Date

2019

Document Type

Thesis

Degree

Master of Science

Department

Mechanical Engineering

First Adviser

Voloshin, Arkady

Abstract

Live cells move in the body in response to physiological and mechanical stimuli. Cells move using lamellipodium which extend beyond the leading edge of the cell. This lamellipodium is part of the cytoskeleton of the cell which pulls the cell forward in cell migration. It is observed that cells will move directionally depending on the stiffness of the substrate the cell comes into contact with. It is hypothesized that cells probe their environment to test the stiffness of their substrate. As a cell comes into contact with a substrate, the resulting force is dependent on how rigid or soft the substrate is, which impacts cell deformation as has been observed in this simulation. If the cell probes a soft substrate, the resultant force is greater causing a larger deformation. If the substrate is stiffer, the resultant forces is less thus causing less deformation. These resultant forces are important because the surface integral of these forces is the strain energy of the cell. This is investigated using finite element analysis of the tensegrity model of the cell where the cell is modeled as a tensed cable network, which simulates the deformability of a live cell’s cytoskeleton. The tensegrity approach is used to understand how the internal strain energy of the tensed cable network is affected by the substrate stiffness. Each member of this model carries either a tension or compression load to give the model a stable shape in space. This model reacts to various substrate stiffness values and prestress values, but it is seen that prestress has very little effect on the model’s internal strain energy while substrate stiffness has a much greater effect on internal strain energy. Knowing that substrate stiffness constitutes a larger role on internal strain energy of a cell, models are created to observe what has been seen in lab experiments. As substrate stiffness increases, internal strain energy of the cell model decreases which has a direct effect on cell movement. It is hypothesized that live cells prefer to stay in a lower strain energy state thus cells will move to the area of s substrate that will cause a lower strain energy. More rigid substrates will cause a lower strain energy compared to soft substrates therefore cells will move towards stiff substrates.The purpose of this thesis is to investigate the internal strain energy of a 3T3 cell with a lamellipodium using a cell model based on the tensegrity approach. This model is connected to a substrate with varying stiffness values. The tensegrity approach is used on this model the same way it was used on a cell without a lamellipodium in previous computational experiments where a cell without a lamellipodium was attached to a substrate of varying stiffness. Studies found the strong relationship between substrate stiffness and internal strain energy. The computational results from this investigation are consistent with the results seen from lab experiments.

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