Showing papers by "Gerhard Holzapfel published in 2017"

A family of hyperelastic models for human brain tissue

Abstract: Experiments on brain samples under multiaxial loading have shown that human brain tissue is both extremely soft when compared to other biological tissues and characterized by a peculiar elastic response under combined shear and compression/tension: there is a significant increase in shear stress with increasing axial compression compared to a moderate increase with increasing axial tension Recent studies have revealed that many widely used constitutive models for soft biological tissues fail to capture this characteristic response Here, guided by experiments of human brain tissue, we develop a family of modeling approaches that capture the elasticity of brain tissue under varying simple shear superposed on varying axial stretch by exploiting key observations about the behavior of the nonlinear shear modulus, which can be obtained directly from the experimental data

Viscoelastic parameter identification of human brain tissue.

Abstract: Understanding the constitutive behavior of the human brain is critical to interpret the physical environment during neurodevelopment, neurosurgery, and neurodegeneration. A wide variety of constitutive models has been proposed to characterize the brain at different temporal and spatial scales. Yet, their model parameters are typically calibrated with a single loading mode and fail to predict the behavior under arbitrary loading conditions. Here we used a finite viscoelastic Ogden model with six material parameters–an elastic stiffness, two viscoelastic stiffnesses, a nonlinearity parameter, and two viscous time constants–to model the characteristic nonlinearity, conditioning, hysteresis and tension-compression asymmetry of the human brain. We calibrated the model under shear, shear relaxation, compression, compression relaxation, and tension for four different regions of the human brain, the cortex, basal ganglia, corona radiata, and corpus callosum. Strikingly, unconditioned gray matter with 0.36 kPa and white matter with 0.35 kPa were equally stiff, whereas conditioned gray matter with 0.52 kPa was three times stiffer than white matter with 0.18 kPa. While both unconditioned viscous time constants were larger in gray than in white matter, both conditioned constants were smaller. These rheological differences suggest a different porosity between both tissues and explain–at least in part–the ongoing controversy between reported stiffness differences in gray and white matter. Our unconditioned and conditioned parameter sets are readily available for finite element simulations with commercial software packages that feature Ogden type models at finite deformations. As such, our results have direct implications on improving the accuracy of human brain simulations in health and disease.

On Fiber Dispersion Models: Exclusion of Compressed Fibers and Spurious Model Comparisons

Abstract: Fiber dispersion in collagenous soft tissues has an important influence on the mechanical response, and the modeling of the collagen fiber architecture and its mechanics has developed significantly over the last few years. The purpose of this paper is twofold, first to develop a method for excluding compressed fibers within a dispersion for the generalized structure tensor (GST) model, which several times in the literature has been claimed not to be possible, and second to draw attention to several erroneous and misleading statements in the literature concerning the relative values of the GST and the angular integration (AI) models. For the GST model we develop a rather simple method involving a deformation dependent dispersion parameter that allows the mechanical influence of compressed fibers within a dispersion to be excluded. The theory is illustrated by application to simple extension and simple shear in order to highlight the effect of exclusion. By means of two examples we also show that the GST and the AI models have equivalent predictive power, contrary to some claims in the literature. We conclude that from the theoretical point of view neither of these two models is superior to the other. However, as is well known and as we now emphasize, the GST model has proved to be very successful in modeling the data from experiments on a wide range of tissues, and it is easier to analyze and simpler to implement than the AI approach, and the related computational effort is much lower.

A Mechanobiological model for damage-induced growth in arterial tissue with application to in-stent restenosis

Abstract: In-stent restenosis (ISR) is one of the main drawbacks of stent implementation which limits the long-term success of the procedure. Morphological changes occurring within the arterial wall due to stent-induced mechanical injury are a major cause for activation of vascular smooth muscle cells (VSMCs), and the subsequent development of ISR. Considering the theory of volumetric mass growth and adopting a multiplicative decomposition of the deformation gradient into an elastic part and a growth part, we present a mechanobiological model for ISR. An evolution equation is developed for mass growth of the neointima, in which the activation of VSMCs due to stent-induced damage (injury) and the proliferation rate of the activated cells are considered. By introducing the mass evolution into the mass balance equation, we obtain the evolution of the growth tensor over time. The model is implemented in a finite element code and the procedure of angioplasty is simulated, whereby the features of the proposed growth model are illustrated.

Comparison of two model frameworks for fiber dispersion in the elasticity of soft biological tissues

Abstract: This study compares two models that are used to describe the elastic properties of fiber-reinforced materials with dispersed fibers, in particular some soft biological tissues such as arterial walls and cartilages. The two model approaches involve different constitutive frameworks, one being based on a generalized structure tensor (GST) and the other on the method of angular integration (AI). By using two representative examples, with the same number of parameters for each model, it is shown that the predictions of the two models are virtually identical for a significant range of large deformations, which contradicts conclusions contained in several papers that are based on faulty analysis. Additionally, each of the models is fitted to sets of uniaxial data from the circumferential and axial directions of the adventitia of a human aorta, both models providing excellent agreement with the data. While the predictions of the two models are comparable and exclusion of compressed fibers can be accommodated by either model, it is well known that the AI model requires more computational time than the GST model when used within a finite element environment, in particular if compressed fibers are excluded.

Modeling of damage in soft biological tissues

Abstract: The mechanical responses of biological tissues are well characterized by hyperelastic or viscoelastic models within the physiological loading range. However, during supra-physiological mechanical loading, as occurs during interventional procedures such as balloon angioplasty and arterial clamping, damage may occur in the tissue. The continuum and computational treatments of damage in soft biological tissues have attracted considerable attention over the recent years. In this chapter, we review the state of the art of this challenging area. We summarize and critically discuss various damage models, which are based on continuum damage mechanics, the theory of pseudo-elasticity, and the softening hyperelasticity approach. Finally, we provide a recent account of finite element implementations and highlight open questions, challenges, and methods for further development.

Computational Biomechanics of Soft Biological Tissues: Arterial Walls, Hearts Walls, and Ligaments

Abstract: Soft tissues are diverse biological materials in which the cells are separated by extracellular material. They connect, support, and protect our body and form structures such as organs. Soft tissues include blood vessels, heart tissues, ligaments, tendons, skin or articular cartilage just to name a few. Soft tissues are complex fiber-reinforced composite structures. In a microscopic sense they are non-homogeneous materials because of their composition. Most of them exhibit an anisotropic behavior because of their embedded fibers, which tend to have preferred directions. The tensile response of soft tissues is nonlinear stiffening and the tensile strength depends on the strain rate. In contrast to hard (mineralized) tissues such as bones, soft tissues may experience large

Microstructure and Mechanics of Human Aortas in Health and Disease

Abstract: Human aortas are three-layered fibrous composites assembled by a ground matrix and embedded families of dispersed collagen fibers. The microstructural arrangement of the collagen fibers alters due to diseases such as aneurysms. We review a general dispersion model that is required to describe the mechanical response of a variety of collagenous tissues such as aortic walls considering three structural and three material parameters. The dispersion model is used to capture the remarkable differences in the microstructure and mechanics of healthy and aneurysmatic aortas. Related modeling/simulation of an aortic dissection is provided using the recently developed phase-field approach. An energy-based anisotropic failure criterion is used to numerically simulate the evolution of the crack phase-field in a simple shear test. Model parameters are provided and numerical results agree favorably with the experimental findings. Finally, an aortic clamping simulation is described by considering the individual aortic layers, residual stresses, nonsymmetric blood pressure after clamping, patient-specific data and damage-induced inelastic phenomena, i.e., stress softening and permanent deformations.