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A Computational Model of Continuous Hollow Cerebrovascular Arterioles Using a Fractal L-System

There is a need for better 3-D model representations of cerebrovasculature particularly on the order of arterioles. Such a model would have many applications and could be a useful tool for those conducting studies involving the brain and its function. The load bearing effects of the vasculature can be better studied with such a model, such as in the case of large strains. In addition, by having a continuous hollow structure, studies involving flow properties can be conducted at a whole scale rather than in a segmented view. Such studies are critical to the advancement of knowledge about the brain and its mechanics which can lead to advancements in preventative and curative care, as well as preventative safety measures. The model developed in this paper could serve as a tool in such studies. A fractal L-system is used to define the branching nature of the model. As such a growing tree structure is developed and characterized by its bifurcation at the end of a vessel segment. The index of bifurcation, α, is a parameter that controls the behavior of the two generated daughter vessels. The model presented here grows from a single parent branch into a bifurcation each of which then bifurcates as many times as specified. The length and diameter of the two daughter vessels will be a function of the respective parent’s length and diameter as well as a value α. The branching angle of the two daughter vessels will be entirely controlled by α. The hollow continuous nature of the model allows for it to be used as a representation of the arteriole structures in the brain. There is also use for such a model in other areas of the body, however, this study will focus on the representation of the cerebrovasculature. The end result is a branching tree model generated in Abaqus which is continuous, hollow and capable of extensive generation with uses in modeling complex cerebrovascular mechanics.