Chemotaxis is the major cytotaxic mechanism that leads the movement of phagocytes in the tissue towards the harmful agents. Loss of phagocytes ability to track and respond to danger signals can lead to chronic infections, sepsis or even death. This thesis examines the consequences of anomalous diffusion of chemokines on the chemotaxis of phagocytes in the event of acute inflammatory responses.
The main driver of any chemotactic system is the corresponding chemo-attractant, which is the role given to chemokines. Allowing anomalous (fractional) diffusion with the tail index of $0<\alpha<2$, leads to the front propagation rate proportional to $t^{1/\alpha}$: faster than the traditional Gaussian spread ($t^{1/2}$). Moreover, fractional chemokine concentration profiles obey power laws, which results in slower tail decays leading to heavy tails; whereas in the Gaussian scenario tail decays are exponential and rapid.
Changing the morphology of chemokine profile over the domain will affect all other entities that depend on chemokine concentration: the likes of tactic motility, sensitivity and velocity. Our study aims at understanding the influences of chemokine gradient field variations on phagocyte chemotaxis and hence on the acute inflammatory response. We show various circumstances in which normally diffusing chemokines fail to recruit adequate phagocytes and more importantly this behaviour stays the same even if the source of chemokine production is multiplied by several orders of magnitude. Another challenge is to insure the presence of an optimum number of phagocytes in the tissue, which is governed by a timely initiation of infiltration.
Overall, we observe differences in the outcomes of the inflammatory responses of the two different diffusion schemes. The consideration of fractional diffusion enables us to give new interpretation of how signals spread in the heterogeneous tissues and why in some cases the traditional Gaussian mechanism may fall short.
