Mathematical Model of BCG Immunotherapy in Superficial Bladder Cancer

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. However, the mode of action has not yet been fully elucidated, despite much extensive biological experience. The purpose of this paper is to develop a first mathematical model that describes tumor-immune interactions in the bladder as a result of BCG therapy. A mathematical analysis of the ODE model identifies multiple equilibrium points, their stability properties, and bifurcation points. Intriguing regimes of bistability are identified in which treatment has potential to result in a tumor-free equilibrium or a full-blown tumor depending only on initial conditions. Attention is given to estimating parameters and validating the model using published data taken from in vitro, mouse and human studies. The model makes clear that intensity of immunotherapy must be kept in limited bounds. While small treatment levels may fail to clear the tumor, a treatment that is too large can lead to an over-stimulated immune system having dangerous side effects for the patient.

Cancer as Multifaceted Disease

“…Bunimovich-Mendrazitsky et al [7] [8] developed an ODE model of BCG therapy. The model predicts that the intensity of immunotherapy must not exceed certain bounds which depend on the initial size of the tumor.…”

Mathematical model of tumor immunotherapy for bladder carcinoma identifies the limitations of the innate immune response

“…We therefore chose a logistic model (i.e., the Verhulst model) to describe the dynamics of the tumor cell population in absence of BCG therapy. 36,37 We estimate the postresection tumor burden to be in the range of 10 5 -10 7 tumor cells for papillary tumors (i.e., microscopic lesions -10 6 cells occupying ~1 mm 3 ) and 10 7 -10 9 tumor cells for CIS lesions (n.b., some treatment practices do not resect CIS due to its sessile nature and lesions may reach a tumor burden of 10 10 cells). As a starting point for our model, we use 10 6 , but have evaluated the effect of starting tumor burden as one of the determinants of tumor elimination (Fig.…”

A mathematical model of tumour growth with Beddington–DeAngelis functional response: a case of cancer without disease

“…Many mathematical models of tumour growth use nonlinear ordinary differential equations (ODEs) [10][11][12][16][17][18][24][25][26]31,35,36]. This work is based on a mathematical model developed by de Pillis et al [18].…”