Showing papers by "Gerhard Holzapfel published in 2013"

Influence of myocardial fiber/sheet orientations on left ventricular mechanical contraction:

Abstract: At any point in space the material properties of the myocardium are characterized as orthotropic, that is, there are three mutually orthogonal axes along which both electrical and mechanical parame ...

An automated approach for three-dimensional quantification of fibrillar structures in optically cleared soft biological tissues

Abstract: We present a novel approach allowing for a simple, fast and automated morphological analysis of three-dimensional image stacks (z-stacks) featuring fibrillar structures from optically cleared soft biological tissues. Five non-atherosclerotic tissue samples from human abdominal aortas were used to outline the multi-purpose methodology, applicable to various tissue types. It yields a three-dimensional orientational distribution of relative amplitudes, representing the original collagen fibre morphology, identifies regions of isotropy where no preferred fibre orientations are observed and determines structural parameters throughout anisotropic regions for the analysis and numerical modelling of biomechanical quantities such as stress and strain. Our method combines optical tissue clearing with second-harmonic generation imaging, Fourier-based image analysis and maximum-likelihood estimation for distribution fitting. With a new sample preparation method for arteries, we present, for the first time to our knowledge, a continuous three-dimensional distribution of collagen fibres throughout the entire thickness of the aortic wall, revealing novel structural and organizational insights into the three arterial layers.

A finite element-based constrained mixture implementation for arterial growth, remodeling, and adaptation: theory and numerical verification.

Abstract: We implemented a constrained mixture model of arterial growth and remodeling in a nonlinear finite element framework to facilitate numerical analyses of diverse cases of arterial adaptation and mal ...

A hyperelastic biphasic fibre-reinforced model of articular cartilage considering distributed collagen fibre orientations: continuum basis, computational aspects and applications.

Abstract: Cartilage is a multi-phase material composed of fluid and electrolytes (68-85% by wet weight), proteoglycans (5-10% by wet weight), chondrocytes, collagen fibres and other glycoproteins The solid phase constitutes an isotropic proteoglycan gel and a fibre network of predominantly type II collagen, which provides tensile strength and mechanical stiffness The same two components control diffusion of the fluid phase, eg as visualised by diffusion tensor MRI: (i) the proteoglycan gel (giving a baseline isotropic diffusivity) and (ii) the highly anisotropic collagenous fibre network We propose a new constitutive model and finite element implementation that focus on the essential load-bearing morphology: an incompressible, poroelastic solid matrix reinforced by an inhomogeneous, dispersed fibre fabric, which is saturated with an incompressible fluid residing in strain-dependent pores of the collagen-proteoglycan solid matrix The inhomogeneous, dispersed fibre fabric of the solid further influences the fluid permeability, as well as an intrafibrillar portion that cannot be 'squeezed out' from the tissue Using representative numerical examples on the mechanical response of cartilage, we reproduce several features that have been demonstrated experimentally in the cartilage mechanics literature

Modeling the dispersion in electromechanically coupled myocardium

Abstract: We present an approach to model the dispersion of fiber and sheet orientations in the myocardium By utilizing structure parameters, an existing orthotropic and invariant-based constitutive model developed to describe the passive behavior of the myocardium is augmented Two dispersion parameters are fitted to experimentally observed angular dispersion data of the myocardial tissue Computations are performed on a unit myocardium tissue cube and on a slice of the left ventricle indicating that the dispersion parameter has an effect on the myocardial deformation and stress development The use of fiber dispersions relating to a pathological myocardium had a rather big effect The final example represents an ellipsoidal model of the left ventricle indicating the influence of fiber and sheet dispersions upon contraction over a cardiac cycle Although only a minor shift in the pressure-volume (PV) loops between the cases with no dispersions and with fiber and sheet dispersions for a healthy myocardium was observed, a remarkably different behavior is obtained with a fiber dispersion relating to a diseased myocardium In future simulations, this dispersion model for myocardial tissue may advantageously be used together with models of, for example, growth and remodeling of various cardiac diseases

A new approach to model cross-linked actin networks: multi-scale continuum formulation and computational analysis.

Abstract: The mechanical properties of a cell are defined mainly by the cytoskeleton. One contributor within this three-dimensional structure is the actin cortex which is located underneath the lipid bilayer ...

Modeling sample/patient-specific structural and diffusional responses of cartilage using DT-MRI.

Abstract: We propose a new 3D biphasic constitutive model designed to incorporate structural data on the sample/patient-specific collagen fiber network. The finite strain model focuses on the load-bearing morphology, that is, an incompressible, poroelastic solid matrix, reinforced by an inhomogeneous, dispersed fiber fabric, saturated with an incompressible fluid at constant electrolytic conditions residing in strain-dependent pores of the collagen-proteoglycan solid matrix. In addition, the fiber network of the solid influences the fluid permeability and an intrafibrillar portion that cannot be 'squeezed out' from the tissue. We implement the model into a finite element code. To demonstrate the utility of our proposed modeling approach, we test two hypotheses by simulating an indentation experiment for a human tissue sample. The simulations use ultra-high field diffusion tensor magnetic resonance imaging that was performed on the tissue sample. We test the following hypotheses: (i) the through-thickness structural arrangement of the collagen fiber network adjusts fluid permeation to maintain fluid pressure (Biomech. Model. Mechanobiol. 7:367-378, 2008); and (ii) the inhomogeneity of mechanical properties through the cartilage thickness acts to maintain fluid pressure at the articular surface (J. Biomech. Eng. 125:569-577, 2003). For the tissue sample investigated, both through-thickness inhomogeneities of the collagen fiber distribution and of the material properties serve to influence the interstitial fluid pressure distribution and maintain fluid pressure underneath the indenter at the cartilage surface. Tissue inhomogeneity appears to have a larger effect on fluid pressure retention in this tissue sample and on the advantageous pressure distribution.

Biomechanical Properties of the Human Ventricular Myocardium

Abstract: In the multidisciplinary field of heart research it is of utmost importance, for the description of phenomena such as mechano-electric feedback or heart wall thickening, to accurately identify the biomechanical properties of the myocardium. Hence, this study aims at determining biaxial tensile and triaxial shear properties of the passive human myocardium. This novel combination of biaxial and shear testing, together with the investigation of the myocardial microstructure, yields new innovative and essential information of the material properties to fulfil the short term goals of constructing realistic myocardial models. Through such modeling efforts, capable to capture the biomechanical behaviour of the heart, it is possible to improve some methods of medical treatment, and hence the quality of life for people suffering from heart diseases - at least as a long-term goal.

Cardiovascular Tissue Damage: An Experimental and Computational Framework

Abstract: Tissue overload during medical procedures can lead to severe complications. This chapter presents an experimental and computational framework to define and predict damage due to mechanical loading and applies this framework to arterial clamping. An extension of the Holzapfel-material model for arterial tissue is presented, incorporating smooth muscle cell activation and damage to the different constituents. It is implemented in a finite element framework and used to simulate arterial clamping and subsequent damage evaluation through an isometric contraction test. These simulations are compared to actual experiments and repeated for a different clamp design, thereby demonstrating the capability of the framework.

Peng Li: Boundary Element Method for Wave Propagtion in Partially Saturated Poroelastic Continua

Abstract: Wave propagation in partially saturated porous continua is an interesting subject in Civil Engineering, Petroleum Engineering, Bioengineering, Earthquake Engineering, and Geophysics, etc. For such problems, there exist different theories, e.g., an extension of Biot’s theory, the Theory of Porous Media and the Mixture theory. Based on the Mixture theory, a dynamic three–phase model for partially saturated poroelasticity is established as well as the corresponding governing equations in Laplace domain. This model is applied to a one dimensional column and the related analytical solution in Laplace domain is deduced.The three different compressional waves, the fast wave, the second, and the third slow waves are calculated and validated with the Biot–Gassmann prediction and Murphy’s experimental results. The time domain results are obtained with the convolution quadrature method. Within the limit of a saturation nearly to one the results are as well compared with the corresponding results of saturated poroelasticity. For the three-dimensional governing equations, the fundamental solutions are deduced following Hörmander’s method. The boundary integral equations are established based on the weighted residual method. After regularization, spatial discretization, and the time discretization with the convolution quadrature method the boundary element formulation in time domain for partial saturated media is obtained. The implementation is done with the help of the open source C++ BEM library HyENA. Finally, the code is validated with the analytical one-dimensional solutions of the column. Two half-space applications are as well presented.

Modeling of Smooth Muscle Activation

Abstract: Smooth muscle contraction is governed by a complex chain of events including both mechanical and electrochemical stimuli such as stretch and calcium ion concentration. A homogeneous model for smooth muscle contraction is derived in this paper by using a continuum thermodynamical framework. The model is based on an additive decomposition of the deformation, and balance laws for the mechanical and electrochemical scales are obtained using the principle of virtual power. Constitutive equations are derived by applying the dissipation inequality, and a first-order kinetic model for the chemical state of myosin and standard linear or nonlinear mechanical models for the tissue are introduced. The constitutive equations also provide couplings between the scales. The model includes experimentally observed features like stretch dependent active force generation and hyperbolic relation between shortening velocity and afterload. The model is applied to an experimentally relevant example to illustrate its potential.

Material Modeling of the Damage Behavior of Arterial Tissues.

Abstract: In this contribution we present a damage model for collagenous soft tissues such as arterial walls, which takes into account the statistical distributions of microscopic parameters. This approach extends the constitutive framework proposed in [1] by specific damage functions arising from microscopical considerations. In detail, statistical distributions of proteoglycan (PG) orientations, fibril length parameters and ultimate proteoglycan stretch can be considered, cf. [2]. The influence of each distributed quantity on the damage behavior is investigated by adjusting the model to uniaxial experimental data of a human carotid artery. Furthermore, the proposed model is implemented into a finite element framework and used within a numerical example in order to show its applicability to inhomogeneous boundary-value problems.

Method for Incorporating Three-Dimensional Residual Stresses Into Patient-Specific Simulations of Arteries

Abstract: METHOD FOR INCORPORATING THREE-DIMENSIONAL RESIDUAL STRESSES INTO PATIENT-SPECIFIC SIMULATIONS OF ARTERIES

A Mathematical Approach for Studying Ca2+-Regulated Smooth Muscle Contraction

Abstract: Smooth muscle is found in various organs. It has mutual purposes such as providing mechanical stability and regulating organ size. To better understand the physiology and the function of smooth muscle different experimental setups and techniques are available. However, to interpret and analyze the experimental results basic models of smooth muscle are necessary. Advanced mathematical models of smooth muscle contraction further allow, to not, only investigate the experimental behavior but also to simulate and predict behaviors in complex boundary conditions that are not easy or even impossible to perform through in vitro experiments. In this chapter the characteristic behaviors of vascular smooth muscle, specially those relevant from a biomechanical point of view, and the mathematical models able to simulate and mimic those behaviors are reviewed and studied.

A hyperelastic biphasic fiber reinforced model for articular cartilage considering the distribution and orientation of collagen fibers

Abstract: Royal Institute of Technology, Department of Solid Mechanics, Osquars Backe 1, 100 44 Stockholm, SwedenArticular cartilage is a multiphase material consisting of fluids and electrolytes, which is described with the Theory of PorousMedia. The mechanical characteristics of articular cartilage are porosity, incompressible material behavior combined withtransversely isotropic behavior for solid and fluid phases. There are two central points to model articular cartilage: theporo-viscosity of the porous matrix and the visco elasticity, and orientation of the collagen fibers. A numerical example ispresented.

Determination of Mechanical and Microstructural Tissue Quantities for Modeling Damage in Arterial Tissues.

Abstract: The overstretching of arterial walls as it occurs, eg, during balloon angioplasty, results in a stress-softening of the collagenous wall which is believed to arise from microscopic tissue damage To model such damage we use a macroscopic, fiber-reinforced constitutive framework including a characterization of the individual tissue components We employed traditional and novel experimental investigations to determine and quantify the required mechanical and microstructural tissue parameters for the constitutive model Herein we present some of our experimental approaches and the resulting preliminary findings