Fractal characteristics of vascular structure and modeling of blood flow in three dimensions

This thesis improves our understanding of blood flow physiology in tree-like, arterial vascular systems of complete organs such as the kidneys, lungs, and heart. Models of blood flow and experimental data of kidney morphology are presented based on the concept of volume ordering. A perfused volume of tissue is assigned to each segment within the vascular tree. This volume serves as a measure of scale and defines the volume order number of the segment. The dependence of vascular parameters such as vessel diameter and conductance on scale is examined and termed 'fractal' if it follows a power law as a function of scale. A theoretical, non-geometric model, which assumes fractal vessel segment conductance and scale-independent branching asymmetry, is introduced that produces perfusion heterogeneities similar to experimental observations in sheep hearts.; Three-dimensional data of arterial trees in mouse and rat kidneys are obtained using high-resolution computed tomography (microCT). The performance of the General Electric MS8 microCT scanner and different vascular contrast agents are evaluated. Fractal relationships are observed for vessel diameter and conductance but not for segment length. Branching is found to be asymmetric for large vessels but becomes symmetric at smaller scales. The advantages of volume ordering over previous vessel ordering schemes are demonstrated and results are compared with theoretical expectations. The microCT data reveals a fully connected vascular tree with vessels down to 44 mum in mice and 76 mum in rats. Subtree conductances and blood flow in this structure are predicted based on extrapolating segment conductances down to the capillary level. It is the first model of blood flow in a complete organ that is based on the actual three-dimensional geometry of the vascular tree. Subsequent experiments to measure perfusion and vascular structure in the same organ are proposed to validate the model. Validated three-dimensional models of vascular systems are needed to eventually understand and be able to model the development, function, and pathology of complete organs and organisms. They will serve as gold standards for less sophisticated models.