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Stability and Bifurcation Analysis of Tumor–Macrophages Response Model and Inhibitory Role of Treg Cells. IRANIAN JOURNAL OF SCIENCE AND TECHNOLOGY, TRANSACTIONS A: SCIENCE 2022. [DOI: 10.1007/s40995-022-01381-8] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
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Dynamics of an Antitumour Model with Pulsed Radioimmunotherapy. COMPUTATIONAL AND MATHEMATICAL METHODS IN MEDICINE 2022; 2022:4692772. [PMID: 35677181 PMCID: PMC9168186 DOI: 10.1155/2022/4692772] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 12/11/2021] [Accepted: 04/20/2022] [Indexed: 11/18/2022]
Abstract
In this paper, an antitumour model for characterising radiotherapy and immunotherapy processes at different fixed times is proposed. The global attractiveness of the positive periodic solution for each corresponding subsystem is proved with the integral inequality technique. Then, based on the differentiability of the solutions with respect to the initial values, the eigenvalues of the Jacobian matrix at a fixed point corresponding to the tumour-free periodic solution are determined, resulting in a sufficient condition for local stability. The solutions to the ordinary differential equations are compared, the threshold condition for the global attractiveness of the tumour-free periodic solution is provided in terms of an indicator
, and the permanence of a system with at least one tumour-present periodic solution is investigated. Furthermore, the effects of the death rate, effector cell injection dosage, therapeutic period, and effector cell activation rate on indicator
are determined through numerical simulations, and the results indicate that radioimmunotherapy is more effective than either radiotherapy or immunotherapy alone.
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Bitsouni V, Tsilidis V. Mathematical modeling of tumor-immune system interactions: the effect of rituximab on breast cancer immune response. J Theor Biol 2022; 539:111001. [PMID: 34998860 DOI: 10.1016/j.jtbi.2021.111001] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/02/2021] [Accepted: 12/25/2021] [Indexed: 12/11/2022]
Abstract
tBregs are a newly discovered subcategory of B regulatory cells, which are generated by breast cancer, resulting in the increase of Tregs and therefore in the death of NK cells. In this study, we use a mathematical and computational approach to investigate the complex interactions between the aforementioned cells as well as CD8+ T cells, CD4+ T cells and B cells. Furthermore, we use data fitting to prove that the functional response regarding the lysis of breast cancer cells by NK cells has a ratio-dependent form. Additionally, we include in our model the concentration of rituximab - a monoclonal antibody that has been suggested as a potential breast cancer therapy - and test its effect, when the standard, as well as experimental dosages, are administered.
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Affiliation(s)
- Vasiliki Bitsouni
- Department of Mathematics, National and Kapodistrian University of Athens, Panepistimioupolis, GR-15784 Athens, Greece; School of Science and Technology, Hellenic Open University, 18 Parodos Aristotelous Str., GR-26335 Patras, Greece.
| | - Vasilis Tsilidis
- School of Science and Technology, Hellenic Open University, 18 Parodos Aristotelous Str., GR-26335 Patras, Greece.
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Brummer AB, Yang X, Ma E, Gutova M, Brown CE, Rockne RC. Dose-dependent thresholds of dexamethasone destabilize CAR T-cell treatment efficacy. PLoS Comput Biol 2022; 18:e1009504. [PMID: 35081104 PMCID: PMC8820647 DOI: 10.1371/journal.pcbi.1009504] [Citation(s) in RCA: 7] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/04/2021] [Revised: 02/07/2022] [Accepted: 01/12/2022] [Indexed: 12/14/2022] Open
Abstract
Chimeric antigen receptor (CAR) T-cell therapy is potentially an effective targeted immunotherapy for glioblastoma, yet there is presently little known about the efficacy of CAR T-cell treatment when combined with the widely used anti-inflammatory and immunosuppressant glucocorticoid, dexamethasone. Here we present a mathematical model-based analysis of three patient-derived glioblastoma cell lines treated in vitro with CAR T-cells and dexamethasone. Advanced in vitro experimental cell killing assay technologies allow for highly resolved temporal dynamics of tumor cells treated with CAR T-cells and dexamethasone, making this a valuable model system for studying the rich dynamics of nonlinear biological processes with translational applications. We model the system as a nonautonomous, two-species predator-prey interaction of tumor cells and CAR T-cells, with explicit time-dependence in the clearance rate of dexamethasone. Using time as a bifurcation parameter, we show that (1) dexamethasone destabilizes coexistence equilibria between CAR T-cells and tumor cells in a dose-dependent manner and (2) as dexamethasone is cleared from the system, a stable coexistence equilibrium returns in the form of a Hopf bifurcation. With the model fit to experimental data, we demonstrate that high concentrations of dexamethasone antagonizes CAR T-cell efficacy by exhausting, or reducing the activity of CAR T-cells, and by promoting tumor cell growth. Finally, we identify a critical threshold in the ratio of CAR T-cell death to CAR T-cell proliferation rates that predicts eventual treatment success or failure that may be used to guide the dose and timing of CAR T-cell therapy in the presence of dexamethasone in patients. Bioengineering and gene-editing technologies have paved the way for advance immunotherapies that can target patient-specific tumor cells. One of these therapies, chimeric antigen receptor (CAR) T-cell therapy has recently shown promise in treating glioblastoma, an aggressive brain cancer often with poor patient prognosis. Dexamethasone is a commonly prescribed anti-inflammatory medication due to the health complications of tumor associated swelling in the brain. However, the immunosuppressant effects of dexamethasone on the immunotherapeutic CAR T-cells are not well understood. To address this issue, we use mathematical modeling to study in vitro dynamics of dexamethasone and CAR T-cells in three patient-derived glioblastoma cell lines. We find that in each cell line studied there is a threshold of tolerable dexamethasone concentration. Below this threshold, CAR T-cells are successful at eliminating the cancer cells, while above this threshold, dexamethasone critically inhibits CAR T-cell efficacy. Our modeling suggests that in the presence of high dexamethasone reduced CAR T-cell efficacy, or increased exhaustion, can occur and result in CAR T-cell treatment failure.
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Affiliation(s)
- Alexander B. Brummer
- Department of Computational and Quantitative Medicine, Division of Mathematical Oncology, Beckman Research Institute, City of Hope National Medical Center, Duarte, California, United States of America
- * E-mail: (ABB); (CEB); (RCR)
| | - Xin Yang
- Department of Hematology and Hematopoietic Cell Translation and Immuno-Oncology, Beckman Research Institute, City of Hope National Medical Center, Duarte, California, United States of America
| | - Eric Ma
- Department of Hematology and Hematopoietic Cell Translation and Immuno-Oncology, Beckman Research Institute, City of Hope National Medical Center, Duarte, California, United States of America
| | - Margarita Gutova
- Department of Stem Cell Biology and Regenerative Medicine, Beckman Research Institute, City of Hope National Medical Center, Duarte, California, United States of America
| | - Christine E. Brown
- Department of Hematology and Hematopoietic Cell Translation and Immuno-Oncology, Beckman Research Institute, City of Hope National Medical Center, Duarte, California, United States of America
- * E-mail: (ABB); (CEB); (RCR)
| | - Russell C. Rockne
- Department of Computational and Quantitative Medicine, Division of Mathematical Oncology, Beckman Research Institute, City of Hope National Medical Center, Duarte, California, United States of America
- * E-mail: (ABB); (CEB); (RCR)
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Dehingia K, Sarmah HK, Alharbi Y, Hosseini K. Mathematical analysis of a cancer model with time-delay in tumor-immune interaction and stimulation processes. ADVANCES IN DIFFERENCE EQUATIONS 2021; 2021:473. [PMID: 34721555 PMCID: PMC8546790 DOI: 10.1186/s13662-021-03621-4] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 04/18/2021] [Accepted: 09/22/2021] [Indexed: 06/13/2023]
Abstract
In this study, we discuss a cancer model considering discrete time-delay in tumor-immune interaction and stimulation processes. This study aims to analyze and observe the dynamics of the model along with variation of vital parameters and the delay effect on anti-tumor immune responses. We obtain sufficient conditions for the existence of equilibrium points and their stability. Existence of Hopf bifurcation at co-axial equilibrium is investigated. The stability of bifurcating periodic solutions is discussed, and the time length for which the solutions preserve the stability is estimated. Furthermore, we have derived the conditions for the direction of bifurcating periodic solutions. Theoretically, it was observed that the system undergoes different states if we vary the system's parameters. Some numerical simulations are presented to verify the obtained mathematical results.
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Affiliation(s)
- Kaushik Dehingia
- Department of Mathematics, Gauhati University, Guwahati, Assam India
| | | | - Yamen Alharbi
- Department of Mathematics, King Abdul Aziz University, Jeddah, Saudi Arabia
| | - Kamyar Hosseini
- Department of Mathematics, Rasht Branch, Islamic Azad University, Rasht, Iran
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Beck RJ, Weigelin B, Beltman JB. Mathematical Modelling Based on In Vivo Imaging Suggests CD137-Stimulated Cytotoxic T Lymphocytes Exert Superior Tumour Control Due to an Enhanced Antimitotic Effect on Tumour Cells. Cancers (Basel) 2021; 13:cancers13112567. [PMID: 34073822 PMCID: PMC8197176 DOI: 10.3390/cancers13112567] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/06/2021] [Revised: 05/18/2021] [Accepted: 05/19/2021] [Indexed: 01/12/2023] Open
Abstract
Simple Summary Cytotoxic T lymphocytes (CTLs) play an important role in controlling tumours, and an improved understanding of how they accomplish this will benefit immunotherapeutic cancer treatment strategies. Stimulation of CTLs by targeting their CD137 receptor is a strategy currently under investigation for enhancing responses against tumours, yet so far only limited quantitative knowledge regarding the effects of such stimulation upon CTLs has been obtained. Here, we develop mathematical models to describe dynamic in vivo two-photon imaging of tumour infiltrating CTLs, to characterise differences in their function either in the presence or absence of a CD137 agonist antibody. We showed that an increased antiproliferative effect and a more sustained presence of CTLs within the tumour were the most important effects associated with anti-CD137 treatment. Abstract Several immunotherapeutic strategies for the treatment of cancer are under development. Two prominent strategies are adoptive cell transfer (ACT) of CTLs and modulation of CTL function with immune checkpoint inhibitors or with costimulatory antibodies. Despite some success with these approaches, there remains a lack of detailed and quantitative descriptions of the events following CTL transfer and the impact of immunomodulation. Here, we have applied ordinary differential equation models to two photon imaging data derived from a B16F10 murine melanoma. Models were parameterised with data from two different treatment conditions: either ACT-only, or ACT with intratumoural costimulation using a CD137 targeted antibody. Model dynamics and best fitting parameters were compared, in order to assess the mode of action of the CTLs and examine how the CD137 antibody influenced their activities. We found that the cytolytic activity of the transferred CTLs was minimal without CD137 costimulation, and that the CD137 targeted antibody did not enhance the per-capita killing ability of the transferred CTLs. Instead, the results of our modelling study suggest that an antiproliferative effect of CTLs exerted upon the tumour likely accounted for the majority of the reduction in tumour growth after CTL transfer. Moreover, we found that CD137 most likely improved tumour control via enhancement of this antiproliferative effect, as well as prolonging the period in which CTLs were inside the tumour, leading to a sustained duration of their antitumour effects following CD137 stimulation.
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Affiliation(s)
- Richard J. Beck
- Leiden Academic Centre for Drug Research, Division of Drug Discovery and Safety, Leiden University, 2333 CC Leiden, The Netherlands;
| | - Bettina Weigelin
- Department of Preclinical Imaging and Radiopharmacy, Eberhard Karls University of Tübingen, 72076 Tübingen, Germany;
- Cluster of Excellence iFIT (EXC 2180) “Image-Guided and Functionally Instructed Tumor Therapies”, University of Tübingen, 72076 Tübingen, Germany
| | - Joost B. Beltman
- Leiden Academic Centre for Drug Research, Division of Drug Discovery and Safety, Leiden University, 2333 CC Leiden, The Netherlands;
- Correspondence:
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Ottesen JT, Stiehl T, Andersen M. Blood Cancer and Immune Surveillance. SYSTEMS MEDICINE 2021. [DOI: 10.1016/b978-0-12-801238-3.11510-7] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022] Open
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Peskov K, Azarov I, Chu L, Voronova V, Kosinsky Y, Helmlinger G. Quantitative Mechanistic Modeling in Support of Pharmacological Therapeutics Development in Immuno-Oncology. Front Immunol 2019; 10:924. [PMID: 31134058 PMCID: PMC6524731 DOI: 10.3389/fimmu.2019.00924] [Citation(s) in RCA: 28] [Impact Index Per Article: 5.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/28/2019] [Accepted: 04/10/2019] [Indexed: 12/15/2022] Open
Abstract
Following the approval, in recent years, of the first immune checkpoint inhibitor, there has been an explosion in the development of immuno-modulating pharmacological modalities for the treatment of various cancers. From the discovery phase to late-stage clinical testing and regulatory approval, challenges in the development of immuno-oncology (IO) drugs are multi-fold and complex. In the preclinical setting, the multiplicity of potential drug targets around immune checkpoints, the growing list of immuno-modulatory molecular and cellular forces in the tumor microenvironment-with additional opportunities for IO drug targets, the emergence of exploratory biomarkers, and the unleashed potential of modality combinations all have necessitated the development of quantitative, mechanistically-oriented systems models which incorporate key biology and patho-physiology aspects of immuno-oncology and the pharmacokinetics of IO-modulating agents. In the clinical setting, the qualification of surrogate biomarkers predictive of IO treatment efficacy or outcome, and the corresponding optimization of IO trial design have become major challenges. This mini-review focuses on the evolution and state-of-the-art of quantitative systems models describing the tumor vs. immune system interplay, and their merging with quantitative pharmacology models of IO-modulating agents, as companion tools to support the addressing of these challenges.
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Affiliation(s)
- Kirill Peskov
- M&S Decisions, Moscow, Russia.,Computational Oncology Group, I.M. Sechenov First Moscow State Medical University of the Russian Ministry of Health, Moscow, Russia
| | | | - Lulu Chu
- Quantitative Clinical Pharmacology, Early Clinical Development, IMED Biotech Unit, AstraZeneca Pharmaceuticals, Boston, MA, United States
| | | | | | - Gabriel Helmlinger
- Quantitative Clinical Pharmacology, Early Clinical Development, IMED Biotech Unit, AstraZeneca Pharmaceuticals, Boston, MA, United States
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Ottesen JT, Pedersen RK, Sajid Z, Gudmand-Hoeyer J, Bangsgaard KO, Skov V, Kjær L, Knudsen TA, Pallisgaard N, Hasselbalch HC, Andersen M. Bridging blood cancers and inflammation: The reduced Cancitis model. J Theor Biol 2019; 465:90-108. [PMID: 30615883 DOI: 10.1016/j.jtbi.2019.01.001] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/05/2018] [Revised: 12/11/2018] [Accepted: 01/02/2019] [Indexed: 11/28/2022]
Abstract
A novel mechanism-based model - the Cancitis model - describing the interaction of blood cancer and the inflammatory system is proposed, analyzed and validated. The immune response is divided into two components, one where the elimination rate of malignant stem cells is independent of the level of the blood cancer and one where the elimination rate depends on the level of the blood cancer. A dimensional analysis shows that the full 6-dimensional system of nonlinear ordinary differential equations may be reduced to a 2-dimensional system - the reduced Cancitis model - using Fenichel theory. The original 18 parameters appear in the reduced model in 8 groups of parameters. The reduced model is analyzed. Especially the steady states and their dependence on the exogenous inflammatory stimuli are analyzed. A semi-analytic investigation reveals the stability properties of the steady states. Finally, positivity of the system and the existence of an attracting trapping region in the positive octahedron guaranteeing global existence and uniqueness of solutions are proved. The possible topologies of the dynamical system are completely determined as having a Janus structure, where two qualitatively different topologies appear for different sets of parameters. To classify this Janus structure we propose a novel concept in blood cancer - a reproduction ratio R. It determines the topological structure depending on whether it is larger or smaller than a threshold value. Furthermore, it follows that inflammation, affected by the exogenous inflammatory stimulation, may determine the onset and development of blood cancers. The body may manage initial blood cancer as long as the self-renewal rate is not too high, but fails to manage it if an inflammation appears. Thus, inflammation may trigger and drive blood cancers. Finally, the mathematical analysis suggests novel treatment strategies and it is used to discuss the in silico effect of existing treatment, e.g. interferon-α or T-cell therapy, and the impact of malignant cells becoming resistant.
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Affiliation(s)
- Johnny T Ottesen
- Department of Science and Environment, Roskilde University, Denmark.
| | | | - Zamra Sajid
- Department of Science and Environment, Roskilde University, Denmark
| | | | | | - Vibe Skov
- Department of Hematology, Zealand University Hospital, University of Copenhagen, Denmark
| | - Lasse Kjær
- Department of Hematology, Zealand University Hospital, University of Copenhagen, Denmark
| | - Trine A Knudsen
- Department of Hematology, Zealand University Hospital, University of Copenhagen, Denmark
| | - Niels Pallisgaard
- Department of Hematology, Zealand University Hospital, University of Copenhagen, Denmark
| | - Hans C Hasselbalch
- Department of Hematology, Zealand University Hospital, University of Copenhagen, Denmark
| | - Morten Andersen
- Department of Science and Environment, Roskilde University, Denmark
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Yu M, Dong Y, Takeuchi Y. Dual role of delay effects in a tumour-immune system. JOURNAL OF BIOLOGICAL DYNAMICS 2017; 11:334-347. [PMID: 27648645 DOI: 10.1080/17513758.2016.1231347] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/09/2023]
Abstract
In this paper, a previous tumour-immune interaction model is simplified by neglecting a relatively weak direct immune activation by the tumour cells, which can still keep the essential dynamics properties of the original model. As the immune activation process is not instantaneous, we now incorporate one delay for the activation of the effector cells (ECs) by helper T cells (HTCs) into the model. Furthermore, we investigate the stability and instability regions of the tumour-presence equilibrium state of the delay-induced system with respect to two parameters, the activation rate of ECs by HTCs and the HTCs stimulation rate by the presence of identified tumour antigens. We show the dual role of this delay that can induce stability switches exhibiting destabilization as well as stabilization of the tumour-presence equilibrium. Besides, our results reveal that an appropriate immune activation time delay plays a significant role in control of tumour growth.
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Affiliation(s)
- Min Yu
- a College of Science and Engineering , Aoyama Gakuin University , Sagamihara , Japan
| | - Yueping Dong
- b Graduate school of Medicine , The University of Tokyo , Tokyo , Japan
| | - Yasuhiro Takeuchi
- a College of Science and Engineering , Aoyama Gakuin University , Sagamihara , Japan
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Pradeep BGSA, Ma W, Wang W. Stability and Hopf bifurcation analysis of an SEIR model with nonlinear incidence rate and relapse. JOURNAL OF STATISTICS & MANAGEMENT SYSTEMS 2017. [DOI: 10.1080/09720510.2016.1228321] [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]
Affiliation(s)
| | - Wanbiao Ma
- Department of Applied Mathematics and Physics, University of Science and Technology Beijing, Beijing-100083, China
| | - Wei Wang
- Department of Applied Mathematics and Physics, University of Science and Technology Beijing, Beijing-100083, China
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Ordinary Differential Equation Models for Adoptive Immunotherapy. Bull Math Biol 2017; 80:1059-1083. [PMID: 28382423 DOI: 10.1007/s11538-017-0263-8] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/06/2016] [Accepted: 02/24/2017] [Indexed: 10/19/2022]
Abstract
Modified T cells that have been engineered to recognize the CD19 surface marker have recently been shown to be very successful at treating acute lymphocytic leukemias. Here, we explore four previous approaches that have used ordinary differential equations to model this type of therapy, compare their properties, and modify the models to address their deficiencies. Although the four models treat the workings of the immune system in slightly different ways, they all predict that adoptive immunotherapy can be successful to move a patient from the large tumor fixed point to an equilibrium with little or no tumor.
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dePillis LG, Eladdadi A, Radunskaya AE. Modeling cancer-immune responses to therapy. J Pharmacokinet Pharmacodyn 2014; 41:461-78. [DOI: 10.1007/s10928-014-9386-9] [Citation(s) in RCA: 47] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/01/2014] [Accepted: 09/17/2014] [Indexed: 12/26/2022]
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