Wavefront invasion for a chemotaxis model of Multiple Sclerosis

Barresi, Rita; Bilotta, Eleonora; Gargano, Francesco; Lombardo, Maria Carmela; Pantano, Pietro; Sammartino, M.

doi:10.1007/s11587-016-0265-0

Cited by 6 publications

(1 citation statement)

References 27 publications

(32 reference statements)

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“…All the details of the derivation of the coefficients in Eq. ( 25) can be found in [4], where we have performed the weakly non linear analysis to investigate the pattern invasion as a travelling wave front.…”

Section: Weakly Nonlinear Analysismentioning

confidence: 99%

Demyelination patterns in a mathematical model of multiple sclerosis

et al. 2016

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In this paper we derive a reaction-diffusion-chemotaxis model for the dynamics of multiple sclerosis. We focus on the early inflammatory phase of the disease characterized by activated local microglia, with the recruitment of a systemically activated immune response, and by oligodendrocyte apoptosis. The model consists of three equations describing the evolution of macrophages, cytokine and apoptotic oligodendrocytes. The main driving mechanism is the chemotactic motion of macrophages in response to a chemical gradient provided by the cytokines. Our model generalizes the 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's sclerosis, a rare and aggressive form of multiple sclerosis. We use a combination of analytical and numerical approaches to show the formation of different demyelinating patterns. In particular, a Turing instability analysis demonstrates the existence of a threshold value for the chemotactic coefficient above which stationary structures develop. In the case of subcritical transition to the patterned state, the numerical investigations performed on a 1-dimensional domain show the existence, far from the bifurcation, of complex spatio-temporal dynamics coexisting with the Turing pattern. On a 2-dimensional domain the proposed model supports the emergence of different demyelination patterns: localized areas of apoptotic oligodendrocytes, which closely fit existing MRI findings on the active MS lesion during acute relapses; concentric rings, typical of Baló's sclerosis; small clusters of activated microglia in absence of oligodendrocytes apoptosis, observed in the pathology of preactive lesions.

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Section: Weakly Nonlinear Analysismentioning

confidence: 99%

Demyelination patterns in a mathematical model of multiple sclerosis

et al. 2016

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Axisymmetric solutions for a chemotaxis model of Multiple Sclerosis

et al. 2018

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A chemotaxis reaction–diffusion model for Multiple Sclerosis with Allee effect

et al. 2023

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In this paper, we study a modification of the mathematical model describing inflammation and demyelination patterns in the brain caused by Multiple Sclerosis proposed in Lombardo et al. (J Math Biol 75:373–417, 2017). In particular, we hypothesize a minimal amount of macrophages to be able to start and sustain the inflammatory response. Thus, the model function for macrophage activation includes an Allee effect. We investigate the emergence of Turing patterns by combining linearised and weakly nonlinear analysis, bifurcation diagrams and numerical simulations, focusing on the comparison with the previous model.

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Wavefront invasion for a chemotaxis model of Multiple Sclerosis

Cited by 6 publications

References 27 publications

Demyelination patterns in a mathematical model of multiple sclerosis

Demyelination patterns in a mathematical model of multiple sclerosis

Axisymmetric solutions for a chemotaxis model of Multiple Sclerosis

A chemotaxis reaction–diffusion model for Multiple Sclerosis with Allee effect

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