We consider a continuum mechanical model for the migration of multiple cell populations through parts of tissue separated by thin membranes. In this model, cells belonging to different populations may be characterised by different proliferative abilities and mobility, which may vary from part to part of the tissue, as well as by different invasion potentials within the membranes. The original transmission problem, consisting of a set of mass balance equations for the volume fraction of cells of every population complemented with continuity of stresses and mass flux across the surfaces of the membranes, is then reduced to a limiting transmission problem whereby each thin membrane is replaced by an effective interface. In order to close the limiting problem, a set of biophysically-consistent transmission conditions is derived through a formal asymptotic method. Models based on such a limiting transmission problem may find fruitful application in a variety of research areas in the biological and medical sciences, including developmental biology, immunology and cancer growth and invasion.

我们考虑了多个细胞群通过由薄膜分隔的组织部分迁移的连续机械模型。在这个模型中，属于不同群体的细胞可能具有不同的增殖能力和流动性，这可能因组织的一部分而异，以及膜内的不同侵袭潜力。最初的传输问题由一组每个群体的细胞体积分数的质量平衡方程组成，并辅以膜表面的应力和质量通量的连续性，然后被简化为限制传输问题，其中每个薄膜是取而代之的是一个有效的界面。为了封闭极限问题，一组生物物理一致的传输条件是通过形式渐近方法推导出来的。基于这种限制性传输问题的模型可能会在生物和医学科学的各种研究领域得到卓有成效的应用，包括发育生物学、免疫学以及癌症的生长和侵袭。