Abstract
A new optimality principle for the branching angles of blood vessels in the cardiovascular system is proposed: the principle of minimum drag. The results are examined in the light of general observations and compared with those obtained from the principles of minimum work and minimum volume. It is shown that in some aspects the new principle is equally consistent with observations, and, in other aspects, it is perhaps more plausible than the other two principles.
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Selected References
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- Caro C. G., Fitz-Gerald J. M., Schroter R. C. Atheroma and arterial wall shear. Observation, correlation and proposal of a shear dependent mass transfer mechanism for atherogenesis. Proc R Soc Lond B Biol Sci. 1971 Feb 16;177(1046):109–159. doi: 10.1098/rspb.1971.0019. [DOI] [PubMed] [Google Scholar]
- Fry D. L. Acute vascular endothelial changes associated with increased blood velocity gradients. Circ Res. 1968 Feb;22(2):165–197. doi: 10.1161/01.res.22.2.165. [DOI] [PubMed] [Google Scholar]
- Kamiya A., Togawa T. Optimal branching structure of the vascular tree. Bull Math Biophys. 1972 Dec;34(4):431–438. doi: 10.1007/BF02476705. [DOI] [PubMed] [Google Scholar]
- Leopold L. B. Trees and streams: the efficiency of branching patterns. J Theor Biol. 1971 May;31(2):339–354. doi: 10.1016/0022-5193(71)90192-5. [DOI] [PubMed] [Google Scholar]
- Murray C. D. A RELATIONSHIP BETWEEN CIRCUMFERENCE AND WEIGHT IN TREES AND ITS BEARING ON BRANCHING ANGLES. J Gen Physiol. 1927 May 20;10(5):725–729. doi: 10.1085/jgp.10.5.725. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Murray C. D. THE PHYSIOLOGICAL PRINCIPLE OF MINIMUM WORK APPLIED TO THE ANGLE OF BRANCHING OF ARTERIES. J Gen Physiol. 1926 Jul 20;9(6):835–841. doi: 10.1085/jgp.9.6.835. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Roach M. R., Scott S., Ferguson G. G. The hemodynamic importance of the geometry of bifurcations in the circle of Willis (glass model studies). Stroke. 1972 May-Jun;3(3):255–267. doi: 10.1161/01.str.3.3.255. [DOI] [PubMed] [Google Scholar]
- Turner R. S. The geometry of the human cerebellar vermis. Anat Rec. 1968 Apr;160(4):691–696. doi: 10.1002/ar.1091600404. [DOI] [PubMed] [Google Scholar]
- Warren B. A. Changes following emboli in small veins. Vasc Surg. 1968 Dec;2(4):205–213. doi: 10.1177/153857446800200404. [DOI] [PubMed] [Google Scholar]
- Zamir M., Roach M. R. Blood flow downstream of a two-dimensional bifurcation. J Theor Biol. 1973 Nov 5;42(1):33–48. doi: 10.1016/0022-5193(73)90146-x. [DOI] [PubMed] [Google Scholar]
- Zamir M., Roach M. R. Blood flow, slip, and viscometry. Biophys J. 1972 Jun;12(6):703–704. doi: 10.1016/S0006-3495(72)86113-7. [DOI] [PMC free article] [PubMed] [Google Scholar]
