A model for transit time distributions through organs that accounts for fractal heterogeneity

It has been shown that density functions of organ transit time distributions of vascular markers (washout curves) are characterized by a power-law tail, reflecting the fractal nature of the vascular network. Yet, thus far, no closed-form model is available that can be fitted to such organ outflow data. Here we propose a model that accounts for the existing data. The model is a continuous mixture of inverse Gaussian densities, implying flow heterogeneity in the organ. It has been fitted to outflow data from the rabbit heart and rat liver. The power-law decay with exponent -3 observed in the heart, corresponds to an intra-organ flow distribution with a relative dispersion of about 35%.