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Khan MS, Samreen M, Khan MA, De la Sen M. A Dynamically Consistent Nonstandard Difference Scheme for a Discrete-Time Immunogenic Tumors Model. ENTROPY (BASEL, SWITZERLAND) 2022; 24:949. [PMID: 35885172 PMCID: PMC9317731 DOI: 10.3390/e24070949] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 05/06/2022] [Revised: 06/27/2022] [Accepted: 06/30/2022] [Indexed: 12/29/2022]
Abstract
This manuscript deals with the qualitative study of certain properties of an immunogenic tumors model. Mainly, we obtain a dynamically consistent discrete-time immunogenic tumors model using a nonstandard difference scheme. The existence of fixed points and their stability are discussed. It is shown that a continuous system experiences Hopf bifurcation at one and only one positive fixed point, whereas its discrete-time counterpart experiences Neimark-Sacker bifurcation at one and only one positive fixed point. It is shown that there is no chance of period-doubling bifurcation in our discrete-time system. Additionally, numerical simulations are carried out in support of our theoretical discussion.
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Affiliation(s)
| | - Maria Samreen
- Department of Mathematics, Quaid-I-Azam University, Islamabad 44230, Pakistan;
| | - Muhammad Asif Khan
- Department of Mathematics, Kahota-Haveli Campus, University of the Poonch Rawalakot, Rawalakot 12350, Pakistan;
| | - Manuel De la Sen
- Department of Electricity and Electronics, Institute of Research and Development of Processes, Faculty of Science and Technology, University of the Basque Country (UPV/EHU), Campus of Leioa, 48940 Leioa, Bizkaia, Spain;
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Sardar M, Khajanchi S, Biswas S, Abdelwahab SF, Nisar KS. Exploring the dynamics of a tumor-immune interplay with time delay. ALEXANDRIA ENGINEERING JOURNAL 2021; 60:4875-4888. [DOI: 10.1016/j.aej.2021.03.041] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 02/05/2023]
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Agur Z, Halevi-Tobias K, Kogan Y, Shlagman O. Employing dynamical computational models for personalizing cancer immunotherapy. Expert Opin Biol Ther 2016; 16:1373-1385. [PMID: 27564141 DOI: 10.1080/14712598.2016.1223622] [Citation(s) in RCA: 20] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/21/2022]
Abstract
INTRODUCTION Recently, cancer immunotherapy has shown considerable success, but due to the complexity of the immune-cancer interactions, clinical outcomes vary largely between patients. A possible approach to overcome this difficulty may be to develop new methodologies for personal predictions of therapy outcomes, by the integration of patient data with dynamical mathematical models of the drug-affected pathophysiological processes. AREAS COVERED This review unfolds the story of mathematical modeling in cancer immunotherapy, and examines the feasibility of using these models for immunotherapy personalization. The reviewed studies suggest that response to immunotherapy can be improved by patient-specific regimens, which can be worked out by personalized mathematical models. The studies further indicate that personalized models can be constructed and validated relatively early in treatment. EXPERT OPINION The suggested methodology has the potential to raise the overall efficacy of the developed immunotherapy. If implemented already during drug development it may increase the prospects of the technology being approved for clinical use. However, schedule personalization, per se, does not comply with the current, 'one size fits all,' paradigm of clinical trials. It is worthwhile considering adjustment of the current paradigm to involve personally tailored immunotherapy regimens.
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Affiliation(s)
- Zvia Agur
- a Institute for Medical BioMathematics (IMBM) , Bene Ataroth , Israel
| | | | - Yuri Kogan
- a Institute for Medical BioMathematics (IMBM) , Bene Ataroth , Israel
| | - Ofer Shlagman
- a Institute for Medical BioMathematics (IMBM) , Bene Ataroth , Israel
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DE PILLIS LG, FISTER KR, GU W, HEAD TIFFANY, MAPLES KENNY, NEAL TODD, MURUGAN ANAND, KOZAI KENJI. OPTIMAL CONTROL OF MIXED IMMUNOTHERAPY AND CHEMOTHERAPY OF TUMORS. J BIOL SYST 2011. [DOI: 10.1142/s0218339008002435] [Citation(s) in RCA: 64] [Impact Index Per Article: 4.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
We investigate a mathematical population model of tumor-immune interactions. The populations involved are tumor cells, specific and non-specific immune cells, and concentrations of therapeutic treatments. We establish the existence of an optimal control for this model and provide necessary conditions for the optimal control triple for simultaneous application of chemotherapy, tumor infiltrating lymphocyte (TIL) therapy, and interleukin-2 (IL-2) treatment. We discuss numerical results for the combination of the chemo-immunotherapy regimens. We find that the qualitative nature of our results indicates that chemotherapy is the dominant intervention with TIL interacting in a complementary fashion with the chemotherapy. However, within the optimal control context, the interleukin-2 treatment does not become activated for the estimated parameter ranges.
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Affiliation(s)
- L. G. DE PILLIS
- Department of Mathematics, Harvey Mudd College, Claremont, CA 91711, USA
| | - K. R. FISTER
- Department of Mathematics, Murray State University, Murray, KY 42071, USA
| | - W. GU
- Department of Mathematics, Harvey Mudd College, Claremont, CA 91711, USA
| | - TIFFANY HEAD
- Department of Mathematics, Harvey Mudd College, Claremont, CA 91711, USA
| | - KENNY MAPLES
- Department of Mathematics, Harvey Mudd College, Claremont, CA 91711, USA
| | - TODD NEAL
- Department of Mathematics, Murray State University, Murray, KY 42071, USA
| | - ANAND MURUGAN
- Department of Mathematics, Pomona College, Claremont, CA 91711, USA
| | - KENJI KOZAI
- Department of Mathematics, Harvey Mudd College, Claremont, CA 91711, USA
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CHAKRABARTY SIDDHARTHAP, BANERJEE SANDIP. A CONTROL THEORY APPROACH TO CANCER REMISSION AIDED BY AN OPTIMAL THERAPY. J BIOL SYST 2011. [DOI: 10.1142/s0218339010003226] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
The mathematical model depicting cancer remission as presented by Banerjee and Sarkar1is reinvestigated here. Mathematical tools from control theory have been used to analyze and determine how an optimal external treatment of Adaptive Cellular Immunotherapy and interleukin-2 can result in more effective remission of malignant tumors while minimizing any adverse affect on the immune response.
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Affiliation(s)
| | - SANDIP BANERJEE
- Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee, Uttarakhand 247667, India
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Abstract
During the past 20 years, there has been considerable interest in lymphocyte therapy as a treatment for renal cell carcinoma. There is no therapeutic role for B-lymphocyte therapy, but their products, monoclonal antibodies, now have widespread clinical applications. The major types of autologous lymphocyte therapy that have been explored in clinical trials are cytotoxic lymphokine-activated killer cells, which are natural killer cells and T-cells that have been stimulated in vitro by interleukin-2 or other similar cytokines; cytotoxic and noncytotoxic tumor infiltrating lymphocytes, which are T-cells derived from tumor tissue; other tumor antigen-stimulated T-lymphocytes derived from regional lymph nodes or peripheral blood; and noncytotoxic lymphocytes of the memory/helper phenotype. More recently, allogeneic immune therapy using nonmyeloablative hematopoietic stem cell transplant and/or donor lymphocyte therapy has also shown promise.
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de Pillis LG, Gu W, Radunskaya AE. Mixed immunotherapy and chemotherapy of tumors: modeling, applications and biological interpretations. J Theor Biol 2006; 238:841-62. [PMID: 16153659 DOI: 10.1016/j.jtbi.2005.06.037] [Citation(s) in RCA: 208] [Impact Index Per Article: 10.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/28/2004] [Revised: 05/31/2005] [Accepted: 06/28/2005] [Indexed: 01/12/2023]
Abstract
We develop and analyze a mathematical model, in the form of a system of ordinary differential equations (ODEs), governing cancer growth on a cell population level with combination immune, vaccine and chemotherapy treatments. We characterize the ODE system dynamics by locating equilibrium points, determining stability properties, performing a bifurcation analysis, and identifying basins of attraction. These system characteristics are useful not only to gain a broad understanding of the specific system dynamics, but also to help guide the development of combination therapies. Numerical simulations of mixed chemo-immuno and vaccine therapy using both mouse and human parameters are presented. We illustrate situations for which neither chemotherapy nor immunotherapy alone are sufficient to control tumor growth, but in combination the therapies are able to eliminate the entire tumor.
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Fulgenzi A, Casati R, Colombo FR, Gasparini M, Ferrero E, Bondanza A, Gerundini P, Ferrero ME. Distribution of 99mTc-labeled lymphocytes in control and inflamed rats. Nucl Med Biol 2004; 31:631-8. [PMID: 15219282 DOI: 10.1016/j.nucmedbio.2004.01.004] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/22/2003] [Revised: 01/14/2004] [Accepted: 01/18/2004] [Indexed: 10/26/2022]
Abstract
We studied the in vivo fate of CD8(+) lymphocytes, of naive (CD8(+)CD45RC(bright)) or memory (CD8(+)CD45RC(dim)) phenotype, injected in syngeneic rats, after their sorting and labeling with [(99m)Tc] HM-PAO. By using the scintigrafic method we showed that memory CD8(+) lymphocytes were able to recirculate into liver and lungs. The same method was also successfully used to in vivo study the homing of total blood lymphocytes obtained from inflamed rats.
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Affiliation(s)
- Alessandro Fulgenzi
- Istituto di Patologia Generale, Universita degli Studi di Milano, Milano, Italy
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Laport GG, Levine BL, Stadtmauer EA, Schuster SJ, Luger SM, Grupp S, Bunin N, Strobl FJ, Cotte J, Zheng Z, Gregson B, Rivers P, Vonderheide RH, Liebowitz DN, Porter DL, June CH. Adoptive transfer of costimulated T cells induces lymphocytosis in patients with relapsed/refractory non-Hodgkin lymphoma following CD34+-selected hematopoietic cell transplantation. Blood 2003; 102:2004-13. [PMID: 12763934 DOI: 10.1182/blood-2003-01-0095] [Citation(s) in RCA: 166] [Impact Index Per Article: 7.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/01/2023] Open
Abstract
We explored the feasibility and toxicity of administering escalating doses of anti-CD3/CD28 ex vivo costimulated T cells as a therapeutic adjunct for patients with relapsed, refractory, or chemotherapy-resistant, aggressive non-Hodgkin lymphoma (NHL) following high-dose chemotherapy and CD34+-selected hematopoietic cell transplantation (HCT). Sixteen patients had infusions on day 14 after HCT of autologous T cells that had been stimulated using beads coated with anti-CD3 and anti-CD28 monoclonal antibodies. At baseline, the subjects had severe quantitative and functional T-cell impairments. The culture procedure partially reversed impaired cytokine responsiveness in T cells in vitro and in vivo. Transient dose-dependent infusion toxicities were observed. There was a rapid reconstitution of lymphocytes; however, there were persistent defects in CD4 T cells. Most interestingly, 5 patients had a delayed lymphocytosis between day 30 and day 120 after HCT. Maximal clinical responses included 5 patients with a complete response (CR), 7 patients with a partial response (PR), and 4 patients with stable disease. At a median follow-up of 33 months (range, 26-60 months), 5 patients are alive with stable or relapsed disease and 3 patients remain in CR. In conclusion, this phase 1 trial demonstrates that adoptive transfer of autologous costimulated T cells (1) is feasible in heavily pretreated patients with advanced NHL, (2) is associated with a rapid recovery of lymphocyte counts, (3) reverses cytokine activation deficits in vitro, and (4) is associated with delayed lymphocytosis in a subset of patients.
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Affiliation(s)
- Ginna G Laport
- Translational Research Program, Abramsonm Family Cancer Research Institute, University of Pennsylvania School of Medicine, 421 Curie Blvd, Philadelphia, PA 19104-6160, USA
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Chang AE, Li Q, Jiang G, Sayre DM, Braun TM, Redman BG. Phase II trial of autologous tumor vaccination, anti-CD3-activated vaccine-primed lymphocytes, and interleukin-2 in stage IV renal cell cancer. J Clin Oncol 2003; 21:884-90. [PMID: 12610189 DOI: 10.1200/jco.2003.08.023] [Citation(s) in RCA: 83] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/29/2023] Open
Abstract
PURPOSE Previous preclinical and clinical studies have demonstrated that autologous tumor vaccines can induce relatively specific tumor-reactive T cells in draining lymph nodes. The adoptive transfer of these cells can result in tumor regression. PATIENTS AND METHODS Patients with stage IV renal cell cancer (RCC) were vaccinated with irradiated autologous tumor cells admixed with Calmette-Guérin bacillus. Approximately 7 days later, vaccine-primed lymph nodes (VPLNs) were harvested and the lymphoid cells secondarily activated with anti-CD3 monoclonal antibody and expanded in interleukin 2 (IL-2). The activated cells were subsequently infused intravenously along with the concomitant administration of bolus IL-2 (360,000 U/kg intravenously x 15 doses). RESULTS Thirty-nine patients were entered onto the study, of whom 34 completed an initial course of cell therapy consisting of a mean (SEM) number of 4.3 (2.2) x 10(10) VPLN cells. Among subjects who received cell therapy, there were nine responses (four complete responses [CRs] and five partial responses [PRs]), for an overall response rate of 27%. The durations of the CRs were > 48, 45, > 35, and 12 months, and the durations of the PRs were > 63, 48, 15, 12, and 4 months. Cultured tumor cells were available to assess in vitro cytokine release of VPLN cells in 24 subjects. The median cytokine release ratio of interferon gamma (IFNgamma) to IL-10 for responders and nonresponders was 992 and 5, respectively, which was significantly different (P =.047). CONCLUSION The treatment protocol resulted in durable tumor responses in patients with advanced RCC. The ratio of IFNgamma and IL-10 cytokines released in response to tumor by the VPLN cells was a significant correlate with tumor response.
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Affiliation(s)
- Alfred E Chang
- Department of Surgery, University of Michigan, Ann Arbor, MI, USA.
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GARLIE NINAK, SIEBENLIST RUTHE, LEFEVER ANNV. T CELLS ACTIVATED IN VITRO AS IMMUNOTHERAPY FOR RENAL CELL CARCINOMA: CHARACTERIZATION OF 2 EFFECTOR T-CELL POPULATIONS. J Urol 2001. [DOI: 10.1016/s0022-5347(05)66149-6] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
Affiliation(s)
- NINA K. GARLIE
- From the Immunotherapy Program, St. Luke’s Medical Center, Milwaukee, Wisconsin
| | - RUTH E. SIEBENLIST
- From the Immunotherapy Program, St. Luke’s Medical Center, Milwaukee, Wisconsin
| | - ANN V. LEFEVER
- From the Immunotherapy Program, St. Luke’s Medical Center, Milwaukee, Wisconsin
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T CELLS ACTIVATED IN VITRO AS IMMUNOTHERAPY FOR RENAL CELL CARCINOMA: CHARACTERIZATION OF 2 EFFECTOR T-CELL POPULATIONS. J Urol 2001. [DOI: 10.1097/00005392-200107000-00087] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/26/2022]
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Abstract
Cellular and cytokine adjuvants, often immune effector cells and soluble factors, respectively, are supplemental and/or follow-up treatments of human origin for cancer patients who have unsatisfactory clinical responses to conventional chemotherapy, radiotherapy, and surgery. Since many human studies with these reagents are in their infancy, extensive data collection is only now being performed to determine which strategy provides the greatest therapeutic benefit. Research published in the literature since the genesis of this approach to cancer treatment is summarized in this report. Methodologies attempting to generate anticancer responses by provoking or enhancing the patient's own immune system are new compared with the other standard types of cancer treatment. Although a few encouraging human studies can be discussed, many of the most promising techniques are only now being transferred from the laboratory to the clinic. The administration of immune effector cells in combination with immunomodulators, such as interferons or interleukins, often enhances clinical outcome. The literature cited in this report indicate that immune-cell- and cytokine-based therapies hold promise in our attempts to improve the quality and duration of life in those with cancer. With each report reaching the literature, more effective clinical trials are being designed and implemented.
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Affiliation(s)
- M L Salgaller
- Pacific Northwest Cancer Foundation and Immunotherapeutics Division, Northwest Biotherapeutics, L.L.C., Seattle, Washington 98125, USA.
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