A mathematical model of inflammation during ischemic stroke

Abstract

Abstract. In this article we propose a model to describe the inflammatory process which occurs during ischemic stroke. First, an introduction to some basic concepts about the biological phenomenon is given. Then, a detailed derivation of the model and the numerical scheme used are presented. Finally, the studies of the model robustness and sensitivity are showed and some numerical results on the time and space evolution of the process are presented and discussed.Résumé. Dans cet article, nous nous attachons à modéliser le processus inflammatoire lors d'un accident vasculaire cérébral ischémique. Tout d'abord, nous expliquons brièvement les bases biologiques de ce phénomène. Puis, nous décrivons les équations et les schémas numériques retenus pour le modéliser et l'implémenter. Nous présentons ensuite des études de robustesse et de sensibilité et montrons et discutons les premiers résultats de simulation obtenus.

Modeling Molecular Pathways of Neuronal Ischemia

“…22 The model uses proportional densities of healthy, dying, and dead cells, as well as leukocytic cells, to evaluate the diffusive effects of inflammatory chemokines and cytokines that react with local cells to modify the ischemic insult. Partial differential equations are used to describe how these molecular factors alter the densities of dead, dying and healthy cells over time.…”

Computer modeling of ischemic stroke

“…Caspase is activated by binding of surface receptors or in response to oxidative stress. Modeling has identify factors that lead to the heterogeneity of cell fates, protein interactions that can promote or suppress apoptosis and have the potential for in silico drug development [20, 21, 22, 23]. Intracellular Ca 2+ plays vital role in neuronal signalling and biophysiology, so has been extensively modeled in both physiological [24] and pathological conditions [25], it is also a principle agent in the ischemic cascade (Fig.…”

“…After around 24 hours, macrophages enter and perform further phayocytosis, clearing dead tissue from the infarct core. A detailed mathematical model was developed that considered the densities of these cells in different tissue states – healthy, necortic, aptotpic and undergoing aptotosis [22]. That model revealed a nonlinear relationship between initial core volume and the ultimate size of the infarction.…”

“…Inflammation is a response to injury which causes further injury, particularly in the skull-case which provides no room for expansion. General cell density models for inflammation can distinguish between microglial and leukocyte inflammation to begin to calculate how inhibition of aggregation could affect infarct size in each case [22]. However these models lack key features that are peculiar to the brain and to ischemic stroke, such as the effects of production and diffusion of ROS, which activate microglia and can be produced by them.…”

Computer modeling of ischemic stroke

“…A model by Di Russo et al (2010) was used to evaluate the contribution of inflammatory processes to the further development of edema in the penumbra. The model used proportional densities of healthy, dying, and dead cells, as well as leukocytic cells, to evaluate how diffusion of inflammatory chemokines and cytokines would react with local cells to modify the ischemic insult.…”