| Abstract: |
| In this work, we develop a model for the evolution of the Multiple Sclerosis pathology that considers the modulatory influence of cytokines on the activation rate of macrophages. Our starting point is the reaction-diffusion-chemotaxis model proposed in (Lombardo, Barresi, Bilotta, Gargano, Pantano, Sammartino, J.Math.Biol. (2017)), and we modify the macrophage activation mechanism. We explore the hypothesis, e.g., Lassmann, (2018), that cytokines mediate the activation mechanism.
Through a weakly nonlinear analysis, we characterize the chemotaxis-driven Turing instability and construct the stationary patterns that emerge from this instability. Using biologically relevant parameter values, we show that the asymptotic solutions of our model system reproduce the concentric demyelinating rings, confluent plaques, and preactive lesions observed in Bal\`{o} sclerosis and type III Multiple Sclerosis. Furthermore, we explore the initiation and progression of demyelinated plaques through extensive numerical simulations on two-dimensional domains. Our findings reveal that the alternative scenario proposed here results in a less aggressive pathology and slower disease progression.
Under the appropriate regularity conditions on the initial data, we prove the existence of a unique global solution to our proposed system.
This study provides insights into the role of cytokines in the pathogenesis of Multiple Sclerosis and offers potential avenues for therapeutic interventions. |
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