A Gibbs point field model for the spatial pattern of coronary capillaries

Physica A: Statistical Mechanics and its Applications

Volumn 369, Issue 2, 2006, Pages 599-611

  Karch, R ^a   Neumann, M ^b   Neumann, F ^a   Ullrich, R ^a   Neumuller J ^a   Schreiner, W ^a  

^a MEDICAL UNIVERSITY OF VIENNA   (Austria)

^b INSTITUT FÜR EXPERIMENTALPHYSIK   (Austria)

Author keywords

Capillaries; Cardiomyopathy; Computer simulation; One component plasma; Point field process

Indexed keywords

BIOLOGICAL ORGANS; CAPILLARITY; COMPUTER SIMULATION; DIFFUSION; ELECTROSTATICS; GIBBS FREE ENERGY; MATHEMATICAL MODELS; OXYGEN SUPPLY; PHYSIOLOGY; PLASMAS; POISSON EQUATION; POTENTIAL ENERGY; THERMAL EFFECTS; TISSUE;

CAPILLARIES; CARDIOMYOPATHY; ONE-COMPONENT PLASMAS; POINT FIELD PROCESSES;

HISTOLOGY;

EID: 33745684691     PISSN: 03784371     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physa.2006.02.018     Document Type: Article

References (43)

1. Hudlicka O., Brown M., and Egginton S. Angiogenesis in skeletal and cardiac muscle. Physiol. Rev. 72 2 (1992) 369-417
2. Rakusan K., Flanagan M.F., Geva T., Southern J., and Van Praagh R. Morphometry of human coronary capillaries during normal growth and the effect of age in left ventricular pressure-overload hypertrophy. Circulation 86 1 (1992) 38-46
3. Krogh A. The number and distribution of capillaries in muscles with calculations of the oxygen pressure head necessary for supplying the tissue. J. Physiol. (London) 52 (1919) 409-415
4. Hoofd L. Calculation of oxygen pressures in tissue with anisotropic capillary orientation. I. Two-dimensional analytical solution for arbitrary capillary characteristics. Math. Biosci. 129 1 (1995) 1-23
5. Goldman D., and Popel A.S. A computational study of the effect of vasomotion on oxygen transport from capillary networks. J. Theor. Biol. 209 2 (2001) 189-199
6. Popel A.S. Theory of oxygen transport to tissue. Crit. Rev. Biomed. Eng. 17 3 (1989) 257-321
7. Pittman R.N. Influence of microvascular architecture on oxygen exchange in skeletal muscle. Microcirculation 2 1 (1995) 1-18
8. Gavin J.B., Maxwell L., and Edgar S.G. Microvascular involvement in cardiac pathology. J. Mol. Cell. Cardiol. 30 12 (1998) 2531-2540
9. Pisani B., Taylor D.O., and Mason J.W. Inflammatory myocardial diseases and cardiomyopathies. Am. J. Med. 102 5 (1997) 459-469
10. Calabrese F., and Thiene G. Myocarditis and inflammatory cardiomyopathy: microbiological and molecular biological aspects. Cardiovasc. Res. 60 1 (2003) 11-25
11. Diggle P.J. Statistical Analysis of Spatial Point Patterns (1983), Academic Press, London
12. Cressie N.A.C. Statistics for Spatial Data. revised ed. (1993), Wiley, New York
13. Stoyan D., Kendall W.S., and Mecke J. Stochastic Geometry and its Applications. second ed. (1995), Wiley, Chichester
14. Stoyan D. Basic ideas of spatial statistics. In: Mecke K.R., and Stoyan D. (Eds). Statistical Physics and Spatial Statistics, Lecture Notes in Physics vol. 554 (2000), Springer, Berlin 3-21
15. Ripley B.D. Tests of 'randomness' for spatial point patterns. J. R. Stat. Soc. B 41 3 (1979) 368-374
16. Karch R., Neumann F., Ullrich R., Neumüller J., Podesser B.K., Neumann M., and Schreiner W. The spatial pattern of coronary capillaries in patients with dilated. ischemic, or inflammatory cardiomyopathy, Cardiovasc. Pathol. 14 3 (2005) 135-144
17. Jancovici B. Exact results for the two-dimensional one-component plasma. Phys. Rev. Lett. 46 6 (1981) 386-388
18. Caillol J.M., Levesque D., Weis J.J., and Hansen J.P. A Monte Carlo study of the classical two-dimensional one-component plasma. J. Stat. Phys. 28 2 (1982) 325-349
19. de Leeuw S.W., and Perram J.W. Statistical mechanics of two-dimensional Coulomb systems. II. The two-dimensional one-component plasma. Physica A 113 3 (1982) 546-558
20. Okabe A., Boots B., Sugihara K., and Chiu S.N. Spatial Tessellations: Concepts and Applications of Voronoi Diagrams. second ed. (1999), Wiley, Chichester
21. Hermann H., Wendrock H., and Stoyan D. Cell-area distributions of planar Voronoi mosaics. Metallography 23 3 (1989) 189-200
22. C.B. Barber, H. Huhdanpaa, Qhull version 2.6, The Geometry Center, University of Minnesota, Minneapolis, 1998 〈http://www.qhull.org/〉.
23. Hansen J.P., and McDonald I.R. Theory of Simple Liquids. second ed. (1986), Academic Press, London
24. Allen M.P., and Tildesley D.J. Computer Simulation of Liquids (1987), Clarendon Press, Oxford
25. Ogata Y., and Tanemura M. Likelihood analysis of spatial point patterns. J. R. Stat. Soc. B 46 3 (1984) 496-518
26. Popel A.S. Analysis of capillary-tissue diffusion in multicapillary systems. Math. Biosci. 39 3-4 (1978) 187-211
27. Hsu R., and Secomb T.W. A Green's function method for analysis of oxygen delivery to tissue by microvascular networks. Math. Biosci. 96 1 (1989) 61-78
28. Berg H.C. Random Walks in Biology. expanded ed. (1993), Princeton University Press, Princeton
29. Brush S.G., Sahlin H.L., and Teller E. Monte Carlo study of one-component plasma. I. J. Chem. Phys. 45 6 (1966) 2102-2118
30. Hansen J.P. Molecular-dynamics simulation of Coulomb systems in two and three dimensions. In: Ciccotti G., and Hoover W.G. (Eds). Proceedings of the 97th International School of Physics "Enrico Fermi" on Molecular-Dynamics Simulations of Statistical-Mechanical Systems (1986), North-Holland, Amsterdam 89-129
31. M. Abramowitz, I.A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, Ninth printing, Dover Publications, New York, 1972.
32. Metropolis N., Rosenbluth A.W., Rosenbluth M.N., Teller A.H., and Teller E. Equation of state calculations by fast computing machines. J. Chem. Phys. 21 6 (1953) 1087-1092
33. Egginton S. Morphometric analysis of tissue capillary supply. Adv. Comp. Environ. Physiol. 6 (1990) 73-141
34. Hoofd L., Turek Z., Kubat K., Ringnalda B.E.M., and Kazda S. Variability of intercapillary distance estimated on histological sections of rat heart. Adv. Exp. Med. Biol. 191 (1985) 239-247
35. H. Kurz, K. Sandau, Modelling of blood vessel development. Bifurcation pattern and hemodynamics, optimality and allometry, Comment. Theor. Biol. 4(4) (1997) 261-291.
36. Duyckaerts C., and Godefroy G. Voronoi tessellation to study the numerical density and the spatial distribution of neurones. J. Chem. Neuroanat. 20 1 (2000) 83-92
37. Levesque D., Weis J.J., and Lebowitz J.L. Charge fluctuations in the two-dimensional one-component plasma. J. Stat. Phys. 100 1-2 (2000) 209-222
38. Turek Z., and Rakusan K. Lognormal distribution of intercapillary distance in normal and hypertrophic rat heart as estimated by the method of concentric circles: its effect on tissue oxygenation. Pflügers Arch. 391 (1981) 17-21
39. Turek Z., Hoofd L., and Rakusan K. Myocardial capillaries and tissue oxygenation. Can. J. Cardiol. 2 2 (1986) 98-103
40. Carmeliet P. Angiogenesis in health and disease. Nat. Med. 9 6 (2003) 653-660
41. Zou G., and Wu H. Nearest-neighbor distribution of interacting biological entities. J. Theor. Biol. 172 4 (1995) 347-353
42. Gamba A., Ambrosi D., Coniglio A., de Candia A., Di Talia S., Giraudo E., Serini G., Preziosi L., and Bussolino F. Percolation, morphogenesis, and burgers dynamics in blood vessels formation. Phys. Rev. Lett. 90 11 (2003) 118101
43. Abraham D., Hofbauer R., Schafer R., Blumer R., Paulus P., Miksovsky A., Traxler H., Kocher A., and Aharinejad S. Selective downregulation of VEGF-A(165), VEGF-R(1), and decreased capillary density in patients with dilative but not ischemic cardiomyopathy. Circ. Res. 87 8 (2000) 644-647