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Arora G, Bairagi N, Chatterjee S. A mathematical model to study low-dose metronomic scheduling for chemotherapy. Math Biosci 2024; 372:109186. [PMID: 38580078 DOI: 10.1016/j.mbs.2024.109186] [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: 12/15/2023] [Revised: 02/21/2024] [Accepted: 03/27/2024] [Indexed: 04/07/2024]
Abstract
Metronomic chemotherapy refers to the frequent administration of chemotherapeutic agents at a lower dose and presents an attractive alternative to conventional chemotherapy with encouraging response rates. However, the schedule of the therapy, including the dosage of the drug, is usually based on empiricism. The confounding effects of tumor-endothelial-immune interactions during metronomic administration of drugs have not yet been explored in detail, resulting in an incomplete assessment of drug dose and frequency evaluations. The present study aimed to gain a mechanistic understanding of different actions of metronomic chemotherapy using a mathematical model. We have established an analytical condition for determining the dosage and frequency of the drug depending on its clearance rate for complete tumor elimination. The model also brings forward the immune-mediated clearance of the tumor during the metronomic administration of the chemotherapeutic agent. The results from the global sensitivity analysis showed an increase in the sensitivity of drug and immune-mediated killing factors toward the tumor population during metronomic scheduling. Our results emphasize metronomic scheduling over the maximum tolerated dose (MTD) and define a model-based approach for approximating the optimal schedule of drug administration to eliminate tumors while minimizing harm to the immune cells and the patient's body.
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Affiliation(s)
- Garhima Arora
- Complex Analysis Group, Translational Health Science and Technology Institute, NCR Biotech Science Cluster, Faridabad, 121001, India
| | - Nandadulal Bairagi
- Department of Mathematics, Centre for Mathematical Biology and Ecology, Jadavpur University, Kolkata, 700032, India
| | - Samrat Chatterjee
- Complex Analysis Group, Translational Health Science and Technology Institute, NCR Biotech Science Cluster, Faridabad, 121001, India.
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2
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Matsuo K, Hayashi R, Iwasa Y. Multiple colonies of cancer involved in mutual suppression with the immune system. J Theor Biol 2023; 572:111577. [PMID: 37423483 DOI: 10.1016/j.jtbi.2023.111577] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/09/2023] [Revised: 05/28/2023] [Accepted: 07/03/2023] [Indexed: 07/11/2023]
Abstract
We study the effects of the immune system on multiple cancer colonies. When cancer cells proliferate, cytotoxic T lymphocytes (CTLs) reactive to the cancer-specific antigens are activated, suppressing the growth of cancer colonies. The immune reaction activated by a large cancer colony may suppress and eliminate smaller colonies. However, cancer cells mitigate immune reactions by slowing down the activation of CTLs in dendritic cells with regulatory T cells and by inactivating CTLs attacking cancer cells with immune checkpoints. If cancer cells strongly suppress the immune reaction, the system may become bistable, where both the cancer-dominated and immunity-dominated states are locally stable. We study several models differing in the distance between colonies and the migration speeds of CTLs and regulatory T cells. We examine how the domains of attraction for multiple equilibria change with parameters. Nonlinear cancer-immunity dynamics may produce a sharp transition from a state with a small number of colonies and strong immunity to one with many colonies and weak immunity, resulting in the rapid emergence of many cancer colonies in the same organ or metastatic sites.
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Affiliation(s)
- Kosei Matsuo
- Department of Biology, Faculty of Science, Kyushu University, 744 Motooka, Nishi-ku, Fukuoka 819-0035, Japan
| | - Rena Hayashi
- Department of Biology, Faculty of Science, Kyushu University, 744 Motooka, Nishi-ku, Fukuoka 819-0035, Japan
| | - Yoh Iwasa
- Department of Biology, Faculty of Science, Kyushu University, 744 Motooka, Nishi-ku, Fukuoka 819-0035, Japan; Institute of Freshwater Biology, Nagano University, Komaki, Ueda, Nagano 386-0031, Japan.
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3
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West J, Adler F, Gallaher J, Strobl M, Brady-Nicholls R, Brown J, Roberson-Tessi M, Kim E, Noble R, Viossat Y, Basanta D, Anderson ARA. A survey of open questions in adaptive therapy: Bridging mathematics and clinical translation. eLife 2023; 12:e84263. [PMID: 36952376 PMCID: PMC10036119 DOI: 10.7554/elife.84263] [Citation(s) in RCA: 11] [Impact Index Per Article: 11.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/18/2022] [Accepted: 02/27/2023] [Indexed: 03/24/2023] Open
Abstract
Adaptive therapy is a dynamic cancer treatment protocol that updates (or 'adapts') treatment decisions in anticipation of evolving tumor dynamics. This broad term encompasses many possible dynamic treatment protocols of patient-specific dose modulation or dose timing. Adaptive therapy maintains high levels of tumor burden to benefit from the competitive suppression of treatment-sensitive subpopulations on treatment-resistant subpopulations. This evolution-based approach to cancer treatment has been integrated into several ongoing or planned clinical trials, including treatment of metastatic castrate resistant prostate cancer, ovarian cancer, and BRAF-mutant melanoma. In the previous few decades, experimental and clinical investigation of adaptive therapy has progressed synergistically with mathematical and computational modeling. In this work, we discuss 11 open questions in cancer adaptive therapy mathematical modeling. The questions are split into three sections: (1) integrating the appropriate components into mathematical models (2) design and validation of dosing protocols, and (3) challenges and opportunities in clinical translation.
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Affiliation(s)
- Jeffrey West
- Department of Integrated Mathematical Oncology, H. Lee Moffitt Cancer Center & Research InstituteTampaUnited States
| | - Fred Adler
- Department of Mathematics, University of UtahSalt Lake CityUnited States
- School of Biological Sciences, University of UtahSalt Lake CityUnited States
| | - Jill Gallaher
- Department of Integrated Mathematical Oncology, H. Lee Moffitt Cancer Center & Research InstituteTampaUnited States
| | - Maximilian Strobl
- Department of Integrated Mathematical Oncology, H. Lee Moffitt Cancer Center & Research InstituteTampaUnited States
| | - Renee Brady-Nicholls
- Department of Integrated Mathematical Oncology, H. Lee Moffitt Cancer Center & Research InstituteTampaUnited States
| | - Joel Brown
- Department of Integrated Mathematical Oncology, H. Lee Moffitt Cancer Center & Research InstituteTampaUnited States
| | - Mark Roberson-Tessi
- Department of Integrated Mathematical Oncology, H. Lee Moffitt Cancer Center & Research InstituteTampaUnited States
| | - Eunjung Kim
- Natural Product Informatics Research Center, Korea Institute of Science and TechnologyGangneungRepublic of Korea
| | - Robert Noble
- Department of Mathematics, University of LondonLondonUnited Kingdom
| | - Yannick Viossat
- Ceremade, Université Paris-Dauphine, Université Paris Sciences et LettresParisFrance
| | - David Basanta
- Department of Integrated Mathematical Oncology, H. Lee Moffitt Cancer Center & Research InstituteTampaUnited States
| | - Alexander RA Anderson
- Department of Integrated Mathematical Oncology, H. Lee Moffitt Cancer Center & Research InstituteTampaUnited States
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Mpekris F, Voutouri C, Panagi M, Baish JW, Jain RK, Stylianopoulos T. Normalizing tumor microenvironment with nanomedicine and metronomic therapy to improve immunotherapy. J Control Release 2022; 345:190-199. [PMID: 35271911 PMCID: PMC9168447 DOI: 10.1016/j.jconrel.2022.03.008] [Citation(s) in RCA: 25] [Impact Index Per Article: 12.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/27/2021] [Revised: 01/17/2022] [Accepted: 03/03/2022] [Indexed: 12/25/2022]
Abstract
Nanomedicine offered hope for improving the treatment of cancer but the survival benefits of the clinically approved nanomedicines are modest in many cases when compared to conventional chemotherapy. Metronomic therapy, defined as the frequent, low dose administration of chemotherapeutics – is being tested in clinical trials as an alternative to the conventional maximum tolerated dose (MTD) chemotherapy schedule. Although metronomic chemotherapy has not been clinically approved yet, it has shown better survival than MTD in many preclinical studies. When beneficial, metronomic therapy seems to be associated with normalization of the tumor microenvironment including improvements in tumor perfusion, tissue oxygenation and drug delivery as well as activation of the immune system. Recent preclinical studies suggest that nanomedicines can cause similar changes in the tumor microenvironment. Here, by employing a mathematical framework, we show that both approaches can serve as normalization strategies to enhance treatment. Furthermore, employing murine breast and fibrosarcoma tumor models as well as ultrasound shear wave elastography and contrast-enhanced ultrasound, we provide evidence that the approved nanomedicine Doxil can induce normalization in a dose-dependent manner by improving tumor perfusion as a result of tissue softening. Finally, we show that pretreatment with a normalizing dose of Doxil can improve the efficacy of immune checkpoint inhibition.
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Affiliation(s)
- Fotios Mpekris
- Cancer Biophysics Laboratory, Department of Mechanical and Manufacturing Engineering, University of Cyprus, Nicosia, Cyprus
| | - Chrysovalantis Voutouri
- Cancer Biophysics Laboratory, Department of Mechanical and Manufacturing Engineering, University of Cyprus, Nicosia, Cyprus; Edwin L. Steele Laboratories, Department of Radiation Oncology, Massachusetts General Hospital and Harvard Medical School, Boston, MA, USA
| | - Myrofora Panagi
- Cancer Biophysics Laboratory, Department of Mechanical and Manufacturing Engineering, University of Cyprus, Nicosia, Cyprus
| | - James W Baish
- Department of Biomedical Engineering, Bucknell University, Lewisburg, PA, USA
| | - Rakesh K Jain
- Edwin L. Steele Laboratories, Department of Radiation Oncology, Massachusetts General Hospital and Harvard Medical School, Boston, MA, USA.
| | - Triantafyllos Stylianopoulos
- Cancer Biophysics Laboratory, Department of Mechanical and Manufacturing Engineering, University of Cyprus, Nicosia, Cyprus.
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5
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Tang TQ, Shah Z, Bonyah E, Jan R, Shutaywi M, Alreshidi N. Modeling and Analysis of Breast Cancer with Adverse Reactions of Chemotherapy Treatment through Fractional Derivative. COMPUTATIONAL AND MATHEMATICAL METHODS IN MEDICINE 2022; 2022:5636844. [PMID: 35190752 PMCID: PMC8858052 DOI: 10.1155/2022/5636844] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 07/12/2021] [Accepted: 01/19/2022] [Indexed: 01/09/2023]
Abstract
The abnormal growth of cells in the breast is called malignancy or breast cancer; it is a life-threatening and dangerous cancer in women around the world. In the treatment of cancer, the doctors apply different techniques to stop cancer cell development, remove cancer cells through surgery, or kill cancer cells. In chemotherapy treatment, powerful drugs are used to kill abnormal cells; however, it has adverse reactions on the patient heart which is called cardiotoxicity. In this paper, we formulate the dynamics of cancer in the breast with adverse reactions of chemotherapy treatment on the heart of a patient in the fractional framework to visualize its dynamical behaviour. We listed the fundamental results of the fractional calculus for the analysis of our model. The model is then analyzed for the basic properties, and the existence and uniqueness of the proposed breast cancer system are investigated through fixed point theory. Furthermore, the Adams-Bashforth numerical technique is presented for the solution of fractional-order system to illustrate the time series of breast cancer model. The dynamical behaviour of different stages of breast cancer is then highlighted numerically to show the effect of fractional-order ϑ and to visualize the role of input parameter on the dynamics of breast cancer.
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Affiliation(s)
- Tao-Qian Tang
- International Intercollegiate Ph.D. Program, National Tsing Hua University, Hsinchu 30013, Taiwan
- Department of Internal Medicine, E-Da Hospital, Kaohsiung 82445, Taiwan
- School of Medicine, College of Medicine, I-Shou University, Kaohsiung 82445, Taiwan
- Department of Family and Community Medicine, E-Da Hospital, Kaohsiung 82445, Taiwan
- Department of Engineering and System Science, National Tsing Hua University, Hsinchu 30013, Taiwan
| | - Zahir Shah
- Department of Mathematical Sciences, University of Lakki Marwat, Lakki Marwat, 28420 KPK, Pakistan
| | - Ebenezer Bonyah
- Department of Mathematics Education, University of Education Winneba Kumasi (Kumasicompus), Kumasi 00233, Ghana
| | - Rashid Jan
- Department of Mathematics, University of Swabi, Swabi, 23561 KPK, Pakistan
| | - Meshal Shutaywi
- King Abdulaziz University, College of Science & Arts, Department of Mathematics, Rabigh, Saudi Arabia
| | - Nasser Alreshidi
- Department of Mathematics College of Science Northern Border University, Arar 73222, Saudi Arabia
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6
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Agossou C, Atchadé MN, Djibril AM, Kurisheva SV. Mathematical modeling and machine learning for public health decision-making: the case of breast cancer in Benin. MATHEMATICAL BIOSCIENCES AND ENGINEERING : MBE 2022; 19:1697-1720. [PMID: 35135225 DOI: 10.3934/mbe.2022080] [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: 06/14/2023]
Abstract
Breast cancer is the most common type of cancer in women. Its mortality rate is high due to late detection and cardiotoxic effects of chemotherapy. In this work, we used the Support Vector Machine (SVM) method to classify tumors and proposed a new mathematical model of the patient dynamics of the breast cancer population. Numerical simulations were performed to study the behavior of the solutions around the equilibrium point. The findings revealed that the equilibrium point is stable regardless of the initial conditions. Moreover, this study will help public health decision-making as the results can be used to minimize the number of cardiotoxic patients and increase the number of recovered patients after chemotherapy.
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Affiliation(s)
- Cyrille Agossou
- National Higher School of Mathematics Genius and Modelization, National University of Sciences, Technologies, Engineering and Mathematics, Abomey, Benin Republic
| | - Mintodê Nicodème Atchadé
- National Higher School of Mathematics Genius and Modelization, National University of Sciences, Technologies, Engineering and Mathematics, Abomey, Benin Republic
- University of Abomey-Calavi/ International Chair in Mathematical Physics and Applications (ICMPA : UNESCO-Chair), 072 BP 50 Cotonou, Benin Republic
- Saint-Petersburg State University of Economics, Department of Statistics and Econometrics, Russian Federation
| | - Aliou Moussa Djibril
- National Higher School of Mathematics Genius and Modelization, National University of Sciences, Technologies, Engineering and Mathematics, Abomey, Benin Republic
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7
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Terterov IN, Chubenko VA, Knyazev NA, Klimenko VV, Bogdanov AA, Moiseyenko VM, Bogdanov AA. Minimal PK/PD model for simultaneous description of the maximal tolerated dose and metronomic treatment outcomes in mouse tumor models. Cancer Chemother Pharmacol 2021; 88:867-878. [PMID: 34351468 DOI: 10.1007/s00280-021-04326-x] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/04/2021] [Accepted: 07/06/2021] [Indexed: 01/08/2023]
Abstract
PURPOSE Metronomic chemotherapy (MC) is a promising approach where, in contrast to the conventional maximal tolerated dose (MTD) strategy, regular fractionated doses of the drug are used. This approach has proven its efficacy, although drug dosing and scheduling are often chosen empirically. Pharmacokinetic/pharmacodynamic (PK/PD) models provide a way to choose optimal protocols with computational methods. Existing models are usually too complicated and are valid for only a subset of drug schedules. To address this issue, we propose herein a simple model that can describe MC and MTD regimens simultaneously. METHODS The minimal model comprises tumor suppression due to antiangiogenic drug effect together with a cell-kill term, responsible for its cytotoxicity. The model was tested on data obtained on tumor-bearing mice treated with gemcitabine in ether MTD, MC, or combined (MTD + MC) regimens. RESULTS We conducted a number of tests in which data were divided in various ways into training and validation sets. The model successfully described different trends in the MTD and MC regimens. With parameters obtained by fitting the model to MTD data, the simulations correctly predicted trends in both the MC and combined therapy groups. CONCLUSION Our results demonstrate that the proposed model presents a minimal yet efficient tool for modeling outcomes in different treatment regimens in mice. We hope that this model has the potential for use in clinical practice in the development of patient-specific chemotherapy scheduling protocols based on observed treatment response.
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Affiliation(s)
- Ivan N Terterov
- Saint-Petersburg Clinical Scientific and Practical Center of Specialized Types of Medical Care (Oncological), St. Petersburg, Russia.
| | - Vyacheslav A Chubenko
- Saint-Petersburg Clinical Scientific and Practical Center of Specialized Types of Medical Care (Oncological), St. Petersburg, Russia
| | - Nikolay A Knyazev
- Saint-Petersburg Clinical Scientific and Practical Center of Specialized Types of Medical Care (Oncological), St. Petersburg, Russia
| | - Vladimir V Klimenko
- Saint-Petersburg Clinical Scientific and Practical Center of Specialized Types of Medical Care (Oncological), St. Petersburg, Russia
| | - Andrei A Bogdanov
- Saint-Petersburg Clinical Scientific and Practical Center of Specialized Types of Medical Care (Oncological), St. Petersburg, Russia
| | - Vladimir M Moiseyenko
- Saint-Petersburg Clinical Scientific and Practical Center of Specialized Types of Medical Care (Oncological), St. Petersburg, Russia
| | - Alexey A Bogdanov
- Saint-Petersburg Clinical Scientific and Practical Center of Specialized Types of Medical Care (Oncological), St. Petersburg, Russia
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8
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Buhler CK, Terry RS, Link KG, Adler FR. Do mechanisms matter? Comparing cancer treatment strategies across mathematical models and outcome objectives. MATHEMATICAL BIOSCIENCES AND ENGINEERING : MBE 2021; 18:6305-6327. [PMID: 34517535 PMCID: PMC10625481 DOI: 10.3934/mbe.2021315] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/13/2023]
Abstract
When eradication is impossible, cancer treatment aims to delay the emergence of resistance while minimizing cancer burden and treatment. Adaptive therapies may achieve these aims, with success based on three assumptions: resistance is costly, sensitive cells compete with resistant cells, and therapy reduces the population of sensitive cells. We use a range of mathematical models and treatment strategies to investigate the tradeoff between controlling cell populations and delaying the emergence of resistance. These models extend game theoretic and competition models with four additional components: 1) an Allee effect where cell populations grow more slowly at low population sizes, 2) healthy cells that compete with cancer cells, 3) immune cells that suppress cancer cells, and 4) resource competition for a growth factor like androgen. In comparing maximum tolerable dose, intermittent treatment, and adaptive therapy strategies, no therapeutic choice robustly breaks the three-way tradeoff among the three therapeutic aims. Almost all models show a tight tradeoff between time to emergence of resistant cells and cancer cell burden, with intermittent and adaptive therapies following identical curves. For most models, some adaptive therapies delay overall tumor growth more than intermittent therapies, but at the cost of higher cell populations. The Allee effect breaks these relationships, with some adaptive therapies performing poorly due to their failure to treat sufficiently to drive populations below the threshold. When eradication is impossible, no treatment can simultaneously delay emergence of resistance, limit total cancer cell numbers, and minimize treatment. Simple mathematical models can play a role in designing the next generation of therapies that balance these competing objectives.
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Affiliation(s)
- Cassidy K. Buhler
- Department of Decision Sciences and MIS, Drexel University, 3220 Market St, Philadelphia, PA 19104, USA
- Department of Mathematics, University of Utah, 155 S 1400 E, Salt Lake City, UT 84112, USA
| | - Rebecca S. Terry
- Department of Mathematics, University of Utah, 155 S 1400 E, Salt Lake City, UT 84112, USA
- Department of Mathematics, Computer Science and Statistics, St. Lawrence University, 23 Romoda Drive, Canton, NY 13617, USA
| | - Kathryn G. Link
- Department of Mathematics, University of California, Davis, One Shields Avenue, CA 95616, USA
| | - Frederick R. Adler
- Department of Mathematics, University of Utah, 155 S 1400 E, Salt Lake City, UT 84112, USA
- School of Biological Sciences, University of Utah, 257 S 1400 E, Salt Lake City, UT 84112, USA
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Tran AP, Ali Al-Radhawi M, Kareva I, Wu J, Waxman DJ, Sontag ED. Delicate Balances in Cancer Chemotherapy: Modeling Immune Recruitment and Emergence of Systemic Drug Resistance. Front Immunol 2020; 11:1376. [PMID: 32695118 PMCID: PMC7338613 DOI: 10.3389/fimmu.2020.01376] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/31/2020] [Accepted: 05/29/2020] [Indexed: 01/21/2023] Open
Abstract
Metronomic chemotherapy can drastically enhance immunogenic tumor cell death. However, the mechanisms responsible are still incompletely understood. Here, we develop a mathematical model to elucidate the underlying complex interactions between tumor growth, immune system activation, and therapy-mediated immunogenic cell death. Our model is conceptually simple, yet it provides a surprisingly excellent fit to empirical data obtained from a GL261 SCID mouse glioma model treated with cyclophosphamide on a metronomic schedule. The model includes terms representing immune recruitment as well as the emergence of drug resistance during prolonged metronomic treatments. Strikingly, a single fixed set of parameters, adjusted neither for individuals nor for drug schedule, recapitulates experimental data across various drug regimens remarkably well, including treatments administered at intervals ranging from 6 to 12 days. Additionally, the model predicts peak immune activation times, rediscovering experimental data that had not been used in parameter fitting or in model construction. Notably, the validated model suggests that immunostimulatory and immunosuppressive intermediates are responsible for the observed phenomena of resistance and immune cell recruitment, and thus for variation of responses with respect to different schedules of drug administration.
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Affiliation(s)
- Anh Phong Tran
- Department of Chemical Engineering, Northeastern University, Boston, MA, United States
| | - M Ali Al-Radhawi
- Department of Electrical and Computer Engineering, Northeastern University, Boston, MA, United States
| | - Irina Kareva
- Mathematical and Computational Sciences Center, School of Human Evolution and Social Change, Arizona State University, Tempe, AZ, United States
| | - Junjie Wu
- Clinical Research Institute, Key Laboratory of Tumor Molecular Diagnosis and Individualized Medicine of Zhejiang Province, Zhejiang Provincial People's Hospital, People's Hospital of Hangzhou Medical College, Hangzhou, China
| | - David J Waxman
- Department of Biology and Bioinformatics Program, Boston University, Boston, MA, United States
| | - Eduardo D Sontag
- Department of Electrical and Computer Engineering, Northeastern University, Boston, MA, United States
- Department of Bioengineering, Northeastern University, Boston, MA, United States
- Laboratory of Systems Pharmacology, Program in Therapeutic Science, Harvard Medical School, Boston, MA, United States
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Böttcher MA, Held-Feindt J, Synowitz M, Lucius R, Traulsen A, Hattermann K. Modeling treatment-dependent glioma growth including a dormant tumor cell subpopulation. BMC Cancer 2018; 18:376. [PMID: 29614985 PMCID: PMC5883287 DOI: 10.1186/s12885-018-4281-1] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/18/2018] [Accepted: 03/21/2018] [Indexed: 02/07/2023] Open
Abstract
Background Tumors comprise a variety of specialized cell phenotypes adapted to different ecological niches that massively influence the tumor growth and its response to treatment. Methods In the background of glioblastoma multiforme, a highly malignant brain tumor, we consider a rapid proliferating phenotype that appears susceptible to treatment, and a dormant phenotype which lacks this pronounced proliferative ability and is not affected by standard therapeutic strategies. To gain insight in the dynamically changing proportions of different tumor cell phenotypes under different treatment conditions, we develop a mathematical model and underline our assumptions with experimental data. Results We show that both cell phenotypes contribute to the distinct composition of the tumor, especially in cycling low and high dose treatment, and therefore may influence the tumor growth in a phenotype specific way. Conclusion Our model of the dynamic proportions of dormant and rapidly growing glioblastoma cells in different therapy settings suggests that phenotypically different cells should be considered to plan dose and duration of treatment schedules.
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Affiliation(s)
- Marvin A Böttcher
- Department Evolutionary Theory, Max Planck Institute for Evolutionary Biology, 24306, Plön, Germany
| | - Janka Held-Feindt
- Department of Neurosurgery, University Medical Center Schleswig-Holstein UKSH, Campus Kiel, 24105, Kiel, Germany
| | - Michael Synowitz
- Department of Neurosurgery, University Medical Center Schleswig-Holstein UKSH, Campus Kiel, 24105, Kiel, Germany
| | - Ralph Lucius
- Department of Anatomy, University of Kiel, 24098, Kiel, Germany
| | - Arne Traulsen
- Department Evolutionary Theory, Max Planck Institute for Evolutionary Biology, 24306, Plön, Germany
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11
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Ledzewicz U, Schättler H. Application of mathematical models to metronomic chemotherapy: What can be inferred from minimal parameterized models? Cancer Lett 2017; 401:74-80. [PMID: 28323033 DOI: 10.1016/j.canlet.2017.03.021] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/10/2017] [Revised: 03/10/2017] [Accepted: 03/10/2017] [Indexed: 01/11/2023]
Abstract
Metronomic chemotherapy refers to the frequent administration of chemotherapy at relatively low, minimally toxic doses without prolonged treatment interruptions. Different from conventional or maximum-tolerated-dose chemotherapy which aims at an eradication of all malignant cells, in a metronomic dosing the goal often lies in the long-term management of the disease when eradication proves elusive. Mathematical modeling and subsequent analysis (theoretical as well as numerical) have become an increasingly more valuable tool (in silico) both for determining conditions under which specific treatment strategies should be preferred and for numerically optimizing treatment regimens. While elaborate, computationally-driven patient specific schemes that would optimize the timing and drug dose levels are still a part of the future, such procedures may become instrumental in making chemotherapy effective in situations where it currently fails. Ideally, mathematical modeling and analysis will develop into an additional decision making tool in the complicated process that is the determination of efficient chemotherapy regimens. In this article, we review some of the results that have been obtained about metronomic chemotherapy from mathematical models and what they infer about the structure of optimal treatment regimens.
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Affiliation(s)
- Urszula Ledzewicz
- Dept. of Mathematics and Statistics, Southern Illinois University Edwardsville, Edwardsville, IL, 62026-1653, USA; Institute of Mathematics, Lodz University of Technology, 90-924, Lodz, Poland.
| | - Heinz Schättler
- Dept. of Electrical and Systems Engineering Washington University, St. Louis, MO, 63130, USA.
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12
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Abstract
Metronomic dosing of chemotherapy-defined as frequent administration at lower doses-has been shown to be more efficacious than maximum tolerated dose treatment in preclinical studies, and is currently being tested in the clinic. Although multiple mechanisms of benefit from metronomic chemotherapy have been proposed, how these mechanisms are related to one another and which one is dominant for a given tumor-drug combination is not known. To this end, we have developed a mathematical model that incorporates various proposed mechanisms, and report here that improved function of tumor vessels is a key determinant of benefit from metronomic chemotherapy. In our analysis, we used multiple dosage schedules and incorporated interactions among cancer cells, stem-like cancer cells, immune cells, and the tumor vasculature. We found that metronomic chemotherapy induces functional normalization of tumor blood vessels, resulting in improved tumor perfusion. Improved perfusion alleviates hypoxia, which reprograms the immunosuppressive tumor microenvironment toward immunostimulation and improves drug delivery and therapeutic outcomes. Indeed, in our model, improved vessel function enhanced the delivery of oxygen and drugs, increased the number of effector immune cells, and decreased the number of regulatory T cells, which in turn killed a larger number of cancer cells, including cancer stem-like cells. Vessel function was further improved owing to decompression of intratumoral vessels as a result of increased killing of cancer cells, setting up a positive feedback loop. Our model enables evaluation of the relative importance of these mechanisms, and suggests guidelines for the optimal use of metronomic therapy.
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13
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Ledzewicz U, Wang S, Schattler H, Andre N, Heng MA, Pasquier E. On drug resistance and metronomic chemotherapy: A mathematical modeling and optimal control approach. MATHEMATICAL BIOSCIENCES AND ENGINEERING : MBE 2017; 14:217-235. [PMID: 27879129 DOI: 10.3934/mbe.2017014] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
Effects that tumor heterogeneity and drug resistance have on the structure of chemotherapy protocols are discussed from a mathematical modeling and optimal control point of view. In the case when two compartments consisting of sensitive and resistant cells are considered, optimal protocols consist of full dose chemotherapy as long as the relative proportion of sensitive cells is high. When resistant cells become more dominant, optimal controls switch to lower dose regimens defined by so-called singular controls. The role that singular controls play in the structure of optimal therapy protocols for cell populations with a large number of traits is explored in mathematical models.
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Affiliation(s)
- Urszula Ledzewicz
- Institute of Mathematics, Lodz University of Technology, 90-924 Lodz, Poland.
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14
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Munzone E, Colleoni M. Metronomics in the neoadjuvant and adjuvant treatment of breast cancer. Cancer Lett 2017; 400:259-266. [PMID: 28093280 DOI: 10.1016/j.canlet.2016.12.041] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/18/2016] [Revised: 12/22/2016] [Accepted: 12/24/2016] [Indexed: 12/23/2022]
Abstract
The concept of metronomic chemotherapy (MC) has evolved from a descriptive preclinical phenomenon encompassing inhibition of angiogenesis to a clinically validated treatment concept involving multiple potential mechanisms of action. Clinicians are progressively more incline to consider MC as a component of mainstream medical oncology practice in advanced breast cancer. However, more recently MC has been tested even in the adjuvant/neoadjuvant setting, taking the opportunity to obtain tumor specimens and blood samples, in order to identify tumor-specific or patient-specific biomarkers for personalizing treatments. In addition, the antiangiogenic and pro-immune nature of metronomic chemotherapy made triple negative breast cancer (TNBC) a good candidate for exploring low-dose maintenance treatment in the adjuvant setting or in combination with immunomodulatory drugs. The potential development of MC in breast cancer pass through the research to identify biomarkers and individual tumor characteristics that can better address the use of this treatment strategy in the future. Finally, the subjective attitude of patients represents one of the major factors that influence the choice and acceptance of a therapeutic program. Personal preference and considerations about quality of life should guide the treatment choice eventually prioritizing the use of MC. Nevertheless, more robust data from randomized phase III trials are needed in the future, in order to make clinicians more confident in using metronomic strategies.
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Affiliation(s)
- Elisabetta Munzone
- Division of Medical Senology, European Institute of Oncology, Milan, Italy
| | - Marco Colleoni
- Division of Medical Senology, European Institute of Oncology, Milan, Italy.
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15
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Chisholm RH, Lorenzi T, Clairambault J. Cell population heterogeneity and evolution towards drug resistance in cancer: Biological and mathematical assessment, theoretical treatment optimisation. Biochim Biophys Acta Gen Subj 2016; 1860:2627-45. [PMID: 27339473 DOI: 10.1016/j.bbagen.2016.06.009] [Citation(s) in RCA: 55] [Impact Index Per Article: 6.9] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/01/2016] [Revised: 05/25/2016] [Accepted: 06/05/2016] [Indexed: 12/14/2022]
Abstract
BACKGROUND Drug-induced drug resistance in cancer has been attributed to diverse biological mechanisms at the individual cell or cell population scale, relying on stochastically or epigenetically varying expression of phenotypes at the single cell level, and on the adaptability of tumours at the cell population level. SCOPE OF REVIEW We focus on intra-tumour heterogeneity, namely between-cell variability within cancer cell populations, to account for drug resistance. To shed light on such heterogeneity, we review evolutionary mechanisms that encompass the great evolution that has designed multicellular organisms, as well as smaller windows of evolution on the time scale of human disease. We also present mathematical models used to predict drug resistance in cancer and optimal control methods that can circumvent it in combined therapeutic strategies. MAJOR CONCLUSIONS Plasticity in cancer cells, i.e., partial reversal to a stem-like status in individual cells and resulting adaptability of cancer cell populations, may be viewed as backward evolution making cancer cell populations resistant to drug insult. This reversible plasticity is captured by mathematical models that incorporate between-cell heterogeneity through continuous phenotypic variables. Such models have the benefit of being compatible with optimal control methods for the design of optimised therapeutic protocols involving combinations of cytotoxic and cytostatic treatments with epigenetic drugs and immunotherapies. GENERAL SIGNIFICANCE Gathering knowledge from cancer and evolutionary biology with physiologically based mathematical models of cell population dynamics should provide oncologists with a rationale to design optimised therapeutic strategies to circumvent drug resistance, that still remains a major pitfall of cancer therapeutics. This article is part of a Special Issue entitled "System Genetics" Guest Editor: Dr. Yudong Cai and Dr. Tao Huang.
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Affiliation(s)
- Rebecca H Chisholm
- School of Biotechnology and Biomolecular Sciences, University of New South Wales, Sydney, Australia
| | - Tommaso Lorenzi
- School of Mathematics and Statistics, University of St Andrews, North Haugh, KY16 9SS, St Andrews, Scotland, United Kingdom. http://www.tommasolorenzi.com
| | - Jean Clairambault
- INRIA Paris, MAMBA team, 2, rue Simone Iff, CS 42112, 75589 Paris Cedex 12, France; Sorbonne Universités, UPMC Univ. Paris 6, UMR 7598, Laboratoire Jacques-Louis Lions, Boîte courrier 187, 4 Place Jussieu, 75252 Paris Cedex 05, France.
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16
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Ledzewicz U, Schaettler H. Optimizing Chemotherapeutic Anti-cancer Treatment and the Tumor Microenvironment: An Analysis of Mathematical Models. ADVANCES IN EXPERIMENTAL MEDICINE AND BIOLOGY 2016; 936:209-223. [PMID: 27739050 DOI: 10.1007/978-3-319-42023-3_11] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/10/2022]
Abstract
We review results about the structure of administration of chemotherapeutic anti-cancer treatment that we have obtained from an analysis of minimally parameterized mathematical models using methods of optimal control. This is a branch of continuous-time optimization that studies the minimization of a performance criterion imposed on an underlying dynamical system subject to constraints. The scheduling of anti-cancer treatments has all the features of such a problem: treatments are administered in time and the interactions of the drugs with the tumor and its microenvironment determine the efficacy of therapy. At the same time, constraints on the toxicity of the treatments need to be taken into account. The models we consider are low-dimensional and do not include more refined details, but they capture the essence of the underlying biology and our results give robust and rather conclusive qualitative information about the administration of optimal treatment protocols that strongly correlate with approaches taken in medical practice. We describe the changes that arise in optimal administration schedules as the mathematical models are increasingly refined to progress from models that only consider the cancerous cells to models that include the major components of the tumor microenvironment, namely the tumor vasculature and tumor-immune system interactions.
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Affiliation(s)
- Urszula Ledzewicz
- Department of Mathematics and Statistics, Southern Illinois University Edwardsville, Edwardsville, IL, USA, 62026.
- Institute of Mathematics, Lodz University of Technology, Lodz, Poland.
| | - Heinz Schaettler
- Department of Electrical and Systems Engineering, Washington University, St. Louis, MO, USA, 63130
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