Date of Award
The structure of vascular networks represents a great, unsolved problem in anatomy. Network geometry and topology differ dramatically from left to right and person to person as evidenced by the superficial venation of the hands and the vasculature of the retinae. Mathematically, we may state that there is no conserved topology in vascular networks. Efficiency demands that these networks be regular on a statistical level and perhaps optimal. We have taken the first steps towards elucidating the principles underlying vascular organization, creating the rst map of the hierarchical vasculature (above the capillaries) of an entire organ. Using serial blockface microscopy and fluorescence imaging, we are able to identify vasculature at 5 μm resolution. We have designed image analysis software to segment, align, and skeletonize the resulting data, yielding a map of the individual vessels. We transformed these data into a mathematical graph, allowing computationally efficient storage and the calculation of geometric and topological statistics for the network. Our data revealed a complexity of structure unexpected by theory. We observe loops at all scales that complicate the assignment of hierarchy within the network and the existence of set length scales, implying a distinctly non-fractal structure of components within.
Jacob, Oppenheim N., "High Resolution Maps of the Vasculature of An Entire Organ" (2014). Student Theses and Dissertations. 210.