Mathematical Discovery of Natural Laws in Biomedical Sciences with Application to Metastasis

Document Type

Presentation Abstract

Presentation Date

9-27-2021

Abstract

Mathematical modeling of systemic biomedical processes faces two principal challenges: (1) enormous complexity of these processes and (2) variability and heterogeneity of individual characteristics of biological systems and organisms. As a result, in the grand scheme of things, mathematical models have played so far an auxiliary role in biomedical sciences. I propose a new methodology of mathematical modeling that would allow mathematics to give, in certain cases, definitive answers to important biomedical questions that elude empirical resolution. The new methodology is based on two ideas: (1) to employ mathematical models that are so general and flexible that they can account for many possible mechanisms, both known and unknown, of biomedical processes of interest; (2) to find those model parameters whose optimal values are independent of observations. These universal parameter values may reveal general regularities in biomedical processes (that can be called natural laws). Existence of such universal parameters presupposes that the model does not meet the conditions required for the consistency of the maximum likelihood estimator.

I illustrate this approach with the discovery of a natural law governing cancer metastasis. Specifically, I will show that under minimal mathematical and biological assumptions the likelihood-maximizing scenario of metastatic cancer progression is always the same: complete suppression of metastatic growth before primary tumor resection followed by an abrupt growth acceleration after surgery. This scenario is widely observed in clinical practice, represents a common knowledge among veterinarians, and is supported by a wealth of experimental studies on animals and clinical observations accumulated over the last 115 years. Furthermore, several biological mechanisms, both hypothetical and experimentally verified, have been proposed that could explain this natural law. The above scenario does not preclude other possibilities that are also observed in clinical practice. In particular, metastases may surface before surgery or may remain dormant thereafter.

Additional Details

September 27, 2021 at 3:00 p.m. in Math 305

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