PDE Modeling of Bladder Cancer Treatment Using BCG Immunotherapy

T. Lazebnik; S. Yanetz; S. Bunimovich-Mendrazitsky

doi:10.1007/978-981-16-6297-3_9

PDE Modeling of Bladder Cancer Treatment Using BCG Immunotherapy

T. Lazebnik
, S. Yanetz
, S. Bunimovich-Mendrazitsky

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

2 Scopus citations

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. Bunimovich-Mendrazitsky et al. [16] studied the role of BCG immunotherapy in bladder cancer dynamics in a system of nonlinear ODEs. The purpose of this paper is to develop a first mathematical model that uses PDEs to describe tumor-immune interactions in the bladder as a result of BCG therapy considering the geometrical configuration of the human bladder. A mathematical analysis of the BCG as a PDE model identifies multiple equilibrium points, and their stability properties are identified so that treatment that has the potential to result in a tumor-free equilibrium can be determined. Estimating parameters and validating the model using published data are taken from in vitro, mouse, and human studies. The model makes clear that the intensity of immunotherapy must be kept within limited bounds. We use numerical analysis methods to find the solution of the PDE describing the tumor-immune interaction; in particular, analysis of the solution’s stability for given parameters is presented using Computer Vision methodologies.

Original language	English
Title of host publication	Functional Differential Equations and Applications - FDEA-2019
Editors	Alexander Domoshnitsky, Alexander Rasin, Seshadev Padhi
Publisher	Springer
Pages	119-129
Number of pages	11
ISBN (Print)	9789811662966
DOIs	https://doi.org/10.1007/978-981-16-6297-3_9
State	Published - 2021
Event	7th International Conference on Functional Differential Equations and Applications, FDEA 2019 - Ariel, Israel Duration: 22 Aug 2019 → 27 Aug 2019

Publication series

Name	Springer Proceedings in Mathematics and Statistics
Volume	379
ISSN (Print)	2194-1009
ISSN (Electronic)	2194-1017

Conference

Conference	7th International Conference on Functional Differential Equations and Applications, FDEA 2019
Country/Territory	Israel
City	Ariel
Period	22/08/19 → 27/08/19

Bibliographical note

Publisher Copyright:
© 2021, The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.

UN SDGs

This output contributes to the following UN Sustainable Development Goals (SDGs)

SDG 3 Good Health and Well-being

Keywords

34A34
35A25
35A30
65M60
68W25
Numerical analysis
PDE’s parameters’ sensitivity analysis
PDE’s solution stability

Access to Document

10.1007/978-981-16-6297-3_9

Cite this

Lazebnik, T., Yanetz, S., & Bunimovich-Mendrazitsky, S. (2021). PDE Modeling of Bladder Cancer Treatment Using BCG Immunotherapy. In A. Domoshnitsky, A. Rasin, & S. Padhi (Eds.), Functional Differential Equations and Applications - FDEA-2019 (pp. 119-129). (Springer Proceedings in Mathematics and Statistics; Vol. 379). Springer. https://doi.org/10.1007/978-981-16-6297-3_9

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title = "PDE Modeling of Bladder Cancer Treatment Using BCG Immunotherapy",

abstract = "Immunotherapy with Bacillus Calmette-Gu{\'e}rin (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. Bunimovich-Mendrazitsky et al. [16] studied the role of BCG immunotherapy in bladder cancer dynamics in a system of nonlinear ODEs. The purpose of this paper is to develop a first mathematical model that uses PDEs to describe tumor-immune interactions in the bladder as a result of BCG therapy considering the geometrical configuration of the human bladder. A mathematical analysis of the BCG as a PDE model identifies multiple equilibrium points, and their stability properties are identified so that treatment that has the potential to result in a tumor-free equilibrium can be determined. Estimating parameters and validating the model using published data are taken from in vitro, mouse, and human studies. The model makes clear that the intensity of immunotherapy must be kept within limited bounds. We use numerical analysis methods to find the solution of the PDE describing the tumor-immune interaction; in particular, analysis of the solution{\textquoteright}s stability for given parameters is presented using Computer Vision methodologies.",

keywords = "34A34, 35A25, 35A30, 65M60, 68W25, Numerical analysis, PDE{\textquoteright}s parameters{\textquoteright} sensitivity analysis, PDE{\textquoteright}s solution stability",

author = "T. Lazebnik and S. Yanetz and S. Bunimovich-Mendrazitsky",

note = "Publisher Copyright: {\textcopyright} 2021, The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.; 7th International Conference on Functional Differential Equations and Applications, FDEA 2019 ; Conference date: 22-08-2019 Through 27-08-2019",

year = "2021",

doi = "10.1007/978-981-16-6297-3\_9",

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Lazebnik, T, Yanetz, S & Bunimovich-Mendrazitsky, S 2021, PDE Modeling of Bladder Cancer Treatment Using BCG Immunotherapy. in A Domoshnitsky, A Rasin & S Padhi (eds), Functional Differential Equations and Applications - FDEA-2019. Springer Proceedings in Mathematics and Statistics, vol. 379, Springer, pp. 119-129, 7th International Conference on Functional Differential Equations and Applications, FDEA 2019, Ariel, Israel, 22/08/19. https://doi.org/10.1007/978-981-16-6297-3_9

PDE Modeling of Bladder Cancer Treatment Using BCG Immunotherapy. / Lazebnik, T.; Yanetz, S.; Bunimovich-Mendrazitsky, S.
Functional Differential Equations and Applications - FDEA-2019. ed. / Alexander Domoshnitsky; Alexander Rasin; Seshadev Padhi. Springer, 2021. p. 119-129 (Springer Proceedings in Mathematics and Statistics; Vol. 379).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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AB - 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. Bunimovich-Mendrazitsky et al. [16] studied the role of BCG immunotherapy in bladder cancer dynamics in a system of nonlinear ODEs. The purpose of this paper is to develop a first mathematical model that uses PDEs to describe tumor-immune interactions in the bladder as a result of BCG therapy considering the geometrical configuration of the human bladder. A mathematical analysis of the BCG as a PDE model identifies multiple equilibrium points, and their stability properties are identified so that treatment that has the potential to result in a tumor-free equilibrium can be determined. Estimating parameters and validating the model using published data are taken from in vitro, mouse, and human studies. The model makes clear that the intensity of immunotherapy must be kept within limited bounds. We use numerical analysis methods to find the solution of the PDE describing the tumor-immune interaction; in particular, analysis of the solution’s stability for given parameters is presented using Computer Vision methodologies.

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ER -

PDE Modeling of Bladder Cancer Treatment Using BCG Immunotherapy

Abstract

Publication series

Conference

Bibliographical note

UN SDGs

Keywords

Access to Document

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