Journal of Biomedicine and Biotechnology
Volume 2009 (2009), Article ID 928286, 16 pages
doi:10.1155/2009/928286
Research Article
Quantification of Spatial Parameters in 3D Cellular Constructs Using Graph Theory
1Department of Biology, Rensselaer Polytechnic Institute, Troy, NY 12180, USA
2Department of Computer Science, Rensselaer Polytechnic Institute, Troy, NY 12180, USA
3Department of Biomedical Engineering, University of Michigan, Ann Arbor, MI 48109, USA
Received 16 December 2008; Revised 22 June 2009; Accepted 16 August 2009
Academic Editor: Satoru Miyano
Copyright © 2009 A. W. Lund et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
Multispectral three-dimensional (3D) imaging provides spatial information for biological structures that cannot be measured by traditional methods. This work presents a method of tracking 3D biological structures to quantify changes over time using graph theory. Cell-graphs were generated based on the pairwise distances, in 3D-Euclidean space, between nuclei during collagen I gel compaction. From these graphs quantitative features are extracted that measure both the global topography and the frequently occurring local structures of the “tissue constructs.” The feature trends can be controlled by manipulating compaction through cell density and are significant when compared to random graphs. This work presents a novel methodology to track a simple 3D biological event and quantitatively analyze the underlying structural change. Further application of this method will allow for the study of complex biological problems that require the quantification of temporal-spatial information in 3D and establish a new paradigm in understanding structure-function relationships.