Investigating the Limits of Predictability of Magnetic Resonance Imaging-Based Mathematical Models of Tumor Growth

We provide a framework for determining how far into the future the spatiotemporal dynamics of tumor growth can be accurately predicted using routinely available magnetic resonance imaging (MRI) data. Our analysis is applied to a coupled set of reaction-diffusion equations describing the spatiotemporal development of tumor cellularity and vascularity, initialized and constrained with diffusion-weighted (DW) and dynamic contrast-enhanced (DCE) MRI data, respectively.

Motivated by experimentally acquired murine glioma data, the rat brain serves as the computational domain within which we seed an in silico tumor. We generate a set of 13 virtual tumors defined by different combinations of model parameters. The first parameter combination was selected as it generated a tumor with a necrotic core during our simulated ten-day experiment. We then tested 12 additional parameter combinations to study a range of high and low tumor cell proliferation and diffusion values. Each tumor is grown for ten days via our model system to establish "ground truth" spatiotemporal tumor dynamics with an infinite signal-to-noise ratio (SNR). We then systematically reduce the quality of the imaging data by decreasing the SNR, downsampling the spatial resolution (SR), and decreasing the sampling frequency, our proxy for reduced temporal resolution (TR). With each decrement in image quality, we assess the accuracy of the calibration and subsequent prediction by comparing it to the corresponding ground truth data using the concordance correlation coefficient (CCC) for both tumor and vasculature volume fractions, as well as the Dice similarity coefficient for tumor volume fraction.

All tumor CCC and Dice scores for each of the 13 virtual tumors are >0.9 regardless of the SNR/SR/TR combination. Vasculature CCC scores with any SR/TR combination are >0.9 provided the SNR ≥ 80 for all virtual tumors; for the special case of high-proliferating tumors (i.e., proliferation > 0.0263 day^-1), any SR/TR combination yields CCC and Dice scores > 0.9 provided the SNR ≥ 40.

Our systematic evaluation demonstrates that reaction-diffusion models can maintain acceptable longitudinal prediction accuracy-especially for tumor predictions-despite limitations in the quality and quantity of experimental data.