Diffusion

Theoretically the mean squared diffusion distance is proportional to the diffusion time and the proportional constant is called the diffusion coefficient (D). The diffusion coefficient is dependent on the temperature, and for pure water at 37" C, D=3.4 m2/s (43). The above mentioned relation, the Einstein relation, is based on a truly random passage of the water molecule. In normal brain tissue the diffusion coefficient is less than the diffusion coefficient in pure water. At least four possible mechanisms may be responsible for this reduction (1 12). Firstly, the water molecules may encounter barriers (e.g. myelin membranes) during the time interval of the pulse sequence, thereby restricting their diffusion. These barriers may be either permeable or inpermeable. Secondly, the passage of the molecule may be obstructed by macromolecules and subcellular organelles. Thirdly, a portion of the water may be 'bound' to macromolecular surfaces and therefore not freely diffusive. Fourthly, the presence and nature of the numerous subcellular surfaces may affect the physical properties of a substantial portion of the water i.e. the viscosity may be increased. The relative significance of these factors is not known at present, and usually it is not known whether the diffusion path is truly random. Therefore we only speak of the apparent diffusion coefficient. It is, however, well known that the values of the relaxation times as well as the diffusion coefficient of intracellular water protons are reduced compared with corresponding values for pure bulk water which has a low content of macromolecules (1 13). Furthermore, if restriction takes place, the Einstein relation shows that if the diffusion time is increased, the diffusion constant will decrease once the root-mean-square diffusional displacement reaches the characteristic value of the restrictive structure. The diffusion coefficient of tissue is an averaged measurement of the tissue water in various compartments. However, unlike the relaxation times, D is heavily weighted by the free portion of the water in a given tissue (112). Thus the measured apparent diffusion coefficient may be depend-