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Abstrakty
Vascular networks develop by way of angiogenesis, a growth process that involves the biological mechanisms of vessel sprouting (budding) and splitting (intussusception). Graph theory is excellently suited to model vascular networks and to analyze their properties (invariants). In particular, a random graph process model can simulate the development of a vascular network that has been modeled using graph theory. The renal glomerulus is one example of such a vascular network. Here the correlation between the invariants of this vascular network modeled as a graph and the mechanisms of the network growth using a random graph process are studied. It is proposed that the relative frequencies of sprouting and splitting during the growth of a given renal glomerulus can be estimated by the invariants (root distance, radius, and diameter) of the graph representing the renal glomerulus network. Experimental evidence has been given to support this conjecture.
Czasopismo
Rocznik
Tom
Strony
91--103
Opis fizyczny
Bibliogr. 17 poz., rys., tab., wykr.
Twórcy
autor
autor
autor
autor
autor
- Computer Science Department, Pace University, New York, NY 10038 USA
Bibliografia
- [1] Feller W.: An introduction to probability theory and its applications. Volume 1, Third Edition, John Wiley & Sons, New York, 1968.
- [2] Shea S. M.: Glomerular hemodynamics and vasculature. Microvascular Research, 18, 129-143, 1979.
- [3] Armstrong M. A.: Basic topology, Springer, New York, 1983.
- [4] Shea S. M., Raskova J.: Glomerular hemodynamics and vasculature structure in uremic: a network analysisof glomerular path lengths and maximal blood transit times computed for a microvascular model reconstructed from subserial ultrathin sections. Microvascular Research, 28, 37-50, 1984.
- [5] Wahl E. M., Daniels F. H., Leonard E. F., Levinthal C., Cortell S.: A Graph theory model of the glomerular capillary network and its development. Microvascular Research, 27, 96-109, 1984.
- [6] Buckley F., Harary F.: Distance in graphs. Addison-Wesley Pub Co., Reading, MA, 1990 .
- [7] Winkler D., Elger M., Sakai T., Kriz W.: Branching and confluence pattern of glomerular arterioles in the rat. Kidney International, 39 (Suppl. 32), S2-S8, 1991.
- [8] Remuzzi A., Brenner B., Pata V., Tebaldi G., Mariano R., Belloro A., Remuzzi G.: Threedimensional recostructed glomerular capilary network: blood flow distribution and local filtration. Am. J. Physiol., 26, F562-F572, 1992.
- [9] Balińska K. T., Quintas L. V.: The random f-graph process. Quo Vadis, Graph Theory, Annals of Discrete Math., 55, 333-340, 1993.
- [10] Nyengaard J. R., Marcussen N.: The number of glomerular capillaries estimated by an unbiased and efficient stereological method. J. Microsc., 171 (1), 27-37, 1993.
- [11] Risau W., Flamme L.: Vasculogenesis. Annu. Rev. Celi Dev. Biol., 11, 73-91, 1995.
- [12] Risau W.: Mechanisms of Angiogenesis. Nature, 386, 671-674, 1997.
- [13] Carmeliet P.: Mechanisms of angiogenesis and arteriogenesis. Nature Medicine, 6 (3), 389-395, 2000.
- [14] Antiga L., Ene-Iordache B., Remuzzi G., Remuzzi A.: Automatic generation of glomerular capillary organization. Microvascular Research, 62, 346-354, 2001.
- [15] Carmaliet P.: Angiogenesis in Health and Disease. Angiogenesis, 9 (6), 653-660, 2003.
- [16] Gargano M. L., Lurie L. L., Quintas L. V., Wahl E. M.: A graph theory analysis of renal glomerular microvascular networks. Microvascular Research, 67, 223-230, 2004.
- [17] Cha S.-H., Gargano M. L., Quintas L. V., Wahl E. M.: A vascular network growth Estimation algorithm using random graphs. Lecture Notes in Computer Science, Vol 3434, 45-53, 2005.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BWA1-0032-0005