A monte carlo study of restricted diffusion: Implications for diffusion MRI of prostate cancer

Purpose: Diffusion MRI is frequently used to assess prostate cancer. The prostate consists of cellular tissue surrounding fluid filled ducts. Here, the diffusion properties of the ductal fluid alone were studied. Monte Carlo simulations were used to investigate ductal residence times to determine whether ducts can be regarded as forming a separate compartment and whether ductal radius could determine the ADC of the ductal fluid. Methods: Random walks were simulated in cavities. Average residence times were estimated for permeable cavities. Signal reductions resulting from application of a Stejskal-Tanner pulse sequence were calculated in impermeable cavities. Simulations were repeated for cavities of different radii and different diffusion times. Results: Residence times are at least comparable with diffusion times even in relatively high grade tumours. ADCs asymptotically approach theoretical limiting values. At large radii and short diffusion times, ADCs are similar to free diffusion. At small radii and long diffusion times, ADCs are reduced towards zero, and kurtosis approaches a value of -1.2. Conclusions: Restricted diffusion in cavities of similar sizes to prostate ducts may reduce ductal ADCs. This may contribute to reductions in total ADC seen in prostate cancer