Name: Bunimovich-Mendrazitsky2007 - Mathematical model of BCG immunotherapy
Keywords: Immuno-oncology

Dataset Information

Bunimovich-Mendrazitsky2007 - Mathematical model of BCG immunotherapy

ABSTRACT: This ordinary differential equation model, simulating the tumor-immune interactions involved in BCG immunotherapy to treat superficial bladder cancer, is described by the publication: Bunimovich-Mendrazitsky, S., Shochat, E., Stone, L. "Mathematical Model of BCG Immunotherapy in Superficial Bladder Cancer". Bull. Math. Biol. 69, 1847–1870 (2007). DOI: 10.1007/s11538-007-9195-z Comment: This model is based on the system of ODEs given in Equation 4 of the publication manuscript. Reproduction of Figure 4 was achieved by setting p4 = 0.085. Abstract: Immunotherapy with Bacillus Calmette-Guérin (BCG)-an attenuated strain of Mycobacterium bovis (M. bovis) used for anti tuberculosis immunization-is a clinically established procedure for the treatment of superficial bladder cancer. However, the mode of action has not yet been fully elucidated, despite much extensive biological experience. The purpose of this paper is to develop a first mathematical model that describes tumor-immune interactions in the bladder as a result of BCG therapy. A mathematical analysis of the ODE model identifies multiple equilibrium points, their stability properties, and bifurcation points. Intriguing regimes of bistability are identified in which treatment has potential to result in a tumor-free equilibrium or a full-blown tumor depending only on initial conditions. Attention is given to estimating parameters and validating the model using published data taken from in vitro, mouse and human studies. The model makes clear that intensity of immunotherapy must be kept in limited bounds. While small treatment levels may fail to clear the tumor, a treatment that is too large can lead to an over-stimulated immune system having dangerous side effects for the patient.

DISEASE(S): Urinary Bladder Cancer

SUBMITTER: Emilia Chen

PROVIDER: BIOMD0000001034 | BioModels | 2021-08-19

REPOSITORIES: BioModels

ACCESS DATA

Publications

Mathematical model of BCG immunotherapy in superficial bladder cancer.

Bunimovich-Mendrazitsky Svetlana S Shochat Eliezer E Stone Lewi L

Bulletin of mathematical biology 20070425 6

Immunotherapy with Bacillus Calmette-Guérin (BCG)-an attenuated strain of Mycobacterium bovis (M. bovis) used for anti tuberculosis immunization-is a clinically established procedure for the treatment of superficial bladder cancer. However, the mode of action has not yet been fully elucidated, despite much extensive biological experience. The purpose of this paper is to develop a first mathematical model that describes tumor-immune interactions in the bladder as a result of BCG therapy. A mathem ...[more]

PMID: 17457655

Similar Datasets

Project description:This ordinary differential equation model simulating the interactions between tumor and immune cells is detailed in the publication: Ahmed M. Makhlouf, Lamiaa El-Shennawy, Hesham A. Elkaranshawy, "Mathematical Modelling for the Role of CD4+T Cells in Tumor-Immune Interactions", Comput Math Methods Med. 2020 Feb 19;2020:7187602. doi: 10.1155/2020/7187602 Comment: This no treatment model is described by equations 1-7 of the publication manuscript. Abstract: Mathematical modelling has been used to study tumor-immune cell interaction. Some models were proposed to examine the effect of circulating lymphocytes, natural killer cells, and CD8+T cells, but they neglected the role of CD4+T cells. Other models were constructed to study the role of CD4+T cells but did not consider the role of other immune cells. In this study, we propose a mathematical model, in the form of a system of nonlinear ordinary differential equations, that predicts the interaction between tumor cells and natural killer cells, CD4+T cells, CD8+T cells, and circulating lymphocytes with or without immunotherapy and/or chemotherapy. This system is stiff, and the Runge–Kutta method failed to solve it. Consequently, the “Adams predictor-corrector” method is used. The results reveal that the patient’s immune system can overcome small tumors; however, if the tumor is large, adoptive therapy with CD4+T cells can be an alternative to both CD8+T cell therapy and cytokines in some cases. Moreover, CD4+T cell therapy could replace chemotherapy depending upon tumor size. Even if a combination of chemotherapy and immunotherapy is necessary, using CD4+T cell therapy can better reduce the dose of the associated chemotherapy compared to using combined CD8+T cells and cytokine therapy. Stability analysis is performed for the studied patients. It has been found that all equilibrium points are unstable, and a condition for preventing tumor recurrence after treatment has been deduced. Finally, a bifurcation analysis is performed to study the effect of varying system parameters on the stability, and bifurcation points are specified. New equilibrium points are created or demolished at some bifurcation points, and stability is changed at some others. Hence, for systems turning to be stable, tumors can be eradicated without the possibility of recurrence. The proposed mathematical model provides a valuable tool for designing patients’ treatment intervention strategies.

Project description:The paper describes a simple model of tumor immunotherapy. Created by COPASI 4.25 (Build 207) This model is described in the article: Predicting success or failure of immunotherapy for cancer: insights from a clinically applicable mathematical model Charles F Babbs Am J Cancer Res 2012;2(2):204-213 Abstract: The objective of this study was to create a clinically applicable mathematical model of immunotherapy for cancer and use it to explore differences between successful and unsuccessful treatment scenarios. The simplified predator-prey model includes four lumped parameters: tumor growth rate, g; immune cell killing efficiency, k; immune cell signaling factor, λ; and immune cell half-life decay, μ. The predator-prey equations as functions of time, t, for nor- malized tumor cell numbers, y, (the prey) and immunocyte numbers, x, (the predators) are: dy/dt = gy – kx and dx/dt = λxy – μx. A parameter estimation procedure that capitalizes on available clinical data and the timing of clinically observable phenomena gives mid-range benchmarks for parameters representing the unstable equilibrium case in which the tumor neither grows nor shrinks. Departure from this equilibrium results in oscillations in tumor cell num- bers and in many cases complete elimination of the tumor. Several paradoxical phenomena are predicted, including increasing tumor cell numbers prior to a population crash, apparent cure with late recurrence, one or more cycles of tumor growth prior to eventual tumor elimination, and improved tumor killing with initially weaker immune parame- ters or smaller initial populations of immune cells. The model and the parameter estimation techniques are easily adapted to various human cancers that evoke an immune response. They may help clinicians understand and predict certain strange and unexpected effects in the world of tumor immunity and lead to the design of clinical trials to test improved treatment protocols for patients. To cite BioModels Database, please use: BioModels Database: An enhanced, curated and annotated resource for published quantitative kinetic models . To the extent possible under law, all copyright and related or neighbouring rights to this encoded model have been dedicated to the public domain worldwide. Please refer to CC0 Public Domain Dedication for more information.

Project description:This ordinary differential equation model simulating the mechanisms that govern cancer-immune dynamics and their role in tumor responses to immunotherapy is described by the publication: Creemers JHA, Lesterhuis WJ, Mehra N, et al. "A tipping point in cancer-immune dynamics leads to divergent immunotherapy responses and hampers biomarker discovery." Journal for ImmunoTherapy of Cancer 2021;9:e002032. doi:10.1136/jitc-2020-002032 Comment: Simulation parameters in supplementary table 1 mismatch with figure 1 in manuscript. Therefore, to clarify, the following parameter values were used: Reproduction of Fig. 1(C), xi = 0.0005 Reproduction of Fig. 1(D), xi = 0.00025 Abstract: Background: Predicting treatment response or survival of cancer patients remains challenging in immuno-oncology. Efforts to overcome these challenges focus, among others, on the discovery of new biomarkers. Despite advances in cellular and molecular approaches, only a limited number of candidate biomarkers eventually enter clinical practice. Methods: A computational modeling approach based on ordinary differential equations was used to simulate the fundamental mechanisms that dictate tumor-immune dynamics and to investigate its implications on responses to immune checkpoint inhibition (ICI) and patient survival. Using in silico biomarker discovery trials, we revealed fundamental principles that explain the diverging success rates of biomarker discovery programs. Results: Our model shows that a tipping point—a sharp state transition between immune control and immune evasion—induces a strongly non-linear relationship between patient survival and both immunological and tumor-related parameters. In patients close to the tipping point, ICI therapy may lead to long-lasting survival benefits, whereas patients far from the tipping point may fail to benefit from these potent treatments. Conclusion: These findings have two important implications for clinical oncology. First, the apparent conundrum that ICI induces substantial benefits in some patients yet completely fails in others could be, to a large extent, explained by the presence of a tipping point. Second, predictive biomarkers for immunotherapy should ideally combine both immunological and tumor-related markers, as a patient’s distance from the tipping point can typically not be reliably determined from solely one of these. The notion of a tipping point in cancer-immune dynamics helps to devise more accurate strategies to select appropriate treatments for patients with cancer.

Project description:This ordinary differential equation model is the Panetta-Kirschner model of tumor-immune interactions is described in the publication: Cappuccio A, Castiglione F, Piccoli B." Determination of the optimal therapeutic protocols in cancer immunotherapy." Math Biosci. 2007 Sep;209(1):1-13. doi: 10.1016/j.mbs.2007.02.009. Comment: The model represented in Equations 1-3 is the Panetta-Kirschner model and was used to reproduce Fig. 1. N.B.: Labelling of Fig. 1 graphs in manuscript mismatches with simulation results - CTL and tumor cell plots swapped. Abstract: Cancer immunotherapy aims at eliciting an immune system response against the tumor. However, it is often characterized by toxic side-effects. Limiting the tumor growth and, concurrently, avoiding the toxicity of a drug, is the problem of protocol design. We formulate this question as an optimization problem and derive an algorithm for its solution. Unlike the standard optimal control approach, the algorithm simulates impulse-like drug administrations. It relies on an exact computation of the gradient of the cost function with respect to any protocol by means of the variational equations, that can be solved in parallel with the system. In comparison with previous versions of this method [F. Castiglione, B. Piccoli, Optimal control in a model of dendritic cell transfection cancer immunotherapy, Bull. Math. Biol. 68 (2006) 255-274; B. Piccoli, F. Castiglione, Optimal vaccine scheduling in cancer immunotherapy, Physica A. 370 (2) (2007) 672-680], we optimize both the timing and the dosage of each administration and introduce a penalty term to avoid clustering of subsequent injections, a requirement consistent with the clinical practice. In addition, we implement the optimization scheme to simulate the case of multi-therapies. The procedure works for any ODE system describing the pharmacokinetics and pharmacodynamics of an arbitrary number of therapeutic agents. In this work, it was tested for a well known model of the tumor-immune system interaction [D. Kirschner, J.C. Panetta, Modeling immunotherapy of tumor-immune interaction, J. Math. Biol. 37 (1998) 235-252]. Exploring three immunotherapeutic scenarios (CTL therapy, IL-2 therapy and combined therapy), we display the stability and efficacy of the optimization method, obtaining protocols that are successful compromises between various clinical requirements.

Dataset Information

Bunimovich-Mendrazitsky2007 - Mathematical model of BCG immunotherapy

Publications

Mathematical model of BCG immunotherapy in superficial bladder cancer.

Similar Datasets

OmicsDI is part of the ELIXIR infrastructure