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A Mathematical Study of the Role of tBregs in Breast Cancer. Bull Math Biol 2022; 84:112. [PMID: 36048369 DOI: 10.1007/s11538-022-01054-y] [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: 03/03/2022] [Accepted: 07/12/2022] [Indexed: 12/24/2022]
Abstract
A model for the mathematical study of immune response to breast cancer is proposed and studied, both analytically and numerically. It is a simplification of a complex one, recently introduced by two of the present authors. It serves for a compact study of the dynamical role in cancer promotion of a relatively recently described subgroup of regulatory B cells, which are evoked by the tumour.
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Shafiekhani S, Dehghanbanadaki H, Fatemi AS, Rahbar S, Hadjati J, Jafari AH. Prediction of anti-CD25 and 5-FU treatments efficacy for pancreatic cancer using a mathematical model. BMC Cancer 2021; 21:1226. [PMID: 34781899 PMCID: PMC8594222 DOI: 10.1186/s12885-021-08770-z] [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: 02/13/2021] [Accepted: 09/09/2021] [Indexed: 02/18/2023] Open
Abstract
BACKGROUND Pancreatic ductal adenocarcinoma (PDAC) is a highly lethal disease with rising incidence and with 5-years overall survival of less than 8%. PDAC creates an immune-suppressive tumor microenvironment to escape immune-mediated eradication. Regulatory T (Treg) cells and myeloid-derived suppressor cells (MDSC) are critical components of the immune-suppressive tumor microenvironment. Shifting from tumor escape or tolerance to elimination is the major challenge in the treatment of PDAC. RESULTS In a mathematical model, we combine distinct treatment modalities for PDAC, including 5-FU chemotherapy and anti- CD25 immunotherapy to improve clinical outcome and therapeutic efficacy. To address and optimize 5-FU and anti- CD25 treatment (to suppress MDSCs and Tregs, respectively) schedule in-silico and simultaneously unravel the processes driving therapeutic responses, we designed an in vivo calibrated mathematical model of tumor-immune system (TIS) interactions. We designed a user-friendly graphical user interface (GUI) unit which is configurable for treatment timings to implement an in-silico clinical trial to test different timings of both 5-FU and anti- CD25 therapies. By optimizing combination regimens, we improved treatment efficacy. In-silico assessment of 5-FU and anti- CD25 combination therapy for PDAC significantly showed better treatment outcomes when compared to 5-FU and anti- CD25 therapies separately. Due to imprecise, missing, or incomplete experimental data, the kinetic parameters of the TIS model are uncertain that this can be captured by the fuzzy theorem. We have predicted the uncertainty band of cell/cytokines dynamics based on the parametric uncertainty, and we have shown the effect of the treatments on the displacement of the uncertainty band of the cells/cytokines. We performed global sensitivity analysis methods to identify the most influential kinetic parameters and simulate the effect of the perturbation on kinetic parameters on the dynamics of cells/cytokines. CONCLUSION Our findings outline a rational approach to therapy optimization with meaningful consequences for how we effectively design treatment schedules (timing) to maximize their success, and how we treat PDAC with combined 5-FU and anti- CD25 therapies. Our data revealed that a synergistic combinatorial regimen targeting the Tregs and MDSCs in both crisp and fuzzy settings of model parameters can lead to tumor eradication.
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Affiliation(s)
- Sajad Shafiekhani
- Departments of Biomedical Engineering, School of Medicine, Tehran University of Medical Sciences, Tehran, Iran.,Research Center for Biomedical Technologies and Robotics, Tehran, Iran.,Students' Scientific Research Center, Tehran University of Medical Sciences, Tehran, Iran
| | - Hojat Dehghanbanadaki
- Students' Scientific Research Center, Tehran University of Medical Sciences, Tehran, Iran.,Metabolic Disorders Research Center, Endocrinology and Metabolism Molecular-Cellular Sciences Institute, Tehran University of Medical Sciences, Tehran, Iran
| | - Azam Sadat Fatemi
- Departments of Biomedical Engineering, School of Medicine, Tehran University of Medical Sciences, Tehran, Iran.,Research Center for Biomedical Technologies and Robotics, Tehran, Iran
| | - Sara Rahbar
- Departments of Biomedical Engineering, School of Medicine, Tehran University of Medical Sciences, Tehran, Iran.,Research Center for Biomedical Technologies and Robotics, Tehran, Iran
| | - Jamshid Hadjati
- Departments of Medical Immunology, School of Medicine, Tehran University of Medical Sciences, Tehran, Iran
| | - Amir Homayoun Jafari
- Departments of Biomedical Engineering, School of Medicine, Tehran University of Medical Sciences, Tehran, Iran. .,Research Center for Biomedical Technologies and Robotics, Tehran, Iran.
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YILDIZ TUĞBAAKMAN, KÖSE EMEK, ELLIOTT SAMANTHAL. MATHEMATICAL MODELING OF PANCREATIC CANCER TREATMENT WITH CANCER STEM CELLS. J BIOL SYST 2021. [DOI: 10.1142/s0218339021500182] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/24/2022]
Abstract
Of all cancers, pancreatic cancer has a significantly low rate of survival, mostly due to lack of early screening. Thus, once detected, pancreatic cancer is usually in later stages, reducing the likelihood of full recovery. The most common treatment strategy is chemotherapy, although several immunotherapeutic drugs show promising results in extending the patient’s lifespan. In this paper, we provide a validated mathematical model for the pancreatic cancer after fitting the parameter values, such as tumor growth rate, inverse carrying capacity, activation and decay rate of pancreatic stellate cells, with the use of the experimental data presented by Cioffi et al. cioffi2015inhibition For treatments with the chemotherapeutic drugs, Abraxane and Gemcitabine, and the immunotherapeutic drug, Anti-CD47, we modified the model accurately and compared the simulation results with the experimental data not only to model pancreatic cancer treatment correctly but also to move forward with other drug trials. Then, we include the cancer stem cells, which are known to initiate tumors and cause a relapse post-chemotherapy, per cancer stem cell hypothesis so that cancer progression can be assessed based on this phenomenon. In addition, we investigate optimal drug protocols. We find out that the most effective treatment is dual therapy due to extending survival time when compared to other drugs. Moreover, this study reveals that drug dose is more effectual than frequency of drug injection on account of different treatment scheduling with the same dose over a week. The model could be a starting point to investigate pancreatic cancer progression based on cancer stem cell hypothesis and shed light on novel drug discoveries.
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Affiliation(s)
- TUĞBA AKMAN YILDIZ
- Department of Computer Engineering, University of Turkish Aeronautical Association, 06790 Ankara, Turkey
| | - EMEK KÖSE
- Department of Mathematics and Computer Science, St. Mary’s College of Maryland, St. Mary’s City, MD 20619, USA
| | - SAMANTHA L. ELLIOTT
- Department of Biology, St. Mary’s College of Maryland, St. Mary’s City, MD 20619, USA
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Hu X, Ke G, Jang SRJ. Modeling Pancreatic Cancer Dynamics with Immunotherapy. Bull Math Biol 2019; 81:1885-1915. [PMID: 30843136 DOI: 10.1007/s11538-019-00591-3] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/28/2018] [Accepted: 02/22/2019] [Indexed: 12/11/2022]
Abstract
We develop a mathematical model of pancreatic cancer that includes pancreatic cancer cells, pancreatic stellate cells, effector cells and tumor-promoting and tumor-suppressing cytokines to investigate the effects of immunotherapies on patient survival. The model is first validated using the survival data of two clinical trials. Local sensitivity analysis of the parameters indicates there exists a critical activation rate of pro-tumor cytokines beyond which the cancer can be eradicated if four adoptive transfers of immune cells are applied. Optimal control theory is explored as a potential tool for searching the best adoptive cellular immunotherapies. Combined immunotherapies between adoptive ex vivo expanded immune cells and TGF-[Formula: see text] inhibition by siRNA treatments are investigated. This study concludes that mono-immunotherapy is unlikely to control the pancreatic cancer and combined immunotherapies between anti-TGF-[Formula: see text] and adoptive transfers of immune cells can prolong patient survival. We show through numerical explorations that how these two types of immunotherapies are scheduled is important to survival. Applying TGF-[Formula: see text] inhibition first followed by adoptive immune cell transfers can yield better survival outcomes.
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Affiliation(s)
- Xiaochuan Hu
- Department of Mathematics and Statistics, Texas Tech University, Lubbock, TX, 79409-1042, USA.,Department of Mathematics and Statistics, University of the Incarnate Word, San Antonio, TX, 78209, USA
| | - Guoyi Ke
- Department of Mathematics and Statistics, Texas Tech University, Lubbock, TX, 79409-1042, USA.,Department of Mathematics and Physical Sciences, Louisiana State University of Alexandria, Alexandria, LA, 71302, USA
| | - Sophia R-J Jang
- Department of Mathematics and Statistics, Texas Tech University, Lubbock, TX, 79409-1042, USA.
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A structural methodology for modeling immune-tumor interactions including pro- and anti-tumor factors for clinical applications. Math Biosci 2018; 304:48-61. [PMID: 30055212 DOI: 10.1016/j.mbs.2018.07.006] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/26/2018] [Revised: 07/10/2018] [Accepted: 07/17/2018] [Indexed: 12/17/2022]
Abstract
The immune system turns out to have both stimulatory and inhibitory factors influencing on tumor growth. In recent years, the pro-tumor role of immunity factors such as regulatory T cells and TGF-β cytokines has specially been considered in mathematical modeling of tumor-immune interactions. This paper presents a novel structural methodology for reviewing these models and classifies them into five subgroups on the basis of immune factors included. By using our experimental data due to immunotherapy experimentation in mice, these five modeling groups are evaluated and scored. The results show that a model with a small number of variables and coefficients performs efficiently in predicting the tumor-immune system interactions. Though immunology theorems suggest to employ a larger number of variables and coefficients, more complicated models are here shown to be inefficient due to redundant parallel pathways. So, these models are trapped in local minima and restricted in prediction capability. This paper investigates the mathematical models that were previously developed and proposes variables and pathways that are essential for modeling tumor-immune. Using these variables and pathways, a minimal structure for modeling tumor-immune interactions is proposed for future studies.
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ARABAMERI ABAZAR, ASEMANI DAVUD, HAJATI JAMSHID. MATHEMATICAL MODELING OF IN-VIVO TUMOR-IMMUNE INTERACTIONS FOR THE CANCER IMMUNOTHERAPY USING MATURED DENDRITIC CELLS. J BIOL SYST 2018. [DOI: 10.1142/s0218339018500080] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
To develop an anticancer drug, the mathematical models are nowadays indispensable because of complex immunological mechanisms defying with high experimentation costs as well as a large number of parameters. Based on immunological theories and vision of experimentation data, a simple and sufficient compartment model is designed that can accurately interpret and predict the effects of dendritic cell (DC)-based immunotherapy in accordance with experimentation data. The model includes effector cells, regulatory T cells, helper T cells, and DCs. A new key feature is the inclusion of immunotherapy with DCs matured with different materials. All the parameters of the model have been optimally obtained by fitting the experimental data using genetic algorithm. The proposed model has been used to predict a near-optimal pattern that minimizes tumor size after vaccination. This pattern has been validated by carrying out the associated in-vivo experimentation. The model recommends maturation materials and doses that activate a small amount of Treg in the early days and a large Th1/Treg ratio in the next days. The performance of the model compared with the previous study was shown to be superior, both qualitatively and quantitatively.
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Affiliation(s)
- ABAZAR ARABAMERI
- Laboratory of Signals and Electronic Systems, K.N. Toosi University of Technology, Tehran, Iran
| | - DAVUD ASEMANI
- Laboratory of Signals and Electronic Systems, K.N. Toosi University of Technology, Tehran, Iran
- Darby Children Research Institute (DCRI), Sixth Floor, Medical University of South Carolina, Charleston, SC 29407, USA
| | - JAMSHID HAJATI
- Department of Immunology, School of Medicine, Tehran University of Medical Sciences, Tehran, Iran
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