Pier Paolo Delsanto

Does tumor growth follow a “universal law”?

A general model for the ontogenetic growth of living organisms has been recently proposed. Here we investigate the extension of this model to the growth of solid malignant tumors. A variety of in vitro and in vivo data are analysed and compared with the prediction of a universal law, relating properly rescaled tumor masses and tumor growth times. The results support the notion that tumor growth follows such a universal law. Several important implications of this finding are discussed, including its relevance for tumor metastasis and recurrence, cell turnover rates, angiogenesis and invasion.

Physical aspects of cancer invasion.

Invasiveness, one of the hallmarks of tumor progression, represents the tumors ability to expand into the host tissue by means of several complex biochemical and biomechanical processes. Since certain aspects of the problem present a striking resemblance with well-known physical mechanisms, such as the mechanical insertion of a solid inclusion in an elastic material specimen (G Eaves 1973 The invasive growth of malignant tumours as a purely mechanical process J. Pathol. 109 233; C Guiot, N Pugno and P P Delsanto 2006 Elastomechanical model of tumor invasion Appl. Phys. Lett. 89 233901) or a water drop impinging on a surface (C Guiot, P P Delsanto and T S Deisboeck 2007 Morphological instability and cancer invasion: a splashing water drop analogy Theor. Biol. Med. Model 4 4), we propose here an analogy between these physical processes and a cancer systems invasive branching into the surrounding tissue. Accounting for its solid and viscous properties, we then arrive, as a unifying model, to an analogy with a granular solid. While our model has been explicitly formulated for multicellular tumor spheroids in vitro, it should also contribute to a better understanding of tumor invasion in vivo.