Morphological instability and cancer invasion: a 'splashing water drop' analogy

We present an analogy between two unrelated instabilities. One is caused by the impact of a drop of water on a solid surface while the other concerns a tumor that develops invasive cellular branches into the surrounding host tissue. In spite of the apparent abstractness of the idea, it yields a very practical result, i.e. an index that predicts tumor invasion based on a few measurable parameters. We discuss its application in the context of experimental data and suggest potential clinical implications.Tissue invasion is one of the hallmarks of cancer [1]. From the primary tumor mass, cells are able to move out and infiltrate adjacent tissues by means of degrading enzymes (e.g., [2]). Depending on the cancer type, these cells may form distant settlements, i.e. metastases (e.g., [3]). Tumor expansion therefore results from the complex interplay between the developmental ability of the tumor itself and the characteristics of the host tissue in which its growth occurs (e.g., [4]).It has been recently proposed [5] that cancer invasion can be described as a morphological instability that occurs during solid tumor growth and results in invasive 'fingering', i.e. branching patterns (see Figure 1). This instability may be driven by any physical or chemical condition (oxygen, glucose, acid and drug concentration gradients), provided that the average cohesion among tumor cells decreases and/or their adhesion to the stroma increases (for a recent review on related molecular aspects, such as the cadherin-'switch', see [6]). In fact, the aforementioned model of Cristini et al. [5] shows that reductions in the surface tension at the tumor-tissue interface may generate and control tumor branching in the nearby tissues. A previous investigation from the same group [7] had analyzed different tumor growth regimes and shown that invasive fingering in vivo could be driven by vascular and elastic anisotropies in highly vascularized tumors. A recent advance [8] shows that the competition