{
  "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.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.08479",
  "author_total": 4,
  "authors": [
    {
      "name": "Dhiraj S. Bombarde"
    },
    {
      "name": "Carlotta Giannelli"
    },
    {
      "name": "Alessandro Reali"
    },
    {
      "name": "Guillermo Lorenzo"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4b80mrbw0t6z0.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.08479",
  "fulltext_url": null,
  "id": "4b80mrbw0t6z0",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.08479",
  "language": null,
  "licence": "CC-BY-NC-SA-4.0",
  "licence_label": "CC BY-NC-SA 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.NA"
    ],
    [
      "arxiv",
      "math.NA"
    ],
    [
      "openalex",
      "2611|Mathematical Biology Tumor Growth"
    ]
  ],
  "openalex": "W7212057604",
  "pdf_url": "https://arxiv.org/pdf/2609.08479",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4b80mrbw0t6z0.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:50Z",
      "native_id": "2609.08479",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.08479"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "Cahn-Hilliard phase-field modeling of tumor growth via locally adaptive isogeometric analysis with THB-splines",
  "title_text": "Cahn-Hilliard phase-field modeling of tumor growth via locally adaptive isogeometric analysis with THB-splines",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:50Z",
  "url": "https://research.draconitic.com/paper/4b80mrbw0t6z0",
  "venue": "arXiv",
  "versions": []
}