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...
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Published in | Bulletin of mathematical biology Vol. 58; no. 3; pp. 409 - 424 |
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Main Authors | , , , |
Format | Journal Article |
Language | English |
Published |
United States
01.05.1996
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Subjects | |
Online Access | Get full text |
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Summary: | 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. |
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Bibliography: | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 23 |
ISSN: | 0092-8240 1522-9602 |
DOI: | 10.1007/BF02460590 |