Corneal vascularisation and its relation to the physical properties of the tissue: a fractal analysis

References

• Klintworth G. K., Burger P. C. Neovascularisation of the cornea: current concepts of its pathogenesis. Int. Ophthalmol. Clin. 1983; 23: 27–39
   PubMedGoogle Scholar
• Klintworth G. K. The contribution of morphology to our understanding of the pathogenesis of experimentally produced corneal vascularisation. Invest. Ophthalmol. Vis. Sci. 1977; 16: 281–285
   PubMed Web of Science ®Google Scholar
• Gimbrone M. A., Cotran R. S., Folkman J. Tumor growth neovascularisation: an experimental model using rabbit cornea. J. Natl. Cancer. Inst. 1974; 52: 413–427
   PubMed Web of Science ®Google Scholar
• Landini G., Misson G. Simulation of corneal neovascularisation by inverted diffusion limited aggregation. Invest. Ophthalmol. Vis. Sci. 1993; 34: 1872–1875
   PubMed Web of Science ®Google Scholar
• Mandelbrot B. B. The fractal geometry of nature. Freeman, New York 1983
   Google Scholar
• Masters B. R., Platt D. E. Development of human retinal vessels: a fractal analysis. Invest. Ophthalmol. Vis. Sci. 1989; 30: 391
   Google Scholar
• Obert M., Pfeifer P., Sernetz M. Microbial growth patterns described by fractal geometry. J. Bacteriol. 1990; 172: 1180–1185
   PubMed Web of Science ®Google Scholar
• McNamee J. E. Fractal character of pulmonary microvascular permeability. Ann. Biomed. Eng. 1990; 18: 123–133
   PubMed Web of Science ®Google Scholar
• Masters B. R. Fractal analysis of human retinal blood vessel patterns: developmental and diagnostic aspects. Noninvasive diagnostic techniques in ophthalmology., B. R. Masters. Springer Verlag, New York 1990; 515–527
   Google Scholar
• Masters B. R., Sernetz M., Wiczek P. Image analysis of human retinal blood vessels and their characterisation as fractals. Acta Stereol. 1992; 11: 355–360
   Google Scholar
• Family F., Masters B. R., Platt D. E. Fractal pattern formation in human retinal vessels. Physica D 1989; 38: 98–103
   Web of Science ®Google Scholar
• Mainster M. A. The fractal properties of retinal vessels: embryological and clinical implications. Eye 1990; 4: 235–241
   PubMed Web of Science ®Google Scholar
• Daxer A. Fractals and retinal vessels. Lancet 1992; 339: 618
   PubMed Web of Science ®Google Scholar
• Daxer A. The fractal geometry of proliferative diabetic retinopathy: implications for the diagnosis and the process of retinal vasculogenesis. Curr. Eye Res. 1993; 12: 1103–1109
   PubMed Web of Science ®Google Scholar
• Daxer A. Characterisation of the neovascularisation process in diabetic retinopathy by means of fractal geometry: diagnostic implications. Graefes Arch. Clin. Exp. Ophthalmol. 1993; 231: 681–686
   PubMed Web of Science ®Google Scholar
• Liebovitch L. S. The fractal random telegraph signal: analysis and application. Ann. Biomed. Eng. 1988; 16: 483–494
   PubMed Web of Science ®Google Scholar
• Morse D. R., Lawton J. H., Dodson M. M., Williamson M. H. Fractal dimension of vegetation and the distribution of arthropod body lengths. Nature 1985; 314: 731–733
   Web of Science ®Google Scholar
• Meakin P. A new model for biological pattern formation. J. Theor. Biol. 1986; 118: 101–113
   PubMed Web of Science ®Google Scholar
• Smith T. G., Marks W. B., Lange G. D., Sheriff W. H., Neale E. A. A fractal analysis of cell images. J. Neurosci. Meth. 1989; 27: 173–180
   PubMed Web of Science ®Google Scholar
• Vicsek T. Fractal growth phenomena. World Scientific, Singapore 1989
   Google Scholar
• Ahorony A. Fractal growth. Fractals and disordered systems., A. Bunde, S. Havlin. Springer Verlag, Berlin 1991; 153–173
   Google Scholar
• Bunde A., Havlin S. Percolation I and II. Fractals and disordered systems., A. Bunde, S. Havlin. Springer Verlag, Berlin 1991; 51–149
   Google Scholar
• Straub W., Köhler U. Krankheiten der Hornhaut. Lehrbuch der Augenheilkunde., T. Axenfeld, H. Pau. Fischer, Stuttgart 1992; 237–238
   Google Scholar
• Witten T. A., Sander L. M. Diffusion-limited aggregation. Phys. Rev. B 1983; 27: 5686–5697
   Web of Science ®Google Scholar
• Casserta F., Stanley H. E., Eldred W. D., Daccord G., Hausman R. E., Nittman J. Physical mechanisms underlying neurite outgrowth: a quantitative analysis of neuronal shape. Phys. Rev. Lett. 1990; 64: 95–98
   PubMed Web of Science ®Google Scholar
• Guyton A. C. Physics of blood, blood flow, and pressure: Hemodynamics. Textbook of medical physiology., A. C. Guyton. WB Saunders, Philadelphia 1981; 206–218
   Google Scholar
• Feder J. Fractals. Plenum Press, New York 1988; 104–149
   Google Scholar
• Maurice D. M., Zauberman H., Michaelson I. C. The stimulus to neovascularisation in the cornea. Exp. Eye Res. 1966; 5: 168–184
   PubMed Web of Science ®Google Scholar
• Gray's Anatomy 36th Edition, P. L. Williams, R. Warwick. Churchill Livingstone, London 1980
   Google Scholar
• Fratzl P., Daxer A. Structural transformation of collagen fibrils in corneal stroma during drying: an X-ray scattering study. Biophys. J. 1993; 64: 1210–1214
   PubMed Web of Science ®Google Scholar
• Benedek G. B. Theory of transparency of the eye. Appl. Opt. 1971; 10: 459–473
   PubMed Web of Science ®Google Scholar
• Eliason J. A. Leucocytes and experimental corneal vascularisation. Invest. Ophthalmol. Vis. Sci. 1978; 17: 1087–1095
   PubMed Web of Science ®Google Scholar
• Robins S. L., Cotran R. S., Cumar V. Inflamation and repair. Pathologic basis of disease., S. L. Robins, R. S. Cotran, V. Kumar. WB Saunders, Philadelphia 1984; 40–84
   Google Scholar
• Lin M. T., Chen Y. Effect of copper ion on collagenase release. Its implication in corneal neovascularisation. Invest. Ophthalmol. Vis. Sci. 1992; 33: 558–563
   PubMed Web of Science ®Google Scholar
• Stark C. P. An invasion percolation model of drainage network evolution. Nature 1991; 352: 423–425
   Web of Science ®Google Scholar
• Carey D. J. Control of growth and differentiation of vascular cells by extracellular matrix proteins. Ann. Rev. Physiol. 1991; 53: 161–177
   PubMed Web of Science ®Google Scholar
• Montesano R., Orci L., Vassalli P. In vitro rapid organisation of endothelial cells into capillary-like networks is promoted by collagen matrices. J. Cell. Biol. 1983; 97: 1648–1652
   PubMed Web of Science ®Google Scholar
• Nakayasu K., Hayashi N., Sato N. Formation of capillary-like tubes by vascular endothelial cells cocultivated with keratocytes. Invest. Ophthalmol. Vis. Sci. 1992; 33: 3050–3057
   PubMed Web of Science ®Google Scholar
• Klagsbrun M., D'Amore P. A. Regulators of angiogenesis. Ann. Rev. Physiol. 1991; 53: 217–239
   PubMed Web of Science ®Google Scholar