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Introduction: Patients with locally advanced, triple-negative breast cancer (TNBC) typically receive neoadjuvant systemic therapy (NAST). However, the response of TNBC to NAST is varied and a prognostic marker is still lacking. Since angiogenesis plays an important role in cancer progression, the quantification of changes in the tumor vasculature during treatment has the potential to provide useful information for characterizing the treatment response. We have recently developed a method to quantify changes in tumor-associated vasculature through a novel analysis of dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI). In this study, we investigated its ability to monitor the response of TNBC to NAST. Methods: Dynamic contrast-enhanced (DCE) MRI was acquired in TNBC patients (N = 50; 25 pathological complete response (pCR), 25 non-pCR) before, after 2 and 4 cycles of Adriamycin/Cyclophosphamide (A/C), as part of the ARTEMIS trial (NCT02276433). Using DCE-MRI, we identified the tumor-associated vessels via a breast vasculature analysis. Specifically, the difference between pre- and post-contrast DCE-MRI images was enhanced by a histogram-based intensity transfer function. The 3D vasculature in the breast was then segmented by applying a Hessian filter. Given the vasculature segmented by the algorithms and the tumor masks segmented by radiologists, a lowest-cost tracking algorithm was used to automatically detect the vessels that are most likely to contact the tumor. These vessels are defined as tumor-associated vessels (TAV). The number of TAVs per patient was tabulated and the Wilcoxon rank sum test compared the TAV values before (V1), after 2 cycles (V2), and after 4 cycles of NAST (V3). Additionally, we compared the percent change of TAV from V1 to V3 between the pCR patients and non-pCR patients. Statistical significance was defined as P < 0.05. Results: A significant decrease in the number of TAVs was observed during the NAST. In particular, the number of TAVs has a median (interquartile range) of 15 (7 - 24), 7 (3 - 14), and 2 (0 - 8) at V1, V2, V3, respectively, which are (pair-wise) significantly different (P < 0.01). Moreover, pCR patients showed a significantly greater decrease in the number of TAVs as compared to non-pCR patients. The percent changes in the number of TAVs from V1 to V3 have a median (range) of -88.89% (-100.00% - -60.00%) and -66.67% (-87.85% - -40.88%) in the pCR and non-pCR patients, respectively (P < 0.05). Conclusion: These preliminary results demonstrate that tumor-associated vasculature may be a valuable imaging biomarker for monitoring the response of TNBC to NAST. Ongoing efforts include additional investigation of the TAVs beyond their number, as well as applying the analysis to more patients. Citation Format: Chengyue Wu, Casey E. Stowers, Zhan Xu, Ernesto A. B. F. Lima, Clinton Yam, Jong Bum Son, Jingfei Ma, Gaiane M. Rauch, Thomas E. Yankeelov. Quantification of tumor-associated vasculature as an imaging biomarker for monitoring the response of triple-negative breast cancer to neoadjuvant chemotherapy. [abstract]. In: Proceedings of the American Association for Cancer Research Annual Meeting 2023; Part 1 (Regular and Invited Abstracts); 2023 Apr 14-19; Orlando, FL. Philadelphia (PA): AACR; Cancer Res 2023;83(7_Suppl):Abstract nr 5569.

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., Low-resource settings can face additional challenges in managing the COVID-19 pandemic. Here, the authors use mathematical modelling to investigate transmission in the state of Bahia, Brazil, and quantify control measures needed to prevent the hospital system becoming overwhelmed.

Digital twins employ mathematical and computational models to virtually represent a physical object (e.g., planes and human organs), predict the behavior of the object, and enable decision-making to optimize the future behavior of the object. While digital twins have been widely used in engineering for decades, their applications to oncology are only just emerging. Due to advances in experimental techniques quantitatively characterizing cancer, as well as advances in the mathematical and computational sciences, the notion of building and applying digital twins to understand tumor dynamics and personalize the care of cancer patients has been increasingly appreciated. In this review, we present the opportunities and challenges of applying digital twins in clinical oncology, with a particular focus on integrating medical imaging with mechanism-based, tissue-scale mathematical modeling. Specifically, we first introduce the general digital twin framework and then illustrate existing applications of image-guided digital twins in healthcare. Next, we detail both the imaging and modeling techniques that provide practical opportunities to build patient-specific digital twins for oncology. We then describe the current challenges and limitations in developing image-guided, mechanism-based digital twins for oncology along with potential solutions. We conclude by outlining five fundamental questions that can serve as a roadmap when designing and building a practical digital twin for oncology and attempt to provide answers for a specific application to brain cancer. We hope that this contribution provides motivation for the imaging science, oncology, and computational communities to develop practical digital twin technologies to improve the care of patients battling cancer.

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.

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.

Simple Summary The recruitment of new vasculature via angiogenesis is a critical component of tumor development, which fundamentally influences tumor growth and response to treatment. The characterization of tumor-induced angiogenesis via mathematical models could enable approaches to forecast tumor response and improve patient care. In this review, we discuss how time-resolved imaging data integrated with mathematical modeling can be used to systematically investigate angiogenesis from the cell to tissue scale and ultimately forecast response to therapy. Abstract 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.

A mathematical analysis of local and nonlocal phase-field models of tumor growth is presented that includes time-dependent Darcy–Forchheimer–Brinkman models of convective velocity fields and models of long-range cell interactions. A complete existence analysis is provided. In addition, a parameter-sensitivity analysis is described that quantifies the sensitivity of key quantities of interest to changes in parameter values. Two sensitivity analyses are examined; one employing statistical variances of model outputs and another employing the notion of active subspaces based on existing observational data. Remarkably, the two approaches yield very similar conclusions on sensitivity for certain quantities of interest. The work concludes with the presentation of numerical approximations of solutions of the governing equations and results of numerical experiments on tumor growth produced using finite element discretizations of the full tumor model for representative cases.

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 due to probabilistic phenotypic transitions, and numerous model parameters that are difficult to measure directly 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) calibrated with 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 and data, we perform a global sensitivity analysis to identify the relative importance of the model parameters. The subsequent cgABM with a reduced parameter space 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 in model parameters and observational data. The results indicate that the cgABM can reliably predict the spatiotemporal 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 [[EQUATION]] 2.01 and 5.78 [[EQUATION]] 1.13, respectively.

Here we present a general compartment model with a time-varying transmission rate to describe the dynamics of the COVID-19 epidemic, parameterized with the demographics of Bahia, a state in northeast Brazil. The dynamics of the model are influenced by the number of asymptomatic cases, hospitalization requirements and mortality due to the disease. A locally-informed model was determined using actual hospitalization records. Together with cases and casualty data, optimized estimates for model parameters were obtained within a metaheuristic framework based on Particle Swarm Optimization. Our strategy is supported by a statistical sensitivity analysis on the model parameters, adequate to properly account for the simulated scenarios. First, we evaluated the effect of previously enforced interventions on the transmission rate. Then, we studied its effects on the number of deaths as well as hospitalization requirements, considering the state as a whole. Special attention is given to the impact of asymptomatic individuals on the dynamic of COVID-19 transmission, as these were estimated to contribute to a 68% increase in the basic reproductive number. Finally, we delineated scenarios that can set guides to protect the health care system, particularly by keeping demand below total bed occupancy. Our results underscore the challenges related to maintaining a fully capable health infrastructure during the ongoing COVID-19 pandemic, specially in a low-resource setting such as the one focused in this work. The evidences produced by our modelling-based analysis show that decreasing the transmission rate is paramount to success in maintaining health resources availability, but that current local efforts, leading to a 38% decrease in the transmission rate, are still insufficient to prevent its collapse at peak demand. Carefully planned and timely applied interventions, that result in stark decreases in transmission rate, were found to be the most effective in preventing hospital bed shortages for the longest periods.

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.

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 incompressible 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.

Neste trabalho realizamos um estudo comparativo do uso de tres metodos de in- ferencia Bayesiana em modelos matematicos estocasticos. Consideramos que nao dispomos de funcao de verossimilhanca, de modo que a calibracao e realizada tendo como base a abordagem bayesiana aproximada. Utilizamos dois metodos classicos de computacao bayesiana aproximada (ABC), o ABC Rejeicao e o ABC Monte Carlo Sequencial, e um terceiro metodo que propoe o uso conjunto de um metamodelo com o ABC, requerendo um numero limitado de simulacoes, denominado AABC. Os metodos foram utilizados para a resolucao de dois problemas inversos simples, um deles tendo solucao exata. Apesar de sensiveis a escolha dos parametros, todos os tres metodos se mostraram adequados, com o AABC apresentando potencial destaque na reducao do custo computacional.

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.

The use of mathematical and computational models for reliable predictions of tumor growth and decline in living organisms is one of the foremost challenges in modern predictive science, as it must cope with uncertainties in observational data, model selection, model parameters, and model inadequacy, all for very complex physical and biological systems. In this paper, large classes of parametric models of tumor growth in vascular tissue are discussed including models for radiation therapy. Observational data is obtained from MRI of a murine model of glioma and observed over a period of about three weeks, with X-ray radiation administered 14.5 days into the experimental program. Parametric models of tumor proliferation and decline are presented based on the balance laws of continuum mixture theory, particularly mass balance, and from accepted biological hypotheses on tumor growth. Among these are new model classes that include characterizations of effects of radiation and simple models of mechanical deformation of tumors. The Occam Plausibility Algorithm (OPAL) is implemented to provide a Bayesian statistical calibration of the model classes, 39 models in all, as well as the determination of the most plausible models in these classes relative to the observational data, and to assess model inadequacy through statistical validation processes. Discussions of the numerical analysis of finite element approximations of the system of stochastic, nonlinear partial differential equations characterizing the model classes, as well as the sampling algorithms for Monte Carlo and Markov chain Monte Carlo (MCMC) methods employed in solving the forward stochastic problem, and in computing posterior distributions of parameters and model plausibilities are provided. The results of the analyses described suggest that the general framework developed can provide a useful approach for predicting tumor growth and the effects of radiation.

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., Author summary The calibration of agent-based models of tumor cell growth to experimental data remains a challenge in computational oncology. Besides the computational cost of modeling thousands of agents, the model’s intrinsic stochasticity demands numerous realizations of the simulations to accurately represent the statistical features of the model predictions. We developed a hybrid, multiscale, coarse-grain, agent-based model that captures the growth and decline of human breast carcinoma cells under different initial conditions. We determined the effects of coarse-graining the ABM on the multiscale model output and the number of repetitions necessary to capture the stochastic transitions present in the model. We identified the most influential parameters on the model prediction through a sensitivity analysis and selected which parameters can be fixed and which ones should be calibrated. Using Bayesian calibration, we show that the model can accurately represent the experimental data. The validation step indicates that our model can reliably predict the in vitro temporal data, depending on the choice of the training (calibration data) sets.

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., Graphical Abstract ‘Two Beasts’ (2017) Artist: Ben Day Todd. Acrylic, gouache on canvas ’Two Beasts’ is an exploration of form and colour. By adding and subtracting paint, pushing and pulling colour, new information is found and previously unknown dialogues are recorded.

We present and analyze new multi-species phase-field mathematical models of tumor growth and ECM invasion. The local and nonlocal mathematical models describe the evolution of volume fractions of tumor cells, viable cells (proliferative and hypoxic cells), necrotic cells, and the evolution of matrix-degenerative enzyme (MDE) and extracellular matrix (ECM), together with chemotaxis, haptotaxis, apoptosis, nutrient distribution, and cell-to-matrix adhesion. We provide a rigorous proof of the existence of solutions of the coupled system with gradient-based and adhesion-based haptotaxis effects. In addition, we discuss finite element discretizations of the model, and we present the results of numerical experiments designed to show the relative importance and roles of various effects, including cell mobility, proliferation, necrosis, hypoxia, and nutrient concentration on the generation of MDEs and the degradation of the ECM.

Summary 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., Graphical Abstract, Bioengineering; Systems Biology; Cancer; In Silico Biology

Introduction: We show that the combination of quantitative magnetic resonance imaging (MRI) and mathematical modeling can accurately predict tumor response for individual patients, and we demonstrate the selection of personalized therapeutic regimens using our mathematical model to vary, in silico, a range of clinically feasible treatment plans to achieve the greatest tumor control. Methods: Breast cancer patients (N = 18) were scanned by MRI at three time points during neoadjuvant therapy (NAT): 1) prior to NAT, 2) after one cycle of their initial NAT regimen, and 3) after the completion of their initial NAT regimen. Specifically, diffusion-weighted MRI data characterizing tumor cellularity was collected to estimate tumor cell burden, and dynamic contrast-enhanced MRI data was collected to estimate the local drug delivery using pharmacokinetic analysis and population-derived plasma curves of the administered chemotherapies. To predict tumor response, we calibrated our tissue scale, 3D, biophysical mathematical model to each patient's MRI data set using their first two scans. Using the calibrated, patient-specific parameters, the model was projected forward to the third scan time. The predicted total tumor cellularity, volume, and longest axis were compared to the actual values measured from the patient's third scan. Following evaluation of the model's predictive ability, we then employed the model to identify potentially superior, clinically relevant, alternative dosing regimens for each patient. The alternative regimens were defined using the same total amount of drug each patient received during their standard regimen, while varying dosages and frequency between their second and third scans. Statistical analysis was completed with Pearson correlation and Wilcoxon signed rank test. Results: The model's predictions of tumor response are significantly correlated to the measured tumor burden at the time of scan 3 (r2 > 0.88, p < 0.01) for total cellularity, total volume, and longest axis. For the alternative dosing regimens assessed, the model predicted that individual patients could have achieved, on average, an additional 21% (0-46%) reduction in total cellularity. The optimal dosing regimens chosen by the model were predicted to significantly outperform standard regimens for tumor control (p < 0.001). Conclusions: These results suggest that the mathematical model can be predictive of tumor response by MRI in the clinical setting using data at the earliest times of therapy. With in silico studies, we illustrate how therapeutic regimens can be selected for individual patients for better tumor control, revealing that standard regimens may not be the most effective for every patient. These results represent a first step towards mathematically-based, personalized patient regimens. Future work aims to optimize therapy regimens via established optimal control theory methods. Citation Format: Angela M. Jarrett, Ernesto A. Lima, David A. Hormuth, Chengyue Wu, John Virostko, Anna G. Sorace, Julie C. DiCarlo, Debra Patt, Boone Goodgame, Sarah Avery, Thomas E. Yankeelov. Patient-specific neoadjuvant regimens for breast cancer identified via image-driven mathematical modeling [abstract]. In: Proceedings of the Annual Meeting of the American Association for Cancer Research 2020; 2020 Apr 27-28 and Jun 22-24. Philadelphia (PA): AACR; Cancer Res 2020;80(16 Suppl):Abstract nr 5485.

Two of the central challenges of using mathematical models for predicting the spatiotemporal development of tumors is the lack of appropriate data to calibrate the parameters of the model, and quantitative characterization of the uncertainties in both the experimental data and the modeling process itself. We present a sequence of experiments, with increasing complexity, designed to systematically calibrate the rates of apoptosis, proliferation, and necrosis, as well as mobility, within a phase-field tumor growth model. The in vitro experiments characterize the proliferation and death of human liver carcinoma cells under different initial cell concentrations, nutrient availabilities, and treatment conditions. A Bayesian framework is employed to quantify the uncertainties in model parameters. The average difference between the calibration and the data, across all time points is between 11.54% and 14.04% for the apoptosis experiments, 7.33% and 23.30% for the proliferation experiments, and 8.12% and 31.55% for the necrosis experiments. The results indicate the proposed experiment-computational approach is generalizable and appropriate for step-by-step calibration of multi-parameter models, yielding accurate estimations of model parameters related to rates of proliferation, apoptosis, and necrosis.

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.

New directions in medical and biomedical sciences have gradually emerged over recent years that will change the way diseases are diagnosed and treated and are leading to the redirection of medicine toward patient-specific treatments. We refer to these new approaches for studying biomedical systems as predictive medicine, a new version of medical science that involves the use of advanced computer models of biomedical phenomena, high-performance computing, new experimental methods for model data calibration, modern imaging technologies, cutting-edge numerical algorithms for treating large stochastic systems, modern methods for model selection, calibration, validation, verification, and uncertainty quantification, and new approaches for drug design and delivery, all based on predictive models. The methodologies are designed to study events at multiple scales, from genetic data, to sub-cellular signaling mechanisms, to cell interactions, to tissue physics and chemistry, to organs in living human subjects. The present document surveys work on the development and implementation of predictive models of vascular tumor growth, covering aspects of what might be called modeling-and-experimentally based computational oncology. The work described is that of a multi-institutional team, centered at ICES with strong participation by members at M. D. Anderson Cancer Center and University of Texas at San Antonio. This exposition covers topics on signaling models, cell and cell-interaction models, tissue models based on multi-species mixture theories, models of angiogenesis, and beginning work of drug effects. A number of new parallel computer codes for implementing finite-element methods, multi-level Markov Chain Monte Carlo sampling methods, data classification methods, stochastic PDE solvers, statistical inverse algorithms for model calibration and validation, models of events at different spatial and temporal scales is presented. Importantly, new methods for model selection in the presence of uncertainties fundamental to predictive medical science, are described which are based on the notion of Bayesian model plausibilities. Also, as part of this general approach, new codes for determining the sensitivity of model outputs to variations in model parameters are described that provide a basis for assessing the importance of model parameters and controlling and reducing the number of relevant model parameters. Model specific data is to be accessible through careful and model-specific platforms in the Tumor Engineering Laboratory. We describe parallel computer platforms on which large-scale calculations are run as well as specific time-marching algorithms needed to treat stiff systems encountered in some phase-field mixture models. We also cover new non-invasive imaging and data classification methods that provide in vivo data for model validation. The study concludes with a brief discussion of future work and open challenges.

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.

This paper presents general approaches for addressing some of the most important issues in predictive computational oncology concerned with developing classes of predictive models of tumor growth. First, the process of developing mathematical models of vascular tumors evolving in the complex, heterogeneous, macroenvironment of living tissue; second, the selection of the most plausible models among these classes, given relevant observational data; third, the statistical calibration and validation of models in these classes, and finally, the prediction of key Quantities of Interest (QOIs) relevant to patient survival and the effect of various therapies. The most challenging aspects of this endeavor is that all of these issues often involve confounding uncertainties: in observational data, in model parameters, in model selection, and in the features targeted in the prediction. Our approach can be referred to as “model agnostic” in that no single model is advocated; rather, a general approach that explores powerful mixture-theory representations of tissue behavior while accounting for a range of relevant biological factors is presented, which leads to many potentially predictive models. Then representative classes are identified which provide a starting point for the implementation of OPAL, the Occam Plausibility Algorithm (OPAL) which enables the modeler to select the most plausible models (for given data) and to determine if the model is a valid tool for predicting tumor growth and morphology (in vivo). All of these approaches account for uncertainties in the model, the observational data, the model parameters, and the target QOI. We demonstrate these processes by comparing a list of models for tumor growth, including reaction–diffusion models, phase-fields models, and models with and without mechanical deformation effects, for glioma growth measured in murine experiments. Examples are provided that exhibit quite acceptable predictions of tumor growth in laboratory animals while demonstrating successful implementations of OPAL.

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.

crescimento tumoral e resultado de uma serie de complexos fenomenos que ocorrem em multiplas escalas de tempo e espaco. Na escala sub-celular ocorre uma variedade de cascatas de reacoes moleculares que regulam as atividades celulares. Na escala da celula, destacam-se os mecanismos de agregacao, adesao e sinalizacao entre celulas e entre os componentes do microambiente. Fenomenos tipicos dos meios continuos ocorrem na escala do tecido, tais como difusao de nutrientes, fatores de crescimento, etc. Eventos que ocorrem em uma escala interferem com os que ocorrem em outras e vice-versa, de modo que o entendimento destes mecanismos e fundamental para a compreensao da doenca e para o desenvolvimento de terapias. Neste trabalho, desenvolvemos um modelo hibrido que representa fenomenos que ocorrem nas escalas tecidual e celular. A escala celular e descrita atraves de um modelo baseado em agentes (MBA), que possibilita tratar cada celula individualmente e descrever seu comportamento no microambiente. Na escala do tecido representamos a dispersao de nutrientes no meio atraves de uma equacao diferencial parcial de difusao-reacao. Sem perda de generalidade, este modelo e usado para descrever o crescimento tumoral do carcinoma avascular e experimentos computacionais sao realizados para demonstrar o potencial uso da metodologia desenvolvida.

The development of predictive computational models of tumor initiation, growth, and decline is faced with many formidable challenges. Phenomenological models which attempt to capture the complex interactions of multiple tissue and cellular species must cope with moving interfaces of heterogeneous media and the sprouting vascular structures due to angiogenesis and their evolution. They must be able to deliver predictions consistent with events that take place at cellular scales, and they must faithfully depict biological mechanisms and events that are known to be associated with various forms of cancer. In the present work, a ten-species vascular model for the tumor growth is presented which falls within the framework of phase-field (or diffuse-interface) models suggested by continuum mixture theory. This framework provides for the simultaneous treatment of interactions of multiple evolving species, such as tumor cells, necrotic cell cores, nutrients, and other cellular and tissue types that exist and interact in living tissue. We develop a hybrid model that couples the tumor growth with sprouting through angiogenesis. The model is able to represent the branching of new vessels through coupling a discrete model for which the angiogenesis is started upon pre-defined conditions on the nutrient deprivation in the continuum model. Such conditions are represented by hypoxic cells that release tumor growth factors that ultimately trigger vascular growth. We discuss the numerical approximation of the model using mixed finite elements. The results of numerical experiments are also presented and discussed.

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., This study applied principles that describe the growth dynamics of species within an ecosystem in a novel attempt to understand the growth of tumors. At low cell densities, cooperative interactions among cancer cells may influence growth in a manner reminiscent of the ecological “Allee effect,” in contrast to conventional logistic growth models.

Like every biological process, tumor development is not purely deterministic, as it is subject to random perturbations from the environment. Moreover, mathematical and computational tumor growth models are subject to uncertainties in the parameters, which may arise from experimental variations or intratumor and intrapatient heterogeneities. Tumor growth models are typically deterministic representations of growth, neglecting the aforementioned uncertainties. However, carcinogenesis must be modeled as a stochastic process to generate more informative predictions of the tumor microenvironment, which is particularly important when describing the action of various therapies. The model developed here aims to reflect the stochastic proliferation and differentiation of tumor cells. We present, for the first time, a methodology for performing a stochastic calibration of an agent-based tumor growth model. The agent-based model reproduces the interactions among different tumor cell phenotypes (e.g., proliferative and dead cells). The cell movement is driven by the balance of a variety of forces (e.g., cell-cell adhesion and repulsion) according to Newton’s second law. Transitions among cell phenotypes are defined by rules that depend on glucose concentration and time spent in each phase of cell cycle. The model captures the phenomena at the cell scale, tracking the velocity, position, and confluence, as well as the glucose concentration in the microenvironment. The experiments were done using a HER2+ breast cancer line (BT-474). Cells were seeded at a density of 3.2×104, 4.0×104 and 4.8×104 cells/well on a 96-well tissue culture plate, with four glucose levels (0, 2, 5 and 10 mM), and four replicates for each combination of initial density and glucose levels. The cells were incubated in the IncuCyte live cell imaging system (Essen BioScience, USA). Multiple images were acquired and stitched together automatically by this system with a 4× objective to obtain whole well images for each well. IncuCyte Cytotox Red Reagents (Essen BioScience, USA), a highly sensitive cyanine nucleic acid dye was added into the medium to estimate cell death. The wells were imaged every 2 hours and cell segmentation was performed in Matlab (The Mathworks, Inc., USA). Segmented images from phase-contrast and fluorescent images were employed to determine the confluence of the live cells. The dead and live cells from our agent-based model were calibrated using a Bayesian framework. The likelihood used during the calibration process considers the stochasticity from our model and the variance in the in vitro experiments. Preliminary efforts indicate the average difference between the calibrated model and the experimental data is below 5.6±4.5%. The results of the proposed model suggest that the computational framework developed can correctly calibrate the agent-based model while considering the stochasticity of the model and data. Citation Format: Ernesto A. Lima, Danial Faghihi, Russel Philley, Jianchen Yang, Jack Virostko, Thomas E. Yankeelov. Stochastic calibration of an agent-based tumor growth model using time-resolved microscopy data [abstract]. In: Proceedings of the American Association for Cancer Research Annual Meeting 2019; 2019 Mar 29-Apr 3; Atlanta, GA. Philadelphia (PA): AACR; Cancer Res 2019;79(13 Suppl):Abstract nr 2446.

We performed a computational analysis employing a cellular automata model to investigate the larval dispersal behavior of blowflies. The spatially discrete model developed here, incorporates simple behavioral rules in local interactions to produce the large-scale patterns observed in the larval dispersal process. We were able to find parameter ranges that could simulate the required experimental dispersal patterns in the study. In particular, oscillations, initially explained as a response to larval aggregation, could be explained by the combination of different mechanisms acting during the dispersal process. Peaks have characterized the interaction between dispersing larvae, but as a function of time. Then, the number of larvae decreased as a result of the pupation process, and neighborhood interaction became stingy.

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.

As a result of the highly heterogeneous tumor microenvironment and a series of complex phenomena that occur at different scales, several modeling approaches have emerged. The tumor growth models can be categorized by the behaviors they aim to capture, the hallmarks of cancer that are being considered, and the temporal and biological scales represented. Moreover, these models can also be differentiated according to the mathematical framework that is being employed, being either discrete models, continuum models, or hybrid models. Therefore, with this large set of possible models, and with each model choice having many unknown parameters, it is important to develop an adaptive model selection and validation framework in order to choose the best model for the desired application. In this work, we employ the Occam Plausibility Algorithm (OPAL) framework [1] for model selection and validation of a large body of tumor growth models. We select several continuum tumor growth models, half of them using the phase-field modeling approach, derived from the models developed in [2], and the other half being reaction-diffusion type models derived from [3]. The OPAL framework brings together model calibration, determination of sensitivities of outputs to parameter variances, and calculation of model plausibilities for model selection. Firstly, we identify the model classes and compute the sensitivity of the quantity of interest (QoI), here the tumor volume as a function of time. The models with parameters that do not influence the QoI are eliminated. The next step consists in dividing the models into Occam categories according to their number of parameters, where the models with fewer parameters are assembled to category 1. Following the principle of Occam's Razor, one of main goals of OPAL is to select the simplest model among the several models that leads to the same prediction. The models from the first category are calibrated using Bayes' rule for a specific calibration scenario. The next step is to compute the plausibilities for the models in this category and choose the most plausible model. Finally, with the most plausible model known, we solve the problem in the validation scenario. The model is valid depending on the accuracy with which the model predictions of the QoI agree with experimental data. If the model is not valid, we move to the next category; otherwise, we select this model as being the simplest and the most plausible valid model. We demonstrate that the OPAL is able to assist in the selection of the best tumor growth model from a defined set of models. The model selected is valid for particular scenarios. In this work, we consider avascular tumor growth models to reproduce the data obtained in a murine model of glioma growth. The brain data is generated with diffusion weighted magnetic resonance imaging over a period of ten days. The methodologies and results confirm that the OPAL strategy provides a powerful framework for model selection, parameters estimation, and model validation in the presence of uncertainties. References [1] K. Farrell, J. T. Oden, and D. Faghihi. A bayesian framework for adaptive selection, calibration, and validation of coarse-grained models of atomistic systems. J Comput Phys, 295(0):189 - 208, 2015. [2] E. A. B. F. Lima, J. T. Oden, and R. C. Almeida. A hybrid ten-species phase-field model of tumor growth. Math Mod Meth Appl S, 24(13):2569-2599, 2014. [3] J. A. Weis, M. I. Miga, L. R. Arlinghaus, X. Li, A. B. Chakravarthy, V. Abramson, J. Farley, and T. E. Yankeelov. A mechanically coupled reaction-diffusion model for predicting the response of breast tumors to neoadjuvant chemotherapy. Phys Med Biol, 58(17):5851-66, 2013. Citation Format: Ernesto A. B. F. Lima, Regina C. Almeida, David A. Hormuth, Thomas E. Yankeelov, J. T. Oden. Calibration, selection and validation of tumor growth models. [abstract]. In: Proceedings of the AACR Special Conference on Engineering and Physical Sciences in Oncology; 2016 Jun 25-28; Boston, MA. Philadelphia (PA): AACR; Cancer Res 2017;77(2 Suppl):Abstract nr A11.

A compartmental model was developed to describe the temporal course of an exotic amphipod's population, Talitroides topitotum, in an Atlantic Forest habitat in Brazil. Extensive biological information — including breeding pattern, development and mortality rates, and temperature dependence of the parameters — were considered in the model. A genetic algorithm was used to estimate model parameters by comparing simulation results with field data. This allowed us to discuss the reproductive strategies adopted by this species and to analyze the potential influence of global climate changes on its populations dynamics.

During long time pest control was associated only to insecticides. The formulations were produced as an attempt of improving the insect control. However, some undesirable effects emerged in this time, mainly the toxin action and resistance. Insecticides are substances produced from chemical or biological products to control insect pests. The most common mode of action for insecticides is to kill insects by blocking physiological or biochemical processes (Ware & Whitacre, 2004). Usually, insecticides act on the nervous system, resulting in high efficacy and rapid responses in pest-control programs. Insecticides can be classified as physical, protoplasmic, metabolic inhibitors, neurotoxins, and hormone agonists (Matsumura, 1985). Mineral oil is an example of a physical insecticide, and heavy metals are protoplasmic insecticides (Amiri-Besheli, 2008; Gallo et al, 2002). Some examples of metabolic inhibitors are the inhibitors of multi-function oxidases, carbohydrate and amino-acid metabolism inhibitors, and chitin-synthesis inhibitors (Krieger, 2001). The neurotoxins act through acetylcholinesterase, the neurotoxin that affects ion permeability, intervening in the nerve receptors of insects (Haynes, 1988), killing the arthropod by disrupting the membrane integrity (Gill et al, 1992). The main groups of insecticides can be studied using the following classification: neurotoxins, insect growth regulators, cellular respiration inhibitors, and others. Of the neurotoxins, the organophosphates and carbamates act on synaptic transmission, accumulating acetylcholine molecules in the synapse, which in insects can produce a cholinergic syndrome characterized by nerve hyperexcitation (Costa et al, 2008; Thacker, 2002). The acetylcholine agonists nicotines, neonicotinoids (the newest group of synthetic insecticides) and spinosines connect to the nicotine receptors of acetylcholine located in the pre-synaptic neuron (Thacker, 2002). In this case, the nerve impulses are continuously transmitted, also resulting in nerve hyper-excitation in the insect (Thacker, 2002). The acetylcholine antagonists avermectin and milbemycin block the nerve stimulus, immobilizing the insect. Cyclodienes and phenyl-pyrazoles act differently from avermectin and milbemycin, killing insects by inducing hyperexcitability (Thacker, 2002). DDT (dichlorodiphenyltrichloroethane) and pyrethroids are sodium-channel modulators, acting on sodium channels of nerve cells in insects (Thacker, 2002). Action potentials can be repetitive, 1

Made available in DSpace on 2013-08-12T18:40:40Z (GMT). No. of bitstreams: 0 Previous issue date: 2009-11-01 Made available in DSpace on 2013-09-30T18:35:28Z (GMT). No. of bitstreams: 0 Previous issue date: 2009-11-01 Submitted by Vitor Silverio Rodrigues (vitorsrodrigues@reitoria.unesp.br) on 2014-05-20T13:48:01Z No. of bitstreams: 0 Made available in DSpace on 2014-05-20T13:48:01Z (GMT). No. of bitstreams: 0 Previous issue date: 2009-11-01 Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) 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 demográfi cos 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 trófi cos, 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. 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. Univ Estadual Paulista, Inst Biociencias, Depto Bioestatist, BR-18618000 Botucatu, SP, Brazil USP, Escola Super Agr Luiz de Queiroz, Depto Entomol & Acarol, BR-13418900 Piracicaba, SP, Brazil Univ Estadual Paulista, Inst Biociencias, Depto Bioestatist, BR-18618000 Botucatu, SP, Brazil

While the past decade has seen the development of a myriad of targeted therapeutics, immunotherapies, and radiotherapy technologies, coordinated optimized delivery of novel and existing therapeutic...