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Mathematical Models of Cellular Immunotherapies in Cancer

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A special issue of Cancers (ISSN 2072-6694). This special issue belongs to the section "Cancer Therapy".

Deadline for manuscript submissions: closed (31 May 2022) | Viewed by 36508

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Prof. Dr. Víctor M. Pérez-García

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Mathematical Oncology Laboratory, University of Castilla-La Mancha, 13071 Ciudad Real, SpainMathematical Oncology Laboratory, University of Castilla-La Mancha, 13071 Ciudad Real, Spain
Interests: mathematical oncology; imaging biomarkers; mathematical modelling; tumor growth laws; evolutionary dynamics; tumor heterogeneity; CAR-T cell modelling

Prof. Dr. Lisette de Pillis

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Department of Mathematics, Harvey Mudd College, Claremont, CA, USA
Interests: mathematical immunology; mathematical oncology; type I diabetes modeling; mathematical modeling of oncolytic viral therapy

Dr. Philipp Altrock

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Guest Editor

Department of Integrated Mathematical Oncology, H. Lee Moffitt Cancer Center and Research Institute, Tampa, FL 33647, USA
Interests: mathematical oncology; evolutionary dynamics, cellular immunotherapy, single cell RNA sequencing

Dr. Russell Rockne

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City of Hope National Med Center, Duarte, CA, USA
Interests: mathematical oncology; personalized medicine; mathematical modeling; state transition; model discovery; radiation therapy; targeted radionuclides; glioblastoma; acute myeloid leukemia
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Dear Colleagues,

Cellular therapies in cancer constitute an emerging field including many different therapeutic strategies. Many of these strategies typically work by collecting a specific set of cells from patients, modifying them to produce some kind of attack on a patient's cancer cells, and then reinjecting them into the patient. Some examples are tumor-infiltrating lymphocytes, engineered T-cell receptor, chimeric antigen receptor (CAR)-T cells, cytotoxic T lymphocytes, natural killer cells, and mesenchymal stem cells.

In this Special Issue, we plan to address cellular therapies from a mathematical and computational modeling perspective. Mathematical modeling has the potential to help in finding optimal administration protocols, provide a deeper understanding of the mechanisms and dynamics, help in the design of new clinical trials, and more. Despite the immense potential of these treatments, applied mathematicians and computational modelers have started to study these processes only very recently.

With this Special Issue we plan to stimulate further much needed research in the field and provide a way for disseminating state-of-the-art research on mathematical models of cell therapies in cancer.

Prof. Dr. Víctor Pérez-García
Prof. Dr. Lisette de Pillis
Dr. Philipp Altrock
Prof. Dr. Russell Rockne
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Cancers is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2900 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

mathematical oncology
CAR-T cells
mesenchymal stem cells
natural killer cells
cellular therapies
mathematical modelling

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Published Papers (9 papers)

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Research

23 pages, 2347 KiB

Open AccessArticle

A Model-Based Framework to Identify Optimal Administration Protocols for Immunotherapies in Castration-Resistance Prostate Cancer

by Roberta Coletti, Andrea Pugliese, Andrea Lunardi, Orazio Caffo and Luca Marchetti

Cancers 2022, 14(1), 135; https://doi.org/10.3390/cancers14010135 - 28 Dec 2021

Cited by 2 | Viewed by 2206

Abstract

Prostate cancer (PCa) is one of the most frequent cancer in male population. Androgen deprivation therapy is the first-line strategy for the metastatic stage of the disease, but, inevitably, PCa develops resistance to castration (CRPC), becoming incurable. In recent years, clinical trials are testing the efficacy of anti-CTLA4 on CRPC. However, this tumor seems to be resistant to immunotherapies that are very effective in other types of cancers, and, so far, only the dendritic cell vaccine sipuleucel-T has been approved. In this work, we employ a mathematical model of CRPC to determine the optimal administration protocol of ipilimumab, a particular anti-CTLA4, as single treatment or in combination with the sipuleucel-T, by considering both the effect on tumor population and the drug toxicity. To this end, we first introduce a dose-depending function of toxicity, estimated from experimental data, then we define two different optimization problems. We show the results obtained by imposing different constraints, and how these change by varying drug efficacy. Our results suggest administration of high-doses for a brief period, which is predicted to be more efficient than solutions with prolonged low-doses. The model also highlights a synergy between ipilimumab and sipuleucel-T, which leads to a better tumor control with lower doses of ipilimumab. Finally, tumor eradication is also conceivable, but it depends on patient-specific parameters. Full article

(This article belongs to the Special Issue Mathematical Models of Cellular Immunotherapies in Cancer)

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14 pages, 2693 KiB

Open AccessArticle

A Mathematical Modeling Approach for Targeted Radionuclide and Chimeric Antigen Receptor T Cell Combination Therapy

by Vikram Adhikarla, Dennis Awuah, Alexander B. Brummer, Enrico Caserta, Amrita Krishnan, Flavia Pichiorri, Megan Minnix, John E. Shively, Jeffrey Y. C. Wong, Xiuli Wang and Russell C. Rockne

Cancers 2021, 13(20), 5171; https://doi.org/10.3390/cancers13205171 - 15 Oct 2021

Cited by 7 | Viewed by 2861

Abstract

Targeted radionuclide therapy (TRT) has recently seen a surge in popularity with the use of radionuclides conjugated to small molecules and antibodies. Similarly, immunotherapy also has shown promising results, an example being chimeric antigen receptor T cell (CAR-T) therapy in hematologic malignancies. Moreover, TRT and CAR-T therapies possess unique features that require special consideration when determining how to dose as well as the timing and sequence of combination treatments including the distribution of the TRT dose in the body, the decay rate of the radionuclide, and the proliferation and persistence of the CAR-T cells. These characteristics complicate the additive or synergistic effects of combination therapies and warrant a mathematical treatment that includes these dynamics in relation to the proliferation and clearance rates of the target tumor cells. Here, we combine two previously published mathematical models to explore the effects of dose, timing, and sequencing of TRT and CAR-T cell-based therapies in a multiple myeloma setting. We find that, for a fixed TRT and CAR-T cell dose, the tumor proliferation rate is the most important parameter in determining the best timing of TRT and CAR-T therapies. Full article

(This article belongs to the Special Issue Mathematical Models of Cellular Immunotherapies in Cancer)

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20 pages, 747 KiB

Open AccessArticle

Potential of Immunotherapies in Treating Hematological Cancer-Infection Comorbidities—A Mathematical Modelling Approach

by Johnny T. Ottesen and Morten Andersen

Cancers 2021, 13(15), 3789; https://doi.org/10.3390/cancers13153789 - 27 Jul 2021

Cited by 2 | Viewed by 2527

Abstract

Background: The immune system attacks threats like an emerging cancer or infections like COVID-19 but it also plays a role in dealing with autoimmune disease, e.g., inflammatory bowel diseases, and aging. Malignant cells may tend to be eradicated, to appraoch a dormant state or escape the immune system resulting in uncontrolled growth leading to cancer progression. If the immune system is busy fighting a cancer, a severe infection on top of it may compromise the immunoediting and the comorbidity may be too taxing for the immune system to control. Method: A novel mechanism based computational model coupling a cancer-infection development to the adaptive immune system is presented and analyzed. The model maps the outcome to the underlying physiological mechanisms and agree with numerous evidence based medical observations. Results and Conclusions: Progression of a cancer and the effect of treatments depend on the cancer size, the level of infection, and on the efficiency of the adaptive immune system. The model exhibits bi-stability, i.e., virtual patient trajectories gravitate towards one of two stable steady states: a dormant state or a full-blown cancer-infection disease state. An infectious threshold curve exists and if infection exceed this separatrix for sufficiently long time the cancer escapes. Thus, early treatment is vital for remission and severe infections may instigate cancer progression. CAR T-cell Immunotherapy may sufficiently control cancer progression back into a dormant state but the therapy significantly gains efficiency in combination with antibiotics or immunomodulation. Full article

(This article belongs to the Special Issue Mathematical Models of Cellular Immunotherapies in Cancer)

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22 pages, 1745 KiB

Open AccessArticle

CARTmath—A Mathematical Model of CAR-T Immunotherapy in Preclinical Studies of Hematological Cancers

by Luciana R. C. Barros, Emanuelle A. Paixão, Andrea M. P. Valli, Gustavo T. Naozuka, Artur C. Fassoni and Regina C. Almeida

Cancers 2021, 13(12), 2941; https://doi.org/10.3390/cancers13122941 - 11 Jun 2021

Cited by 27 | Viewed by 5793

Abstract

Immunotherapy has gained great momentum with chimeric antigen receptor T cell (CAR-T) therapy, in which patient’s T lymphocytes are genetically manipulated to recognize tumor-specific antigens, increasing tumor elimination efficiency. In recent years, CAR-T cell immunotherapy for hematological malignancies achieved a great response rate in patients and is a very promising therapy for several other malignancies. Each new CAR design requires a preclinical proof-of-concept experiment using immunodeficient mouse models. The absence of a functional immune system in these mice makes them simple and suitable for use as mathematical models. In this work, we develop a three-population mathematical model to describe tumor response to CAR-T cell immunotherapy in immunodeficient mouse models, encompassing interactions between a non-solid tumor and CAR-T cells (effector and long-term memory). We account for several phenomena, such as tumor-induced immunosuppression, memory pool formation, and conversion of memory into effector CAR-T cells in the presence of new tumor cells. Individual donor and tumor specificities are considered uncertainties in the model parameters. Our model is able to reproduce several CAR-T cell immunotherapy scenarios, with different CAR receptors and tumor targets reported in the literature. We found that therapy effectiveness mostly depends on specific parameters such as the differentiation of effector to memory CAR-T cells, CAR-T cytotoxic capacity, tumor growth rate, and tumor-induced immunosuppression. In summary, our model can contribute to reducing and optimizing the number of in vivo experiments with in silico tests to select specific scenarios that could be tested in experimental research. Such an in silico laboratory is an easy-to-run open-source simulator, built on a Shiny R-based platform called CARTmath. It contains the results of this manuscript as examples and documentation. The developed model together with the CARTmath platform have potential use in assessing different CAR-T cell immunotherapy protocols and its associated efficacy, becoming an accessory for in silico trials. Full article

(This article belongs to the Special Issue Mathematical Models of Cellular Immunotherapies in Cancer)

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28 pages, 7217 KiB

Open AccessArticle

Early Survival Prediction Framework in CD19-Specific CAR-T Cell Immunotherapy Using a Quantitative Systems Pharmacology Model

by Anna Mueller-Schoell, Nahum Puebla-Osorio, Robin Michelet, Michael R. Green, Annette Künkele, Wilhelm Huisinga, Paolo Strati, Beth Chasen, Sattva S. Neelapu, Cassian Yee and Charlotte Kloft

Cancers 2021, 13(11), 2782; https://doi.org/10.3390/cancers13112782 - 3 Jun 2021

Cited by 24 | Viewed by 7257

Abstract

Chimeric antigen receptor (CAR)-T cell therapy has revolutionized treatment of relapsed/refractory non-Hodgkin lymphoma (NHL). However, since 36–60% of patients relapse, early response prediction is crucial. We present a novel population quantitative systems pharmacology model, integrating literature knowledge on physiology, immunology, and adoptive cell therapy together with 133 CAR-T cell phenotype, 1943 cytokine, and 48 metabolic tumor measurements. The model well described post-infusion concentrations of four CAR-T cell phenotypes and CD19⁺ metabolic tumor volume over 3 months after CAR-T cell infusion. Leveraging the model, we identified a low expansion subpopulation with significantly lower CAR-T cell expansion capacities amongst 19 NHL patients. Together with two patient-/therapy-related factors (autologous stem cell transplantation, CD4⁺/CD8⁺ T cells), the low expansion subpopulation explained 2/3 of the interindividual variability in the CAR-T cell expansion capacities. Moreover, the low expansion subpopulation had poor prognosis as only 1/4 of the low expansion subpopulation compared to 2/3 of the reference population were still alive after 24 months. We translated the expansion capacities into a clinical composite score (CCS) of ‘Maximum naïve CAR-T cell concentrations/Baseline tumor burden’ ratio and propose a CCS_TN-value > 0.00136 (cells·µL⁻¹·mL⁻¹ as predictor for survival. Once validated in a larger cohort, the model will foster refining survival prediction and solutions to enhance NHL CAR-T cell therapy response. Full article

(This article belongs to the Special Issue Mathematical Models of Cellular Immunotherapies in Cancer)

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19 pages, 3613 KiB

Open AccessArticle

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

by Richard J. Beck, Bettina Weigelin and Joost B. Beltman

Cancers 2021, 13(11), 2567; https://doi.org/10.3390/cancers13112567 - 24 May 2021

Cited by 4 | Viewed by 2695

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. Full article

(This article belongs to the Special Issue Mathematical Models of Cellular Immunotherapies in Cancer)

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22 pages, 1922 KiB

Open AccessArticle

Personalized Immunotherapy Treatment Strategies for a Dynamical System of Chronic Myelogenous Leukemia

by Paul A. Valle, Luis N. Coria and Corina Plata

Cancers 2021, 13(9), 2030; https://doi.org/10.3390/cancers13092030 - 22 Apr 2021

Cited by 9 | Viewed by 2860

Abstract

This paper is devoted to exploring personalized applications of cellular immunotherapy as a control strategy for the treatment of chronic myelogenous leukemia described by a dynamical system of three first-order ordinary differential equations. The latter was achieved by applying both the Localization of Compact Invariant Sets and Lyapunov’s stability theory. Combination of these two approaches allows us to establish sufficient conditions on the immunotherapy treatment parameter to ensure the complete eradication of the leukemia cancer cells. These conditions are given in terms of the system parameters and by performing several in silico experimentations, we formulated a protocol for the therapy application that completely eradicates the leukemia cancer cells population for different initial tumour concentrations. The formulated protocol does not dangerously increase the effector T cells population. Further, complete eradication is considered when solutions go below a finite critical value below which cancer cells cannot longer persist; i.e., one cancer cell. Numerical simulations are consistent with our analytical results. Full article

(This article belongs to the Special Issue Mathematical Models of Cellular Immunotherapies in Cancer)

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20 pages, 1818 KiB

Open AccessArticle

Dual-Target CAR-Ts with On- and Off-Tumour Activity May Override Immune Suppression in Solid Cancers: A Mathematical Proof of Concept

by Odelaisy León-Triana, Antonio Pérez-Martínez, Manuel Ramírez-Orellana and Víctor M. Pérez-García

Cancers 2021, 13(4), 703; https://doi.org/10.3390/cancers13040703 - 9 Feb 2021

Cited by 18 | Viewed by 4015

Abstract

Chimeric antigen receptor (CAR)-T cell-based therapies have achieved substantial success against B-cell malignancies, which has led to a growing scientific and clinical interest in extending their use to solid cancers. However, results for solid tumours have been limited up to now, in part due to the immunosuppressive tumour microenvironment, which is able to inactivate CAR-T cell clones. In this paper we put forward a mathematical model describing the competition of CAR-T and tumour cells, taking into account their immunosuppressive capacity. Using the mathematical model, we show that the use of large numbers of CAR-T cells targetting the solid tumour antigens could overcome the immunosuppressive potential of cancer. To achieve such high levels of CAR-T cells we propose, and study computationally, the manufacture and injection of CAR-T cells targetting two antigens: CD19 and a tumour-associated antigen. We study in silico the resulting dynamics of the disease after the injection of this product and find that the expansion of the CAR-T cell population in the blood and lymphopoietic organs could lead to the massive production of an army of CAR-T cells targetting the solid tumour, and potentially overcoming its immune suppression capabilities. This strategy could benefit from the combination with PD-1 inhibitors and low tumour loads. Our computational results provide theoretical support for the treatment of different types of solid tumours using T cells engineered with combination treatments of dual CARs with on- and off-tumour activity and anti-PD-1 drugs after completion of classical cytoreductive treatments. Full article

(This article belongs to the Special Issue Mathematical Models of Cellular Immunotherapies in Cancer)

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18 pages, 2737 KiB

Open AccessArticle

Dormant Tumor Cell Vaccination: A Mathematical Model of Immunological Dormancy in Triple-Negative Breast Cancer

by Reza Mehdizadeh, Seyed Peyman Shariatpanahi, Bahram Goliaei, Sanam Peyvandi and Curzio Rüegg

Cancers 2021, 13(2), 245; https://doi.org/10.3390/cancers13020245 - 11 Jan 2021

Cited by 12 | Viewed by 4043

Abstract

Triple-negative breast cancer (TNBC) is a molecular subtype of breast malignancy with a poor clinical prognosis. There is growing evidence that some chemotherapeutic agents induce an adaptive anti-tumor immune response. This reaction has been proposed to maintain the equilibrium phase of the immunoediting process and to control tumor growth by immunological cancer dormancy. We recently reported a model of immunological breast cancer dormancy based on the murine 4T1 TNBC model. Treatment of 4T1 cells in vitro with high-dose chemotherapy activated the type I interferon (type I IFN) signaling pathway, causing a switch from immunosuppressive to cytotoxic T lymphocyte-dependent immune response in vivo, resulting in sustained dormancy. Here, we developed a deterministic mathematical model based on the assumption that two cell subpopulations exist within the treated tumor: one population with high type I IFN signaling and immunogenicity and lower growth rate; the other population with low type I IFN signaling and immunogenicity and higher growth rate. The model reproduced cancer dormancy, elimination, and immune-escape in agreement with our previously reported experimental data. It predicted that the injection of dormant tumor cells with active type I IFN signaling results in complete growth control of the aggressive parental cancer cells injected at a later time point, but also of an already established aggressive tumor. Taken together, our results indicate that a dormant cell population can suppress the growth of an aggressive counterpart by eliciting a cytotoxic T lymphocyte-dependent immune response. Full article

(This article belongs to the Special Issue Mathematical Models of Cellular Immunotherapies in Cancer)

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