The growth and treatment of tumors is an important problem to society that involves the manifestation of cellular phenomena at length scales on the order of centimeters. Continuum mechanical approaches are being increasingly used to model tumors at the largest length scales of concern. The issue of how to best connect such descriptions to smaller-scale descriptions remains open. We formulate a framework to derive macroscale models of tumor behavior using the thermodynamically constrained averaging theory (TCAT), which provides a firm connection with the microscale and constraints on permissible forms of closure relations. We build on developments in the porous medium mechanics literature to formulate fundamental entropy inequality expressions for a general class of three-phase, compositional models at the macroscale. We use the general framework derived to formulate two classes of models, a two-phase model and a three-phase model. The general TCAT framework derived forms the basis for a wide range of potential models of varying sophistication, which can be derived, approximated, and applied to understand not only tumor growth but also the effectiveness of various treatment modalities.

肿瘤的生长和治疗是社会的一个重要问题，它涉及以厘米数量级的长度尺度表现出细胞现象。连续机械方法越来越多地用于在最大关注尺度上对肿瘤进行建模。如何最好地将这些描述与较小规模的描述联系起来的问题仍然悬而未决。我们使用热力学约束平均理论 (TCAT) 制定了一个框架来推导肿瘤行为的宏观模型，该理论提供了与微观尺度的牢固联系以及对允许的闭合关系形式的约束。我们以多孔介质力学文献的发展为基础，为宏观尺度的一般三相成分模型制定基本熵不等式表达式。我们使用导出的通用框架来制定两类模型，两相模型和三相模型。衍生的通用 TCAT 框架构成了各种复杂程度的潜在模型的基础，这些模型可以被推导、近似和应用，不仅可以理解肿瘤生长，还可以理解各种治疗方式的有效性。