Demyelination patterns in a mathematical model of multiple sclerosis

被引:46
作者
Lombardo, M. C. [1 ]
Barresi, R. [1 ]
Bilotta, E. [2 ]
Gargano, F. [1 ]
Pantano, P. [2 ]
Sammartino, M. [1 ]
机构
[1] Univ Palermo, Dept Math, Via Archirafi 34, I-90123 Palermo, Italy
[2] Univ Calabria, Dept Phys, Via Pietro Bucci, I-87036 Arcavacata Di Rende, CS, Italy
基金
美国国家科学基金会;
关键词
Multiple sclerosis; Inflammation; Chemotaxis PDE model; Turing instability; Patterns; REACTION-DIFFUSION MODEL; DISEASE SENILE PLAQUES; KELLER-SEGEL MODEL; CHEMOTAXIS MODEL; CONCENTRIC DEMYELINATION; NONLINEAR STABILITY; GLOBAL BIFURCATION; SELF-ORGANIZATION; STEADY-STATES; LESIONS;
D O I
10.1007/s00285-016-1087-0
中图分类号
Q [生物科学];
学科分类号
07 ; 0710 ; 09 ;
摘要
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 Bal'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 Bal's sclerosis; small clusters of activated microglia in absence of oligodendrocytes apoptosis, observed in the pathology of preactive lesions.
引用
收藏
页码:373 / 417
页数:45
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