Fractal analysis of the vascular tree in the human retina

Annual Review of Biomedical Engineering

Volumn 6, Issue , 2004, Pages 427-452

  Masters, Barry R ^a  

^a UNIVERSITY OF BERN   (Switzerland)

Author keywords

Bronchial tree; Eye; Fractal structures; Fractals; Human bronchial tree; Human lung; Murray Principle; Optimal vascular tree; Retinal blood vessel patterns; Retinal circulation

Indexed keywords

ANGIOGENESIS; BRONCHUS; EMBRYO DEVELOPMENT; EYE DEVELOPMENT; FRACTAL ANALYSIS; HUMAN; RETINA BLOOD FLOW; RETINA BLOOD VESSEL; REVIEW; STATISTICAL MODEL;

ANIMALS; BIOMECHANICS; BRONCHI; DIFFUSION; FRACTALS; HUMANS; LUNG; MODELS, ANATOMIC; RETINA; TISSUE ENGINEERING;

BRONCHUS;

EID: 4544298453     PISSN: 15239829     EISSN: None     Source Type: Book Series    
DOI: 10.1146/annurev.bioeng.6.040803.140100     Document Type: Review

References (93)

1. Wong D. 1991. The fundus camera. In Duane's Clinical Ophthalmology, eds. W Tasman, EA Jaeger, 61:1-14. Philadelphia, PA: J.B. Lippincott
2. Rashevsky N. 1960. Mathematical Biophysics. Physico-Mathematical Foundations of Biology. New York: Dover Publ. 3rd ed.
3. West BJ. 1990. Fractal Physiology and Chaos in Medicine. Singapore: World Sci.
4. Schroeder M. 1991. Fractals, Chaos, Power Laws: Minutes from an Infinite Paradise. San Francisco: W.H. Freeman. 429 pp.
5. Bassingthwaighte JB, Liebovitch LS, West BJ. 1994. Fractal Physiology. New York: Oxford Univ. Press
6. Iannaccone PM, Khokha M, eds. 1996. Fractal Geometry in Biological Systems, An Analytical Approach. Boca Raton, FL: CRC Press. 360 pp.
7. Stanley HE, Amaral LAN, Buldyrev SV, Goldberger AL, Havlin S, et al. 1996. Scaling and universality in living systems. Fractals 4:427-51
8. Smith TG Jr, Marks WB, Lange GD, Sheriff WH Jr, Neale EA. 1989. A fractal analysis of cell images. J. Neurosci. Methods 27:173-80
9. Caserta F, Stanley HE, Eldred WD, Daccord G, Hausman RE, Nittmann J. 1990. Physical mechanisms underlying neurite outgrowth: a quantitative analysis of neuronal shape. Phys. Rev. Lett. 64:95-98
10. Porter R, Ghosh S, Lange GD, Smith TG Jr. 1991. A fractal analysis of pyramidal neurons in mammalian motor cortex. Neurosci. Lett. 130:112-16
11. Reichenbach A, Siegel A, Senitz D, Smith TGJr. 1992. A comparative fractal analysis of various mammalian astroglial cell types. Neuroimage 1:69-77
12. Smith TG Jr, Behar TN, Lange GD, Marks WB, Sheriff WH Jr. 1991. A fractal analysis of cultured rat optic nerve glial growth and differentiation. Neuroscience 41:159-66
13. Goldberger AL, Peng C-K, Hausdorff J, Mietus J, Havlin S, Stanley HE. 1996. Fractals and the heart. See Ref. 6, pp. 249-66
14. Einstein AJ, Wu H-S, Gil G. 1998. Self-affinity and lacunarity of chromatin texture in benign and malignant breast epithelial cell nuclei. Phys. Rev. Lett. 80:397-400
15. Peiss J, Verlande M, Ameling W, Gunther RW 1996. Classification of lung tumors on chest radiographs by fractal texture analysis. Invest. Radiol. 31:625-29
16. Floyd CE Jr, Patz EF, Lo JY, Vittitoe NF, Stambaugh LW. 1996. Diffuse nodular lung disease on chest radiographs: a pilot study of characterization by fractal dimension. Am. J. Radiol. 167:1185-87
17. West BJ, Bhargava V, Goldberger AL. 1986. Beyond the principle of similitude: renormalization in the bronchial tree. J Appl. Physiol. 60:189-97
18. Uppaluri R, Hoffman EA, Sonka M, Hartley PG, Hunninghake GW, McLennan G. 1999. Computer recognition of regional lung disease patterns. Am. J. Respir. Crit. Care Med. 160:648-54
19. Weibel ER. 1963. Morphometry of the Human Lung. Berlin: Springer-Verlag
20. Horsfield K, Cumming G. 1967. Angles of branching and diameters of branches in the human bronchial tree. Bull. Math. Biophys. 29:245-59
21. Weibel ER. 1987. Scaling of structural and functional variables in the respiratory system. Annu. Rev. Physiol. 49:147-59
22. Horsfield K, Cumming G. 1968. Morphology of the bronchial tree in man. J. Appl. Physiol. 24:373-83
23. Horsfield K, Dart G, Olson DE, Filley GF, Cumming G. 1971. Models of the human bronchial tree. J. Appl. Physiol. 31:207-17
24. Horsfield K. 1978. Morphometry of the small pulmonary arteries in man. Circ. Res. 42:593-97
25. Sernetz M, Justen M, Jestczemski F. 1995. Dispersive fractal characterization of kidney arteries by three-dimensional mass-radius-analysis. Fractals 3:879-91
26. Masters BR, Family F, Platt DE. 1989. Fractal analysis of human retinal vessels. Biophys. J. 55:575a (Suppl.)
27. Masters BR. 1989. Fractal analysis of human retinal vessels. SPIE Proc. 1357:250-56
28. Masters BR. 1989. Fractal analysis of human retina blood vessel patterns: developmental aspects. Int. Symp. Ocular Circ. Neovascularization, 2nd, Wilmer Inst., Johns Hopkins Med. Inst., p. 45. Baltimore, MD
29. Tsonis AA, Tsonis PA. 1987. Fractals: a new look at biological shape and patterning. Perspect. Biol. Med. 30:355-60
30. Wornell GW. 1998. Fractal signals. In The Digital Signal Processing Handbook, ed. VK Madisetti, DB Smith, pp. 73-1-13. Boca Raton, FL: CRC Press
31. Goldberger AL, Bhargava V, West BJ, Mandell AJ. 1985. On a mechanism of cardiac electrical stability: the fractal hypothesis. Biophys. J. 48:525-28
32. Liebovitch LS. 1996. Ion channel kinetics. See Ref. 6, pp. 31-56
33. Folkman J. 1976. The vascularization of tumors. Sci. Am. 234:58-73
34. Folkman J, Haudenschild C. 1980. Angiogenesis in vitro. Nature 288:551-56
35. Yancopoulos GD, Klagsbrun M, Folkman J. 1998. Vasculogenesis, angiogenesis, and growth factors: ephrins enter the fray at the border. Cell 93:661-64
36. Masters BR. 1990. Fractal analysis of human retinal blood vessel patterns: developmental and diagnostic aspects. In Noninvasive Diagnostic Techniques in Ophthalmology, ed. BR Masters, pp. 515-27. New York: Springer Verlag
37. Landini G, Misson GP. 1993. Simulation of corneal neovascularization by inverted diffusion limited aggregation. Invest. Ophthalmol. Vis. Sci. 34:1872-76
38. Thompson DW. 1942. On Growth and Form. Cambridge: Cambridge Univ. Press
39. Stanley HE, Ostrowsky N, eds. 1986. On Growth and Form. Dordrecht: Martinus Nijhoff
40. West GB, Brown JH, Enquist BJ. 1997. A general model for the origin of allometric scaling laws in biology. Science 276:122-26
41. Cook TA. 1979. The Curves of Life. New York: Dover Publ.
42. Ball P. 1999. The Self-Made Tapestry: Pattern Formation in Nature. New York: Oxford Univ. Press
43. Livio M. 2002. The Golden Ratio: The Story of Phi, The World's Most Astonishing Number. New York: Random House
44. Mandelbrot BB. 1967. How long is the coast of Britain? Statistical self-similarity and fractional dimension. Science 156:636-38
45. Mandelbrot BB. 1982. The Fractal Geometry of Nature. San Francisco: WH Freeman. 460 pp.
46. Sander LM. 1987. Fractal Growth. Sci. Am. 256:94-100
47. Ben-Jacob E, Garik P. 1990. The formation of patterns in non-equilibrium growth. Nature 343:523-30
48. Peitgen H-O, Jürgens H, Saupe D. 1992. Chaos and Fractals. New Frontiers of Science. Berlin: Springer-Verlag. 984 pp.
49. Feder J. 1988. Fractals. New York: Plenum
50. Falconer K. 1997. Techniques of Fractal Geometry. New York: Wiley
51. Pietronero L, Erzan A, Evertsz C. 1988. Theory of Laplacian fractals: diffusion limited aggregation and dielectric breakdown model. Physica A 151:207-45
52. Vicsek T. 1992. Fractal Growth Phenomena. Singapore: World Sci. 488 pp. 2nd ed.
53. Landini G. 1996. Applications of fractal geometry in pathology. See Ref. 6, pp. 205-46
54. Bittner HR, Wlczek P, Sernetz M. 1989. Characterization of fractal biological objects by image analysis. Acta Stereol. 8:31-40
55. Bunde A, Havlin S, eds. 1991. Fractals and Disordered Systems. New York: Springer-Verlag
56. Weitz DA, Oliveria M. 1984. Fractal structures formed by kinetic aggregation of aqueous gold colloids. Phys. Rev. Lett. 52:1433-36
57. Witten TA, Sander LM. 1981. Diffusion-limited aggregation, a kinetic phenomena. Phys. Rev. Lett. 47:1400-3
58. Meakin P. 1986. A new model for biological pattern formation. J. Theor. Biol. 118:101-13
59. Ryan SJ. 1989. Retina. St. Louis: Mosby. Vols. 1, 2, 3
60. Hogan MJ, Alvarado JA, Weddel JE. 1971. Histology of the Human Eye. Philadelphia, PA: Saunders
61. Klein GJ, Baumgartner RH, Flower RW. 1990. An image processing approach to characterizing choroidal blood flow. Invest. Ophthalmol. 31:23-31
62. Lambrou GN. 1993. Choroidal Plerometry: A Method for Evaluating the Choroidal Blood Supply in Clinical Practice. The Hague: Kugler Publ.
63. Lutty GA, McLeod DS. 2003. Retinal vascular development and oxygen-induced retinopathy: a role for adenosine. Prog. Retin. Eye Res. 22:95-111
64. Gariano RF. 2002. Cellular mechanisms in retinal vascular development. Prog. Retin. Eye Res. 22:295-306
65. Ozanics V, Jakobiec FA. 1982. Prenatal development of the eye and its adnexa. In Ocular Anatomy, Embryology and Teratology, ed. FA Jakobiec, pp. 11-96. Philadelphia, PA: Harper Row
66. Kretzer FL, Hittner HM. 1988. Retinopathy of prematurity: clinical implications of retinal development. Arch. Dis. Child. 63:1151-67
67. Maxwell PH, Ratcliffe PJ. 2002. Oxygen sensors and angiogenesis. Cell Develop. Biol. 13:29-37
68. Masters BR, Platt DF. 1989. Development of human retinal vessels: a fractal analysis. Invest. Ophthalmol. Vis. Sci. 30:391 (Suppl.)
69. Family F, Masters BR, Platt DE. 1989. Fractal pattern formation in human retinal vessels. Physica D 38:98-103
70. Daxer A. 1993. Fractal analysis of new vessels in diabetic retinopathy. Invest. Ophthalmol. Vis. Sci. 34(Suppl.):718
71. Landini G, Misson GP, Murray P. 1993. Fractal analysis of the normal human retinal fluorescein angiogram. Curr. Eye Res. 12:23-27
72. Mainster MA. 1990. The fractal properties of retinal vessels: embryological and clinical implications. Eye 4:235-41
73. Masters BR, Sernetz M, Wlczek P. 1992. Image analysis of human retinal blood vessels and their characterization as fractals. Acta Stereol. 11(Suppl. 1):355-60
74. Masters BR. 1994. Fractal analysis of normal human retinal blood vessels. Fractals 2:103-10
75. Masters BR. 1991. Fractal patterns in the human retina and their physiological correlates. Proc. SPIE 1380:218-26
76. Fleury V, Schwartz L. 1999. Diffusion limited aggregation from shear stress as a simple model of vasculogenesis. Fractals 7:33-39
77. Fleury V, Schwartz L. 2000. Modelisation of 3-D microvasculature by interlaced diffusion limited aggregation. Fractals 8:255-59
78. Kyriacos S, Nekka F, Cartilier L, Vico P. 1997. Insights into the formation process of the retinal vasculature. Fractals 5:615-24
79. Sun T, Meakin P, Jossang T. 1995. Minimum energy dissipation and fractal structures of vascular systems. Fractals 3:123-53
80. Wong TY, Klein R, Klein BEK, Tielsch JM, Hubbard L, Nieto FJ. 2001. Retinal microvascular abnormalities and their relationship with hypertension, cardiovascular disease, and mortality. Surv. Ophthalmol. 46:59-80
81. Obert M. 1993. Numerical estimates of the fractal dimension D and the lacunarity L by the mass radius relation. Fractals 1:711-21
82. Landini G, Murray P, Misson GP. 1995. Local connected fractal dimensions and lacunarity analysis of 60° fluorescein angiograms. Invest. Ophthalmol. Vis. Sci. 36:2749-55
83. Meinhardt H. 1982. Models of Biological Pattern Formation. London: Academic. 225 pp.
84. MacDonald N. 1983. Trees and Networks in Biological Models. New York: Wiley. 215 pp.
85. LaBarbera M. 1990. Principles of design of fluid transport systems in zoology. Science 249:992-1000
86. Murray CD. 1926. The physiological principle of minimum work. I. The vascular system and the cost of blood volume. Proc. Natl. Acad. Sci. USA. 12:207-14
87. Murray CD. 1926. The physiological principle of minimum work applied to the angle of branching arteries. J. Gen. Physiol. 9:835-41
88. Zamir M, Medeiros JS, Cunningham TK. 1979. Arterial bifurcations in the human retina. J. Gen. Physiol. 74:537-48
89. Zamir M. 2001. Fractal dimensions and multifractility in vascular branching. J. Theor. Biol. 212:183-90
90. Sherman TF, Popel AS, Koller A, Johnson PC. 1989. The cost of departure from optimal radii in microvascular networks. J. Theor. Biol. 136:245-65
91. Mayrovitz HN, Roy J. 1983. Microvascular blood flow: evidence indicating a cubic dependence on arteriolar diameter. Am. J. Physiol. Heart Circ. Physiol. 245(14):H1031-38
92. Zamir M, Medeiros JA, Cunningham TK. 1979. Arterial bifurcations in the human retina. J. Gen. Physiol. 74:537-48
93. Metzger RJ, Krasnow MA 1999. Genetic control of branching morphogenesis. Science 284:1635-39