Bayesian combination of mechanistic modeling and machine learning (BaM3): improving clinical tumor growth predictions

Biomedical problems are highly complex and multidimensional. Commonly, only a small subset of the relevant variables can be modeled by virtue of mathematical modeling due to lack of knowledge of the involved phenomena. Although, these models are effective in analyzing the approximate dynamics of the system, their predictive accuracy is generally limited. On the other hand, statistical learning methods are well-suited for quantitative reproduction of data, but they do not provide mechanistic understanding of the investigated problem. Herein, we propose a novel method, based on the Bayesian coupling of mathematical modeling and machine learning (BaM3). We evaluate the proposed BaM3 method on a synthetic dataset for brain tumor growth as a proof of concept and analyze its performance in predicting two major clinical outputs, namely tumor burden and infiltration. Combining these two approaches result in improved predictions in almost all simulated patients, especially for those with a late clinical presentation. We finally discuss some limitations of the proposed BaM3 method and suggest future research directions.