The application of porous-media theory to the investigation of time-dependent diffusion in in vivo systems

Recent developments in solid-boundary porous-media theory have shown that useful structural information can be extracted from the time-dependent diffusion coefficient, D(t), of the fluid filling the interstitial space, This theoretical framework provides a basis from which to understand the results from diffusion experiments performed in other types of systems (e.g. biological). Structural information about porous media can be obtained from the short-time behavior of D(t) in the form of the ratio of the surface area to pore volume, S/V The long-time behavior of D(t) in porous media provides an indirect measure of the macroscopic structure, In this case, the longtime diffusion coefficient, D-eff, reflects the tortuosity, T, of the medium; a property of both the connectivity of the diffusion paths and the volume fraction of the sample. Measurements of D(t) were performed in RIF-1 tumors, using both spectroscopy and imaging, and the data were used to calculate S/V and T, The results were compared with histological sections in order to correlate S/V and T with differences in tissue structure (i.e. necrotic vs nonnecrotic tumor tissue), Based on spectroscopic measurements, there is a trend towards decreasing S/V and T with increasing tumor volume, consistent with the interpretation that water in necrotic tissue Is experiencing relatively fewer restricting barriers (as compared to non-necrotic tumor tissue). Based on D(t) maps generated from RIF-1 tumors, D-eff, and hence T appears to be much more sensitive than S/V in differentiating between necrotic and nonnecrotic tissue, In addition to characterizing diseased tissue, S/V and particularly T appear to be sensitive to structural changes that would accompany tumor treatment and should therefore provide a useful tool for monitoring the progress of therapeutic interventions.