{
  "abstract": "Spatially restricted immune access can undermine tumour control even when total immune recruitment appears sufficient. We develop a nondimensional reaction--diffusion--chemotaxis model for hepatocellular carcinoma that couples tumour growth and immune-mediated killing with effector diffusion, saturating chemokine-dependent recruitment, and migration along an effective CXCL9/CXCL10/CXCL11--CXCR3 signal. We establish nonnegativity, uniform tumour and mass bounds, and global boundedness of classical solutions in one dimension and, in arbitrary dimensions, when chemokine production is tumour-driven. Analysis of the homogeneous dynamics shows that the threshold $σ_0>δ$ is only local and does not preclude bistable tumour persistence. A mode-wise dispersion relation identifies stationary finite-wavelength and oscillatory instabilities, whose critical sensitivities, dominant modes, growth rates, and frequencies are quantitatively recovered by conservative finite-volume simulations. Using matched initial states and identical mean recruitment, we show that a well-mixed model may predict clearance while margin-limited recruitment preserves a stable interior tumour refuge. Chemotaxis improves interior effector access and reduces, but need not eliminate, this refuge. Spatial-overlap biomarkers further connect model-generated phenotypes to pathology and spatial-omics observables. These results distinguish immune abundance from effective spatial access and identify access-limited recruitment as a mechanism of incomplete tumour control.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.27949",
  "author_total": 2,
  "authors": [
    {
      "name": "Jiguang Yu"
    },
    {
      "name": "Louis Shuo Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/df6kvrh0kweha.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.27949",
  "fulltext_url": null,
  "id": "df6kvrh0kweha",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.27949",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AP"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2609.27949",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/df6kvrh0kweha.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:00Z",
      "native_id": "2609.27949",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.27949"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Spatially Limited Immune Access Creates Tumour Refugia in Hepatocellular Carcinoma",
  "title_text": "Spatially Limited Immune Access Creates Tumour Refugia in Hepatocellular Carcinoma",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:00Z",
  "url": "https://research.draconitic.com/paper/df6kvrh0kweha",
  "venue": "arXiv",
  "versions": []
}