Exact Pharmacokinetic Washout Bounds, Cycle Conservation Laws, and Model-Free Resistance Observers in Adaptive Cancer Containment
- 1Independent Researcher, Lisburn, Northern Ireland
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.
In this paper we prove three exact analytical results for evolutionary containment under finite PK clearance:
Exact 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.
Volterra–Oncology Cycle Conservation Law: Over any periodic adaptive cycle of period T, the time-averaged clonal burdens satisfy ⟨S⟩_T + β⟨R⟩_T = K(1 - k_d⟨C⟩_T / r_S), yielding the universal dosing speed limit k_d⟨C⟩_T < r_S(1 - 1/α).
Model-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.
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BibTeX
@misc{montgomery2026exact,
title = {{Exact Pharmacokinetic Washout Bounds, Cycle Conservation Laws, and Model-Free Resistance Observers in Adaptive Cancer Containment}},
author = {Gareth Montgomery},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23611278},
url = {https://zenodo.org/records/23611278},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Exact Pharmacokinetic Washout Bounds, Cycle Conservation Laws, and Model-Free Resistance Observers in Adaptive Cancer Containment
AU - Gareth Montgomery
PY - 2026
DA - 2026/10/24
PB - Zenodo
DO - 10.5281/zenodo.23611278
UR - https://zenodo.org/records/23611278
AB - 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. In this paper we prove three exact analytical results for evolutionary containment under finite PK clearance: Exact 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. Volterra–Oncology Cycle Conservation Law: Over any periodic adaptive cycle of period T, the time-averaged clonal burdens satisfy ⟨S⟩_T + β⟨R⟩_T = K(1 - k_d⟨C⟩_T / r_S), yielding the universal dosing speed limit k_d⟨C⟩_T < r_S(1 - 1/α). Model-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.
ER -