Svetlana Bunimovich-Mendrazitsky

Mathematical Model of Pulsed Immunotherapy for Superficial Bladder Cancer

We present a theoretical study of superficial bladder cancer growth and its treatment via pulsed immunotherapy with Bacillus Calmette–Guérin (BCG), an attenuated strain of Mycobacterium bovis. BCG pulsed immunotherapy is a clinically established procedure for the treatment of superficial bladder cancer. In this paper, periodic BCG instillations are modeled using impulsive differential equations, which are studied using a combination of analytical and numerical techniques. In this way, we determine critical threshold values of the BCG instillation dose and rate of pulsing for successful treatment. We also identify treatment regimes in which tumor destruction occurs, but undesirable side effects are maintained at low levels by the immune system.

Treatment of non-muscle invasive bladder cancer with Bacillus Calmette-Guerin (BCG): Biological markers and simulation studies

Intravesical Bacillus Calmette–Guerin (BCG) vaccine is the preferred first line treatment for non-muscle invasive bladder carcinoma (NMIBC) in order to prevent recurrence and progression of cancer. There is ongoing need for the rational selection of i) BCG dose, ii) frequency of BCG administration along with iii) synergistic adjuvant therapy and iv) a reliable set of biochemical markers relevant to tumor response. In this review we evaluate cellular and molecular markers pertinent to the immunological response triggered by the BCG instillation and respective mathematical models of the treatment. Specific examples of markers include diverse immune cells, genetic polymorphisms, miRNAs, epigenetics, immunohistochemistry and molecular biology ‘beacons’ as exemplified by cell surface proteins, cytokines, signaling proteins and enzymes. We identified tumor associated macrophages (TAMs), human leukocyte antigen (HLA) class I, a combination of Ki-67/CK20, IL-2, IL-8 and IL-6/IL-10 ratio as the most promising markers for both pre-BCG and post-BCG treatment suitable for the simulation studies. The intricate and patient-specific nature of these data warrants the use of powerful multi-parametral mathematical methods in combination with molecular/cellular biology insight and clinical input.

Reconstruction of the natural history of metastatic cancer and assessment of the effects of surgery: Gompertzian growth of the primary tumor

This work deals with retrospective reconstruction of the individual natural history of solid cancer and assessment of the effects of treatment on metastatic progression. This is achieved through a mathematical model of cancer progression accounting for the growth of the primary tumor, shedding of metastases, their dormancy and growth at secondary sites. To describe dynamics of the primary tumor, we used the Gompertz law, a parsimonious model of tumor growth accounting for its saturation. Parameters of the model were estimated from the age and volume of the primary tumor at surgery and volumes of detectable bone metastases collected from one breast cancer patient and one prostate cancer patient. This allowed us to estimate, for each patient, the ages at cancer onset and inception of all detected metastases, the expected metastasis latency time, parameters of the Gompertzian growth of the primary tumor, and the rates of growth of metastases before and after surgery. We found that for both patients: (1) onset of metastasis occurred when primary tumor was undetectable; (2) inception of all surveyed metastases except one occurred before surgery; and most importantly, (3) resection of the primary tumor led to a dramatic increase in the rate of growth of metastases. The model provides an excellent fit to the observed volumes of bone metastases in both patients. Our results agree well with those obtained previously based on exponential growth of the primary tumor, which serves as model validation. Our findings support the notion of metastatic dormancy and indirectly confirm the existence of stem-like cancer cells in breast and prostate tumors. We also explored the logistic law of primary tumor growth; however, it degenerated into the exponential law for both patients analyzed. The conclusions of this work are supported by a vast body of experimental, clinical and epidemiological knowledge accumulated over the last century.

Improving Bacillus Calmette-Guérin (BCG) immunotherapy for bladder cancer by adding interleukin 2 (IL-2): a mathematical model

One of the treatments offered to non-invasive bladder cancer patients is BCG instillations, using a well-established, time-honoured protocol. Some of the patients, however, do not respond to this protocol. To examine possible changes in the protocol, we provide a platform for in silico testing of alternative protocols for BCG instillations and combinations with IL-2, to be used by urologists in planning new treatment strategies for subpopulations of bladder cancer patients who may benefit from a personalized protocol. We use a systems biology approach to describe the BCG-tumour-immune interplay and translate it into a set of mathematical differential equations. The variables of the equation set are the number of tumour cells, bacteria cells, immune cells, and cytokines participating in the tumour-immune response. Relevant parameters that describe the systems dynamics are taken from a variety of independent literature, unrelated to the clinical trial results assessed by the model predictions. Model simulations use a clinically relevant range of initial tumour sizes (tumour volume) and tumour growth rates (tumour grade), representative of a virtual population of fifty patients. Our model successfully retrieved previous clinical results for BCG induction treatment and BCG maintenance therapy with a complete response (CR) rate of 82%. Furthermore, we designed alternative maintenance protocols, using IL-2 combinations with BCG, which improved success rates up to 86% and 100% of the patients, albeit without considering possible side effects. We have shown our simulation platform to be reliable by demonstrating its ability to retrieve published clinical trial results. We used this platform to predict the outcome of treatment combinations. Our results suggest that the subpopulation of non-responsive patients may benefit from an intensified combined BCG IL-2 maintenance treatment.

Key signaling pathways in the muscle-invasive bladder carcinoma: Clinical markers for disease modeling and optimized treatment

In this review, we evaluate key molecular pathways and markers of muscle‐invasive bladder cancer (MIBC). Overexpression and activation of EGFR, p63, and EMT genes are suggestive of basal MIBC subtype generally responsive to chemotherapy. Alterations in PPARγ, ERBB2/3, and FGFR3 gene products and their signaling along with deregulated p53, cytokeratins KRT5/6/14 in combination with the cellular proliferation (Ki‐67), and cell cycle markers (p16) indicate the need for more radical treatment protocols. Similarly, the “bell‐shape” dynamics of Shh expression levels may suggest aggressive MIBC. A panel of diverse biological markers may be suitable for simulation studies of MIBC and development of an optimized treatment protocol. We conducted a critical evaluation of PubMed/Medline and SciFinder databases related to MIBC covering the period 2009–2015. The free‐text search was extended by adding the following keywords and phrases: bladder cancer, metastatic, muscle‐invasive, basal, luminal, epithelial‐to‐mesenchymal transition, cancer stem cell, mutations, immune response, signaling, biological markers, molecular markers, mathematical models, simulation, epigenetics, transmembrane, transcription factor, kinase, predictor, prognosis. The resulting selection of ca 500 abstracts was further analyzed in order to select the latest publications relevant to MIBC molecular markers of immediate clinical significance.

Dynamical properties and tumor clearance conditions for a nine-dimensional model of bladder cancer immunotherapy

Understanding the global interaction dynamics between tumor and the immune system plays a key role in the advancement of cancer therapy. Bunimovich-Mendrazitsky et al. (2015) developed a mathematical model for the study of the immune system response to combined therapy for bladder cancer with Bacillus Calmette-Guérin (BCG) and interleukin-2 (IL-2) . We utilized a mathematical approach for bladder cancer treatment model for derivation of ultimate upper and lower bounds and proving dissipativity property in the sense of Levinson. Furthermore, tumor clearance conditions for BCG treatment of bladder cancer are presented. Our method is based on localization of compact invariant sets and may be exploited for a prediction of the cells populations dynamics involved into the model.

Modeling and simulation of a low-grade urinary bladder carcinoma

In this work, we present a mathematical model of the initiation and progression of a low-grade urinary bladder carcinoma. We simulate the crucial processes affecting tumor growth, such as oxygen diffusion, carcinogen penetration, and angiogenesis, within the framework of the urothelial cell dynamics. The cell dynamics are modeled using the discrete technique of cellular automata, while the continuous processes of carcinogen penetration and oxygen diffusion are described by nonlinear diffusion-absorption equations. As the availability of oxygen is necessary for tumor progression, processes of oxygen transport to the tumor growth site seem most important. Our model yields a theoretical insight into the main stages of development and growth of urinary bladder carcinoma with emphasis on the two most common types: bladder polyps and carcinoma in situ. Analysis of histological structure of bladder tumor is important to avoid misdiagnosis and wrong treatment. We expect our model to be a valuable tool in the study of bladder cancer progression due to the exposure to carcinogens and the oxygen dependent expression of genes promoting tumor growth. Our numerical simulations have good qualitative agreement with in vivo results reported in the corresponding medical literature.

Hybrid discrete-continuous model of invasive bladder cancer

Bladder cancer is the seventh most common cancer worldwide. Epidemiological studies and experiments implicated chemical penetration into urothelium (epithelial tissue surrounding bladder) in the etiology of bladder cancer. In this work we model invasive bladder cancer. This type of cancer starts in the urothelium and progresses towards surrounding muscles and tissues, causing metastatic disease. Our mathematical model of invasive BC consists of two coupled sub-models: (i) living cycle of the urothelial cells (normal and mutated) simulated using discrete technique of Cellular Automata and (ii) mechanism of tumor invasion described by the system of reaction-diffusion equations. Numerical simulations presented here are in good qualitative agreement with the experimental results and reproduce in vitro observations described in medical literature.

A mathematical model with time-varying delays in the combined treatment of chronic myeloid leukemia

In this paper, we propose and analyze a mathematical model for the treatment of chronic myelogenous (myeloid) leukemia (CML), a cancer of the blood. Our main focus is on the combined treatment of CML based on imatinib therapy and immunotherapy. Treatment with imatinib is a molecular targeted therapy that inhibits the cells involved in the chronic CML pathogenesis. Immunotherapy based on interferon alfa-2a (IFN-α) increases cancer cell mortality and leads to improvement of outcomes of the combined therapy. Interaction between CML cancer cells and effector cells of the immune system is modeled by a system of non-linear differential equations, where we introduced biologically motivated time-varying delays in the treatment terms. The analysis of the described system shows the existence of a unique global positive solution and a unique non-trivial equilibrium. We also derive explicit local and global stability conditions for the non-trivial equilibrium.

Use of quasi-normal form to examine stability of tumor-free equilibrium in a mathematical model of bcg treatment of bladder cancer

Understanding the dynamics of human hosts and tumors is of critical importance. A mathematical model was developed by Bunimovich-Mendrazitsky et al., who explored the immune response in bladder cancer as an effect of BCG treatment. This treatment exploits the hosts own immune system to boost a response that will enable the host to rid itself of the tumor. Although this model was extensively studied using numerical simulation, no analytical results on global tumor dynamics were originally presented. In this work, we analyze stability in a mathematical model for BCG treatment of bladder cancer based on the use of quasi-normal form and stability theory. These tools are employed in the critical cases, especially when analysis of the linearized system is insufficient. Our goal is to gain a deeper insight into the BCG treatment of bladder cancer, which is based on a mathematical model and biological considerations, and thereby to bring us one step closer to the design of a relevant clinical protocol.