3D Structural Model and Visualization of Blood Vessels Based on L-System

Abstract

The insight in structures of the blood vessels is a basis for study of blood flows to help understanding the abnormalities of blood vessels that can cause vascular diseases. Basic concept used for constructing structures of blood vessels in organs is arterial branching, which is usually characterized by fractal similarity in the bifurcation pattern. In this work, the concept of Lindenmayer system (L-system) is modified for three-dimensional (3D) tree-like structures to model structures of blood vessels in organs, and then, applied to construct and visualize structural blood vessels via our software created based on openGL and Lazarus program. The structure of blood vessels is constructed based on the physiological law of arterial branching proposed Murray (Murray’s law) under additional assumptions and constraints such as the spreading of blood vessels to cover all directions, the angle condition and the non-overlapping vessels condition. The concept is applied to simulate structures of blood vessels in 3 study cases, including symmetric arterial branching, non-symmetric arterial branching and structure of blood vessel on different domains. The results of structures of blood vessels generated from all cases are measured based on the number of segments, the total blood volume and the fractal dimension. The results of modeling and simulation in this work are illustrated by comparing with other results appeared literature. Moreover, the constructed structures of the blood vessels based on this 3D L-system could be useful for future research such as blood flow, pressure and other properties involving in structures of blood vessels in different organs of human and animals.
 HIGHLIGHTS
 
 A new 3D L-system is developed based on directional vectors for construction of 3D tree-like structures such as structures of blood vessels
 The model of structures of blood vessels is constructed based on the physiological laws of arterial branching (Murray’s law) with additional assumptions on the spreading of blood vessels, the angle condition, and the non-overlapping of blood vessels
 Algorithm and software are developed based on L-system to simulate and visualize 3D structures of blood vessels
 
 GRAPHICAL ABSTRACT