SIAM News Blog

Predicting Post-Surgery Cancer Metastasis with Mathematical Modeling

By Lina Sorg

Consistent advancements in the detection and removal of cancerous tumors continue to influence decisions regarding cancer treatment and the possibility of metastatic return after surgery. Although tumor cells may metastasize unpredictably, making the rate of spread challenging to gauge, a common assumption presumes that the size of a surgically removed tumor directly correlates with the chance of cancer spreading within the body post-removal. As a result, surgical removal of localized tumors is considered one of the best ways to limit the likelihood of subsequent disease spread.

However, a recent study conducted by scientists at Roswell Park Cancer Institute and Inria, the French National Institute for Research in Computer Science and Automation, indicates that mathematical models may be able to more accurately predict the risk of post-surgery metastasis.

In a paper entitled “Modeling spontaneous metastasis following surgery: an in vivo-in silico approach,” the authors created laboratory mouse models with implanted tumors meant to mimic the progression of cancer in humans. The in vivo tumor data represented all stages of cancer progression. Using a population approach to statistically estimate the key parameters (metastatic spread and primary tumor size), the authors then generated a mathematical model based on growth and dissemination, the laws of the disease. They converted the subsequent outputs to longitudinal readings of initial tumor size, metastatic burden, and chance of survival. Bioluminescence allowed for the observation of cancer cells that are otherwise indistinguishable and the tracking of primary tumor and metastatic growth.

Upon surgically removing implanted tumors from the mice, the authors conducted subsequent analysis of presurgical growth and postsurgical spread while accounting for individual variability. Although the modeling did confirm a correlation between presurigcal tumor size and postsurgical cancer spread, that correlation was highly nonlinear. For tumors that were either unusually large or unusually small, size did not seem to be an accurate predictor of survival or recurrence. This nonlinearity identifies the possible existence of threshold limits for tumor size’s predictability of metastasis. A retrospective analysis of breast cancer patient data confirmed the results.

The study represents the first combined usage of preclinical animal models and data-based mathematical models for post-surgery disease growth. The resulting findings will likely influence the ideal timing of both presurgical and postsurgical cancer treatment, help predict the risk of metastasis from a cancerous tumor, and could even extend the length of cancer remissions.

Read more about the study, and about Roswell Park and Inria, here.

Lina Sorg is the associate editor of SIAM News
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