{
  "abstract": "Standard Zhang–Gatenby adaptive cancer therapy protocols pause dosing when a tumor biomarker (such as PSA or ctDNA) reaches 50% of baseline, assuming instantaneous drug clearance. In clinical reality, finite pharmacokinetic (PK) elimination half-lives (e.g., abiraterone, enzalutamide, osimertinib) drive a post-cessation washout nadir that can breach the competitive containment floor K/α and trigger competitive release of resistant clones.\n\nIn this paper we prove three exact analytical results for evolutionary containment under finite PK clearance:\n\nExact Poisson–Bernoulli Solution & Inverse Safe-Stopping Law: We integrate the non-autonomous PK-washout Bernoulli ODE in closed form via Poisson expectations and derive the exact stopping threshold S*_stop(S_floor, C_off) guaranteeing min_{t ≥ 0} S(t) = S_floor = K/α.\n\nVolterra–Oncology Cycle Conservation Law: Over any periodic adaptive cycle of period T, the time-averaged clonal burdens satisfy &langle;S&rangle;_T + β&langle;R&rangle;_T = K(1 - k_d&langle;C&rangle;_T / r_S), yielding the universal dosing speed limit k_d&langle;C&rangle;_T < r_S(1 - 1/α).\n\nModel-Free Equal-Burden Hysteresis Slope Observer: We prove that the hidden resistant population R(t) can be reconstructed directly from total biomarker slopes at equal total burden N on the off-treatment and on-treatment branches without knowing r_S, K, α, or β.",
  "abstract_shown": true,
  "affiliations": [
    "Independent Researcher, Lisburn, Northern Ireland"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Gareth Montgomery"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bwnnn1df4ng5q.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23611278",
  "fulltext_url": null,
  "id": "bwnnn1df4ng5q",
  "issns": [],
  "landing_url": "https://zenodo.org/records/23611278",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [],
  "openalex": null,
  "pdf_url": "https://zenodo.org/api/records/23611278/files/Montgomery_2026_Adaptive_Oncology_PK_Washout_Containment.pdf/content",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-24",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bwnnn1df4ng5q.ris",
  "sources": [
    {
      "first_seen": "2026-11-07T12:21:33Z",
      "native_id": "23611278",
      "source": "zenodo",
      "url": "https://zenodo.org/records/23611278"
    }
  ],
  "subjects": [],
  "title": "Exact Pharmacokinetic Washout Bounds, Cycle Conservation Laws, and Model-Free Resistance Observers in Adaptive Cancer Containment",
  "title_text": "Exact Pharmacokinetic Washout Bounds, Cycle Conservation Laws, and Model-Free Resistance Observers in Adaptive Cancer Containment",
  "type": "preprint",
  "updated_at": "2026-11-07T12:21:33Z",
  "url": "https://research.draconitic.com/paper/bwnnn1df4ng5q",
  "venue": "Zenodo",
  "versions": []
}