Fractal models of circulatory system. Symmetrical and asymmetrical approach comparison

Chaos, Solitons and Fractals

Volumn 24, Issue 3, 2005, Pages 707-715

  Gabryś, Elzbieta ^a   Rybaczuk, Marek ^a   Kȩdzia, Alicja ^b  

^a WROCLAW UNIVERSITY OF TECHNOLOGY   (Poland)

^b WROCLAW MEDICAL UNIVERSITY   (Poland)

Author keywords

[No Author keywords available]

Indexed keywords

BIFURCATION (MATHEMATICS); BLOOD VESSELS; DISEASES; HEMODYNAMICS; MATHEMATICAL MODELS; OPTIMIZATION; TREES (MATHEMATICS);

BIOLOGICAL STRUCTURES; CIRULATORY SYSTEMS; FRACTAL MODELS; TREE GENERATION;

FRACTALS;

EID: 12244313919     PISSN: 09600779     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.chaos.2004.09.087     Document Type: Article

References (28)

1. Boryczko K. Computational model of blood dynamics in capillary vessels, Doctoral thesis, 2003
2. M.A. Changizi, and C. Cherniak Modeling the large-scale geometry of human coronary arteries Can. J. Physiol. Pharmacol. 78 2000 603 611
3. Cieślicki K. Hydrodynamiczne uwarunkowania kra̧żenia mózgowego, AOW EXIT Warsaw, 2001
4. D. Cohn Optimal systems I: the vascular system Bull. Math. Biophys. 16 1954 59 74
5. D. Cohn Optimal systems II: the vascular system Bull. Math. Biophys. 17 1955 219 227
6. Kȩdzia A, Rybaczuk M, Dymecki J. The fractal analysis of subdural haematoma. Folia Neuropathol 2001;39(3):203-7
7. H. Kurz, and K.S. Sandau Modeling of blood vessel development-bifurcation pattern and hemodynamics, optimality and allometry Comments Theor. Biol. 4 1997 261 281
8. L.S. Liebovitch, and T. Toth A fast algorithm to determine fractal dimensions by box counting Physics Letters A 141 8,9 1989 386 390
9. B. Mandelbrot The fractal geometry of nature 1977 Freeman
10. C.D. Murray The physiological principle of minimum work I. The vascular system and the cost of the blood volume Proc. Natl. Adac. Sci. USA 12 1926 207 214
11. C.D. Murray The physiological principle of minimum work applied to the angle of branching of arteries J. Gen. Physiol. 9 1926 835 841
12. Nonnenmacher TF. Fractal in biology and medicine, 1993
13. R. Rosen Optimal principles in biology 1967 Butterworths London
14. M. Rybaczuk, A. Kȩdzia, and E. Błaszczyk Fractal description of cerebellum surface during fetal period Folia Morphol. 55 1996 434 436
15. M. Rybaczuk, A. Kȩdzia, and R. Andrzejak Fractal dimension of human brain cortex vessel during the fetal period Med. Sci. Monit. 8 3 2002
16. M. Rybaczuk, A. Kȩdzia, and L. Paradowski Fractal characteristic of brain vessel microangioarchitecture during the fetal period Med. Sci. Monit. 8 8 2002 MT145 MT152 (in polish)
17. W. Schreiner Structural quantification and bifurcation symmetry in arterial tree models generated by constrained constructive optimization J. Theor. Biol. 180 1996 161 174
18. W. Schreiner, F. Neumann, and R. Karch Shear stress distribution in arterial tree models generated by constrained constructive optimization J. Theor. Biol. 198 1999 27 45
19. W. Schreiner, and R. Karch Heterogeneous perfusion is a consequence of uniform shear stress in optimized arterial tree models J Theor Biol 220 2003 285 301
20. N. Suwa, H. Fukasawa, and Y. Sasaki Estimation of intravascular blood pressure gradient by mathematical analysis of arterial casts Tohoku J. Exp. Med. 79 1963 168 198
21. Traczyk W, Trzebski A. Fizjologia człowieka z elementami fizjologii stosowanej i klinicznej PZWL, 2001 (in Polish)
22. H. Uylings Optimization of diameters and bifurcation angles in lung and vascular tree structures Bull. Math. Biol. 39 1977 509 520
23. S. Weinbaum, and L.M. Jiji Theory and experiment for the effect of vascular microstructure on surface tissue heat transfer-Part I: Anatomical foundation and model conceptualization Trans. ASME J. Biomed. Eng. 106 1984 321 330
24. M. Zamir Optimal principles in arterial branching J. Theor. Biol. 62 1976 227 251
25. M. Zamir The role of shear forces in arterial branching J. Gen. Physiol. 67 1976 213 222
26. M. Zamir, and N. Braun Arterial branching in various parts of the cardiovascular system Am. J. Anat. 163 1982 295 307
27. M. Zamir The branching structure of arterial trees Comm. Theor. Biol. 91 1988 15 37
28. M. Zamir Distributing and delivering vessels of the human heart J. Gen. Physiol. 91 1988 725 735