Quantification of spatial parameters in 3D cellular constructs using graph theory

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.