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1.
PLoS Comput Biol ; 17(11): e1008845, 2021 11.
Artigo em Inglês | MEDLINE | ID: mdl-34843457

RESUMO

Hybrid multiscale agent-based models (ABMs) are unique in their ability to simulate individual cell interactions and microenvironmental dynamics. Unfortunately, the high computational cost of modeling individual cells, the inherent stochasticity of cell dynamics, and numerous model parameters are fundamental limitations of applying such models to predict tumor dynamics. To overcome these challenges, we have developed a coarse-grained two-scale ABM (cgABM) with a reduced parameter space that allows for an accurate and efficient calibration using a set of time-resolved microscopy measurements of cancer cells grown with different initial conditions. The multiscale model consists of a reaction-diffusion type model capturing the spatio-temporal evolution of glucose and growth factors in the tumor microenvironment (at tissue scale), coupled with a lattice-free ABM to simulate individual cell dynamics (at cellular scale). The experimental data consists of BT474 human breast carcinoma cells initialized with different glucose concentrations and tumor cell confluences. The confluence of live and dead cells was measured every three hours over four days. Given this model, we perform a time-dependent global sensitivity analysis to identify the relative importance of the model parameters. The subsequent cgABM is calibrated within a Bayesian framework to the experimental data to estimate model parameters, which are then used to predict the temporal evolution of the living and dead cell populations. To this end, a moment-based Bayesian inference is proposed to account for the stochasticity of the cgABM while quantifying uncertainties due to limited temporal observational data. The cgABM reduces the computational time of ABM simulations by 93% to 97% while staying within a 3% difference in prediction compared to ABM. Additionally, the cgABM can reliably predict the temporal evolution of breast cancer cells observed by the microscopy data with an average error and standard deviation for live and dead cells being 7.61±2.01 and 5.78±1.13, respectively.

2.
Cancers (Basel) ; 13(12)2021 Jun 16.
Artigo em Inglês | MEDLINE | ID: mdl-34208448

RESUMO

Tumor-associated vasculature is responsible for the delivery of nutrients, removal of waste, and allowing growth beyond 2-3 mm3. Additionally, the vascular network, which is changing in both space and time, fundamentally influences tumor response to both systemic and radiation therapy. Thus, a robust understanding of vascular dynamics is necessary to accurately predict tumor growth, as well as establish optimal treatment protocols to achieve optimal tumor control. Such a goal requires the intimate integration of both theory and experiment. Quantitative and time-resolved imaging methods have emerged as technologies able to visualize and characterize tumor vascular properties before and during therapy at the tissue and cell scale. Parallel to, but separate from those developments, mathematical modeling techniques have been developed to enable in silico investigations into theoretical tumor and vascular dynamics. In particular, recent efforts have sought to integrate both theory and experiment to enable data-driven mathematical modeling. Such mathematical models are calibrated by data obtained from individual tumor-vascular systems to predict future vascular growth, delivery of systemic agents, and response to radiotherapy. In this review, we discuss experimental techniques for visualizing and quantifying vascular dynamics including magnetic resonance imaging, microfluidic devices, and confocal microscopy. We then focus on the integration of these experimental measures with biologically based mathematical models to generate testable predictions.

4.
Nat Commun ; 12(1): 333, 2021 01 12.
Artigo em Inglês | MEDLINE | ID: mdl-33436608

RESUMO

COVID-19 is affecting healthcare resources worldwide, with lower and middle-income countries being particularly disadvantaged to mitigate the challenges imposed by the disease, including the availability of a sufficient number of infirmary/ICU hospital beds, ventilators, and medical supplies. Here, we use mathematical modelling to study the dynamics of COVID-19 in Bahia, a state in northeastern Brazil, considering the influences of asymptomatic/non-detected cases, hospitalizations, and mortality. The impacts of policies on the transmission rate were also examined. Our results underscore the difficulties in maintaining a fully operational health infrastructure amidst the pandemic. Lowering the transmission rate is paramount to this objective, but current local efforts, leading to a 36% decrease, remain insufficient to prevent systemic collapse at peak demand, which could be accomplished using periodic interventions. Non-detected cases contribute to a ∽55% increase in R0. Finally, we discuss our results in light of epidemiological data that became available after the initial analyses.


Assuntos
COVID-19/epidemiologia , Modelos Teóricos , Pandemias , SARS-CoV-2 , Doenças Assintomáticas , Brasil/epidemiologia , COVID-19/prevenção & controle , COVID-19/transmissão , Métodos Epidemiológicos , Hospitalização/estatística & dados numéricos , Humanos , Unidades de Terapia Intensiva , Distanciamento Físico
5.
iScience ; 23(12): 101807, 2020 Dec 18.
Artigo em Inglês | MEDLINE | ID: mdl-33299976

RESUMO

We provide an overview on the use of biological assays to calibrate and initialize mechanism-based models of cancer phenomena. Although artificial intelligence methods currently dominate the landscape in computational oncology, mathematical models that seek to explicitly incorporate biological mechanisms into their formalism are of increasing interest. These models can guide experimental design and provide insights into the underlying mechanisms of cancer progression. Historically, these models have included a myriad of parameters that have been difficult to quantify in biologically relevant systems, limiting their practical insights. Recently, however, there has been much interest calibrating biologically based models with the quantitative measurements available from (for example) RNA sequencing, time-resolved microscopy, and in vivo imaging. In this contribution, we summarize how a variety of experimental methods quantify tumor characteristics from the molecular to tissue scales and describe how such data can be directly integrated with mechanism-based models to improve predictions of tumor growth and treatment response.

6.
J Clin Med ; 9(5)2020 May 02.
Artigo em Inglês | MEDLINE | ID: mdl-32370195

RESUMO

Optimal control theory is branch of mathematics that aims to optimize a solution to a dynamical system. While the concept of using optimal control theory to improve treatment regimens in oncology is not novel, many of the early applications of this mathematical technique were not designed to work with routinely available data or produce results that can eventually be translated to the clinical setting. The purpose of this review is to discuss clinically relevant considerations for formulating and solving optimal control problems for treating cancer patients. Our review focuses on two of the most widely used cancer treatments, radiation therapy and systemic therapy, as they naturally lend themselves to optimal control theory as a means to personalize therapeutic plans in a rigorous fashion. To provide context for optimal control theory to address either of these two modalities, we first discuss the major limitations and difficulties oncologists face when considering alternate regimens for their patients. We then provide a brief introduction to optimal control theory before formulating the optimal control problem in the context of radiation and systemic therapy. We also summarize examples from the literature that illustrate these concepts. Finally, we present both challenges and opportunities for dramatically improving patient outcomes via the integration of clinically relevant, patient-specific, mathematical models and optimal control theory.

7.
J Mech Phys Solids ; 1392020 Jun.
Artigo em Inglês | MEDLINE | ID: mdl-32394987

RESUMO

We develop a general class of thermodynamically consistent, continuum models based on mixture theory with phase effects that describe the behavior of a mass of multiple interacting constituents. The constituents consist of solid species undergoing large elastic deformations and compressible viscous fluids. The fundamental building blocks framing the mixture theories consist of the mass balance law of diffusing species and microscopic (cellular scale) and macroscopic (tissue scale) force balances, as well as energy balance and the entropy production inequality derived from the first and second laws of thermodynamics. A general phase-field framework is developed by closing the system through postulating constitutive equations (i.e., specific forms of free energy and rate of dissipation potentials) to depict the growth of tumors in a microenvironment. A notable feature of this theory is that it contains a unified continuum mechanics framework for addressing the interactions of multiple species evolving in both space and time and involved in biological growth of soft tissues (e.g., tumor cells and nutrients). The formulation also accounts for the regulating roles of the mechanical deformation on the growth of tumors, through a physically and mathematically consistent coupled diffusion and deformation framework. A new algorithm for numerical approximation of the proposed model using mixed finite elements is presented. The results of numerical experiments indicate that the proposed theory captures critical features of avascular tumor growth in the various microenvironment of living tissue, in agreement with the experimental studies in the literature.

8.
PLoS One ; 15(4): e0231137, 2020.
Artigo em Inglês | MEDLINE | ID: mdl-32275674

RESUMO

Tumor associated angiogenesis is the development of new blood vessels in response to proteins secreted by tumor cells. These new blood vessels allow tumors to continue to grow beyond what the pre-existing vasculature could support. Here, we construct a mathematical model to simulate tumor angiogenesis by considering each endothelial cell as an agent, and allowing the vascular endothelial growth factor (VEGF) and nutrient fields to impact the dynamics and phenotypic transitions of each tumor and endothelial cell. The phenotypes of the endothelial cells (i.e., tip, stalk, and phalanx cells) are selected by the local VEGF field, and govern the migration and growth of vessel sprouts at the cellular level. Over time, these vessels grow and migrate to the tumor, forming anastomotic loops to supply nutrients, while interacting with the tumor through mechanical forces and the consumption of VEGF. The model is able to capture collapsing and breaking of vessels caused by tumor-endothelial cell interactions. This is accomplished through modeling the physical interaction between the vasculature and the tumor, resulting in vessel occlusion and tumor heterogeneity over time due to the stages of response in angiogenesis. Key parameters are identified through a sensitivity analysis based on the Sobol method, establishing which parameters should be the focus of subsequent experimental efforts. During the avascular phase (i.e., before angiogenesis is triggered), the nutrient consumption rate, followed by the rate of nutrient diffusion, yield the greatest influence on the number and distribution of tumor cells. Similarly, the consumption and diffusion of VEGF yield the greatest influence on the endothelial and tumor cell numbers during angiogenesis. In summary, we present a hybrid mathematical approach that characterizes vascular changes via an agent-based model, while treating nutrient and VEGF changes through a continuum model. The model describes the physical interaction between a tumor and the surrounding blood vessels, explicitly allowing the forces of the growing tumor to influence the nutrient delivery of the vasculature.


Assuntos
Células Endoteliais/patologia , Modelos Biológicos , Neoplasias/patologia , Neovascularização Patológica/patologia , Fator A de Crescimento do Endotélio Vascular/metabolismo , Animais , Simulação por Computador , Humanos , Neoplasias/irrigação sanguínea
9.
PLoS Biol ; 17(8): e3000399, 2019 08.
Artigo em Inglês | MEDLINE | ID: mdl-31381560

RESUMO

Most models of cancer cell population expansion assume exponential growth kinetics at low cell densities, with deviations to account for observed slowing of growth rate only at higher densities due to limited resources such as space and nutrients. However, recent preclinical and clinical observations of tumor initiation or recurrence indicate the presence of tumor growth kinetics in which growth rates scale positively with cell numbers. These observations are analogous to the cooperative behavior of species in an ecosystem described by the ecological principle of the Allee effect. In preclinical and clinical models, however, tumor growth data are limited by the lower limit of detection (i.e., a measurable lesion) and confounding variables, such as tumor microenvironment, and immune responses may cause and mask deviations from exponential growth models. In this work, we present alternative growth models to investigate the presence of an Allee effect in cancer cells seeded at low cell densities in a controlled in vitro setting. We propose a stochastic modeling framework to disentangle expected deviations due to small population size stochastic effects from cooperative growth and use the moment approach for stochastic parameter estimation to calibrate the observed growth trajectories. We validate the framework on simulated data and apply this approach to longitudinal cell proliferation data of BT-474 luminal B breast cancer cells. We find that cell population growth kinetics are best described by a model structure that considers the Allee effect, in that the birth rate of tumor cells increases with cell number in the regime of small population size. This indicates a potentially critical role of cooperative behavior among tumor cells at low cell densities with relevance to early stage growth patterns of emerging and relapsed tumors.


Assuntos
Contagem de Células/métodos , Proliferação de Células/fisiologia , Neoplasias/metabolismo , Linhagem Celular Tumoral , Ecossistema , Humanos , Cinética , Modelos Biológicos , Modelos Teóricos
10.
Phys Biol ; 16(4): 041005, 2019 06 19.
Artigo em Inglês | MEDLINE | ID: mdl-30991381

RESUMO

Whether the nom de guerre is Mathematical Oncology, Computational or Systems Biology, Theoretical Biology, Evolutionary Oncology, Bioinformatics, or simply Basic Science, there is no denying that mathematics continues to play an increasingly prominent role in cancer research. Mathematical Oncology-defined here simply as the use of mathematics in cancer research-complements and overlaps with a number of other fields that rely on mathematics as a core methodology. As a result, Mathematical Oncology has a broad scope, ranging from theoretical studies to clinical trials designed with mathematical models. This Roadmap differentiates Mathematical Oncology from related fields and demonstrates specific areas of focus within this unique field of research. The dominant theme of this Roadmap is the personalization of medicine through mathematics, modelling, and simulation. This is achieved through the use of patient-specific clinical data to: develop individualized screening strategies to detect cancer earlier; make predictions of response to therapy; design adaptive, patient-specific treatment plans to overcome therapy resistance; and establish domain-specific standards to share model predictions and to make models and simulations reproducible. The cover art for this Roadmap was chosen as an apt metaphor for the beautiful, strange, and evolving relationship between mathematics and cancer.


Assuntos
Matemática/métodos , Oncologia/métodos , Biologia de Sistemas/métodos , Biologia Computacional , Simulação por Computador , Humanos , Modelos Biológicos , Modelos Teóricos , Neoplasias/diagnóstico , Neoplasias/terapia , Análise de Célula Única/métodos
11.
JCO Clin Cancer Inform ; 3: 1-10, 2019 02.
Artigo em Inglês | MEDLINE | ID: mdl-30807209

RESUMO

Multiparametric imaging is a critical tool in the noninvasive study and assessment of cancer. Imaging methods have evolved over the past several decades to provide quantitative measures of tumor and healthy tissue characteristics related to, for example, cell number, blood volume fraction, blood flow, hypoxia, and metabolism. Mechanistic models of tumor growth also have matured to a point where the incorporation of patient-specific measures could provide clinically relevant predictions of tumor growth and response. In this review, we identify and discuss approaches that use multiparametric imaging data, including diffusion-weighted magnetic resonance imaging, dynamic contrast-enhanced magnetic resonance imaging, diffusion tensor imaging, contrast-enhanced computed tomography, [18F]fluorodeoxyglucose positron emission tomography, and [18F]fluoromisonidazole positron emission tomography to initialize and calibrate mechanistic models of tumor growth and response. We focus the discussion on brain and breast cancers; however, we also identify three emerging areas of application in kidney, pancreatic, and lung cancers. We conclude with a discussion of the future directions for incorporating multiparametric imaging data and mechanistic modeling into clinical decision making for patients with cancer.


Assuntos
Processamento de Imagem Assistida por Computador/métodos , Imageamento por Ressonância Magnética Multiparamétrica/métodos , Neoplasias/diagnóstico por imagem , Neoplasias/terapia , Tomografia por Emissão de Pósitrons/métodos , Tomografia Computadorizada por Raios X/métodos , Terapia Combinada , Simulação por Computador , Fluordesoxiglucose F18 , Humanos , Neoplasias/patologia , Compostos Radiofarmacêuticos , Resultado do Tratamento , Carga Tumoral
12.
Expert Rev Anticancer Ther ; 18(12): 1271-1286, 2018 12.
Artigo em Inglês | MEDLINE | ID: mdl-30252552

RESUMO

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.


Assuntos
Proliferação de Células/fisiologia , Modelos Teóricos , Neoplasias/patologia , Diagnóstico por Imagem/métodos , Humanos , Modelos Biológicos
13.
Neotrop. entomol ; 38(6): 699-707, Nov.-Dec. 2009. graf, ilus
Artigo em Inglês | LILACS | ID: lil-537392

RESUMO

Ecological modeling is an important tool for investigating dynamic behavior patterns in populations, trophic interactions, and behavioral ecology. However, the ecological patterns that reflect population oscillation trends are often not clearly visible without analytical instruments such as ecological models. Thus, ecological modeling plays a fundamental role in describing demographic processes that are important for population dynamics. Ecological models, besides making possible the visualization of ecological patterns, may also reveal patterns of population persistence in many trophic systems, including prey-predator or host-parasitoid relationships, interactions that are commonly present in integrated pest management programs. In this forum, we present the main ecological aspects important for model building and implementation of integrated pest management programs for insects. Particularly, in this study, we analyze the combination between host-parasitoid models and the concept of economic threshold level on a spatio-temporal scale. As a conclusion about the model combination, spatial structure is essential for models of this nature, since its introduction into the system significantly alters the economic threshold-level values.


A modelagem ecológica é uma ferramenta importante para a investigação de padrões de comportamento dinâmico em populações, interações tróficas e também em ecologia comportamental. Contudo, os padrões ecológicos que refletem tendências de oscilação populacional muitas vezes não são claramente visíveis sem instrumentos analíticos, como os modelos ecológicos. Dessa forma, a modelagem ecológica exerce papel fundamental na descrição de processos demográficos importantes para a dinâmica populacional. Os modelos ecológicos, além de tornarem possível a visualização de padrões ecológicos, podem também revelar padrões de persistência populacional nos diversos sistemas tróficos, incluindo as relações presa-predador ou hospedeiro-parasitóide, interações comumente presentes em programas de manejo integrado de pragas. Neste fórum apresentamos os principais aspectos ecológicos importantes para a construção de modelos e implementação de programa de manejo de pragas em insetos. Em particular, analisamos a combinação entre modelos hospedeiro-parasitóide e o conceito de nível de dano em escala espaço-temporal. Como conclusão sobre a combinação de modelos, evidencia-se que a estrutura espacial é essencial para modelos desta natureza, já que sua introdução no sistema altera significativamente os valores de nível de dano econômico.


Assuntos
Fenômenos Ecológicos e Ambientais , Interações Hospedeiro-Parasita , Modelos Teóricos , Controle de Pragas
14.
Neotrop Entomol ; 38(6): 699-707, 2009.
Artigo em Inglês | MEDLINE | ID: mdl-20098914

RESUMO

Ecological modeling is an important tool for investigating dynamic behavior patterns in populations, trophic interactions, and behavioral ecology. However, the ecological patterns that reflect population oscillation trends are often not clearly visible without analytical instruments such as ecological models. Thus, ecological modeling plays a fundamental role in describing demographic processes that are important for population dynamics. Ecological models, besides making possible the visualization of ecological patterns, may also reveal patterns of population persistence in many trophic systems, including prey-predator or host-parasitoid relationships, interactions that are commonly present in integrated pest management programs. In this forum, we present the main ecological aspects important for model building and implementation of integrated pest management programs for insects. Particularly, in this study, we analyze the combination between host-parasitoid models and the concept of economic threshold level on a spatio-temporal scale. As a conclusion about the model combination, spatial structure is essential for models of this nature, since its introduction into the system significantly alters the economic threshold-level values.


Assuntos
Fenômenos Ecológicos e Ambientais , Interações Hospedeiro-Parasita , Modelos Teóricos , Controle de Pragas
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