A model for transport and dispersion in the circulatory system based on the vascular fractal tree

Materials are distributed throughout the body of mammals by fractal networks of branching tubes. Based on the scaling laws of the fractal structure, the vascular tree is reduced to an equivalent one-dimensional, tube model. A dispersion-convection partial differential equation with constant coefficients describes the heterogeneous concentration profile of an intravascular tracer in the vascular tree. A simple model for the mammalian circulatory system is built in entirely physiological terms consisting of a ring shaped, one-dimensional tube which corresponds to the arterial, venular, and pulmonary trees, successively. The model incorporates the blood flow heterogeneity of the mammalian circulatory system. Model predictions are fitted to published concentration-time data of indocyanine green injected in humans and dogs. Close agreement was found with parameter values within the expected physiological range.