Gibbs point field model quantifies disorder in microvasculature of U87-glioblastoma.

Microvascular proliferation in glioblastoma multiforme is a biological key mechanism to facilitate tumor growth and infiltration and a main target for treatment interventions. The vascular architecture can be obtained by Single Plane Illumination Microscopy (SPIM) to evaluate vascular heterogeneity in tumorous tissue. We make use of the Gibbs point field model to quantify the order of regularity in capillary distributions found in the U87 glioblastoma model in a murine model and to compare tumorous and healthy brain tissue. A single model parameter Γ was assigned that is linked to tissue-specific vascular topology through Monte-Carlo simulations. Distributions of the model parameter Γ differ significantly between glioblastoma tissue with mean 〈Γ〉=2.1±0.4, as compared to healthy brain tissue with mean 〈Γ〉=4.9±0.4, suggesting that the average Γ-value allows for tissue differentiation. These results may be used for diagnostic magnetic resonance imaging, where it has been shown recently that Γ is linked to tissue-inherent relaxation parameters.