Showing papers by "Gerhard Holzapfel published in 2016"

Microstructure and mechanics of healthy and aneurysmatic abdominal aortas: experimental analysis and modelling.

Abstract: Soft biological tissues such as aortic walls can be viewed as fibrous composites assembled by a ground matrix and embedded families of collagen fibres. Changes in the structural components of aortic walls such as the ground matrix and the embedded families of collagen fibres have been shown to play a significant role in the pathogenesis of aortic degeneration. Hence, there is a need to develop a deeper understanding of the microstructure and the related mechanics of aortic walls. In this study, tissue samples from 17 human abdominal aortas (AA) and from 11 abdominal aortic aneurysms (AAA) are systematically analysed and compared with respect to their structural and mechanical differences. The collagen microstructure is examined by analysing data from second-harmonic generation imaging after optical clearing. Samples from the intact AA wall, their individual layers and the AAA wall are mechanically investigated using biaxial stretching tests. A bivariate von Mises distribution was used to represent the continuous fibre dispersion throughout the entire thickness, and to provide two independent dispersion parameters to be used in a recently proposed material model. Remarkable differences were found between healthy and diseased tissues. The out-of-plane dispersion was significantly higher in AAA when compared with AA tissues, and with the exception of one AAA sample, the characteristic wall structure, as visible in healthy AAs with three distinct layers, could not be identified in AAA samples. The collagen fibres in the abluminal layer of AAAs lost their waviness and exhibited rather straight and thick struts of collagen. A novel set of three structural and three material parameters is provided. With the structural parameters fixed, the material model was fitted to the mechanical experimental data, giving a very satisfying fit although there are only three material parameters involved. The results highlight the need to incorporate the structural differences into finite-element simulations as otherwise simulations of AAA tissues might not be good predictors for the actual in vivo stress state.

An orthotropic viscoelastic model for the passive myocardium: continuum basis and numerical treatment

Abstract: This study deals with the viscoelastic constitutive modeling and the respective computational analysis of the human passive myocardium. We start by recapitulating the locally orthotropic inner structure of the human myocardial tissue and model the mechanical response through invariants and structure tensors associated with three orthonormal basis vectors. In accordance with recent experimental findings the ventricular myocardial tissue is assumed to be incompressible, thick-walled, orthotropic and viscoelastic. In particular, one spring element coupled with Maxwell elements in parallel endows the model with viscoelastic features such that four dashpots describe the viscous response due to matrix, fiber, sheet and fiber-sheet fragments. In order to alleviate the numerical obstacles, the strictly incompressible model is altered by decomposing the free-energy function into volumetric-isochoric elastic and isochoric-viscoelastic parts along with the multiplicative split of the deformation gradient which enables the three-field mixed finite element method. The crucial aspect of the viscoelastic formulation is linked to the rate equations of the viscous overstresses resulting from a 3-D analogy of a generalized 1-D Maxwell model. We provide algorithmic updates for second Piola-Kirchhoff stress and elasticity tensors. In the sequel, we address some numerical aspects of the constitutive model by applying it to elastic, cyclic and relaxation test data obtained from biaxial extension and triaxial shear tests whereby we assess the fitting capacity of the model. With the tissue parameters identified, we conduct (elastic and viscoelastic) finite element simulations for an ellipsoidal geometry retrieved from a human specimen.

A microstructurally based continuum model of cartilage viscoelasticity and permeability incorporating measured statistical fiber orientations

Abstract: The remarkable mechanical properties of cartilage derive from an interplay of isotropically distributed, densely packed and negatively charged proteoglycans; a highly anisotropic and inhomogeneously oriented fiber network of collagens; and an interstitial electrolytic fluid We propose a new 3D finite strain constitutive model capable of simultaneously addressing both solid (reinforcement) and fluid (permeability) dependence of the tissue’s mechanical response on the patient-specific collagen fiber network To represent fiber reinforcement, we integrate the strain energies of single collagen fibers—weighted by an orientation distribution function (ODF) defined over a unit sphere—over the distributed fiber orientations in 3D We define the anisotropic intrinsic permeability of the tissue with a structure tensor based again on the integration of the local ODF over all spatial fiber orientations By design, our modeling formulation accepts structural data on patient-specific collagen fiber networks as determined via diffusion tensor MRI We implement our new model in 3D large strain finite elements and study the distributions of interstitial fluid pressure, fluid pressure load support and shear stress within a cartilage sample under indentation Results show that the fiber network dramatically increases interstitial fluid pressure and focuses it near the surface Inhomogeneity in the tissue’s composition also increases fluid pressure and reduces shear stress in the solid Finally, a biphasic neo-Hookean material model, as is available in commercial finite element codes, does not capture important features of the intra-tissue response, eg, distributions of interstitial fluid pressure and principal shear stress

Stress softening and permanent deformation in human aortas: Continuum and computational modeling with application to arterial clamping

Abstract: Inelastic phenomena such as stress softening and unrecoverable inelastic deformations induced by supra-physiological loading have been observed experimentally in soft tissues such as arteries. These phenomena need to be accounted for in constitutive models of arterial tissues so that computational models can properly predict the outcome of interventional procedures such as arterial clamping and balloon angioplasty that involve non-physiological tissue loading. Motivated by experimental data, a novel pseudo-elastic damage model is proposed to describe discontinuous softening and permanent deformation in arterial tissues. The model is fitted to experimental data and specific material parameters for 9 abdominal and 14 thoracic aortas are provided. Furthermore, the model was implemented in a finite element code and numerically analyzed with respect to experimental tests, i.e. cyclic uniaxial tension in circumferential and longitudinal directions. Results showed that the model is able to capture specific features including anisotropy, nonlinearity, and damage-induced inelastic phenomena, i.e. stress softening and permanent deformation. Finite element results of a more complex boundary-value problem, i.e. aortic clamping considering the three aortic layers, residual stress, non-symmetric blood pressure after clamping, and patient-specific data are also presented.

Computational method for excluding fibers under compression in modeling soft fibrous solids

Abstract: Soft fibrous solids often consist of a matrix reinforced by fibers that render the material anisotropic. Recently a fiber dispersion model was proposed on the basis of a weighted strain-energy function using an angular integration approach for both planar and three-dimensional fiber dispersions (G.A. Holzapfel and R.W. Ogden: Eur. J. Mech. A/Solids, 49 (2015) 561–569). This model allows the exclusion of fibers under compression. In the present study computational aspects of the model are documented. In particular, we provide expressions for the elasticity tensor and the integration boundary that admits only fibers which are extended. In addition, we give a brief description of the finite element implementation for both 2D and 3D models which make use of the von Mises distribution to describe the dispersion of the fibers. The performance and the finite element implementations of the 2D and 3D fiber dispersion models are illustrated by means of uniaxial extension in the mean fiber direction and more general directions, and simple shear with different mean fiber directions. The finite element results are in perfect agreement with the solutions computed from analytical formulas.

Pleiotropic roles of the matricellular protein Sparc in tendon maturation and ageing.

Abstract: Acute and chronic tendinopathies remain clinically challenging and tendons are predisposed to degeneration or injury with age. Despite the high prevalence of tendon disease in the elderly, our current understanding of the mechanisms underlying the age-dependent deterioration of tendon function remains very limited. Here, we show that Secreted protein acidic and rich in cysteine (Sparc) expression significantly decreases in healthy-aged mouse Achilles tendons. Loss of Sparc results in tendon collagen fibrillogenesis defects and Sparc−/− tendons are less able to withstand force in comparison with their respective wild type counterparts. On the cellular level, Sparc-null and healthy-aged tendon-derived cells exhibited a more contracted phenotype and an altered actin cytoskeleton. Additionally, an elevated expression of the adipogenic marker genes PPARγ and Cebpα with a concomitant increase in lipid deposits in aged and Sparc−/− tendons was observed. In summary, we propose that Sparc levels in tendons are critical for proper collagen fibril maturation and its age-related decrease, together with a change in ECM properties favors lipid accretion in tendons.

On the thermodynamics of smooth muscle contraction

Abstract: Cell function is based on many dynamically complex networks of interacting biochemical reactions. Enzymes may increase the rate of only those reactions that are thermodynamically consistent. In this paper we specifically treat the contraction of smooth muscle cells from the continuum thermodynamics point of view by considering them as an open system where matter passes through the cell membrane. We systematically set up a well-known four-state kinetic model for the cross-bridge interaction of actin and myosin in smooth muscle, where the transition between each state is driven by forward and reverse reactions. Chemical, mechanical and energy balance laws are provided in local forms, while energy balance is also formulated in the more convenient temperature form. We derive the local (non-negative) production of entropy from which we deduce the reduced entropy inequality and the constitutive equations for the first Piola–Kirchhoff stress tensor, the heat flux, the ion and molecular flux and the entropy. One example for smooth muscle contraction is analyzed in more detail in order to provide orientation within the established general thermodynamic framework. In particular the stress evolution, heat generation, muscle shorting rate and a condition for muscle cooling are derived.

A Kernel Interpolation Based Fast Multipole Method for Elastodynamic Problems

Abstract: The boundary element method (BEM) is a well-established method and particularly well suited to treat wave propagation phenomena in unbounded domains. However, the occurrence of dense system matrices is prohibitive, limiting the classical BEM to small and mid-sized problems. In the present work we propose a Chebyshev interpolation based multi-level fast multipole method (FMM) to reduce memory and computational cost of the 3D elastodynamic boundary integral operators. We present two versions for the proposed algorithm: Firstly, the direct approximation of the tensorial elastodynamic displacement and traction kernels and secondly, a version using a representation of the fundamental solutions based on scalar Helmholtz kernels. The former offers easy extensibility to more complicated kernel functions, which arise for instance in poroelastic problems. The latter minimizes the number of moment-to-local (M2L) operations and, additionally, offers the possibility to exploit the rotational invariance of the scalar kernel to further reduce memory requirements. For both approaches a directional clustering scheme in combination with a plane wave modification of the kernel function is implemented to treat the high frequency case. In order to validate the proposed numerical schemes, the FMM approximation error is investigated for both the low and high frequency regime. Furthermore, convergence results are given for a Dirichlet as well as a mixed boundary value problem in Laplace domain. Finally, the applicability of the proposed FMM to transient problems treated with the Convolution Quadrature Method is investigated.