kuhl, E., Darve, E. 2015; 102 (12): 1784-1814
View details for DOI 10.1002/nme.4865

View details for Web of Science ID 000354625300002
Mechanical properties of gray and white matter brain tissue by indentation. Journal of the mechanical behavior of biomedical materials Budday, S., Nay, R., de Rooij, R., Steinmann, P., Wyrobek, T., Ovaert, T. C., Kuhl, E. 2015; 46: 318-330
Abstract

The mammalian brain is composed of an outer layer of gray matter, consisting of cell bodies, dendrites, and unmyelinated axons, and an inner core of white matter, consisting primarily of myelinated axons. Recent evidence suggests that microstructural differences between gray and white matter play an important role during neurodevelopment. While brain tissue as a whole is rheologically well characterized, the individual features of gray and white matter remain poorly understood. Here we quantify the mechanical properties of gray and white matter using a robust, reliable, and repeatable method, flat-punch indentation. To systematically characterize gray and white matter moduli for varying indenter diameters, loading rates, holding times, post-mortem times, and locations we performed a series of n=192 indentation tests. We found that indenting thick, intact coronal slices eliminates the common challenges associated with small specimens: it naturally minimizes boundary effects, dehydration, swelling, and structural degradation. When kept intact and hydrated, brain slices maintained their mechanical characteristics with standard deviations as low as 5% throughout the entire testing period of five days post mortem. White matter, with an average modulus of 1.895kPa±0.592kPa, was on average 39% stiffer than gray matter, p<0.01, with an average modulus of 1.389kPa±0.289kPa, and displayed larger regional variations. It was also more viscous than gray matter and responded less rapidly to mechanical loading. Understanding the rheological differences between gray and white matter may have direct implications on diagnosing and understanding the mechanical environment in neurodevelopment and neurological disorders.

View details for DOI 10.1016/j.jmbbm.2015.02.024

View details for PubMedID 25819199
Segmental Aortic Stiffening Contributes to Experimental Abdominal Aortic Aneurysm Development CIRCULATION Raaz, U., Zoellner, A. M., Schellinger, I. N., Toh, R., Nakagami, F., Brandt, M., Emrich, F. C., Kayama, Y., Eken, S., Adam, M., Maegdefessel, L., Hertel, T., Deng, A., Jagger, A., Buerke, M., Dalman, R. L., Spin, J. M., Kuhl, E., Tsao, P. S. 2015; 131 (20): 1783-1795
Abstract

Stiffening of the aortic wall is a phenomenon consistently observed in age and in abdominal aortic aneurysm (AAA). However, its role in AAA pathophysiology is largely undefined.Using an established murine elastase-induced AAA model, we demonstrate that segmental aortic stiffening precedes aneurysm growth. Finite-element analysis reveals that early stiffening of the aneurysm-prone aortic segment leads to axial (longitudinal) wall stress generated by cyclic (systolic) tethering of adjacent, more compliant wall segments. Interventional stiffening of AAA-adjacent aortic segments (via external application of surgical adhesive) significantly reduces aneurysm growth. These changes correlate with the reduced segmental stiffness of the AAA-prone aorta (attributable to equalized stiffness in adjacent segments), reduced axial wall stress, decreased production of reactive oxygen species, attenuated elastin breakdown, and decreased expression of inflammatory cytokines and macrophage infiltration, and attenuated apoptosis within the aortic wall, as well. Cyclic pressurization of segmentally stiffened aortic segments ex vivo increases the expression of genes related to inflammation and extracellular matrix remodeling. Finally, human ultrasound studies reveal that aging, a significant AAA risk factor, is accompanied by segmental infrarenal aortic stiffening.The present study introduces the novel concept of segmental aortic stiffening as an early pathomechanism generating aortic wall stress and triggering aneurysmal growth, thereby delineating potential underlying molecular mechanisms and therapeutic targets. In addition, monitoring segmental aortic stiffening may aid the identification of patients at risk for AAA.

View details for DOI 10.1161/CIRCULATIONAHA.114.012377

View details for Web of Science ID 000354610300015

View details for PubMedID 25904646
Morphoelastic control of gastro-intestinal organogenesis: Theoretical predictions and numerical insights JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS Balbi, V., Kuhl, E., Ciarletta, P. 2015; 78: 493-510
View details for DOI 10.1016/j.jmps.2015.02.016

View details for Web of Science ID 000356733700026
Use it or lose it: multiscale skeletal muscle adaptation to mechanical stimuli. Biomechanics and modeling in mechanobiology Wisdom, K. M., Delp, S. L., Kuhl, E. 2015; 14 (2): 195-215
View details for DOI 10.1007/s10237-014-0607-3

View details for PubMedID 25199941
A computational model that predicts reverse growth in response to mechanical unloading BIOMECHANICS AND MODELING IN MECHANOBIOLOGY Lee, L. C., Genet, M., Acevedo-Bolton, G., Ordovas, K., Guccione, J. M., Kuhl, E. 2015; 14 (2): 217-229
Abstract

Ventricular growth is widely considered to be an important feature in the adverse progression of heart diseases, whereas reverse ventricular growth (or reverse remodeling) is often considered to be a favorable response to clinical intervention. In recent years, a number of theoretical models have been proposed to model the process of ventricular growth while little has been done to model its reverse. Based on the framework of volumetric strain-driven finite growth with a homeostatic equilibrium range for the elastic myofiber stretch, we propose here a reversible growth model capable of describing both ventricular growth and its reversal. We used this model to construct a semi-analytical solution based on an idealized cylindrical tube model, as well as numerical solutions based on a truncated ellipsoidal model and a human left ventricular model that was reconstructed from magnetic resonance images. We show that our model is able to predict key features in the end-diastolic pressure-volume relationship that were observed experimentally and clinically during ventricular growth and reverse growth. We also show that the residual stress fields generated as a result of differential growth in the cylindrical tube model are similar to those in other nonidentical models utilizing the same geometry.

View details for DOI 10.1007/s10237-014-0598-0

View details for Web of Science ID 000350871000002

View details for PubMedID 24888270
Use it or lose it: multiscale skeletal muscle adaptation to mechanical stimuli. Biomechanics and modeling in mechanobiology Wisdom, K. M., Delp, S. L., Kuhl, E. 2015; 14 (2): 195-215
Abstract

Skeletal muscle undergoes continuous turnover to adapt to changes in its mechanical environment. Overload increases muscle mass, whereas underload decreases muscle mass. These changes are correlated with, and enabled by, structural alterations across the molecular, subcellular, cellular, tissue, and organ scales. Despite extensive research on muscle adaptation at the individual scales, the interaction of the underlying mechanisms across the scales remains poorly understood. Here, we present a thorough review and a broad classification of multiscale muscle adaptation in response to a variety of mechanical stimuli. From this classification, we suggest that a mathematical model for skeletal muscle adaptation should include the four major stimuli, overstretch, understretch, overload, and underload, and the five key players in skeletal muscle adaptation, myosin heavy chain isoform, serial sarcomere number, parallel sarcomere number, pennation angle, and extracellular matrix composition. Including this information in multiscale computational models of muscle will shape our understanding of the interacting mechanisms of skeletal muscle adaptation across the scales. Ultimately, this will allow us to rationalize the design of exercise and rehabilitation programs, and improve the long-term success of interventional treatment in musculoskeletal disease.

View details for DOI 10.1007/s10237-014-0607-3

View details for PubMedID 25199941
On high heels and short muscles: a multiscale model for sarcomere loss in the gastrocnemius muscle. Journal of theoretical biology Zöllner, A. M., Pok, J. M., McWalter, E. J., Gold, G. E., Kuhl, E. 2015; 365: 301-310
Abstract

High heels are a major source of chronic lower limb pain. Yet, more than one third of all women compromise health for looks and wear high heels on a daily basis. Changing from flat footwear to high heels induces chronic muscle shortening associated with discomfort, fatigue, reduced shock absorption, and increased injury risk. However, the long-term effects of high-heeled footwear on the musculoskeletal kinematics of the lower extremities remain poorly understood. Here we create a multiscale computational model for chronic muscle adaptation to characterize the acute and chronic effects of global muscle shortening on local sarcomere lengths. We perform a case study of a healthy female subject and show that raising the heel by 13cm shortens the gastrocnemius muscle by 5% while the Achilles tendon remains virtually unaffected. Our computational simulation indicates that muscle shortening displays significant regional variations with extreme values of 22% in the central gastrocnemius. Our model suggests that the muscle gradually adjusts to its new functional length by a chronic loss of sarcomeres in series. Sarcomere loss varies significantly across the muscle with an average loss of 9%, virtually no loss at the proximal and distal ends, and a maximum loss of 39% in the central region. These changes reposition the remaining sarcomeres back into their optimal operating regime. Computational modeling of chronic muscle shortening provides a valuable tool to shape our understanding of the underlying mechanisms of muscle adaptation. Our study could open new avenues in orthopedic surgery and enhance treatment for patients with muscle contracture caused by other conditions than high heel wear such as paralysis, muscular atrophy, and muscular dystrophy.

View details for DOI 10.1016/j.jtbi.2014.10.036

View details for PubMedID 25451524
On high heels and short muscles: A multiscale model for sarcomere loss in the gastrocnemius muscle. Journal of theoretical biology Zöllner, A. M., Pok, J. M., McWalter, E. J., Gold, G. E., Kuhl, E. 2015; 365: 301-310
View details for DOI 10.1016/j.jtbi.2014.10.036

View details for PubMedID 25451524
The emergence of extracellular matrix mechanics and cell traction forces as important regulators of cellular self-organization BIOMECHANICS AND MODELING IN MECHANOBIOLOGY Checa, S., Rausch, M. K., Petersen, A., Kuhl, E., Duda, G. N. 2015; 14 (1): 1-13
Abstract

Physical cues play a fundamental role in a wide range of biological processes, such as embryogenesis, wound healing, tumour invasion and connective tissue morphogenesis. Although it is well known that during these processes, cells continuously interact with the local extracellular matrix (ECM) through cell traction forces, the role of these mechanical interactions on large scale cellular and matrix organization remains largely unknown. In this study, we use a simple theoretical model to investigate cellular and matrix organization as a result of mechanical feedback signals between cells and the surrounding ECM. The model includes bi-directional coupling through cellular traction forces to deform the ECM and through matrix deformation to trigger cellular migration. In addition, we incorporate the mechanical contribution of matrix fibres and their reorganization by the cells. We show that a group of contractile cells will self-polarize at a large scale, even in homogeneous environments. In addition, our simulations mimic the experimentally observed alignment of cells in the direction of maximum stiffness and the building up of tension as a consequence of cell and fibre reorganization. Moreover, we demonstrate that cellular organization is tightly linked to the mechanical feedback loop between cells and matrix. Cells with a preference for stiff environments have a tendency to form chains, while cells with a tendency for soft environments tend to form clusters. The model presented here illustrates the potential of simple physical cues and their impact on cellular self-organization. It can be used in applications where cell-matrix interactions play a key role, such as in the design of tissue engineering scaffolds and to gain a basic understanding of pattern formation in organogenesis or tissue regeneration.

View details for DOI 10.1007/s10237-014-0581-9

View details for Web of Science ID 000347250500001

View details for PubMedID 24718853
Neuromechanics: From Neurons to Brain ADVANCES IN APPLIED MECHANICS, VOL 48 Goriely, A., Budday, S., Kuhl, E. 2015; 48: 79-139
View details for DOI 10.1016/bs.aams.2015.10.002

View details for Web of Science ID 000370509200003
Human Cardiac Function Simulator for the Optimal Design of a Novel Annuloplasty Ring with a Sub-valvular Element for Correction of Ischemic Mitral Regurgitation. Cardiovascular engineering and technology Baillargeon, B., Costa, I., Leach, J. R., Lee, L. C., Genet, M., Toutain, A., Wenk, J. F., Rausch, M. K., Rebelo, N., Acevedo-Bolton, G., Kuhl, E., Navia, J. L., Guccione, J. M. 2015; 6 (2): 105-116
Abstract

Ischemic mitral regurgitation is associated with substantial risk of death. We sought to: (1) detail significant recent improvements to the Dassault Systèmes human cardiac function simulator (HCFS); (2) use the HCFS to simulate normal cardiac function as well as pathologic function in the setting of posterior left ventricular (LV) papillary muscle infarction; and (3) debut our novel device for correction of ischemic mitral regurgitation. We synthesized two recent studies of human myocardial mechanics. The first study presented the robust and integrative finite element HCFS. Its primary limitation was its poor diastolic performance with an LV ejection fraction below 20% caused by overly stiff ex vivo porcine tissue parameters. The second study derived improved diastolic myocardial material parameters using in vivo MRI data from five normal human subjects. We combined these models to simulate ischemic mitral regurgitation by computationally infarcting an LV region including the posterior papillary muscle. Contact between our novel device and the mitral valve apparatus was simulated using Dassault Systèmes SIMULIA software. Incorporating improved cardiac geometry and diastolic myocardial material properties in the HCFS resulted in a realistic LV ejection fraction of 55%. Simulating infarction of posterior papillary muscle caused regurgitant mitral valve mechanics. Implementation of our novel device corrected valve dysfunction. Improvements in the current study to the HCFS permit increasingly accurate study of myocardial mechanics. The first application of this simulator to abnormal human cardiac function suggests that our novel annuloplasty ring with a sub-valvular element will correct ischemic mitral regurgitation.

View details for DOI 10.1007/s13239-015-0216-z

View details for PubMedID 25984248
Pattern Selection in Growing Tubular Tissues PHYSICAL REVIEW LETTERS Ciarletta, P., Balbi, V., Kuhl, E. 2014; 113 (24)
Abstract

Tubular organs display a wide variety of surface morphologies including circumferential and longitudinal folds, square and hexagonal undulations, and finger-type protrusions. Surface morphology is closely correlated to tissue function and serves as a clinical indicator for physiological and pathological conditions, but the regulators of surface morphology remain poorly understood. Here, we explore the role of geometry and elasticity on the formation of surface patterns. We establish morphological phase diagrams for patterns selection and show that increasing the thickness or stiffness ratio between the outer and inner tubular layers induces a gradual transition from circumferential to longitudinal folding. Our results suggest that physical forces act as regulators during organogenesis and give rise to the characteristic circular folds in the esophagus, the longitudinal folds in the valves of Kerckring, the surface networks in villi, and the crypts in the large intestine.

View details for DOI 10.1103/PhysRevLett.113.248101

View details for Web of Science ID 000346387700022

View details for PubMedID 25541805
The role of mechanics during brain development JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS Budday, S., Steinmann, P., Kuhl, E. 2014; 72: 75-92
View details for DOI 10.1016/j.jmps.2014.07.010

View details for Web of Science ID 000343841900005
The generalized Hill model: A kinematic approach towards active muscle contraction JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS Goktepe, S., Menzel, A., Kuhl, E. 2014; 72: 20-39
View details for DOI 10.1016/j.jmps.2014.07.015

View details for Web of Science ID 000343841900002
Modeling and simulation of viscous electro-active polymers EUROPEAN JOURNAL OF MECHANICS A-SOLIDS Vogel, F., Goktepe, S., Steinmann, P., Kuhl, E. 2014; 48: 112-128
View details for DOI 10.1016/j.euromechsol.2014.02.001

View details for Web of Science ID 000342879100011
Characterization of living skin using multi-view stereo and isogeometric analysis. Acta biomaterialia Buganza Tepole, A., Gart, M., Gosain, A. K., Kuhl, E. 2014; 10 (11): 4822-4831
Abstract

Skin is our interface with the outside world. In its natural environment, it displays unique mechanical characteristics, such as prestretch and growth. While there is a general agreement on the physiological importance of these features, they remain poorly characterized, mainly because they are difficult to access with standard laboratory techniques. Here we present a new, inexpensive technique to characterize living skin using multi-view stereo and isogeometric analysis. Based on easy-to-create hand-held camera images, we quantify prestretch, deformation and growth in a controlled porcine model of chronic skin expansion. Over a period of 5 weeks, we gradually inflate an implanted tissue expander, take weekly photographs of the experimental scene, reconstruct the geometry from a tattooed surface grid and create parametric representations of the skin surface. After 5 weeks of expansion, our method reveals an average area prestretch of 1.44, an average area stretch of 1.87 and an average area growth of 2.25. Area prestretch is maximal in the ventral region with a value of 2.37, whereas area stretch and area growth are maximal above the center of the expander, with values of 4.05 and 4.81, respectively. Our study has immediate impact on understanding living skin to optimize treatment planning and decision making in plastic and reconstructive surgery. Beyond these direct implications, our experimental design has broad applications in clinical research and basic sciences: it serves as a simple, robust, low cost, easy-to-use tool to reconstruct living membranes, which are difficult to characterize in a conventional laboratory setup.

View details for DOI 10.1016/j.actbio.2014.06.037

View details for PubMedID 25016279
Application of Finite Element Modeling to Optimize Flap Design with Tissue Expansion PLASTIC AND RECONSTRUCTIVE SURGERY Buganza-Tepole, A., Steinberg, J. P., Kuhl, E., Gosain, A. K. 2014; 134 (4): 785-792
View details for DOI 10.1097/PRS.0000000000000553

View details for Web of Science ID 000343105400054
Application of finite element modeling to optimize flap design with tissue expansion. Plastic and reconstructive surgery Buganza-Tepole, A., Steinberg, J. P., Kuhl, E., Gosain, A. K. 2014; 134 (4): 785-792
Abstract

Tissue expansion is a widely used technique to create skin flaps for the correction of sizable defects in reconstructive plastic surgery. Major complications following the inset of expanded flaps include breakdown and uncontrolled scarring secondary to excessive tissue tension. Although it is recognized that mechanical forces may significantly impact the success of defect repair with tissue expansion, a mechanical analysis of tissue stresses has not previously been attempted. Such analyses have the potential to optimize flap design preoperatively.The authors establish computer-aided design as a tool with which to explore stress profiles for two commonly used flap designs, the direct advancement flap and the double back-cut flap. The authors advanced both flaps parallel and perpendicular to the relaxed skin tension lines to quantify the impact of tissue anisotropy on stress distribution profiles.Stress profiles were highly sensitive to flap design and orientation of relaxed skin tension lines, with stress minimized when flaps were advanced perpendicular to relaxed skin tension lines. Maximum stresses in advancement flaps occurred at the distal end of the flap, followed by the base. The double back-cut design increased stress at the lateral edges of the flap.The authors conclude that finite element modeling may be used to effectively predict areas of increased flap tension. Performed preoperatively, such modeling can allow for the optimization of flap design and a potential reduction in complications such as flap dehiscence and hypertrophic scarring.

View details for DOI 10.1097/PRS.0000000000000553

View details for PubMedID 24945952
Computational modeling of skin: Using stress profiles as predictor for tissue necrosis in reconstructive surgery COMPUTERS & STRUCTURES Tepole, A. B., Gosain, A. K., Kuhl, E. 2014; 143: 32-39
View details for DOI 10.1016/j.compstruc.2014.07.004

View details for Web of Science ID 000341481500004
Generating fibre orientation maps in human heart models using Poisson interpolation COMPUTER METHODS IN BIOMECHANICS AND BIOMEDICAL ENGINEERING Wong, J., Kuhl, E. 2014; 17 (11): 1217-1226
Abstract

Smoothly varying muscle fibre orientations in the heart are critical to its electrical and mechanical function. From detailed histological studies and diffusion tensor imaging, we now know that fibre orientations in humans vary gradually from approximately - 70° in the outer wall to +80° in the inner wall. However, the creation of fibre orientation maps for computational analyses remains one of the most challenging problems in cardiac electrophysiology and cardiac mechanics. Here, we show that Poisson interpolation generates smoothly varying vector fields that satisfy a set of user-defined constraints in arbitrary domains. Specifically, we enforce the Poisson interpolation in the weak sense using a standard linear finite element algorithm for scalar-valued second-order boundary value problems and introduce the feature to be interpolated as a global unknown. User-defined constraints are then simply enforced in the strong sense as Dirichlet boundary conditions. We demonstrate that the proposed concept is capable of generating smoothly varying fibre orientations, quickly, efficiently and robustly, both in a generic bi-ventricular model and in a patient-specific human heart. Sensitivity analyses demonstrate that the underlying algorithm is conceptually able to handle both arbitrarily and uniformly distributed user-defined constraints; however, the quality of the interpolation is best for uniformly distributed constraints. We anticipate our algorithm to be immediately transformative to experimental and clinical settings, in which it will allow us to quickly and reliably create smooth interpolations of arbitrary fields from data-sets, which are sparse but uniformly distributed.

View details for DOI 10.1080/10255842.2012.739167

View details for Web of Science ID 000334018600006

View details for PubMedID 23210529

View details for PubMedCentralID PMC3656979
Computational modelling of electrocardiograms: repolarisation and T-wave polarity in the human heart COMPUTER METHODS IN BIOMECHANICS AND BIOMEDICAL ENGINEERING Hurtado, D. E., Kuhl, E. 2014; 17 (9): 986-996
Abstract

For more than a century, electrophysiologists, cardiologists and engineers have studied the electrical activity of the human heart to better understand rhythm disorders and possible treatment options. Although the depolarisation sequence of the heart is relatively well characterised, the repolarisation sequence remains a subject of great controversy. Here, we study regional and temporal variations in both depolarisation and repolarisation using a finite element approach. We discretise the governing equations in time using an unconditionally stable implicit Euler backward scheme and in space using a consistently linearised Newton-Raphson-based finite element solver. Through systematic parameter-sensitivity studies, we establish a direct relation between a normal positive T-wave and the non-uniform distribution of the controlling parameter, which we have termed refractoriness. To establish a healthy baseline model, we calibrate the refractoriness using clinically measured action potential durations at different locations in the human heart. We demonstrate the potential of our model by comparing the computationally predicted and clinically measured depolarisation and repolarisation profiles across the left ventricle. The proposed framework allows us to explore how local action potential durations on the microscopic scale translate into global repolarisation sequences on the macroscopic scale. We anticipate that our calibrated human heart model can be widely used to explore cardiac excitation in health and disease. For example, our model can serve to identify optimal pacing sites in patients with heart failure and to localise optimal ablation sites in patients with cardiac fibrillation.

View details for DOI 10.1080/10255842.2012.729582

View details for Web of Science ID 000333954600006

View details for PubMedID 23113842
Computational modeling of hypertensive growth in the human carotid artery COMPUTATIONAL MECHANICS Saez, P., Pena, E., Martinez, M. A., Kuhl, E. 2014; 53 (6): 1183-1196
View details for DOI 10.1007/s00466-013-0959-z

View details for Web of Science ID 000335669100006
On the mechanics of growing thin biological membranes JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS Rausch, M. K., Kuhl, E. 2014; 63: 128-140
View details for DOI 10.1016/j.jmps.2013.09.015

View details for Web of Science ID 000331006900009
A novel strategy to identify the critical conditions for growth-induced instabilities JOURNAL OF THE MECHANICAL BEHAVIOR OF BIOMEDICAL MATERIALS Javili, A., Steinmann, P., Kuhl, E. 2014; 29: 20-32
Abstract

Geometric instabilities in living structures can be critical for healthy biological function, and abnormal buckling, folding, or wrinkling patterns are often important indicators of disease. Mathematical models typically attribute these instabilities to differential growth, and characterize them using the concept of fictitious configurations. This kinematic approach toward growth-induced instabilities is based on the multiplicative decomposition of the total deformation gradient into a reversible elastic part and an irreversible growth part. While this generic concept is generally accepted and well established today, the critical conditions for the formation of growth-induced instabilities remain elusive and poorly understood. Here we propose a novel strategy for the stability analysis of growing structures motivated by the idea of replacing growth by prestress. Conceptually speaking, we kinematically map the stress-free grown configuration onto a prestressed initial configuration. This allows us to adopt a classical infinitesimal stability analysis to identify critical material parameter ranges beyond which growth-induced instabilities may occur. We illustrate the proposed concept by a series of numerical examples using the finite element method. Understanding the critical conditions for growth-induced instabilities may have immediate applications in plastic and reconstructive surgery, asthma, obstructive sleep apnoea, and brain development.

View details for DOI 10.1016/j.jmbbm.2013.08.017

View details for Web of Science ID 000330085700003

View details for PubMedID 24041754
Human pluripotent stem cell tools for cardiac optogenetics. Conference proceedings : ... Annual International Conference of the IEEE Engineering in Medicine and Biology Society. IEEE Engineering in Medicine and Biology Society. Annual Conference Zhuge, Y., Patlolla, B., Ramakrishnan, C., Beygui, R. E., Zarins, C. K., Deisseroth, K., Kuhl, E., Abilez, O. J. 2014; 2014: 6171-6174
Abstract

It is likely that arrhythmias should be avoided for therapies based on human pluripotent stem cell (hPSC)-derived cardiomyocytes (CM) to be effective. Towards achieving this goal, we introduced light-activated channelrhodopsin-2 (ChR2), a cation channel activated with 480 nm light, into human embryonic stem cells (hESC). By using in vitro approaches, hESC-CM are able to be activated with light. ChR2 is stably transduced into undifferentiated hESC via a lentiviral vector. Via directed differentiation, hESC(ChR2)-CM are produced and subjected to optical stimulation. hESC(ChR2)-CM respond to traditional electrical stimulation and produce similar contractility features as their wild-type counterparts but only hESC(ChR2)-CM can be activated by optical stimulation. Here it is shown that a light sensitive protein can enable in vitro optical control of hESC-CM and that this activation occurs optimally above specific light stimulation intensity and pulse width thresholds. For future therapy, in vivo optical stimulation along with optical inhibition could allow for acute synchronization of implanted hPSC-CM with patient cardiac rhythms.

View details for DOI 10.1109/EMBC.2014.6945038

View details for PubMedID 25571406
Mathematical modeling of collagen turnover in biological tissue JOURNAL OF MATHEMATICAL BIOLOGY Saez, P., Pena, E., Angel Martinez, M., Kuhl, E. 2013; 67 (6-7): 1765-1793
Abstract

We present a theoretical and computational model for collagen turnover in soft biological tissues. Driven by alterations in the mechanical environment, collagen fiber bundles may undergo important chronic changes, characterized primarily by alterations in collagen synthesis and degradation rates. In particular, hypertension triggers an increase in tropocollagen synthesis and a decrease in collagen degradation, which lead to the well-documented overall increase in collagen content. These changes are the result of a cascade of events, initiated mainly by the endothelial and smooth muscle cells. Here, we represent these events collectively in terms of two internal variables, the concentration of growth factor TGF-[Formula: see text] and tissue inhibitors of metalloproteinases TIMP. The upregulation of TGF-[Formula: see text] increases the collagen density. The upregulation of TIMP also increases the collagen density through decreasing matrix metalloproteinase MMP. We establish a mathematical theory for mechanically-induced collagen turnover and introduce a computational algorithm for its robust and efficient solution. We demonstrate that our model can accurately predict the experimentally observed collagen increase in response to hypertension reported in literature. Ultimately, the model can serve as a valuable tool to predict the chronic adaptation of collagen content to restore the homeostatic equilibrium state in vessels with arbitrary micro-structure and geometry.

View details for DOI 10.1007/s00285-012-0613-y

View details for Web of Science ID 000326898300016

View details for PubMedID 23129392
On the Role of Mechanics in Chronic Lung Disease MATERIALS Eskandari, M., Pfaller, M. R., Kuhl, E. 2013; 6 (12): 5639-5658
View details for DOI 10.3390/ma6125639

View details for Web of Science ID 000330297600014
Growth on demand: Reviewing the mechanobiology of stretched skin JOURNAL OF THE MECHANICAL BEHAVIOR OF BIOMEDICAL MATERIALS Zoellner, A. M., Holland, M. A., Honda, K. S., Gosain, A. K., Kuhl, E. 2013; 28: 495-509
View details for DOI 10.1016/j.jmbbm.2013.03.018

View details for Web of Science ID 000328234500044
Computational modeling of chemo-electro-mechanical coupling: A novel implicit monolithic finite element approach INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING Wong, J., Goektepe, S., Kuhl, E. 2013; 29 (10): 1104-1133
Abstract

Computational modeling of the human heart allows us to predict how chemical, electrical, and mechanical fields interact throughout a cardiac cycle. Pharmacological treatment of cardiac disease has advanced significantly over the past decades, yet it remains unclear how the local biochemistry of an individual heart cell translates into global cardiac function. Here, we propose a novel, unified strategy to simulate excitable biological systems across three biological scales. To discretize the governing chemical, electrical, and mechanical equations in space, we propose a monolithic finite element scheme. We apply a highly efficient and inherently modular global-local split, in which the deformation and the transmembrane potential are introduced globally as nodal degrees of freedom, whereas the chemical state variables are treated locally as internal variables. To ensure unconditional algorithmic stability, we apply an implicit backward Euler finite difference scheme to discretize the resulting system in time. To increase algorithmic robustness and guarantee optimal quadratic convergence, we suggest an incremental iterative Newton-Raphson scheme. The proposed algorithm allows us to simulate the interaction of chemical, electrical, and mechanical fields during a representative cardiac cycle on a patient-specific geometry, robust and stable, with calculation times on the order of 4 days on a standard desktop computer.Copyright © 2013 John Wiley & Sons, Ltd.

View details for DOI 10.1002/cnm.2565

View details for Web of Science ID 000325500200006

View details for PubMedID 23798328
Mechanics of the mitral valve: a critical review, an in vivo parameter identification, and the effect of prestrain. Biomechanics and modeling in mechanobiology Rausch, M. K., Famaey, N., Shultz, T. O., Bothe, W., Miller, D. C., Kuhl, E. 2013; 12 (5): 1053-1071
Abstract

Alterations in mitral valve mechanics are classical indicators of valvular heart disease, such as mitral valve prolapse, mitral regurgitation, and mitral stenosis. Computational modeling is a powerful technique to quantify these alterations, to explore mitral valve physiology and pathology, and to classify the impact of novel treatment strategies. The selection of the appropriate constitutive model and the choice of its material parameters are paramount to the success of these models. However, the in vivo parameters values for these models are unknown. Here, we identify the in vivo material parameters for three common hyperelastic models for mitral valve tissue, an isotropic one and two anisotropic ones, using an inverse finite element approach. We demonstrate that the two anisotropic models provide an excellent fit to the in vivo data, with local displacement errors in the sub-millimeter range. In a complementary sensitivity analysis, we show that the identified parameter values are highly sensitive to prestrain, with some parameters varying up to four orders of magnitude. For the coupled anisotropic model, the stiffness varied from 119,021 kPa at 0 % prestrain via 36 kPa at 30 % prestrain to 9 kPa at 60 % prestrain. These results may, at least in part, explain the discrepancy between previously reported ex vivo and in vivo measurements of mitral leaflet stiffness. We believe that our study provides valuable guidelines for modeling mitral valve mechanics, selecting appropriate constitutive models, and choosing physiologically meaningful parameter values. Future studies will be necessary to experimentally and computationally investigate prestrain, to verify its existence, to quantify its magnitude, and to clarify its role in mitral valve mechanics.

View details for DOI 10.1007/s10237-012-0462-z

View details for PubMedID 23263365
Mechanics of the Mitral Annulus in Chronic Ischemic Cardiomyopathy ANNALS OF BIOMEDICAL ENGINEERING Rausch, M. K., Tibayan, F. A., Ingels, N. B., Miller, D. C., Kuhl, E. 2013; 41 (10): 2171-2180
Abstract

Approximately one third of all patients undergoing open-heart surgery for repair of ischemic mitral regurgitation present with residual and recurrent mitral valve leakage upon follow up. A fundamental quantitative understanding of mitral valve remodeling following myocardial infarction may hold the key to improved medical devices and better treatment outcomes. Here we quantify mitral annular strains and curvature in nine sheep 5 ± 1 weeks after controlled inferior myocardial infarction of the left ventricle. We complement our marker-based mechanical analysis of the remodeling mitral valve by common clinical measures of annular geometry before and after the infarct. After 5 ± 1 weeks, the mitral annulus dilated in septal-lateral direction by 15.2% (p = 0.003) and in commissure-commissure direction by 14.2% (p < 0.001). The septal annulus dilated by 10.4% (p = 0.013) and the lateral annulus dilated by 18.4% (p < 0.001). Remarkably, in animals with large degree of mitral regurgitation and annular remodeling, the annulus dilated asymmetrically with larger distortions toward the lateral-posterior segment. Strain analysis revealed average tensile strains of 25% over most of the annulus with exception for the lateral-posterior segment, where tensile strains were 50% and higher. Annular dilation and peak strains were closely correlated to the degree of mitral regurgitation. A complementary relative curvature analysis revealed a homogenous curvature decrease associated with significant annular circularization. All curvature profiles displayed distinct points of peak curvature disturbing the overall homogenous pattern. These hinge points may be the mechanistic origin for the asymmetric annular deformation following inferior myocardial infarction. In the future, this new insight into the mechanism of asymmetric annular dilation may support improved device designs and possibly aid surgeons in reconstructing healthy annular geometry during mitral valve repair.

View details for DOI 10.1007/s10439-013-0813-7

View details for Web of Science ID 000324073200014

View details for PubMedID 23636575
On the effect of prestrain and residual stress in thin biological membranes JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS Rausch, M. K., Kuhl, E. 2013; 61 (9): 1955-1969
View details for DOI 10.1016/j.jmps.2013.04.005

View details for Web of Science ID 000322296900005
On the mechanics of thin films and growing surfaces MATHEMATICS AND MECHANICS OF SOLIDS Holland, M. A., Kosmata, T., Goriely, A., Kuhl, E. 2013; 18 (6): 561-575
View details for DOI 10.1177/1081286513485776

View details for Web of Science ID 000323118900002
On the mechanics of continua with boundary energies and growing surfaces JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS Papastavrou, A., Steinmann, P., Kuhl, E. 2013; 61 (6): 1446-1463
View details for DOI 10.1016/j.jmps.2013.01.007

View details for Web of Science ID 000318579500012
Systems-based approaches toward wound healing PEDIATRIC RESEARCH Tepole, A. B., Kuhl, E. 2013; 73 (4): 553-563
Abstract

Wound healing in the pediatric patient is of utmost clinical and social importance because hypertrophic scarring can have aesthetic and psychological sequelae, from early childhood to late adolescence. Wound healing is a well-orchestrated reparative response affecting the damaged tissue at the cellular, tissue, organ, and system scales. Although tremendous progress has been made toward understanding wound healing at the individual temporal and spatial scales, its effects across the scales remain severely understudied and poorly understood. Here, we discuss the critical need for systems-based computational modeling of wound healing across the scales, from short-term to long-term and from small to large. We illustrate the state of the art in systems modeling by means of three key signaling mechanisms: oxygen tension-regulating angiogenesis and revascularization; transforming growth factor-β (TGF-β) kinetics controlling collagen deposition; and mechanical stretch stimulating cellular mitosis and extracellular matrix (ECM) remodeling. The complex network of biochemical and biomechanical signaling mechanisms and the multiscale character of the healing process make systems modeling an integral tool in exploring personalized strategies for wound repair. A better mechanistic understanding of wound healing in the pediatric patient could open new avenues in treating children with skin disorders such as birth defects, skin cancer, wounds, and burn injuries.

View details for DOI 10.1038/pr.2013.3

View details for Web of Science ID 000317554900008

View details for PubMedID 23314298
Characterisation of electrophysiological conduction in cardiomyocyte co-cultures using co-occurrence analysis COMPUTER METHODS IN BIOMECHANICS AND BIOMEDICAL ENGINEERING Chen, M. Q., Wong, J., Kuhl, E., Giovangrandi, L., Kovacs, G. T. 2013; 16 (2): 185-197
Abstract

Cardiac arrhythmias are disturbances of the electrical conduction pattern in the heart with severe clinical implications. The damage of existing cells or the transplantation of foreign cells may disturb functional conduction pathways and may increase the risk of arrhythmias. Although these conduction disturbances are easily accessible with the human eye, there is no algorithmic method to extract quantitative features that quickly portray the conduction pattern. Here, we show that co-occurrence analysis, a well-established method for feature recognition in texture analysis, provides insightful quantitative information about the uniformity and the homogeneity of an excitation wave. As a first proof-of-principle, we illustrate the potential of co-occurrence analysis by means of conduction patterns of cardiomyocyte-fibroblast co-cultures, generated both in vitro and in silico. To characterise signal propagation in vitro, we perform a conduction analysis of co-cultured murine HL-1 cardiomyocytes and murine 3T3 fibroblasts using microelectrode arrays. To characterise signal propagation in silico, we establish a conduction analysis of co-cultured electrically active, conductive cardiomyocytes and non-conductive fibroblasts using the finite element method. Our results demonstrate that co-occurrence analysis is a powerful tool to create purity-conduction relationships and to quickly quantify conduction patterns in terms of co-occurrence energy and contrast. We anticipate this first preliminary study to be a starting point for more sophisticated analyses of different co-culture systems. In particular, in view of stem cell therapies, we expect co-occurrence analysis to provide valuable quantitative insight into the integration of foreign cells into a functional host system.

View details for DOI 10.1080/10255842.2011.615310

View details for Web of Science ID 000314564900007

View details for PubMedID 21970595
A three-constituent damage model for arterial clamping in computer-assisted surgery BIOMECHANICS AND MODELING IN MECHANOBIOLOGY Famaey, N., Vander Sloten, J., Kuhl, E. 2013; 12 (1): 123-136
Abstract

Robotic surgery is an attractive, minimally invasive and high precision alternative to conventional surgical procedures. However, it lacks the natural touch and force feedback that allows the surgeon to control safe tissue manipulation. This is an important problem in standard surgical procedures such as clamping, which might induce severe tissue damage. In complex, heterogeneous, large deformation scenarios, the limits of the safe loading regime beyond which tissue damage occurs are unknown. Here, we show that a continuum damage model for arteries, implemented in a finite element setting, can help to predict arterial stiffness degradation and to identify critical loading regimes. The model consists of the main mechanical constituents of arterial tissue: extracellular matrix, collagen fibres and smooth muscle cells. All constituents are allowed to degrade independently in response to mechanical overload. To demonstrate the modularity and portability of the proposed model, we implement it in a commercial finite element programme, which allows to keep track of damage progression via internal variables. The loading history during arterial clamping is simulated through four successive steps, incorporating residual strains. The results of our first prototype simulation demonstrate significant regional variations in smooth muscle cell damage. In three additional steps, this damage is evaluated by simulating an isometric contraction experiment. The entire finite element simulation is finally compared with actual in vivo experiments. In the short term, our computational simulation tool can be useful to optimise surgical tools with the goal to minimise tissue damage. In the long term, it can potentially be used to inform computer-assisted surgery and identify safe loading regimes, in real time, to minimise tissue damage during robotic tissue manipulation.

View details for DOI 10.1007/s10237-012-0386-7

View details for Web of Science ID 000313480100011

View details for PubMedID 22446834
A fully implicit finite element method for bidomain models of cardiac electromechanics COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING Dal, H., Goektepe, S., Kaliske, M., Kuhl, E. 2013; 253: 323-336
View details for DOI 10.1016/j.cma.2012.07.004

View details for Web of Science ID 000313134600021
Evidence of adaptive mitral leaflet growth JOURNAL OF THE MECHANICAL BEHAVIOR OF BIOMEDICAL MATERIALS Rausch, M. K., Tibayan, F. A., Miller, D. C., Kuhl, E. 2012; 15: 208-217
Abstract

Ischemic mitral regurgitation is mitral insufficiency caused by myocardial infarction. Recent studies suggest that mitral leaflets have the potential to grow and reduce the degree of regurgitation. Leaflet growth has been associated with papillary muscle displacement, but role of annular dilation in leaflet growth is unclear. We tested the hypothesis that chronic leaflet stretch, induced by papillary muscle tethering and annular dilation, triggers chronic leaflet growth. To decipher the mechanisms that drive the growth process, we further quantified regional and directional variations of growth. Five adult sheep underwent coronary snare and marker placement on the left ventricle, papillary muscles, mitral annulus, and mitral leaflet. After eight days, we tightened the snares to create inferior myocardial infarction. We recorded marker coordinates at baseline, acutely (immediately post-infarction), and chronically (five weeks post-infarction). From these coordinates, we calculated acute and chronic changes in ventricular, papillary muscle, and annular geometry along with acute and chronic leaflet strains. Chronic left ventricular dilation of 17.15% (p<0.001) induced chronic posterior papillary muscle displacement of 13.49 mm (p=0.07). Chronic mitral annular area, commissural and septal-lateral distances increased by 32.50% (p=0.010), 14.11% (p=0.007), and 10.84% (p=0.010). Chronic area, circumferential, and radial growth were 15.57%, 5.91%, and 3.58%, with non-significant regional variations (p=0.868). Our study demonstrates that mechanical stretch, induced by annular dilation and papillary muscle tethering, triggers mitral leaflet growth. Understanding the mechanisms of leaflet adaptation may open new avenues to pharmacologically or surgically manipulate mechanotransduction pathways to augment mitral leaflet area and reduce the degree of regurgitation.

View details for DOI 10.1016/j.jmbbm.2012.07.001

View details for Web of Science ID 000313598800020

View details for PubMedID 23159489
Stretching Skeletal Muscle: Chronic Muscle Lengthening through Sarcomerogenesis PLOS ONE Zoellner, A. M., Abilez, O. J., Boel, M., Kuhl, E. 2012; 7 (10)
Abstract

Skeletal muscle responds to passive overstretch through sarcomerogenesis, the creation and serial deposition of new sarcomere units. Sarcomerogenesis is critical to muscle function: It gradually re-positions the muscle back into its optimal operating regime. Animal models of immobilization, limb lengthening, and tendon transfer have provided significant insight into muscle adaptation in vivo. Yet, to date, there is no mathematical model that allows us to predict how skeletal muscle adapts to mechanical stretch in silico. Here we propose a novel mechanistic model for chronic longitudinal muscle growth in response to passive mechanical stretch. We characterize growth through a single scalar-valued internal variable, the serial sarcomere number. Sarcomerogenesis, the evolution of this variable, is driven by the elastic mechanical stretch. To analyze realistic three-dimensional muscle geometries, we embed our model into a nonlinear finite element framework. In a chronic limb lengthening study with a muscle stretch of 1.14, the model predicts an acute sarcomere lengthening from 3.09[Formula: see text]m to 3.51[Formula: see text]m, and a chronic gradual return to the initial sarcomere length within two weeks. Compared to the experiment, the acute model error was 0.00% by design of the model; the chronic model error was 2.13%, which lies within the rage of the experimental standard deviation. Our model explains, from a mechanistic point of view, why gradual multi-step muscle lengthening is less invasive than single-step lengthening. It also explains regional variations in sarcomere length, shorter close to and longer away from the muscle-tendon interface. Once calibrated with a richer data set, our model may help surgeons to prevent muscle overstretch and make informed decisions about optimal stretch increments, stretch timing, and stretch amplitudes. We anticipate our study to open new avenues in orthopedic and reconstructive surgery and enhance treatment for patients with ill proportioned limbs, tendon lengthening, tendon transfer, tendon tear, and chronically retracted muscles.

View details for DOI 10.1371/journal.pone.0045661

View details for Web of Science ID 000309388500010

View details for PubMedID 23049683
Stretching skin: The physiological limit and beyond INTERNATIONAL JOURNAL OF NON-LINEAR MECHANICS Tepole, A. B., Gosain, A. K., Kuhl, E. 2012; 47 (8): 938-949
Abstract

The goal of this manuscript is to establish a novel computational model for skin to characterize its constitutive behavior when stretched within and beyond its physiological limits. Within the physiological regime, skin displays a reversible, highly nonlinear, stretch locking, and anisotropic behavior. We model these characteristics using a transversely isotropic chain network model composed of eight wormlike chains. Beyond the physiological limit, skin undergoes an irreversible area growth triggered through mechanical stretch. We model skin growth as a transversely isotropic process characterized through a single internal variable, the scalar-valued growth multiplier. To discretize the evolution of growth in time, we apply an unconditionally stable, implicit Euler backward scheme. To discretize it in space, we utilize the finite element method. For maximum algorithmic efficiency and optimal convergence, we suggest an inner Newton iteration to locally update the growth multiplier at each integration point. This iteration is embedded within an outer Newton iteration to globally update the deformation at each finite element node. To illustrate the characteristic features of skin growth, we first compare the two simple model problems of displacement- and force-driven growth. Then, we model the process of stretch-induced skin growth during tissue expansion. In particular, we compare the spatio-temporal evolution of stress, strain, and area gain for four commonly available tissue expander geometries. We believe that the proposed model has the potential to open new avenues in reconstructive surgery and rationalize critical process parameters in tissue expansion, such as expander geometry, expander size, expander placement, and inflation timing.

View details for DOI 10.1016/j.ijnonlinmec.2011.07.006

View details for Web of Science ID 000307613200010
How Do Annuloplasty Rings Affect Mitral Annular Strains in the Normal Beating Ovine Heart? Meeting of the American-Heart-Association Bothe, W., Rausch, M. K., Kvitting, J. E., Echtner, D. K., Walther, M., Ingels, N. B., Kuhl, E., Miller, D. C. LIPPINCOTT WILLIAMS & WILKINS. 2012: S231–S238
Abstract

We hypothesized that annuloplasty ring implantation alters mitral annular strains in a normal beating ovine heart preparation.Sheep had 16 radiopaque markers sewn equally spaced around the mitral annulus. Edwards Cosgrove partial flexible band (COS; n=12), St Jude complete rigid saddle-shaped annuloplasty ring (RSA; n=10), Carpentier-Edwards Physio (PHY; n=11), Edwards IMR ETlogix (ETL; n=11), and GeoForm (GEO; n=12) annuloplasty rings were implanted in a releasable fashion. Four-dimensional marker coordinates were obtained using biplane videofluoroscopy with the ring inserted (ring) and after ring release (control). From marker coordinates, a functional spatio-temporal representation of each annulus was generated through a best fit using 16 piecewise cubic Hermitian splines. Absolute total mitral annular ring strains were calculated from the relative change in length of the tangent vector to the annular curve as strains occurring from control to ring state at end-systole. In addition, average Green-Lagrange strains occurring from control to ring state at end-systole along the annulus were calculated. Absolute total mitral annular ring strains were smallest for COS and greatest for ETL. Strains for RSA, PHY, and GEO were similar. Except for COS in the septal mitral annular segment, all rings induced compressive strains along the entire annulus, with greatest values occurring at the lateral mitral annular segment.In healthy, beating ovine hearts, annuloplasty rings (COS, RSA, PHY, ETL, and GEO) induce compressive strains that are predominate in the lateral annular region, smallest for flexible partial bands (COS) and greatest for an asymmetrical rigid ring type with intrinsic septal-lateral downsizing (ETL). However, the ring type with the most drastic intrinsic septal-lateral downsizing (GEO) introduced strains similar to physiologically shaped rings (RSA and PHY), indicating that ring effects on annular strain profiles cannot be estimated from the degree of septal-lateral downsizing.

View details for DOI 10.1161/CIRCULATIONAHA.111.084046

View details for Web of Science ID 000314150200032

View details for PubMedID 22965988
Growing skin: tissue expansion in pediatric forehead reconstruction. Biomechanics and modeling in mechanobiology Zöllner, A. M., Buganza Tepole, A., Gosain, A. K., Kuhl, E. 2012; 11 (6): 855-867
Abstract

Tissue expansion is a common surgical procedure to grow extra skin through controlled mechanical over-stretch. It creates skin that matches the color, texture, and thickness of the surrounding tissue, while minimizing scars and risk of rejection. Despite intense research in tissue expansion and skin growth, there is a clear knowledge gap between heuristic observation and mechanistic understanding of the key phenomena that drive the growth process. Here, we show that a continuum mechanics approach, embedded in a custom-designed finite element model, informed by medical imaging, provides valuable insight into the biomechanics of skin growth. In particular, we model skin growth using the concept of an incompatible growth configuration. We characterize its evolution in time using a second-order growth tensor parameterized in terms of a scalar-valued internal variable, the in-plane area growth. When stretched beyond the physiological level, new skin is created, and the in-plane area growth increases. For the first time, we simulate tissue expansion on a patient-specific geometric model, and predict stress, strain, and area gain at three expanded locations in a pediatric skull: in the scalp, in the forehead, and in the cheek. Our results may help the surgeon to prevent tissue over-stretch and make informed decisions about expander geometry, size, placement, and inflation. We anticipate our study to open new avenues in reconstructive surgery and enhance treatment for patients with birth defects, burn injuries, or breast tumor removal.

View details for DOI 10.1007/s10237-011-0357-4

View details for PubMedID 22052000
Growing skin: tissue expansion in pediatric forehead reconstruction BIOMECHANICS AND MODELING IN MECHANOBIOLOGY Zoellner, A. M., Tepole, A. B., Gosain, A. K., Kuhl, E. 2012; 11 (6): 855-867
View details for DOI 10.1007/s10237-011-0357-4

View details for Web of Science ID 000304814100010
Anisotropic density growth of bone-A computational micro-sphere approach INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES Waffenschmidt, T., Menzel, A., Kuhl, E. 2012; 49 (14): 1928-1946
View details for DOI 10.1016/j.ijsolstr.2012.03.035

View details for Web of Science ID 000305441600002
Computational optogenetics: A novel continuum framework for the photoelectrochemistry of living systems JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS Wong, J., Abilez, O. J., Kuhl, E. 2012; 60 (6): 1158-1178
Abstract

Electrical stimulation is currently the gold standard treatment for heart rhythm disorders. However, electrical pacing is associated with technical limitations and unavoidable potential complications. Recent developments now enable the stimulation of mammalian cells with light using a novel technology known as optogenetics. The optical stimulation of genetically engineered cells has significantly changed our understanding of electrically excitable tissues, paving the way towards controlling heart rhythm disorders by means of photostimulation. Controlling these disorders, in turn, restores coordinated force generation to avoid sudden cardiac death. Here, we report a novel continuum framework for the photoelectrochemistry of living systems that allows us to decipher the mechanisms by which this technology regulates the electrical and mechanical function of the heart. Using a modular multiscale approach, we introduce a non-selective cation channel, channelrhodopsin-2, into a conventional cardiac muscle cell model via an additional photocurrent governed by a light-sensitive gating variable. Upon optical stimulation, this channel opens and allows sodium ions to enter the cell, inducing electrical activation. In side-by-side comparisons with conventional heart muscle cells, we show that photostimulation directly increases the sodium concentration, which indirectly decreases the potassium concentration in the cell, while all other characteristics of the cell remain virtually unchanged. We integrate our model cells into a continuum model for excitable tissue using a nonlinear parabolic second order partial differential equation, which we discretize in time using finite differences and in space using finite elements. To illustrate the potential of this computational model, we virtually inject our photosensitive cells into different locations of a human heart, and explore its activation sequences upon photostimulation. Our computational optogenetics tool box allows us to virtually probe landscapes of process parameters, and to identify optimal photostimulation sequences with the goal to pace human hearts with light and, ultimately, to restore mechanical function.

View details for DOI 10.1016/j.jmps.2012.02.004

View details for Web of Science ID 000303285600007

View details for PubMedCentralID PMC3388516
Frontiers in growth and remodeling MECHANICS RESEARCH COMMUNICATIONS Menzel, A., Kuhl, E. 2012; 42: 1-14
View details for DOI 10.1016/j.mechrescom.2012.02.007

View details for Web of Science ID 000304847400001
Growth and remodeling of the left ventricle: A case study of myocardial infarction and surgical ventricular restoration MECHANICS RESEARCH COMMUNICATIONS Klepach, D., Lee, L. C., Wenk, J. F., Ratcliffe, M. B., Zohdi, T. I., Navia, J. L., Kassab, G. S., Kuhl, E., Guccione, J. M. 2012; 42: 134-141
View details for DOI 10.1016/j.mechrescom.2012.03.005

View details for Web of Science ID 000304847400015
Kinematics of cardiac growth: In vivo characterization of growth tensors and strains JOURNAL OF THE MECHANICAL BEHAVIOR OF BIOMEDICAL MATERIALS Tsamis, A., Cheng, A., Nguyen, T. C., Langer, F., Miller, D. C., Kuhl, E. 2012; 8: 165-177
Abstract

Progressive growth and remodeling of the left ventricle are part of the natural history of chronic heart failure and strong clinical indicators for survival. Accompanied by changes in cardiac form and function, they manifest themselves in alterations of cardiac strains, fiber stretches, and muscle volume. Recent attempts to shed light on the mechanistic origin of heart failure utilize continuum theories of growth to predict the maladaptation of the heart in response to pressure or volume overload. However, despite a general consensus on the representation of growth through a second order tensor, the precise format of this growth tensor remains unknown. Here we show that infarct-induced cardiac dilation is associated with a chronic longitudinal growth, accompanied by a chronic thinning of the ventricular wall. In controlled in vivo experiments throughout a period of seven weeks, we found that the lateral left ventricular wall adjacent to the infarct grows longitudinally by more than 10%, thins by more than 25%, lengthens in fiber direction by more than 5%, and decreases its volume by more than 15%. Our results illustrate how a local loss of blood supply induces chronic alterations in structure and function in adjacent regions of the ventricular wall. We anticipate our findings to be the starting point for a series of in vivo studies to calibrate and validate constitutive models for cardiac growth. Ultimately, these models could be useful to guide the design of novel therapies, which allow us to control the progression of heart failure.

View details for DOI 10.1016/j.jmbbm.2011.12.006

View details for Web of Science ID 000302586300015

View details for PubMedID 22402163

View details for PubMedCentralID PMC3298662
On the biomechanics and mechanobiology of growing skin JOURNAL OF THEORETICAL BIOLOGY Zoellner, A. M., Tepole, A. B., Kuhl, E. 2012; 297: 166-175
Abstract

Skin displays an impressive functional plasticity, which allows it to adapt gradually to environmental changes. Tissue expansion takes advantage of this adaptation, and induces a controlled in situ skin growth for defect correction in plastic and reconstructive surgery. Stretches beyond the skin's physiological limit invoke several mechanotransduction pathways, which increase mitotic activity and collagen synthesis, ultimately resulting in a net gain in skin surface area. However, the interplay between mechanics and biology during tissue expansion remains unquantified. Here, we present a continuum model for skin growth that summarizes the underlying mechanotransduction pathways collectively in a single phenomenological variable, the strain-driven area growth. We illustrate the governing equations for growing biological membranes, and demonstrate their computational solution within a nonlinear finite element setting. In displacement-controlled equi-biaxial extension tests, the model accurately predicts the experimentally observed histological, mechanical, and structural features of growing skin, both qualitatively and quantitatively. Acute and chronic elastic uniaxial stretches are 25% and 10%, compared to 36% and 10% reported in the literature. Acute and chronic thickness changes are -28% and -12%, compared to -22% and -7% reported in the literature. Chronic fractional weight gain is 3.3, compared to 2.7 for wet weight and 3.3 for dry weight reported in the literature. In two clinical cases of skin expansion in pediatric forehead reconstruction, the model captures the clinically observed mechanical and structural responses, both acutely and chronically. Our results demonstrate that the field theories of continuum mechanics can reliably predict the mechanical manipulation of thin biological membranes by controlling their mechanotransduction pathways through mechanical overstretch. We anticipate that the proposed skin growth model can be generalized to arbitrary biological membranes, and that it can serve as a valuable tool to virtually manipulate living tissues, simply by means of changes in the mechanical environment.

View details for DOI 10.1016/j.jtbi.2011.12.022

View details for Web of Science ID 000300652000016

View details for PubMedID 22227432
Computational modeling of bone density profiles in response to gait: a subject-specific approach BIOMECHANICS AND MODELING IN MECHANOBIOLOGY Pang, H., Shiwalkar, A. P., Madormo, C. M., Taylor, R. E., Andriacchi, T. P., Kuhl, E. 2012; 11 (3-4): 379-390
Abstract

The goal of this study is to explore the potential of computational growth models to predict bone density profiles in the proximal tibia in response to gait-induced loading. From a modeling point of view, we design a finite element-based computational algorithm using the theory of open system thermodynamics. In this algorithm, the biological problem, the balance of mass, is solved locally on the integration point level, while the mechanical problem, the balance of linear momentum, is solved globally on the node point level. Specifically, the local bone mineral density is treated as an internal variable, which is allowed to change in response to mechanical loading. From an experimental point of view, we perform a subject-specific gait analysis to identify the relevant forces during walking using an inverse dynamics approach. These forces are directly applied as loads in the finite element simulation. To validate the model, we take a Dual-Energy X-ray Absorptiometry scan of the subject's right knee from which we create a geometric model of the proximal tibia. For qualitative validation, we compare the computationally predicted density profiles to the bone mineral density extracted from this scan. For quantitative validation, we adopt the region of interest method and determine the density values at fourteen discrete locations using standard and custom-designed image analysis tools. Qualitatively, our two- and three-dimensional density predictions are in excellent agreement with the experimental measurements. Quantitatively, errors are less than 3% for the two-dimensional analysis and less than 10% for the three-dimensional analysis. The proposed approach has the potential to ultimately improve the long-term success of possible treatment options for chronic diseases such as osteoarthritis on a patient-specific basis by accurately addressing the complex interactions between ambulatory loads and tissue changes.

View details for DOI 10.1007/s10237-011-0318-y

View details for Web of Science ID 000300518000008

View details for PubMedID 21604146
Mitral Valve Annuloplasty A Quantitative Clinical and Mechanical Comparison of Different Annuloplasty Devices ANNALS OF BIOMEDICAL ENGINEERING Rausch, M. K., Bothe, W., Kvitting, J. E., Swanson, J. C., Miller, D. C., Kuhl, E. 2012; 40 (3): 750-761
Abstract

Mitral valve annuloplasty is a common surgical technique used in the repair of a leaking valve by implanting an annuloplasty device. To enhance repair durability, these devices are designed to increase leaflet coaptation, while preserving the native annular shape and motion; however, the precise impact of device implantation on annular deformation, strain, and curvature is unknown. In this article, we quantify how three frequently used devices significantly impair native annular dynamics. In controlled in vivo experiments, we surgically implanted 11 flexible-incomplete, 11 semi-rigid-complete, and 12 rigid-complete devices around the mitral annuli of 34 sheep, each tagged with 16 equally spaced tantalum markers. We recorded four-dimensional marker coordinates using biplane videofluoroscopy, first with device and then without, which were used to create mathematical models using piecewise cubic splines. Clinical metrics (characteristic anatomical distances) revealed significant global reduction in annular dynamics upon device implantation. Mechanical metrics (strain and curvature fields) explained this reduction via a local loss of anterior dilation and posterior contraction. Overall, all three devices unfavorably caused reduction in annular dynamics. The flexible-incomplete device, however, preserved native annular dynamics to a larger extent than the complete devices. Heterogeneous strain and curvature profiles suggest the need for heterogeneous support, which may spawn more rational design of annuloplasty devices using design concepts of functionally graded materials.

View details for DOI 10.1007/s10439-011-0442-y

View details for Web of Science ID 000300770200018

View details for PubMedID 22037916
MODELING GROWTH IN TISSUE EXPANSION ASME Summer Bioengineering Conference (SBC) Zoellner, A. M., Tepole, A. B., Kuhl, E. AMER SOC MECHANICAL ENGINEERS. 2012: 213–214
View details for Web of Science ID 000325036600106
CHRONIC MITRAL VALVE LEAFLET GROWTH FOLLOWING MYOCARDIAL INFARCTION ASME Summer Bioengineering Conference (SBC) Rausch, M. K., Tibayan, F. A., Miller, D. C., Kuhl, E. AMER SOC MECHANICAL ENGINEERS. 2012: 1015–1016
View details for Web of Science ID 000325036600507
Computational modeling of electrocardiograms: Repolarization and T-wave polarity in the human heart Comp Meth Biomech Biomed Eng, accepted for publication. Hurtado D, Kuhl E 2012
Consistent formulation of the growth process at the kinematic and constitutive level for soft tissues composed of multiple constituents COMPUTER METHODS IN BIOMECHANICS AND BIOMEDICAL ENGINEERING Schmid, H., PAULI, L., Paulus, A., Kuhl, E., Itskov, M. 2012; 15 (5): 547-561
Abstract

Previous studies have investigated the possibilities of modelling the change in volume and change in density of biomaterials. This can be modelled at the constitutive or the kinematic level. This work introduces a consistent formulation at the kinematic and constitutive level for growth processes. Most biomaterials consist of many constituents and can be approximated as being incompressible. These two conditions (many constituents and incompressibility) suggest a straightforward implementation in the context of the finite element (FE) method which could now be validated more easily against histological measurements. Its key characteristic variable is the normalised partial mass change. Using the concept of homeostatic equilibrium, we suggest two complementary growth laws in which the evolution of the normalised partial mass change is governed by an ordinary differential equation in terms of either the Piola-Kirchhoff stress or the Green-Lagrange strain. We combine this approach with the classical incompatibility condition and illustrate its algorithmic implementation within a fully nonlinear FE approach. This approach is first illustrated for a simple uniaxial tension and extension test for pure volume change and pure density change and is validated against previous numerical results. Finally, a physiologically based example of a two-phase model is presented which is a combination of volume and density changes. It can be concluded that the effect of hyper-restoration may be due to the systemic effect of degradation and adaptation of given constituents.

View details for DOI 10.1080/10255842.2010.548325

View details for Web of Science ID 000303561200010

View details for PubMedID 21347909
A fully implicit finite element method for bidomain models of cardiac electrophysiology COMPUTER METHODS IN BIOMECHANICS AND BIOMEDICAL ENGINEERING Dal, H., Goktepe, S., Kaliske, M., Kuhl, E. 2012; 15 (6): 645-656
Abstract

This work introduces a novel, unconditionally stable and fully coupled finite element method for the bidomain system of equations of cardiac electrophysiology. The transmembrane potential Φ(i)-Φ(e) and the extracellular potential Φ(e) are treated as independent variables. To this end, the respective reaction-diffusion equations are recast into weak forms via a conventional isoparametric Galerkin approach. The resultant nonlinear set of residual equations is consistently linearised. The method results in a symmetric set of equations, which reduces the computational time significantly compared to the conventional solution algorithms. The proposed method is inherently modular and can be combined with phenomenological or ionic models across the cell membrane. The efficiency of the method and the comparison of its computational cost with respect to the simplified monodomain models are demonstrated through representative numerical examples.

View details for DOI 10.1080/10255842.2011.554410

View details for Web of Science ID 000303560100008

View details for PubMedID 21491253
IN VITRO/IN SILICO CHARACTERIZATION OF ACTIVE AND PASSIVE STRESSES IN CARDIAC MUSCLE INTERNATIONAL JOURNAL FOR MULTISCALE COMPUTATIONAL ENGINEERING Boel, M., Abilez, O. J., Assar, A. N., Zarins, C. K., Kuhl, E. 2012; 10 (2): 171-188
View details for Web of Science ID 000302835000006
SPECIAL ISSUE ACTIVE TISSUE MODELING: FROM SINGLE MUSCLE CELLS TO MUSCULAR CONTRACTION INTERNATIONAL JOURNAL FOR MULTISCALE COMPUTATIONAL ENGINEERING Boel, M., Kuhl, E. 2012; 10 (2): VII-VIII
View details for Web of Science ID 000302835000001
COMPUTATIONAL MODELLING OF OPTOGENETICS IN CARDIAC CELLS ASME Summer Bioengineering Conference (SBC) Wong, J., Abilez, O., Kuhl, E. AMER SOC MECHANICAL ENGINEERS. 2012: 355–356
View details for Web of Science ID 000325036600177
FINITE ELEMENT MODELING OF FLAP DESIGN AFTER SKIN EXPANSION ASME Summer Bioengineering Conference (SBC) Tepole, A. B., Zollner, A. M., Kuhl, E. AMER SOC MECHANICAL ENGINEERS. 2012: 1017–1018
View details for Web of Science ID 000325036600508
Computational modeling of growth: systemic and pulmonary hypertension in the heart BIOMECHANICS AND MODELING IN MECHANOBIOLOGY Rausch, M. K., Dam, A., Goktepe, S., Abilez, O. J., Kuhl, E. 2011; 10 (6): 799-811
Abstract

We introduce a novel constitutive model for growing soft biological tissue and study its performance in two characteristic cases of mechanically induced wall thickening of the heart. We adopt the concept of an incompatible growth configuration introducing the multiplicative decomposition of the deformation gradient into an elastic and a growth part. The key feature of the model is the definition of the evolution equation for the growth tensor which we motivate by pressure-overload-induced sarcomerogenesis. In response to the deposition of sarcomere units on the molecular level, the individual heart muscle cells increase in diameter, and the wall of the heart becomes progressively thicker. We present the underlying constitutive equations and their algorithmic implementation within an implicit nonlinear finite element framework. To demonstrate the features of the proposed approach, we study two classical growth phenomena in the heart: left and right ventricular wall thickening in response to systemic and pulmonary hypertension.

View details for DOI 10.1007/s10237-010-0275-x

View details for Web of Science ID 000296634000001

View details for PubMedID 21188611
Growing skin: A computational model for skin expansion in reconstructive surgery JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS Tepole, A. B., Ploch, C. J., Wong, J., Gosain, A. K., Kuhl, E. 2011; 59 (10): 2177-2190
Abstract

The goal of this manuscript is to establish a novel computational model for stretch-induced skin growth during tissue expansion. Tissue expansion is a common surgical procedure to grow extra skin for reconstructing birth defects, burn injuries, or cancerous breasts. To model skin growth within the framework of nonlinear continuum mechanics, we adopt the multiplicative decomposition of the deformation gradient into an elastic and a growth part. Within this concept, we characterize growth as an irreversible, stretch-driven, transversely isotropic process parameterized in terms of a single scalar-valued growth multiplier, the in-plane area growth. To discretize its evolution in time, we apply an unconditionally stable, implicit Euler backward scheme. To discretize it in space, we utilize the finite element method. For maximum algorithmic efficiency and optimal convergence, we suggest an inner Newton iteration to locally update the growth multiplier at each integration point. This iteration is embedded within an outer Newton iteration to globally update the deformation at each finite element node. To demonstrate the characteristic features of skin growth, we simulate the process of gradual tissue expander inflation. To visualize growth-induced residual stresses, we simulate a subsequent tissue expander deflation. In particular, we compare the spatio-temporal evolution of area growth, elastic strains, and residual stresses for four commonly available tissue expander geometries. We believe that predictive computational modeling can open new avenues in reconstructive surgery to rationalize and standardize clinical process parameters such as expander geometry, expander size, expander placement, and inflation timing.

View details for DOI 10.1016/j.jmps.2011.05.004

View details for Web of Science ID 000295549500013

View details for PubMedCentralID PMC3212404
Active contraction of cardiac muscle: In vivo characterization of mechanical activation sequences in the beating heart JOURNAL OF THE MECHANICAL BEHAVIOR OF BIOMEDICAL MATERIALS Tsamis, A., Bothe, W., Kvitting, J. E., Swanson, J. C., Miller, D. C., Kuhl, E. 2011; 4 (7): 1167-1176
Abstract

Progressive alterations in cardiac wall strains are a classic hallmark of chronic heart failure. Accordingly, the objectives of this study are to establish a baseline characterization of cardiac strains throughout the cardiac cycle, to quantify temporal, regional, and transmural variations of active fiber contraction, and to identify pathways of mechanical activation in the healthy beating heart. To this end, we insert two sets of twelve radiopaque beads into the heart muscle of nine sheep; one in the anterior-basal and one in the lateral-equatorial left ventricular wall. During three consecutive heartbeats, we record the bead coordinates via biplane videofluoroscopy. From the resulting four-dimensional data sets, we calculate the temporally and transmurally varying Green-Lagrange strains in the anterior and lateral wall. To quantify active contraction, we project the strains onto the local muscle fiber directions. We observe that mechanical activation is initiated at the endocardium slightly after end diastole and progresses transmurally outward, reaching the epicardium slightly before end systole. Accordingly, fibers near the outer wall are in contraction for approximately half of the cardiac cycle while fibers near the inner wall are in contraction almost throughout the entire cardiac cycle. In summary, cardiac wall strains display significant temporal, regional, and transmural variations. Quantifying wall strain profiles might be of particular clinical significance when characterizing stages of left ventricular remodeling, but also of engineering relevance when designing new biomaterials of similar structure and function.

View details for DOI 10.1016/j.jmbbm.2011.03.027

View details for Web of Science ID 000294187500025

View details for PubMedID 21783125
Multiscale Computational Models for Optogenetic Control of Cardiac Function BIOPHYSICAL JOURNAL Abilez, O. J., Wong, J., Prakash, R., Deisseroth, K., Zarins, C. K., Kuhl, E. 2011; 101 (6): 1326-1334
Abstract

The ability to stimulate mammalian cells with light has significantly changed our understanding of electrically excitable tissues in health and disease, paving the way toward various novel therapeutic applications. Here, we demonstrate the potential of optogenetic control in cardiac cells using a hybrid experimental/computational technique. Experimentally, we introduced channelrhodopsin-2 into undifferentiated human embryonic stem cells via a lentiviral vector, and sorted and expanded the genetically engineered cells. Via directed differentiation, we created channelrhodopsin-expressing cardiomyocytes, which we subjected to optical stimulation. To quantify the impact of photostimulation, we assessed electrical, biochemical, and mechanical signals using patch-clamping, multielectrode array recordings, and video microscopy. Computationally, we introduced channelrhodopsin-2 into a classic autorhythmic cardiac cell model via an additional photocurrent governed by a light-sensitive gating variable. Upon optical stimulation, the channel opens and allows sodium ions to enter the cell, inducing a fast upstroke of the transmembrane potential. We calibrated the channelrhodopsin-expressing cell model using single action potential readings for different photostimulation amplitudes, pulse widths, and frequencies. To illustrate the potential of the proposed approach, we virtually injected channelrhodopsin-expressing cells into different locations of a human heart, and explored its activation sequences upon optical stimulation. Our experimentally calibrated computational toolbox allows us to virtually probe landscapes of process parameters, and identify optimal photostimulation sequences toward pacing hearts with light.

View details for DOI 10.1016/j.bpj.2011.08.004

View details for Web of Science ID 000295197300006

View details for PubMedID 21943413

View details for PubMedCentralID PMC3177076
Rigid, Complete Annuloplasty Rings Increase Anterior Mitral Leaflet Strains in the Normal Beating Ovine Heart Annual Meeting of the American-Heart-Association Bothe, W., Kuhl, E., Kvitting, J. E., Rausch, M. K., Goektepe, S., Swanson, J. C., Farahmandnia, S., Ingels, N. B., Miller, D. C. LIPPINCOTT WILLIAMS & WILKINS. 2011: S81–S96
Abstract

Annuloplasty ring or band implantation during surgical mitral valve repair perturbs mitral annular dimensions, dynamics, and shape, which have been associated with changes in anterior mitral leaflet (AML) strain patterns and suboptimal long-term repair durability. We hypothesized that rigid rings with nonphysiological three-dimensional shapes, but not saddle-shaped rigid rings or flexible bands, increase AML strains.Sheep had 23 radiopaque markers inserted: 7 along the anterior mitral annulus and 16 equally spaced on the AML. True-sized Cosgrove-Edwards flexible, partial band (n=12), rigid, complete St Jude Medical rigid saddle-shaped (n=12), Carpentier-Edwards Physio (n=12), Edwards IMR ETlogix (n=11), and Edwards GeoForm (n=12) annuloplasty rings were implanted in a releasable fashion. Under acute open-chest conditions, 4-dimensional marker coordinates were obtained using biplane videofluoroscopy along with hemodynamic parameters with the ring inserted and after release. Marker coordinates were triangulated, and the largest maximum principal AML strains were determined during isovolumetric relaxation. No relevant changes in hemodynamics occurred. Compared with the respective control state, strains increased significantly with rigid saddle-shaped annuloplasty ring, Carpentier-Edwards Physio, Edwards IMR ETlogix, and Edwards GeoForm (0.14 ± 0.05 versus 0.16 ± 0.05, P=0.024, 0.15 ± 0.03 versus 0.18 ± 0.04, P=0.020, 0.11 ± 0.05 versus 0.14 ± 0.05, P=0.042, and 0.13 ± 0.05 versus 0.16 ± 0.05, P=0.009), but not with Cosgrove-Edwards band (0.15 ± 0.05 versus 0.15 ± 0.04, P=0.973).Regardless of three-dimensional shape, rigid, complete annuloplasty rings, but not a flexible, partial band, increased AML strains in the normal beating ovine heart. Clinical studies are needed to determine whether annuloplasty rings affect AML strains in patients, and, if so, whether ring-induced perturbations in leaflet strain states are linked to repair failure.

View details for DOI 10.1161/CIRCULATIONAHA.110.011163

View details for Web of Science ID 000294782800011

View details for PubMedID 21911823
A novel method for quantifying the in-vivo mechanical effect of material injected into a myocardial infarction. Annals of thoracic surgery Wenk, J. F., Eslami, P., Zhang, Z., Xu, C., Kuhl, E., Gorman, J. H., Robb, J. D., Ratcliffe, M. B., Gorman, R. C., Guccione, J. M. 2011; 92 (3): 935-941
Abstract

Infarcted regions of myocardium exhibit functional impairment ranging in severity from hypokinesis to dyskinesis. We sought to quantify the effects of injecting a calcium hydroxyapatite-based tissue filler on the passive material response of infarcted left ventricles.Three-dimensional finite element models of the left ventricle were developed using three-dimensional echocardiography data from sheep with a treated and untreated anteroapical infarct, to estimate the material properties (stiffness) in the infarct and remote regions. This was accomplished by matching experimentally determined left ventricular volumes, and minimizing radial strain in the treated infarct, which is indicative of akinesia. The nonlinear stress-strain relationship for the diastolic myocardium was anisotropic with respect to the local muscle fiber direction, and an elastance model for active fiber stress was incorporated.It was found that the passive stiffness parameter, C, in the treated infarct region is increased by nearly 345 times the healthy remote value. Additionally, the average myofiber stress in the treated left ventricle was significantly reduced in both the remote and infarct regions.Overall, injection of tissue filler into the infarct was found to render it akinetic and reduce stress in the left ventricle, which could limit the adverse remodeling that leads to heart failure.

View details for DOI 10.1016/j.athoracsur.2011.04.089

View details for PubMedID 21871280
Characterization of Mitral Valve Annular Dynamics in the Beating Heart ANNALS OF BIOMEDICAL ENGINEERING Rausch, M. K., Bothe, W., Kvitting, J. E., Swanson, J. C., Ingels, N. B., Miller, D. C., Kuhl, E. 2011; 39 (6): 1690-1702
Abstract

The objective of this study is to establish a mathematical characterization of the mitral valve annulus that allows a precise qualitative and quantitative assessment of annular dynamics in the beating heart. We define annular geometry through 16 miniature markers sewn onto the annuli of 55 sheep. Using biplane videofluoroscopy, we record marker coordinates in vivo. By approximating these 16 marker coordinates through piecewise cubic splines, we generate a smooth mathematical representation of the 55 mitral annuli. We time-align these 55 annulus representations with respect to characteristic hemodynamic time points to generate an averaged baseline annulus representation. To characterize annular physiology, we extract classical clinical metrics of annular form and function throughout the cardiac cycle. To characterize annular dynamics, we calculate displacements, strains, and curvature from the discrete mathematical representations. To illustrate potential future applications of this approach, we create rapid prototypes of the averaged mitral annulus at characteristic hemodynamic time points. In summary, this study introduces a novel mathematical model that allows us to identify temporal, regional, and inter-subject variations of clinical and mechanical metrics that characterize mitral annular form and function. Ultimately, this model can serve as a valuable tool to optimize both surgical and interventional approaches that aim at restoring mitral valve competence.

View details for DOI 10.1007/s10439-011-0272-y

View details for Web of Science ID 000290724900009

View details for PubMedID 21336803
In vivo dynamic strains of the ovine anterior mitral valve leaflet JOURNAL OF BIOMECHANICS Rausch, M. K., Bothe, W., Kvitting, J. E., Goektepe, S., Miller, D. C., Kuhl, E. 2011; 44 (6): 1149-1157
Abstract

Understanding the mechanics of the mitral valve is crucial in terms of designing and evaluating medical devices and techniques for mitral valve repair. In the current study we characterize the in vivo strains of the anterior mitral valve leaflet. On cardiopulmonary bypass, we sew miniature markers onto the leaflets of 57 sheep. During the cardiac cycle, the coordinates of these markers are recorded via biplane fluoroscopy. From the resulting four-dimensional data sets, we calculate areal, maximum principal, circumferential, and radial leaflet strains and display their profiles on the averaged leaflet geometry. Average peak areal strains are 13.8±6.3%, maximum principal strains are 13.0±4.7%, circumferential strains are 5.0±2.7%, and radial strains are 7.8±4.3%. Maximum principal strains are largest in the belly region, where they are aligned with the circumferential direction during diastole switching into the radial direction during systole. Circumferential strains are concentrated at the distal portion of the belly region close to the free edge of the leaflet, while radial strains are highest in the center of the leaflet, stretching from the posterior to the anterior commissure. In summary, leaflet strains display significant temporal, regional, and directional variations with largest values inside the belly region and toward the free edge. Characterizing strain distribution profiles might be of particular clinical significance when optimizing mitral valve repair techniques in terms of forces on suture lines and on medical devices.

View details for DOI 10.1016/j.jbiomech.2011.01.020

View details for Web of Science ID 000290187500025

View details for PubMedID 21306716
Perspectives on biological growth and remodeling JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS Ambrosi, D., Ateshian, G. A., Arruda, E. M., Cowin, S. C., Dumais, J., Goriely, A., Holzapfel, G. A., Humphrey, J. D., Kemkemer, R., Kuhl, E., Olberding, J. E., Taber, L. A., Garikipati, K. 2011; 59 (4): 863-883
Abstract

The continuum mechanical treatment of biological growth and remodeling has attracted considerable attention over the past fifteen years. Many aspects of these problems are now well-understood, yet there remain areas in need of significant development from the standpoint of experiments, theory, and computation. In this perspective paper we review the state of the field and highlight open questions, challenges, and avenues for further development.

View details for DOI 10.1016/j.jmps.2010.12.011

View details for Web of Science ID 000289136300008
Computational modeling of electrochemical coupling: A novel finite element approach towards ionic models for cardiac electrophysiology COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING Wong, J., Goktepe, S., Kuhl, E. 2011; 200 (45-46): 3139-3158
View details for DOI 10.1016/j.cma.2011.07.003

View details for Web of Science ID 000295753800016
Computational modeling of passive myocardium INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING Goektepe, S., Acharya, S. N., Wong, J., Kuhl, E. 2011; 27 (1): 1-12
View details for DOI 10.1002/cnm.1402

View details for Web of Science ID 000287141000001
Anterior Mitral Leaflet Curvature During the Cardiac Cycle in the Normal Ovine Heart CIRCULATION Kvitting, J. E., Bothe, W., Goektepe, S., Rausch, M. K., Swanson, J. C., Kuhl, E., Ingels, N. B., Miller, D. C. 2010; 122 (17): 1683-1689
Abstract

The dynamic changes of anterior mitral leaflet (AML) curvature are of primary importance for optimal left ventricular filling and emptying but are incompletely characterized.Sixteen radiopaque markers were sutured to the AML in 11 sheep, and 4-dimensional marker coordinates were acquired with biplane videofluoroscopy. A surface subdivision algorithm was applied to compute the curvature across the AML at midsystole and at maximal valve opening. Septal-lateral (SL) and commissure-commissure (CC) curvature profiles were calculated along the SL AML meridian (M(SL))and CC AML meridian (M(CC)), respectively, with positive curvature being concave toward the left atrium. At midsystole, the M(SL) was concave near the mitral annulus, turned from concave to convex across the belly, and was convex along the free edge. At maximal valve opening, the M(SL) was flat near the annulus, turned from slightly concave to convex across the belly, and flattened toward the free edge. In contrast, the M(CC) was concave near both commissures and convex at the belly at midsystole but convex near both commissures and concave at the belly at maximal valve opening.While the SL curvature of the AML along the M(SL) is similar across the belly region at midsystole and early diastole, the CC curvature of the AML along the M(CC) flips, with the belly being convex to the left atrium at midsystole and concave at maximal valve opening. These curvature orientations suggest optimal left ventricular inflow and outflow shapes of the AML and should be preserved during catheter or surgical interventions.

View details for DOI 10.1161/CIRCULATIONAHA.110.961243

View details for Web of Science ID 000283440600012

View details for PubMedID 20937973
A generic approach towards finite growth with examples of athlete's heart, cardiac dilation, and cardiac wall thickening JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS Goktepe, S., Abilez, O. J., Kuhl, E. 2010; 58 (10): 1661-1680
View details for DOI 10.1016/j.jmps.2010.07.003

View details for Web of Science ID 000282856200014
A multiscale model for eccentric and concentric cardiac growth through sarcomerogenesis JOURNAL OF THEORETICAL BIOLOGY Goktepe, S., Abilez, O. J., Parker, K. K., Kuhl, E. 2010; 265 (3): 433-442
Abstract

We present a novel computational model for maladaptive cardiac growth in which kinematic changes of the cardiac chambers are attributed to alterations in cytoskeletal architecture and in cellular morphology. We adopt the concept of finite volume growth characterized through the multiplicative decomposition of the deformation gradient into an elastic part and a growth part. The functional form of its growth tensor is correlated to sarcomerogenesis, the creation and deposition of new sarcomere units. In response to chronic volume-overload, an increased diastolic wall strain leads to the addition of sarcomeres in series, resulting in a relative increase in cardiomyocyte length, associated with eccentric hypertrophy and ventricular dilation. In response to chronic pressure-overload, an increased systolic wall stress leads to the addition of sacromeres in parallel, resulting in a relative increase in myocyte cross sectional area, associated with concentric hypertrophy and ventricular wall thickening. The continuum equations for both forms of maladaptive growth are discretized in space using a nonlinear finite element approach, and discretized in time using the implicit Euler backward scheme. We explore a generic bi-ventricular heart model in response to volume- and pressure-overload to demonstrate how local changes in cellular morphology translate into global alterations in cardiac form and function.

View details for DOI 10.1016/j.jtbi.2010.04.023

View details for Web of Science ID 000280374100023

View details for PubMedID 20447409
Natural element analysis of the Cahn-Hilliard phase-field model COMPUTATIONAL MECHANICS Rajagopal, A., Fischer, P., Kuhl, E., Steinmann, P. 2010; 46 (3): 471-493
View details for DOI 10.1007/s00466-010-0490-4

View details for Web of Science ID 000277937300008
Anterior mitral leaflet curvature in the beating ovine heart: a case study using videofluoroscopic markers and subdivision surfaces BIOMECHANICS AND MODELING IN MECHANOBIOLOGY Goektepe, S., Bothe, W., Kvitting, J. E., Swanson, J. C., Ingels, N. B., Miller, D. C., Kuhl, E. 2010; 9 (3): 281-293
View details for DOI 10.1007/s10237-009-0176-z

View details for Web of Science ID 000277711400003
Anterior mitral leaflet curvature in the beating ovine heart: a case study using videofluoroscopic markers and subdivision surfaces. Biomechanics and modeling in mechanobiology Göktepe, S., Bothe, W., Kvitting, J. E., Swanson, J. C., Ingels, N. B., Miller, D. C., Kuhl, E. 2010; 9 (3): 281-293
Abstract

The implantation of annuloplasty rings is a common surgical treatment targeted to re-establish mitral valve competence in patients with mitral regurgitation. It is hypothesized that annuloplasty ring implantation influences leaflet curvature, which in turn may considerably impair repair durability. This research is driven by the vision to design repair devices that optimize leaflet curvature to reduce valvular stress. In pursuit of this goal, the objective of this manuscript is to quantify leaflet curvature in ovine models with and without annuloplasty ring using in vivo animal data from videofluoroscopic marker analysis. We represent the surface of the anterior mitral leaflet based on 23 radiopaque markers using subdivision surfaces techniques. Quartic box-spline functions are applied to determine leaflet curvature on overlapping subdivision patches. We illustrate the virtual reconstruction of the leaflet surface for both interpolating and approximating algorithms. Different scalar-valued metrics are introduced to quantify leaflet curvature in the beating heart using the approximating subdivision scheme. To explore the impact of annuloplasty ring implantation, we analyze ring-induced curvature changes at characteristic instances throughout the cardiac cycle. The presented results demonstrate that the fully automated subdivision surface procedure can successfully reconstruct a smooth representation of the anterior mitral valve from a limited number of markers at a high temporal resolution of approximately 60 frames per minute.

View details for DOI 10.1007/s10237-009-0176-z

View details for PubMedID 19890668
Atrial and ventricular fibrillation: computational simulation of spiral waves in cardiac tissue ARCHIVE OF APPLIED MECHANICS Goktepe, S., Wong, J., Kuhl, E. 2010; 80 (5): 569-580
View details for DOI 10.1007/s00419-009-0384-0

View details for Web of Science ID 000275787600011
Stress concentrations in fractured compact bone simulated with a special class of anisotropic gradient elasticity INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES Gitman, I. M., Askes, H., Kuhl, E., Aifantis, E. C. 2010; 47 (9): 1099-1107
View details for DOI 10.1016/j.ijsolstr.2009.11.020

View details for Web of Science ID 000276127200001
Computational modeling of electrocardiograms: A finite element approach toward cardiac excitation INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING Kotikanyadanam, M., Goktepe, S., Kuhl, E. 2010; 26 (5): 524-533
View details for DOI 10.1002/cnm.1273

View details for Web of Science ID 000277552200003
Characterization of indentation response and stiffness reduction of bone using a continuum damage model JOURNAL OF THE MECHANICAL BEHAVIOR OF BIOMEDICAL MATERIALS Zhang, J., Michalenko, M. M., Kuhl, E., Ovaert, T. C. 2010; 3 (2): 189-202
Abstract

Indentation tests can be used to characterize the mechanical properties of bone at small load/length scales offering the possibility of utilizing very small test specimens, which can be excised using minimally-invasive procedures. In addition, the need for mechanical property data from bone may be a requirement for fundamental multi-scale experiments, changes in nano- and micro-mechanical properties (e.g., as affected by changes in bone mineral density) due to drug therapies, and/or the development of computational models. Load vs. indentation depth data, however, is more complex than those obtained from typical macro-scale experiments, primarily due to the mixed state of stress, and thus interpretation of the data and extraction of mechanical properties is more challenging. Previous studies have shown that cortical bone exhibits a visco-elastic response combined with permanent deformation during indentation tests, and that the load vs. indentation depth response can be simulated using a visco-elastic/plastic material model. The model successfully captures the loading and creep displacement behavior, however, it does not adequately reproduce the unloading response near the end of the unloading cycle, where a pronounced decrease in contact stiffness is observed. It is proposed that the stiffness reduction observed in bone results from an increase in damage; therefore, a plastic-damage model was investigated and shown capable of simulating a typical bone indentation response through an axisymmetric finite element simulation. The plastic-damage model was able to reproduce the full indentation response, especially the reduced stiffness behavior exhibited during the latter stages of unloading. The results suggest that the plastic-damage model is suitable for describing the complex indentation response of bone and may provide further insight into the relationship between model parameters and mechanical/physical properties.

View details for DOI 10.1016/j.jmbbm.2009.08.001

View details for Web of Science ID 000274987000007

View details for PubMedID 20129418
Electromechanics of the heart: a unified approach to the strongly coupled excitation-contraction problem COMPUTATIONAL MECHANICS Goektepe, S., Kuhl, E. 2010; 45 (2-3): 227-243
View details for DOI 10.1007/s00466-009-0434-z

View details for Web of Science ID 000272118100009
Computational Homogenization of Confined Frictional Granular Matter IUTAM Symposium on Variational Concepts with Applications to the Mechanics of Materials Meier, H. A., Steinmann, P., Kuhl, E. SPRINGER. 2010: 157–169
View details for DOI 10.1007/978-90-481-9195-6_12

View details for Web of Science ID 000290694500012
Dilation and Hypertrophy: A Cell-Based Continuum Mechanics Approach Towards Ventricular Growth and Remodeling International-Union-of-Theoretical-and-Applied-Mechanics Symposium on Cellular, Molecular and Tissue Mechanics Ulerich, J., Goektepe, S., Kuhl, E. SPRINGER. 2010: 237–244
View details for DOI 10.1007/978-90-481-3348-2_20

View details for Web of Science ID 000276397800020
IN VITRO ASSESSMENT OF RAT HEART FORCE GENERATION: A QUANTITATIVE APPROACH FOR PREDICTING OUTCOMES FROM PLURIPOTENT STEM CELL-DERIVED THERAPY FOR MYOCARDIAL INFARCTION 12th ASME Summer Bioengineering Conference Guillou, L., Abilez, O. J., Baugh, J., Billakanti, G., Zarins, C. K., Kuhl, E. AMER SOC MECHANICAL ENGINEERS. 2010: 717–718
View details for Web of Science ID 000290705300359
Regional stiffening of the mitral valve anterior leaflet in the beating ovine heart JOURNAL OF BIOMECHANICS Krishnamurthy, G., Itoh, A., Swanson, J. C., Bothe, W., Karlsson, M., Kuhl, E., Miller, D. C., Ingels, N. B. 2009; 42 (16): 2697-2701
Abstract

Left atrial muscle extends into the proximal third of the mitral valve (MV) anterior leaflet and transient tensing of this muscle has been proposed as a mechanism aiding valve closure. If such tensing occurs, regional stiffness in the proximal anterior mitral leaflet will be greater during isovolumic contraction (IVC) than isovolumic relaxation (IVR) and this regional stiffness difference will be selectively abolished by beta-receptor blockade. We tested this hypothesis in the beating ovine heart. Radiopaque markers were sewn around the MV annulus and on the anterior MV leaflet in 10 sheep hearts. Four-dimensional marker coordinates were obtained from biplane videofluoroscopy before (CRTL) and after administration of esmolol (ESML). Heterogeneous finite element models of each anterior leaflet were developed using marker coordinates over matched pressures during IVC and IVR for CRTL and ESML. Leaflet displacements were simulated using measured left ventricular and atrial pressures and a response function was computed as the difference between simulated and measured displacements. Circumferential and radial elastic moduli for ANNULAR, BELLY and EDGE leaflet regions were iteratively varied until the response function reached a minimum. The stiffness values at this minimum were interpreted as the in vivo regional material properties of the anterior leaflet. For all regions and all CTRL beats IVC stiffness was 40-58% greater than IVR stiffness. ESML reduced ANNULAR IVC stiffness to ANNULAR IVR stiffness values. These results strongly implicate transient tensing of leaflet atrial muscle during IVC as the basis of the ANNULAR IVC-IVR stiffness difference.

View details for DOI 10.1016/j.jbiomech.2009.08.028

View details for Web of Science ID 000273135200011

View details for PubMedID 19766222
Towards the treatment of boundary conditions for global crack path tracking in three-dimensional brittle fracture COMPUTATIONAL MECHANICS Jaeger, P., Steinmann, P., Kuhl, E. 2009; 45 (1): 91-107
View details for DOI 10.1007/s00466-009-0417-0

View details for Web of Science ID 000270428100007
Mechanics in biology: cells and tissues PREFACE PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES Ambrosi, D., Garikipati, K., Kuhl, E. 2009; 367 (1902): 3335-3337
View details for DOI 10.1098/rsta.2009.0122

View details for Web of Science ID 000268735700001

View details for PubMedID 19657002
Stress-strain behavior of mitral valve leaflets in the beating ovine heart JOURNAL OF BIOMECHANICS Krishnamurthy, G., Itoh, A., Bothe, W., Swanson, J. C., Kuhl, E., Karlsson, M., Miller, D. C., Ingels, N. B. 2009; 42 (12): 1909-1916
Abstract

Excised anterior mitral leaflets exhibit anisotropic, non-linear material behavior with pre-transitional stiffness ranging from 0.06 to 0.09 N/mm(2) and post-transitional stiffness from 2 to 9 N/mm(2). We used inverse finite element (FE) analysis to test, for the first time, whether the anterior mitral leaflet (AML), in vivo, exhibits similar non-linear behavior during isovolumic relaxation (IVR). Miniature radiopaque markers were sewn to the mitral annulus, AML, and papillary muscles in 8 sheep. Four-dimensional marker coordinates were obtained using biplane videofluoroscopic imaging during three consecutive cardiac cycles. A FE model of the AML was developed using marker coordinates at the end of isovolumic relaxation (when pressure difference across the valve is approximately zero), as the reference state. AML displacements were simulated during IVR using measured left ventricular and atrial pressures. AML elastic moduli in the radial and circumferential directions were obtained for each heartbeat by inverse FEA, minimizing the difference between simulated and measured displacements. Stress-strain curves for each beat were obtained from the FE model at incrementally increasing transmitral pressure intervals during IVR. Linear regression of 24 individual stress-strain curves (8 hearts, 3 beats each) yielded a mean (+/-SD) linear correlation coefficient (r(2)) of 0.994+/-0.003 for the circumferential direction and 0.995+/-0.003 for the radial direction. Thus, unlike isolated leaflets, the AML, in vivo, operates linearly over a physiologic range of pressures in the closed mitral valve.

View details for DOI 10.1016/j.jbiomech.2009.05.018

View details for Web of Science ID 000269734200015

View details for PubMedID 19535081
Computational modeling of cardiac electrophysiology: A novel finite element approach INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING Goektepe, S., Kuhl, E. 2009; 79 (2): 156-178
View details for DOI 10.1002/nme.2571

View details for Web of Science ID 000267788300002
Active stiffening of mitral valve leaflets in the beating heart AMERICAN JOURNAL OF PHYSIOLOGY-HEART AND CIRCULATORY PHYSIOLOGY Itoh, A., Krishnamurthy, G., Swanson, J. C., Ennis, D. B., Bothe, W., Kuhl, E., Karlsson, M., Davis, L. R., Miller, D. C., Ingels, N. B. 2009; 296 (6): H1766-H1773
Abstract

The anterior leaflet of the mitral valve (MV), viewed traditionally as a passive membrane, is shown to be a highly active structure in the beating heart. Two types of leaflet contractile activity are demonstrated: 1) a brief twitch at the beginning of each beat (reflecting contraction of myocytes in the leaflet in communication with and excited by left atrial muscle) that is relaxed by midsystole and whose contractile activity is eliminated with beta-receptor blockade and 2) sustained tone during isovolumic relaxation, insensitive to beta-blockade, but doubled by stimulation of the neurally rich region of aortic-mitral continuity. These findings raise the possibility that these leaflets are neurally controlled tissues, with potentially adaptive capabilities to meet the changing physiological demands on the heart. They also provide a basis for a permanent paradigm shift from one viewing the leaflets as passive flaps to one viewing them as active tissues whose complex function and dysfunction must be taken into account when considering not only therapeutic approaches to MV disease, but even the definitions of MV disease itself.

View details for DOI 10.1152/ajpheart.00120.2009

View details for Web of Science ID 000266397500009

View details for PubMedID 19363135
Computational modeling of muscular thin films for cardiac repair COMPUTATIONAL MECHANICS Boel, M., Reese, S., Parker, K. K., Kuhl, E. 2009; 43 (4): 535-544
View details for DOI 10.1007/s00466-008-0328-5

View details for Web of Science ID 000263059500008
COMPUTATIONAL SIMULATION OF TRAVELING ARRHYTHMIC WAVES IN MYOCARDIAL TISSUE ASME Summer Bioengineering Conference Wong, J., Goektepe, S., Kuhl, E. AMER SOC MECHANICAL ENGINEERS. 2009: 829–830
View details for Web of Science ID 000280089000415
EXPLORING CELLULAR TENSEGRITY: PHYSICAL MODELING AND COMPUTATIONAL SIMULATION ASME Summer Bioengineering Conference Zheng, C. H., Doll, J., Gu, E., Hager-Barnard, E., Huang, Z., Kia, A., Ortiz, M., Petzold, B., Usul, T., Kwon, R., Jacobs, C., Kuhl, E. AMER SOC MECHANICAL ENGINEERS. 2009: 283–284
View details for Web of Science ID 000263364700142
FIRST ATTEMPTS TOWARDS THE COMPUTATIONAL SIMULATION OF NOVEL STEM-CELL BASED POST INFARCT THERAPIES ASME Summer Bioengineering Conference Ulerich, J. P., Goktepe, S., Kuhl, E. AMER SOC MECHANICAL ENGINEERS. 2009: 417–418
View details for Web of Science ID 000263364700209
HOW TO TREAT THE LOSS OF BEAT: MODELING AND SIMULATION OF VENTRICULAR GROWTH AND REMODELING AND NOVEL POST-INFARCTION THERAPIES ASME Summer Bioengineering Conference Goktepe, S., Ulerich, J. P., Kuhl, E. AMER SOC MECHANICAL ENGINEERS. 2009: 971–972
View details for Web of Science ID 000263364700486
QUANTIFICATION OF IN VIVO STRESSES IN THE OVINE ANTERIOR MITRAL VALVE LEAFLET ASME Summer Bioengineering Conference Krishnamurthy, G., Ltoh, A., Bothe, W., Ennis, D. B., Swanson, J. C., Kuhl, E., Miller, D. C., Ingels, N. B. AMER SOC MECHANICAL ENGINEERS. 2009: 131–132
View details for Web of Science ID 000263364700066
On the Multiscale Computation of Con"ned Granular Media ECCOMAS Multidisciplinary Jubilee Symposium on Computational Challenges in Materials, Structures and Fluids Meier, H. A., Steinmann, P., Kuhl, E. SPRINGER-VERLAG BERLIN. 2009: 121–133
View details for Web of Science ID 000267056200009
CRITICAL LOADING DURING SERVE: MODELING STRESS-INDUCED BONE GROWTH IN PERFORMANCE TENNIS PLAYERS ASME Summer Bioengineering Conference Taylor, R. E., Zheng, C., Jackson, R. P., Doll, J. C., Chen, J., Holzbaur, K. R., Besier, T., Kuhl, E. AMER SOC MECHANICAL ENGINEERS. 2009: 201–202
View details for Web of Science ID 000263364700101
The phenomenon of twisted growth: humeral torsion in dominant arms of high performance tennis players COMPUTER METHODS IN BIOMECHANICS AND BIOMEDICAL ENGINEERING Taylor, R. E., Zheng, C., Jackson, R. P., Doll, J. C., Chen, J. C., Holzbaur, K. R., Besier, T., Kuhl, E. 2009; 12 (1): 83-93
Abstract

This manuscript is driven by the need to understand the fundamental mechanisms that cause twisted bone growth and shoulder pain in high performance tennis players. Our ultimate goal is to predict bone mass density in the humerus through computational analysis. The underlying study spans a unique four level complete analysis consisting of a high-speed video analysis, a musculoskeletal analysis, a finite element based density growth analysis and an X-ray based bone mass density analysis. For high performance tennis players, critical loads are postulated to occur during the serve. From high-speed video analyses, the serve phases of maximum external shoulder rotation and ball impact are identified as most critical loading situations for the humerus. The corresponding posts from the video analysis are reproduced with a musculoskeletal analysis tool to determine muscle attachment points, muscle force vectors and overall forces of relevant muscle groups. Collective representative muscle forces of the deltoid, latissimus dorsi, pectoralis major and triceps are then applied as external loads in a fully 3D finite element analysis. A problem specific nonlinear finite element based density analysis tool is developed to predict functional adaptation over time. The density profiles in response to the identified critical muscle forces during serve are qualitatively compared to X-ray based bone mass density analyses.

View details for DOI 10.1080/10255840802178046

View details for Web of Science ID 000262182900008

View details for PubMedID 18654877
Acceleration insensitive encapsulated silicon microresonator APPLIED PHYSICS LETTERS Jha, C. M., Salvia, J., Chandorkar, S. A., Melamud, R., Kuhl, E., Kenny, T. W. 2008; 93 (23)
View details for DOI 10.1063/1.3036536

View details for Web of Science ID 000261699700087
Modeling three-dimensional crack propagation-A comparison of crack path tracking strategies INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING Jaeger, R., Steinmann, R., Kuhl, E. 2008; 76 (9): 1328-1352
View details for DOI 10.1002/nme.2353

View details for Web of Science ID 000261111400002
Visualization of particle interactions in granular media IEEE TRANSACTIONS ON VISUALIZATION AND COMPUTER GRAPHICS Meier, H. A., Schlemmer, M., Wagner, C., Kerren, A., Hagen, H., Kuhl, E., Steinmann, P. 2008; 14 (5): 1110-1125
Abstract

Interaction between particles in so-called granular media, such as soil and sand, plays an important role in the context of geomechanical phenomena and numerous industrial applications. A two scale homogenization approach based on a micro and a macro scale level is briefly introduced in this paper. Computation of granular material in such a way gives a deeper insight into the context of discontinuous materials and at the same time reduces the computational costs. However, the description and the understanding of the phenomena in granular materials are not yet satisfactory. A sophisticated problem-specific visualization technique would significantly help to illustrate failure phenomena on the microscopic level. As main contribution, we present a novel 2D approach for the visualization of simulation data, based on the above outlined homogenization technique. Our visualization tool supports visualization on micro scale level as well as on macro scale level. The tool shows both aspects closely arranged in form of multiple coordinated views to give users the possibility to analyze the particle behavior effectively. A novel type of interactive rose diagrams was developed to represent the dynamic contact networks on the micro scale level in a condensed and efficient way.

View details for DOI 10.1109/TVCG.2008.65

View details for Web of Science ID 000257371400011

View details for PubMedID 18599921
Material properties of the ovine mitral valve anterior leaflet in vivo from inverse finite element analysis AMERICAN JOURNAL OF PHYSIOLOGY-HEART AND CIRCULATORY PHYSIOLOGY Krishnamurthy, G., Ennis, D. B., Itoh, A., Bothe, W., Swanson, J. C., Karlsson, M., Kuhl, E., Miller, D. C., Ingels, N. B. 2008; 295 (3): H1141-H1149
Abstract

We measured leaflet displacements and used inverse finite-element analysis to define, for the first time, the material properties of mitral valve (MV) leaflets in vivo. Sixteen miniature radiopaque markers were sewn to the MV annulus, 16 to the anterior MV leaflet, and 1 on each papillary muscle tip in 17 sheep. Four-dimensional coordinates were obtained from biplane videofluoroscopic marker images (60 frames/s) during three complete cardiac cycles. A finite-element model of the anterior MV leaflet was developed using marker coordinates at the end of isovolumic relaxation (IVR; when the pressure difference across the valve is approximately 0), as the minimum stress reference state. Leaflet displacements were simulated during IVR using measured left ventricular and atrial pressures. The leaflet shear modulus (G(circ-rad)) and elastic moduli in both the commisure-commisure (E(circ)) and radial (E(rad)) directions were obtained using the method of feasible directions to minimize the difference between simulated and measured displacements. Group mean (+/-SD) values (17 animals, 3 heartbeats each, i.e., 51 cardiac cycles) were as follows: G(circ-rad) = 121 +/- 22 N/mm2, E(circ) = 43 +/- 18 N/mm2, and E(rad) = 11 +/- 3 N/mm2 (E(circ) > E(rad), P < 0.01). These values, much greater than those previously reported from in vitro studies, may result from activated neurally controlled contractile tissue within the leaflet that is inactive in excised tissues. This could have important implications, not only to our understanding of mitral valve physiology in the beating heart but for providing additional information to aid the development of more durable tissue-engineered bioprosthetic valves.

View details for DOI 10.1152/ajpheart.00284.2008

View details for Web of Science ID 000258949200031

View details for PubMedID 18621858
On local tracking algorithms for the simulation of three-dimensional discontinuities COMPUTATIONAL MECHANICS Jaeger, P., Steinmann, P., Kuhl, E. 2008; 42 (3): 395-406
View details for DOI 10.1007/s00466-008-0249-3

View details for Web of Science ID 000256254000005
A note on the generation of periodic granular microstructures based on grain size distributions INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS MEIER, H. A., Kuhl, E., Steinmann, P. 2008; 32 (5): 509-522
View details for DOI 10.1002/nag.635

View details for Web of Science ID 000255319200004
Time-dependent fibre reorientation of transversely isotropic continua - Finite element formulation and consistent linearization INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING Himpel, G., Menzel, A., Kuhl, E., Steinmann, P. 2008; 73 (10): 1413-1433
View details for DOI 10.1002/nme.2124

View details for Web of Science ID 000253694300004
Brittle fracture during folding of rocks: A finite element study PHILOSOPHICAL MAGAZINE Jager, P., Schmalholz, S. M., Schmid, D. W., Kuhl, E. 2008; 88 (28-29): 3245-3263
View details for DOI 10.1080/14786430802320101

View details for Web of Science ID 000261803800004
Computational modelling of thermal impact welded PEEK/steel single lap tensile specimens COMPUTATIONAL MATERIALS SCIENCE Utzinger, J., Bos, M., Floeck, M., Menzel, A., Kuhl, E., Renz, R., Friedrich, K., Schlarb, A. K., Steinmann, P. 2008; 41 (3): 287-296
View details for DOI 10.1016/j.commatsci.2007.04.015

View details for Web of Science ID 000254338500004
Towards mulitscale computation of confined granular media - Contact forces, stresses and tangent operators Techn Mech Meier HA, Steinmann P, Kuhl E 2008; 28: 32-42
A continuum model for remodeling in living structures JOURNAL OF MATERIALS SCIENCE Kuhl, E., Holzapfel, G. A. 2007; 42 (21): 8811-8823
View details for DOI 10.1007/s10853-007-1917-y

View details for Web of Science ID 000249213300006
Diamond elements: A finite element/discrete-mechanics approximation scheme with guaranteed optimal convergence in incompressible elasticity INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING Hauret, P., Kuhl, E., Ortiz, M. 2007; 72 (3): 253-294
View details for DOI 10.1002/nme.1992

View details for Web of Science ID 000250277400001
Computational modeling of arterial wall growth - Attempts towards patient-specific simulations based on computer tomography Workshop on Mathematical Methods and Models of Continuum Biomechanics Kuhl, E., Maas, R., Himpel, G., Menzel, A. SPRINGER HEIDELBERG. 2007: 321–31
Abstract

The present manuscript documents our first experiences with a computational model for stress-induced arterial wall growth and in-stent restenosis related to atherosclerosis. The underlying theoretical framework is provided by the kinematics of finite growth combined with open system thermodynamics. The computational simulation is embedded in a finite element approach in which growth is essentially captured by a single scalar-valued growth factor introduced as internal variable on the integration point level. The conceptual simplicity of the model enables its straightforward implementation into standard commercial finite element codes. Qualitative studies of stress-induced changes of the arterial wall thickness in response to balloon angioplasty or stenting are presented to illustrate the features of the suggested growth model. First attempts towards a patient-specific simulation based on realistic artery morphologies generated from computer tomography data are discussed.

View details for DOI 10.1007/s10237-006-0062-x

View details for Web of Science ID 000249307500005

View details for PubMedID 17119902
Computational modeling of mineral unmixing and growth - An application of the Cahn-Hilliard equation COMPUTATIONAL MECHANICS Kuhl, E., Schmid, D. W. 2007; 39 (4): 439-451
View details for DOI 10.1007/s00466-006-0041-1

View details for Web of Science ID 000243968400008
Towards the algorithmic treatment of 3D strong discontinuities COMMUNICATIONS IN NUMERICAL METHODS IN ENGINEERING Mergheim, J., Kuhl, E., Steinmann, P. 2007; 23 (2): 97-108
View details for DOI 10.1002/cnm.885

View details for Web of Science ID 000244089800002
Diamond elements: A finite-element / discrete-mechanics approximation scheme with guaranteed optimal convergence in incompressible elasticity Int J Num Meth Eng Hauret P, Kuhl E, Ortiz M 2007; 72: 8811-8823
On deformational and configurational mechanics of micromorphic hyperelasticity - Theory and computation COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING Hirschberger, C. B., Kuhl, E., Steinmann, P. 2007; 196 (41-44): 4027-4044
View details for DOI 10.1016/j.cma.2007.02.015

View details for Web of Science ID 000249301500002
On the application of Hansbo's method for interface problems IUTAM Symposium on Discretization Methods for Evolving Discontinuities Kuhl, E., Jaeger, P., Mergheim, J., Steinmann, P. SPRINGER. 2007: 255–265
View details for Web of Science ID 000251312200015
A discontinuous Galerkin method for the Cahn-Hilliard equation JOURNAL OF COMPUTATIONAL PHYSICS Wells, G. N., Kuhl, E., Garikipati, K. 2006; 218 (2): 860-877
View details for DOI 10.1016/j.jcp.2006.03.010

View details for Web of Science ID 000242461200021
On the convexity of transversely isotropic chain network models Symposium on Instabilities Across the Scales Kuhl, E., Menzel, A., Garikipati, K. TAYLOR & FRANCIS LTD. 2006: 3241–58
View details for DOI 10.1080/14786430500080296

View details for Web of Science ID 000237931000007
An illustration of the equivalence of the loss of ellipticity conditions in spatial and material settings of hyperelasticity EUROPEAN JOURNAL OF MECHANICS A-SOLIDS Kuhl, E., Askes, H., Steinmann, P. 2006; 25 (2): 199-214
View details for DOI 10.1016/j.euromechsol.2005.07.008

View details for Web of Science ID 000236610600001
Modeling and simulation of remodeling in soft biological tissues IUTAM Symposium on Mechanics of Biological Tissue Kuhl, E., Menzel, A., Garikipati, K., Arruda, E. M., Grosh, K. SPRINGER-VERLAG BERLIN. 2006: 77–89
View details for Web of Science ID 000237286900006
Structural optimization by simultaneous equilibration of spatial and material forces COMMUNICATIONS IN NUMERICAL METHODS IN ENGINEERING Askes, H., Bargmann, S., Kuhl, E., Steinmann, P. 2005; 21 (8): 433-442
View details for DOI 10.1002/cnm.758

View details for Web of Science ID 000231331400004
Remodeling of biological tissue: Mechanically induced reorientation of a transversely isotropic chain network JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS Kuhl, E., Garikipati, K., Arruda, E. M., Grosh, K. 2005; 53 (7): 1552-1573
View details for DOI 10.1016/j.jmps.2005.03.002

View details for Web of Science ID 000230058500005
A finite element method for the computational modelling of cohesive cracks INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING Mergheim, J., Kuhl, E., Steinmann, P. 2005; 63 (2): 276-289
View details for Web of Science ID 000228913400007
Computational modelling of isotropic multiplicative growth CMES-COMPUTER MODELING IN ENGINEERING & SCIENCES Himpel, G., Kuhl, E., Menzel, A., Steinmann, P. 2005; 8 (2): 119-134
View details for Web of Science ID 000230077000003
A hyperelastodynamic ALE formulation based on referential, spatial and material settings of continuum mechanics ACTA MECHANICA Kuhl, E., Steinmann, P. 2005; 174 (3-4): 201-222
View details for DOI 10.1007/s00707-004-0200-4

View details for Web of Science ID 000227999700005
Computational modeling of hip replacement surgery - Total hip replacement vs. hip resurfacing Techn Mech Kuhl E, Balle F 2005; 25: 107-114
Material force method. Continuum damage & thermo-hyperelasticity EUROMECH Colloquium 445 Denzer, R., Liebe, T., Kuhl, E., Barth, F. J., Steinmann, P. SPRINGER. 2005: 95–104
View details for Web of Science ID 000233193400010
Computational spatial and material settings of continuum mechanics. An Arbitrary Lagrangian Eulerian formulation EUROMECH Colloquium 445 Kuhl, E., Askes, H., Steinmann, P. SPRINGER. 2005: 115–125
View details for Web of Science ID 000233193400012
A hybrid discontinuous Galerkin/interface method for the computational modelling of failure COMMUNICATIONS IN NUMERICAL METHODS IN ENGINEERING Mergheim, J., Kuhl, E., Steinmann, P. 2004; 20 (7): 511-519
View details for DOI 10.1002/cnm.689

View details for Web of Science ID 000222538700002
Computational modeling of healing: an application of the material force method BIOMECHANICS AND MODELING IN MECHANOBIOLOGY Kuhl, E., Steinmann, P. 2004; 2 (4): 187-203
Abstract

The basic aim of the present contribution is the qualitative simulation of healing phenomena typically encountered in hard and soft tissue mechanics. The mechanical framework is provided by the theory of open system thermodynamics, which will be formulated in the spatial as well as in the material motion context. While the former typically aims at deriving the density and the spatial motion deformation field in response to given spatial forces, the latter will be applied to determine the material forces in response to a given density and material deformation field. We derive a general computational framework within the finite element context that will serve to evaluate both the spatial and the material motion problem. However, once the spatial motion problem has been solved, the solution of the material motion problem represents a mere post-processing step and is thus extremely cheap from a computational point of view. The underlying algorithm will be elaborated systematically by means of two prototype geometries subjected to three different representative loading scenarios, tension, torsion, and bending. Particular focus will be dedicated to the discussion of the additional information provided by the material force method. Since the discrete material node point forces typically point in the direction of potential material deposition, they can be interpreted as a driving force for the healing mechanism.

View details for DOI 10.1007/s10237-003-0034-3

View details for Web of Science ID 000208283300001

View details for PubMedID 14872320
On the impact of configurational mechanics on computational mechanics Symposium on Configurational Mechanics held at the 5th Euromech Solid Mechanics Conference Kuhl, E., Steinmann, P. A A BALKEMA PUBLISHERS. 2004: 15–29
View details for Web of Science ID 000189444500002
Material forces in open system mechanics COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING Kuhl, E., Steinmann, P. 2004; 193 (23-26): 2357-2381
View details for DOI 10.1016/j.cma.2004.01.022

View details for Web of Science ID 000221274800013
Application of the material force method to thermo-hyperelasticity COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING Kuhl, E., Denzer, R., Barth, F. J., Steinmann, P. 2004; 193 (30-32): 3303-3325
View details for DOI 10.1016/j.cma.2003.09.021

View details for Web of Science ID 000222540900008
An ALE formulation based on spatial and material settings of continuum mechanics. Part 1: Generic hyperelastic formulation COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING Kuhl, E., Askes, H., Steinmann, P. 2004; 193 (39-41): 4207-4222
View details for DOI 10.1016/j.cma.2003.09.030

View details for Web of Science ID 000224018200008
An ALE formulation based on spatial and material settings of continuum mechanics. Part 2: Classification and applications COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING Askes, H., Kuhl, E., Steinmann, P. 2004; 193 (39-41): 4223-4245
View details for DOI 10.1016/j.cma.2003.09.031

View details for Web of Science ID 000224018200009
Theory and numerics of geometrically non-linear open system mechanics INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING Kuhl, E., Steinmann, P. 2003; 58 (11): 1593-1615
View details for DOI 10.1002/nme.827

View details for Web of Science ID 000186438000001
Mass- and volume-specific views on thermodynamics for open systems PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES Kuhl, E., Steinmann, P. 2003; 459 (2038): 2547-2568
View details for DOI 10.1098/rspa.2003.1119

View details for Web of Science ID 000185739200009
Computational modeling of growth - A critical review, a classification of concepts and two new consistent approaches COMPUTATIONAL MECHANICS Kuhl, E., Menzel, A., Steinmann, P. 2003; 32 (1-2): 71-88
View details for DOI 10.1007/S00466-003-0463-Y

View details for Web of Science ID 000185915200008
An arbitrary Lagrangian Eulerian finite-element approach for fluid-structure interaction phenomena Int J Num Meth Eng Kuhl E, Hulshoff S, de Borst R 2003; 57: 117-142
On spatial and material settings of thermo-hyperelastodynamics for open systems ACTA MECHANICA Kuhl, E., Steinmann, P. 2003; 160 (3-4): 179-217
View details for DOI 10.1007/s00707-002-0974-1

View details for Web of Science ID 000181493700004
Thermodynamics of open systems with application to chemomechanical problems EURO-C 2003 Conference Kuhl, E., Steinmann, P. A A BALKEMA PUBLISHERS. 2003: 463–472
View details for Web of Science ID 000182406800050
A thermodynamically consistent approach to microplane theory. Part II. Dissipation and inelastic constitutive modeling INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES Kuhl, E., Steinmann, P., Carol, I. 2001; 38 (17): 2933-2952
View details for Web of Science ID 000167747700003
New thermodynamic approach to microplane model. Part II: Dissipation and inelastic constitutive modelling Int J Solids Structures Kuhl E, Carol I, Steinmann P 2001; 38: 2933-2952
A comparison of discrete granular material models with continuous microplane formulations Granular Matter Kuhl E, D'Addetta GA, Herrmann HJ, Ramm E 2000; 2: 123-135
Failure analysis for elasto-plastic material models on different levels of observation Int J Solids Structures Kuhl E, Ramm E, Willam KJ 2000; 37: 7259-7280
Microplane modelling of cohesive frictional materials Eur J Mech/A:Solids Kuhl E, Ramm E 2000; 19: S121-S143
An anisotropic gradient damage model for quasi-brittle materials Comp Meth Appl Mech Eng Kuhl E, Ramm E, de Borst R 2000; 183: 87-103
Parameter identification of gradient enhanced damage models with the finite element method Eur J Mech/A: Solids Mahnken R, Kuhl E 1999; 18: 819-835
Simulation of strain localization with gradient enhanced damage models Comp Mat Sci Kuhl E, Ramm E 1999; 16: 176-185
Aspects of non-associated single crystal plasticity: Influence of non-Schmid effects and localization analysis INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES Steinmann, P., Kuhl, E., Stein, E. 1998; 35 (33): 4437-4456
View details for Web of Science ID 000075278600007
On the linearization of the microplane model Mech Coh Fric Mat Kuhl E, Ramm E 1998; 2: 343-364
Modelling and computations of instability phenomena in multisurface plasticity Comp Mech Sawischlewski E, Steinmann P, Stein E 1996; 18: 245-258

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