Is in Vivo Drug Dissolution a Fractal Process

This structure is generated via the modified diffusion-limited aggregation (DLA) algorithm of [205] using the law p = a (m/N). Here, N = 2, 000 (the number of particles of the DLA clusters), a = 10 and ft = 0.5 are constants that determine the shape of the cluster, p is the radius of the circle in which the cluster is embedded, pc = 0.1 is the lower limit of p (always pc p), and to is the number of particles sticking to the downstream portion of the cluster. This example corresponds to a radial Hele-Shaw cell where water has been injected radially from the central hole. Due to heterogeneity a sample cannot be used to calculate the dissolved amount at any time, i.e., an average value for the percent dissolved amount at any time does not exist. This property is characteristic of fractal objects and processes. 

According to van Damme [201], fractal fingering is in many respects a chaotic phenomenon because it exhibits a sensitive dependence on the initial conditions. Although this kind of performance for a dissolution system is currently unacceptable, it might mirror more realistically the erratic dissolution of drugs with very low extent of absorption. 

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