Computational frameworks for modelling cancer across scales

Abstract

Purpose: Cancer progression is a non-linear, multiscale process driven by the interaction of molecular, cellular and tissue systems, which ultimately leads to tumour growth, invasion and metastasis. Understanding and predicting these dynamics is essential for improving diagnostics and personalising therapy. Mathematical and computational modelling has become central to this effort, enabling in silico simulations of progression and treatment response.

Methods: This survey outlines computational frameworks for modelling cancer across biological scales, incorporating mathematical formalisms and algorithmic paradigms. These frameworks include: ordinary and partial differential equation models of growth, angiogenesis and invasion; agent-based and hybrid multiscale approaches that capture heterogeneity and microenvironmental feedback; emerging digital twin platforms that integrate mechanistic and data-driven modelling for patient-specific predictions. Recent advances in artificial intelligence (AI), such as graph neural networks, transformer-based architectures and multimodal data fusion, enhance these frameworks by combining interpretability with predictive power through mechanistic learning pipelines.

Results: Based on these advances, the survey presents a conceptual roadmap for multiscale cancer modelling. This roadmap offers a structured workflow that begins with defining the biological question and modelling scale and continues through selecting appropriate paradigms, calibrating and validating models with experimental or clinical data and integrating multimodal information into individualised simulations. The long-term goal is to develop digital twins of cancer that can personalise and optimise therapy and ultimately guide clinical decisions. These models will capture processes ranging from single-cell dynamics and cancer progression to angiogenesis, tumour evolution and treatment response. To achieve this vision, we need advances in parameter calibration, multimodal dataset integration and cross-scale model validation.

Conclusion: Computational oncology bridges the gap between biological mechanisms and predictive modelling, offering a framework for reproducible, data-driven precision medicine. The convergence of mechanistic modelling, AI-assisted inference and digital twin technologies establishes a continuum for translating research into real-time, patient-specific decision support in oncology.

Keywords

agent-based models / cancer / computational oncology / digital twins / hybrid models / machine learning / mathematical modelling / mechanistic learning / multiscale modelling / precision medicine

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2025 The Author(s). Clinical and Translational Discovery published by John Wiley & Sons Australia, Ltd on behalf of Shanghai Institute of Clinical Bioinformatics.