The integration of quantitative multi-modality imaging data into mathematical models of tumors

Quantitative imaging data obtained from multiple modalities may be integrated into mathematical models of tumor growth and treatment response to achieve additional insights of practical predictive value. We show how this approach can describe the development of tumors that appear realistic in terms of producing proliferating tumor rims and necrotic cores. Two established models (the logistic model with and without the effects of treatment) and one novel model built a priori from available imaging data have been studied. We modify the logistic model to predict the spatial expansion of a tumor driven by tumor cell migration after a voxel's carrying capacity has been reached. Depending on the efficacy of a simulated cytotoxic treatment, we show that the tumor may either continue to expand, or contract. The novel model includes hypoxia as a driver of tumor cell movement. The starting conditions for these models are based on imaging data related to the tumor cell number (as estimated from diffusion-weighted MRI), apoptosis (from 99mTc-Annexin-V SPECT), cell proliferation and hypoxia (from PET). We conclude that integrating multi-modality imaging data into mathematical models of tumor growth is a promising combination that can capture the salient features of tumor growth and treatment response and this indicates the direction for additional research.