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Invasiveness, one of the hallmarks of tumor progression, represents the tumor's 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 [1, 2] or a water drop impinging on a surface [3], we propose here an analogy between these physical processes and a cancer system's invasive branching into the surrounding tissue. Accounting for its solid and viscous properties, we present a unifying concept that the tumor behaves as 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., Comment: 20 pages, 2 figures

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 one 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., Comment: 14 pages, 3 figures

We argue that volumetric growth dynamics of a solid cancer depend on the tumor system's overall surface extension. While this at first may seem evident, to our knowledge, so far no theoretical argument has been presented explaining this relationship explicitly. In here, we therefore develop a conceptual framework based on the universal scaling law and then support our conjecture through evaluation with experimental data., Comment: 11 pages, 1 figure

We have previously reported that a universal growth law, as proposed by West and collaborators for all living organisms, appears to be able to describe also the growth of tumors in vivo. In contrast to the assumption of a fixed power exponent p (assumed by West et al. to be equal to 3/4), we show in this paper the dynamic evolution of p from 2/3 to 1, using experimental data from the cancer literature and in analogy with results obtained by applying scaling laws to the study of fragmentation of solids. The dynamic behaviour of p is related to the evolution of the fractal topology of neoplastic vascular systems and might be applied for diagnostic purposes to mark the emergence of a functionally sufficient (or effective) neo-angiogenetic structure.

We have previously reported that a 'universal' growth law with fixed scaling exponent p, as proposed by West and collaborators for all living organisms, appears to be able to describe also the growth of tumors in vivo. Here, we investigate in more detail the dynamic behaviour of p using data from the literature. We show that p initially decreases before it again increases up to or even beyond 3/4. These results support the notion that p can vary over time and yet its dynamics are independent from the cancer type., Comment: 8 pages, 1 figure

Using our previously developed model we demonstrate here, that (1) solid tumor growth and cell invasion are linked, not only qualitatively but also quantitatively, that (2) the onset of invasion marks the time point when the tumor cell density exceeds a compaction maximum, and that (3) tumor cell invasion, reduction of mechanical confinement and angiogenesis can act synergistically to increase the actual tumor mass towards the level predicted by West et al. universal growth curve.

Most organisms grow according to simple laws, which in principle can be derived from energy conservation and scaling arguments, critically dependent on the relation between the metabolic rate B of energy flow and the organism mass m. Although this relation is generally recognized to be of the form B(m) = mp, the specific value of the exponent p is the object of an ongoing debate, with many mechanisms being postulated to support different predictions. We propose that multicellular tumor spheroids provide an ideal experimental model system for testing these allometric growth theories, especially under controlled conditions of malnourishment and applied mechanical stress.

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 analyzed 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.