Quantitation of non-Einstein diffusion behavior of water in biological tissues by proton MR diffusion imaging: synthetic image calculations.

The non-Einstein diffusion behavior of water in a model biological tissue system, intact duck embryos, has been investigated by the use of an in vivo proton pulsed-gradient spin-echo (PGSE) MR imaging technique. Multiple-frame MR images of the intact duck embryos and control solution (0.5 mM CuSO4 doped water) were acquired systematically at different diffusion times and strengths of the diffusion-sensitizing magnetic field gradients of the PGSE sequence. These raw images were then used to generate various dynamic (self-diffusion coefficient) and structural (fractal, residual attenuation, and compartment fraction) diffusion parameter maps of water in the imaging objects on the basis of different Einstein and higher order (non-Brownian, Residual, and 2-compartment) diffusion models. The self-diffusion coefficients of the body tissues of the embryos obtained from all diffusion models were significantly lower than those of the surrounding embryonic fluid. The structural diffusion parameter maps obtained from the higher order diffusion models revealed that water molecules exhibited either non-Brownian, restricted, or compartmentalized diffusion behavior in the embryonic tissues, but Einstein or Brownian diffusion behavior in the embryonic fluid and control solution. The diffusion parameter maps, both dynamic and structural, were found to provide much better contrasts than the conventional relaxation time (T1, T2, and biexponential T2) maps in separating the tissues from the surrounding embryonic fluid in the duck embryos. The mathematical models and procedures for generating the dynamic and structural diffusion parameter maps are also presented in this paper.