DUROTAXIS MODELLING FOR TISSUE ENGINEERING APPLICATIONS

Tissue Engineering is a very promising research field for the development of natural biological substitutes that restore damaged tissue functions. Cells play a crucial role in tissue regeneration and repair due to their characteristics of proliferation and differentiation, cell-to-cell interaction, biomolecular production and extracellular matrix formation. In particular cell migration is a phenomenon that is involved in different physiological processes such as morphogenesis, wound healing and new tissue deposition. In the absence of external guiding factors it is essentially a phenomenon that shares quite a few analogies with Brownian motion. The presence of biochemical or biophysical cues, on the other hand, can influence cell migration in terms of speed, direction and persistence, transforming it in a biased random movement. Recent studies have shown that cells, in particular fibroblasts, are able to recognize the mechanical properties of a substratum over which they move and that these properties direct the motion through a phenomenon called durotaxis. The aim of this thesis is to study this phenomenon for a better understanding of cell behaviour in durotaxis conditions and for Tissue Engineering applications. In order to do that, in the first part of the work a mathematical model for the description of durotaxis is presented. The model is based on a stochastic differential equation for the cell velocity which is derived from the Langevin equation: cell movement is affected by two forces, namely a deterministic one representing the dissipative effects of the system, and a stochastic one which is due to all the probabilistic processes that might affect cell motility (random fluctuations in motile sensing, response mechanisms, etc.). The original contribution of this work concerns the stochastic force, which has been modified to account for the directions of highest perceived local stiffness through a finite element scheme that reminds the cellular probing mechanism. Numerical simulations of the model provide individual cell tracks that can be qualitatively compared with experimental observations. The present model is solved for two important cases that are reported in literature and a comparison with experimental data obtained on PDMS substrata is presented. The degree of agreement is satisfactory thus the model could be utilized to quantify relevant parameters of cell migration as a function of substratum mechanical properties. The second part of the work is concerned on the study and development of a durotaxis-based substratum, able to guide cells in their migration and in particular, able to guide cells along straight path. It was proved, in fact, that a relation exist between the alignment of collagen produced by fibroblasts or others tissue cells and their migration. Thus, the idea is to obtain an aligned tissue made of new collagen, giving to the cells the conditions to move along straight-lines through the mechanical properties of the substratum. To realize this substratum Polyethylenglycole (PEG) was used. First, smooth PEG was synthesized and cell migration experiments was performed over it to better understand its response. Then a specific technique was developed to produce durotaxis-based PEG substrata, and preliminary experiments of cell adhesion over it were performed showing aligned adhesion of cells over them.