The migration of vascular endothelial cells (ECs), the cells lining the inner surfaces of all blood vessels, is critical for several physiological and pathological processes including vascular wound healing after injury, tumor angiogenesis, and the development of viable and biocompatible tissue engineered vascular constructs. The goal of the proposed doctoral research is to develop a predictive computational model of EC migration under flow. A number of previous studies have demonstrated that EC migration is regulated by the intracellular concentration of adenosine triphosphate (ATP) and recent experiments on ECs cultured on line patterns, i.e. on surfaces where cellular adhesion is confined to narrow lines that confer physical confinement to the cells, have demonstrated that these cells exhibit very different migration behavior than cells on unpatterned surfaces where the cells are not confined. In light of the above, the initial focus of the project is on the development of a mathematical model that describes the changes in intracellular ATP concentration experienced by ECs on line patterns. In this regard, the focus is on the physical phenomena that provoke changes in intracellular ATP including modifications in cytoskeletal organization and the flow environment to which the cells are subjected. The equations governing intracellular ATP dynamics are solved numerically; successively an appropriate theoretical analysis of the equations will be performed.
Once a predictive model of ATP dynamics is developed, the study will proceed to couple the computed intracellular ATP concentrations to migration. The proposed research is highly novel. While some computational models of cell migration certainly exist, there are very few models of the effect of flow on EC migration. Furthermore, no models exist for the regulation of cellular migration on patterned surfaces under flow.
It is now recognized that patterned surfaces that allow fine control of cellular shape and cytoskeletal organization constitute a powerful tool for studying relationships between cell structure and function. In spite of the rapidly increasing use of these surfaces among experimentalists, no mathematical models currently exist of cellular migration on such surfaces. Therefore, the proposed research is highly novel. If we succeed in developing a robust model that accurately predicts cellular migration on patterned surfaces, then this model can be used for exploring how line patterns of different dimensions influence cell migration and how other types of surface patterns may modulate cell migratory phenotypes.
One application where patterned surfaces hold particular promise is in the field of implantable devices. An important consideration in the performance of these devices is how rapidly after implantation their surfaces become covered with cells. For instance, in the specific case of implantable endovascular devices such as stents or valves, it is essential for endothelial cells around the device to migrate onto the device surface and cover the surface in order to minimize the incidence of thrombosis (blood clot formation). Thus, one idea might be to pattern the surfaces of such devices in such a manner as to optimize endothelial migration, Therefore, a mathematical model such as the one proposed here promises to be an important tool in the design flow path of endovascular devices.
Another novelty concerning the model is the presence and influence of ATP on cell behavior. Previous mathematical models of migration mainly include properties of the cells such as adhesion to the substrate and contractility of the cytoskeleton, but none of them take into account the main engine of the cell: its energy. Furthermore, investigations on the relations between intracellular ATP concentration, cell elongation and cytoskeletal remodeling might open new paths in the development of new experimental methods in the measurement of ATP, which is a field of research in part still unknown. Thus a mathematical model that includes it, might be considered as a starting point for further research towards always more complex and detailed models that give a better description of the cell. From the mathematical point of view, we want to deeper explore the theory of bifurcation, studying analytically the problem of ordinary differential equations in order to find a proper set of parameters that can allow us to discriminate and predict the three different cases under analysis. This field is challenging and requires the use of sophisticated methods that we want to explore. From the point of view of partial differential equations, we want to find new methods to study the system that might include the different effects of diffusion and reaction and this is something interesting also from the numerical point of view since we want to develop new strategies to solve our equations.