A Study on the Validity of the Tortuosity Approximation for Extracellular Diffusion Using Monte Carlo Simulations

Hubert Martinus Fonteijn¹, Matt G. Hall¹, Daniel C. Alexander¹

Models of extracellular diffusion in biological tissue rely on two assumptions: 1. diffusion is approximately Gaussian for long diffusion times and 2. The relationship between the apparent diffusion coefficient in hindered directions and the free diffusion coefficient is only dependent on the intracellular volume fraction and not on the specific tissue geometry. We have tested these assumptions using Monte Carlo simulations for the diffusion weighted signal using cylinders with gamma-distributed radii. We have found a mono-exponentially decaying signal for only a limited range of b-values. Moreover, the ADC is to some extent related to the distribution of cylinder radii.