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Schattler2016 - Dynamical properties of a minimally parameterized mathematical model for metronomic chemotherapy

ABSTRACT: A minimally parameterized mathematical model for low-dose metronomic chemotherapy is formulated that takes into account angiogenic signaling between the tumor and its vasculature and tumor inhibiting effects of tumor-immune system interactions. The dynamical equations combine a model for tumor development under angiogenic signaling formulated by Hahnfeldt et al. with a model for tumor-immune system interactions by Stepanova. The dynamical properties of the model are analyzed. Depending on the parameter values, the system encompasses a variety of medically realistic scenarios that range from cases when (i) low-dose metronomic chemotherapy is able to eradicate the tumor (all trajectories converge to a tumor-free equilibrium point) to situations when (ii) tumor dormancy is induced (a unique, globally asymp- totically stable benign equilibrium point exists) to (iii) multi-stable situations that have both persistent benign and malignant behaviors separated by the stable manifold of an unstable equilibrium point and finally to (iv) situations when tumor growth can- not be overcome by low-dose metronomic chemotherapy. The model forms a basis for a more general study of chemotherapy when the main components of a tumor’s microenvironment are taken into account

SUBMITTER: Mohammad Umer Sharif Shohan

PROVIDER: MODEL2002030001 | BioModels | 2020-02-03

REPOSITORIES: BioModels

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Dynamical properties of a minimally parameterized mathematical model for metronomic chemotherapy.

Schättler Heinz H Ledzewicz Urszula U Amini Behrooz B

Journal of mathematical biology 20150619 5

A minimally parameterized mathematical model for low-dose metronomic chemotherapy is formulated that takes into account angiogenic signaling between the tumor and its vasculature and tumor inhibiting effects of tumor-immune system interactions. The dynamical equations combine a model for tumor development under angiogenic signaling formulated by Hahnfeldt et al. with a model for tumor-immune system interactions by Stepanova. The dynamical properties of the model are analyzed. Depending on the pa ...[more]

PMID: 26089097

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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:Ribba2012 - Low-grade gliomas, tumour growth inhibition model Using longitudinal mean tumour diameter (MTD) data, this model describe the size evolution of low-grade glioma (LGG) in patients treated with chemotherapy or radiotherapy. This model is described in the article: A tumour growth inhibition model for low-grade glioma treated with chemotherapy or radiotherapy Ribba B, Kaloshi G, Peyre M, Ricard D, Calvez V, Tod M, Cajavec-Bernard B, Idbaih A, Psimaras D, Dainese L, Pallud J, Cartalat-Carel S, Delattre JY, Honnorat J, Grenier E, Ducray F. Clin. Cancer Res. 2012 Sep; 18(18): 5071-5080 Abstract: PURPOSE: To develop a tumor growth inhibition model for adult diffuse low-grade gliomas (LGG) able to describe tumor size evolution in patients treated with chemotherapy or radiotherapy. EXPERIMENTAL DESIGN: Using longitudinal mean tumor diameter (MTD) data from 21 patients treated with first-line procarbazine, 1-(2-chloroethyl)-3-cyclohexyl-l-nitrosourea, and vincristine (PCV) chemotherapy, we formulated a model consisting of a system of differential equations, incorporating tumor-specific and treatment-related parameters that reflect the response of proliferative and quiescent tumor tissue to treatment. The model was then applied to the analysis of longitudinal tumor size data in 24 patients treated with first-line temozolomide (TMZ) chemotherapy and in 25 patients treated with first-line radiotherapy. RESULTS: The model successfully described the MTD dynamics of LGG before, during, and after PCV chemotherapy. Using the same model structure, we were also able to successfully describe the MTD dynamics in LGG patients treated with TMZ chemotherapy or radiotherapy. Tumor-specific parameters were found to be consistent across the three treatment modalities. The model is robust to sensitivity analysis, and preliminary results suggest that it can predict treatment response on the basis of pretreatment tumor size data. CONCLUSIONS: Using MTD data, we propose a tumor growth inhibition model able to describe LGG tumor size evolution in patients treated with chemotherapy or radiotherapy. In the future, this model might be used to predict treatment efficacy in LGG patients and could constitute a rational tool to conceive more effective chemotherapy schedules. This model is hosted on BioModels Database and identified by: BIOMD0000000521 . 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.

Dataset Information

Schattler2016 - Dynamical properties of a minimally parameterized mathematical model for metronomic chemotherapy

Publications

Dynamical properties of a minimally parameterized mathematical model for metronomic chemotherapy.

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