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Medical Engineering & Physics
Volume 28, Issue 5
, Pages 416-429
, June 2006
Optimized arterial trees supplying hollow organs
References
- . The pattern of coronary arteriolar bifurcations and the uniform shear hypothesis. Ann Biomed Eng. 1995;23:13–20
- . Epicardial coronary blood flow including the presence of stenoses and aorto-coronary bypasses I: model and numerical method. J Biomech Eng. 1985;107:361–367
- . Generation of an anatomically based geometric coronary model. Ann Biomed Eng. 2000;28:14–25
- . A mathematical model of cardiac anatomy. In: Panfilov AV, Holden AV editor. Computational biology of the heart. Chichester: John Wiley & Sons; 1997;p. 171–215
- . Staged growth of optimized arterial model trees. Ann Biomed Eng. 2000;28:495–511
- . A three-dimensional model for arterial tree representation, generated by constrained constructive optimization. Comput Biol Med. 1999;29:19–38
- . Three-dimensional optimization of arterial tree models. In: Power H, Brebbia CA, Kenny J editor. Simulation in biomedicine IV. Southampton: Computational Mechanics Publications; 1997;p. 3–12
- . Computer-optimization of vascular trees. IEEE Trans Biomed Eng. 1993;40:482–491
- . On the bifurcation of blood vessels—Wilhelm Roux's doctoral thesis (Jena 1878)—a seminal work for biophysical modelling in developmental biology. Anat Anz. 1997;179:33–36
- . Branching patterns in the porcine coronary arterial tree. Estimation of flow heterogeneity. Circ Res. 1992;71:1200–1212
- . Relation between diameter and flow in major branches of the arch of the aorta. J Biomech. 1992;25:1303–1310
- . The branching structure of arterial trees. Comments Theor Biol. 1988;1:15–37
- . On connecting large vessels to small: the meaning of MURRAY's law. J Gen Physiol. 1981;78:431–453
- . Propagation velocity and reflection of pressure waves in the canine coronary artery. Am J Physiol. 1979;237:H469–H474
- . The influence of optimization target selection on the structure of arterial tree models generated by constrained constructive optimization. J Gen Physiol. 1995;106:583–599
- . Redistribution of microvascular resistance produced by dipyridamole. Am J Physiol. 1989;256:H383–H390
- . Optimal branching structure of the vascular tree. Bull Math Biophys. 1972;34:431–438
- . Biomechanics. Circulation. New York: Springer-Verlag; 1997;
- . Evolution and optimum seeking. New York: John Wiley & Sons Inc.; 1995;
- . Principles of design of fluid transport systems in zoology. Science. 1990;249:992–999
- . Cost of deparature from optimality in arterial branching. J Theor Biol. 1984;109:401–409
- . Generation of biological pattern and form. IMA J Math Appl Med Biol. 1984;1:51–75
- . Teleonomical optimization of a fractal model of the pulmonary arterial bed. J Theor Biol. 1983;102:225–248
- . Teleonomical representation of the pulmonary arterial bed of the dog by a fractal tree. In: Kenner T, Busse R, Hinghofer-Szalkay H editor. Cardiovascular system dynamics: models and measurements. New York, London: Plenum Press; 1982;p. 137–146
- . Optimization of diameters and bifurcation angles in lung and vascular tree structures. Bull Math Biol. 1977;39:509–519
- . Optimality principles in biology. London: Butterworth & Co. Ltd.; 1967;
- . Optimal systems: I. The vascular system. Bull Math Biophys. 1954;16:59–74
- . On growth and form. Cambridge: Cambridge University Press; 1942;
- . The physiological principle of minimum work. I. The vascular system and the cost of blood volume. Proc Natl Acad Sci USA. 1926;12:207–214
- . Optimality principles in arterial branching. J Theor Biol. 1976;62:227–251
- . Theoretical relationship between the optimal models of the vascular tree. Bull Math Biol. 1974;36:311–323
- . A model of the mechanics of the left ventricle. Ann Biomed Eng. 1979;7:299–318
- . A computer study of the left ventricular performance based on fiber structure, sacomere dynamics, and transmural electrical propagation velocity. Circ Res. 1984;55:358–374
- . Relating left ventricular dimension to maximum elastance by fiber mechanics. Am J Physiol. 1986;251:R627–R635
- . Laminar structure of the heart: ventricular myocyte arrangement and connective tissue architecture in the dog. Am J Physiol. 1995;269:H571–H582
- . Laminar structure of the heart: a mathematical model. Am J Physiol. 1997;272:H2466–H2476
- . A unique mathematic model of the geometry of the human eyeball. Ann Ophthalmol. 1992;24:114–117
- . A model of the peritoneal cavity for use in internal dosimetry. J Nucl Med. 1989;30:2002–2011
- . Methode der finiten elemente. Stuttgart: Teubner; 1991;
- Amira™ advanced visualization, data analysis and geometry reconstruction. User's guide and reference manual. Berlin: Konrad-Zuse-Zentrum für Informationstechnik; 2001.
- . Monte Carlo methods. New York: Wiley; 1986;
- . Simulated annealing and Boltzmann machines. Chichester, New York, Brisbane, Toronto, Singapore: Wiley; 1989;
- . Micro-architecture and composition of artery walls: relationship to location, diameter and the distribution of mechanical stress. J Hypertens. 1992;10:101–104
- NAG fortran library manual, mark 16. Oxford: The Numerical Algorithms Group; 1993.
- . Application of stereology to coronary microcirculation. Basic Res Cardiol. 1981;76:411–415
- . A computerized method for determination of microvascular density. Microvasc Res. 1995;49:180–189
- . Heterogeneous perfusion is a consequence of uniform shear stress in optimized arterial tree models. J Theor Biol. 2003;220:285–301
- . An optimal bronchial tree may be dangerous. Nature. 2004;427:633–666
- . Smaller is better—but not too small: a physical scale for the design of the mammalian pulmonary acinus. Proc Natl Acad Sci USA. 2002;99:10411–10416
- . Shear stress distribution in arterial tree models, generated by constrained constructive optimization. J Theor Biol. 1999;198:27–45
- . Segment analysis of human coronary arteries. Blood Vessels. 1987;24:76–84
- . Distributing and delivering vessels of the human heart. J Gen Physiol. 1988;91:725–735
- . Limited bifurcation asymmetry in coronary arterial tree models generated by constrained constructive optimization. J Gen Physiol. 1997;109:129–140
- . Branching characteristics of human coronary arteries. Can J Physiol Pharmacol. 1986;64:661–668
- The branching angles in computer-generated optimized models of arterial trees. J Gen Physiol. 1994;103:975–989
- . Structural quantification and bifurcation symmetry in arterial tree models generated by constrained constructive optimization. J Theor Biol. 1996;180:161–174
- . Fractal nature of regional myocardial blood flow heterogeneity. Circ Res. 1989;65:578–590
- . Fractals describe blood flow heterogeneity within skeletal muscle and within myocardium. Am J Physiol. 1995;268:H112–H116
- . Myocardial blood flow heterogeneity in shock and small-volume resuscitation in pigs with coronary stenosis. J Appl Physiol. 1997;83:1832–1841
- Local continuity of myocardial blood flow studied by monochromatic synchrotron radiation-excited X-ray fluorescence spectrometry. Circ Res. 1995;76:1088–1100
- . Fractal properties of perfusion heterogeneity in optimized arterial trees: a model study. J Gen Physiol. 2003;122:307–321
- . Concepts and features of arterial tree models generated by constrained constructive optimization. Comments Theor Biol. 2001;6:103–136
- . Analysis of coronary blood flow interaction with myocardial mechanics based on anatomical models. Philos Trans R Soc Lond. Series A: Math Phys Eng Sci. 2001;359:1251–1262
- . Squeezing tubes: a case of remodeling and regulation: coronary reserve in hypertensive heart disease. Cardiovasc Res. 1998;40:4–8
- Coronary back flow pressure is elevated in association with increased left ventricular end-diastolic pressure in humans. Angiology. 1996;47:1047–1051
- . Effects of myocardial contraction on coronary blood flow: an integrated model. Ann Biomed Eng. 1994;22:638–652
- . Mechanical compression of small coronary vessels during the cardiac cycle. Biorheology. 1993;30:387–396
- . Effects of left ventricular pressure unloading during LVAD support on right ventricular contractility. ASAIO J. 1992;38:M473–M476
- . Coronary oscillatory flow amplitude is more affected by perfusion pressure than ventricular pressure. Am J Physiol. 1990;258:H1889–H1898
- . Small vessel phenomena in the coronary microcirculation: phasic intramyocardial perfusion and coronary microvascular dynamics. Prog Cardiovasc Dis. 1988;31:17–38
- . The interaction of extravascular pressure fields and fluid exchange in capillary networks. Math Biosci. 1986;82:141–151
PII: S1350-4533(05)00157-8
doi: 10.1016/j.medengphy.2005.07.019
© 2005 IPEM. Published by Elsevier Inc. All rights reserved.
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Medical Engineering & Physics
Volume 28, Issue 5
, Pages 416-429
, June 2006
