title: Demyelination patterns in a mathematical model of multiple sclerosis.
abstract: 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.
authors.affiliation: Department of Mathematics, University of Palermo, Via Archirafi 34, 90123, Palermo, Italy.
authors.forename: M C
authors.initials: MC
authors.lastname: Lombardo
authors.affiliation: Department of Mathematics, University of Palermo, Via Archirafi 34, 90123, Palermo, Italy.
authors.forename: R
authors.initials: R
authors.lastname: Barresi
authors.affiliation: Department of Physics, University of Calabria, Via Pietro Bucci, 87036, Rende, CS, Italy.
authors.forename: E
authors.initials: E
authors.lastname: Bilotta
authors.affiliation: Department of Mathematics, University of Palermo, Via Archirafi 34, 90123, Palermo, Italy.
authors.forename: F
authors.initials: F
authors.lastname: Gargano
authors.affiliation: Department of Physics, University of Calabria, Via Pietro Bucci, 87036, Rende, CS, Italy.
authors.forename: P
authors.initials: P
authors.lastname: Pantano
authors.affiliation: Department of Mathematics, University of Palermo, Via Archirafi 34, 90123, Palermo, Italy. marcomarialuigi.sammartino@unipa.it.
authors.forename: M
authors.identifier: 0000-0002-1135-0167
authors.initials: M
authors.lastname: Sammartino
mesh_terms: D017209:Apoptosis; D003711:Demyelinating Diseases / Q000473:pathology*; D006801:Humans; D008279:Magnetic Resonance Imaging; D008954:Models, Biological; D009103:Multiple Sclerosis / Q000473:pathology*
keywords: Chemotaxis PDE model; Inflammation; Multiple sclerosis; Patterns; Turing instability