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Volumn 31, Issue 5, 2003, Pages 548-563

Voronoi polyhedra analysis of optimized arterial tree models

Author keywords

Blood flow; Computer simulation; Gamma distribution; Lognormal distribution; Relative dispersion; Scaling; Voronoi cell

Indexed keywords

BLOOD; BLOOD VESSELS; COMPUTER SIMULATION; HEMODYNAMICS; MEDICAL IMAGING; METABOLISM; OPTIMIZATION; TOPOLOGY;

EID: 0038543206     PISSN: 00906964     EISSN: None     Source Type: Journal    
DOI: 10.1114/1.1566444     Document Type: Article
Times cited : (33)

References (63)
  • 3
    • 0001781555 scopus 로고    scopus 로고
    • Voronoi diagrams
    • edited by J. R. Sack and J. Urrutia. Amsterdam: Elsevier Science B. V.
    • Aurenhammer, F., and R. Klein. Voronoi Diagrams. In: Handbook of Computational Geometry, edited by J. R. Sack and J. Urrutia. Amsterdam: Elsevier Science B. V., 2000, pp. 201-290.
    • (2000) Handbook of Computational Geometry , pp. 201-290
    • Aurenhammer, F.1    Klein, R.2
  • 4
    • 0037991142 scopus 로고    scopus 로고
    • The Geometry Center, University of Minnesota, Minneapolis
    • Barber, C. B., and H. Huhdanpaa. Qhull version 2.6. The Geometry Center, University of Minnesota, Minneapolis, 1998. http://www.geom.umn.edu/locate/qhull
    • (1998) Qhull Version 2.6
    • Barber, C.B.1    Huhdanpaa, H.2
  • 6
    • 0024440958 scopus 로고
    • Fractal nature of regional myocardial blood flow heterogeneity
    • Bassingthwaighte, J. B., R. B. King, and S. A. Roger. Fractal nature of regional myocardial blood flow heterogeneity. Circ. Res. 65:578-590, 1989.
    • (1989) Circ. Res. , vol.65 , pp. 578-590
    • Bassingthwaighte, J.B.1    King, R.B.2    Roger, S.A.3
  • 7
    • 0033798526 scopus 로고    scopus 로고
    • The fractal nature of myocardial blood flow emerges from a whole-organ model of arterial network
    • Beard, D. A., and J. B. Bassingthwaighte. The fractal nature of myocardial blood flow emerges from a whole-organ model of arterial network. J. Vasc. Res. 37:282-296, 2000.
    • (2000) J. Vasc. Res. , vol.37 , pp. 282-296
    • Beard, D.A.1    Bassingthwaighte, J.B.2
  • 8
    • 0034743998 scopus 로고    scopus 로고
    • Modeling advection and diffusion of oxygen in complex vascular networks
    • Beard, D. A., and J. B. Bassingthwaighte. Modeling advection and diffusion of oxygen in complex vascular networks. Ann. Biomed. Eng. 29:298-310, 2001.
    • (2001) Ann. Biomed. Eng. , vol.29 , pp. 298-310
    • Beard, D.A.1    Bassingthwaighte, J.B.2
  • 9
    • 0018768186 scopus 로고
    • Voronoi diagrams from convex hulls
    • Brown, D. Voronoi diagrams from convex hulls. Inf. Process. Lett. 9:223-228, 1979.
    • (1979) Inf. Process. Lett. , vol.9 , pp. 223-228
    • Brown, D.1
  • 11
    • 0026096218 scopus 로고
    • Microvascular pressures and resistances in the left ventricular subepicardium and subendocardium
    • Chilian, W. M. Microvascular pressures and resistances in the left ventricular subepicardium and subendocardium. Circ. Res. 69:561-570, 1991.
    • (1991) Circ. Res. , vol.69 , pp. 561-570
    • Chilian, W.M.1
  • 12
    • 84941433641 scopus 로고
    • Uber die Reduction der positiven quadratischen Formen mit drei unbestimmten ganzen Zahlen
    • Dirichlet, G. L. Uber die Reduction der positiven quadratischen Formen mit drei unbestimmten ganzen Zahlen. J. Reine Angew: Math. 40:209-227, 1850.
    • (1850) J. Reine Angew: Math. , vol.40 , pp. 209-227
    • Dirichlet, G.L.1
  • 14
    • 0025144428 scopus 로고
    • Fractal properties of pulmonary blood flow: Characterization of spatial heterogeneity
    • Glenny, R. W., and H. T. Robertson. Fractal properties of pulmonary blood flow: Characterization of spatial heterogeneity. J. Appl. Physiol. 69:532-55, 1990.
    • (1990) J. Appl. Physiol. , vol.69 , pp. 532-545
    • Glenny, R.W.1    Robertson, H.T.2
  • 15
    • 0029135072 scopus 로고
    • A computer simulation of pulmonary perfusion in three dimensions
    • Glenny R. W., and H. T. Robertson. A computer simulation of pulmonary perfusion in three dimensions. J. Appl. Physiol. 79:357-369, 1995.
    • (1995) J. Appl. Physiol. , vol.79 , pp. 357-369
    • Glenny, R.W.1    Robertson, H.T.2
  • 16
    • 33644889705 scopus 로고
    • The voronoi polyhedra as tools for structure determination in simple disordered systems
    • Gil Montoro, J. C., and J.L.F. Abascal. The Voronoi polyhedra as tools for structure determination in simple disordered systems. J. Phys. Chem. 97:4211-4215, 1993.
    • (1993) J. Phys. Chem. , vol.97 , pp. 4211-4215
    • Montoro, J.C.G.1    Abascal, J.L.F.2
  • 17
    • 0000993485 scopus 로고
    • Ionic association in electrolyte solutions: A Voronoi polyhedra analysis
    • Gil Montoro, J. C., F. Bresme, and J. L. F. Abascal. Ionic association in electrolyte solutions: A Voronoi polyhedra analysis. J. Chem. Phys. 101:10892-10898, 1994.
    • (1994) J. Chem. Phys. , vol.101 , pp. 10892-10898
    • Montoro, J.C.G.1    Bresme, F.2    Abascal, J.L.F.3
  • 18
    • 0035087563 scopus 로고    scopus 로고
    • Structural and biophysical simulation of angieogenesis and vascular remodeling
    • Gödde, R., and H. Kurz. Structural and biophysical simulation of angiogenesis and vascular remodeling. Dev. Dyn. 220:387-401, 2001.
    • (2001) Dev. Dyn. , vol.220 , pp. 387-401
    • Gödde, R.1    Kurz, H.2
  • 19
    • 84945017550 scopus 로고
    • Monte Carlo estimates of the distributions of the random polygons of the Voronoi tessellation with respect to a Poisson process
    • Hinde, A. L., and R. E. Miles. Monte Carlo estimates of the distributions of the random polygons of the Voronoi tessellation with respect to a Poisson process. J. Stat. Comput. Simul. 10:205-223, 1980.
    • (1980) J. Stat. Comput. Simul. , vol.10 , pp. 205-223
    • Hinde, A.L.1    Miles, R.E.2
  • 20
    • 0017829092 scopus 로고
    • Description of cellular patterns by Dirichlet domains: The two-dimensional case
    • Honda, H. Description of cellular patterns by Dirichlet domains: The two-dimensional case. J. Theor. Biol. 72:523-543, 1978.
    • (1978) J. Theor. Biol. , vol.72 , pp. 523-543
    • Honda, H.1
  • 21
    • 0022335441 scopus 로고
    • Variability of intercapillary distance estimated on histological sections of rat heart
    • Hoofd, L., Z. Turek, K. Kubat, B. E. M. Ringnalda, and S. Kazda. Variability of intercapillary distance estimated on histological sections of rat heart. Adv. Exp. Med. Biol. 191:239-247, 1985.
    • (1985) Adv. Exp. Med. Biol. , vol.191 , pp. 239-247
    • Hoofd, L.1    Turek, Z.2    Kubat, K.3    Ringnalda, B.E.M.4    Kazda, S.5
  • 22
    • 0022654143 scopus 로고
    • Angiogenesis in the heart and skeletal muscle
    • Hudlicka, O., A. J. Wright, and A. M. Ziada. Angiogenesis in the heart and skeletal muscle. Can. J. Cardiol. 2:120-123, 1986.
    • (1986) Can. J. Cardiol. , vol.2 , pp. 120-123
    • Hudlicka, O.1    Wright, A.J.2    Ziada, A.M.3
  • 23
    • 0011627860 scopus 로고    scopus 로고
    • Voronoi polyhedra analysis of the local structure of water from ambient to supercritical conditions
    • Jedlovszky, P. Voronoi polyhedra analysis of the local structure of water from ambient to supercritical conditions. J. Chem. Phys. 111;5975-5985, 1999.
    • (1999) J. Chem. Phys. , vol.111 , pp. 5975-5985
    • Jedlovszky, P.1
  • 24
    • 0015444264 scopus 로고
    • Optimal branching structure of the vascular tree
    • Kamiya, A., and T. Togawa. Optimal branching structure of the vascular tree. Bull. Math. Biophys. 34:431-438, 1972.
    • (1972) Bull. Math. Biophys. , vol.34 , pp. 431-438
    • Kamiya, A.1    Togawa, T.2
  • 25
    • 0032623656 scopus 로고    scopus 로고
    • A three-dimensional model for arterial tree representation, generated by constrained constructive optimization
    • Karch, R., F. Neumann, M. Neumann, and W. Schreiner. A three-dimensional model for arterial tree representation, generated by constrained constructive optimization. Comput. Biol. Med. 29:19-38, 1999.
    • (1999) Comput. Biol. Med. , vol.29 , pp. 19-38
    • Karch, R.1    Neumann, F.2    Neumann, M.3    Schreiner, W.4
  • 28
    • 0031019212 scopus 로고    scopus 로고
    • Analysis of pig's coronary arterial blood flow with detailed anatomical data
    • Kassab, G. S., J. Berkley, and Y. C. B. Fung. Analysis of pig's coronary arterial blood flow with detailed anatomical data. Ann. Biomed. Eng. 25:204-217, 1997.
    • (1997) Ann. Biomed. Eng. , vol.25 , pp. 204-217
    • Kassab, G.S.1    Berkley, J.2    Fung, Y.C.B.3
  • 30
    • 34249840947 scopus 로고
    • Properties of a three-dimensioanl Poisson-Voronoi tesselation: A Monte Carlo study
    • Kumar, S., S. K. Kurtz, J. R. Banavar, and M. G. Sharma. Properties of a three-dimensional Poisson-Voronoi tesselation: A Monte Carlo study. J. Stat. Phys. 67:523-551, 1992.
    • (1992) J. Stat. Phys. , vol.67 , pp. 523-551
    • Kumar, S.1    Kurtz, S.K.2    Banavar, J.R.3    Sharma, M.G.4
  • 31
    • 0027624499 scopus 로고
    • Properties of a two-dimensional Poisson-Voronoi tesselation: A Monte-Carlo study
    • Kumar, S., and S. K. Kurtz. Properties of a two-dimensional Poisson-Voronoi tesselation: A Monte-Carlo study. Mater. Charact. 31;55-68, 1993.
    • (1993) Mater. Charact. , vol.31 , pp. 55-68
    • Kumar, S.1    Kurtz, S.K.2
  • 32
    • 0000330240 scopus 로고    scopus 로고
    • Modelling of blood vessel development. Bifurcation pattern and hemodynamics, optimality and allometry
    • Kurz, H., and K. Sandau. Modelling of blood vessel development. Bifurcation pattern and hemodynamics, optimality and allometry. Comments Theor. Biol. 4;261-291, 1997.
    • (1997) Comments Theor. Biol. , vol.4 , pp. 261-291
    • Kurz, H.1    Sandau, K.2
  • 34
    • 0017585237 scopus 로고
    • Methods for the simultaneous measurement of pressure differentials and flows in single unbranched vessels of the microcirculation for rheological studies
    • Lipowsky, H. H., and B. W. Zweifach. Methods for the simultaneous measurement of pressure differentials and flows in single unbranched vessels of the microcirculation for rheological studies. Microvasc. Res. 14:345-361, 1977.
    • (1977) Microvasc. Res. , vol.14 , pp. 345-361
    • Lipowsky, H.H.1    Zweifach, B.W.2
  • 35
    • 0003746585 scopus 로고
    • Interface area, edge length, and number of vertices in crystal aggregates with random nucleation
    • Meijering, J. L. Interface area, edge length, and number of vertices in crystal aggregates with random nucleation. Philips Res. Rep. 8:270-290, 1953.
    • (1953) Philips Res. Rep. , vol.8 , pp. 270-290
    • Meijering, J.L.1
  • 36
    • 0000205972 scopus 로고
    • The physiological principle of minimum work. I. The vascular system and the cost of blood volume
    • Murray, C. D. The physiological principle of minimum work. I. The vascular system and the cost of blood volume. Proc. Natl. Acad. Sci. U.S.A. 12:207-214, 1926.
    • (1926) Proc. Natl. Acad. Sci. U.S.A. , vol.12 , pp. 207-214
    • Murray, C.D.1
  • 37
    • 0038667469 scopus 로고
    • Solvation of large dipoles. I. A molecular dynamics study
    • Neumann, M., F. J. Vesely, O. Steinhauser, and P. Schuster. Solvation of large dipoles. I. A molecular dynamics study. Mol. Phys. 35:841-855, 1978.
    • (1978) Mol. Phys. , vol.35 , pp. 841-855
    • Neumann, M.1    Vesely, F.J.2    Steinhauser, O.3    Schuster, P.4
  • 38
    • 0030380284 scopus 로고    scopus 로고
    • Visualization of computer-generated arterial model trees
    • edited by M. Cerrolaza, D. Jugo, and C. A. Brebbia, Southampton: Computational Mechanics
    • Neumann, F., M. Neumann, R. Karch, and W. Schreiner. Visualization of computer-generated arterial model trees. In: Simulation Modelling in Bioengineering, edited by M. Cerrolaza, D. Jugo, and C. A. Brebbia, Southampton: Computational Mechanics, 1996, pp. 259-268.
    • (1996) Simulation Modelling in Bioengineering , pp. 259-268
    • Neumann, F.1    Neumann, M.2    Karch, R.3    Schreiner, W.4
  • 39
    • 0003760944 scopus 로고    scopus 로고
    • Spatial tessellations: Concepts and applications of voronoi diagrams, second edition
    • Chichester, Wiley
    • Okabe, A., B. Boots, K. Sugihara, and S. N. Chiu. Spatial Tessellations: Concepts and Applications of Voronoi Diagrams, Second Edition, Chichester, Wiley, 1999.
    • (1999)
    • Okabe, A.1    Boots, B.2    Sugihara, K.3    Chiu, S.N.4
  • 41
    • 45949129450 scopus 로고
    • Scaling of blood parameters in mammals
    • Prothero, J. W. Scaling of blood parameters in mammals. Comparative Biochem. Physiol. 67A:649-657, 1980.
    • (1980) Comparative Biochem. Physiol. , vol.67 A , pp. 649-657
    • Prothero, J.W.1
  • 42
    • 0034698013 scopus 로고    scopus 로고
    • A class of flow bifurcation models with lognormal distribution and fractal dispersion
    • Qian, H., and J. B. Bassingthwaighte, A class of flow bifurcation models with lognormal distribution and fractal dispersion. J. Theor. Biol. 205:261-268, 2000.
    • (2000) J. Theor. Biol. , vol.205 , pp. 261-268
    • Qian, H.1    Bassingthwaighte, J.B.2
  • 43
    • 0000612686 scopus 로고
    • Liquid structure and self-diffusion
    • Rahman, A. Liquid structure and self-diffusion. J. Chem. Phys. 45:2584-2592, 1966.
    • (1966) J. Chem. Phys. , vol.45 , pp. 2584-2592
    • Rahman, A.1
  • 44
    • 0000135847 scopus 로고
    • Test of 'randomness' for spatial point patterns
    • Ripley, B. D. Test of 'randomness' for spatial point patterns. J. R. Statist. Soc. B 41:368-374, 1979.
    • (1979) J. R. Statist. Soc. B , vol.41 , pp. 368-374
    • Ripley, B.D.1
  • 46
    • 0001522973 scopus 로고
    • Analysis of the network topology in liquid water and hydrogen sulphide by computer simulation
    • Ruocco, G., M. Sampoli, and R. Vallauri. Analysis of the network topology in liquid water and hydrogen sulphide by computer simulation. J. Chem. Phys. 96:6167-6176, 1992.
    • (1992) J. Chem. Phys. , vol.96 , pp. 6167-6176
    • Ruocco, G.1    Sampoli, M.2    Vallauri, R.3
  • 47
    • 0028070419 scopus 로고
    • Modelling of vascular growth processes: A stochastic biophysical approach to embryonic angiogenesis
    • Sandau, K., and H. Kurz. Modelling of vascular growth processes: A stochastic biophysical approach to embryonic angiogenesis. J. Microsc. 175:205-213, 1994.
    • (1994) J. Microsc. , vol.175 , pp. 205-213
    • Sandau, K.1    Kurz, H.2
  • 48
    • 0027499061 scopus 로고
    • Computer generation of complex arterial tree models
    • Schreiner, W. Computer generation of complex arterial tree models. J. Biomed. Eng. 15:148-149, 1993.
    • (1993) J. Biomed. Eng. , vol.15 , pp. 148-149
    • Schreiner, W.1
  • 49
    • 0027588995 scopus 로고
    • Computer-optimization of vascular trees
    • Schreiner, W., and P. Buxbaum. Computer-optimization of vascular trees. IEEE Trans. Biomed. Eng. 40:482-491, 1993.
    • (1993) IEEE Trans. Biomed. Eng. , vol.40 , pp. 482-491
    • Schreiner, W.1    Buxbaum, P.2
  • 51
    • 0026654958 scopus 로고
    • Basic structure-function relations of the epicardial coronary vascular tree
    • Seiler, C., R. L. Kirkeeide, and K. L. Gould. Basic structure-function relations of the epicardial coronary vascular tree. Circulation 85:1987-2003, 1992.
    • (1992) Circulation , vol.85 , pp. 1987-2003
    • Seiler, C.1    Kirkeeide, R.L.2    Gould, K.L.3
  • 53
    • 84975030700 scopus 로고
    • Quantitative analysis of watershed geomorphology
    • Strahler, A. N. Quantitative analysis of watershed geomorphology. Trans. Am. Geophys. Union 38:913-920, 1957.
    • (1957) Trans. Am. Geophys. Union , vol.38 , pp. 913-920
    • Strahler, A.N.1
  • 54
    • 0003720769 scopus 로고
    • Cambridge, MA: Cambridge University Press
    • Thompson, D. W. On Growth and Form. Cambridge, MA: Cambridge University Press, 1917.
    • (1917) On Growth and Form
    • Thompson, D.W.1
  • 55
    • 0026774222 scopus 로고
    • Branching patterns in the porcine coronary arterial tree. Estimation of flow heterogeneity
    • Van Bavel, E., and J. A. E. Spaan, Branching patterns in the porcine coronary arterial tree. Estimation of flow heterogeneity. Circ. Res. 71:1200-1212, 1992.
    • (1992) Circ. Res. , vol.71 , pp. 1200-1212
    • Van Bavel, E.1    Spaan, J.A.E.2
  • 56
    • 0024368647 scopus 로고
    • Regional myocardial flow heterogeneity explained with fractal networks
    • Van Beek, J. H. G. M., S. A. Roger, and J. B. Bassingthwaighte. Regional myocardial flow heterogeneity explained with fractal networks. Am. J. Physiol. 257:H1670-H1680, 1989.
    • (1989) Am. J. Physiol. , vol.257
    • Van Beek, J.H.G.M.1    Roger, S.A.2    Bassingthwaighte, J.B.3
  • 57
    • 0023825658 scopus 로고
    • Grain size distribution: The lognormal and the gamma distribution functions
    • Vaz, M. F., and M. A. Fortes. Grain size distribution: The lognormal and the gamma distribution functions. Scr. Metall. 22:35-40, 1988.
    • (1988) Scr. Metall. , vol.22 , pp. 35-40
    • Vaz, M.F.1    Fortes, M.A.2
  • 58
    • 84927514013 scopus 로고
    • Nouvelles applications des parametres continus a la theorie des formes quadratiques
    • Voronoi, G. Nouvelles applications des parametres continus a la theorie des formes quadratiques. J. Reine Angew. Math. 134:198-287, 1908.
    • (1908) J. Reine Angew. Math. , vol.134 , pp. 198-287
    • Voronoi, G.1
  • 60
    • 0030932272 scopus 로고    scopus 로고
    • A general model for the origin of allometric scaling laws in biology
    • West, G. B., J. H. Brown, and B. J. Enquist. A general model for the origin of allometric scaling laws in biology. Science 276:122-126, 1997.
    • (1997) Science , vol.276 , pp. 122-126
    • West, G.B.1    Brown, J.H.2    Enquist, B.J.3
  • 61
    • 0023054712 scopus 로고
    • Relation of branching angles to optimality for four cost principles
    • Woldenberg, M. J., and K. Horsfield. Relation of branching angles to optimality for four cost principles. J. Theor. Biol. 122:187-204, 1986.
    • (1986) J. Theor. Biol. , vol.122 , pp. 187-204
    • Woldenberg, M.J.1    Horsfield, K.2
  • 62
    • 0017152558 scopus 로고
    • Optimality principles in arterial branching
    • Zamir, M. Optimality principles in arterial branching. J. Theor. Biol. 62:227-251, 1976.
    • (1976) J. Theor. Biol. , vol.62 , pp. 227-251
    • Zamir, M.1


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