Functional Differential Equations conference · 2020

PDE Modeling of Bladder Cancer Treatment Using BCG Immunotherapy

Teddy Lazebnik, Shlomo Yanetz, Svetlana Bunimovich-Mendrazitsky

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ACML authorsTeddy LazebnikPI
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  1. Abstract

Abstract

Immunotherapy with Bacillus Calmette-Guérin (BCG) – an attenuated strain of Mycobacterium bovis (M. bovis) used for antituberculosis immunization – is a clinically established procedure for the treatment of superficial bladder cancer. Bunimovich-Mendrazitsky et al. 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 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 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 a given parameters is presented using Computer Vision methodologies.

This is the conference version of Treatment of Bladder Cancer Using BCG Immunotherapy: PDE Modeling, which has the full text.
Research projectBiomathematical Modeling of Cancer and BeyondDeveloping bio-mathematical models for cancer spread and treatment, and for additional diseases, using ODEs, PDEs, and simulations.Paper · 2020PDE based geometry model for BCG immunotherapy of bladder cancerbiosystemsPaper · 2021Improved Geometric Configuration for the Bladder Cancer BCG-Based Immunotherapy Treatment ModelInternational Symposium on Mathematical and Computational Oncology

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APA

Lazebnik, T., Yanetz, S., & Bunimovich-Mendrazitsky, S. (2020). PDE Modeling of Bladder Cancer Treatment Using BCG Immunotherapy. Functional Differential Equations conference.

BibTeX

@article{lazebnik2020pde,
  title = {PDE Modeling of Bladder Cancer Treatment Using BCG Immunotherapy},
  author = {Lazebnik, Teddy and Yanetz, Shlomo and Bunimovich-Mendrazitsky, Svetlana},
  journal = {Functional Differential Equations conference},
  year = {2020}
}