Saber Dini, Fariba Bahrami
Astrocyte, remyelination, glial scar, OPC, mathematicalmodel, Partial Differential Equation (PDE), Neumannboundary condition.
Astrocytes play an important role in remyelination. Normally, they mediate an appropriate environment for oligodendrocyte progenitor cells (OPC) to migrate to the damaged region and differentiate into new myelin sheaths. However, it is reported that they can be harmful in some conditions. Astrocytes secrete pro-inflammatory cytokines and growth factors which are essential for recruiting OPCs to the damaged oligodendrocytes. However their accumulation around the lesion and creating glial scar can impede recruitment of OPCs by obstructing their path. In this work we investigate the role of astrocytes in recruitment phase of remyelination using a new mathematical model. We introduce a new technique to relate cell concentrations in the partial differential equations (PDE) to concrete objects in the model using circles of Neumann boundary conditions. The positions of these circles are obtained by solving five PDEs describing physiological processes. The novelty of this model is in relating continuous variables for cell concentration in PDEs to discrete objects. This approach is useful when objective characteristics of the cells are important to us. In contrast to agent based models, in this modelling process no extended rules were assigned to discrete cells.
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