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Roy S, Pan Z, Abu Qarnayn N, Alajmi M, Alatawi A, Alghamdi A, Alshaoosh I, Asiri Z, Batista B, Chaturvedi S, Dehinsilu O, Edduweh H, El-Adawy R, Hossen E, Mojra B, Rana J. A robust optimal control framework for controlling aberrant RTK signaling pathways in esophageal cancer. J Math Biol 2024; 88:14. [PMID: 38180543 DOI: 10.1007/s00285-023-02033-0] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/02/2023] [Revised: 09/18/2023] [Accepted: 11/27/2023] [Indexed: 01/06/2024]
Abstract
This study presents a new framework for obtaining personalized optimal treatment strategies targeting aberrant signaling pathways in esophageal cancer, such as the epidermal growth factor (EGF) and vascular endothelial growth factor (VEGF) signaling pathways. A new pharmacokinetic model is developed taking into account specific heterogeneities of these signaling mechanisms. The optimal therapies are designed to be obtained using a three step process. First, a finite-dimensional constrained optimization problem is solved to obtain the parameters of the pharmacokinetic model, using discrete patient data measurements. Next, a sensitivity analysis is carried out to determine which of the parameters are sensitive to the evolution of the variants of EGF receptors and VEGF receptors. Finally, a second optimal control problem is solved based on the sensitivity analysis results, using a modified pharmacokinetic model that incorporates two representative drugs Trastuzumab and Bevacizumab, targeting EGF and VEGF, respectively. Numerical results with the combination of the two drugs demonstrate the efficiency of the proposed framework.
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Affiliation(s)
- Souvik Roy
- Department of Mathematics, The University of Texas at Arlington, Arlington, TX, 76019-0407, USA.
| | - Zui Pan
- College of Nursing and Health Innovation, The University of Texas at Arlington, Arlington, TX, 76019-0407, USA
| | - Naif Abu Qarnayn
- Department of Mathematics, The University of Texas at Arlington, Arlington, TX, 76019-0407, USA
| | - Mesfer Alajmi
- Department of Mathematics, The University of Texas at Arlington, Arlington, TX, 76019-0407, USA
| | - Ali Alatawi
- Department of Mathematics, The University of Texas at Arlington, Arlington, TX, 76019-0407, USA
| | - Asma Alghamdi
- Department of Mathematics, The University of Texas at Arlington, Arlington, TX, 76019-0407, USA
| | - Ibrahem Alshaoosh
- Department of Mathematics, The University of Texas at Arlington, Arlington, TX, 76019-0407, USA
| | - Zahra Asiri
- Department of Mathematics, The University of Texas at Arlington, Arlington, TX, 76019-0407, USA
| | - Berlinda Batista
- Department of Mathematics, The University of Texas at Arlington, Arlington, TX, 76019-0407, USA
| | - Shreshtha Chaturvedi
- Department of Mathematics, The University of Texas at Arlington, Arlington, TX, 76019-0407, USA
| | - Olusola Dehinsilu
- Department of Mathematics, The University of Texas at Arlington, Arlington, TX, 76019-0407, USA
| | - Hussein Edduweh
- Department of Mathematics, The University of Texas at Arlington, Arlington, TX, 76019-0407, USA
| | - Rodina El-Adawy
- Department of Mathematics, The University of Texas at Arlington, Arlington, TX, 76019-0407, USA
| | - Emran Hossen
- Department of Mathematics, The University of Texas at Arlington, Arlington, TX, 76019-0407, USA
| | - Bardia Mojra
- Department of Computer Science, The University of Texas at Arlington, Arlington, TX, 76019-0407, USA
| | - Jashmon Rana
- Department of Mathematics, The University of Texas at Arlington, Arlington, TX, 76019-0407, USA
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Pal S, Roy S. On the parameter estimation of Box-Cox transformation cure model. Stat Med 2023. [PMID: 37019798 DOI: 10.1002/sim.9739] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/19/2022] [Revised: 01/17/2023] [Accepted: 03/27/2023] [Indexed: 04/07/2023]
Abstract
We propose an improved estimation method for the Box-Cox transformation (BCT) cure rate model parameters. Specifically, we propose a generic maximum likelihood estimation algorithm through a non-linear conjugate gradient (NCG) method with an efficient line search technique. We then apply the proposed NCG algorithm to BCT cure model. Through a detailed simulation study, we compare the model fitting results of the NCG algorithm with those obtained by the existing expectation maximization (EM) algorithm. First, we show that our proposed NCG algorithm allows simultaneous maximization of all model parameters unlike the EM algorithm when the likelihood surface is flat with respect to the BCT index parameter. Then, we show that the NCG algorithm results in smaller bias and noticeably smaller root mean square error of the estimates of the model parameters that are associated with the cure rate. This results in more accurate and precise inference on the cure rate. In addition, we show that when the sample size is large the NCG algorithm, which only needs the computation of the gradient and not the Hessian, takes less CPU time to produce the estimates. These advantages of the NCG algorithm allows us to conclude that the NCG method should be the preferred estimation method over the already existing EM algorithm in the context of BCT cure model. Finally, we apply the NCG algorithm to analyze a well-known melanoma data and show that it results in a better fit when compared to the EM algorithm.
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Affiliation(s)
- Suvra Pal
- Department of Mathematics, University of Texas at Arlington, 411 S Nedderman Drive, Arlington, Texas, 76019, USA
| | - Souvik Roy
- Department of Mathematics, University of Texas at Arlington, 411 S Nedderman Drive, Arlington, Texas, 76019, USA
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