Stability Analysis of Delayed Immune Response BCG Infection in Bladder Cancer Treatment Model by Stochastic Perturbations

Mathematical Modeling of Tumor Immune Interactions: The Role of Anti-FGFR and Anti-PD-1 in the Combination Therapy

Bladder cancer poses a significant global health burden with high incidence and recurrence rates. This study addresses the therapeutic challenges in advanced bladder cancer, focusing on the competitive mechanisms of ligand or drug binding to receptors. We developed a refined mathematical model that integrates the dynamics of tumor cells and immune responses, particularly targeting fibroblast growth factor receptor 3 (FGFR3) and immune checkpoint inhibitors (ICIs). This study contributes to understanding combination therapies by elucidating the competitive binding dynamics and quantifying the synergistic effects. The findings highlight the importance of personalized immunotherapeutic strategies, considering factors such as drug dosage, dosing schedules, and patient-specific parameters. Our model further reveals that ligand-independent activated-state receptors are the most essential drivers of tumor proliferation. Moreover, we found that PD-L1 expression rate was more important than PD-1 in driving the dynamic evolution of tumor and immune cells. The proposed mathematical model provides a comprehensive framework for unraveling the complexities of combination therapies in advanced bladder cancer. As research progresses, this multidisciplinary approach contributes valuable insights toward optimizing therapeutic strategies and advancing cancer treatment paradigms.

Mathematical model of MMC chemotherapy for non-invasive bladder cancer treatment

Mitomycin-C (MMC) chemotherapy is a well-established anti-cancer treatment for non-muscle-invasive bladder cancer (NMIBC). However, despite comprehensive biological research, the complete mechanism of action and an ideal regimen of MMC have not been elucidated. In this study, we present a theoretical investigation of NMIBC growth and its treatment by continuous administration of MMC chemotherapy. Using temporal ordinary differential equations (ODEs) to describe cell populations and drug molecules, we formulated the first mathematical model of tumor-immune interactions in the treatment of MMC for NMIBC, based on biological sources. Several hypothetical scenarios for NMIBC under the assumption that tumor size correlates with cell count are presented, depicting the evolution of tumors classified as small, medium, and large. These scenarios align qualitatively with clinical observations of lower recurrence rates for tumor size ≤ 30[mm] with MMC treatment, demonstrating that cure appears up to a theoretical x[mm] tumor size threshold, given specific parameters within a feasible biological range. The unique use of mole units allows to introduce a new method for theoretical pre-treatment assessments by determining MMC drug doses required for a cure. In this way, our approach provides initial steps toward personalized MMC chemotherapy for NMIBC patients, offering the possibility of new insights and potentially holding the key to unlocking some of its mysteries.

Investigation toward the economic feasibility of personalized medicine for healthcare service providers: the case of bladder cancer

In today's complex healthcare landscape, the pursuit of delivering optimal patient care while navigating intricate economic dynamics poses a significant challenge for healthcare service providers (HSPs). In this already complex dynamic, the emergence of clinically promising personalized medicine-based treatment aims to revolutionize medicine. While personalized medicine holds tremendous potential for enhancing therapeutic outcomes, its integration within resource-constrained HSPs presents formidable challenges. In this study, we investigate the economic feasibility of implementing personalized medicine. The central objective is to strike a balance between catering to individual patient needs and making economically viable decisions. Unlike conventional binary approaches to personalized treatment, we propose a more nuanced perspective by treating personalization as a spectrum. This approach allows for greater flexibility in decision-making and resource allocation. To this end, we propose a mathematical framework to investigate our proposal, focusing on Bladder Cancer (BC) as a case study. Our results show that while it is feasible to introduce personalized medicine, a highly efficient but highly expensive one would be short-lived relative to its less effective but cheaper alternative as the latter can be provided to a larger cohort of patients, optimizing the HSP's objective better.

Mathematical modeling of BCG-based bladder cancer treatment using socio-demographics

Cancer is one of the most widespread diseases around the world with millions of new patients each year. Bladder cancer is one of the most prevalent types of cancer affecting all individuals alike with no obvious "prototypical patient". The current standard treatment for BC follows a routine weekly Bacillus Calmette-Guérin (BCG) immunotherapy-based therapy protocol which is applied to all patients alike. The clinical outcomes associated with BCG treatment vary significantly among patients due to the biological and clinical complexity of the interaction between the immune system, treatments, and cancer cells. In this study, we take advantage of the patient's socio-demographics to offer a personalized mathematical model that describes the clinical dynamics associated with BCG-based treatment. To this end, we adopt a well-established BCG treatment model and integrate a machine learning component to temporally adjust and reconfigure key parameters within the model thus promoting its personalization. Using real clinical data, we show that our personalized model favorably compares with the original one in predicting the number of cancer cells at the end of the treatment, with [Formula: see text] improvement, on average.

Cell-Level Spatio-Temporal Model for a Bacillus Calmette–Guérin-Based Immunotherapy Treatment Protocol of Superficial Bladder Cancer

Bladder cancer is one of the most widespread types of cancer. Multiple treatments for non-invasive, superficial bladder cancer have been proposed over the last several decades with a weekly Bacillus Calmette–Guérin immunotherapy-based therapy protocol, which is considered the gold standard today. Nonetheless, due to the complexity of the interactions between the immune system, healthy cells, and cancer cells in the bladder’s microenvironment, clinical outcomes vary significantly among patients. Mathematical models are shown to be effective in predicting the treatment outcome based on the patient’s clinical condition at the beginning of the treatment. Even so, these models still have large errors for long-term treatments and patients that they do not fit. In this work, we utilize modern mathematical tools and propose a novel cell-level spatio-temporal mathematical model that takes into consideration the cell–cell and cell–environment interactions occurring in a realistic bladder’s geometric configuration in order to reduce these errors. We implement the model using the agent-based simulation approach, showing the impacts of different cancer tumor sizes and locations at the beginning of the treatment on the clinical outcomes for today’s gold-standard treatment protocol. In addition, we propose a genetic-algorithm-based approach to finding a successful and time-optimal treatment protocol for a given patient’s initial condition. Our results show that the current standard treatment protocol can be modified to produce cancer-free equilibrium for deeper cancer cells in the urothelium if the cancer cells’ spatial distribution is known, resulting in a greater success rate.

STABILITY ANALYSIS OF A MATHEMATICAL MODEL FOR CHRONIC MYELOID LEUKEMIA ERADICATION

We analyze a mathematical model for the treatment of chronic myeloid leukemia (CML). The model is designed for complete recovery of CML patients after treatment. The model developed in the paper [Bunimovich-Mendrazitsky S, Kronik N, Vainstein V, Optimization of interferon-alpha and imatinib combination therapy for CML: A modeling approach, Adv Theory Simul 2(1):1800081, 2018] introduced a combined treatment of CML based on imatinib therapy and immunotherapy. Immunotherapy based on Interferon alpha-2a (IFN-[Formula: see text]) affects stem and mature cancer cell mortality, and leads to outcome improvements in the combined therapy. The qualitative character of our results shows that additional therapy for the complete cure of CML patients is required. This additional treatment is tumor infiltrating lymphocytes (TIL) along with a combination imatinib and IFN-[Formula: see text] treatment. The model examines the interaction between CML cancer cells and effector cells, using an ODE system. Stability analysis of the model defines conditions when imatinib treatment might lead to the eradication of CML with IFN-[Formula: see text] and TIL. Three equilibria are investigated for the proposed model. Stability conditions for equilibria are formulated in terms of the linear matrix inequalities (LMIs).

PDE based geometry model for BCG immunotherapy of bladder cancer

BCG immunotherapy has shown significant success for bladder cancer treatment, but due to the complexity of the interaction between immunity and cancer, clinical outcomes vary significantly between patients. A possible approach to overcome this difficulty may be to develop new methodologies for personally predicting the results of therapy by integrating patient data with dynamic mathematical model. We present a model describing a BCG immunotherapy dynamic taking into consideration an approximation of the bladder's geometry using PDE. We show that the proposed model takes into account the initial distribution of the cancer cells in the geometry of the bladder and as such can provide more customized treatment by providing tumor polyp depth in the urothelium. In addition, time optimal treatment protocol for the average case and recover-rate optimal, personalized treatment protocol based on initial tumor distribution have been analyzed.

Stability Analysis of Delayed Tumor-Antigen-ActivatedImmune Response in Combined BCG and IL-2Immunotherapy of Bladder Cancer

We use a system biology approach to translate the interaction of Bacillus Calmette-Gurin (BCG) + interleukin 2 (IL-2) for the treatment of bladder cancer into a mathematical model. The main goal of this research is to predict the outcome of BCG + IL-2 treatment combinations. We examined whether the delay effect caused by the proliferation of tumor antigen-specific effector cells after the immune system destroys BCG-infected urothelium cells after BCG and IL-2 immunotherapy influences success in bladder cancer treatment. To do this, we introduce a system of differential equations where the variables are the main participants in the immune response after BCG installations to fight cancer: the number of tumor cells, BCG cells, immune cells, and cytokines involved in the tumor-immune response. The relevant parameters describing the dynamics of the system are taken from a variety of biological, clinical literature and estimated using the mathematical models. We examine the local stability analysis of non-negative equilibrium states of the model. In theory, treatment could improve system stability, and we analyze the stability of all equilibria using the method of Lyapunov functionals construction and the method of linear matrix inequalities (LMIs). Our results prove that the period for the proliferation of tumor antigen-specific effector cells does not influence to the success of the non-responsive patients after an intensified combined BCG + IL-2 treatment.