Fig. 3. Variability in human islet size distributions influences functional outcomes.

a Schematic illustrating the procedure for calculating the effect of size distribution variability on BAP device functional outcomes. b Overlaid traces of human islet diameter probability density functions (n = 129 distributions). c Values of the number-basis shape and scale parameters (${\alpha }_n$ and ${\beta }_n$, respectively) from b (n = 129 values; bars represent mean ± SD). d Traces of simulated human islet diameter probability density functions generated through the hierarchical probabilistic Monte Carlo model (n = 200 simulated distributions). e Schematic of the simulated cylindrical system containing islets of size distributions selected by the hierarchical probabilistic Monte Carlo model. f–i Correlations of the loss of insulin secretion capacity ($\Psi$) to the following distribution properties: mean diameter (${\overline{d}}_n$) (f), islet size index (ISI) (g), standard deviation (SD) (h), and volume-basis 3rd quartile diameter (i) (n = 200 simulated devices). Center dashed lines indicate the best-fit line and peripheral dashed lines indicate 95% confidence intervals. Pearson’s correlation coefficient, $r$, is displayed in the bottom right text. j, k Necrotic fraction ($N_c$) (j) and fractional loss of insulin secretion capacity (${\Psi }_c$) (k) of individual simulated islets (n = 60,583 simulated islets). l Islet volume (IEQ) versus functional islet volume (fIEQ) for all individual islets. Line of identity is shown in red. m Schematic showing that large islets reduce oxygenation of smaller ones localized nearby. n Mean islet pO₂ (${\overline{p}}_c$) versus proximity to nearest large islet (n = 14,627 simulated islets). o, p Net loss of function (o) and necrosis (p) of the islet populations in the simulated construct when islets of all sizes were encapsulated (“none replaced”, n = 200 simulated devices), or when the ones over 300 or 250 μm were excluded and replaced with smaller ones (n = 100 simulated devices). Solid black lines indicate median value, dashed black lines indicate first and third quartiles. f ****p = 3.5e–25, g ****p = 1.1e–59, h ****p = 1.2e–100, i ****p = 4.0e–88; two-sided Pearson’s correlation. o ****p = 5.7e–6 (“none” versus “>300 μm replaced”), ****p = 3.4e–15 (“none” versus “>250 μm replaced”); p ****p = 1.5e–10 (“none” versus “>300 μm replaced”), ****p = 1.1e–14 (“none” versus “>250 μm replaced”); Brown–Forsythe and Welch ANOVA tests with two-sided Games–Howell post hoc p value adjustment for multiple comparisons. Source data are provided as a Source Data file.