Bio

Bio


I am an Associate Professor of Mechanical Engineering, Bioengineering (affiliate), and Cardiothoracic Surgery (courtesy). My area of professional expertise is Computational Biomechanics, the creation of theoretical and computational models to predict the acute and chronic response of living biological tissue to environmental changes during development and disease progression. My specific interest is the multiscale modeling of growth and remodeling, the study of how biological tissues adapt their form and function to changes in mechanical loading, and how this adaptation could be traced back to structural alterations on the cellular or molecular levels. Growth and remodeling might be induced naturally, e.g., through elevated pressure, stress, or strain, or interventionally, e.g., through prostheses, stents, tissue grafts, or stem cell injection. Combining theories of electrophysiology, biophysics, and continuum mechanics, my lab has specialized in predicting the chronic loss of form and function in growing and remodeling cardiac tissue using patient-specific custom-designed finite element models.

Academic Appointments


Administrative Appointments


  • Editorial Board, Journal of the Mechanics and Physics of Solids (2013 - Present)
  • Editorial Board, Applied Mechanics Reviews (2012 - Present)
  • Editorial Board, Journal of Computational Surgery (2012 - Present)
  • Editorial Board, Computer Methods in Biomechanics and Biomedical Engineering (2011 - Present)
  • Editorial Board, International Journal for Numerical Methods in Biomedical Engineering (2011 - Present)
  • Editorial Board, Acta Mechanica Sinica (2011 - Present)

Honors & Awards


  • Graduate Research Fellowship, German National Science Foundation (DFG) (1996-1999)
  • Habilitation Research Fellowship, German National Science Foundation (DFG) (2001-2004)
  • Hellman Faculty Scholar, Hellman Faculty Scholar (2009)
  • NSF CAREER Award, National Science Foundation (2010-2014)

Professional Education


  • Habilitation, TU Kaiserslautern, Germany, Mechanics (2004)
  • PhD, University of Stuttgart, Germany, Civil Engineering (2000)
  • Dipl.-Ing., Leibniz University of Hannover, Germany, Computational Engineering (1995)

Research & Scholarship

Current Research and Scholarly Interests


I am an Associate Professor of Mechanical Engineering, Bioengineering (courtesy), and Cardiothoracic Surgery (courtesy). My area of professional expertise is living matter physics, the creation of theoretical and computational models to predict the acute and chronic response of living structures to environmental changes during development and disease progression. My specific interest is the multiscale modeling of growth and remodeling, the study of how living matter adapts its form and function to changes in mechanical loading, and how this adaptation could be traced back to structural alterations on the cellular or molecular levels. Growth and remodeling might be induced naturally, e.g., through elevated pressure, stress, or strain, or interventionally, e.g., through prostheses, stents, tissue grafts, or stem cell injection. Combining theories of electrophysiology, photoelectrochemistry, biophysics, and continuum mechanics, my lab has specialized in predicting the chronic loss of form and function in growing and remodeling cardiac tissue using patient-specific custom-designed finite element models.

Teaching

2013-14 Courses


Publications

Journal Articles


  • 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

  • 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-? (TGF-?) 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

  • On the effect of prestrain and residual stress in thin biological membranes J Mech Phys Solids, doi:10.1016/j.jmps.2013.04.005 Rausch MK, Kuhl E 2013
  • 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

  • How Do Annuloplasty Rings Affect Mitral Annular Strains in the Normal Beating Ovine Heart? CIRCULATION Bothe, W., Rausch, M. K., Kvitting, J. E., Echtner, D. K., Walther, M., Ingels, N. B., Kuhl, E., Miller, D. C. 2012; 126 (11): 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

  • 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

  • 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

  • Growth on demand: Reviewing the mechanobiology of stretched skin. Journal of the mechanical behavior of biomedical materials Zöllner, A. M., Holland, M. A., Honda, K. S., Gosain, A. K., Kuhl, E. 2013; 28: 495-509

    Abstract

    Skin is a highly dynamic, autoregulated, living system that responds to mechanical stretch through a net gain in skin surface area. Tissue expansion uses the concept of controlled overstretch to grow extra skin for defect repair in situ. While the short-term mechanics of stretched skin have been studied intensely by testing explanted tissue samples ex vivo, we know very little about the long-term biomechanics and mechanobiology of living skin in vivo. Here we explore the long-term effects of mechanical stretch on the characteristics of living skin using a mathematical model for skin growth. We review the molecular mechanisms by which skin responds to mechanical loading and model their effects collectively in a single scalar-valued internal variable, the surface area growth. This allows us to adopt a continuum model for growing skin based on the multiplicative decomposition of the deformation gradient into a reversible elastic and an irreversible growth part. To demonstrate the inherent modularity of this approach, we implement growth as a user-defined constitutive subroutine into the general purpose implicit finite element program Abaqus/Standard. To illustrate the features of the model, we simulate the controlled area growth of skin in response to tissue expansion with multiple filling points in time. Our results demonstrate that the field theories of continuum mechanics can reliably predict the manipulation of thin biological membranes through mechanical overstretch. Our model could serve as a valuable tool to rationalize clinical process parameters such as expander geometry, expander size, filling volume, filling pressure, and inflation timing to minimize tissue necrosis and maximize patient comfort in plastic and reconstructive surgery. While initially developed for growing skin, our model can easily be generalized to arbitrary biological structures to explore the physiology and pathology of stretch-induced growth of other living systems such as hearts, arteries, bladders, intestines, ureters, muscles, and nerves.

    View details for DOI 10.1016/j.jmbbm.2013.03.018

    View details for PubMedID 23623569

  • 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 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

  • Mathematical modeling of collagen turnover in biological tissue J Math Bio. doi:10.1007/s00285-012-0613-y Saez P, Pena E, Martinez MA, Kuhl E
  • 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
  • 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

  • On the mechanics of thin films and growing surfaces Math Mech Solids. doi:10.1177/1081286513485776 Holland MA, Kosmata T, Goriely A, Kuhl E 2013
  • 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
  • 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

  • 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 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

    View details for PubMedID 23459410

  • 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
  • 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
  • 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
  • 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 PubMedID 22773861

  • Frontiers in growth and remodeling MECHANICS RESEARCH COMMUNICATIONS Menzel, A., Kuhl, E. 2012; 42: 1-14
  • 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

  • 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

  • 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
  • Generating fibre orientation maps in human heart models using Poisson interpolation. Computer methods in biomechanics and biomedical engineering Wong, J., Kuhl, E. 2012

    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 PubMedID 23210529

  • 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
  • Mathematical modeling of collagen turnover in biological tissue. Journal of mathematical biology Sáez, P., Peña, E., Angel Martínez, M., Kuhl, E. 2012

    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 PubMedID 23129392

  • 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
  • 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 ?(i)-?(e) and the extracellular potential ?(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

  • COMPUTATIONAL MODELLING OF OPTOGENETICS IN CARDIAC CELLS PROCEEDINGS OF THE ASME SUMMER BIOENGINEERING CONFERENCE, PTS A AND B Wong, J., Abilez, O., Kuhl, E. 2012: 355-356
  • CHRONIC MITRAL VALVE LEAFLET GROWTH FOLLOWING MYOCARDIAL INFARCTION PROCEEDINGS OF THE ASME SUMMER BIOENGINEERING CONFERENCE, PTS A AND B Rausch, M. K., Tibayan, F. A., Miller, D. C., Kuhl, E. 2012: 1015-1016
  • FINITE ELEMENT MODELING OF FLAP DESIGN AFTER SKIN EXPANSION PROCEEDINGS OF THE ASME SUMMER BIOENGINEERING CONFERENCE, PTS A AND B Tepole, A. B., Zollner, A. M., Kuhl, E. 2012: 1017-1018
  • MODELING GROWTH IN TISSUE EXPANSION PROCEEDINGS OF THE ASME SUMMER BIOENGINEERING CONFERENCE, PTS A AND B Zoellner, A. M., Tepole, A. B., Kuhl, E. 2012: 213-214
  • 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 PubMedID 22081726

  • 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

  • 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

    View details for PubMedID 21532929

  • 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
  • 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
  • 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
  • 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
  • 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

  • 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

  • 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
  • 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
  • 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

  • IN VITRO ASSESSMENT OF RAT HEART FORCE GENERATION: A QUANTITATIVE APPROACH FOR PREDICTING OUTCOMES FROM PLURIPOTENT STEM CELL-DERIVED THERAPY FOR MYOCARDIAL INFARCTION PROCEEDINGS OF THE ASME SUMMER BIOENGINEERING CONFERENCE, 2010 Guillou, L., Abilez, O. J., Baugh, J., Billakanti, G., Zarins, C. K., Kuhl, E. 2010: 717-718
  • 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
  • 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. 2010; 21: 157-169
  • Dilation and Hypertrophy: A Cell-Based Continuum Mechanics Approach Towards Ventricular Growth and Remodeling IUTAM SYMPOSIUM ON CELLULAR, MOLECULAR AND TISSUE MECHANICS, PROCEEDINGS Ulerich, J., Goektepe, S., Kuhl, E. 2010; 16: 237-244
  • 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
  • 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
  • CRITICAL LOADING DURING SERVE: MODELING STRESS-INDUCED BONE GROWTH IN PERFORMANCE TENNIS PLAYERS PROCEEDINGS OF THE ASME SUMMER BIOENGINEERING CONFERENCE 2008, PTS A AND B Taylor, R. E., Zheng, C., Jackson, R. P., Doll, J. C., Chen, J., Holzbaur, K. R., Besier, T., Kuhl, E. 2009: 201-202
  • 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

  • FIRST ATTEMPTS TOWARDS THE COMPUTATIONAL SIMULATION OF NOVEL STEM-CELL BASED POST INFARCT THERAPIES PROCEEDINGS OF THE ASME SUMMER BIOENGINEERING CONFERENCE 2008, PTS A AND B Ulerich, J. P., Goktepe, S., Kuhl, E. 2009: 417-418
  • COMPUTATIONAL SIMULATION OF TRAVELING ARRHYTHMIC WAVES IN MYOCARDIAL TISSUE PROCEEDINGS OF THE ASME SUMMER BIOENGINEERING CONFERENCE - 2009, PT A AND B Wong, J., Goektepe, S., Kuhl, E. 2009: 829-830
  • HOW TO TREAT THE LOSS OF BEAT: MODELING AND SIMULATION OF VENTRICULAR GROWTH AND REMODELING AND NOVEL POST-INFARCTION THERAPIES PROCEEDINGS OF THE ASME SUMMER BIOENGINEERING CONFERENCE 2008, PTS A AND B Goktepe, S., Ulerich, J. P., Kuhl, E. 2009: 971-972
  • QUANTIFICATION OF IN VIVO STRESSES IN THE OVINE ANTERIOR MITRAL VALVE LEAFLET PROCEEDINGS OF THE ASME SUMMER BIOENGINEERING CONFERENCE 2008, PTS A AND B Krishnamurthy, G., Ltoh, A., Bothe, W., Ennis, D. B., Swanson, J. C., Kuhl, E., Miller, D. C., Ingels, N. B. 2009: 131-132
  • On the Multiscale Computation of Con"ned Granular Media ECCOMAS MULTIDISCIPLINARY JUBILEE SYMPOSIUM Meier, H. A., Steinmann, P., Kuhl, E. 2009; 14: 121-133
  • 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
  • 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
  • Computational modelling of thermal impact welded PEEK/steel single lap tensile specimens Comp Mat Sci Utzinger J, Bos M, Floeck M, Menzel A, Kuhl E, Renz R, Friedrich K, Schlarb AK, Steinmann P 2008; 41: 287-296
  • 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
  • Computational modeling of arterial wall growth - Attempts towards patient-specific simulations based on computer tomography BIOMECHANICS AND MODELING IN MECHANOBIOLOGY Kuhl, E., Maas, R., Himpel, G., Menzel, A. 2007; 6 (5): 321-331

    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

  • 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

  • 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. 2007; 5: 255-265
  • On deformational and configurational mechanics of micromorphic hyperelasticity - Theory and computation Comp Meth Appl Mech Eng Hirschberger CB, Kuhl E, Steinmann P 2007; 196: 4027-4044
  • 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
  • Computational modeling of mineral unmixing and growth - An application of the Cahn-Hilliard equation Comp Mech Kuhl E, Schmid DW 2007; 39: 439-451
  • 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
  • On the convexity of transversely isotropic chain network models PHILOSOPHICAL MAGAZINE Kuhl, E., Menzel, A., Garikipati, K. 2006; 86 (21-22): 3241-3258
  • 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
  • Modeling and simulation of remodeling in soft biological tissues MECHANICS OF BIOLOGICAL TISSUE Kuhl, E., Menzel, A., Garikipati, K., Arruda, E. M., Grosh, K. 2006: 77-89
  • 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
  • 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
  • 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
  • Computational spatial and material settings of continuum mechanics. An Arbitrary Lagrangian Eulerian formulation MECHANICS OF MATERIAL FORCES Kuhl, E., Askes, H., Steinmann, P. 2005; 11: 115-125
  • Computational modeling of hip replacement surgery - Total hip replacement vs. hip resurfacing Techn Mech Kuhl E, Balle F 2005; 25: 107-114
  • A hyperelastodynamic ALE formulation based on referential, spatial and material forces Acta Mech Kuhl E, Steinmann P 2005; 174: 201-222
  • 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 CONFIGURATIONAL MECHANICS Kuhl, E., Steinmann, P. 2004: 15-29
  • Application of the material force method to thermo-hyperelasticity Comp Meth Appl Mech Eng Kuhl E, Denzer R, Barth FJ, Steinmann P 2004; 193: 3303-3326
  • Material forces in open system mechanics Comp Meth Appl Mech Eng Kuhl E, Steinmann P 2004; 193: 2357-2381
  • 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
  • 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
  • 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
  • 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
  • Mass- and volume specific views on thermodynamics for open systems Proc Roy Soc London Kuhl E, Steinmann P 2003; 459: 2547-2568
  • Theory and numerics of geometrically nonlinear open systems Int J Num Meth Eng Kuhl E, Steinmann P 2003; 58: 1593-1615
  • On spatial and material settings of thermo-hyperelastodynamics for open systems Acta Mech Kuhl E, Steinmann P 2003; 160: 179-217
  • Thermodynamics of open systems with application to chemomechanical problems COMPUTATIONAL MODELLING OF CONCRETE STRUCTURES Kuhl, E., Steinmann, P. 2003: 463-472
  • 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
  • On the linearization of the microplane model Mech Coh Fric Mat Kuhl E, Ramm E 1998; 2: 343-364
  • Aspects of non-associated single crystal plasticity: Influence of Non-Schmid effects and localization analysis Int J Solids Structures Steinmann P, Kuhl E, Stein E 1998; 35: 4437-4456
  • Modelling and computations of instability phenomena in multisurface plasticity Comp Mech Sawischlewski E, Steinmann P, Stein E 1996; 18: 245-258

Conference Proceedings


  • Rigid, Complete Annuloplasty Rings Increase Anterior Mitral Leaflet Strains in the Normal Beating Ovine Heart 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

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