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...

Full description

Saved in:
Bibliographic Details
Published inBulletin of mathematical biology Vol. 58; no. 3; pp. 409 - 424
Main Authors Nekka, F, Kyriacos, S, Kerrigan, C, Cartilier, L
Format Journal Article
LanguageEnglish
Published United States 01.05.1996
Subjects
Adult
Animals
Blood Vessels - anatomy & histology
Blood Vessels - embryology
Blood Vessels - growth & development
Humans
Mathematics
Models, Biological
Neovascularization, Physiologic
Online AccessGet full text

Cover

More Information
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.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 23
ISSN:0092-8240
1522-9602
DOI:10.1007/BF02460590