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To infer unmeasurable biophysical drivers of lumen morphogenesis, the authors coupled phase-field simulations with SampEuler—a topological descriptor based on the Euler Characteristic Transform—inside an Approximate Bayesian Computation (ABC) rejection framework. Inferring latent mechanics like luminal osmotic pressure and cell proliferation directly from non-destructive imaging has traditionally been bottlenecked by the inability of classical geometric descriptors to handle variable, highly connected architectures. Evaluating the pipeline via the SampEuler Wasserstein distance accurately recovered ground-truth parameters from both time-lapse and static snapshots, revealed a latent compensatory trade-off between proliferation and pressure, and yielded posteriors consistent with biological ground truth on experimental pancreatic organoids.
Hidden biophysical forces like osmotic pressure can now be reliably inferred from a single static tissue snapshot by swapping conventional geometric descriptors for topological Euler characteristics.
The reproducibility of organ morphology and the extent to which computational models can predict morphogenesis remain difficult to quantify, particularly for organs with complex networks of fluid-filled lumina. Here, we combine Topological Data Analysis (TDA), biophysical simulation, and Bayesian inference to study lumen morphogenesis in pancreatic organoids. Lumen formation is governed by physical processes that are challenging to measure directly, including cell proliferation and luminal osmotic pressure. We simulate organoid development using a phase-field model and address the inverse problem of inferring these parameters from either time-lapse images or single morphological snapshots. Since lumen architectures vary substantially in size, structure, and connectivity, conventional geometric descriptors provide only a partial representation of their morphology. We therefore represent each organoid using SampEuler, a topological descriptor derived from the Euler Characteristic Transform (ECT). We first show that SampEuler captures morphological information encoded by established morphometrics. We then perform parameter inference using an approximate Bayesian computation (ABC) rejection framework with the SampEuler Wasserstein distance. Using synthetic organoids with known ground-truth parameters, our approach accurately recovers the osmotic pressure and the proliferation rate while revealing a compensatory trade-off between the two processes. Applied to experimental data from ten pancreatic organoids, the inferred posterior distributions are consistent with biological expectations. Together, these results establish a non-destructive, image-based pipeline for estimating otherwise inaccessible physical parameters governing lumen formation and highlight the potential of topological representations for linking complex biological morphology to mechanistic models.