Predictive Mathematical Modeling in Metastasis
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Mathematical modeling is emerging as a powerful predictive tool in many areas of biology and medicine, with applications to cancer metastasis increasingly widespread and effective. This type of modeling involves quantitatively accurate representations of specific cellular activities, and is quite different from more traditional applications of mathematics to cancer, such as the simple fitting of experimental data to Gompertzian growth curves. It is made possible by the twin revolutions in molecular biology and nonlinear mathematics over the last two decades, and involves using experimental data at the cell and molecular level to construct mathematical models, which can then be used to predict the macroscopic implications of this data.
Mathematical models have been in use for biological prediction since the early part of the century, initially in ecology and embryology. These early models were phenomenological, that is, they acted as a convenient way to express and explore theories, but did not represent particular postulated mechanisms. Establishment of mathematical biology as a recognized scientific field was achieved by a number of major successes for these early models. Most notable amongst these is the work of Hodgkin and Huxley on electrical signaling in nerve axons, which underlies much of neurophysiology, and for which they were awarded the Nobel Prize for Physiology and Medicine in 1963. More recently, the ability to isolate biological mechanisms at the molecular level has led to a new type of mathematical model, which represents specific low-level mechanisms, either known or hypothesised.
