Mathematical models of pancreatic islet size distributions

The islets of Langerhans, ranging in size from clusters of a few cells to several thousand cells, are scattered near large blood vessels. While the β-cell mass in mammals is proportional to body weight, the size ranges of islets are similar between species with different body sizes, possibly reflecting an optimal functional size. The large range of islet sizes suggests a stochastic developmental process. It is not fully understood how islets develop to reach such size distributions, and how their sizes change under certain physiological and pathological conditions such as development, pregnancy, aging, obesity, and diabetes. The lack of a high-resolution in vivo imaging technique for pancreatic islets implies that the only data available to elucidate the dynamics of islet development are cross-sectional quantifications of islet size distributions. In this review, we infer biological processes affecting islet morphology in the large by examining changes of islet size distributions. Neonatal islet formation and growth is shown as a particular example of developing a mathematical model of islet size distribution. Application of this modeling to elucidate islet changes under other conditions is also discussed.