A geometry-informed continuous 3D IEQ framework enables more accurate dose estimation in stem cell-derived islet transplantation

Abstract

Accurate quantification of islet mass is critical for the preclinical evaluation and therapeutic application of stem cell-derived pancreatic islet organoids. Traditional methods, including Ricordi’s islet equivalent (IEQ) approach and its equivalent circle diameter adaptations, often overestimate islet volume due to reliance on maximal diameters and discrete size bins. To address these limitations, we developed an automated image segmentation and three-dimensional modeling framework to quantify individual islet clusters from brightfield images. Clusters were fitted with ellipses and modeled as ellipsoids using rotation about either the minor or major axis, allowing IEQs to be calculated continuously relative to a reference 150 μm spherical islet. Major-axis (prolate) rotation provided the most conservative and physically plausible volume estimates, whereas minor-axis (oblate) rotation and diameter-based approaches systematically overestimated IEQs. Functional assessment with glucose-stimulated insulin secretion assays across multiple size categories demonstrated consistent insulin output for clusters below 250 μm, supporting the reproducibility of our 3D differentiation system. In vivo, streptozotocin-induced diabetic mice transplanted with islet doses based on major-axis modeling exhibited faster and more stable restoration of glycemia compared with groups receiving doses derived from overestimated approaches. These findings establish that major-axis ellipsoid modeling offers a mathematically consistent, conservative, and biologically relevant method for estimating IEQs, providing a practical framework to guide dosing in preclinical studies and supporting the translational development of stem cell-derived islet therapies.

1. Introduction

Type 1 diabetes mellitus (T1D) is characterized by autoimmune destruction of pancreatic β cells, resulting in lifelong dependence on exogenous insulin therapy.¹ Although insulin replacement remains the standard of care, it does not fully recapitulate endogenous glucose regulation and fails to prevent long-term complications in a substantial proportion of patients.^2-4 Pancreatic islet transplantation has demonstrated the potential to restore physiological glycemic control, particularly following the development of the Edmonton protocol.^5,6 However, widespread clinical adoption remains constrained by limited donor availability, variability in islet isolation, substantial cell loss during processing, and high procedural costs.⁷

Recent advances in stem cell biology have provided a promising alternative to donor-derived islets. The development of embryonic stem cells (ESCs) and induced pluripotent stem cells (iPSCs), and refined differentiation protocols now enable the generation of stem cell-derived islet-like clusters capable of glucose-responsive insulin secretion both in vitro and in vivo.^7-10 These advances have accelerated the translation of stem cell-derived islet products toward clinical application and highlighted the need for scalable, standardized, and quantitatively robust manufacturing and evaluation frameworks.

A critical component of islet transplantation is the accurate quantification of islet mass for dosing, functional assessment, and cross-study comparability. The islet equivalent (IEQ), originally defined by Ricordi et al. as the volume of a spherical islet with a diameter of 150 μm, remains the most widely used metric.^11,12 However, this approach is subject to several inherent limitations, including discretization into size bins, reliance on maximal diameter measurements, and the implicit assumption of spherical geometry.¹³ These factors can lead to systematic overestimation of islet mass, particularly in preparations containing irregular or elongated clusters, and introduce variability that may affect both experimental interpretation and therapeutic dosing.¹⁴

To improve objectivity and reproducibility, computer-assisted image analysis methods have been developed. Estimation based on the equivalent circle diameter (ECD), derived from two-dimensional projected area, reduces operator bias and improves measurement consistency.^15-17 Nevertheless, many implementations retain Ricordi’s categorical binning system, limiting volumetric resolution and preserving discretization artefacts. More recently, ellipse-fitting approaches have enabled the modeling of islet clusters as three-dimensional ellipsoids, allowing continuous volume estimation relative to a 150 μm reference sphere.^18,19

Despite these methodological advances, a key geometric assumption remains insufficiently examined: the choice of rotational axis when reconstructing three-dimensional volume from two-dimensional projections. Several existing approaches implicitly assume rotation about the minor axis, effectively modeling islet clusters as oblate (lentil-shaped) spheroids oriented on their thin edges (Figure 1(a)).^18-20 However, under standard culture conditions, islet clusters settle onto the substrate and are more likely to adopt a physically stable orientation consistent with prolate (olive-shaped) geometries when inferred from their projected morphology (Figure 1(b)). Minor-axis rotation may therefore introduce systematic overestimation of volume and misrepresent the true three-dimensional structure of the clusters.

Figure 1.

Conceptual illustration of two possible three-dimensional orientations of islet clusters inferred from a two-dimensional projection.

When viewed from above under brightfield imaging, islet clusters appear as elliptical projections (blue contour on the X-Y imaging plane). Two alternative three-dimensional geometries may produce this projection. (a) An oblate, lentil-shaped spheroid that would present a circular profile if viewed from the side (gray contour on the X-Z plane). (b) A prolate, olive-shaped spheroid that would retain an elliptical profile when viewed from the side (gray contour on the X-Z contour). These alternative geometries correspond to volume estimation models based on rotation around the minor axis (oblate assumption) or the major axis (prolate assumption), respectively.

In this study, we present a computer-assisted segmentation and quantification framework for the analysis of stem cell-derived islet clusters from standard brightfield images. We systematically compare IEQ estimation methods based on maximal diameter, equivalent circle diameter, and continuous volumetric modeling using both spherical and ellipsoidal assumptions. Importantly, we evaluate the impact of rotational axis selection and propose a major-axis (prolate) ellipsoid model as a more physically consistent and conservative approach for volume estimation.

To assess the practical implications of these modeling strategies, we further examine the relationship between IEQ estimates and biological function. Structural validation is performed by correlating IEQ with total cell number following dissociation, while functional consistency is evaluated using glucose-stimulated insulin secretion (GSIS) assays. Finally, we explore the translational relevance of these findings in in vivo transplantation models, demonstrating how differences in IEQ estimation can influence dosing strategies and therapeutic outcomes.

Together, this work establishes a continuous, geometry-informed framework for IEQ estimation, with direct implications for standardizing islet quantification and improving dosing accuracy in stem cell-derived islet transplantation.

2. Materials and methods

2.1. Human embryonic stem cell source and maintenance

The EB03 human embryonic stem cell (ESC) line was obtained from the China National Stem Cell Resource Center. Cells were maintained under feeder-free conditions using a defined extracellular matrix, specifically recombinant human vitronectin-coated culture vessels. ESCs were cultured in 2D in complete mTeSR1 medium (STEMCELL Technologies, #85850) supplemented with 10 μM Y-27632 (Sigma0Aldrich, #Y0503) during routine passaging. T25 (Corning, #431463) and T75 (Corning, #430720U) culture vessels were coated with vitronectin (STEMCELL Technologies, #100-0763) according to the manufacturer’s instructions. Medium was replaced daily. Cells were passaged every 3-4 days at 85-90% confluence using 0.5 mM EDTA in PBS (Corning, #46-034-CI). Only cultures exhibiting typical compact colony morphology and minimal spontaneous differentiation were used for 3D adaptation and downstream differentiation experiments.

2.2. Adaptation to 3D suspension culture

Following thawing from liquid nitrogen, EB03 cells were expanded for at least two passages in 2D culture prior to transfer to suspension conditions.

For 3D adaptation, cells were dissociated into single cells using Accutase (STEMCELL Technologies, #07920) for approximately 6 minutes at room temperature. After neutralization and centrifugation, cells were resuspended in complete mTeSR1 medium containing 10 μM Y-27632 and seeded into 100 mL or 500 mL single-use mini vertical-wheel bioreactors (PBS-0.1 or PBS-0.5, PBS Biotech) at a density of 1 × 10⁶ cells/mL.

Bioreactors were mounted on a magnetic stir platform (PBS-Mini base unit, PBS Biotech) within a humidified incubator at 37 °C and 5% CO₂. Agitation was maintained at 60 rpm, optimized according to vessel volume and cell line characteristics to ensure aggregate uniformity without excessive shear stress.

Cells were cultured in suspension for 48 hours to allow spontaneous cluster formation. Medium was exchanged daily by allowing aggregates to settle by gravity and replacing spent medium with fresh mTeSR1 without Y-27632 after the initial 24 hours.

Cells were considered fully adapted to suspension culture when uniform spherical clusters formed with an average diameter around 150 μm and were ready for directed differentiation.

2.3. Directed differentiation of ESC clusters into pancreatic islet organoids

Differentiation was initiated 72 hours after the 3D adaption, when clusters reached a diameter of 200−300 μm. A six-stage, 20-day directed differentiation protocol²¹ was carried out in the suspension bioreactors, followed by a 4-5 week maturation phase. The basal medium for Stages 1-6 was RPMI 1640 (Gibco, #11875-127) supplemented with 1 × B27 (Gibco, #17504-044) and 1 × GlutaMAX (Gibco, #35050-061). All media were prepared fresh and supplemented with factors immediately before use. Bioreactors were fed daily during the differentiation process by allowing clusters to settle by gravity for 5-10 minutes, gently aspirating spent medium, and replacing it with fresh stage-specific medium.

Stage 1 (Definitive Endoderm): Days 1-3. Basal medium was supplemented with 100 ng/mL Activin A (R&D Systems, #338-AC) and 3 μM CHIR99021 (Tocris, #4423).

Stage 2 (Primitive Gut Tube): Days 4-6. Basal medium was supplemented with 50 ng/mL FGF7 (PeproTech, #100-19) and 0.25 μM SANT-1 (Sigma, #S4572).

Stage 3 (Posterior Foregut): Days 7-9. Basal medium was supplemented with 50 ng/mL FGF7, 0.25 μM SANT-1, 2 μM Retinoic Acid (Sigma, #R2625), and 100 nM LDN-193189 (Sigma, #SML0559).

Stage 4 (Pancreatic Progenitor): Days 10-12. Basal medium was supplemented with 50 ng/mL FGF7, 0.25 μM SANT-1, 0.1 μM Retinoic Acid, 10 μM Alk5i II (Enzo, #ALX-270-445), and 200 nM LDN-193189.

Stage 5 (Endocrine Progenitor): Days 13-16. Basal medium was supplemented with 10 μM Alk5i II, 10 μM Zinc Sulfate (Sigma, #Z0251), and 10 μg/mL Heparin (Sigma, #H3149).

Stage 6 (Immature Islet Cells): Days 17-20. Basal medium was supplemented with 10 μM Alk5i II, 10 μM Zinc Sulfate, 10 μg/mL Heparin, and 1 μM T3 (Sigma, #T6397).

Maturation (Islet-like Organoids): Days 21 onwards. Clusters were matured for an additional 4-5 weeks in CMRL 1066 medium (Gibco, #11530-037) supplemented with 1 × B27, 1 × GlutaMAX, 10 μM Alk5i II, 10 μM Zinc Sulfate, 10 μg/mL Heparin, 1 μM T3, and 10 μM Forskolin (Tocris, #1099). Media changes were performed every other day during this phase.

2.4. Imaging and image analysis

Approximately 300 ESC-derived islet organoids were randomly sampled from independent differentiation batches for morphological analysis. Brightfield images were acquired using an inverted phase-contrast microscope (M140, Mshot) at fixed magnification under standardized illumination settings to ensure consistency across samples.

2.4.1. Image segmentation and morphometric analysis

Two-dimensional brightfield images were analyzed using an in-house developed computational pipeline implemented in Python (Version 3.14).

Individual ESC-derived islet organoids were identified using an automated image segmentation pipeline developed in-house. As illustrated in Figure 2, original RGB images (Figure 2(a)) were first converted to grayscale and subsequently binarized (Figure 2(b)). Image noise was reduced using Gaussian blur filtering to smooth intensity variations and improve boundary definition (Figure 2(c)). Adaptive thresholding was then applied to distinguish foreground objects from background, followed by morphological operations (erosion and dilation) to refine cluster boundaries and eliminate small artefacts (Figure 2(d)). Connected-component analysis was subsequently performed to identify and isolate individual clusters as discrete objects (Figure 2(e)). Each correctly identified islet organoid was automatically outlined, labeled, and subjected to downstream morphometric analysis (Figure 2(f)).

Figure 2.

Stepwise illustration of the automated image segmentation algorithm with representative intermediate outputs. (a) Original brightfield image of ESC-derived islet organoids; (b) Conversion to grayscale and binary image; (c) Noise reduction using Gaussian blur filtering; (d) Adaptive thresholding followed by morphological operations (erosion and dilation) to refine object boundaries; (e) Connected-component analysis to identify and separate attaching islet clusters; (f) Final segmentation output showing outlined and labeled islets selected for morphometric analysis.

Objects below a predefined area threshold (debris) and objects intersecting the image border (partially captured clusters) were excluded from analysis to avoid segmentation artefacts and measurement bias.

2.4.2. Equivalent circle diameter calculation

For each segmented cluster, the projected area (A) was computed.

The equivalent circle diameter (ECD) was then calculated as:

$$\mathit{ECD}=2\sqrt{\frac{A}{\pi }}$$

This diameter represents the diameter of a circle with the same projected area as the segmented cluster.

2.4.3. Ellipse fitting and 3D volume modeling

To account for non-circular morphology, each segmented cluster boundary was fitted using least-squares ellipse fitting.²² This yielded the major axis length (2·a) and the minor axis length (2·b).

Stem cell-derived islet clusters typically form compact and relatively uniform aggregates under controlled culture conditions,²¹ supporting the use of simplified geometric approximations with assumed rotational symmetry. Based on this assumption, two ellipsoidal models were evaluated:

Volume was calculated assuming rotational symmetry about the minor semi-axis, generating an oblate spheroid model:

$$V_{\mathit{minor}}=\frac{4}{3}\pi a^{2}b$$

Volume was calculated assuming rotational symmetry about the major semi-axis, generating a prolate spheroid model:

$$V_{\mathit{major}}=\frac{4}{3}\pi a{b}^2$$

The major-axis rotation model was proposed as a more physically realistic approximation for islet organoids that settle in suspension and exhibit rounder projected profiles under gravity (Figure 1(b)).

For comparison, a spherical model was also evaluated using the equivalent circle diameter (ECD):

$$V_{\mathit{sp}h\mathit{ere}}=\frac{4}{3}\pi {\left(\frac{\mathit{ECD}}{2}\right)}^3$$

2.5. IEQ calculation

IEQ values were estimated using three independent methods:

2.5.1. Ricordi bin method (Staggered IEQ)

Equivalent circle diameters were categorized into predefined Ricordi diameter bins, and IEQ was assigned according to standard bin-based conversion factors.

2.5.2. IEQ based on ellipsoid volume (Continuous IEQ)

For ellipsoid-derived volumes, IEQ was calculated by normalizing cluster volume to the volume of a reference 150 μm diameter (i.e., radius of 75 μm) sphere:

$$\mathit{IE}{Q}_{\mathit{ellipsoid}}=\frac{V_{\mathit{model}}}{V_{150}}$$

where:

$$V_{150}=\frac{4}{3}\pi {(75)}^3$$

2.5.3. Continuous IEQ based on equivalent sphere volume

Similarly:

$$\mathit{IE}{Q}_{\mathit{sphere}}=\frac{V_{\mathit{sphere}}}{V_{150}}$$

IEQs estimated by Ricordi binning, equivalent sphere modeling, minor- and major-axis ellipsoid rotation were plotted against equivalent circle diameter for direct comparison of scaling behavior and deviation patterns.

2.6. In vitro static glucose-stimulated insulin secretion (GSIS) assay

ESC-derived islet organoids were randomly hand-picked from independent differentiation batches and categorized into four size groups based on their diameters: 50−100, 100−150, 150−200, and 200−250 μm. For each size category, approximately 30 organoids were randomly selected and transferred into a single Transwell insert (Corning, #3421) placed within one well of a 24-well plate (Corning, #3738) for each GSIS replicate.

Organoids were washed three times with pre-warmed Krebs-Ringer bicarbonate buffer (KRB) to remove residual culture medium. KRB was freshly prepared and contained 120 mM NaCl (Sigma-Aldrich, #S7653), 5 mM KCl (Sigma-Aldrich, #P9333), 2 mM CaCl₂ (Sigma-Aldrich, #C1016), 1 mM MgCl₂ (Sigma-Aldrich, #M8266), 25 mM NaHCO₃ (Sigma-Aldrich, #S5761), and 10 mM HEPES (Thermo Fisher Scientific, #15630080).

Following washing, clusters were pre-incubated in 1 mL KRB supplemented with 2 mM D-glucose (Sigma-Aldrich, #G8270) for 1 hour at 37 °C in a humidified atmosphere with 5% CO₂. The supernatant was discarded after this equilibration step.

For basal insulin secretion measurement, organoids were transferred to a fresh well containing 1 mL KRB supplemented with 2 mM glucose and incubated for 1 hour at 37 °C. The supernatant was collected and immediately stored at −80 °C to minimize insulin degradation.

For stimulated secretion, organoids were subsequently transferred to a new well containing 1 mL KRB supplemented with 20 mM glucose and incubated for an additional 1 hour under the same conditions. The supernatant was collected and immediately frozen at −80 °C until analysis. The islet clusters were then dissociated with TrypLE Express (Gibco, #12604013) as described.

When GSIS has been performed, the organoids were dissociated using TrypLE Express in 3-4 sequential short incubations (5 min at RT) to minimize over-digestion and preserve cell viability. The resulting single cells were quantified using an automated cell counter (Countstar Mira BF, Alit Biotech) to enable normalization of insulin secretion to cell number.

Frozen samples were thawed on ice and diluted 1:500 prior to analysis. Insulin concentrations were measured using the human insulin ELIZA kit (Mercodia, #10-1132-01) according to the manufacturer’s instructions. Absorbance was read using a microplate reader (Varioskan LUX, Thermo Scientific).

Insulin concentrations were calculated based on the standard curve generated for each assay. Secretion levels were normalized to total viable cell number and expressed as μIU per 1,000 cells. Basal (2 mM) and stimulated (20 mM) insulin secretion values were presented as column plots.

2.7. In vivo transplantation studies in diabetic animal models

2.7.1. Streptozotocin-induced diabetic mouse model and islet transplantation

Streptozotocin (STZ; Merck Millipore, #572201) was freshly prepared immediately prior to use. For example, for ten mice, 36 mg STZ was dissolved in 2 mL of cold 0.1 M sodium citrate (Sigma-Aldrich, #1613859) buffer (pH 4.5) to obtain an 18 mg/mL solution. The solution was prepared on ice, protected from light, sterile-filtered, and used within 30 minutes of preparation. All procedures involving STZ handling were performed on ice to preserve stability.

Injection volume was adjusted according to body weight to achieve a final dose of 180 mg/kg.

2.7.2. Induction of diabetes in mice

Six- to eight-week-old NOD/SCID mice were used for diabetes induction. Mice were fasted for 12 hours prior to STZ administration, with free access to water.

A single intraperitoneal injection of STZ was administered at 180 mg/kg. For a 20 g mouse, this corresponded to approximately 0.2 mL of the prepared STZ solution.

One week after STZ injection, blood glucose levels were measured following a 4-hour fasting period. Mice with fasting blood glucose ≥11.1 mM were considered diabetic and included in subsequent transplantation experiments.^23,24

Baseline (pre-STZ) blood glucose measurements were recorded after acclimatization to serve as normal reference values.

2.7.3. Experimental groups and transplantation

Diabetic mice were randomly assigned to one control group and three treatment groups as shown in Table 1.

Table 1.

Experimental design of the in vivo study.

Group	Strain	Age (weeks)	n (primary + backup)	Treatment	Route	Dose	Volume
Control	NOD/SCID	6–8	4 + 2	Saline	Kidney capsule	—	50 μL
Treatment (3 Groups)	NOD/SCID	6–8	10 + 2	ESC-derived islets	Kidney capsule	2,000 IEQ per mouse	50 μL

For each transplantation, the number of ESC-derived islets administered per mouse was determined to achieve a target dose of 2,000 IEQ, as estimated using the equivalent circle diameter (ECD), oblate (minor-axis rotation), or prolate (major-axis rotation) modeling approaches. Islet preparations were resuspended in sterile saline and delivered at a volume of 50 μL per mouse.

Islets were transplanted under the kidney capsule under appropriate anesthesia using standard microsurgical techniques.

2.7.4. Blood glucose monitoring

Tail vein blood glucose levels were measured using a handheld glucometer (i-STAT 1, Abbott) following a 4-hour fasting period every day.

3. Results

3.1. Automated segmentation accurately identifies individual organoids

Brightfield images of stem cell-derived islet clusters were processed using our automated segmentation algorithm. Individual clusters were successfully identified and sequentially labeled following image segmentation, as illustrated in Figure 3. Objects below a predefined size threshold, including single cells and debris, as well as clusters intersecting the image boundary were excluded from analysis.

Figure 3.

Automated segmentation of stem cell-derived islet clusters. (Scale bar = 200 μm).

In cases where clusters were closely attached or partially overlapping, accurate separation of individual objects became more challenging. Under these conditions, the algorithm performed segmentation based on the most distinct boundaries detectable within the image, while regions with ambiguous boundaries were excluded from subsequent analysis (for example, the area enclosed by clusters 22, 25, 30, and 34 in Figure 2).

To minimize segmentation ambiguity, clusters were gently resuspended prior to imaging to reduce aggregation and ensure adequate separation between individual organoids.

3.2. Major-axis modeling yields lower and continuous IEQ estimates compared with Ricordi binning

The segmented islet clusters were first fitted with ellipses using the Direct Least Squares Fitting of Ellipses algorithm.²³ The fitted ellipses were then converted into 3D ellipsoids by assuming rotation around the major axis, based on the rationale that islet clusters tend to settle in a physically stable orientation when resting on the culture surface. Using this approach, the total islet equivalent (IEQ) calculated for the example image was 47.424 IEQ.

Since individual clusters had already been segmented, the same dataset was subsequently analyzed using alternative IEQ estimation approaches for comparison (Figure 4). These included: (i) the modified Ricordi binning method based on equivalent circle diameter (ECD); (ii) a sphere model using the ECD as the sphere diameter; and (iii) an ellipsoid model rotated about the minor axis.

Figure 4.

Segmented clusters subjected to ellipsoid fitting for volumetric modeling using the developed algorithm. (Scale bar = 200 μm).

Among the evaluated approaches, the major-axis ellipsoid model produced the lowest total IEQ estimate, whereas other methods yielded higher values. Specifically, the sphere model based on ECD produced a total of 49.589 IEQ, the modified Ricordi binning method yielded 53.496 IEQ, and the minor-axis ellipsoid model resulted in the highest estimate of 55.773 IEQ.

These results demonstrate that modeling islet clusters as prolate ellipsoids rotated about their major axis provides a more conservative and continuous estimate of IEQ, in contrast to the discretized values produced by Ricordi binning.

Islet size is a key determinant of transplantation outcome. To quantitatively assess the impact of different IEQ estimation methods, over 300 ESC-derived islet clusters were then analyzed using the automated segmentation and modeling pipeline. Total IEQ values were calculated using the Ricordi method based on ECD, as well as ellipsoid models generated by minor-axis (oblate) and major-axis (prolate) rotation. As shown in Figure 5(a), the total IEQ estimated by the ECD-based Ricordi method was 174.485, exhibiting a staggered distribution due to categorical binning. In contrast, ellipsoid-based approaches produced continuous distributions, with total IEQ values of 174.186 for minor-axis modeling and 145.311 for major-axis modeling.

Figure 5.

Comparison of IEQ estimation methods and their relationship with islet size.

A strong linear correlation was observed between ECD and both the major and minor axes of the fitted ellipses (both p-value < 0.0001; Figure 5(b)). This relationship supports the use of ECD as a common reference for comparing IEQ estimates derived from different methods. When plotted against ECD, IEQ values obtained from ellipsoid models followed continuous trends, whereas the Ricordi method retained a stepwise (discretized) profile. The ellipsoid-based estimates followed cubic relationships (R² = 0.9878 for minor-axis and R² = 0.9926 for major-axis modeling; Figure 5(c)), which is indicative of the relatively uniform, near-spheroidal morphology of ESC-derived islet clusters compared with the greater structural heterogeneity of donor-derived islets. Notably, the curve corresponding to major-axis modeling consistently lay below that of minor-axis modeling, indicating a more conservative estimation of IEQ.

To further examine the distribution of islet size and contribution to total IEQ, clusters were grouped into four size categories based on ECD (50−100, 100−150, 150−200, and 200−250 μm) using IEQ values derived from the major-axis model. Clusters within the 50−100 μm range accounted for 44% of total islet number but contributed only 19% of total IEQ. In contrast, the 100−150 μm group comprised 49% of islets and contributed the majority (56%) of total IEQ. Larger islets in the 150−200 μm range represented 6% of clusters but contributed 18% of IEQ, while the 200−250 μm group constituted only 1% of clusters yet contributed 7% of total IEQ.

3.3. Glucose-stimulated insulin secretion

In vitro functional assessment was performed using static glucose-stimulated insulin secretion (GSIS) assays. ESC-derived islet clusters were grouped into four size categories based on ECD (50–100, 100–150, 150–200, and 200–250 μm), and insulin secretion was measured under low- and high-glucose conditions and normalized to 1,000 cells.

When normalized on a per-cell basis, insulin secretion did not differ significantly across size categories (Figure 6). It indicates that, within the examined size range (<250 μm), ESC-derived islet cells exhibit comparable glucose responsiveness irrespective of cluster size. While larger clusters contain more cells and would therefore be expected to produce higher absolute insulin output, this effect is accounted for by cell number normalization in the present analysis.

Figure 6.

GSIS of ESC-derived islet clusters across size-defined groups.

These results suggest that functional capacity, when assessed at the cellular level, is largely independent of cluster size within this range. Consequently, different approaches in IEQ estimation are unlikely to be compensated by intrinsic functional differences between small and large clusters. Rather, accurate quantification of islet mass remains essential for reliable interpretation of functional output and for appropriate dose determination.

This finding further supports the robustness of the 3D suspension differentiation system, indicating its ability to generate islet organoids with consistent functional performance, which may be advantageous for scalable manufacturing applications.²⁰

3.4. Pilot study in diabetic mice

A diabetic mouse model was established by administration of STZ. Following a 12-day induction period, diabetic mice underwent transplantation of ESC-derived islets under the kidney capsule using standard microsurgical techniques. For each recipient, a nominal dose of 2000 IEQ was targeted. However, the actual number of transplanted islet clusters differed between groups, as it was back-calculated based on three distinct IEQ estimation methods: ECD-based Ricordi method, minor-axis (oblate) ellipsoid modeling, and major-axis (prolate) ellipsoid modeling.

Following transplantation, all treatment groups exhibited a gradual reduction in blood glucose levels compared with untreated diabetic controls, which remained persistently hyperglycemic (Figure 7). Notably, mice receiving grafts dosed based on the major-axis (prolate) model demonstrated a more rapid decline in blood glucose and achieved stable glycemic control at approximately 11.1 mM, although full euglycemia was not reached during the period of studies.

Figure 7.

Blood glucose profiles in diabetic mice following transplantation of ESC-derived islets dosed using different IEQ estimation methods (mean ± SD). Streptozotocin (STZ) was administered on Day 2 following baseline blood glucose measurement, and ESC-derived islets were transplanted on Day 9. Grafts were standardized to 2000 IEQ using equivalent circle diameter (ECD), minor-axis, or major-axis modeling. The horizontal dotted line denotes the threshold for stable glycemic control (approximately 11.1 mM).

4. Discussions

Accurate quantification of islet mass remains a fundamental challenge in both experimental and clinical islet transplantation.¹⁴ In this study, we demonstrate that commonly used IEQ estimation approaches (particularly those derived from the traditional Ricordi framework) can introduce systematic bias due to simplifying geometric assumptions and discretized binning strategies. By contrast, our proposed continuous three-dimensional modeling framework, based on ellipsoidal fitting and major-axis (prolate) rotation, provides a more conservative and physically consistent estimation of islet volume.^20,25

A key limitation of conventional IEQ methodologies lies in their reliance on maximal diameter measurements and categorical size binning. As shown in our analysis, these approaches can lead to overestimation of islet mass, particularly for elongated or irregular clusters. Even when improved through equivalent circle diameter (ECD)-based computation, discretization artefacts persist, limiting volumetric precision. Our results demonstrate that continuous IEQ estimation derived from volumetric modeling eliminates these discontinuities and produces smoother, more biologically plausible distributions. Notably, while minor-axis (oblate) and major-axis (prolate) ellipsoid models both yield continuous outputs, the prolate model consistently generates lower IEQ estimates, reflecting a more conservative interpretation of islet volume.

The distinction between oblate and prolate modeling is not merely mathematical but also reflects underlying physical assumptions regarding islet morphology and orientation. Islet clusters cultured in suspension and imaged under standard conditions are expected to settle in orientations that favor stable contact with the culture surface. Under such conditions, assuming rotational symmetry about the minor axis implies a geometrically less stable, edge-balanced configuration, which is unlikely to predominate in practice. In contrast, major-axis rotation better captures the expected morphology of elongated aggregates and avoids systematic inflation of volume estimates. This conceptual refinement is supported by our quantitative data, where prolate modeling consistently yields lower IEQ values compared with oblate modeling for the same projected geometry.

Importantly, the implications of these findings extend beyond geometric accuracy to the interpretation of function and the determination of transplantation dose. Our GSIS data demonstrate that, when normalized on a per-cell basis, ESC-derived islet clusters exhibit comparable glucose responsiveness across the examined size range (<250 μm). This indicates that intrinsic cellular function is largely independent of cluster size within this range,²⁶ and that functional heterogeneity attributable to size is limited in relatively uniform stem cell-derived preparations. However, an additional refinement would be to quantify intracellular insulin content and express GSIS as fractional insulin release, which may provide further insight into secretory efficiency across different cluster sizes.^27,28

These observations have direct relevance for IEQ-based quantification. As IEQ is fundamentally a volumetric metric, its application in transplantation implicitly assumes that larger clusters contribute proportionally greater functional output due to increased cell number rather than enhanced per-cell activity. Consequently, inaccuracies in IEQ estimation arising from geometric assumptions are unlikely to be mitigated by functional differences between clusters. Instead, such inaccuracies may translate directly into misestimation of effective dose.

This point is further illustrated in our pilot in vivo study. Although all treatment groups were nominally dosed at 2000 IEQ, the actual number of transplanted islet clusters differed substantially depending on the estimation method used. Groups dosed based on ECD or oblate modeling, both of which tend to overestimate IEQ, received fewer physical islets, resulting in comparatively slower or less effective glycemic control. In contrast, prolate model-based dosing, by providing a more conservative IEQ estimate, led to transplantation of a greater number of islet clusters and correspondingly improved glycemic outcomes. These findings highlight a critical but often overlooked issue: inaccuracies in IEQ estimation can directly translate into underdosing or overdosing in transplantation settings, with tangible consequences for therapeutic efficacy.

While this study provides a strong proof-of-concept, several limitations should be acknowledged. The in vivo experiments represent an initial pilot with a limited sample size, and further studies will be required to validate the observed differences across larger cohorts with extended follow-up. Although ellipsoidal modeling offers a tractable and computationally efficient approximation, real islet clusters may exhibit more complex and irregular geometries that are not fully captured by simple parametric shapes. Future work may incorporate more advanced three-dimensional imaging or machine learning-based shape reconstruction to further refine volumetric estimation. In addition, integration of the proposed framework into automated, high-throughput pipelines will be essential for its application in GMP manufacturing and clinical workflows.^29,30

A further consideration is that the present framework is based primarily on morphology-driven segmentation and therefore does not inherently distinguish endocrine tissue from non-endocrine contamination. This limitation is particularly relevant when analyzing donor-isolated pancreatic islets, where exocrine fragments, ductal tissue, or mantled peripheral material may contribute to the apparent cluster volume. In contrast, the proof-of-concept experiments here were performed using ESC-derived islet organoids generated in a defined 3D suspension differentiation system, where the analyzed clusters exhibit relatively homogeneous endocrine composition. Under these conditions, whole-cluster segmentation and volumetric modeling were considered appropriate.

Importantly, although this study was developed and validated using ESC-derived islets, the computational principles are broadly transferable. Automated cluster segmentation, ellipse fitting, and continuous IEQ conversion can in principle be extended to donor-derived human islets, porcine islets, or other endocrine preparations used in research and transplantation. For such heterogeneous clinical samples, integration of Dithizone (DTZ)-based color masking,^31,32 purity correction, or endocrine-specific fluorescence imaging prior to volumetric modeling would further enhance biological specificity by excluding non-islet tissue from analysis. Therefore, this platform may serve not only as a quantification tool for stem cell-derived products, but also as a foundation for future standardized IEQ assessment across conventional and emerging islet transplantation settings.

In conclusion, we describe a continuous, geometry-informed framework for IEQ estimation that addresses several important limitations of existing methodologies. By adopting a prolate ellipsoidal model with major-axis rotation, this approach provides a more conservative and physically plausible estimate of islet volume, reduces discretization artefacts, and improves the translational relevance of IEQ-based dosing. These findings support the need for more physically consistent islet mass quantification and may contribute to more accurate dose determination in both preclinical and clinical islet transplantation.

Funding Statement

This work was supported by internal research and development funding from Beijing Essentia Biosciences Ltd.

Disclosure statement

The authors are employees of Beijing Essentia Biosciences Ltd. and its subsidiary, Aceso Biosciences.