Demyelination patterns in a mathematical model of multiple sclerosis
Demyelination patterns in a mathematical model of multiple sclerosis
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DOI：
10.1007/s00285-016-1087-0
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发表时间：
2016-12
影响因子：
1.9
通讯作者：
M. Lombardo;R. Barresi;E. Bilotta;F. Gargano;Pietro S. Pantano;M. Sammartino
中科院分区：
文献类型：
--
作者：
M. Lombardo;R. Barresi;E. Bilotta;F. Gargano;Pietro S. Pantano;M. Sammartino
本文推导了多发性硬化症动力学的反应-扩散-趋化模型。我们关注的是该疾病的早期炎症阶段，其特征是局部小胶质细胞被激活，伴随着系统性激活的免疫反应的募集，以及少突胶质细胞凋亡。该模型由描述巨噬细胞、细胞因子和凋亡少突胶质细胞进化的三个方程组成。主要驱动机制是巨噬细胞响应细胞因子提供的化学梯度的趋化运动。我们的模型概括了Calvez和Khonsari（数学计算模型47(7-8):726-742,2008）和Khonsari和Calvez （PLos ONE 2(1):e150, 2007）提出的描述Baló硬化症的系统，这是一种罕见的侵袭性多发性硬化症。我们使用分析和数值方法的结合来显示不同脱髓鞘模式的形成。特别地，图灵不稳定性分析证明了趋化系数的一个阈值的存在，超过这个阈值，固定结构就会发展。在亚临界过渡到图形状态的情况下，在一维域上进行的数值研究表明，与图灵模式共存的复杂时空动力学存在，而不是分岔。在二维领域，提出的模型支持不同脱髓鞘模式的出现：局部区域的凋亡少突胶质细胞，这与MS急性复发期间活动性病变的现有MRI结果非常吻合；同心环，Baló硬化症的典型特征；在未发生少突胶质细胞凋亡的情况下，观察到小簇激活的小胶质细胞。
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.