Lauffenburger D A, Kennedy C R
J Math Biol. 1983;16(2):141-63. doi: 10.1007/BF00276054.
Phagocyte motility and chemotaxis are included in a distributed mathematical model for the inflammatory response to bacterial invasion of tissue. Both uniform and non-uniform steady state solutions may occur for the model equations governing bacteria and phagocyte densities in a macroscopic tissue region. The non-uniform states appear to be more dangerous because they allow large bacteria densities concentrated in local foci, and in some cases greater total bacteria and phagocyte populations. Using a linear stability analysis, it is shown that a phagocyte chemotactic response smaller than a critical value can lead to a non-uniform state, while a chemotactic response greater than this critical value stabilizes the uniform state. This result is the opposite of that found for the role of chemotaxis in aggregation of slimemold amoebae because, in the inflammatory response, the chemotactic population serves as an inhibitor rather than an activator. We speculate that these non-uniform steady states could be related to the localized cell aggregation seen in chronic granulomatous inflammation. The formation of non-uniform states is not necessarily a consequence of defective phagocyte chemotaxis, however. Rather, certain values of the kinetic parameters can yield values for the critical chemotactic response which are greater than the normal response. Numerical computations of the transient inflammatory response to bacterial challenge are presented, using parameter values estimated from the experimental literature wherever possible.
吞噬细胞的运动性和趋化性被纳入一个针对组织细菌入侵的炎症反应的分布式数学模型中。对于宏观组织区域中控制细菌和吞噬细胞密度的模型方程，可能会出现均匀和非均匀稳态解。非均匀状态似乎更危险，因为它们会使大量细菌密度集中在局部病灶中，并且在某些情况下，细菌和吞噬细胞的总数更多。通过线性稳定性分析表明，小于临界值的吞噬细胞趋化反应会导致非均匀状态，而大于此临界值的趋化反应会使均匀状态稳定。这一结果与在黏菌变形虫聚集过程中趋化作用的结果相反，因为在炎症反应中，趋化群体起到抑制剂而非激活剂的作用。我们推测这些非均匀稳态可能与慢性肉芽肿性炎症中观察到的局部细胞聚集有关。然而，非均匀状态的形成不一定是吞噬细胞趋化缺陷的结果。相反，动力学参数的某些值可以产生大于正常反应的临界趋化反应值。本文给出了对细菌攻击的瞬态炎症反应的数值计算，尽可能使用从实验文献中估计的参数值。
