Dendritic flow networks: the link between patterns and design with purpose in biosystems
摘要
This study presents a comprehensive methodology, based on physics laws, for predicting the architecture of symmetric and asymmetric dendritic flow networks. These flow networks, found in vascular systems and respiratory trees, exhibit prefractal patterns that can be described by using recursive processes based on the concept of self-similarity, and the definition of a dimension that represents the degree of the system occupancy in space. Prefractal dendritic networks are thought that ensure the best possible access to flow transport.
MethodsAccording to the second law of thermodynamics, the path with the lowest impedance uses the least amount of energy to perform its task. The methodology employed in this study is the minimizing of flow impedance within constraints. The constraints are defined as the path's volume and lateral area.
Results and conclusionThe homothety ratios for sizes of the network that ensure maximum flow access are presented. We also examine the relationship between the fractality of dendritic flow networks and the design obtained from physical laws in this study. Based on the homothetic relations obtained here, the prefractal dimension is defined in terms of physics quantities, giving it meaning beyond the degree of space occupation and potentially shedding light on predicting issues in specific systems when the measured fractality differs from the predicted. Our study can be also very valuable in designing flow networks, which are crucial in the bioengineering sciences.