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Arterial Growth From Optimisation Principles

This study explores the optimization principles governing the growth of arterial trees, particularly in the context of coronary arteries. By applying computational methods, including simulated annealing and constrained constructive optimization, the research examines the topological and geometrical factors that influence energy requirements and blood volume maintenance. Key findings highlight the asymmetry in bifurcation patterns under varying metabolic costs and propose future applications in medical imaging, artificial tissue development, and statistical modeling of strokes. The results advance our understanding of vascular structure optimization.

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Arterial Growth From Optimisation Principles

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  1. Arterial Growth From Optimisation Principles Jonathan J. Keelan, The Open University (Global metabolic optimality in the structure of the coronary arteries, arXiv:1403.6450, J. Keelan, E.M.L. Chung and J.P. Hague)

  2. Arterial Trees • Approximately Binary (3% Trifurcation) • Delivery and Transport • Topology and Geometry

  3. Energy Requirements • Blood volume maintenance • Pumping power / vascular resistance • Murrays Law

  4. Modelling • Fractal Models • Constrained Constructive Optimisation (CCO) • Morphological Models [2] [1] CCO Morphological 1. Schreiner, W., et al (2006). Optimized arterial trees supplying hollow organs. Medical Engineering & Physics, 28(5), 416-429 2. Kaimovitz, B., et al. (2010). A full 3-D reconstruction of the entire porcine coronary. Am J Phys. Heart Circ. Phys

  5. Modelling • Blood Supply • Arterial Exclusion • Volume and Power arXiv:1403.6450

  6. Simulated Annealing • Geometry • Topology • Boundary Constraints arXiv:1403.6450

  7. Results arXiv:1403.6450

  8. Results • Bifurcation asymmetry over various metabolic costs arXiv:1403.6450

  9. Results Anterior Posterior arXiv:1403.6450

  10. Future Work • Use real tissue geometries (e.g. Brain MRI data) • Model various organs • Incorporate into statistical stroke model

  11. Applications [1] • Medical Imaging Augmentation • Artificial tissue / Organs [1] Kolesky, David B. etc al, 3D Bioprinting of Vascularized, Heterogeneous Cell-Laden Tissue Constructs, Advanced Materials, 1521-4095

  12. Summary • Computational growth of arterial trees • Simulated Annealing algorithm for arbitrary tissue geometries • Accurate reproduction of Morphological / Structural properties

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