Multiscale PDE–Agent-Based Modeling in Health and Disease

Dear Colleagues,

Mathematical models that marry spatially resolved continuum descriptions with discrete, stochastic representations of cells are uniquely powerful for studying health and disease. Partial differential equations (PDEs) naturally describe how signaling molecules, oxygen, drugs and other microenvironmental fields evolve in space and time; agent-based and other cell-level stochastic models capture the heterogeneity, discreteness and decision-making of individual cells. When coupled, these approaches provide a multiscale framework that links molecular and tissue scale transport and reactions to emergent cellular behaviors enabling mechanistic insight that neither paradigm can supply alone.

This Special Issue seeks papers that advance the theory, computation, and application of PDE-based and hybrid PDE–agent-based models in biomedical settings. We welcome rigorous analysis (well-posedness, continuum limits, multiscale asymptotics), methodological innovation (stable and efficient hybrid coupling schemes, adaptive meshing, stochastic–deterministic operator splitting, GPU/HPC implementations), and advances in parameter estimation, uncertainty quantification, model selection and surrogate/model-reduction techniques that make large-scale, data-driven simulation practical and trustworthy.

Equally important are contributions that close the loop with experiment and clinic: studies that calibrate and validate models against in vitro systems (organoids, microfluidics), animal data, or clinical imaging and molecular biomarkers; works that demonstrate how models can inform experimental design, optimize drug delivery or combination therapies, stratify patients, or support trial design and decision-making. We particularly encourage submissions that provide open, reproducible workflows (code, data, benchmarks) and that integrate modern data-science tools—from data assimilation to machine-learning surrogates—without sacrificing interpretability.

Topics of interest:

• Hybrid PDE–ABM and multiscale frameworks for angiogenesis, vascular patterning, and microcirculation.
• Reaction–diffusion theory, Turing instabilities, and linear stability analysis on finite domains.
• Modeling perfusion heterogeneity and its impact on metabolism, pharmacokinetics/pharmacodynamics and drug resistance.
• Mechanistic studies of chemotaxis, endothelial, inflammatory and cancer cell motility, and bidirectional signaling feedback (e.g., endothelial secretion of TAF).
• Image-driven, disease models, patient-specific, and 3D computational models; high-performance implementations.
• Data assimilation, machine learning, and Bayesian inference for parameter estimation and model selection.
• Uncertainty quantification, inverse problems, and optimal control strategies to homogenize perfusion or improve therapy.
• Experimental validation and translational studies linking model predictions to biomarkers, imaging, or clinical protocols.

We welcome original research articles, methodological papers (numerics, inference, high-performance computing), short communications demonstrating novel hypotheses, and review articles synthesizing PDE-based approaches across biological and clinical domains.

Dr. José Alberto Rodrigues
Dr. Jacinta Serpa
Guest Editors

Manuscript Submission Information

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