PDE Modeling of Bladder Cancer Treatment Using BCG Immunotherapy

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

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

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 languageEnglish
Title of host publicationFunctional Differential Equations and Applications - FDEA-2019
EditorsAlexander Domoshnitsky, Alexander Rasin, Seshadev Padhi
PublisherSpringer
Pages119-129
Number of pages11
ISBN (Print)9789811662966
DOIs
StatePublished - 2021
Externally publishedYes
Event7th International Conference on Functional Differential Equations and Applications, FDEA 2019 - Ariel, Israel
Duration: 22 Aug 201927 Aug 2019

Publication series

NameSpringer Proceedings in Mathematics and Statistics
Volume379
ISSN (Print)2194-1009
ISSN (Electronic)2194-1017

Conference

Conference7th International Conference on Functional Differential Equations and Applications, FDEA 2019
Country/TerritoryIsrael
CityAriel
Period22/08/1927/08/19

Bibliographical note

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

Keywords

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

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