Abstract

It is well-known that expanding glioblastomas typically induce significant deformations of the surrounding parenchyma (i.e., the so-called “mass effect”). In this study, we evaluate the performance of three mathematical models of tumor growth: 1) a reaction-diffusion-advection model which accounts for mass effect (RDAM), 2) a reaction-diffusion model with mass effect that is consistent only in the case of small deformations (RDM), and 3) a reaction-diffusion model that does not include the mass effect (RD). The models were calibrated with magnetic resonance imaging (MRI) data obtained during tumor development in a murine model of glioma (n = 9). We obtained <inline-formula><tex-math notation="LaTeX">$\boldsymbol{{\it T}_2}$</tex-math></inline-formula>-weighted and contrast-enhanced <inline-formula><tex-math notation="LaTeX">$\boldsymbol{{\it T}_1}$</tex-math></inline-formula>-weighted MRI at 6 time points over 10 days to determine the spatiotemporal variation in the mass effect and the volume fraction of tumor cells, respectively. We calibrated the three models using data 1) at the first four, 2) only at the first and fourth, and 3) only at the third and fourth time points. Each of these calibrations were run forward in time to predict the volume fraction of tumor cells at the conclusion of the experiment. The diffusion coefficient for the RDAM model (median of 10.65 × 10<inline-formula><tex-math notation="LaTeX">$\boldsymbol{^{-3}}$</tex-math></inline-formula> mm<inline-formula><tex-math notation="LaTeX">$\boldsymbol{^2\cdot }$</tex-math></inline-formula> d<inline-formula><tex-math notation="LaTeX">$\boldsymbol{^{-1}}$</tex-math></inline-formula>) is significantly less than those for the RD and RDM models (17.46 × 10<inline-formula><tex-math notation="LaTeX">$\boldsymbol{^{-3}}$</tex-math></inline-formula> mm<inline-formula><tex-math notation="LaTeX">$\boldsymbol{^2\cdot }$</tex-math></inline-formula> d<inline-formula><tex-math notation="LaTeX">$\boldsymbol{^{-1}}$</tex-math></inline-formula> and 19.38 × 10<inline-formula><tex-math notation="LaTeX">$\boldsymbol{^{-3}}$</tex-math></inline-formula> mm<inline-formula><tex-math notation="LaTeX">$\boldsymbol{^2\cdot }$</tex-math></inline-formula> d<inline-formula><tex-math notation="LaTeX">$\boldsymbol{^{-1}}$</tex-math></inline-formula>, respectively). The error in the tumor volume fraction for the RD, RDM, and RDAM models have medians of 40.2%, 32.1%, and 44.7%, respectively, for the calibration using data from the first four time points. The RDM model most accurately predicts tumor growth, while the RDAM model presents the least variation in its estimates of the diffusion coefficient and proliferation rate. This study demonstrates that the mathematical models capture both tumor development and mass effect observed in experiments.