In this paper we derive a reaction-diffusion-chemotaxis model for thedynamics of multiple sclerosis. We focus on the early inflammatory phase of the diseasecharacterized by activated local microglia, with the recruitment of a systemicallyactivated immune response, and by oligodendrocyte apoptosis. The model consists ofthree equations describing the evolution of macrophages, cytokine and apoptotic oligodendrocytes.The main driving mechanism is the chemotactic motion of macrophagesin response to a chemical gradient provided by the cytokines. Our model generalizesthe system proposed by Calvez and Khonsari (Math Comput Model 47(7–8):726–742, 2008) and Khonsari and Calvez (PLos ONE 2(1):e150, 2007) to describe Baló’ssclerosis, a rare and aggressive form of multiple sclerosis. We use a combination of analytical and numerical approaches to show the formation of different demyelinatingpatterns. In particular, a Turing instability analysis demonstrates the existenceof a threshold value for the chemotactic coefficient above which stationary structuresdevelop. In the case of subcritical transition to the patterned state, the numericalinvestigations performed on a 1-dimensional domain show the existence, far from thebifurcation, of complex spatio-temporal dynamics coexisting with the Turing pattern.On a 2-dimensional domain the proposed model supports the emergence of differentdemyelination patterns: localized areas of apoptotic oligodendrocytes, which closelyfit existing MRI findings on the active MS lesion during acute relapses; concentricrings, typical of Baló’s sclerosis; small clusters of activated microglia in absence ofoligodendrocytes apoptosis, observed in the pathology of preactive lesions.

Demyelination patterns in a mathematical model of multiple sclerosis

BILOTTA, Eleonora;PANTANO, Pietro Salvatore;
2017

Abstract

In this paper we derive a reaction-diffusion-chemotaxis model for thedynamics of multiple sclerosis. We focus on the early inflammatory phase of the diseasecharacterized by activated local microglia, with the recruitment of a systemicallyactivated immune response, and by oligodendrocyte apoptosis. The model consists ofthree equations describing the evolution of macrophages, cytokine and apoptotic oligodendrocytes.The main driving mechanism is the chemotactic motion of macrophagesin response to a chemical gradient provided by the cytokines. Our model generalizesthe system proposed by Calvez and Khonsari (Math Comput Model 47(7–8):726–742, 2008) and Khonsari and Calvez (PLos ONE 2(1):e150, 2007) to describe Baló’ssclerosis, a rare and aggressive form of multiple sclerosis. We use a combination of analytical and numerical approaches to show the formation of different demyelinatingpatterns. In particular, a Turing instability analysis demonstrates the existenceof a threshold value for the chemotactic coefficient above which stationary structuresdevelop. In the case of subcritical transition to the patterned state, the numericalinvestigations performed on a 1-dimensional domain show the existence, far from thebifurcation, of complex spatio-temporal dynamics coexisting with the Turing pattern.On a 2-dimensional domain the proposed model supports the emergence of differentdemyelination patterns: localized areas of apoptotic oligodendrocytes, which closelyfit existing MRI findings on the active MS lesion during acute relapses; concentricrings, typical of Baló’s sclerosis; small clusters of activated microglia in absence ofoligodendrocytes apoptosis, observed in the pathology of preactive lesions.
Multiple sclerosis; Chemotaxis PDE model; Turing instability
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/20.500.11770/133061
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