Blood Vessel Growth: Mathematical Analysis and Computer Simulation, Fractality, and Optimality

The structural complexity of the circulatory system exceeds the available genetic information. In the developmental process, therefore, self-organization on epigenetic levels can be postulated, which exploits information that is being generated during embryogenesis. We used mathematical tools to analyze patterns and complexity, and designed a computer model to predict geometrical and biophysical properties of bifurcating vessel systems. In particular, some boundary conditions during development, and the problem of optimality are addressed. We propose that the complexity of blood vessel formation in vivo and in sapio may be adequately described with a combination of various classical geometrical and physical concepts, supplemented by concepts of fractal geometry.

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