Theoretical model for water diffusion in tissues

Water diffusion in a tissue model is studied both analytically and numerically. Tissue is regarded as a periodic array of boxes surrounded by partially permeable membranes (cells), embedded in an extracellular medium. intracellular and extracellular diffusion coefficients may differ. Expressions for the apparent diffusion coefficients (ADC) in isotropic and nonisotropic tissues are derived and compared with Monte Carlo simulations. Calculated ADCs disagree with values obtained from the widely used "fast exchange" formula. Effects of differences between intracellular and extracellular T2 relaxation times on measured values of ADC and T2 are discussed. The general analysis is specifically applied to the changes occurring in ADC following ischemic insults to brain tissue. It is found that although membranes affect ADC significantly, the observed changes in diffusion cannot be due to reduced membrane permeabilities. They may result from the combined effect of changes in cellular volume fraction, extracellular and intracellular diffusion.

An analytical model of restricted diffusion in bovine optic nerve

An analytical model of restricted diffusion in bovine optic nerve is presented. The nerve tissue model is composed of two different objects: prolate ellipsoids (axons) and spheres (glial cells) surrounded by partially permeable membranes. The free diffusion coefficients of intracellular and extracellular water may differ. Analytical formulas for signal loss due to diffusion in the pulsed gradient spin echo (PGSE) experiment for this tissue model are derived. The model is fitted to experimental data for bovine optic nerve. The obtained model parameters are shown to be reasonable. The model describes all of the characteristics of the PGSE data: anisotropy, upward curvature of decay curves, and diffusion time dependence. The validity and sensitivity of the model are also discussed.

Diffusion-weighted imaging in tissues: theoretical models

Typical diffusion measurements use Stejskal-Tanner pulsed gradient spin echo sequences to provide information about the average diffusion and displacement profiles of particles in a sample. To derive structural information, a measured displacement profile has to be related by means of a model to the physical and geometrical properties of the tissue, such as diffusion coefficients and shapes of semi-permeable membranes of compartments in the system. The behavior of the NMR signal and the measured ADC are greatly affected by the cellular architecture of a tissue, mainly because cellular membranes are relatively impermeable to water. For long diffusion times, and small signal attenuations, ADC is relatively insensitive to how it is measured. In general, however, ADC values are not readily interpreted unless the measuring conditions are specified in detail. For given measuring conditions, ADC depends on intra- and extracellular diffusion coefficients, membrane permeabilities, cell sizes and the cellular volume fraction. If intra- and extracellular T2 relaxation rates are different enough, ADC may also depend on the relaxation properties of the system and the echo time. An improved understanding of the precise influence of these factors has been obtained by detailed consideration of theoretical and computer models that can be related to experimental data in simple systems. Further refinements of such models should advance our understanding of water diffusion in tissues.

Effects of osmotically driven cell volume changes on diffusion-weighted imaging of the rat optic nerve

The apparent diffusion coefficient (ADC) of the rat optic nerve was measured in vitro, using magnetic resonance imaging, to determine the effects of changes in cellular volume fraction on the diffusion of tissue water. Nerve ADC was determined under conditions of cell membrane depolarization and (i) increased intracellular volume, (ii) decreased intracellular volume, and (iii) negligible volume change. Depolarization alone had little affect on ADC, whereas volume changes produced strong, reversible effects. Increased cell volume decreased ADC and vice versa. These results are consistent with the view that changes in the extracellular space are the major source of ADC changes in brain tissue.