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.

Mathematical model of coffee tree's rust control using snails as biological agents.

Coffee rust is one of the main diseases that affect coffee plantations worldwide, causing large-scale ecological and economic damage. While multiple methods have been proposed to tackle this challenge, using snails as biological agents have shown to be the most consistent and promising approach. However, snails are an invasive species, and overusing them can cause devastating outcomes. In this paper, we develop and explore an ecological-epidemiological mathematical model for the coffee tree rust pandemic control using snails as biological agents. We analyze the equilibria of the proposed system with their stability properties. In addition, we perform numerical analysis to obtain the sensitivity of the system to different changes and manipulation of the snails pandemic control, under specific conditions. Finally, we propose an in silico mechanism to obtain an analytical connection between the system's initial condition and the number of snails needed to optimally control the rust pandemic spread while preventing the snail population to grow unmanageably. Our model can be used to optimize the usage of snails as biological agents to control the rust pandemic in spatially-small areas, by predicting the number of snails one needs to introduce to the ecosystem in order to obtain a desired outcome.

Early Detection and Control of the Next Epidemic Wave Using Health Communications: Development of an Artificial Intelligence-Based Tool and Its Validation on COVID-19 Data from the US.

Social media networks highly influence on a broad range of global social life, especially in the context of a pandemic. We developed a mathematical model with a computational tool, called EMIT (Epidemic and Media Impact Tool), to detect and control pandemic waves, using mainly topics of relevance on social media networks and pandemic spread. Using EMIT, we analyzed health-related communications on social media networks for early prediction, detection, and control of an outbreak. EMIT is an artificial intelligence-based tool supporting health communication and policy makers decisions. Thus, EMIT, based on historical data, social media trends and disease spread, offers an predictive estimation of the influence of public health interventions such as social media-based communication campaigns. We have validated the EMIT mathematical model on real world data combining COVID-19 pandemic data in the US and social media data from Twitter. EMIT demonstrated a high level of performance in predicting the next epidemiological wave (AUC = 0.909, F1 = 0.899).

Validation of a Mathematical Model Describing the Dynamics of Chemotherapy for Chronic Lymphocytic Leukemia In Vivo.

In recent years, mathematical models have developed into an important tool for cancer research, combining quantitative analysis and natural processes. We have focused on Chronic Lymphocytic Leukemia (CLL), since it is one of the most common adult leukemias, which remains incurable. As the first step toward the mathematical prediction of in vivo drug efficacy, we first found that logistic growth best described the proliferation of fluorescently labeled murine A20 leukemic cells injected in immunocompetent Balb/c mice. Then, we tested the cytotoxic efficacy of Ibrutinib (Ibr) and Cytarabine (Cyt) in A20-bearing mice. The results afforded calculation of the killing rate of the A20 cells as a function of therapy. The experimental data were compared with the simulation model to validate the latter's applicability. On the basis of these results, we developed a new ordinary differential equations (ODEs) model and provided its sensitivity and stability analysis. There was excellent accordance between numerical simulations of the model and results from in vivo experiments. We found that simulations of our model could predict that the combination of Cyt and Ibr would lead to approximately 95% killing of A20 cells. In its current format, the model can be used as a tool for mathematical prediction of in vivo drug efficacy, and could form the basis of software for prediction of personalized chemotherapy.

Predicting acute kidney injury following open partial nephrectomy treatment using SAT-pruned explainable machine learning model.

BACKGROUND: One of the most prevalent complications of Partial Nephrectomy (PN) is Acute Kidney Injury (AKI), which could have a negative impact on subsequent renal function and occurs in up to 24.3% of patients undergoing PN. The aim of this study was to predict the occurrence of AKI following PN using preoperative parameters by applying machine learning algorithms. METHODS: We included all adult patients (n = 723) who underwent open PN in our department since 1995 and on whom we have data on the pre-operative renal function. We developed a random forest (RF) model with Boolean satisfaction-based pruned decision trees for binary classification (AKI or non-AKI). Hyper-parameter grid search was performed to optimize the model's performance. Fivefold cross-validation was applied to evaluate the model. We implemented a RF model with greedy feature selection to binary classify AKI and non-AKI cases based on pre-operative data. RESULTS: The best model obtained a 0.69 precision and 0.69 recall in classifying the AKI and non-AKI groups on average (k = 5). In addition, the model's probability to correctly classify a new prediction is 0.75. The proposed model is available as an online calculator. CONCLUSIONS: Our model predicts the occurrence of AKI following open PN with (75%) accuracy. We plan to externally validate this model and modify it to minimally-invasive PN.

Generic approach for mathematical model of multi-strain pandemics.

Multi-strain pandemics have emerged as a major concern. We introduce a new model for assessing the connection between multi-strain pandemics and mortality rate, basic reproduction number, and maximum infected individuals. The proposed model provides a general mathematical approach for representing multi-strain pandemics, generalizing for an arbitrary number of strains. We show that the proposed model fits well with epidemiological historical world health data over a long time period. From a theoretical point of view, we show that the increasing number of strains increases logarithmically the maximum number of infected individuals and the mean mortality rate. Moreover, the mean basic reproduction number is statistically identical to the single, most aggressive pandemic strain for multi-strain pandemics.

The Signature Features of COVID-19 Pandemic in a Hybrid Mathematical Model-Implications for Optimal Work-School Lockdown Policy.

The new COVID-19 pandemic has challenged policymakers on key issues. Most countries have adopted "lockdown" policies to reduce the spatial spread of COVID-19, but they have damaged the economic and moral fabric of society. Mathematical modeling in non-pharmaceutical intervention policy management has proven to be a major weapon in this fight due to the lack of an effective COVID-19 vaccine. A new hybrid model for COVID-19 dynamics using both an age-structured mathematical model based on the SIRD model and spatio-temporal model in silico is presented, analyzing the data of COVID-19 in Israel. Using the hybrid model, a method for estimating the reproduction number of an epidemic in real-time from the data of daily notification of cases is introduced. The results of the proposed model are confirmed by the Israeli Lockdown experience with a mean square error of 0.205 over 2 weeks. The use of mathematical models promises to reduce the uncertainty in the choice of "Lockdown" policies. The unique use of contact details from 2 classes (children and adults), the interaction of populations depending on the time of day, and several physical locations, allow a new look at the differential dynamics of the spread and control of infection.

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.

Analysis of a breast cancer mathematical model by a new method to find an optimal protocol for HER2-positive cancer.

Treatment of breast cancer (positive for HER2, i.e., ERBB2) is described by a mathematical model involving non-linear ordinary differential equations with a hidden hierarchy. To reveal the hierarchy of dynamical variables of the system being considered, we applied the singular perturbed vector field (SPVF) method, where a system of equations can be decomposed to fast and slow sub-systems with explicit small parameters. This new form of the model, which is called a singular perturbed system, enables us to apply a semi-analytical method called the method of directly defining inverse mapping (MDDiM), which is based on the homotopy analysis asymptotic method. We introduced the treatment protocol in explicit form, through an analytical function that describes the exact dose and intervals between treatments in a cyclical manner. In addition, a new algorithm for the optimal dosage that causes tumour shrinkage is presented in this study. Furthermore, we took the concept of protocol optimisation a step further and derived a differential equation that represents vaccination depending on tumour size and yields an optimal protocol of different doses at every time point. We introduced the treatment protocol in explicit form, through an analytical function that describes the exact dose and intervals between treatments in a cyclical manner. In addition, a new algorithm for finding the optimal dosage that causes tumour shrinkage is presented in this study. Additionally, we took the concept of protocol optimisation a step further and derived a differential equation that represents vaccination depending on tumour size and yields an optimal protocol of different doses at every time point.

Metastasis Initiation Precedes Detection of Primary Cancer-Analysis of Metastasis Growth in vivo in a Colorectal Cancer Test Case.

Most cases of deaths from colorectal cancer (CRC) result from metastases, which are often still undetectable at disease detection time. Even so, in many cases, shedding is assumed to have taken place before that time. The dynamics of metastasis formation and growth are not well-established. This work aims to explore CRC lung metastasis growth rate and dynamics. We analyzed a test case of a metastatic CRC patient with four lung metastases, with data of four serial computed tomography (CT) scans measuring metastasis sizes while untreated. We fitted three mathematical growth models-exponential, logistic, and Gompertzian-to the CT measurements. For each metastasis, a best-fitted model was determined, tumor doubling time (TDT) was assessed, and metastasis inception time was extrapolated. Three of the metastases showed exponential growth, while the fourth showed logistic restraint of the growth. TDT was around 93 days. Predicted metastasis inception time was at least 4-5 years before the primary tumor diagnosis date, though they did not reach detectable sizes until at least 1 year after primary tumor resection. Our results support the exponential growth approximation for most of the metastases, at least for the clinically observed time period. Our analysis shows that metastases can be initiated before the primary tumor is detectable and implies that surgeries accelerate metastasis growth.

BCG and IL - 2 model for bladder cancer treatment with fast and slow dynamics based on SPVF method-stability analysis.

In this study, we apply the method of singularly perturbed vector field (SPVF) and its application to the problem of bladder cancer treatment that takes into account the combination of Bacillus CalmetteGurin vaccine (BCG) and interleukin (IL)-2 immunotherapy (IL - 2). The model is presented with a hidden hierarchy of time scale of the dynamical variables of the system. By applying the SPVF, we transform the model to SPS (Singular Perturbed System) form with explicit hierarchy, i.e., slow and fast sub-systems. The decomposition of the model to fast and slow subsystems, first of all, reduces significantly the time computer calculations as well as the long and complex algebraic expressions when investigating the full model. In addition, this decomposition allows us to explore only the fast subsystem without losing important biological/ mathematical information of the original system.The main results of the paper were that we obtained explicit expressions of the equilibrium points of the model and investigated the stability of these points.

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

We present a revised mathematical model of the immune response to Bacillus Calmette-Guérin (BCG) treatment of bladder cancer, optimized according to biological and clinical data accumulated during the last decade. The improved model accounts for cytotoxic T lymphocyte differentiation as an integral element of the delayed immune response, as well as the logistic growth terms for cancer cell proliferation. Three equilibria are demonstrated for the proposed model, which is assumed to be influenced by white noise stochastic perturbations that are directly proportional to the system state deviation from an equilibrium. Stability conditions for all equilibria are analyzed using the Kolmanovskii-Shaikhet general method of Lyapunov functionals construction.

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.

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.

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 system's 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.

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.

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.

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.

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.

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 host's 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.