NMR study of water exchange across the hepatocyte membrane

An understanding of the cellular permeability for water is needed to evaluate MR images of complex tissues, such as liver, and to interpret the effects of contrast agents. To obtain data essential for such an understanding we measured water exchange across the isolated rodent hepatocyte membrane by proton NMR relaxation with dextranmagnetite as a relaxation agent. The results are treated as water exchange in a two-compartment system, and possible reasons for deviations from that behavior are analyzed. The mean residence time of intracellular water was approximately 40 ms at 37 degrees C. We found the lower limit for the diffusional permeability of the hepatocyte membrane to be 8 x 10(-3) cm s-1. These results, combined with consideration of hepatic anatomy indicate that the failure to observe effects on the T1 of liver from particulate contrast agents such as magnetite, Gd-starch, and liposome encapsulated Mn2+ is due to the localization of these agents in the Kupffer cells. Also, the nonexponential T1 decay observed in normal liver is unlikely to be due to slow exchange of water between compartments.     

Anomalous diffusion expressed through fractional order differential operators in the Bloch-Torrey equation

Diffusion weighted MRI is used clinically to detect and characterize neurodegenerative, malignant and ischemic diseases. The correlation between developing pathology and localized diffusion relies on diffusion-weighted pulse sequences to probe biophysical models of molecular diffusion-typically exp[-(bD)]-where D is the apparent diffusion coefficient (mm(2)/s) and b depends on the specific gradient pulse sequence parameters. Several recent studies have investigated the so-called anomalous diffusion stretched exponential model-exp[-(bD)(alpha)], where alpha is a measure of tissue complexity that can be derived from fractal models of tissue structure. In this paper we propose an alternative derivation for the stretched exponential model using fractional order space and time derivatives. First, we consider the case where the spatial Laplacian in the Bloch-Torrey equation is generalized to incorporate a fractional order Brownian model of diffusivity. Second, we consider the case where the time derivative in the Bloch-Torrey equation is replaced by a Riemann-Liouville fractional order time derivative expressed in the Caputo form. Both cases revert to the classical results for integer order operations. Fractional order dynamics derived for the first case were observed to fit the signal attenuation in diffusion-weighted images obtained from Sephadex gels, human articular cartilage and human brain. Future developments of this approach may be useful for classifying anomalous diffusion in tissues with developing pathology.