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Ajayi T, Hosseinian S, Schaefer AJ, Fuller CD. Combination Chemotherapy Optimization with Discrete Dosing. INFORMS JOURNAL ON COMPUTING 2024; 36:434-455. [PMID: 38883557 PMCID: PMC11178284 DOI: 10.1287/ijoc.2022.0207] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/18/2024]
Abstract
Chemotherapy drug administration is a complex problem that often requires expensive clinical trials to evaluate potential regimens; one way to alleviate this burden and better inform future trials is to build reliable models for drug administration. This paper presents a mixed-integer program for combination chemotherapy (utilization of multiple drugs) optimization that incorporates various important operational constraints and, besides dose and concentration limits, controls treatment toxicity based on its effect on the count of white blood cells. To address the uncertainty of tumor heterogeneity, we also propose chance constraints that guarantee reaching an operable tumor size with a high probability in a neoadjuvant setting. We present analytical results pertinent to the accuracy of the model in representing biological processes of chemotherapy and establish its potential for clinical applications through a numerical study of breast cancer.
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Affiliation(s)
| | | | - Andrew J. Schaefer
- Department of Computational Applied Mathematics and Operations Research, Rice University, Houston, Texas 77005
| | - Clifton D. Fuller
- Department of Radiation Oncology, The University of Texas MD Anderson Cancer Center, Houston, Texas 77030
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Kumar A, Dubey US, Dubey B. The impact of radio-chemotherapy on tumour cells interaction with optimal control and sensitivity analysis. Math Biosci 2024; 369:109146. [PMID: 38246323 DOI: 10.1016/j.mbs.2024.109146] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/20/2023] [Revised: 12/23/2023] [Accepted: 01/17/2024] [Indexed: 01/23/2024]
Abstract
Oncologists and applied mathematicians are interested in understanding the dynamics of cancer-immune interactions, mainly due to the unpredictable nature of tumour cell proliferation. In this regard, mathematical modelling offers a promising approach to comprehend this potentially harmful aspect of cancer biology. This paper presents a novel dynamical model that incorporates the interactions between tumour cells, healthy tissue cells, and immune-stimulated cells when subjected to simultaneous chemotherapy and radiotherapy for treatment. We analysed the equilibria and investigated their local stability behaviour. We also study transcritical, saddle-node, and Hopf bifurcations analytically and numerically. We derive the stability and direction conditions for periodic solutions. We identify conditions that lead to chaotic dynamics and rigorously demonstrate the existence of chaos. Furthermore, we formulated an optimal control problem that describes the dynamics of tumour-immune interactions, considering treatments such as radiotherapy and chemotherapy as control parameters. Our goal is to utilize optimal control theory to reduce the cost of radiotherapy and chemotherapy, minimize the harmful effects of medications on the body, and mitigate the burden of cancer cells by maintaining a sufficient population of healthy cells. Cost-effectiveness analysis is employed to identify the most economical strategy for reducing the disease burden. Additionally, we conduct a Latin hypercube sampling-based uncertainty analysis to observe the impact of parameter uncertainties on tumour growth, followed by a sensitivity analysis. Numerical simulations are presented to elucidate how dynamic behaviour of model is influenced by changes in system parameters. The numerical results validate the analytical findings and illustrate that a multi-therapeutic treatment plan can effectively reduce tumour burden within a given time frame of therapeutic intervention.
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Affiliation(s)
- Arjun Kumar
- Department of Mathematics, BITS Pilani, Pilani Campus, Pilani 333031, Rajasthan, India
| | - Uma S Dubey
- Department of Biological Sciences, BITS Pilani, Pilani Campus, Pilani 333031, Rajasthan, India
| | - Balram Dubey
- Department of Mathematics, BITS Pilani, Pilani Campus, Pilani 333031, Rajasthan, India.
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Ahmadi Z, Razminia A. Safe optimal control of cancer using a Control Barrier Function technique. Math Biosci 2024; 369:109142. [PMID: 38218431 DOI: 10.1016/j.mbs.2024.109142] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/28/2023] [Revised: 12/12/2023] [Accepted: 01/09/2024] [Indexed: 01/15/2024]
Abstract
This paper addresses the problem of designing a safe and optimal control strategy for typical cancer using the Control Barrier Function (CBF) technique. Cancer is a complex and highly dynamic disease characterized by uncontrolled cell growth and proliferation. By formulating the cancer dynamics as a control system, this study introduces a CBF-based controller that guides the cancerous tissue towards safe and controlled behaviors. The controller is designed to simultaneously optimize treatment efficacy and patient safety. The methodology involves modeling the cancer growth dynamics, incorporating relevant biological constraints, and designing the CBF-based controller to regulate the tumor's evolution within acceptable bounds. Simulation results demonstrate the effectiveness of the CBF-based strategy in achieving safe and optimal cancer control. The controller showcases the ability to drive the cancerous tissue towards desired states while respecting predefined safety constraints.
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Affiliation(s)
- Zahra Ahmadi
- Department of Electrical Engineering, Faculty of Intelligent Systems Engineering and Data Science, Persian Gulf University, Bushehr, Iran.
| | - Abolhassan Razminia
- Department of Electrical Engineering, Faculty of Intelligent Systems Engineering and Data Science, Persian Gulf University, Bushehr, Iran; Process Control Laboratory, Faculty of Natural Sciences and Engineering, Å bo Akademi University, Turku, Finland.
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Lee D, V AADLR, Kim Y. Optimal strategies of oncolytic virus-bortezomib therapy via the apoptotic, necroptotic, and oncolysis signaling network. MATHEMATICAL BIOSCIENCES AND ENGINEERING : MBE 2024; 21:3876-3909. [PMID: 38549312 DOI: 10.3934/mbe.2024173] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/02/2024]
Abstract
Bortezomib and oncolytic virotherapy are two emerging targeted cancer therapies. Bortezomib, a proteasome inhibitor, disrupts protein degradation in cells, leading to the accumulation of unfolded proteins that induce apoptosis. On the other hand, virotherapy uses genetically modified oncolytic viruses (OVs) to infect cancer cells, trigger cell lysis, and activate anti-tumor response. Despite progress in cancer treatment, identifying administration protocols for therapeutic agents remains a significant concern, aiming to strike a balance between efficacy, minimizing toxicity, and administrative costs. In this work, optimal control theory was employed to design a cost-effective and efficient co-administration protocols for bortezomib and OVs that could significantly diminish the population of cancer cells via the cell death program with the NF$ \kappa $B-BAX-RIP1 signaling network. Both linear and quadratic control strategies were explored to obtain practical treatment approaches by adapting necroptosis protocols to efficient cell death programs. Our findings demonstrated that a combination therapy commencing with the administration of OVs followed by bortezomib infusions yields an effective tumor-killing outcome. These results could provide valuable guidance for the development of clinical administration protocols in cancer treatment.
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Affiliation(s)
- Donggu Lee
- Department of Mathematics, Konkuk University, Seoul, Republic of Korea
| | - Aurelio A de Los Reyes V
- Institute of Mathematics, University of the Philippines Diliman, Quezon City 1101, Philippines
- Biomedical Mathematics Group, Pioneer Research Center for Mathematical and Computational Sciences, Institute for Basic Science, Daejeon 34126, Republic of Korea
| | - Yangjin Kim
- Department of Mathematics, Konkuk University, Seoul, Republic of Korea
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5
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Samy PG, Kanesan J, Badruddin IA, Kamangar S, Ahammad NA. Optimizing chemotherapy treatment outcomes using metaheuristic optimization algorithms: A case study. Biomed Mater Eng 2024; 35:191-204. [PMID: 38143334 DOI: 10.3233/bme-230149] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/26/2023]
Abstract
BACKGROUND This study explores the dynamics of a mathematical model, utilizing ordinary differential equations (ODE), to depict the interplay between cancer cells and effector cells under chemotherapy. The stability of the equilibrium points in the model is analysed using the Jacobian matrix and eigenvalues. Additionally, bifurcation analysis is conducted to determine the optimal values for the control parameters. OBJECTIVE To evaluate the performance of the model and control strategies, benchmarking simulations are performed using the PlatEMO platform. METHODS The Pure Multi-objective Optimal Control Problem (PMOCP) and the Hybrid Multi-objective Optimal Control Problem (HMOCP) are two different forms of optimal control problems that are solved using revolutionary metaheuristic optimisation algorithms. The utilization of the Hypervolume (HV) performance indicator allows for the comparison of various metaheuristic optimization algorithms in their efficacy for solving the PMOCP and HMOCP. RESULTS Results indicate that the MOPSO algorithm excels in solving the HMOCP, with M-MOPSO outperforming for PMOCP in HV analysis. CONCLUSION Despite not directly addressing immediate clinical concerns, these findings indicates that the stability shifts at critical thresholds may impact treatment efficacy.
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Affiliation(s)
- Prakas Gopal Samy
- Department of Electrical Engineering, Faculty of Engineering, University of Malaya, Kuala Lumpur, Malaysia
- Department of Electrical & Electronics Engineering, Faculty of Engineering, Built Environment & Information Technology, SEGi University & Colleges, Kota Damansara, Petaling Jaya, Selangor, Malaysia
| | - Jeevan Kanesan
- Department of Electrical Engineering, Faculty of Engineering, University of Malaya, Kuala Lumpur, Malaysia
| | - Irfan Anjum Badruddin
- Mechanical Engineering Department, College of Engineering, King Khalid University, Abha, Saudi Arabia
| | - Sarfaraz Kamangar
- Mechanical Engineering Department, College of Engineering, King Khalid University, Abha, Saudi Arabia
| | - N Ameer Ahammad
- Department of Mathematics, Faculty of Science, University of Tabuk, Tabuk, Saudi Arabia
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Saldaña F, Kebir A, Camacho-Gutiérrez JA, Aguiar M. Optimal vaccination strategies for a heterogeneous population using multiple objectives: The case of L 1- and L 2-formulations. Math Biosci 2023; 366:109103. [PMID: 37918477 DOI: 10.1016/j.mbs.2023.109103] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/12/2023] [Revised: 09/29/2023] [Accepted: 10/28/2023] [Indexed: 11/04/2023]
Abstract
The choice of the objective functional in optimization problems coming from biomedical and epidemiological applications plays a key role in optimal control outcomes. In this study, we investigate the role of the objective functional on the structure of the optimal control solution for an epidemic model for sexually transmitted infections that includes a core group with higher sexual activity levels than the rest of the population. An optimal control problem is formulated to find a targeted vaccination program able to control the spread of the infection with minimum vaccine deployment. Both L1- and L2-objectives are considered as an attempt to explore the trade-offs between control dynamics and the functional form characterizing optimality. The results show that the optimal vaccination policies for both the L1- and the L2-formulation share one important qualitative property, that is, immunization of the core group should be prioritized by policymakers to achieve a fast reduction of the epidemic. However, quantitative aspects of this result can be significantly affected depending on the choice of the control weights between formulations. Overall, the results suggest that with appropriate weight constants, the optimal control outcomes are reasonably robust with respect to the L1- or L2-formulation. This is particularly true when the monetary cost of the control policy is substantially lower than the cost associated with the disease burden. Under these conditions, even if the L1-formulation is more realistic from a modeling perspective, the L2-formulation can be used as an approximation and yield qualitatively comparable outcomes.
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Affiliation(s)
| | - Amira Kebir
- Basque Center for Applied Mathematics (BCAM), Bilbao, Spain; IPEIT, Tunis University, Tunis, Tunisia; BIMS-IPT, Tunis El Manar University, Tunis, Tunisia
| | | | - Maíra Aguiar
- Basque Center for Applied Mathematics (BCAM), Bilbao, Spain; Ikerbasque, Basque Foundation for Science, Bilbao, Spain; Dipartimento di Matematica, Università degli Studi di Trento, Trento, Italy
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7
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Sancho-Araiz A, Parra-Guillen ZP, Bragard J, Ardanza S, Mangas-Sanjuan V, Trocóniz IF. Mechanistic characterization of oscillatory patterns in unperturbed tumor growth dynamics: The interplay between cancer cells and components of tumor microenvironment. PLoS Comput Biol 2023; 19:e1011507. [PMID: 37792732 PMCID: PMC10550146 DOI: 10.1371/journal.pcbi.1011507] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/23/2023] [Accepted: 09/11/2023] [Indexed: 10/06/2023] Open
Abstract
Mathematical modeling of unperturbed and perturbed tumor growth dynamics (TGD) in preclinical experiments provides an opportunity to establish translational frameworks. The most commonly used unperturbed tumor growth models (i.e. linear, exponential, Gompertz and Simeoni) describe a monotonic increase and although they capture the mean trend of the data reasonably well, systematic model misspecifications can be identified. This represents an opportunity to investigate possible underlying mechanisms controlling tumor growth dynamics through a mathematical framework. The overall goal of this work is to develop a data-driven semi-mechanistic model describing non-monotonic tumor growth in untreated mice. For this purpose, longitudinal tumor volume profiles from different tumor types and cell lines were pooled together and analyzed using the population approach. After characterizing the oscillatory patterns (oscillator half-periods between 8-11 days) and confirming that they were systematically observed across the different preclinical experiments available (p<10-9), a tumor growth model was built including the interplay between resources (i.e. oxygen or nutrients), angiogenesis and cancer cells. The new structure, in addition to improving the model diagnostic compared to the previously used tumor growth models (i.e. AIC reduction of 71.48 and absence of autocorrelation in the residuals (p>0.05)), allows the evaluation of the different oncologic treatments in a mechanistic way. Drug effects can potentially, be included in relevant processes taking place during tumor growth. In brief, the new model, in addition to describing non-monotonic tumor growth and the interaction between biological factors of the tumor microenvironment, can be used to explore different drug scenarios in monotherapy or combination during preclinical drug development.
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Affiliation(s)
- Aymara Sancho-Araiz
- Pharmacometrics & Systems Pharmacology Group, Department of Pharmaceutical Technology and Chemistry, School of Pharmacy and Nutrition, University of Navarra, Pamplona, Spain
- IdiSNA, Navarra Institute for Health Research, Pamplona, Spain
| | - Zinnia P. Parra-Guillen
- Pharmacometrics & Systems Pharmacology Group, Department of Pharmaceutical Technology and Chemistry, School of Pharmacy and Nutrition, University of Navarra, Pamplona, Spain
- IdiSNA, Navarra Institute for Health Research, Pamplona, Spain
| | - Jean Bragard
- Department of Physics and Applied Math. University of Navarra, Pamplona, Spain
- Institute of Data Science and Artificial Intelligence, DATAI, University of Navarra, Pamplona, Spain
| | - Sergio Ardanza
- Department of Physics and Applied Math. University of Navarra, Pamplona, Spain
- Institute of Data Science and Artificial Intelligence, DATAI, University of Navarra, Pamplona, Spain
| | - Victor Mangas-Sanjuan
- Department of Pharmacy and Pharmaceutical Technology and Parasitology, Faculty of Pharmacy, University of Valencia, Valencia, Spain
- Interuniversity Research Institute for Molecular Recognition and Technological Development, Valencia, Spain
| | - Iñaki F. Trocóniz
- Pharmacometrics & Systems Pharmacology Group, Department of Pharmaceutical Technology and Chemistry, School of Pharmacy and Nutrition, University of Navarra, Pamplona, Spain
- IdiSNA, Navarra Institute for Health Research, Pamplona, Spain
- Institute of Data Science and Artificial Intelligence, DATAI, University of Navarra, Pamplona, Spain
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8
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Handoko H, Wahyudi ST, Setyawan AA, Kartono A. A dynamical model of combination therapy applied to glioma. J Biol Phys 2022; 48:439-459. [PMID: 36367670 PMCID: PMC9727046 DOI: 10.1007/s10867-022-09618-8] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/04/2022] [Accepted: 10/28/2022] [Indexed: 11/13/2022] Open
Abstract
Glioma is a human brain tumor that is very difficult to treat at an advanced stage. Studies of glioma biomarkers have shown that some markers are released into the bloodstream, so data from these markers indicate a decrease in the concentration of blood glucose and serum glucose in patients with glioma; these suggest an association between glucose and glioma. This decrease mechanism in glucose concentration can be described by the coupled ordinary differential equations of the early-stage glioma growth and interactions between glioma cells, immune cells, and glucose concentration. In this paper, we propose developing a new mathematical model to explain how glioma cells evolve and survive combination therapy between chemotherapy and oncolytic virotherapy, as an alternative to glioma treatment. In this study, three therapies were applied for analysis, that is, (1) chemotherapy, (2) virotherapy, and (3) a combination of chemotherapy and virotherapy. Virotherapy uses specialist viruses that only attack tumor cells. Based on the simulation results of the therapy carried out, we conclude that combination therapy can reduce the glioma cells significantly compared to the other two therapies. The simulation results of this combination therapy can be an alternative to glioma therapy.
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Affiliation(s)
- Handoko Handoko
- Department of Physics, Faculty of Mathematical and Natural Science, IPB University (Bogor Agricultural University), Jalan Meranti, Building Wing S, 2nd Floor, Dramaga IPB Campus, 16680, Bogor, Indonesia.
| | - Setyanto Tri Wahyudi
- Department of Physics, Faculty of Mathematical and Natural Science, IPB University (Bogor Agricultural University), Jalan Meranti, Building Wing S, 2nd Floor, Dramaga IPB Campus, 16680, Bogor, Indonesia
| | - Ardian Arif Setyawan
- Department of Physics, Faculty of Mathematical and Natural Science, IPB University (Bogor Agricultural University), Jalan Meranti, Building Wing S, 2nd Floor, Dramaga IPB Campus, 16680, Bogor, Indonesia
| | - Agus Kartono
- Department of Physics, Faculty of Mathematical and Natural Science, IPB University (Bogor Agricultural University), Jalan Meranti, Building Wing S, 2nd Floor, Dramaga IPB Campus, 16680, Bogor, Indonesia.
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9
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Yue R, Dutta A. Computational systems biology in disease modeling and control, review and perspectives. NPJ Syst Biol Appl 2022; 8:37. [PMID: 36192551 PMCID: PMC9528884 DOI: 10.1038/s41540-022-00247-4] [Citation(s) in RCA: 12] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/30/2022] [Accepted: 09/05/2022] [Indexed: 02/02/2023] Open
Abstract
Omics-based approaches have become increasingly influential in identifying disease mechanisms and drug responses. Considering that diseases and drug responses are co-expressed and regulated in the relevant omics data interactions, the traditional way of grabbing omics data from single isolated layers cannot always obtain valuable inference. Also, drugs have adverse effects that may impair patients, and launching new medicines for diseases is costly. To resolve the above difficulties, systems biology is applied to predict potential molecular interactions by integrating omics data from genomic, proteomic, transcriptional, and metabolic layers. Combined with known drug reactions, the resulting models improve medicines' therapeutical performance by re-purposing the existing drugs and combining drug molecules without off-target effects. Based on the identified computational models, drug administration control laws are designed to balance toxicity and efficacy. This review introduces biomedical applications and analyses of interactions among gene, protein and drug molecules for modeling disease mechanisms and drug responses. The therapeutical performance can be improved by combining the predictive and computational models with drug administration designed by control laws. The challenges are also discussed for its clinical uses in this work.
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Affiliation(s)
- Rongting Yue
- Department of Electrical and Computer Engineering, University of Connecticut, 371 Fairfield Way, Storrs, CT, 06269, USA.
| | - Abhishek Dutta
- Department of Electrical and Computer Engineering, University of Connecticut, 371 Fairfield Way, Storrs, CT, 06269, USA
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10
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Mathematical Modeling the Time-Delay Interactions between Tumor Viruses and the Immune System with the Effects of Chemotherapy and Autoimmune Diseases. MATHEMATICS 2022. [DOI: 10.3390/math10050756] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 02/04/2023]
Abstract
The immune system is the body’s defense against pathogens, which are complex living organisms found in many parts in the body including organs, tissues, cells, molecules, and proteins. When the immune system works properly, it can recognize and kill the abnormal cells and the infected cells. Otherwise, it can attack the body’s healthy cells even if there is no invader. Many researchers have developed immunotherapy (or cancer vaccines) and have used chemotherapy for cancer treatment that can kill fast-growing cancer cells or at least slow down tumor growth. However, chemotherapy drugs travel throughout the body and tend to kill both healthy cells and cancer cells. In this study, we consider the fact that chemotherapy can kill tumor cells and that the loss of the immune cells may at the same time stir up cancer growth. We present a dynamic time-delay tumor-immune model with the effects of chemotherapy drugs and autoimmune disease. The modeling results can be used to determine the progression of tumor cells in the human body with the effect of chemotherapy, autoimmune diseases, and time delays based on partial differential equations. It can also be used to predict when the tumor viruses’ free state can be reached as time progresses, as well as the state of the body’s healthy cells as time progresses. We also present a few numerical cases that illustrate that the model can be used to monitor the effects of chemotherapy drug treatment and the growth rate of tumor virus-infected cells and the autoimmune disease.
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de los Reyes AA, Kim Y. Optimal regulation of tumour-associated neutrophils in cancer progression. ROYAL SOCIETY OPEN SCIENCE 2022; 9:210705. [PMID: 35127110 PMCID: PMC8808100 DOI: 10.1098/rsos.210705] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 06/10/2021] [Accepted: 11/19/2021] [Indexed: 06/14/2023]
Abstract
In a tumour microenvironment, tumour-associated neutrophils could display two opposing differential phenotypes: anti-tumour (N1) and pro-tumour (N2) effector cells. Converting N2 to N1 neutrophils provides innovative therapies for cancer treatment. In this study, a mathematical model for N1-N2 dynamics describing the cancer survival and immune inhibition in response to TGF-β and IFN-β is considered. The effects of exogenous intervention of TGF-β inhibitor and IFN-β are examined in order to enhance N1 recruitment to combat tumour progression. Our approach employs optimal control theory to determine drug infusion protocols that could minimize tumour volume with least administration cost possible. Four optimal control scenarios corresponding to different therapeutic strategies are explored, namely, TGF-β inhibitor control only, IFN-β control only, concomitant TGF-β inhibitor and IFN-β controls, and alternating TGF-β inhibitor and IFN-β controls. For each scheme, different initial conditions are varied to depict different pathophysiological condition of a cancer patient, leading to adaptive treatment schedule. TGF-β inhibitor and IFN-β drug dosages, total drug amount, infusion times and relative cost of drug administrations are obtained under various circumstances. The control strategies achieved could guide in designing individualized therapeutic protocols.
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Affiliation(s)
- Aurelio A. de los Reyes
- Biomedical Mathematics Group, Pioneer Research Center for Mathematical and Computational Sciences, Institute for Basic Science, Daejeon 34126, Republic of Korea
- Institute of Mathematics, University of the Philippines Diliman, Quezon City 1101, Philippines
| | - Yangjin Kim
- Department of Mathematics, Konkuk University, Seoul 05029, Republic of Korea
- Mathematical Biosciences Institute, Columbus, OH 43210, USA
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12
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Asnaashari TG, Chang YH. Strategies to Reduce Long-Term Drug Resistance by Considering Effects of Differential Selective Treatments. MATHEMATICAL AND COMPUTATIONAL ONCOLOGY : THIRD INTERNATIONAL SYMPOSIUM, ISMCO 2021, VIRTUAL EVENT, OCTOBER 11-13, 2021 : PROCEEDINGS. ISMCO (SYMPOSIUM) (3RD : 2021 : ONLINE) 2021; 13060:49-60. [PMID: 37342205 PMCID: PMC10280777 DOI: 10.1007/978-3-030-91241-3_5] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/22/2023]
Abstract
Despite great advances in modeling and cancer therapy using optimal control theory, tumor heterogeneity and drug resistance are major obstacles in cancer treatments. Since recent biological studies demonstrated the evidence of tumor heterogeneity and assessed potential biological and clinical implications, tumor heterogeneity should be taken into account in the optimal control problem to improve treatment strategies. Here, first we study the effects of two different treatment strategies (i.e., symmetric and asymmetric) in a minimal two-population model to examine the long-term effects of these treatment methods on the system. Second, by considering tumor adaptation to treatment as a factor of the cost function, the optimal treatment strategy is derived. Numerical examples show that optimal treatment decreases tumor burden for the long-term by decreasing rate of tumor adaptation over time.
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Affiliation(s)
- Tina Ghodsi Asnaashari
- Department of Biomedical Engineering and Computational Biology Program, Oregon Health and Science University, Portland, USA
| | - Young Hwan Chang
- Department of Biomedical Engineering and Computational Biology Program, Oregon Health and Science University, Portland, USA
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13
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Ibrahim M. Optimal harvesting of a predator-prey system with marine reserve. SCIENTIFIC AFRICAN 2021. [DOI: 10.1016/j.sciaf.2021.e01048] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/19/2022] Open
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14
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DARANDIS N, NAZARI M. A NEW MATHEMATICAL MODELING AND SUB-OPTIMAL CHEMOTHERAPY OF CANCER. J BIOL SYST 2021. [DOI: 10.1142/s0218339021500133] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
The development of more accurate cancer mathematical models leads to present more realistic treatment protocols, especially in model-based treatment protocol design. Hence, a cancer mathematical model is presented by considering tumor cells, immune cells, interleukins, macrophages polarization, and chemotherapy based on biological concepts. Both local and global sensitivity analyses are done to examine the effect of changing the parameters on the final tumor population. Then, the tumor-free equilibrium points of the system are derived, and their stabilities are studied. The main target of chemotherapy is to eliminate the tumor while limiting drug toxicity. The SDRE method is used to construct a sub-optimal control strategy by using the developed nonlinear cancer model. For simulation, three patients are considered: a young patient, an old patient, and a pregnant patient. These cases have different immune system strengths. Also, three initial tumor sizes are regarded for each case. So, different treatment strategies are suggested. Eradication of tumor cells in a finite duration with a desired amount of chemo-drug is shown in the simulation results. The results confirmed that the immune system’s ability plays an important role in treatment success. It is shown that there are different treatment protocols for different patients, and the SDRE method is more flexible and effective than the others.
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Affiliation(s)
- N. DARANDIS
- Faculty of Mechanical and Mechatronics Engineering, Shahrood, University of Technology, P. O. Box: 3619995161, Shahrood, Iran
| | - M. NAZARI
- Faculty of Mechanical and Mechatronics Engineering, Shahrood, University of Technology, P. O. Box: 3619995161, Shahrood, Iran
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15
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A Dynamic Model of Multiple Time-Delay Interactions between the Virus-Infected Cells and Body’s Immune System with Autoimmune Diseases. AXIOMS 2021. [DOI: 10.3390/axioms10030216] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/26/2022]
Abstract
The immune system is a complex interconnected network consisting of many parts including organs, tissues, cells, molecules and proteins that work together to protect the body from illness when germs enter the body. An autoimmune disease is a disease in which the body’s immune system attacks healthy cells. It is known that when the immune system is working properly, it can clearly recognize and kill the abnormal cells and virus-infected cells. But when it doesn’t work properly, the human body will not be able to recognize the virus-infected cells and, therefore, it can attack the body’s healthy cells when there is no invader or does not stop an attack after the invader has been killed, resulting in autoimmune disease.; This paper presents a mathematical modeling of the virus-infected development in the body’s immune system considering the multiple time-delay interactions between the immune cells and virus-infected cells with autoimmune disease. The proposed model aims to determine the dynamic progression of virus-infected cell growth in the immune system. The patterns of how the virus-infected cells spread and the development of the body’s immune cells with respect to time delays will be derived in the form of a system of delay partial differential equations. The model can be used to determine whether the virus-infected free state can be reached or not as time progresses. It also can be used to predict the number of the body’s immune cells at any given time. Several numerical examples are discussed to illustrate the proposed model. The model can provide a real understanding of the transmission dynamics and other significant factors of the virus-infected disease and the body’s immune system subject to the time delay, including approaches to reduce the growth rate of virus-infected cell and the autoimmune disease as well as to enhance the immune effector cells.
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16
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Nazari M, Babaei N, Nazari M. Nonlinear SDRE based adaptive fuzzy control approach for age-specific drug delivery in mixed chemotherapy and immunotherapy. Biomed Signal Process Control 2021. [DOI: 10.1016/j.bspc.2021.102687] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
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Javadi A, Keighobadi F, Nekoukar V, Ebrahimi M. Finite-Set Model Predictive Control of Melanoma Cancer Treatment Using Signaling Pathway Inhibitor of Cancer Stem Cell. IEEE/ACM TRANSACTIONS ON COMPUTATIONAL BIOLOGY AND BIOINFORMATICS 2021; 18:1504-1511. [PMID: 31514151 DOI: 10.1109/tcbb.2019.2940658] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
Drug delivery is one of the most important issues in the treatment of cancer and surviving the patient. Recently, with a combination of mathematical models of the tumor growth and control theory, optimal drug delivery can be planned, individually. The goal is reducing the tumor volume with minimum side effects on the patient. One of the most important challenges of the modeling is considering the drug resistance, which may lead to failure of the treatment. In this paper, a mathematical model is proposed for describing the growth dynamics of the melanoma tumor cells. It is assumed that the melanoma cancer is treated with Notch signaling pathway inhibitors of the cancer stem cells. The model parameters are identified based on experimental data obtained from 13 male nude mice with an induced melanoma cancer involved in a dual antiplatelet therapy (DAPT) program. The mathematical model is used to determine if DAPT can reduce the growth rate of the tumor. Then an optimal drug delivery plan for the treatment of every animal model is presented, individually using finite-set model predictive control method. The results show that the proposed model can estimate the drug's effect on the treatment of melanoma cancer.
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Personalized Immunotherapy Treatment Strategies for a Dynamical System of Chronic Myelogenous Leukemia. Cancers (Basel) 2021; 13:cancers13092030. [PMID: 33922302 PMCID: PMC8122842 DOI: 10.3390/cancers13092030] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/30/2021] [Revised: 04/20/2021] [Accepted: 04/21/2021] [Indexed: 11/20/2022] Open
Abstract
Simple Summary As computer performance continues to grow at more affordable costs, mathematical modelling and in silico experimentation begin to play a larger role in understanding cancer evolution. The aim of our work is to formulate a control strategy for the Adaptive Cellular Therapy (ACT) that can fully eradicates the Chronic Myelogenous Leukemia (CML) cells population in a mathematical model describing interactions between naive T cells, effector T cells and CML cancer cells in the circulatory blood system. Mathematical analysis and numerical simulations allow us to conclude that it is possible to design a personalized administration protocol for the ACT in the form of a pulse train with asymmetrical waves and a fixed amplitude to achieve complete CML cancer cells eradication. The amplitude of the impulse on which the treatment is applied is given by an arithmetical combination of the parameters of the system with at least a duty cycle of 45 min/day. Abstract This paper is devoted to exploring personalized applications of cellular immunotherapy as a control strategy for the treatment of chronic myelogenous leukemia described by a dynamical system of three first-order ordinary differential equations. The latter was achieved by applying both the Localization of Compact Invariant Sets and Lyapunov’s stability theory. Combination of these two approaches allows us to establish sufficient conditions on the immunotherapy treatment parameter to ensure the complete eradication of the leukemia cancer cells. These conditions are given in terms of the system parameters and by performing several in silico experimentations, we formulated a protocol for the therapy application that completely eradicates the leukemia cancer cells population for different initial tumour concentrations. The formulated protocol does not dangerously increase the effector T cells population. Further, complete eradication is considered when solutions go below a finite critical value below which cancer cells cannot longer persist; i.e., one cancer cell. Numerical simulations are consistent with our analytical results.
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Tang Q, Zhang G. Stability and Hopf bifurcations in a competitive tumour-immune system with intrinsic recruitment delay and chemotherapy. MATHEMATICAL BIOSCIENCES AND ENGINEERING : MBE 2021; 18:1941-1965. [PMID: 33892531 DOI: 10.3934/mbe.2021101] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/12/2023]
Abstract
In this paper, a three-dimensional nonlinear delay differential system including Tumour cells, cytotoxic-T lymphocytes, T-helper cells is constructed to investigate the effects of intrinsic recruitment delay and chemotherapy. It is found that the introduction of chemotherapy and time delay can generate richer dynamics in tumor-immune system. In particular, there exists bistable phenomenon and the tumour cells would be cleared if the effect of chemotherapy on depletion of the tumour cells is strong enough or the side effect of chemotherapy on the hunting predator cells is under a threshold. It is also shown that a branch of stable periodic solutions bifurcates from the coexistence equilibrium when the intrinsic recruitment delay of tumor crosses the threshold which is new mechanism, which can help understand the short-term oscillations in tumour sizes as well as long-term tumour relapse. Numerical simulations are presented to illustrate that larger intrinsic recruitment delay of tumor leads to larger amplitude and longer period of the bifurcated periodic solution, which indicates that there exists longer relapse time and then contributes to the control of tumour growth.
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Affiliation(s)
- Qingfeng Tang
- School of Mathematics and Statistics, Southwest University, Chongqing 400715, China
| | - Guohong Zhang
- School of Mathematics and Statistics, Southwest University, Chongqing 400715, China
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20
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Parajdi LG, Precup R, Şerban MA, Haplea IŞ. Analysis of the effectiveness of the treatment of solid tumors in two cases of drug administration. MATHEMATICAL BIOSCIENCES AND ENGINEERING : MBE 2021; 18:1845-1863. [PMID: 33757214 DOI: 10.3934/mbe.2021096] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/12/2023]
Abstract
A complete stability analysis of the equilibrium solutions of a system modeling tumor chemotherapy is performed in two cases of administration of the treatment, by continuous infusion and by periodic infusion. Several numerical simulations illustrate and complement the theory.
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Affiliation(s)
| | - Radu Precup
- Department of Mathematics, Babeş-Bolyai University, Cluj-Napoca 400084, Romania
| | | | - Ioan Ştefan Haplea
- Department of Internal Medicine, Iuliu Haţieganu University of Medicine and Pharmacy, Cluj-Napoca 400012, Romania
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21
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Adaptive fuzzy controller design of drug dosage using optimal trajectories in a chemoimmunotherapy cancer treatment model. INFORMATICS IN MEDICINE UNLOCKED 2021. [DOI: 10.1016/j.imu.2021.100782] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/24/2022] Open
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22
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Kaondera-Shava RF, Lungu E, Szomolay B. A novel mathematical model of AIDS-associated Kaposi's sarcoma: Analysis and optimal control. Biosystems 2020; 200:104318. [PMID: 33309554 DOI: 10.1016/j.biosystems.2020.104318] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/08/2020] [Accepted: 11/30/2020] [Indexed: 12/27/2022]
Abstract
Kaposi's sarcoma (KS) has been the most common HHV-8 virus-induced neoplasm associated with HIV-1 infection. Although the standard KS therapy has not changed in 20 years, not all cases of KS will respond to the same therapy. The goal of current AIDS-KS treatment modalities is to reconstitute the immune system and suppress HIV-1 replication, but newer treatment modalities are on horizon. There are very few mathematical models that have included HIV-1 viral load (VL) measures, despite VL being a key determinant of treatment outcome. Here we introduce a mathematical model that consolidates the effect of both HIV-1 and HHV-8 VL on KS tumor progression by incorporating low or high VLs into the proliferation terms of the immune cell populations. Regulation of HIV-1/HHV-8 VL and viral reservoir cells is crucial for restoring a patient to an asymptomatic stage. Therefore, an optimal control strategy given by a combined antiretroviral therapy (cART) is derived. The results indicate that the drug treatment strategies are capable of removing the viral reservoirs faster and consequently, the HIV-1 and KS tumor burden is reduced. The predictions of the mathematical model have the potential to offer more effective therapeutic interventions based on viral and virus-infected cell load and support new studies addressing the superiority of VL over CD4+ T-cell count in HIV-1 pathogenesis.
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Affiliation(s)
- R F Kaondera-Shava
- Department of Mathematics and Statistical Sciences, Botswana International University of Science and Technology, Private Bag 16, Palapye, Botswana.
| | - E Lungu
- Department of Mathematics and Statistical Sciences, Botswana International University of Science and Technology, Private Bag 16, Palapye, Botswana.
| | - B Szomolay
- Systems Immunity Research Institute, Cardiff University School of Medicine, Cardiff, CF14 4XN, United Kingdom.
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23
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Cho H, Wang Z, Levy D. Study of dose-dependent combination immunotherapy using engineered T cells and IL-2 in cervical cancer. J Theor Biol 2020; 505:110403. [PMID: 32693004 DOI: 10.1016/j.jtbi.2020.110403] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/16/2020] [Revised: 07/02/2020] [Accepted: 07/07/2020] [Indexed: 11/26/2022]
Abstract
Adoptive T cell based immunotherapy is gaining significant traction in cancer treatment. Despite its limited efficacy so far in treating solid tumors compared to hematologic cancers, recent advances in T cell engineering render this treatment increasingly more successful in solid tumors, demonstrating its broader therapeutic potential. In this paper we develop a mathematical model to study the efficacy of engineered T cell receptor (TCR) T cell therapy targeting the E7 antigen in cervical cancer cell lines. We consider a dynamical system that follows the population of cancer cells, TCR T cells, and IL-2 treatment concentration. We demonstrate that there exists a TCR T cell dosage window for a successful cancer elimination that can be expressed in terms of the initial tumor size. We obtain the TCR T cell dose for two cervical cancer cell lines: 4050 and CaSki. Finally, a combination therapy of TCR T cell and IL-2 treatment is studied. We show that certain treatment protocols can improve therapy responses in the 4050 cell line, but not in the CaSki cell line.
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Affiliation(s)
- Heyrim Cho
- Department of Mathematics, University of California, Riverside, CA 92521, United States.
| | - Zuping Wang
- Department of Mathematics, University of Maryland, College Park, College Park, MD 20742, United States.
| | - Doron Levy
- Department of Mathematics, University of Maryland, College Park, College Park, MD 20742, United States; Center for Scientific Computation and Mathematical Modeling (CSCAMM), University of Maryland, College Park, College Park, MD 20742, United States.
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Nazari M, Nazari M, Noori Skandari MH. Pseudo-spectral method for controlling the drug dosage in cancer. IET Syst Biol 2020; 14:261-270. [PMID: 33095747 DOI: 10.1049/iet-syb.2020.0054] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022] Open
Abstract
A mixed chemotherapy-immunotherapy treatment protocol is developed for cancer treatment. Chemotherapy pushes the trajectory of the system towards the desired equilibrium point, and then immunotherapy alters the dynamics of the system by affecting the parameters of the system. A co-existing cancerous equilibrium point is considered as the desired equilibrium point instead of the tumour-free equilibrium. Chemotherapy protocol is derived using the pseudo-spectral (PS) controller due to its high convergence rate and simple implementation structure. Thus, one of the contributions of this study is simplifying the design procedure and reducing the controller computational load in comparison with Lyapunov-based controllers. In this method, an infinite-horizon optimal control problem is proposed for a non-linear cancer model. Then, the infinite-horizon optimal control of cancer is transformed into a non-linear programming problem. The efficient Legendre PS scheme is suggested to solve the proposed problem. Then, the dynamics of the system is modified by immunotherapy is another contribution. To restrict the upper limit of the chemo-drug dose based on the age of the patients, a Mamdani fuzzy system is designed, which is not present yet. Simulation results on four different dynamics cases how the efficiency of the proposed treatment strategy.
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Affiliation(s)
- Mostafa Nazari
- Faculty of Mechanical and Mechatronics Engineering, Shahrood University of Technology, Shahrood, P.O. Box 3619995161, Iran.
| | - Morteza Nazari
- Faculty of Mathematical Sciences, Shahrood University of Technology, Shahrood, P.O. Box 3619995161, Iran
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Abernathy K, Abernathy Z, Baxter A, Stevens M. Global Dynamics of a Breast Cancer Competition Model. DIFFERENTIAL EQUATIONS AND DYNAMICAL SYSTEMS 2020; 28:791-805. [PMID: 33487925 PMCID: PMC7821963 DOI: 10.1007/s12591-017-0346-x] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/12/2023]
Abstract
In this paper, we present a system of five ordinary differential equations which consider population dynamics among cancer stem cells, tumor cells, and healthy cells. Additionally, we consider the effects of excess estrogen and the body's natural immune response on the aforementioned cell populations. Employing a variety of analytical methods, we study the global dynamics of the full system, along with various submodels. We find sufficient conditions on parameter values to ensure cancer persistence in the absence of immune cells, and cancer eradication when an immune response is included. We conclude with a discussion on the biological implications of the resulting global dynamics.
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Affiliation(s)
| | | | - Arden Baxter
- Rollins College, 1000 Holt Ave, Winter Park, FL 32789
| | - Meghan Stevens
- Drake University, 2507 University Ave, Des Moines, IA 50311
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26
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Shindi O, Kanesan J, Kendall G, Ramanathan A. The combined effect of optimal control and swarm intelligence on optimization of cancer chemotherapy. COMPUTER METHODS AND PROGRAMS IN BIOMEDICINE 2020; 189:105327. [PMID: 31978808 DOI: 10.1016/j.cmpb.2020.105327] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/28/2019] [Revised: 12/16/2019] [Accepted: 01/08/2020] [Indexed: 06/10/2023]
Abstract
BACKGROUND AND OBJECTIVES In cancer therapy optimization, an optimal amount of drug is determined to not only reduce the tumor size but also to maintain the level of chemo toxicity in the patient's body. The increase in the number of objectives and constraints further burdens the optimization problem. The objective of the present work is to solve a Constrained Multi- Objective Optimization Problem (CMOOP) of the Cancer-Chemotherapy. This optimization results in optimal drug schedule through the minimization of the tumor size and the drug concentration by ensuring the patient's health level during dosing within an acceptable level. METHODS This paper presents two hybrid methodologies that combines optimal control theory with multi-objective swarm and evolutionary algorithms and compares the performance of these methodologies with multi-objective swarm intelligence algorithms such as MOEAD, MODE, MOPSO and M-MOPSO. The hybrid and conventional methodologies are compared by addressing CMOOP. RESULTS The minimized tumor and drug concentration results obtained by the hybrid methodologies demonstrate that they are not only superior to pure swarm intelligence or evolutionary algorithm methodologies but also consumes far less computational time. Further, Second Order Sufficient Condition (SSC) is also used to verify and validate the optimality condition of the constrained multi-objective problem. CONCLUSION The proposed methodologies reduce chemo-medicine administration while maintaining effective tumor killing. This will be helpful for oncologist to discover and find the optimum dose schedule of the chemotherapy that reduces the tumor cells while maintaining the patients' health at a safe level.
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Affiliation(s)
- Omar Shindi
- Department of Electrical Engineering, Faculty of Engineering, University of Malaya, 50603, Kuala Lumpur, Malaysia
| | - Jeevan Kanesan
- Department of Electrical Engineering, Faculty of Engineering, University of Malaya, 50603, Kuala Lumpur, Malaysia.
| | - Graham Kendall
- School of Computer Science, University of Nottingham, Malaysia Campus, 43500 Semenyih, Malaysia.
| | - Anand Ramanathan
- Department of Oral & Maxillofacial Clinical Sciences, Oral Cancer Research - Coordinating Centre, Faculty of Dentistry, University of Malaya, 50603, Kuala Lumpur, Malaysia.
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27
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Sweilam NH, Tharwat AA, Abd El Moniem NK. Different optimization strategies for the optimal control of tumor growth. ARCHIVES OF CANCER SCIENCE AND THERAPY 2019; 3:052-062. [DOI: 10.29328/journal.acst.1001010] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 09/01/2023]
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28
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Yin A, Moes DJAR, van Hasselt JGC, Swen JJ, Guchelaar HJ. A Review of Mathematical Models for Tumor Dynamics and Treatment Resistance Evolution of Solid Tumors. CPT-PHARMACOMETRICS & SYSTEMS PHARMACOLOGY 2019; 8:720-737. [PMID: 31250989 PMCID: PMC6813171 DOI: 10.1002/psp4.12450] [Citation(s) in RCA: 46] [Impact Index Per Article: 9.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 04/01/2019] [Accepted: 05/17/2019] [Indexed: 12/19/2022]
Abstract
Increasing knowledge of intertumor heterogeneity, intratumor heterogeneity, and cancer evolution has improved the understanding of anticancer treatment resistance. A better characterization of cancer evolution and subsequent use of this knowledge for personalized treatment would increase the chance to overcome cancer treatment resistance. Model‐based approaches may help achieve this goal. In this review, we comprehensively summarized mathematical models of tumor dynamics for solid tumors and of drug resistance evolution. Models displayed by ordinary differential equations, algebraic equations, and partial differential equations for characterizing tumor burden dynamics are introduced and discussed. As for tumor resistance evolution, stochastic and deterministic models are introduced and discussed. The results may facilitate a novel model‐based analysis on anticancer treatment response and the occurrence of resistance, which incorporates both tumor dynamics and resistance evolution. The opportunities of a model‐based approach as discussed in this review can be of great benefit for future optimizing and personalizing anticancer treatment.
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Affiliation(s)
- Anyue Yin
- Department of Clinical Pharmacy and Toxicology, Leiden University Medical Center, Leiden, The Netherlands.,Leiden Network for Personalized Therapeutics, Leiden University Medical Center, Leiden, The Netherlands
| | - Dirk Jan A R Moes
- Department of Clinical Pharmacy and Toxicology, Leiden University Medical Center, Leiden, The Netherlands.,Leiden Network for Personalized Therapeutics, Leiden University Medical Center, Leiden, The Netherlands
| | - Johan G C van Hasselt
- Division of Systems Biomedicine and Pharmacology, Leiden Academic Center for Drug Research, Leiden University, Leiden, The Netherlands
| | - Jesse J Swen
- Department of Clinical Pharmacy and Toxicology, Leiden University Medical Center, Leiden, The Netherlands.,Leiden Network for Personalized Therapeutics, Leiden University Medical Center, Leiden, The Netherlands
| | - Henk-Jan Guchelaar
- Department of Clinical Pharmacy and Toxicology, Leiden University Medical Center, Leiden, The Netherlands.,Leiden Network for Personalized Therapeutics, Leiden University Medical Center, Leiden, The Netherlands
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29
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Milberg O, Gong C, Jafarnejad M, Bartelink IH, Wang B, Vicini P, Narwal R, Roskos L, Popel AS. A QSP Model for Predicting Clinical Responses to Monotherapy, Combination and Sequential Therapy Following CTLA-4, PD-1, and PD-L1 Checkpoint Blockade. Sci Rep 2019; 9:11286. [PMID: 31375756 PMCID: PMC6677731 DOI: 10.1038/s41598-019-47802-4] [Citation(s) in RCA: 46] [Impact Index Per Article: 9.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/25/2019] [Accepted: 07/24/2019] [Indexed: 01/12/2023] Open
Abstract
Over the past decade, several immunotherapies have been approved for the treatment of melanoma. The most prominent of these are the immune checkpoint inhibitors, which are antibodies that block the inhibitory effects on the immune system by checkpoint receptors, such as CTLA-4, PD-1 and PD-L1. Preclinically, blocking these receptors has led to increased activation and proliferation of effector cells following stimulation and antigen recognition, and subsequently, more effective elimination of cancer cells. Translation from preclinical to clinical outcomes in solid tumors has shown the existence of a wide diversity of individual patient responses, linked to several patient-specific parameters. We developed a quantitative systems pharmacology (QSP) model that looks at the mentioned checkpoint blockade therapies administered as mono-, combo- and sequential therapies, to show how different combinations of specific patient parameters defined within physiological ranges distinguish different types of virtual patient responders to these therapies for melanoma. Further validation by fitting and subsequent simulations of virtual clinical trials mimicking actual patient trials demonstrated that the model can capture a wide variety of tumor dynamics that are observed in the clinic and can predict median clinical responses. Our aim here is to present a QSP model for combination immunotherapy specific to melanoma.
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Affiliation(s)
- Oleg Milberg
- Department of Biomedical Engineering, Johns Hopkins University School of Medicine, Baltimore, Maryland, USA.
| | - Chang Gong
- Department of Biomedical Engineering, Johns Hopkins University School of Medicine, Baltimore, Maryland, USA
| | - Mohammad Jafarnejad
- Department of Biomedical Engineering, Johns Hopkins University School of Medicine, Baltimore, Maryland, USA
| | - Imke H Bartelink
- Clinical Pharmacology, Pharmacometrics and DMPK (CPD), MedImmune, South San Francisco, California, USA.,Department of Clinical Pharmacology and Pharmacy, Amsterdam UMC, Vrije Universiteit Amsterdam, Amsterdam, The Netherlands
| | - Bing Wang
- Clinical Pharmacology, Pharmacometrics and DMPK (CPD), MedImmune, South San Francisco, California, USA
| | - Paolo Vicini
- Clinical Pharmacology, Pharmacometrics and DMPK, MedImmune, Cambridge, United Kingdom
| | | | | | - Aleksander S Popel
- Department of Biomedical Engineering, Johns Hopkins University School of Medicine, Baltimore, Maryland, USA.,The Sidney Kimmel Comprehensive Cancer Center, Johns Hopkins University School of Medicine, Baltimore, Maryland, USA
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30
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Baleanu D, Jajarmi A, Sajjadi SS, Mozyrska D. A new fractional model and optimal control of a tumor-immune surveillance with non-singular derivative operator. CHAOS (WOODBURY, N.Y.) 2019; 29:083127. [PMID: 31472488 DOI: 10.1063/1.5096159] [Citation(s) in RCA: 33] [Impact Index Per Article: 6.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/03/2023]
Abstract
In this paper, we present a new fractional-order mathematical model for a tumor-immune surveillance mechanism. We analyze the interactions between various tumor cell populations and immune system via a system of fractional differential equations (FDEs). An efficient numerical procedure is suggested to solve these FDEs by considering singular and nonsingular derivative operators. An optimal control strategy for investigating the effect of chemotherapy treatment on the proposed fractional model is also provided. Simulation results show that the new presented model based on the fractional operator with Mittag-Leffler kernel represents various asymptomatic behaviors that tracks the real data more accurately than the other fractional- and integer-order models. Numerical simulations also verify the efficiency of the proposed optimal control strategy and show that the growth of the naive tumor cell population is successfully declined.
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Affiliation(s)
- D Baleanu
- Department of Mathematics, Faculty of Arts and Sciences, Cankaya University, 06530 Ankara, Turkey
| | - A Jajarmi
- Department of Electrical Engineering, University of Bojnord, P.O. Box 94531-1339, Bojnord, Iran
| | - S S Sajjadi
- Department of Electrical and Computer Engineering, Hakim Sabzevari University, Sabzevar, Iran
| | - D Mozyrska
- Faculty of Computer Science, Białystok University of Technology, Wiejska 45A, Białystok, Poland
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31
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Tumor Clearance Analysis on a Cancer Chemo-Immunotherapy Mathematical Model. Bull Math Biol 2019; 81:4144-4173. [PMID: 31264136 DOI: 10.1007/s11538-019-00636-7] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/08/2018] [Accepted: 06/20/2019] [Indexed: 01/08/2023]
Abstract
Mathematical models may allow us to improve our knowledge on tumor evolution and to better comprehend the dynamics between cancer, the immune system and the application of treatments such as chemotherapy and immunotherapy in both short and long term. In this paper, we solve the tumor clearance problem for a six-dimensional mathematical model that describes tumor evolution under immune response and chemo-immunotherapy treatments. First, by means of the localization of compact invariant sets method, we determine lower and upper bounds for all cells populations considered by the model and we use these results to establish sufficient conditions for the existence of a bounded positively invariant domain in the nonnegative orthant by applying LaSalle's invariance principle. Then, by exploiting a candidate Lyapunov function we determine sufficient conditions on the chemotherapy treatment to ensure tumor clearance. Further, we investigate the local stability of the tumor-free equilibrium point and compute conditions for asymptotic stability and tumor persistence. All conditions are given by inequalities in terms of the system parameters, and we perform numerical simulations with different values on the chemotherapy treatment to illustrate our results. Finally, we discuss the biological implications of our work.
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KHAJANCHI SUBHAS, BANERJEE SANDIP. A STRATEGY OF OPTIMAL EFFICACY OF T11 TARGET STRUCTURE IN THE TREATMENT OF BRAIN TUMOR. J BIOL SYST 2019. [DOI: 10.1142/s0218339019500104] [Citation(s) in RCA: 19] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
We report a mathematical model depicting gliomas and immune system interactions by considering the role of immunotherapeutic drug T11 target structure (T11TS). The mathematical model comprises a system of coupled nonlinear ordinary differential equations involving glioma cells, macrophages, activated cytotoxic T-lymphocytes (CTLs), immunosuppressive cytokine transforming growth factor-[Formula: see text] (TGF-[Formula: see text]), immunostimulatory cytokine interferon-[Formula: see text] (IFN-[Formula: see text]) and the concentrations of immunotherapeutic agent T11TS. For the better understanding of the circumstances under which the gliomas can be eradicated from a patient, we use optimal control strategy. We design the objective functional by considering the biomedical goal, which minimizes the glioma burden and maximizes the macrophages and activated CTLs. The existence and the characterization for the optimal control are established. The uniqueness of the quadratic optimal control problem is also analyzed. We demonstrate numerically that the optimal treatment strategies using T11TS reduce the glioma burden and increase the cell count of activated CTLs and macrophages.
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Affiliation(s)
- SUBHAS KHAJANCHI
- Department of Mathematics, Presidency University, Kolkata 700073, West Bengal, India
| | - SANDIP BANERJEE
- Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee 247667, Uttarakhand, India
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33
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Nonlinear composite adaptive control of cancer chemotherapy with online identification of uncertain parameters. Biomed Signal Process Control 2019. [DOI: 10.1016/j.bspc.2018.07.009] [Citation(s) in RCA: 16] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/24/2022]
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34
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Optimal Control Analysis of a Mathematical Model for Breast Cancer. MATHEMATICAL AND COMPUTATIONAL APPLICATIONS 2018. [DOI: 10.3390/mca23020021] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/15/2022]
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35
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Sharifi M, Jamshidi A, Sarvestani NN. An Adaptive Robust Control Strategy in a Cancer Tumor-Immune System under Uncertainties. IEEE/ACM TRANSACTIONS ON COMPUTATIONAL BIOLOGY AND BIOINFORMATICS 2018; 16:865-873. [PMID: 29994095 DOI: 10.1109/tcbb.2018.2803175] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
We propose an adaptive robust control for a second order nonlinear model of the interaction between cancer and immune cells of the body to control the growth of cancer and maintain the number of immune cells in an appropriate level. Most of the control approaches are based on minimizing the drug dosage based on an optimal control structure. However, in many cases, measuring the exact quantity of the model parameters is not possible. This is due to limitation in measuring devices, variational and undetermined characteristics of micro-environmental factors. It is of great importance to present a control strategy that can deal with these unknown factors in a nonlinear model.
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36
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Padmanabhan R, Meskin N, Haddad WM. Reinforcement learning-based control of drug dosing for cancer chemotherapy treatment. Math Biosci 2017; 293:11-20. [DOI: 10.1016/j.mbs.2017.08.004] [Citation(s) in RCA: 41] [Impact Index Per Article: 5.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/28/2016] [Revised: 08/08/2017] [Accepted: 08/09/2017] [Indexed: 11/25/2022]
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37
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Ahn I, Heo S, Ji S, Kim KH, Kim T, Lee EJ, Park J, Sung K. Investigation of nonlinear epidemiological models for analyzing and controlling the MERS outbreak in Korea. J Theor Biol 2017; 437:17-28. [PMID: 29031518 PMCID: PMC7094113 DOI: 10.1016/j.jtbi.2017.10.004] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/08/2016] [Revised: 09/18/2017] [Accepted: 10/05/2017] [Indexed: 12/17/2022]
Abstract
By fitting the SIQ model, which employs a squashing-type function for β(t), to the real data on the confirmed cases and the quarantined cases, we obtained reasonable performance. Also, it turned out that the resultant estimated parameters belonged to plausible ranges. By comparison, the conventional SIQ model utilizing a constant transmission probability could not explain the observed data well. As a practical guideline to avoid another similar unexpected outbreak, we draw the conclusion that combined efforts in the early stage are critically important, and sharing information including the names of affected hospitals or countries, clinical situations, and prevention methods might be important for global public health control. We applied optimal control theory to the controlled SIQ model with the goal of minimizing the infectious compartment population and the cost of implementing the quarantine and isolation strategies. Simulation results show that the number of the MERS cases can be controlled reasonably well via the optimal control approach.
Much concern has arisen regarding serious epidemics due to the Middle East Respiratory Syndrome (MERS) coronavirus. The first MERS case of Korea was reported on 20 May 2015, and since then, the MERS outbreak in Korea has resulted in hundreds of confirmed cases and tens of deaths. Deadly infectious diseases such as MERS have significant direct and indirect social impacts, which include disease-induced mortality and economic losses. Also, a delayed response to the outbreak and underestimating its danger can further aggravate the situation. Hence, an analysis and establishing efficient strategies for preventing the propagation of MERS is a very important and urgent issue. In this paper, we propose a class of nonlinear susceptible-infectious-quarantined (SIQ) models for analyzing and controlling the MERS outbreak in Korea. For the SIQ based ordinary differential equation (ODE) model, we perform the task of parameter estimation, and apply optimal control theory to the controlled SIQ model, with the goal of minimizing the infectious compartment population and the cost of implementing the quarantine and isolation strategies. Simulation results show that the proposed SIQ model can explain the observed data for the confirmed cases and the quarantined cases in the MERS outbreak very well, and the number of the MERS cases can be controlled reasonably well via the optimal control approach.
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Affiliation(s)
- Inkyung Ahn
- Department of Mathematics, College of Science and Technology, Korea University, Sejong, 339-700, Republic of Korea.
| | - Seongman Heo
- Department of Control and Instrumentation Engineering, College of Science and Technology, Korea University, Sejong, 339-700, Republic of Korea
| | - Seunghyun Ji
- Department of Control and Instrumentation Engineering, College of Science and Technology, Korea University, Sejong, 339-700, Republic of Korea
| | - Kyung Hyun Kim
- Department of Biotechnology and Bioinformatics, College of Science and Technology, Korea University, Sejong, 339-700, Republic of Korea
| | - Taehwan Kim
- Department of Control and Instrumentation Engineering, College of Science and Technology, Korea University, Sejong, 339-700, Republic of Korea
| | - Eun Joo Lee
- Department of Internal Medicine, Korea University Anam Hospital, College of Medicine, Korea University, Seoul, 136-705, Republic of Korea
| | - Jooyoung Park
- Department of Control and Instrumentation Engineering, College of Science and Technology, Korea University, Sejong, 339-700, Republic of Korea.
| | - Keehoon Sung
- Department of Control and Instrumentation Engineering, College of Science and Technology, Korea University, Sejong, 339-700, Republic of Korea
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Padmanabhan R, Meskin N, Haddad WM. LEARNING-BASED CONTROL OF CANCER CHEMOTHERAPY TREATMENT. ACTA ACUST UNITED AC 2017. [DOI: 10.1016/j.ifacol.2017.08.2247] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
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Korobeinikov A, Starkov KE, Valle PA. Modeling cancer evolution: evolutionary escape under immune system control. ACTA ACUST UNITED AC 2017. [DOI: 10.1088/1742-6596/811/1/012004] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/21/2023]
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Rodríguez CR, Belmonte-Beitia J. Optimizing the delivery of combination therapy for tumors: A mathematical model. INT J BIOMATH 2017. [DOI: 10.1142/s1793524517500395] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
We present in this paper a new mathematical model for the scheduling of angiogenic inhibitors in combination with a chemotherapeutic agent for a tumor. Our model takes into account the process of angiogenesis and the quality of the vasculature discriminating between stable blood vessels and unstable blood vessels. We characterize theoretically the optimal controls on drug distribution to minimize the number of cancer cells at the end of the treatment in a free horizon time problem with restrictions on the total amount of drug doses. Finally, we solve the optimal control problem by using numerical simulations, obtaining as a result that, despite the number of the tumor cells decrease with anti-angiogenic treatment, the best results are reached at the end of the chemotherapy treatment.
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Affiliation(s)
- Clara Rojas Rodríguez
- Departamento de Matemáticas, E. T. S. de Ingenieros Industriales, Universidad de Castilla-La Mancha, 13071 Ciudad Real, Spain
- Instituto de Matemática Aplicada a la, Ciencia y la Ingeniería (IMACI), Universidad de Castilla-La Mancha, 13071 Ciudad Real, Spain
| | - Juan Belmonte-Beitia
- Departamento de Matemáticas, E. T. S. de Ingenieros Industriales, Universidad de Castilla-La Mancha, 13071 Ciudad Real, Spain
- Instituto de Matemática Aplicada a la, Ciencia y la Ingeniería (IMACI), Universidad de Castilla-La Mancha, 13071 Ciudad Real, Spain
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Chen Y, Zhou Y, Murch R, Kosmas P. Modeling Contrast-Imaging-Assisted Optimal Targeted Drug Delivery: A Touchable Communication Channel Estimation and Waveform Design Perspective. IEEE Trans Nanobioscience 2017; 16:203-215. [PMID: 28212092 DOI: 10.1109/tnb.2017.2669309] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
Abstract
To maximize the effect of treatment and minimize the adverse effect on patients, we propose to optimize nanorobots-assisted targeted drug delivery (TDD) for locoregional treatment of tumor from the perspective of touchable communication channel estimation and waveform design. The drug particles are the information molecules; the loading/injection and unloading of the drug correspond to the transmitting and receiving processes; the concentration-time profile of the drug particles administered corresponds to the signaling pulse. Given this analogy, we first propose to use contrast-enhanced microwave imaging (CMI) as a pretherapeutic evaluation technique to determine the pharmacokinetic model of nanorobots-assisted TDD. The CMI system applies an information-theoretic-criteria-based algorithm to estimate drug accumulation in tumor, which is analogous to the estimation of channel impulse response in the communication context. Subsequently, we present three strategies for optimal targeted therapies from the communication waveform design perspective, which are based on minimization of residual drug molecules at the end of each therapeutic session (i.e., inter-symbol interference), maximization of duration when the drug intensity is above a prespecified threshold during each therapeutic session (i.e., non-fade duration), and minimization of average rate that a therapeutic operation is not received correctly at tumor (i.e., bit error rate). Finally, numerical examples are applied to demonstrate the effectiveness of the proposed analytical framework.
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Mathematical Models for Immunology: Current State of the Art and Future Research Directions. Bull Math Biol 2016; 78:2091-2134. [PMID: 27714570 PMCID: PMC5069344 DOI: 10.1007/s11538-016-0214-9] [Citation(s) in RCA: 79] [Impact Index Per Article: 9.9] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/03/2016] [Accepted: 09/26/2016] [Indexed: 01/01/2023]
Abstract
The advances in genetics and biochemistry that have taken place over the last 10 years led to significant advances in experimental and clinical immunology. In turn, this has led to the development of new mathematical models to investigate qualitatively and quantitatively various open questions in immunology. In this study we present a review of some research areas in mathematical immunology that evolved over the last 10 years. To this end, we take a step-by-step approach in discussing a range of models derived to study the dynamics of both the innate and immune responses at the molecular, cellular and tissue scales. To emphasise the use of mathematics in modelling in this area, we also review some of the mathematical tools used to investigate these models. Finally, we discuss some future trends in both experimental immunology and mathematical immunology for the upcoming years.
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Mellal L, Folio D, Belharet K, Ferreira A. Modeling of Optimal Targeted Therapies Using Drug-Loaded Magnetic Nanoparticles for Liver Cancer. IEEE Trans Nanobioscience 2016; 15:265-74. [PMID: 26955045 DOI: 10.1109/tnb.2016.2535380] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/08/2022]
Abstract
To enhance locoregional therapies for liver cancer treatment, we propose in this study a mathematical model to optimize the transcatheter arterial delivery of therapeutical agents. To maximize the effect of the treatment and minimize adverse effects on the patient, different mathematical models of the tumor growth are considered in this study to find the optimal number of the therapeutic drug-loaded magnetic nanoparticles to be administered. Three types of therapy models are considered, e.g., angiogenesis inhibition therapy, chemotherapy and radiotherapy. We use state-dependent Riccati equations (SDRE) as an optimal control methodology framework to the Hahnfeldt's tumor growth formulation. Based on this, design optimal rules are derived for each therapy to reduce the growth of a tumor through the administration of appropriate dose of antiangiogenic, radio- and chemo-therapeutic agents. Simulation results demonstrate the validity of the proposed optimal delivery approach, leading to reduced intervention time, low drug administration rates and optimal targeted delivery.
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Holder AB, Rodrigo MR. Model for acid-mediated tumour invasion with chemotherapy intervention II: Spatially heterogeneous populations. Math Biosci 2015; 270:10-29. [PMID: 26459059 DOI: 10.1016/j.mbs.2015.09.007] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/04/2014] [Revised: 07/15/2015] [Accepted: 09/28/2015] [Indexed: 11/16/2022]
Abstract
This paper extends the model for acid-mediated tumour invasion with chemotherapy intervention examined in part I. The model presented in part I considers the interaction between tumour cells, normal cells, acid and drug in a well mixed (i.e. spatially homogeneous) setting, which is governed by a system of nonlinear differential equations. The model examined here removes the assumption that the populations are spatially homogeneous resulting in a system of nonlinear partial differential equations. Numerical simulations of this model are presented for different treatment methods displaying several possible behaviours. Asymptotic approximations are also derived for a special case of the treatment method and set of parameter values. This analysis then allows us to draw conclusions about the effectiveness of treating acid-mediated tumours with chemotherapy.
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Affiliation(s)
- Andrew B Holder
- School of Mathematics and Applied Statistics, University of Wollongong, NSW 2522, Australia.
| | - Marianito R Rodrigo
- School of Mathematics and Applied Statistics, University of Wollongong, NSW 2522, Australia.
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Babaei N, Salamci MU. Personalized drug administration for cancer treatment using Model Reference Adaptive Control. J Theor Biol 2015; 371:24-44. [PMID: 25665717 DOI: 10.1016/j.jtbi.2015.01.038] [Citation(s) in RCA: 30] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/04/2014] [Revised: 12/29/2014] [Accepted: 01/27/2015] [Indexed: 10/24/2022]
Abstract
A new Model Reference Adaptive Control (MRAC) approach is proposed for the nonlinear regulation problem of cancer treatment via chemotherapy. We suggest an approach for determining an optimal anticancer drug delivery scenario for cancer patients without prior knowledge of nonlinear model structure and parameters by compounding State Dependent Riccati Equation (SDRE) and MRAC which will lead to personalized drug administration. Several approaches have been proposed for eradicating cancerous cells in nonlinear tumor growth model. The main difficulty in these approaches is the requirement of nonlinear model parameters, which are unknown to physicians in reality. To cope with this shortage, we first determine the drug delivery scenario for a reference patient with known mathematical model and parameters via SDRE technique, and by using the proposed approach we adapt the drug administration scenario for another cancer patient despite unknown nonlinear model structure and model parameters. We propose an efficient approach to determine drug administration which will help physicians for prescribing a chemotherapy protocol for a cancer patient by regulating the drug delivery scenario of the reference patient. Stabilizing the tumor growth nonlinear model has been achieved via full state feedback techniques and yields a near optimal solution to cancer treatment problem. Numerical simulations show the effectiveness of the proposed algorithm for eradicating tumor lumps with different sizes in different patients.
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Affiliation(s)
- Naser Babaei
- Department of Mechanical Engineering, Faculty of Engineering, Gazi University, 06570 Maltepe/Ankara, Turkey.
| | - Metin U Salamci
- Department of Mechanical Engineering, Faculty of Engineering, Gazi University, 06570 Maltepe/Ankara, Turkey.
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NAZARI MOSTAFA, GHAFFARI ALI, ARAB FARHAD. FINITE DURATION TREATMENT OF CANCER BY USING VACCINE THERAPY AND OPTIMAL CHEMOTHERAPY: STATE-DEPENDENT RICCATI EQUATION CONTROL AND EXTENDED KALMAN FILTER. J BIOL SYST 2015. [DOI: 10.1142/s0218339015500011] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
The main purpose of this paper is to propose an optimal finite duration treatment method for preventing tumor growth. The obtained results show that changing the dynamics of the cancer model is essential for a finite duration treatment. Therefore, vaccine therapy is used for changing the parameters of the system and chemotherapy is applied for pushing the system to the domain of attraction of the healthy state. The state-dependent Riccati equation (SDRE)-based optimal control method is used for optimal chemotherapy. In this method, the special conditions of the patients could be considered by choosing suitable weighting matrices in the cost function and restricting the drug dosage. Also, there are infinite ways to choose these state-dependent matrices. In this paper, these interesting features of this method are used for each patient. Since measuring the states of the system is impossible at each time for states feedback; an extended Kalman filter (EKF) is designed as an observer in the nonlinear system. So, the SDRE method is employed just by measuring the population of normal cells. Numerical simulations show the flexibility and effectiveness of this treatment method.
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Affiliation(s)
- MOSTAFA NAZARI
- Center of Excellence in Robotics and Control, K. N. Toosi University of Technology, Pardis Street, Vanak sq, Tehran 1656983911, Iran
| | - ALI GHAFFARI
- Mechanical Engineering Department, K. N. Toosi University of Technology, Pardis Street, Vanak sq, Tehran 1656983911, Iran
| | - FARHAD ARAB
- Center of Excellence in Robotics and Control, K. N. Toosi University of Technology, Pardis Street, Vanak sq, Tehran 1656983911, Iran
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Adaptive robust control of cancer chemotherapy in the presence of parametric uncertainties: A comparison between three hypotheses. Comput Biol Med 2015; 56:145-57. [DOI: 10.1016/j.compbiomed.2014.11.002] [Citation(s) in RCA: 36] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/23/2014] [Revised: 10/29/2014] [Accepted: 11/02/2014] [Indexed: 11/18/2022]
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Hoffmann A, Scherrer A, Küfer KH. Analyzing the quality robustness of chemotherapy plans with respect to model uncertainties. Math Biosci 2014; 259:55-61. [PMID: 25457799 DOI: 10.1016/j.mbs.2014.11.003] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/13/2013] [Revised: 11/07/2014] [Accepted: 11/14/2014] [Indexed: 11/16/2022]
Abstract
Mathematical models of chemotherapy planning problems contain various biomedical parameters, whose values are difficult to quantify and thus subject to some uncertainty. This uncertainty propagates into the therapy plans computed on these models, which poses the question of robustness to the expected therapy quality. This work introduces a combined approach for analyzing the quality robustness of plans in terms of dosing levels with respect to model uncertainties in chemotherapy planning. It uses concepts from multi-criteria decision making for studying parameters related to the balancing between the different therapy goals, and concepts from sensitivity analysis for the examination of parameters describing the underlying biomedical processes and their interplay. This approach allows for a profound assessment of a therapy plan, how stable its quality is with respect to parametric changes in the used mathematical model.
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Affiliation(s)
- Anna Hoffmann
- Department of Optimization, Fraunhofer Institute for Industrial Mathematics (ITWM), Kaiserslautern, Germany.
| | - Alexander Scherrer
- Department of Optimization, Fraunhofer Institute for Industrial Mathematics (ITWM), Kaiserslautern, Germany
| | - Karl-Heinz Küfer
- Department of Optimization, Fraunhofer Institute for Industrial Mathematics (ITWM), Kaiserslautern, Germany
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Sanchez-Tapia C, Wan FYM. Fastest time to cancer by loss of tumor suppressor genes. Bull Math Biol 2014; 76:2737-84. [PMID: 25338553 DOI: 10.1007/s11538-014-0027-7] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/27/2014] [Accepted: 09/11/2014] [Indexed: 11/24/2022]
Abstract
Genetic instability promotes cancer progression (by increasing the probability of cancerous mutations) as well as hinders it (by imposing a higher cell death rate for cells susceptible to cancerous mutation). With the loss of tumor suppressor gene function known to be responsible for a high percentage of breast and colorectal cancer (and a good fraction of lung cancer and other types as well), it is important to understand how genetic instability can be orchestrated toward carcinogenesis. In this context, this paper gives a complete characterization of the optimal (time-varying) cell mutation rate for the fastest time to a target cancerous cell population through the loss of both copies of a tumor suppressor gene. Similar to the (one-step) oncogene activation model previously analyzed, the optimal mutation rate of the present two-step model changes qualitatively with the convexity of the (mutation rate-dependent) cell death rate. However, the structure of the Hamiltonian for the new model differs significantly and intrinsically from that of the one-step model, and a completely new approach is needed for the solution of the present two-step problem. Considerable insight into the biology of optimal switching (between corner controls) is extracted from numerical results for cases with nonconvex death rates.
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Affiliation(s)
- Cynthia Sanchez-Tapia
- Department of Mathematics, University of California, Irvine, Irvine, CA , 92697-3875, USA,
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