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Doxorubicin is a chemotherapy widely used to treat several types of cancer, including triple-negative breast cancer. In this work, we use a Bayesian framework to rigorously assess the ability of ten different mathematical models to describe the dynamics of four TNBC cell lines (SUM-149PT, MDA-MB-231, MDA-MB-453, and MDA-MB-468) in response to treatment with doxorubicin at concentrations ranging from 10 to 2500 nM. Each cell line was plated and serially imaged via fluorescence microscopy for 30 days following 6, 12, or 24 h of in vitro drug exposure. We use the resulting data sets to estimate the parameters of the ten pharmacodynamic models using a Bayesian approach, which accounts for uncertainties in the models, parameters, and observational data. The ten candidate models describe the growth patterns and degree of response to doxorubicin for each cell line by incorporating exponential or logistic tumor growth, and distinct forms of cell death. Cell line and treatment specific model parameters are then estimated from the experimental data for each model. We analyze all competing models using the Bayesian Information Criterion (BIC), and the selection of the best model is made according to the model probabilities (BIC weights). We show that the best model among the candidate set of models depends on the TNBC cell line and the treatment scenario, though, in most cases, there is great uncertainty in choosing the best model. However, we show that the probability of being the best model can be increased by combining treatment data with the same total drug exposure. Our analysis points to the importance of considering multiple models, built on different biological assumptions, to capture the observed variations in tumor growth and treatment response.

Brazil’s continental dimension poses a challenge to the control of the spread of COVID-19. Due to the country specific scenario of high social and demographic heterogeneity, combined with limited testing capacity, lack of reliable data, under-reporting of cases, and restricted testing policy, the focus of this study is twofold: (i) to develop a generalized SEIRD model that implicitly takes into account the quarantine measures, and (ii) to estimate the response of the COVID-19 spread dynamics to perturbations/uncertainties. By investigating the projections of cumulative numbers of confirmed and death cases, as well as the effective reproduction number, we show that the model parameter related to social distancing measures is one of the most influential along all stages of the disease spread and the most influential after the infection peak. Due to such importance in the outcomes, different relaxation strategies of social distancing measures are investigated in order to determine which strategies are viable and less hazardous to the population. The results highlight the need of keeping social distancing policies to control the disease spread. Specifically, the considered scenario of abrupt social distancing relaxation implemented after the occurrence of the peak of positively diagnosed cases can prolong the epidemic, with a significant increase of the projected numbers of confirmed and death cases. An even worse scenario could occur if the quarantine relaxation policy is implemented before evidence of the epidemiological control, indicating the importance of the proper choice of when to start relaxing social distancing measures.

Compressive stresses play important roles on tumor cells proliferation and invasion. In this work we propose to inform a tumor growth model with the recovered deformation coming from in vivo imaging data. We investigated the use of an optical flow technique, the well known Lucas-Kanade method, to capture tumor deformation in a synthetic experimental breast cancer setting. We compare displacements and stresses obtained with this method with those derived from a previously developed reaction-diffusion model with mechanical deformation. We show that the considered optical flow technique may capture deformations appearing in breast cancers, being a useful alternative to integrate in vivo data to mathematical tumor models.

INTRODUCTION: A defining hallmark of cancer is aberrant cell proliferation. Efforts to understand the generative properties of cancer cells span all biological scales: from genetic deviations and alterations of metabolic pathways, to physical stresses due to overcrowding, as well as the effects of therapeutics and the immune system. While these factors have long been studied in the laboratory, mathematical and computational techniques are being increasingly applied to help understand and forecast tumor growth and treatment response. Advantages of mathematical modeling of proliferation include the ability to simulate and predict the spatiotemporal development of tumors across multiple experimental scales. Central to proliferation modeling is the incorporation of available biological data and validation with experimental data. AREAS COVERED: We present an overview of past and current mathematical strategies directed at understanding tumor cell proliferation. We identify areas for mathematical development as motivated by available experimental and clinical evidence, with a particular emphasis on emerging, non-invasive imaging technologies. EXPERT COMMENTARY: The data required to legitimize mathematical models are often difficult or (currently) impossible to obtain. We suggest areas for further investigation to establish mathematical models that more effectively utilize available data to make informed predictions on tumor cell proliferation.

O crescimento tumoral e resultado de mecanismos nao lineares complexos que ocorrem em diversas escalas de tempo e espaco. A modelagem computacional pode ajudar na compreensao de tais mecanismos, assim como auxiliar no desenvolvimento de terapias efetivas. Neste trabalho, desenvolvemos um modelo hibrido avascular que integra tres escalas espaciais (tecidual, celular e molecular) com o objetivo de estudar a influencia da resposta regulatoria intra-celular nos processos de migracao e proliferacao. Essas repostas resultam de reacoes bioquimicas de sinalizacao molecular iniciadas por estimulos extracelulares. Experimentos computacionais sao realizados para demonstrar a importância da diferenciacao fenotipica na dinâmica do crescimento tumoral.

Neste trabalho utilizamos um modelo matematico simples para representar o crescimento de tumores avasculares. Atraves de dados da literatura realizamos a calibracao do modelo proposto tendo como base a abordagem Bayesiana. Nesta abordagem, as distribuicoes a posteriori dos parâmetros sao obtidas utilizando duas tecnicas: amostragem via algoritmo de Metropolis-Hastings, um metodo de Monte Carlo via cadeias de Markov, e amostragem via grade fixa. Ambas conduziram a resultados satisfatorios para os experimentos realizados e sao por natureza mais informativas que os metodos tradicionais de regressao.

Cancer results from a complex interplay of different biological, chemical, and physical phenomena that span a wide range of time and length scales. Computational modeling may help to unfold the role of multiple evolving factors that exist and interact in the tumor microenvironment. Understanding these complex multiscale interactions is a crucial step toward predicting cancer growth and in developing effective therapies. We integrate different modeling approaches in a multiscale, avascular, hybrid tumor growth model encompassing tissue, cell, and sub-cell scales. At the tissue level, we consider the dispersion of nutrients and growth factors in the tumor microenvironment, which are modeled through reaction–diffusion equations. At the cell level, we use an agent-based model (ABM) to describe normal and tumor cell dynamics, with normal cells kept in homeostasis and cancer cells differentiated into quiescent, proliferative, migratory, apoptotic, hypoxic, and necrotic states. Cell movement is driven by the balance of a variety of forces according to Newton’s second law, including those related to growth-induced stresses. Phenotypic transitions are defined by specific rule of behaviors that depend on microenvironment stimuli. We integrate in each cell/agent a branch of the epidermal growth factor receptor (EGFR) pathway. This pathway is modeled by a system of coupled nonlinear differential equations involving the mass laws of 20 molecules. The rates of change in the concentration of some key molecules trigger proliferation or migration advantage response. The bridge between cell and tissue scales is built through the reaction and source terms of the partial differential equations. Our hybrid model is built in a modular way, enabling the investigation of the role of different mechanisms at multiple scales on tumor progression. This strategy allows representing both the collective behavior due to cell assembly as well as microscopic intracellular phenomena described by signal transduction pathways. Here, we investigate the impact of some mechanisms associated with sustained proliferation on cancer progression. Speci- fically, we focus on the intracellular proliferation/migration-advantage-response driven by the EGFR pathway and on proliferation inhibition due to accumulation of growth-induced stresses. Simulations demonstrate that the model can adequately describe some complex mechanisms of tumor dynamics, including growth arrest in avascular tumors. Both the sub-cell model and growth-induced stresses give rise to heterogeneity in the tumor expansion and a rich variety of tumor behaviors.

Cell stresses have a key role on the tumor growth rate, the evolution pattern and on ECM synthesis and organization. In this work, we investigate the interplay between these complex biological phenomena. We develop a heterogeneous tumor growth model subjected to elastic deformation and matrix degradation and remodeling. We incorporate mechanical effects of the surrounding tissue on the growing tumor by assuming that the stress components must satisfy the conservation of linear momentum disregarding inertial effects. We investigate tumor differentiation, morphogenic evolution, and invasion through different feedback mechanism models. Numerical simulations are performed to highlight how mechanical properties of a tissue contribute to cancer progression.Keywords: Mathematical Model, Tumor Growth, Sensitivity Analysis, Mechanical Properties

We propose in this work a simple framework to build a hierarchical family of tumor growth models by selecting a subset of the most important parameters of our base model with respect to the evolution of the tumor volume. The importance of each parameter is identified through a model-free sensitivity analysis technique, the elementary effects (EE), due to its simplicity and low computational cost. This model framework encompasses the essential hypotheses and the limited set of important parameters acquired from the sensitivity analysis. In this way, we are able to create a family of models described by at least the same essential conditions and parameters but with different complexities regarding the number of parameters used. Numerical experiments are conducted to show the reasoning behind the hierarchical developed family of tumor growth modes. The modeling framework in this manner provides a powerful way for studying a model itself or either its simplification or extension. The framework can also be tailored to form the basis for future models, incorporating new processes and phenomena.

The aim of this work is to compare two different sensitivity analysis methods, used to investigate the influence of the input parameters of a tumor model on its outcome. The first method uses a Monte Carlo approach to produce Scatterplots and the second uses the Elementary Effects method. Numerical experiments are conducted to highlight the main strengths of each approach.

O modelo utilizado neste trabalho segue a abordagem da mecânica de meios continuuos e visa simular o crescimento tumoral em meios heterogeneos atraves da representacao das celulas tumorais, normais e capacidade suporte das celulas endoteliais. A solucao numerica do sistema de equacoes diferenciais parciais, baseado em equacoes de reacao-difusao, e obtida utilizando o Metodo de Diferencas Finitas para aproximacaao temporal e o Metodo de Elementos Finitos de Galerkin para a aproximacao espacial. Experimentos numericos sao realizados de forma a demonstrar e destacar as principais caracteristicas do modelo.