3D Structural Model and Visualization of Blood Vessels Based on L-System
DOI:
https://doi.org/10.48048/tis.2021.1407Keywords:
Lindenmayer system (L-system), Structural blood vessel, Arterial branching, Murray’s lawAbstract
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
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References
CD Murray. The physiological principle of minimum work applied to the angle of branching of arteries. J. Gen. Physiol. 1926; 9, 835-41.
E Fanucci, A Orlacchio and M Pocek. The vascular geometry of human arterial bifurcations. Invest. Radiol. 1988; 23, 713-8.
J Yang and Y Wang. Design of vascular networks: A mathematical model approach. Int. J. Numer. Methods Biomed. Eng. 2013; 29, 515-29.
M Zamir. Nonsymmetrical bifurcation in arterial branching. J. Gen. Physiol. 1978; 72, 837-45.
M Zamir, JA Medeiros and TK Cunningham. Arterial bifurcation in the human retina. J. Gen. Physiol. 1979; 74, 537-48.
M Marxen and RM Henkelman. Branching tree model with fractal vascular resistance explains fractal perfusion heterogeneity. Am. J. Physiol. Heart Circ. Physiol. 2003; 284, H1848-H1857.
M Zamir. Distributing and delivering vessels of the human heart. J. Gen. Physiol. 1988; 91, 725-35.
MH Tawhai, AR Clarka, GM Donovan and KS Burrowes. Computational modeling of airway and pulmonary vascular structure and function: Development of a “lung physiome”. Crit. Rev. Biomed. Eng. 2011; 39, 319-36.
DA Nordsletten, S Blackett, MD Bentley, EL Ritman and NP Smith. Structural morphology of renal vasculature. Am. J. Physiol. Heart Circ. Physiol. 2006; 291, 296-309.
M Zamir, SM Wrigley and BL Langille. Arterial bifurcations in the cardiovascular system of a rat. J. Gen. Physiol. 1983; 81, 325-35.
W Schreiner, F Neumann, M Neumann, A End, SM Roedler and S Aharinejad. The influence of optimization target selection on the structure of arterial tree models generated by constrained constructive optimization. J. Gen. Physiol. 1995; 106, 583-99.
W Schreiner, F Neumann, M Neumann, R Karch, A End and SM Roedler. Limited bifurcation asymmetry in coronary arterial tree models generated by constrained constructive optimization. J. Gen. Physiol. 1997; 109, 129-40.
W Schreiner, R Karch, M Neumann, F Neumann, P Szawlowski and S Roedler. Optimized arterial trees supplying hollow organs. Med. Eng. Phys. 2006; 28, 416-29.
R Karch, F Neumann, M Neumann and W Schreiner. Functional characteristics of optimized arterial tree models perfusing volumes of different thickness and shape. J. Vasc. Res. 2000; 37, 250-64.
W Schreiner, M Neumann, F Neumann, SM Roedler, A End, P Buxbaum, MR Muller and P Spieckermann. The branching angles in computer-generated optimized models of arterial trees. J. Gen. Physiol. 1994; 103, 975-89.
E Fanucci, A Orlacchio, M Pocek, A Magrini and E Salomoni. Optimal branching of human arterial bifurcations. Invest. Radiol. 1990; 25, 62-6.
R Karch, F Neumann, BK Podesser, M Neumann, P Szawlowski and W Schreiner. Fractal properties of perfusion heterogeneity in optimized arterial trees: A model study. Invest. Radiol. 2003; 122, 307-21.
M Zamir. Arterial branching within the confines of fractal L-system formalism. J. Gen. Physiol. 2001; 118, 267-75.
MA Galarreta-Valverde, MMG Macedo, C Mekkaoui and MP Jackowski. Three-dimensional synthetic blood vessel generation using stochastic L-systems. In: Proceedings of the International Society for Optical Engineering, Florida. 2013, p. 1-6.
M Zamir and N Brown. Arterial branching in various parts of the cardiovascular system. Am. J. Anat. 1982; 163, 295-307.
P Prusinkiewicz. Graphical applications of L-systems. In: Proceedings of the Graphics Interface '86 - Vision Interface '86, Vancouver, British Columbia, Canada. 1986, p. 247-53.
P Prusinkiewicz and A Lindenmayer. The algorithmic beauty of plants. Springer-Verlag New York, New York, 1990, p. 1-50.
P Prusinkiewicz, J Hanan, M Hammel and R Mech. L-systems: From the theory to visual models of plants. In: Proceedings of the 2nd CSIRO Symposium on Computational Challenges in Life Sciences, Melbourne, Australia. 1996, p. 1-27.
K Guan. The research of the improved 3D L-system and its application in plant modeling. In: Proceedings of the IEEE Conference on Cybernetics and Intelligent Systems, Chengdu, China. 2008, p. 718-23.
G Gutierrez, HD Reines and ME Wulf-Gutierrez. Clinical review: Hemorrhagic shock. Crit. Care 2004; 8, 373-81.
LO Schwenl and T Preusser. Analysis and algorithmic generation of hepatic vascular systems. Int. J. Hepatol. 2012; 2012, 357687.
PJ Blanco, LO Muller and JD Spence. Blood pressure gradients in cerebral arteries: A clue to pathogenesis of cerebral small vessel disease. Stroke Vasc. Neurol. 2017; 2, 108-17.
A Gholipour, M Ghayesh and A Zander. Nonlinear biomechanics of bifurcated atherosclerotic coronary arteries. Int. J. Eng. Sci. 2018; 133, 60-83.
M Dong, W Yang, JS Tamaresis, FP Chan, EJ Zucker, S Kumar, M Rabinovitch, AL Marsden and JA Feinstein. Image-based scaling laws for somatic growth and pulmonary artery morphometry from infancy to adulthood. Am. J. Physiol. Heart Circ. Physiol. 2020; 319, 432-42.
ID Kelch, G Bogle, GB Sands, ARJ Phillips, IJ LeGrice and PR Dunbar. Organ-wide 3D-imaging and topological analysis of the continuous microvascular network in a murine lymph node. Sci. Rep. 2015; 5, 16534.
PJ Blanco, RABD Queiroz and RA Feijoo. A computational approach to generate concurrent arterial networks in vascular territories. Int. J. Numer. Methods Biomed. Eng. 2013; 29, 601-14.
AF Tena and PC Clara. Deposition of inhaled particles in the lungs. Arc. Bronconeumol. 2012; 48, 240-6.
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