Study Compares Continuous and Discrete Mathematical Models for Wound Healing
Researchers developed a model selection pipeline using approximate Bayesian computation to compare partial differential equation (PDE) and agent-based models (ABMs) for spatial biological data, applying it to wound healing. The pipeline evaluates parameter estimation, uncertainty quantification, and out-of-sample forecasting to guide modality choice — a largely unaddressed problem in data-driven modeling. The work provides a preliminary framework that could help researchers choose appropriate mathematical models for spatial biological processes more systematically.
A preprint posted to arXiv presents a computational pipeline designed to address a gap in data-driven biological modeling: there are currently no established guidelines for choosing between continuous models (PDEs) and discrete models (ABMs) when modeling spatial processes. The authors used approximate Bayesian computation to perform parameter estimation, uncertainty quantification, and model selection via both information criteria and out-of-sample forecasting. Testing on artificial datasets generated from ABMs revealed that both model types achieved comparable parameter estimation accuracy, but ABM estimates carried higher uncertainty and PDE models ran over 1,000 times faster. Notably, the mean-field PDE was frequently selected over the true generative ABM by both evaluation methods, a counterintuitive finding. When applied to publicly available wound healing data, the pipeline identified a PDE model incorporating cell pulling and a time delay as the best fit, though this model exhibited high parametric uncertainty. The study establishes a foundational methodology for modality selection in spatial biological modeling, though the authors acknowledge the framework is preliminary.
What's missing
The study is a preprint and has not yet undergone peer review. The authors acknowledge high parametric uncertainty in the best-fit wound healing model, but do not fully explore whether this uncertainty undermines predictive utility in clinical or experimental contexts. The generalizability of the pipeline to spatial biological processes beyond wound healing remains untested. It is also unclear how the pipeline performs when real (rather than artificial) data violate mean-field assumptions underlying the PDE models.
What different sources said
- arXiv q-bioCenter
Spatial Model Selection and Uncertainty Quantification: Comparing Continuous and Discrete Wound Healing Models
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