This paper describes a small-strain poroelasticity model to examine the interstitial fluid pressure and matrix deformation in a non-homogeneous solid tumor consisting of an inner core with a reduced specific microvascular area encapsulated in an outer tissue shell with a regular specific microvascular area. A singular perturbation technique is employed to capture the transitional behavior at the interface between the inner core and outer shell under a cyclic microvascular pressure. The perturbation solution reveals the existence of two boundary layers: one at the interface between the inner core and outer shell, and the other at the tumor surface. The amplitude of the tumor interstitial fluid (TIF) pressure is at a lower constant level in the inner core and increases rapidly in the boundary layer at the interface between the inner core and outer shell to the pressure value of the corresponding homogeneous tumor with the outer shell properties. The radial strain undergoes dramatic changes in the boundary layers, and reaches the peak near the interface between the inner core and outer shell. The behavior of the effective stresses remains similar to that of the TIF pressure.

本文描述了一种小应变多孔弹性模型，用于检查非均质实体瘤中的间质液压力和基质变形，该非均质实体瘤由具有减少的比重微血管区域的内芯包裹在具有规则比重微血管区域的外部组织壳中组成。在循环微血管压力下，采用奇异摄动技术捕获内芯和外壳之间的界面处的过渡行为。摄动解揭示了两个边界层的存在：一个在内核和外壳之间的界面，另一个在肿瘤表面。肿瘤间质液（TIF）压力的幅度在内核中处于较低的恒定水平，并且在内核与外壳之间的界面处的边界层中迅速增加，达到相应的均质肿瘤与外壳之间的压力值外壳属性。径向应变在边界层中发生剧烈变化，并在内芯与外壳之间的界面附近达到峰值。有效应力的行为仍然与TIF压力的行为相似。