Three Dimensional Reconstruction of Branched Tree Structures from Serial Sections

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Abstract
The quantative analysis of oxygen transport to tissue requires knowledge of the spatial configuration of the oxygen sources and sinks, mathematical descriptions of the transport phenomena, and experimentally measured tension. The techniques for measuring the oxygen tension in tissue are readily available. Acceptable mathematical description of the transport phenomena is precluded by defining acceptable spatial configuration of the microcirculation of the tissue. The current mathematical descriptions of the transport rely primarily on deterministic models of the phenomena and an assumed simplistic geometry for the system. To permit the development of usable mathematical models for the transport then requires that a technique be available to construct from cross-section images of tissue the micro-structure of the system. The micro-structure includes both the micro-circulatory system as well as the location of the sinks for oxygen. To this end an automatic three dimensional reconstruction process has been developed which uses serial cross-section images of the tissue. The possibility of automating the reconstruction process has received considerable attention recently by Adair, et al., (1981), Batnitzky, et al., (1981), Edelstein, et al., (1981), Moseley, (1982), Bajcsy, et al., (1983), and Hull, et al., (1984).