Computational modeling of biological cells and soft tissues

Biological materials are complex hierarchical systems subjected to external stimuli like mechanical forces, chemical potentials and electrical signals. A deeper understanding of the behavior of these materials is required for the response characterization of healthy and diseased conditions. The primary aim of this dissertation is to study the mechanics of biological materials like cells and tissues from a computational perspective and relate its behavior with experimental works, so as to provide a framework for the identification and treatment of pathological conditions like cancer and vascular diseases. The first step towards understanding the behavior of a biological cell is to comprehend its response to external mechanical stimuli. Experimentally derived material properties of cells have found to vary by orders of magnitude even for the same cell type. The primary cause of such disparity is attributed to the stimulation process, and the theoretical models used to interpret the experimental data. The variations in mechanical properties obtained from the experimental and theoretical studies can be overcome only through the development of a sound mathematical framework correlating the derived mechanical property with the cellular structure. Such a formulation accounting for the inhomogeneity of the cytoplasm due to stress fibers and actin cortex is developed in this work using Mori-Tanaka method of homogenization. Mechanical modeling of single cells would be extremely useful in understanding its behavior in an experimental setup. Characterization of in-vivo response of cells requires mathematical modeling of the embedding environment like fibers and fluids, which forms the extra cellular matrix. Studies on fluid-tissue interactions in biomechanics have primarily relied on either an iterative solution of the individual solid or tissue phases or a sequential solution of the entire domain using a coupled algorithm. In this dissertation, a new computational methodology for the analysis of fluid-tissue interaction problem is presented. The modeling procedure is based on a biphasic representation of fluid and tissue domain, consisting of fluid and solid phases. The biphasic-fluid interaction model is also implemented to study the transfer of low-density lipoprotein from the blood to the arterial wall, and also the nutrient transfer in the tissue scaffolds of a bioreactor

Bone mechanical properties in healthy and diseased states

The mechanical properties of bone are fundamental to the ability of our skeletons to support movement and to provide protection to our vital organs. As such, deterioration in mechanical behavior with aging and/or diseases such as osteoporosis and diabetes can have profound consequences for individuals’ quality of life. This article reviews current knowledge of the basic mechanical behavior of bone at length scales ranging from hundreds of nanometers to tens of centimeters. We present the basic tenets of bone mechanics and connect them to some of the arcs of research that have brought the field to recent advances. We also discuss cortical bone, trabecular bone, and whole bones, as well as multiple aspects of material behavior, including elasticity, yield, fracture, fatigue, and damage. We describe the roles of bone quantity (e.g., density, porosity) and bone quality (e.g., cross-linking, protein composition), along with several avenues of future research.Author manuscrip

Elastic Anisotropy of Trabecular Bone in the Elderly Human Vertebra

Knowledge of the nature of the elastic symmetry of trabecular bone is fundamental to the study of bone adaptation and failure. Previous studies have classified human vertebral trabecular bone as orthotropic or transversely isotropic but have typically obtained samples from only selected regions of the centrum. In this study, the elastic symmetry of human vertebral trabecular bone was characterized using microfinite element (μFE) analyses performed on 1019 cubic regions of side length equal to 5 mm, obtained via thorough sampling of the centrums of 18 human L1 vertebrae (age = 81.17 ± 7.7 yr; eight males and ten females). An optimization procedure was used to find the closest orthotropic representation of the resulting stiffness tensor for each cube. The orthotropic elastic constants and orientation of the principal elastic axes were then recorded for each cube and were compared to the constants predicted from Cowin's fabric-based constitutive model (Cowin, 1985, “The Relationship Between the Elasticity Tensor and the Fabric Tensor,” Mech. Mater., 4(2), pp. 137–147.) and the orientation of the principal axes of the fabric tensor, respectively. Deviations from orthotropy were quantified by the “orthotropic error” (van Rietbergen et al., 1996, “Direct Mechanics Assessment of Elastic Symmetries and Properties of Trabecular Bone Architecture,” J. Biomech., 29(12), pp. 1653–1657), and deviations from transverse isotropy were determined by statistical comparison of the secondary and tertiary elastic moduli. The orthotropic error was greater than 50% for nearly half of the cubes, and the secondary and tertiary moduli differed from one another (p < 0.0001). Both the orthotropic error and the difference between secondary and tertiary moduli decreased with increasing bone volume fraction (BV/TV; p ≤ 0.007). Considering only the cubes with an orthotropic error less than 50%, only moderate correlations were observed between the fabric-based and the μFE-computed elastic moduli (R(2 )≥ 0.337; p < 0.0001). These results indicate that when using a criterion of 5 mm for a representative volume element (RVE), transverse isotropy or orthotropy cannot be assumed for elderly human vertebral trabecular bone. Particularly at low values of BV/TV, this criterion does not ensure applicability of theories of continuous media. In light of the very sparse and inhomogeneous microstructure found in the specimens analyzed in this study, further work is needed to establish guidelines for selecting a RVE within the aged vertebral centrum

Elastic Anisotropy of Trabecular Bone in the Elderly Human Vertebra

Knowledge of the nature of the elastic symmetry of trabecular bone is fundamental to the study of bone adaptation and failure. Previous studies have classified human vertebral trabecular bone as orthotropic or transversely isotropic but have typically obtained samples from only selected regions of the centrum. In this study, the elastic symmetry of human vertebral trabecular bone was characterized using microfinite element (lFE) analyses performed on 1019 cubic regions of side length equal to 5 mm, obtained via thorough sampling of the centrums of 18 human L1 vertebrae (age ¼ 81.17 6 7.7 yr; eight males and ten females). An optimization procedure was used to find the closest orthotropic representation of the resulting stiffness tensor for each cube. The orthotropic elastic constants and orientation of the principal elastic axes were then recorded for each cube and were compared to the constants predicted from Cowin&apos;s fabric-based constitutive mode