On the Bifurcation of Blood Vessels--Wilhelm Roux's Doctoral Thesis (Jena 1878)--a Seminal Work for Biophysical Modelling in Developmental Biology

Wilhelm Roux's doctoral thesis described the relationship between the angle and diameter of bifurcating blood vessels. We have re-read this work in the light of biophysics and developmental biology and found two remarkable aspects hidden among a multitude of observations, rules and exceptions to these rules. First, the author identified the major determinants involved in vascular development; genetics, cybernetics, and mechanics; moreover, he knew that he could not deal with the genetic and regulatory aspects, and could hardly treat the mechanical part adequately. Second, he was deeply convinced that the laws of physics determine the design of organisms, and that a necessity for optimality was inherent in development. We combined the analysis of diameter relationships with the requirement for optimality in a stochastic biophysical model, and concluded that a constant wall-stress condition could define a minimum wall-tissue optimum during arterial development. Hence, almost 120 years after Wilhelm Roux's pioneering work, our model indicates one possible way in which physical laws have determined the evolution of regulatory and structural properties in vessel wall development.