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Mathematical Modelling for Cancer Metastasis

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The size of a surgically removed tumor is generally thought to relate to the risk of the cancer spreading to other regions of the body. But because tumor cells may metastasize at different times and the rate of spread is difficult to assess, the relationship between tumor size and the relative risk of recurrence after surgery is challenging to calculate. Writing in the journal Cancer Research, scientists at Roswell Park Cancer Institute (RPCI) and Inria, the French National Institute for computer science and applied mathematics in Bordeaux, France, demonstrate that mathematical models can provide useful clues about the impact of surgery on metastasis and may help to predict the risk of cancer spread.

The scientists generated a mathematical model using the key parameters of primary tumor size and metastatic spread based on data generated from laboratory models designed to mimic cancer’s progression in humans. They used tumor cells engineered to express a luminescent marker, allowing for the tracking and quantification of these otherwise-undetectable cancer cells.

The mathematical modeling confirmed a strong dependence between presurgical primary tumor size and postsurgical metastatic growth and survival. However, some surprising developments were noted.

“We found that this relationship was not simply dependent on size,” says the study’s corresponding author,Sebastien Benzekry, PhD, a Research Scientist on the Modeling in ONCology (MONC) team at the Inria Bordeaux Research Center, which is affiliated with the Institute of Mathematics of Bordeaux (University of Bordeaux). “The models indicate that in the case of tumors that are either very large or very small, tumor size does not significantly impact on survival, and therefore loses its predictive value. This, in turn, could impact how treatment decisions, such as the optimal time to start and stop therapy, are made.”

Recent advances allowed the research team to, for the first time, integrate data-based mathematical models for predicting post-surgery disease growth patterns into preclinical animal models.

“These findings represent a novel use of clinically relevant models to assess the impact of surgery on metastatic potential, and may guide the optimal timing of treatments in both the presurgical and postsurgical settings to maximize patient benefit,” notes the study’s senior author, John Ebos, PhD, Assistant Professor of Oncology in the departments of Cancer Genetics and Medicine at Roswell Park Cancer Institute, Buffalo, N.Y.

Importantly, the results from these laboratory studies were confirmed using a retrospective analysis of clinical datasets involving breast cancer patients.