Abstract
At all levels (molecules, cells, organisms, ...), biological systems are made of structural and functional units. Those units are interacting with each other and, tend to use space in an optimal way with respect to their specific function and environmental constraints. Hence, cells can be defined as being the smallest structural and functional units capable of auto-reproduction. The rapid technological advances during the 20th century have made possible to describe the inner architecture of cells at different levels of organization. Our approach is an attempt to study cellular populations at the “sociological” level, i.e. at the level of their spatial organization and interrelationship in a given tissue. The topographies of cellular population have to be considered linked to morphogenesis, structural stabilities and functional state of a given tissue. This approach makes use of the relations that links form to disorder and is based on space partition constructed from a set of points defining the position of cells. This spatial partition consisting of a set of individual forms (Voronoi paving) associated to its dual (Delaunay triangulation) permits the calculation of Ulam trees which are descriptors of the local surrounding of a given cell and the search for characteristic features of the normal and pathological state.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Bowyer A: Computing Dirichlet tesselation. Comput J, 24: 162–166, 1981.
Preparata FP, Shamos MI: Computational geometry. Springer-Verlag, 1985.
Toussaint GT: Pattern recognition and geometrical complexity. In: Proceedings 5th International Conference on Pattern Recognition, IEEE Catalog NO. 80CH1499-3, Miami Beach 1980, pp. 1324–1347.
Ulam S: Patterns of growth of figures: mathematical aspects. Proceedings of symposia in applied mathematics, XIV: Mathematical problems in the biological sciences, American Mathematical Society. 64–75, 1962.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1994 Springer Basel AG
About this chapter
Cite this chapter
Marcelpoil, R., Davoine, F., Robert-Nicoud, M. (1994). Cellular Sociology: Parametrization of Spatial Relationships Based on Voronoi Diagram and Ulam Trees. In: Nonnenmacher, T.F., Losa, G.A., Weibel, E.R. (eds) Fractals in Biology and Medicine. Mathematics and Biosciences in Interaction. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8501-0_17
Download citation
DOI: https://doi.org/10.1007/978-3-0348-8501-0_17
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-9652-8
Online ISBN: 978-3-0348-8501-0
eBook Packages: Springer Book Archive