1. Mathematical Modelling of Remyelination: Astrocytes as Moving Boundary Conditions
- Author
-
Fariba Bahrami and Saber Dini
- Subjects
Continuous variable ,medicine.anatomical_structure ,Computer science ,Myelin sheaths ,medicine ,Oligodendrocyte progenitor ,Boundary value problem ,Remyelination ,Neuroscience ,Simulation - Abstract
Astrocytesplay 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.Astrocytessecrete pro-inflammatory cytokines and growth factors which are essential for recruiting OPCs to the damaged oligodendrocytes. However theiraccumulation around the lesion and creatingglialscarcan impede recruitment of OPCs by obstructing thepath. In this work we investigatethe role ofastrocytesin recruitment phase of remyelination using a new mathematical model.We introduce a new technique torelatecell concentrations in thepartial differential equations (PDE)to concrete objects in the model usingcircles ofNeumann boundary conditions. The positions of these circles are obtained by solving five PDEs describingphysiological processes .The novelty of this model isinrelating continuous variables for cell concentrationin PDEs to discrete objects. This approach is useful when objective characteristics of the cellsare important to us. In contrast to agent based models, in this modelling process no extended rules w ereassigned to discrete cells .
- Published
- 2013