Staged Growth of Optimized Arterial Model Trees

Abstract

There is a marked difference in the structure of the arterial tree between epi- and endocardial layers of the human heart. To model these structural variations, we developed an extension to the computational method of constrained constructive optimization (CCO). Within the framework of CCO, a model tree is represented as a dichotomously branching network of straight cylindrical tubes, with flow conditions governed by Poiseuille's law. The tree is grown by successively adding new terminal segments from randomly selected points within the perfusion volume while optimizing the geometric location and topological site of each new connection with respect to minimum intravascular volume. The proposed method of "staged growth" guides the generation of new terminal sites by means of an additional time-dependent boundary condition, thereby inducing a sequence of domains of vascular growth within the given perfusion volume. Model trees generated in this way are very similar to reality in their visual appearance and predict diameter ratios of parent and daughter segments, the distribution of symmetry, the transmural distribution of flow, the volume of large arteries, as well as the ratio of small arterial volume in subendocardial and subepicardial layers in good agreement with experimental data. From this study we conclude that the method of CCO combined with staged growth reproduces many characteristics of the different arterial branching patterns in the subendocardium and the subepicardium, which could not be obtained by applying the principle of minimum volume alone.

Fast algorithm for 3-D vascular tree modeling

“…These models allow structural and functional features to be changed and pathological vascular modifications to be rendered. They range from the early 2-D models [2] to more recent surface-based ones [1] or to fully 3-D models [3,4] with different objectives such as realistic representations for rendering applications [1], physiological interpretation [3] or organ-based descriptions like coronary arterial trees [4,5]. The present contribution is a continuation of the work described in [6].…”

“…The main concepts of the model presented in [3] and the extension described here are close to those reported in [4]. The vessels (rigid tubes forming a binary tree) grow to irrigate macro-cells distributed into a 3-D organ (static shape in [4], growing in [3,5]). In both cases, blood is considered as a Newtonian fluid whose flow is governed by the Poiseuille's law.…”

Creation of a vascular system for organ manufacturing

“…(iv) The radii of parent and two daughter segments at bifurcations (left and right) obey a power law (bifurcation law) [30,31] of the form:…”

Parallel Implementation of Vascular Network Modeling

“…Many vascular models have been proposed, e.g. Constrained Constructive Optimization (COO) method for an arterial tree generation [11], an algorithm of arterial tree growth inside a defined and gradually expanding shape [1], improved CCO method to simulate the coronary tree [6] or a fractal model [13]. According to our knowledge, all of them use the sequential algorithm to develop vascular systems.…”