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

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Abstract
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, Deff, 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 non‐necrotic 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, Deff, and hence T appears to be much more sensitive than S/V in differentiating between necrotic and non‐necrotic 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.