论文标题
血管系统中的异形缩放定律和千古破坏
Allometric scaling law and ergodicity breaking in the vascular system
论文作者
论文摘要
对体大小与生物生理学关系的关系的异态或定量研究是生物物理缩放研究的重要领域。血管网络中的分形分支的西棕色模型（WBE）模型解释了经验异形kleiber定律（代谢率的3/4缩放指数与动物质量的关系）。 WBE模型提出了许多新问题，例如如何更准确地考虑毛细血管现象，以及哪些对毛细管大小的血流速度更现实的依赖性。我们建议对分支模型进行广义配方，并研究分形血管系统中的终身性。通常，这种系统中的流体流并不是奇异的，而千古的断裂归因于网络的分形结构。因此，除了衰老和大分子拥挤等机制外，分形分支还可以看作是生物物理系统中奇异性破裂的根源。对非熟练性的核算对于多种生物医学应用很重要，因为长期观察时间序列是不切实际的。还讨论了与微流体应用的相关性。
Allometry or the quantitative study of the relationship of body size to living organism physiology is an important area of biophysical scaling research. The West-Brown-Enquist (WBE) model of fractal branching in a vascular network explains the empirical allometric Kleiber law (the 3/4 scaling exponent for metabolic rates as a function of animal's mass). The WBE model raises a number of new questions, such as how to account for capillary phenomena more accurately and what are more realistic dependencies for blood flow velocity on the size of a capillary. We suggest a generalized formulation of the branching model and investigate the ergodicity in the fractal vascular system. In general, the fluid flow in such a system is not ergodic, and ergodicity breaking is attributed to the fractal structure of the network. Consequently, the fractal branching may be viewed as a source of ergodicity breaking in biophysical systems, in addition to such mechanisms as aging and macromolecular crowding. Accounting for non-ergodicity is important for a wide range of biomedical applications where long observations of time series are impractical. The relevance to microfluidics applications is also discussed.
