TY - GEN
T1 - PDE Modeling of Bladder Cancer Treatment Using BCG Immunotherapy
AU - Lazebnik, T.
AU - Yanetz, S.
AU - Bunimovich-Mendrazitsky, S.
N1 - Publisher Copyright:
© 2021, The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.
PY - 2021
Y1 - 2021
N2 - 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.
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.
KW - 34A34
KW - 35A25
KW - 35A30
KW - 65M60
KW - 68W25
KW - Numerical analysis
KW - PDE’s parameters’ sensitivity analysis
KW - PDE’s solution stability
UR - http://www.scopus.com/inward/record.url?scp=85125234510&partnerID=8YFLogxK
U2 - 10.1007/978-981-16-6297-3_9
DO - 10.1007/978-981-16-6297-3_9
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AN - SCOPUS:85125234510
SN - 9789811662966
T3 - Springer Proceedings in Mathematics and Statistics
SP - 119
EP - 129
BT - Functional Differential Equations and Applications - FDEA-2019
A2 - Domoshnitsky, Alexander
A2 - Rasin, Alexander
A2 - Padhi, Seshadev
T2 - 7th International Conference on Functional Differential Equations and Applications, FDEA 2019
Y2 - 22 August 2019 through 27 August 2019
ER -