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Peer-reviewedCC BY 4.0Royal Society Open Science

A Liouville dynamical modelling and control framework for oesophageal cancer-induced immune response

  • Souvik Roy1
  • Naif Abu Qarnayn2
  • Mesfer H. F. Alajmi3
  • Asma Alghamdi4
  • Ibrahem Alshaoosh4
  • Shreshtha Chaturvedi5
  • Olusola Dehinsilu1
  • Rodina El-Adawy1
  • Darsh Gandhi6
  • DeAnna Patterson1
  • Jordan Rodriguez1
6 affiliations
  1. 1Department of Mathematics, The University of Texas at Arlington 1 , Arlington, TX, USA
  2. 2Majmaah University 2 , Al Majmaah, Riyadh Province, Saudi Arabia
  3. 3Najran University 3 , Najran, Najran Province, Saudi Arabia
  4. 4University of Tabouk 4 , Tabuk, Tabuk Province, Saudi Arabia
  5. 5UT Southwestern Medical Center 5 , Dallas, TX, USA
  6. 6University of Maryland College Park 6 , College Park, MD, USA
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Abstract

A Liouville-based framework is developed for optimizing treatment strategies in oesophageal cancer (OC) while accounting for inter-patient heterogeneity. Variability within a patient cohort is represented through uncertain initial cancer and immune cell populations, whose probability distribution is propagated by a Liouville partial differential equation while the underlying individual dynamics remains deterministic. Two optimization problems are considered. First, model parameters are estimated from population-level data using an adjoint-based projected nonlinear conjugate-gradient (NCG) method. Second, optimal time-dependent combinations of chemotherapy and immunotherapy are determined using a sequential quadratic Hamiltonian (SQH) scheme based on Pontryagin’s maximum principle (PMP). The Liouville equation is discretized using a finite-volume method designed to preserve positivity and conservation of the probability density. Numerical experiments with synthetic population data are used to demonstrate the parameter-estimation framework and the ability of the proposed optimal control strategy to determine treatment protocols that effectively modify the population-level cancer–immune response while limiting treatment exposure.

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Cite

BibTeXRIS
BibTeX
@article{roy2026liouville,
  title = {{A Liouville dynamical modelling and control framework for oesophageal cancer-induced immune response}},
  author = {Souvik Roy and Naif Abu Qarnayn and Mesfer H. F. Alajmi and Asma Alghamdi and Ibrahem Alshaoosh and Shreshtha Chaturvedi and Olusola Dehinsilu and Rodina El-Adawy and Darsh Gandhi and DeAnna Patterson and Jordan Rodriguez},
  journal = {Royal Society Open Science},
  year = {2026},
  month = oct,
  doi = {10.1098/rsos.261866},
  url = {https://royalsocietypublishing.org/rsos/article/13/10/261866/483957/A-Liouville-dynamical-modelling-and-control},
  note = {CC BY 4.0},
}
RIS
TY  - JOUR
TI  - A Liouville dynamical modelling and control framework for oesophageal cancer-induced immune response
AU  - Souvik Roy
AU  - Naif Abu Qarnayn
AU  - Mesfer H. F. Alajmi
AU  - Asma Alghamdi
AU  - Ibrahem Alshaoosh
AU  - Shreshtha Chaturvedi
AU  - Olusola Dehinsilu
AU  - Rodina El-Adawy
AU  - Darsh Gandhi
AU  - DeAnna Patterson
AU  - Jordan Rodriguez
PY  - 2026
DA  - 2026/10/07
JO  - Royal Society Open Science
DO  - 10.1098/rsos.261866
UR  - https://royalsocietypublishing.org/rsos/article/13/10/261866/483957/A-Liouville-dynamical-modelling-and-control
AB  - A Liouville-based framework is developed for optimizing treatment strategies in oesophageal cancer (OC) while accounting for inter-patient heterogeneity. Variability within a patient cohort is represented through uncertain initial cancer and immune cell populations, whose probability distribution is propagated by a Liouville partial differential equation while the underlying individual dynamics remains deterministic. Two optimization problems are considered. First, model parameters are estimated from population-level data using an adjoint-based projected nonlinear conjugate-gradient (NCG) method. Second, optimal time-dependent combinations of chemotherapy and immunotherapy are determined using a sequential quadratic Hamiltonian (SQH) scheme based on Pontryagin’s maximum principle (PMP). The Liouville equation is discretized using a finite-volume method designed to preserve positivity and conservation of the probability density. Numerical experiments with synthetic population data are used to demonstrate the parameter-estimation framework and the ability of the proposed optimal control strategy to determine treatment protocols that effectively modify the population-level cancer–immune response while limiting treatment exposure.
SN  - 2054-5703
ER  -