Cahn-Hilliard phase-field modeling of tumor growth via locally adaptive isogeometric analysis with THB-splines

Abstract

Predicting tumor dynamics in biological systems under physiologically relevant conditions using mathematical and computational models remains a challenging problem. Continuum models based on phase-field (diffuse-interface) formulations have proven to be an effective modeling strategy to govern tumor dynamics and interactions of multiple species. Within this framework, the present work investigates a tumor growth model based on the Cahn-Hilliard (CH) equation. The formulation involves a fourth-order differential operator that imposes higher continuity requirement on approximation spaces for a well-defined primal variational formulation. To address this challenge, we use isogeometric analysis (IGA), which inherently satisfies this requirement through spline-based basis functions and eliminates the need for mixed or auxiliary-variable approaches commonly used in standard finite element discretizations. Additionally, a locally adaptive IGA scheme with truncated hierarchical B-splines (THB-splines) is used to reduce computational cost while maintaining accuracy. The model is first evaluated on standard benchmark cases and then applied to an organ-scale, patient-specific geometric model of the breast reconstructed from magnetic resonance imaging (MRI) data. Our results show that the model reproduces known tumor morphologies, ranging from a spheroidal pattern to fingered growth. A series of numerical experiments further shows the diversity of tumor dynamics produced by different model parameter choices. Our findings demonstrate the predictive potential of the CH-based phase-field tumor growth model integrated with a locally adaptive IGA framework.

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BibTeX RIS

BibTeX

@misc{bombarde2026cahnhilliard,
  title = {{Cahn-Hilliard phase-field modeling of tumor growth via locally adaptive isogeometric analysis with THB-splines}},
  author = {Dhiraj S. Bombarde and Carlotta Giannelli and Alessandro Reali and Guillermo Lorenzo},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2609.08479},
  eprint = {2609.08479},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.08479},
  note = {CC BY-NC-SA 4.0},
}

RIS

TY  - UNPB
TI  - Cahn-Hilliard phase-field modeling of tumor growth via locally adaptive isogeometric analysis with THB-splines
AU  - Dhiraj S. Bombarde
AU  - Carlotta Giannelli
AU  - Alessandro Reali
AU  - Guillermo Lorenzo
PY  - 2026
DA  - 2026/10/02
PB  - arXiv
DO  - 10.48550/arxiv.2609.08479
UR  - https://arxiv.org/abs/2609.08479
AB  - Predicting tumor dynamics in biological systems under physiologically relevant conditions using mathematical and computational models remains a challenging problem. Continuum models based on phase-field (diffuse-interface) formulations have proven to be an effective modeling strategy to govern tumor dynamics and interactions of multiple species. Within this framework, the present work investigates a tumor growth model based on the Cahn-Hilliard (CH) equation. The formulation involves a fourth-order differential operator that imposes higher continuity requirement on approximation spaces for a well-defined primal variational formulation. To address this challenge, we use isogeometric analysis (IGA), which inherently satisfies this requirement through spline-based basis functions and eliminates the need for mixed or auxiliary-variable approaches commonly used in standard finite element discretizations. Additionally, a locally adaptive IGA scheme with truncated hierarchical B-splines (THB-splines) is used to reduce computational cost while maintaining accuracy. The model is first evaluated on standard benchmark cases and then applied to an organ-scale, patient-specific geometric model of the breast reconstructed from magnetic resonance imaging (MRI) data. Our results show that the model reproduces known tumor morphologies, ranging from a spheroidal pattern to fingered growth. A series of numerical experiments further shows the diversity of tumor dynamics produced by different model parameter choices. Our findings demonstrate the predictive potential of the CH-based phase-field tumor growth model integrated with a locally adaptive IGA framework.
ER  -

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