The arrangement of endocrine cells in pancreatic islets is critical for optimal insulin production. However, the optimal cytoarchitecture in large human islets is still unclear. Many qualitative descriptions suggest beta-cell clusters are surrounded by a mantle of non-beta cells. Here, we test this hypothesis by applying cyclic graph theory to human islet imaging data to determine if cycles of non-beta cells surround beta cells. We quantify this architecture with graph theory to determine how often alpha and delta cell mantles surround beta cell clusters in human islets. The dataset consisted of 150,000 islets and 2,000,000 alpha, beta, and delta cells imaged from 139 human organ donor pancreata ranging in age from gestation to adult. Graphs consisting of vertices and edges were created for each islet with vertices representing endocrine cells and edges determined by the distance between neighboring cells. Edge existence was based on pair correlation functions, an approach used in crystallography to study distances between atoms. From these graphs we determine if cycles of alpha, delta cells surround beta cells and quantify their occurrence. We found the existence and number of cycles to be islet-size and cell-fraction dependent. However, in our extensive dataset, the number of islets that displayed this architecture was very small. Although cycles could be found for specific cell fraction and islet size values, there were very few islets in our extensive dataset that had these characteristics. It follows that, statistically, most human islets do not show beta cell clusters enclosed by an alpha, delta cell mantle.
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