{
  "abstract": "Once diagnosed, cancer requires a fast, reliable and preferably cost-efficient assessment of the current state and potential progression of the disease. A new method for estimating tumor cell diffusivity $D$ and proliferation rate $γ$ in the context of the mechanistic reaction-diffusion equation from single-point-in-time routine biopsies aims to deliver just that, and quantities computed from the parameter estimates have recently been tested as a new biomarkers for risk-stratification in radiotherapy. Here, we extend the findings of this previous work by providing a first theoretical validation. The method is applied to in-silico biopsies which are generated by solving the two-dimensional reaction-diffusion equation for different growth terms (exponential and logistic) with a Dirac-Delta initial condition, and transforming the continuous results into spatial point patterns via a form of reverse coarse-graining. If no information about tumor age is used, in short-term experiments the original dispersion length $\\sqrt{D/γ}$ could be retrieved with a relative root mean squared error (RRMSE) of around 8% and an $\\text{R}^2$-value of 0.97. In long-term experiments, the RRMSEs ranged from 8 to 14% and the $\\text{R}^2$-values from 0.75 to 0.98. The scaled front velocity $\\sqrt{D \\cdotγ}$, which can only be estimated if information about tumor age is available, was retrieved with an RRMSE of 7% and an $\\text{R}^2$ of 0.98 in both, the short-term and the long-term experiments.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.22363",
  "author_total": 5,
  "authors": [
    {
      "name": "Veronika Hofmann"
    },
    {
      "name": "Pirmin Schlicke"
    },
    {
      "name": "Jan Zawallich"
    },
    {
      "name": "Heiko Enderling"
    },
    {
      "name": "Christina Kuttler"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/agxvy95xnewkp.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.22363",
  "fulltext_url": null,
  "id": "agxvy95xnewkp",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.22363",
  "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",
      "q-bio.OT"
    ],
    [
      "openalex",
      "2611|Mathematical Biology Tumor Growth"
    ]
  ],
  "openalex": "W7214040748",
  "pdf_url": "https://arxiv.org/pdf/2609.22363",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-17",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/agxvy95xnewkp.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:28Z",
      "native_id": "2609.22363",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.22363"
    }
  ],
  "subjects": [
    {
      "field": "biology",
      "origin": "arxiv:q-bio.OT",
      "subfield": "general"
    }
  ],
  "title": "2D reaction-diffusion model-based biopsy simulation for dynamic tumor growth parameter estimation",
  "title_text": "2D reaction-diffusion model-based biopsy simulation for dynamic tumor growth parameter estimation",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:28Z",
  "url": "https://research.draconitic.com/paper/agxvy95xnewkp",
  "venue": "arXiv",
  "versions": []
}