A Computational Model of Cell Movement Linked to Substrate Rigidity

Living cells as physical entities can response the changes of the physiological environment as well as mechanical stimuli occurring in and out of the cell body. It is well documented that cell directional motion is determined by the substrate stiffness. Cells tend to move towards stiffer substrate. Cytoskeleton plays a significant role in intracellular force equilibrium and extracellular force balance between substrate and cell via focal adhesions. Cellular deformations can be evaluated by the use of computational models. In this thesis, a finite element modelling approach that describes the biomechanical behaviors of cells is presented. We model cytoskeleton as a tensegrity structure and substrate as a spring element. The tensegrity structure has many features that are capable to model behavior of a living cell. The structure consists of tension-supporting cables and compression-supporting struts that represent the microfilaments and microtubules, respectively. The effects of substrate stiffness and prestress on strain energy of a cell are investigated by defining several substrate stiffness values and prestress values. The model is placed on a flat surface, which represents a cell anchored to an elastic substrate via focal adhesions. Numerical simulation results reveal that the strain energy of the whole cell decreases as substrate stiffness increases. As prestress of cell increases, the strain energy increases. The change of prestress value does not change behavior pattern of the strain energy: cell's strain energy will decrease when substrate stiffness increases. The findings indicate that both cell prestress and substrate stiffness have certain influences on cells' directional movements and structural deformations.