Water diffusion in a tissue model is studied both analytically and num
erically. Tissue is regarded as a periodic array of boxes surrounded b
y partially permeable membranes (cells), embedded in an extracellular
medium, intracellular and extracellular diffusion coefficients may dif
fer. Expressions for the apparent diffusion coefficients (ADC) in isot
ropic and nonisotropic tissues are derived and compared with Monte Car
te simulations. Calculated ADCs disagree with values obtained from the
widely used ''fast exchange'' formula. Effects of differences between
intracellular and extracellular T-2 relaxation times on measured valu
es of ADC and T-2 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 significa
ntly, the observed changes in diffusion cannot be due to reduced membr
ane permeabilities. They may result from the combined effect of change
s in cellular volume fraction, extracellular and intracellular diffusi
on.