一种基于损伤驱动的杜兴肌肉营养不良模型：早期阶段动态和入侵阈值
A Damage-Driven Model for Duchenne Muscular Dystrophy: Early-Stage Dynamics and Invasion Thresholds
AI总结：
本文提出一个基于损伤驱动的数学模型，研究杜兴肌肉营养不良的早期动态和入侵阈值，通过线性化分析证明扩散不引发图灵不稳定性，疾病进展通过入侵过程实现，推导出入侵起始条件和最小传播速度。
摘要：
我们引入了一个基于损伤驱动范式的空间扩展数学模型，用于杜兴肌肉营养不良，其中免疫细胞的招募由组织损伤触发。该模型被公式化为一个反应-扩散-趋化系统，描述健康组织、受损纤维、免疫细胞和炎症信号之间的相互作用。我们建立了系统的全局良好性，并通过线性化围绕健康平衡点研究早期阶段动态。我们的分析表明，扩散不会引发图灵不稳定性，因此空间异质性不能由扩散驱动机制产生。相反，疾病进展通过入侵过程发生。我们推导出入侵起始的显式条件，解释为有效的损伤再生阈值，并表征病理前沿的最小传播速度，显示动态由拉前沿机制支配。数值模拟支持分析结果并确认衰减与入侵之间的过渡。这些结果为早期阶段疾病进展提供了数学框架，并表明空间扩散源于局部损伤的扩展，而非内在图案形成机制。
英文摘要：
We introduce a spatially extended mathematical model for Duchenne muscular dystrophy based on a damage-driven paradigm, in which immune recruitment is triggered by tissue injury. The model is formulated as a reaction--diffusion--chemotaxis system describing the interaction between healthy tissue, damaged fibers, immune cells and inflammatory signals. We establish the global well-posedness of the system and investigate the early-stage dynamics through linearization around the healthy equilibrium. Our analysis shows that diffusion does not induce Turing instabilities, so that spatial heterogeneity cannot arise from diffusion-driven mechanisms. Instead, disease progression occurs through invasion processes. We derive explicit conditions for the onset of invasion, interpreted as an effective damage reproduction threshold and characterize the minimal propagation speed of pathological fronts, showing that the dynamics is governed by a pulled-front mechanism. Numerical simulations support the analytical results and confirm the transition between decay and invasion. These results provide a mathematical framework for early-stage disease progression and indicate that spatial spreading arise from the expansion of localized damage rather than from intrinsic pattern-forming mechanisms.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
