Does Cancer Growth Depend on Surface Extension?

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 figur

A Growth Model for Multicellular Tumor Spheroids

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

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 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 figure

A New Computational Tool for the Phenomenological Analysis of Multipassage Tumor Growth Curves

Multipassage experiments are performed by subcutaneous implantation in lab animals (usually mice) of a small number of cells from selected human lines. Tumor cells are then passaged from one mouse to another by harvesting them from a growing tumor and implanting them into other healthy animals. This procedure may be extremely useful to investigate the various mechanisms involved in the long term evolution of tumoral growth. It has been observed by several researchers that, contrary to what happens in in vitro experiments, there is a significant growth acceleration at each new passage. This result is explained by a new method of analysis, based on the Phenomenological Universalities approach. It is found that, by means of a simple rescaling of time, it is possible to collapse all the growth curves, corresponding to the successive passages, into a single curve, belonging to the Universality Class U2. Possible applications are proposed and the need of further experimental evidence is discussed

A novel approach to the analysis of human growth

OBJECTIVES: Several formulations have been proposed in order to model human growth from birth to maturity. They are usually based on “ad hoc” heuristic assumptions. In the present contribution we adopt, as an alternative, a completely general (interdisciplinary) approach, based on the formalism of the Phenomenological Universalities (PUN). METHODS: The main PUN class investigated to date, i.e. UN, can only account for the overall growth pattern. For a realistic description it is necessary to add to it one or more “spurts”, as expected on biological grounds, due to the stimulation of growth and sex hormones. RESULTS: A new PUN class (UN + FM) is generated and shown to be able to provide excellent agreement with standard auxological datasets. The accuracy of the fitting and reliability of the model suggest applications both at the diagnostic and therapeutic level. CONCLUSIONS: The developed formalism can be suitably related to the biological description of bone plate growth under selective hormonal stimulation on the bone epiphysis; i.e., the additional increase of stature is the “macroscopic” response to a well defined biological signal

Physical Aspects of Cancer Invasion

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 figure