Incorporation of diffusion-weighted magnetic resonance imaging data into a simple mathematical model of tumor growth

We build on previous work to show how serial diffusion-weighted MRI (DW-MRI) data can be used to estimate proliferation rates in a rat model of brain cancer. Thirteen rats were inoculated intracranially with 9L tumor cells; eight rats were treated with the chemotherapeutic drug 1,3-bis(2-chloroethyl)-1-nitrosourea and five rats were untreated controls. All animals underwent DW-MRI immediately before, one day and three days after treatment. Values of the apparent diffusion coefficient (ADC) were calculated from the DW-MRI data and then used to estimate the number of cells in each voxel and also for whole tumor regions of interest. The data from the first two imaging time points were then used to estimate the proliferation rate of each tumor. The proliferation rates were used to predict the number of tumor cells at day three, and this was correlated with the corresponding experimental data. The voxel-by-voxel analysis yielded Pearson's correlation coefficients ranging from -0.06 to 0.65, whereas the region of interest analysis provided Pearson's and concordance correlation coefficients of 0.88 and 0.80, respectively. Additionally, the ratio of positive to negative proliferation values was used to separate the treated and control animals (p < 0.05) at an earlier point than the mean ADC values. These results further illustrate how quantitative measurements of tumor state obtained non-invasively by imaging can be incorporated into mathematical models that predict tumor growth.