Ellen Kuhl

All Publications

• Physical biology of human brain development FRONTIERS IN CELLULAR NEUROSCIENCE Budday, S., Steinmann, P., Kuhl, E. 2015; 9

  Abstract

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

  View details for DOI 10.3389/fncel.2015.00257

  View details for Web of Science ID 000357831600001

  View details for PubMedID 26217183

• The role of mechanics during brain development JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS Budday, S., Steinmann, P., Kuhl, E. 2014; 72: 75-92

  View details for DOI 10.1016/j.jmps.2014.07.010

  View details for Web of Science ID 000343841900005

• Characterization of living skin using multi-view stereo and isogeometric analysis. Acta biomaterialia Buganza Tepole, A., Gart, M., Gosain, A. K., Kuhl, E. 2014; 10 (11): 4822-4831

  Abstract

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

  View details for DOI 10.1016/j.actbio.2014.06.037

  View details for PubMedID 25016279

• The Living Heart Project: A robust and integrative simulator for human heart function EUROPEAN JOURNAL OF MECHANICS A-SOLIDS Baillargeon, B., Rebelo, N., Fox, D. D., Taylor, R. L., Kuhl, E. 2014; 48: 38-47

  View details for DOI 10.1016/j.euromechsol.2014.04.001

  View details for Web of Science ID 000342879100005

• A mechanical model predicts morphological abnormalities in the developing human brain SCIENTIFIC REPORTS Budday, S., Raybaud, C., Kuhl, E. 2014; 4

  Abstract

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

  View details for DOI 10.1038/srep05644

  View details for Web of Science ID 000338763700006

  View details for PubMedID 25008163

• Growth on demand: Reviewing the mechanobiology of stretched skin JOURNAL OF THE MECHANICAL BEHAVIOR OF BIOMEDICAL MATERIALS Zoellner, A. M., Holland, M. A., Honda, K. S., Gosain, A. K., Kuhl, E. 2013; 28: 495-509

  View details for DOI 10.1016/j.jmbbm.2013.03.018

  View details for Web of Science ID 000328234500044

• On the effect of prestrain and residual stress in thin biological membranes JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS Rausch, M. K., Kuhl, E. 2013; 61 (9): 1955-1969

  View details for DOI 10.1016/j.jmps.2013.04.005

  View details for Web of Science ID 000322296900005

• 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

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

  Abstract

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

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

  View details for PubMedID 25634600

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

  Abstract

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

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

  View details for PubMedID 25821112

• Computational aspects of growth-induced instabilities through eigenvalue analysis COMPUTATIONAL MECHANICS Javili, A., Dortdivanlioglu, B., Kuhl, E., Linder, C. 2015; 56 (3): 405-420

  View details for DOI 10.1007/s00466-015-1178-6

  View details for Web of Science ID 000359381500002

• Isogeometric Kirchhoff-Love shell formulations for biological membranes COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING Tepole, A. B., Kabaria, H., Bletzinger, K., Kuhl, E. 2015; 293: 328-347

  View details for DOI 10.1016/j.cma.2015.05.006

  View details for Web of Science ID 000361475900016

• Heterogeneous growth-induced prestrain in the heart JOURNAL OF BIOMECHANICS Genet, M., Rausch, M. K., Lee, L. C., Choy, S., Zhao, X., Kassab, G. S., Kozerke, S., Guccione, J. M., Kuhl, E. 2015; 48 (10): 2080-2089

  View details for DOI 10.1016/j.jbiomech.2015.03.012

  View details for Web of Science ID 000358459800055

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

  Abstract

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

  View details for DOI 10.1016/j.jbiomech.2015.03.012

  View details for PubMedID 25913241

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

  Abstract

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

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

  View details for Web of Science ID 000358258200014

  View details for PubMedID 25824370

• A new sparse matrix vector multiplication graphics processing unit algorithm designed for finite element problems INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING Wong, J., Kuhl, E., Darve, E. 2015; 102 (12): 1784-1814

  View details for DOI 10.1002/nme.4865

  View details for Web of Science ID 000354625300002

• Mechanical properties of gray and white matter brain tissue by indentation JOURNAL OF THE MECHANICAL BEHAVIOR OF BIOMEDICAL MATERIALS Budday, S., Nay, R., de Rooij, R., Steinmann, P., Wyrobek, T., Ovaert, T. C., Kuhl, E. 2015; 46: 318-330

  Abstract

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

  View details for DOI 10.1016/j.jmbbm.2015.02.024

  View details for Web of Science ID 000353752100030

  View details for PubMedID 25819199

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

  Abstract

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

  View details for DOI 10.1161/CIRCULATIONAHA.114.012377

  View details for Web of Science ID 000354610300015

  View details for PubMedID 25904646

• Morphoelastic control of gastro-intestinal organogenesis: Theoretical predictions and numerical insights JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS Balbi, V., Kuhl, E., Ciarletta, P. 2015; 78: 493-510

  View details for DOI 10.1016/j.jmps.2015.02.016

  View details for Web of Science ID 000356733700026

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

  Abstract

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

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

  View details for PubMedID 25199941

• Use it or lose it: multiscale skeletal muscle adaptation to mechanical stimuli BIOMECHANICS AND MODELING IN MECHANOBIOLOGY Wisdom, K. M., Delp, S. L., Kuhl, E. 2015; 14 (2): 195-215

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

  View details for Web of Science ID 000350871000001

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

  Abstract

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

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

  View details for Web of Science ID 000350871000002

  View details for PubMedID 24888270

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

  Abstract

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

  View details for DOI 10.1016/j.jtbi.2014.10.036

  View details for PubMedID 25451524

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

  Abstract

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

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

  View details for Web of Science ID 000347250500001

  View details for PubMedID 24718853

• Pattern Selection in Growing Tubular Tissues PHYSICAL REVIEW LETTERS Ciarletta, P., Balbi, V., Kuhl, E. 2014; 113 (24)

  Abstract

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

  View details for DOI 10.1103/PhysRevLett.113.248101

  View details for Web of Science ID 000346387700022

  View details for PubMedID 25541805

• The generalized Hill model: A kinematic approach towards active muscle contraction JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS Goktepe, S., Menzel, A., Kuhl, E. 2014; 72: 20-39

  View details for DOI 10.1016/j.jmps.2014.07.015

  View details for Web of Science ID 000343841900002

• Modeling and simulation of viscous electro-active polymers EUROPEAN JOURNAL OF MECHANICS A-SOLIDS Vogel, F., Goktepe, S., Steinmann, P., Kuhl, E. 2014; 48: 112-128

  View details for DOI 10.1016/j.euromechsol.2014.02.001

  View details for Web of Science ID 000342879100011

• Application of Finite Element Modeling to Optimize Flap Design with Tissue Expansion PLASTIC AND RECONSTRUCTIVE SURGERY Buganza-Tepole, A., Steinberg, J. P., Kuhl, E., Gosain, A. K. 2014; 134 (4): 785-792

  View details for DOI 10.1097/PRS.0000000000000553

  View details for Web of Science ID 000343105400054

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

  Abstract

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

  View details for DOI 10.1097/PRS.0000000000000553

  View details for PubMedID 24945952

• Computational modeling of skin: Using stress profiles as predictor for tissue necrosis in reconstructive surgery COMPUTERS & STRUCTURES Tepole, A. B., Gosain, A. K., Kuhl, E. 2014; 143: 32-39

  View details for DOI 10.1016/j.compstruc.2014.07.004

  View details for Web of Science ID 000341481500004

• Generating fibre orientation maps in human heart models using Poisson interpolation COMPUTER METHODS IN BIOMECHANICS AND BIOMEDICAL ENGINEERING Wong, J., Kuhl, E. 2014; 17 (11): 1217-1226

  Abstract

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

  View details for DOI 10.1080/10255842.2012.739167

  View details for Web of Science ID 000334018600006

  View details for PubMedID 23210529

• Computational modeling of hypertensive growth in the human carotid artery COMPUTATIONAL MECHANICS Saez, P., Pena, E., Martinez, M. A., Kuhl, E. 2014; 53 (6): 1183-1196

  View details for DOI 10.1007/s00466-013-0959-z

  View details for Web of Science ID 000335669100006

• On the mechanics of growing thin biological membranes JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS Rausch, M. K., Kuhl, E. 2014; 63: 128-140

  View details for DOI 10.1016/j.jmps.2013.09.015

  View details for Web of Science ID 000331006900009

• A novel strategy to identify the critical conditions for growth-induced instabilities JOURNAL OF THE MECHANICAL BEHAVIOR OF BIOMEDICAL MATERIALS Javili, A., Steinmann, P., Kuhl, E. 2014; 29: 20-32

  Abstract

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

  View details for DOI 10.1016/j.jmbbm.2013.08.017

  View details for Web of Science ID 000330085700003

  View details for PubMedID 24041754

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

  Abstract

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

  View details for DOI 10.1109/EMBC.2014.6945038

  View details for PubMedID 25571406

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

  Abstract

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

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

  View details for Web of Science ID 000326898300016

  View details for PubMedID 23129392

• On the Role of Mechanics in Chronic Lung Disease MATERIALS Eskandari, M., Pfaller, M. R., Kuhl, E. 2013; 6 (12): 5639-5658

  View details for DOI 10.3390/ma6125639

  View details for Web of Science ID 000330297600014

• 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

• 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

• 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

• On the mechanics of thin films and growing surfaces MATHEMATICS AND MECHANICS OF SOLIDS Holland, M. A., Kosmata, T., Goriely, A., Kuhl, E. 2013; 18 (6): 561-575

  View details for DOI 10.1177/1081286513485776

  View details for Web of Science ID 000323118900002

• On the mechanics of continua with boundary energies and growing surfaces JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS Papastavrou, A., Steinmann, P., Kuhl, E. 2013; 61 (6): 1446-1463

  View details for DOI 10.1016/j.jmps.2013.01.007

  View details for Web of Science ID 000318579500012

• Systems-based approaches toward wound healing PEDIATRIC RESEARCH Tepole, A. B., Kuhl, E. 2013; 73 (4): 553-563

  Abstract

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

  View details for DOI 10.1038/pr.2013.3

  View details for Web of Science ID 000317554900008

  View details for PubMedID 23314298

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

  Abstract

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

  View details for DOI 10.1080/10255842.2011.615310

  View details for Web of Science ID 000314564900007

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

  Abstract

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

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

  View details for Web of Science ID 000313480100011

  View details for PubMedID 22446834

• A fully implicit finite element method for bidomain models of cardiac electromechanics COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING Dal, H., Goektepe, S., Kaliske, M., Kuhl, E. 2013; 253: 323-336

  View details for DOI 10.1016/j.cma.2012.07.004

  View details for Web of Science ID 000313134600021

• Evidence of adaptive mitral leaflet growth JOURNAL OF THE MECHANICAL BEHAVIOR OF BIOMEDICAL MATERIALS Rausch, M. K., Tibayan, F. A., Miller, D. C., Kuhl, E. 2012; 15: 208-217

  Abstract

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

  View details for DOI 10.1016/j.jmbbm.2012.07.001

  View details for Web of Science ID 000313598800020

  View details for PubMedID 23159489

• Stretching 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

• 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

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

  Abstract

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

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

  View details for PubMedID 22052000

• Growing skin: tissue expansion in pediatric forehead reconstruction BIOMECHANICS AND MODELING IN MECHANOBIOLOGY Zoellner, A. M., Tepole, A. B., Gosain, A. K., Kuhl, E. 2012; 11 (6): 855-867

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

  View details for Web of Science ID 000304814100010

• Anisotropic density growth of bone-A computational micro-sphere approach INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES Waffenschmidt, T., Menzel, A., Kuhl, E. 2012; 49 (14): 1928-1946

  View details for DOI 10.1016/j.ijsolstr.2012.03.035

  View details for Web of Science ID 000305441600002

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

  Abstract

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

  View details for DOI 10.1016/j.jmps.2012.02.004

  View details for Web of Science ID 000303285600007

  View details for PubMedID 22773861

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

  View details for DOI 10.1016/j.mechrescom.2012.02.007

  View details for Web of Science ID 000304847400001

• Growth and remodeling of the left ventricle: A case study of myocardial infarction and surgical ventricular restoration MECHANICS RESEARCH COMMUNICATIONS Klepach, D., Lee, L. C., Wenk, J. F., Ratcliffe, M. B., Zohdi, T. I., Navia, J. L., Kassab, G. S., Kuhl, E., Guccione, J. M. 2012; 42: 134-141

  View details for DOI 10.1016/j.mechrescom.2012.03.005

  View details for Web of Science ID 000304847400015

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

  Abstract

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

  View details for DOI 10.1016/j.jmbbm.2011.12.006

  View details for Web of Science ID 000302586300015

  View details for PubMedID 22402163

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

  Abstract

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

  View details for DOI 10.1016/j.jtbi.2011.12.022

  View details for Web of Science ID 000300652000016

  View details for PubMedID 22227432

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

  Abstract

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

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

  View details for Web of Science ID 000300518000008

  View details for PubMedID 21604146

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

  Abstract

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

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

  View details for Web of Science ID 000300770200018

  View details for PubMedID 22037916

• MODELING GROWTH IN TISSUE EXPANSION PROCEEDINGS OF THE ASME SUMMER BIOENGINEERING CONFERENCE, PTS A AND B Zoellner, A. M., Tepole, A. B., Kuhl, E. 2012: 213-214

  View details for Web of Science ID 000325036600106

• 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

  View details for Web of Science ID 000325036600177

• 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

  View details for Web of Science ID 000325036600507

• 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

  View details for Web of Science ID 000325036600508

• Computational modeling of electrocardiograms: Repolarization and T-wave polarity in the human heart Comp Meth Biomech Biomed Eng, accepted for publication. Hurtado D, Kuhl E 2012
• Consistent formulation of the growth process at the kinematic and constitutive level for soft tissues composed of multiple constituents COMPUTER METHODS IN BIOMECHANICS AND BIOMEDICAL ENGINEERING Schmid, H., PAULI, L., Paulus, A., Kuhl, E., Itskov, M. 2012; 15 (5): 547-561

  Abstract

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

  View details for DOI 10.1080/10255842.2010.548325

  View details for Web of Science ID 000303561200010

  View details for PubMedID 21347909

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

  Abstract

  This work introduces a novel, unconditionally stable and fully coupled finite element method for the bidomain system of equations of cardiac electrophysiology. The transmembrane potential ?(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

• IN VITRO/IN SILICO CHARACTERIZATION OF ACTIVE AND PASSIVE STRESSES IN CARDIAC MUSCLE INTERNATIONAL JOURNAL FOR MULTISCALE COMPUTATIONAL ENGINEERING Boel, M., Abilez, O. J., Assar, A. N., Zarins, C. K., Kuhl, E. 2012; 10 (2): 171-188

  View details for Web of Science ID 000302835000006

• SPECIAL ISSUE ACTIVE TISSUE MODELING: FROM SINGLE MUSCLE CELLS TO MUSCULAR CONTRACTION INTERNATIONAL JOURNAL FOR MULTISCALE COMPUTATIONAL ENGINEERING Boel, M., Kuhl, E. 2012; 10 (2): VII-VIII

  View details for Web of Science ID 000302835000001

• Computational 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

• 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

• 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

  View details for DOI 10.1016/j.cma.2011.07.003

  View details for Web of Science ID 000295753800016

• Computational modeling of passive myocardium INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING Goektepe, S., Acharya, S. N., Wong, J., Kuhl, E. 2011; 27 (1): 1-12

  View details for DOI 10.1002/cnm.1402

  View details for Web of Science ID 000287141000001

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

  Abstract

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

  View details for DOI 10.1161/CIRCULATIONAHA.110.961243

  View details for Web of Science ID 000283440600012

  View details for PubMedID 20937973

• A generic approach towards finite growth with examples of athlete's heart, cardiac dilation, and cardiac wall thickening JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS Goktepe, S., Abilez, O. J., Kuhl, E. 2010; 58 (10): 1661-1680

  View details for DOI 10.1016/j.jmps.2010.07.003

  View details for Web of Science ID 000282856200014

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

  Abstract

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

  View details for DOI 10.1016/j.jtbi.2010.04.023

  View details for Web of Science ID 000280374100023

  View details for PubMedID 20447409

• Natural element analysis of the Cahn-Hilliard phase-field model COMPUTATIONAL MECHANICS Rajagopal, A., Fischer, P., Kuhl, E., Steinmann, P. 2010; 46 (3): 471-493

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

  View details for Web of Science ID 000277937300008

• Anterior mitral leaflet curvature in the beating ovine heart: a case study using videofluoroscopic markers and subdivision surfaces BIOMECHANICS AND MODELING IN MECHANOBIOLOGY Goektepe, S., Bothe, W., Kvitting, J. E., Swanson, J. C., Ingels, N. B., Miller, D. C., Kuhl, E. 2010; 9 (3): 281-293

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

  View details for Web of Science ID 000277711400003

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

  Abstract

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

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

  View details for PubMedID 19890668

• 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

  View details for DOI 10.1016/j.ijsolstr.2009.11.020

  View details for Web of Science ID 000276127200001

• Atrial and ventricular fibrillation: computational simulation of spiral waves in cardiac tissue ARCHIVE OF APPLIED MECHANICS Goktepe, S., Wong, J., Kuhl, E. 2010; 80 (5): 569-580

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

  View details for Web of Science ID 000275787600011

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

  Abstract

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

  View details for DOI 10.1016/j.jmbbm.2009.08.001

  View details for Web of Science ID 000274987000007

  View details for PubMedID 20129418

• Electromechanics of the heart: a unified approach to the strongly coupled excitation-contraction problem COMPUTATIONAL MECHANICS Goektepe, S., Kuhl, E. 2010; 45 (2-3): 227-243

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

  View details for Web of Science ID 000272118100009

• Computational Homogenization of Confined Frictional Granular Matter IUTAM SYMPOSIUM ON VARIATIONAL CONCEPTS WITH APPLICATIONS TO THE MECHANICS OF MATERIALS Meier, H. A., Steinmann, P., Kuhl, E. 2010; 21: 157-169

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

  View details for Web of Science ID 000290694500012

• Dilation and Hypertrophy: A Cell-Based Continuum Mechanics Approach Towards Ventricular Growth and Remodeling IUTAM SYMPOSIUM ON CELLULAR, MOLECULAR AND TISSUE MECHANICS, PROCEEDINGS Ulerich, J., Goektepe, S., Kuhl, E. 2010; 16: 237-244

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

  View details for Web of Science ID 000276397800020

• IN VITRO ASSESSMENT OF RAT HEART FORCE GENERATION: A QUANTITATIVE APPROACH FOR PREDICTING OUTCOMES FROM PLURIPOTENT STEM CELL-DERIVED THERAPY FOR MYOCARDIAL INFARCTION 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

  View details for Web of Science ID 000290705300359

• Regional stiffening of the mitral valve anterior leaflet in the beating ovine heart JOURNAL OF BIOMECHANICS Krishnamurthy, G., Itoh, A., Swanson, J. C., Bothe, W., Karlsson, M., Kuhl, E., Miller, D. C., Ingels, N. B. 2009; 42 (16): 2697-2701

  Abstract

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

  View details for DOI 10.1016/j.jbiomech.2009.08.028

  View details for Web of Science ID 000273135200011

  View details for PubMedID 19766222

• Towards the treatment of boundary conditions for global crack path tracking in three-dimensional brittle fracture COMPUTATIONAL MECHANICS Jaeger, P., Steinmann, P., Kuhl, E. 2009; 45 (1): 91-107

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

  View details for Web of Science ID 000270428100007

• Mechanics in biology: cells and tissues PREFACE PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES Ambrosi, D., Garikipati, K., Kuhl, E. 2009; 367 (1902): 3335-3337

  View details for DOI 10.1098/rsta.2009.0122

  View details for Web of Science ID 000268735700001

  View details for PubMedID 19657002

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

  Abstract

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

  View details for DOI 10.1016/j.jbiomech.2009.05.018

  View details for Web of Science ID 000269734200015

  View details for PubMedID 19535081

• Computational modeling of cardiac electrophysiology: A novel finite element approach INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING Goektepe, S., Kuhl, E. 2009; 79 (2): 156-178

  View details for DOI 10.1002/nme.2571

  View details for Web of Science ID 000267788300002

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

  Abstract

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

  View details for DOI 10.1152/ajpheart.00120.2009

  View details for Web of Science ID 000266397500009

  View details for PubMedID 19363135

• Computational modeling of muscular thin films for cardiac repair COMPUTATIONAL MECHANICS Boel, M., Reese, S., Parker, K. K., Kuhl, E. 2009; 43 (4): 535-544

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

  View details for Web of Science ID 000263059500008

• 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

• EXPLORING CELLULAR TENSEGRITY: PHYSICAL MODELING AND COMPUTATIONAL SIMULATION PROCEEDINGS OF THE ASME SUMMER BIOENGINEERING CONFERENCE 2008, PTS A AND B Zheng, C. H., Doll, J., Gu, E., Hager-Barnard, E., Huang, Z., Kia, A., Ortiz, M., Petzold, B., Usul, T., Kwon, R., Jacobs, C., Kuhl, E. 2009: 283-284

  View details for Web of Science ID 000263364700142

• FIRST ATTEMPTS TOWARDS THE COMPUTATIONAL SIMULATION OF NOVEL STEM-CELL BASED POST INFARCT THERAPIES PROCEEDINGS OF THE ASME SUMMER BIOENGINEERING CONFERENCE 2008, PTS A AND B Ulerich, J. P., Goktepe, S., Kuhl, E. 2009: 417-418

  View details for Web of Science ID 000263364700209

• 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

  View details for Web of Science ID 000280089000415

• 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

  View details for Web of Science ID 000263364700486

• 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

  View details for Web of Science ID 000263364700066

• On the Multiscale Computation of Con"ned Granular Media ECCOMAS MULTIDISCIPLINARY JUBILEE SYMPOSIUM Meier, H. A., Steinmann, P., Kuhl, E. 2009; 14: 121-133

  View details for Web of Science ID 000267056200009

• 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

  View details for Web of Science ID 000263364700101

• Acceleration insensitive encapsulated silicon microresonator APPLIED PHYSICS LETTERS Jha, C. M., Salvia, J., Chandorkar, S. A., Melamud, R., Kuhl, E., Kenny, T. W. 2008; 93 (23)

  View details for DOI 10.1063/1.3036536

  View details for Web of Science ID 000261699700087

• Modeling three-dimensional crack propagation-A comparison of crack path tracking strategies INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING Jaeger, R., Steinmann, R., Kuhl, E. 2008; 76 (9): 1328-1352

  View details for DOI 10.1002/nme.2353

  View details for Web of Science ID 000261111400002

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

  Abstract

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

  View details for DOI 10.1109/TVCG.2008.65

  View details for Web of Science ID 000257371400011

  View details for PubMedID 18599921

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

  Abstract

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

  View details for DOI 10.1152/ajpheart.00284.2008

  View details for Web of Science ID 000258949200031

  View details for PubMedID 18621858

• On local tracking algorithms for the simulation of three-dimensional discontinuities COMPUTATIONAL MECHANICS Jaeger, P., Steinmann, P., Kuhl, E. 2008; 42 (3): 395-406

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

  View details for Web of Science ID 000256254000005

• A note on the generation of periodic granular microstructures based on grain size distributions INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS MEIER, H. A., Kuhl, E., Steinmann, P. 2008; 32 (5): 509-522

  View details for DOI 10.1002/nag.635

  View details for Web of Science ID 000255319200004

• Time-dependent fibre reorientation of transversely isotropic continua - Finite element formulation and consistent linearization INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING Himpel, G., Menzel, A., Kuhl, E., Steinmann, P. 2008; 73 (10): 1413-1433

  View details for DOI 10.1002/nme.2124

  View details for Web of Science ID 000253694300004

• Brittle fracture during folding of rocks: A finite element study PHILOSOPHICAL MAGAZINE Jager, P., Schmalholz, S. M., Schmid, D. W., Kuhl, E. 2008; 88 (28-29): 3245-3263

  View details for DOI 10.1080/14786430802320101

  View details for Web of Science ID 000261803800004

• Computational modelling of thermal impact welded PEEK/steel single lap tensile specimens COMPUTATIONAL MATERIALS SCIENCE Utzinger, J., Bos, M., Floeck, M., Menzel, A., Kuhl, E., Renz, R., Friedrich, K., Schlarb, A. K., Steinmann, P. 2008; 41 (3): 287-296

  View details for DOI 10.1016/j.commatsci.2007.04.015

  View details for Web of Science ID 000254338500004

• Towards mulitscale computation of confined granular media - Contact forces, stresses and tangent operators Techn Mech Meier HA, Steinmann P, Kuhl E 2008; 28: 32-42
• A continuum model for remodeling in living structures JOURNAL OF MATERIALS SCIENCE Kuhl, E., Holzapfel, G. A. 2007; 42 (21): 8811-8823

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

  View details for Web of Science ID 000249213300006

• Diamond elements: A finite element/discrete-mechanics approximation scheme with guaranteed optimal convergence in incompressible elasticity INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING Hauret, P., Kuhl, E., Ortiz, M. 2007; 72 (3): 253-294

  View details for DOI 10.1002/nme.1992

  View details for Web of Science ID 000250277400001

• Computational modeling of arterial wall growth - Attempts towards patient-specific simulations based on computer tomography 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

• Computational modeling of mineral unmixing and growth - An application of the Cahn-Hilliard equation COMPUTATIONAL MECHANICS Kuhl, E., Schmid, D. W. 2007; 39 (4): 439-451

  View details for DOI 10.1007/s00466-006-0041-1

  View details for Web of Science ID 000243968400008

• Towards the algorithmic treatment of 3D strong discontinuities COMMUNICATIONS IN NUMERICAL METHODS IN ENGINEERING Mergheim, J., Kuhl, E., Steinmann, P. 2007; 23 (2): 97-108

  View details for DOI 10.1002/cnm.885

  View details for Web of Science ID 000244089800002

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

  View details for DOI 10.1016/j.cma.2007.02.015

  View details for Web of Science ID 000249301500002

• On the application of Hansbo's method for interface problems IUTAM SYMPOSIUM ON DISCRETIZATION METHODS FOR EVOLVING DISCONTINUITIES Kuhl, E., Jaeger, P., Mergheim, J., Steinmann, P. 2007; 5: 255-265

  View details for Web of Science ID 000251312200015

• A discontinuous Galerkin method for the Cahn-Hilliard equation JOURNAL OF COMPUTATIONAL PHYSICS Wells, G. N., Kuhl, E., Garikipati, K. 2006; 218 (2): 860-877

  View details for DOI 10.1016/j.jcp.2006.03.010

  View details for Web of Science ID 000242461200021

• On the convexity of transversely isotropic chain network models PHILOSOPHICAL MAGAZINE Kuhl, E., Menzel, A., Garikipati, K. 2006; 86 (21-22): 3241-3258

  View details for DOI 10.1080/14786430500080296

  View details for Web of Science ID 000237931000007

• An illustration of the equivalence of the loss of ellipticity conditions in spatial and material settings of hyperelasticity EUROPEAN JOURNAL OF MECHANICS A-SOLIDS Kuhl, E., Askes, H., Steinmann, P. 2006; 25 (2): 199-214

  View details for DOI 10.1016/j.euromechsol.2005.07.008

  View details for Web of Science ID 000236610600001

• Modeling and simulation of remodeling in soft biological tissues MECHANICS OF BIOLOGICAL TISSUE Kuhl, E., Menzel, A., Garikipati, K., Arruda, E. M., Grosh, K. 2006: 77-89

  View details for Web of Science ID 000237286900006

• Structural optimization by simultaneous equilibration of spatial and material forces COMMUNICATIONS IN NUMERICAL METHODS IN ENGINEERING Askes, H., Bargmann, S., Kuhl, E., Steinmann, P. 2005; 21 (8): 433-442

  View details for DOI 10.1002/cnm.758

  View details for Web of Science ID 000231331400004

• Remodeling of biological tissue: Mechanically induced reorientation of a transversely isotropic chain network JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS Kuhl, E., Garikipati, K., Arruda, E. M., Grosh, K. 2005; 53 (7): 1552-1573

  View details for DOI 10.1016/j.jmps.2005.03.002

  View details for Web of Science ID 000230058500005

• A finite element method for the computational modelling of cohesive cracks INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING Mergheim, J., Kuhl, E., Steinmann, P. 2005; 63 (2): 276-289

  View details for Web of Science ID 000228913400007

• Computational modelling of isotropic multiplicative growth CMES-COMPUTER MODELING IN ENGINEERING & SCIENCES Himpel, G., Kuhl, E., Menzel, A., Steinmann, P. 2005; 8 (2): 119-134

  View details for Web of Science ID 000230077000003

• A hyperelastodynamic ALE formulation based on referential, spatial and material settings of continuum mechanics ACTA MECHANICA Kuhl, E., Steinmann, P. 2005; 174 (3-4): 201-222

  View details for DOI 10.1007/s00707-004-0200-4

  View details for Web of Science ID 000227999700005

• Computational modeling of hip replacement surgery - Total hip replacement vs. hip resurfacing Techn Mech Kuhl E, Balle F 2005; 25: 107-114
• Material force method. Continuum damage & thermo-hyperelasticity MECHANICS OF MATERIAL FORCES Denzer, R., Liebe, T., Kuhl, E., Barth, F. J., Steinmann, P. 2005; 11: 95-104

  View details for Web of Science ID 000233193400010

• 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

  View details for Web of Science ID 000233193400012

• A hybrid discontinuous Galerkin/interface method for the computational modelling of failure COMMUNICATIONS IN NUMERICAL METHODS IN ENGINEERING Mergheim, J., Kuhl, E., Steinmann, P. 2004; 20 (7): 511-519

  View details for DOI 10.1002/cnm.689

  View details for Web of Science ID 000222538700002

• Computational modeling of healing: an application of the material force method BIOMECHANICS AND MODELING IN MECHANOBIOLOGY Kuhl, E., Steinmann, P. 2004; 2 (4): 187-203

  Abstract

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

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

  View details for Web of Science ID 000208283300001

  View details for PubMedID 14872320

• On the impact of configurational mechanics on computational mechanics CONFIGURATIONAL MECHANICS Kuhl, E., Steinmann, P. 2004: 15-29

  View details for Web of Science ID 000189444500002

• Material forces in open system mechanics COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING Kuhl, E., Steinmann, P. 2004; 193 (23-26): 2357-2381

  View details for DOI 10.1016/j.cma.2004.01.022

  View details for Web of Science ID 000221274800013

• Application of the material force method to thermo-hyperelasticity COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING Kuhl, E., Denzer, R., Barth, F. J., Steinmann, P. 2004; 193 (30-32): 3303-3325

  View details for DOI 10.1016/j.cma.2003.09.021

  View details for Web of Science ID 000222540900008

• An ALE formulation based on spatial and material settings of continuum mechanics. Part 1: Generic hyperelastic formulation COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING Kuhl, E., Askes, H., Steinmann, P. 2004; 193 (39-41): 4207-4222

  View details for DOI 10.1016/j.cma.2003.09.030

  View details for Web of Science ID 000224018200008

• An ALE formulation based on spatial and material settings of continuum mechanics. Part 2: Classification and applications COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING Askes, H., Kuhl, E., Steinmann, P. 2004; 193 (39-41): 4223-4245

  View details for DOI 10.1016/j.cma.2003.09.031

  View details for Web of Science ID 000224018200009

• Theory and numerics of geometrically non-linear open system mechanics INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING Kuhl, E., Steinmann, P. 2003; 58 (11): 1593-1615

  View details for DOI 10.1002/nme.827

  View details for Web of Science ID 000186438000001

• Mass- and volume-specific views on thermodynamics for open systems PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES Kuhl, E., Steinmann, P. 2003; 459 (2038): 2547-2568

  View details for DOI 10.1098/rspa.2003.1119

  View details for Web of Science ID 000185739200009

• Computational modeling of growth - A critical review, a classification of concepts and two new consistent approaches COMPUTATIONAL MECHANICS Kuhl, E., Menzel, A., Steinmann, P. 2003; 32 (1-2): 71-88

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

  View details for Web of Science ID 000185915200008

• An arbitrary Lagrangian Eulerian finite-element approach for fluid-structure interaction phenomena Int J Num Meth Eng Kuhl E, Hulshoff S, de Borst R 2003; 57: 117-142
• On spatial and material settings of thermo-hyperelastodynamics for open systems ACTA MECHANICA Kuhl, E., Steinmann, P. 2003; 160 (3-4): 179-217

  View details for DOI 10.1007/s00707-002-0974-1

  View details for Web of Science ID 000181493700004

• Thermodynamics of open systems with application to chemomechanical problems COMPUTATIONAL MODELLING OF CONCRETE STRUCTURES Kuhl, E., Steinmann, P. 2003: 463-472

  View details for Web of Science ID 000182406800050

• A thermodynamically consistent approach to microplane theory. Part II. Dissipation and inelastic constitutive modeling INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES Kuhl, E., Steinmann, P., Carol, I. 2001; 38 (17): 2933-2952

  View details for Web of Science ID 000167747700003

• New thermodynamic approach to microplane model. Part II: Dissipation and inelastic constitutive modelling Int J Solids Structures Kuhl E, Carol I, Steinmann P 2001; 38: 2933-2952
• A comparison of discrete granular material models with continuous microplane formulations Granular Matter Kuhl E, D'Addetta GA, Herrmann HJ, Ramm E 2000; 2: 123-135
• Failure analysis for elasto-plastic material models on different levels of observation Int J Solids Structures Kuhl E, Ramm E, Willam KJ 2000; 37: 7259-7280
• Microplane modelling of cohesive frictional materials Eur J Mech/A:Solids Kuhl E, Ramm E 2000; 19: S121-S143
• An anisotropic gradient damage model for quasi-brittle materials Comp Meth Appl Mech Eng Kuhl E, Ramm E, de Borst R 2000; 183: 87-103
• Parameter identification of gradient enhanced damage models with the finite element method Eur J Mech/A: Solids Mahnken R, Kuhl E 1999; 18: 819-835
• Simulation of strain localization with gradient enhanced damage models Comp Mat Sci Kuhl E, Ramm E 1999; 16: 176-185
• Aspects of non-associated single crystal plasticity: Influence of non-Schmid effects and localization analysis INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES Steinmann, P., Kuhl, E., Stein, E. 1998; 35 (33): 4437-4456

  View details for Web of Science ID 000075278600007

• On the linearization of the microplane model Mech Coh Fric Mat Kuhl E, Ramm E 1998; 2: 343-364
• Modelling and computations of instability phenomena in multisurface plasticity Comp Mech Sawischlewski E, Steinmann P, Stein E 1996; 18: 245-258