Abstract
The branching characteristic of the arterial system is such that blood pressure pulses propagate with minimum loss. This characteristic depends on the geometric and elastic properties of branching vessels. In the current investigation, mathematical relations of branching geometry and elastic properties are formulated and their relative contributions to pulse reflection at an arterial junction are analyzed. Results show that alteration of pulse transmission through the junction is more significantly affected by changes in branching vessel radii and wall thickness than by corresponding percentage changes in vessel wall elastic moduli.
Similar content being viewed by others
Literature
Cohn, D. L. 1954. “Optimal Systems: The Vascular System.”Math. Biophys. 16, 59–74.
Farrar, D. J., M. G. Bond, J. K. Sawyer and H. D. Green. 1984. “Pulse Wave Velocity and Morphological Changes Associated with Early Arteriosclerosis Progression in the Aortas of Cynomolgus Monkeys.”Cardiovasc. Res. 18, 107–118.
Kamiya, A. and T. Togawa. 1972. “Optimal Branching Structure of the Vascular Tree.”Bull. math. Biophys. 34, 431–438.
Karreman, G. 1952. “Some Contributions to the Mathematical Biology of Blood Circulation. Reflections of Pressure Wave in the Arterial System.”Bull. math. Biophys. 14, 327–350.
Learoyd, B. M. and M. G. Taylor. 1966. “Alterations with Age in the Viscoelastic Properties of Human Arterial Walls.”Circulation Res. 18, 278–292.
Li, J. K.-J. 1982. “Cardiovascular Diagnostic Parameters Derived from Pressure and Flow Pulses.”Front. Engng Healthcare 4, 186–189.
—, J. Melbin, K. B. Campbell and A. Noordergraaf. 1980. “Evaluation of a Three-point Pressure Method in the Determination of Arterial Transmission Parameters.”J. Biomech. 13, 1023–1029.
——, R. A. Riffle and A. Noordergraaf. 1981. “Pulse Wave Propagation.”Circulation Res..49, 442–452.
—— and A. Noordergraaf. 1984. “Directional Disparity of Pulse Reflection in the Dog.”Am. J. Physiol. 247, 1495–1499.
Martin, J. D., and M. E. Clark. 1966. “Theoretical and Experimental Analyses of Wave Reflections in Branched Flexible Conduits.”Engng. Mech. Res. 12–14, 441–461.
Moens, A. I., 1878.Die Pulsekurve. Leiden: Brill.
Murray, C. D. 1926. “The Physiological Principle of Minimum Work Applied to the Angle of Branching Arteries.”J. gen. Physiol. 9, 835–841.
Rosen, R. 1967.Optimality Principles in Biology. London: Butterworths.
Uylings, H. B. M. 1977. “Optimization of Diameters and Bifurcation Angles in Lung and Vascular Tree Structure.”Bull. math. Biol. 30, 509–520.
Westerhof, N., F. Bosman, C. J. DeVries and A. Noordergraaf. 1969. “Analog Studies of the Human Systemic Arterial Tree.”J. Biomech. 2, 121–143.
Womersley, J. R. 1958. “Oscillatory Flow in Arteries: The Reflection of the Pulse Wave at Junctions and Rigid Inserts in the Arterial System.”Phys. Med. Biol. 2, 313–323.
Zamir, M. 1976. “Optimality Principles in Arterial Branching.”J. theor. Biol. 62, 227–251.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Li, J.K.J. Dominance of geometric overelastic factors in pulse transmission through arterial branching. Bltn Mathcal Biology 48, 97–103 (1986). https://doi.org/10.1007/BF02460065
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02460065