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 τ in a system of permeable membranes characterized by three parameters (membrane permeability P, membrane distance L, and free diffusivity D0), an equivalent dimensionless model was derived with a probability distribution characterized by only a single (dimensionless) tissue parameter . Evaluating this proposed model function, the dimensionless diffusion coefficient was numerically calculated for 60 values of the dimensionless diffusion time and 35 values of . 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 to determine L, P, and D0. The measured diffusivities followed the simulated dependence of . Determined cell sizes varied from 21 to 76 μm, permeabilities from 0.007 to 0.039 μm−1, and the free diffusivities from 1354 to 1713 μm2 s−1. In conclusion, the proposed dimensionless tissue model can be used to determine tissue parameters (D0, 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.