Imaging Cell Size And Permeability In Biological Tissue Using The Diffusion-Time Dependence Of The Apparent Diffusion Coefficient

The purpose of this study was to analyze and evaluate a model of restricted water diffusion between equidistant permeable membranes for cell-size and permeability measurements in biological tissue. Based on the known probability distribution of diffusion distances after the diffusion time tau in a system of permeable membranes characterized by three parameters (membrane permeability P, membrane distance L, and free diffusivity D-0), an equivalent dimensionless model was derived with a probability distribution characterized by only a single (dimensionless) tissue parameter (P) over tilde. Evaluating this proposed model function, the dimensionless diffusion coefficient (D) over tilde (eff)((tau) over tilde; (P) over tilde was numerically calculated for 60 values of the dimensionless diffusion time (tau) over tilde and 35 values of (P) over tilde. Diffusion coefficients were measured in a carrot by diffusion-weighted magnetic resonance imaging (MRI) at 18 diffusion times between 9.9 and 1022.7 ms and fitted to the simulation results (D) over tilde (eff)((tau) over tilde; (P) over tilde) to determine L, P, and D-0. The measured diffusivities followed the simulated dependence of (D) over tilde (eff)((tau) over tilde; (P) over tilde). Determined cell sizes varied from 21 to 76 mu m, permeabilities from 0.007 to 0.039 mu m(-1), and the free diffusivities from 1354 to 1713 mu m(2) s(-1). In conclusion, the proposed dimensionless tissue model can be used to determine tissue parameters (D-0, L, P) based on diffusion MRI with multiple diffusion times. Measurements in a carrot showed a good agreement of the cell diameter, L, determined by diffusion MRI and by light microscopy.