Ellen Kuhl

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

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

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

View details for DOI 10.1016/j.jmps.2013.01.007

View details for Web of Science ID 000318579500012

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

View details for DOI 10.1016/j.cma.2012.07.004

View details for Web of Science ID 000313134600021

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

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

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

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

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

View details for Web of Science ID 000304814100010

View details for DOI 10.1016/j.ijsolstr.2012.03.035

View details for Web of Science ID 000305441600002

View details for DOI 10.1016/j.mechrescom.2012.03.005

View details for Web of Science ID 000304847400015

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

View details for DOI 10.1016/j.mechrescom.2012.02.007

View details for Web of Science ID 000304847400001

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

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

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

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

View details for Web of Science ID 000302835000001

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

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

View details for Web of Science ID 000302835000006

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

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

View details for Web of Science ID 000325036600177

View details for Web of Science ID 000325036600507

View details for Web of Science ID 000325036600508

View details for Web of Science ID 000325036600106

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

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

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

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

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

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

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

View details for DOI 10.1016/j.cma.2011.07.003

View details for Web of Science ID 000295753800016

View details for DOI 10.1002/cnm.1402

View details for Web of Science ID 000287141000001

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

View details for DOI 10.1016/j.jmps.2010.07.003

View details for Web of Science ID 000282856200014

View details for DOI 10.1007/s00466-010-0490-4

View details for Web of Science ID 000277937300008

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

View details for Web of Science ID 000277711400003

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

View details for DOI 10.1002/cnm.1273

View details for Web of Science ID 000277552200003

View details for DOI 10.1016/j.ijsolstr.2009.11.020

View details for Web of Science ID 000276127200001

View details for DOI 10.1007/s00419-009-0384-0

View details for Web of Science ID 000275787600011

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

View details for Web of Science ID 000290705300359

View details for DOI 10.1007/s00466-009-0434-z

View details for Web of Science ID 000272118100009

View details for DOI 10.1007/978-90-481-9195-6_12

View details for Web of Science ID 000290694500012

View details for DOI 10.1007/978-90-481-3348-2_20

View details for Web of Science ID 000276397800020

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

View details for DOI 10.1007/s00466-009-0417-0

View details for Web of Science ID 000270428100007

View details for DOI 10.1098/rsta.2009.0122

View details for Web of Science ID 000268735700001

View details for PubMedID 19657002

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

View details for DOI 10.1002/nme.2571

View details for Web of Science ID 000267788300002

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

View details for DOI 10.1007/s00466-008-0328-5

View details for Web of Science ID 000263059500008

View details for Web of Science ID 000263364700101

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

View details for Web of Science ID 000263364700209

View details for Web of Science ID 000280089000415

View details for Web of Science ID 000263364700486

View details for Web of Science ID 000263364700066

View details for Web of Science ID 000267056200009

View details for DOI 10.1063/1.3036536

View details for Web of Science ID 000261699700087

View details for DOI 10.1002/nme.2353

View details for Web of Science ID 000261111400002

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

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

View details for DOI 10.1007/s00466-008-0249-3

View details for Web of Science ID 000256254000005

View details for DOI 10.1002/nag.635

View details for Web of Science ID 000255319200004

View details for DOI 10.1002/nme.2124

View details for Web of Science ID 000253694300004

View details for DOI 10.1080/14786430802320101

View details for Web of Science ID 000261803800004

View details for DOI 10.1007/s10853-007-1917-y

View details for Web of Science ID 000249213300006

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

View details for DOI 10.1002/cnm.885

View details for Web of Science ID 000244089800002

View details for Web of Science ID 000251312200015

View details for DOI 10.1016/j.jcp.2006.03.010

View details for Web of Science ID 000242461200021

View details for DOI 10.1080/14786430500080296

View details for Web of Science ID 000237931000007

View details for DOI 10.1016/j.euromechsol.2005.07.008

View details for Web of Science ID 000236610600001

View details for Web of Science ID 000237286900006

View details for DOI 10.1002/cnm.758

View details for Web of Science ID 000231331400004

View details for DOI 10.1016/j.jmps.2005.03.002

View details for Web of Science ID 000230058500005

View details for Web of Science ID 000228913400007

View details for Web of Science ID 000230077000003

View details for Web of Science ID 000233193400012

View details for DOI 10.1002/cnm.689

View details for Web of Science ID 000222538700002

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

View details for Web of Science ID 000189444500002

View details for DOI 10.1016/j.cma.2003.09.030

View details for Web of Science ID 000224018200008

View details for DOI 10.1016/j.cma.2003.09.031

View details for Web of Science ID 000224018200009

View details for DOI 10.1007/S00466-003-0463-Y

View details for Web of Science ID 000185915200008

View details for Web of Science ID 000182406800050