Mathematical Modeling of Inflammatory Processes

The association of inflammation with modern human diseases remains an unsolved mystery of current biology and medicine. Inflammation is a protective response to noxious stimuli that unavoidably destroys normal tissue function. Various types of mathematical models are used, each suited for a different type of disease or to different parts of the immune system, in a multiscale framework. For instance, significant research on the atherosclerosis modeling was done at both, microscale and macroscale levels. In the latter case, the studies address the biomechanical and biochemical blood flow interaction with the vessel walls and tissue, giving rise to complex fluid–structure interaction (FSI) problems. The methods to describe the FSI are of great importance to achieve accurate numerical simulations. The microscale modeling of atherosclerosis concerns circulating monocytes, which form a small subpopulation of the leukocytes. The rheological properties of monocytes play a significant role in flow dynamics and alterations in cell mechanical properties, such as cell deformability, can significantly influence vascular flow and might lead to vascular complications, such as sequestration of monocytes on the vessel wall. This preliminary work proposes the development, analysis, and computer implementation of mathematical models of the inflammatory processes in healthy or diseased states. It will be followed by the validation of these approaches making use of the experimental parameters obtained within the frame of collaborative projects with medical institutions.