Date of Award

Spring 1-1-2011

Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

First Advisor

Franck J. Vernerey

Second Advisor

Ronald Pak

Third Advisor

Richard Regueiro

Fourth Advisor

Harihar Rajaram

Fifth Advisor

Stephanie Bryant

Abstract

Biological tissues are very particular types of materials that have the ability to change their structure, properties and chemistry in response to external cues. Contractile cells, i.e. fibroblasts, are key players of tissue adaptivity as they are capable of reorganizing their surrounding extra-cellular matrix (ECM) by contracting and generating mechanical forces. This contractile behavior is attributed to the development of a stress-fiber (SF) network within the cell's cytoskeleton, a process that is known to be highly dependent of the nature of the mechanical environment (such as ECM stiffness or the presence of stress and strain). To describe these processes in a consistent manner, the present thesis introduces a multiphasic formulation (fluid/solid/solute mixture) that accounts for four major elements of cell contraction: cytoskeleton, cytosol, SF and actin monomers, as well as their interactions. The model represents the cross-talks between mechanics and chemistry through various means: (a) a mechano-sensitive formation and dissociation of an anisotropic SF network described by mass exchange between actin monomer and polymers, (b) a bio-mechanical model for SF contraction that captures the well-known length-tension and velocity-tension relation for muscles cells and (c) a convection/diffusion description for the transport of fluid and monomers within the cell. Numerical investigations show that the multiphasic model is able to capture the dependency of cell contraction on the stiffness of the mechanical environment and accurately describes the development of an oriented SF network observed in contracting fibroblasts. From a numerical view-point, cell and substrate are discretized on a single, regular finite element mesh, while the potentially complex cell geometry is defined in terms of a level-set function that is independent of discretization. Field discontinuities across the cell membrane are then naturally enforced using enriched shape functions traditionally used in the XFEM formulation. The resulting method provides a flexible platform that can handle complex cell geometries, avoid expensive meshing techniques, and can potentially be extended to study cell growth and migration on an elastic substrate. In addition, the XFEM formalism facilitates the consideration of the cell's cortical elasticity, a feature that is known to be important during cell deformation. The proposed method is illustrated with a few biologically relevant examples of cell-substrate interactions. Generally, the method is able to capture some key phenomena observed in biological systems and displays numerical versatility and accuracy at a moderate computational cost.

Recent research have shown that cell spreading is highly dependent on the contractile behavior of the cell and mechanical properties of the environment it is located in. The dynamics of such process is critical for the development of tissue engineering strategy but is also a key player in wound contraction, tissue maintenance and angiogenesis. To better understand the underlying physics of such phenomena, this presentation describes a mathematical formulation of cell spreading and contraction that couples the processes of stress fiber formation, protrusion growth through actin polymerization at the cell edge and dynamics of cross-membrane protein (integrins) enabling cell-substrate attachment. The model is based on mixture model which accurately capture the interactions and mass exchange between three constituents, namely, the cell's cytoskeleton, actin monomers and stress fibers. On the one hand, monomers are allowed to polymerize into stress fiber to generate contraction while on the other hand, they may polymerize into an actin meshwork at the cell's boundary to push the membrane forward. In addition, a mechano-sensitive model of the diffusion and attachment integrins to the substrate permit to quantify the physics of the above processes in terms of substrate mechanical

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