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Is there any similarity between tumour growth and thermal expansion?

To model growth in a soft tissue, the tissue is considered as an open system wherein mass is not conserved. This leads to modifying the basic balance equations to accommodate this mass change. On the other hand, a number of researchers have assumed that there exists an analogy between tumour growth and thermal expansion phenomena. However, no mathematical proof yet has supported this analogy. In this paper, based on a new explanation of growth, the set of modified basic balance equations is closed using a new constitutive equation in conjunction with the Clausius–Duhem inequality to model the residual stresses in a growing solid tumour. Applying the model to two popular tumour types (carcinoma and tumour spheroid), which can be examined experimentally, revealed a perfect similarity between the resulting stresses in the growing tumour and those predicted by thermal expansion analogy, although the predicted displacements are different in these two models. Moreover, it is shown that the coefficient of growth expansion, analogous to the coefficient of thermal expansion, is not an independent variable and is related to the tissue measurable known quantities: Poisson’s ratio and density.