A model of growing vascular structures.

Increasing attention is being paid to the configuration and development of vascular structures and their possible correlations with physiological events. The study of angiogenesis in normal and pathological states as well as in embryo and adult has provided new insights into the mechanism of vessel growth and organization of the vasculature. Various mathematical branching models have been developed. These constructions are mainly geometrical and only involve a branching phenomenon. We propose the use of a deterministic non-linear model based on physiological laws and hydrodynamics. Growth, branching and anastomosis, the three actual main events occurring in vascular growth, are included in this model. Space growth, including cells and vessels, is defined by a decreasing transformation. Space density and the length of new sprouts are controlled by a set of parameters. The conditions on these parameters are well established, which allows the production of realistic patterns.

[1]  Benoit B. Mandelbrot,et al.  Fractal Geometry of Nature , 1984 .

[2]  E Marc.  VASCULAR NETWORKS: FRACTAL ANATOMIES FROM NON-LINEAR PHYSIOLOGIES , 1991 .

[3]  O. Hudlická.  Development of Microcirculation : Capillary Growth and Adaptation , 1984 .

[4]  G M Saidel,et al.  Diffusion model of tumor vascularization and growth , 1977, Bulletin of mathematical biology.

[5]  T. J. Ryan.  FACTORS INFLUENCING THE GEOWTH OF VASCULAR ENDOTHELIUM IN THE SKIN , 1970 .

[6]  M. E. Gottlieb.  Modelling Blood Vessels: A Deterministic Method With Fractal Structure Based On Physiological Rules , 1990, [1990] Proceedings of the Twelfth Annual International Conference of the IEEE Engineering in Medicine and Biology Society.

[7]  J. Folkman,et al.  Migration and proliferation of endothelial cells in preformed and newly formed blood vessels during tumor angiogenesis. , 1977, Microvascular research.

[8]  G. D. Phillips,et al.  Initiation and pattern of angiogenesis in wound healing in the rat. , 1991, The American journal of anatomy.

[9]  C. Jones,et al.  Flow studies in canine artery bifurcations using a numerical simulation method. , 1992, Journal of biomechanical engineering.

[10]  A. Hudetz,et al.  Computer simulation of growth of anastomosing microvascular networks. , 1991, Journal of theoretical biology.

[11]  J. Folkman,et al.  Toward an Understanding of Angiogenesis: Search and Discovery , 2015, Perspectives in biology and medicine.

[12]  D A Lauffenburger,et al.  Analysis of the roles of microvessel endothelial cell random motility and chemotaxis in angiogenesis. , 1991, Journal of theoretical biology.

[13]  T. K. Hunt,et al.  Stimulation of wound blood vessel growth by wound macrophages. , 1979, The Journal of surgical research.

[14]  T. Liem,et al.  Flow measurements in a highly curved atherosclerotic coronary artery cast of man. , 1992, Journal of biomechanical engineering.

[15]  Eliot R. Clark,et al.  Microscopic observations on the growth of blood capillaries in the living mammal , 1939 .

[16]  R. Barnhill,et al.  Angiogenesis and the skin. , 1987, Journal of the American Academy of Dermatology.

[17]  G Landini,et al.  Simulation of corneal neovascularization by inverted diffusion limited aggregation. , 1993, Investigative ophthalmology & visual science.

[18]  M. Barnsley,et al.  Iterated function systems and the global construction of fractals , 1985, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[19]  F. Plum.  Handbook of Physiology. , 1960 .

[20]  J. Brickmann.  B. Mandelbrot: The Fractal Geometry of Nature, Freeman and Co., San Francisco 1982. 460 Seiten, Preis: £ 22,75. , 1985 .

[21]  P. Henkind.  Ocular neovascularization. The Krill memorial lecture. , 1978, American journal of ophthalmology.

[22]  J. Wolf.  Angiogenesis in normal and psoriatic skin. , 1989, Laboratory investigation; a journal of technical methods and pathology.

[23]  R K Jain,et al.  Dynamics of neovascularization in normal tissue. , 1981, Microvascular research.

[24]  A. Waxman,et al.  Blood vessel growth as a problem in morphogenesis: a physical theory. , 1981, Microvascular research.

[25]  T. Vicsek.  Fractal Growth Phenomena , 1989 .

[26]  J. Folkman.  Angiogenesis in psoriasis: therapeutic implications. , 1972, The Journal of investigative dermatology.

[27]  J. Folkman,et al.  Anti‐Angiogenesis: New Concept for Therapy of Solid Tumors , 1972, Annals of surgery.

[28]  M. E. Gottlieb,et al.  Vascular Networks: Fractal Anatonies From Non-linear Physiologies , 1991, Proceedings of the Annual International Conference of the IEEE Engineering in Medicine and Biology Society Volume 13: 1991.

[29]  M. E. Gottlieb.  The VT model: a deterministic model of angiogenesis and biofractals based on physiological rules , 1991, Proceedings of the 1991 IEEE Seventeenth Annual Northeast Bioengineering Conference.

[30]  D. Ingber,et al.  Control of capillary growth and differentiation by extracellular matrix. Use of a tensegrity (tensional integrity) mechanism for signal processing. , 1991, Chest.