An improved model for prostate diffusion incorporating the results of Monte Carlo simulations of diffusion in the cellular compartment.

ABSTRACT

The purpose of this work was to refine a previously published model of prostate diffusion by incorporating improved estimates of cellular diffusivity obtained by Monte Carlo simulation. Stromal and epithelial cell size and intracellular volume fraction in different grades of cancer were determined from histological images. Diffusion in different mixtures of cells, corresponding to different tumor grades, was simulated and cellular apparent diffusion coefficient and kurtosis values determined. These values were incorporated into the previously published model of prostate diffusion and model predictions compared with values found in the literature. Stromal cell radius and intracellular volume fraction were 3.74 ± 0.96 µm and 13 ± 3% respectively in normal peripheral zone (PZ), and were similar in all grades of cancer. Epithelial cell radius and intracellular volume fraction were 3.40 ± 0.15 µm and 45 ± 5% respectively in normal PZ, rising to 4.75 ± 0.20 µm and 70 ± 8% in high grade cancer. Cellular apparent diffusion coefficient and kurtosis were 1.02 µm2 ms-1 and 0.58 respectively in normal PZ, and 0.61 µm2 ms-1 and 1.15 in high grade cancer (variation in simulation values are less than 0.1%). Agreement between model predictions and measurements were good, with a mean square error of 0.22 µm2 ms-1 . Incorporation of cellular diffusion coefficient and kurtosis values obtained by Monte Carlo simulation into a model of prostate diffusion gives good agreement with published results.