Kurz H, Sandau K, Christ B
Anatomisches Institut II, Universität Freiburg.
Ann Anat. 1997 Feb;179(1):33-6. doi: 10.1016/S0940-9602(97)80132-X.
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.
威廉·鲁克斯的博士论文描述了分叉血管的角度与直径之间的关系。我们根据生物物理学和发育生物学重新研读了这项工作，发现在众多观察结果、规则以及这些规则的例外情况中隐藏着两个显著的方面。首先，作者确定了血管发育中涉及的主要决定因素：遗传学、控制论和力学；此外，他知道自己无法处理遗传和调节方面的问题，也很难充分探讨力学部分。其次，他深信物理定律决定了生物体的设计，并且最优性的必要性在发育过程中是固有的。我们在一个随机生物物理模型中将直径关系分析与最优性要求相结合，得出恒定壁应力条件可以在动脉发育过程中定义最小壁组织最优值的结论。因此，在威廉·鲁克斯的开创性工作近120年后，我们的模型指出了物理定律决定血管壁发育中调节和结构特性演变的一种可能方式。
