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Roy S, Pal S, Manoj A, Kakarla S, Padilla JV, Alajmi M. A Fokker-Planck Framework for Parameter Estimation and Sensitivity Analysis in Colon Cancer. AIP CONFERENCE PROCEEDINGS 2022; 2522:070005. [PMID: 36276480 PMCID: PMC9583768 DOI: 10.1063/5.0100741] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/16/2023]
Abstract
A new stochastic framework for parameter estimation and uncertainty quantification in colon cancer-induced immune response is presented. The dynamics of colon cancer is given by a stochastic process that captures the inherent randomness in the system. The stochastic framework is based on the Fokker-Planck equation that represents the evolution of the probability density function corresponding to the stochastic process. An optimization problem is formulated that takes input individual patient data with randomness present, and is solved to obtain the unknown parameters corresponding to the individual tumor characteristics. Furthermore, sensitivity analysis of the optimal parameter set is performed to determine the parameters that need to be controlled, thus, providing information of the type of drugs that can be used for treatment.
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Affiliation(s)
- S. Roy
- Department of Mathematics, The University of Texas at Arlington, Arlington, TX 76019-0408, USA
| | - S. Pal
- Department of Mathematics, The University of Texas at Arlington, Arlington, TX 76019-0408, USA
| | - A. Manoj
- Department of Physics, The University of Texas at Arlington, Arlington, TX 76019-0408, USA
| | - S. Kakarla
- Department of Computer Science, The University of Texas at Arlington, Arlington, TX 76019-0408, USA
| | - J. V. Padilla
- Department of Mathematics, The University of Texas at Arlington, Arlington, TX 76019-0408, USA
| | - M. Alajmi
- Department of Mathematics, The University of Texas at Arlington, Arlington, TX 76019-0408, USA
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Abstract
Chronotherapeutics aim at treating illnesses according to the endogenous biologic rhythms, which moderate xenobiotic metabolism and cellular drug response. The molecular clocks present in individual cells involve approximately fifteen clock genes interconnected in regulatory feedback loops. They are coordinated by the suprachiasmatic nuclei, a hypothalamic pacemaker, which also adjusts the circadian rhythms to environmental cycles. As a result, many mechanisms of diseases and drug effects are controlled by the circadian timing system. Thus, the tolerability of nearly 500 medications varies by up to fivefold according to circadian scheduling, both in experimental models and/or patients. Moreover, treatment itself disrupted, maintained, or improved the circadian timing system as a function of drug timing. Improved patient outcomes on circadian-based treatments (chronotherapy) have been demonstrated in randomized clinical trials, especially for cancer and inflammatory diseases. However, recent technological advances have highlighted large interpatient differences in circadian functions resulting in significant variability in chronotherapy response. Such findings advocate for the advancement of personalized chronotherapeutics through interdisciplinary systems approaches. Thus, the combination of mathematical, statistical, technological, experimental, and clinical expertise is now shaping the development of dedicated devices and diagnostic and delivery algorithms enabling treatment individualization. In particular, multiscale systems chronopharmacology approaches currently combine mathematical modeling based on cellular and whole-body physiology to preclinical and clinical investigations toward the design of patient-tailored chronotherapies. We review recent systems research works aiming to the individualization of disease treatment, with emphasis on both cancer management and circadian timing system–resetting strategies for improving chronic disease control and patient outcomes.
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Affiliation(s)
- Annabelle Ballesta
- Warwick Medical School (A.B., P.F.I., R.D., F.A.L.) and Warwick Mathematics Institute (A.B., D.A.R.), University of Warwick, Coventry, United Kingdom; Warwick Systems Biology and Infectious Disease Epidemiological Research Centre, Senate House, Coventry, United Kingdom (A.B., P.F.I., R.D., D.A.R., F.A.L.); INSERM-Warwick European Associated Laboratory "Personalising Cancer Chronotherapy through Systems Medicine" (C2SysMed), Unité mixte de Recherche Scientifique 935, Centre National de Recherche Scientifique Campus, Villejuif, France (A.B., P.F.I., R.D., D.A.R., F.A.L.); and Queen Elisabeth Hospital Birmingham, University Hospitals Birmingham National Health Service Foundation Trust, Cancer Unit, Edgbaston Birmingham, United Kingdom (P.F.I., F.A.L.)
| | - Pasquale F Innominato
- Warwick Medical School (A.B., P.F.I., R.D., F.A.L.) and Warwick Mathematics Institute (A.B., D.A.R.), University of Warwick, Coventry, United Kingdom; Warwick Systems Biology and Infectious Disease Epidemiological Research Centre, Senate House, Coventry, United Kingdom (A.B., P.F.I., R.D., D.A.R., F.A.L.); INSERM-Warwick European Associated Laboratory "Personalising Cancer Chronotherapy through Systems Medicine" (C2SysMed), Unité mixte de Recherche Scientifique 935, Centre National de Recherche Scientifique Campus, Villejuif, France (A.B., P.F.I., R.D., D.A.R., F.A.L.); and Queen Elisabeth Hospital Birmingham, University Hospitals Birmingham National Health Service Foundation Trust, Cancer Unit, Edgbaston Birmingham, United Kingdom (P.F.I., F.A.L.)
| | - Robert Dallmann
- Warwick Medical School (A.B., P.F.I., R.D., F.A.L.) and Warwick Mathematics Institute (A.B., D.A.R.), University of Warwick, Coventry, United Kingdom; Warwick Systems Biology and Infectious Disease Epidemiological Research Centre, Senate House, Coventry, United Kingdom (A.B., P.F.I., R.D., D.A.R., F.A.L.); INSERM-Warwick European Associated Laboratory "Personalising Cancer Chronotherapy through Systems Medicine" (C2SysMed), Unité mixte de Recherche Scientifique 935, Centre National de Recherche Scientifique Campus, Villejuif, France (A.B., P.F.I., R.D., D.A.R., F.A.L.); and Queen Elisabeth Hospital Birmingham, University Hospitals Birmingham National Health Service Foundation Trust, Cancer Unit, Edgbaston Birmingham, United Kingdom (P.F.I., F.A.L.)
| | - David A Rand
- Warwick Medical School (A.B., P.F.I., R.D., F.A.L.) and Warwick Mathematics Institute (A.B., D.A.R.), University of Warwick, Coventry, United Kingdom; Warwick Systems Biology and Infectious Disease Epidemiological Research Centre, Senate House, Coventry, United Kingdom (A.B., P.F.I., R.D., D.A.R., F.A.L.); INSERM-Warwick European Associated Laboratory "Personalising Cancer Chronotherapy through Systems Medicine" (C2SysMed), Unité mixte de Recherche Scientifique 935, Centre National de Recherche Scientifique Campus, Villejuif, France (A.B., P.F.I., R.D., D.A.R., F.A.L.); and Queen Elisabeth Hospital Birmingham, University Hospitals Birmingham National Health Service Foundation Trust, Cancer Unit, Edgbaston Birmingham, United Kingdom (P.F.I., F.A.L.)
| | - Francis A Lévi
- Warwick Medical School (A.B., P.F.I., R.D., F.A.L.) and Warwick Mathematics Institute (A.B., D.A.R.), University of Warwick, Coventry, United Kingdom; Warwick Systems Biology and Infectious Disease Epidemiological Research Centre, Senate House, Coventry, United Kingdom (A.B., P.F.I., R.D., D.A.R., F.A.L.); INSERM-Warwick European Associated Laboratory "Personalising Cancer Chronotherapy through Systems Medicine" (C2SysMed), Unité mixte de Recherche Scientifique 935, Centre National de Recherche Scientifique Campus, Villejuif, France (A.B., P.F.I., R.D., D.A.R., F.A.L.); and Queen Elisabeth Hospital Birmingham, University Hospitals Birmingham National Health Service Foundation Trust, Cancer Unit, Edgbaston Birmingham, United Kingdom (P.F.I., F.A.L.)
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