Continuum versus discrete model: a comparison for multicellular tumour spheroids

2006 ◽  
Vol 364 (1843) ◽  
pp. 1443-1464 ◽  
Author(s):  
Gernot Schaller ◽  
Michael Meyer-Hermann
Keyword(s):  
Growth Curves ◽  
Cell Number ◽  
Nutrient Concentrations ◽  
Model Parameters ◽  
Agent Based Model ◽  
Growth Data ◽  
Agent Based ◽  
Pde Model ◽  
Viable Cells ◽  
Tumour Spheroids

We study multicellular tumour spheroids with a continuum model based on partial differential equations (PDEs). The model includes viable and necrotic cell densities, as well as oxygen and glucose concentrations. Viable cells consume nutrients and become necrotic below critical nutrient concentrations. Proliferation of viable cells is contact-inhibited if the total cellular density locally exceeds volume carrying capacity. The model is discussed under the assumption of spherical symmetry. Unknown model parameters are determined by simultaneously fitting the cell number to several experimental growth curves for different nutrient concentrations. The outcome of the PDE model is compared with an analogous off-lattice agent-based model for tumour growth. It turns out that the numerically more efficient PDE model suffices to explain the macroscopic growth data. As in the agent-based model, we find that the experimental growth curves are only reproduced when a necrotic core develops. However, evaluation of morphometric properties yields differences between the models and the experiment.

scholarly journals A MODEL OF DYNAMIC REWIRING AND KNOWLEDGE EXCHANGE IN R&D NETWORKS

2016 ◽  
Vol 19 (01n02) ◽  
pp. 1650004 ◽  
Author(s):  
MARIO V. TOMASELLO ◽  
CLAUDIO J. TESSONE ◽  
FRANK SCHWEITZER
Keyword(s):  
Network Performance ◽  
Formation Rate ◽  
Knowledge Exchange ◽  
Model Parameters ◽  
Agent Based Model ◽  
Knowledge Space ◽  
Interaction Radius ◽  
Agent Based ◽  
Knowledge Stocks ◽  
Alliance Partners

This paper investigates the process of knowledge exchange in inter-firm Research and Development (R&D) alliances by means of an agent-based model. Extant research has pointed out that firms select alliance partners considering both network-related and network-unrelated features (e.g., social capital versus complementary knowledge stocks). In our agent-based model, firms are located in a metric knowledge space. The interaction rules incorporate an exploration phase and a knowledge transfer phase, during which firms search for a new partner and then evaluate whether they can establish an alliance to exchange their knowledge stocks. The model parameters determining the overall system properties are the rate at which alliances form and dissolve and the agents’ interaction radius. Next, we define a novel indicator of performance, based on the distance traveled by the firms in the knowledge space. Remarkably, we find that — depending on the alliance formation rate and the interaction radius — firms tend to cluster around one or more attractors in the knowledge space, whose position is an emergent property of the system. And, more importantly, we find that there exists an inverted U-shaped dependence of the network performance on both model parameters.

scholarly journals Understanding transmission and control of the pork tapeworm with CystiAgent: a spatially explicit agent-based model

2020 ◽  
Author(s):  
Ian Wright Pray ◽  
Wayne Wakeland ◽  
William Pan ◽  
William E. Lambert ◽  
Hector H. Garcia ◽  
...  
Keyword(s):  
Taenia Solium ◽  
Model Performance ◽  
Rank Correlation ◽  
Public Health Problem ◽  
Sensitivity Analyses ◽  
Transmission Model ◽  
Spatially Explicit ◽  
Model Parameters ◽  
Agent Based Model ◽  
Agent Based

Abstract Background The pork tapeworm ( Taenia solium ) is a serious public health problem in rural low-resource areas of Latin America, Africa, and Asia, where the associated conditions of nuerocysticercosis (NCC) and porcine cysticercosis cause substantial health and economic harms. An accurate and validated transmission model for T. solium would serve as an important new tool for control and elimination, as it would allow for comparison of available intervention strategies, and prioritization of the most effective strategies for control and elimination efforts. Methods We developed a spatially-explicit agent-based model (ABM) for T. solium (“CystiAgent”) that differs from prior T. solium models by including a spatial framework and behavioral parameters such as pig roaming, open human defecation, and human travel. In this article, we introduce the structure and function of the model, describe the data sources used to parameterize the model, and apply sensitivity analyses (Latin hypercube sampling–partial rank correlation coefficient (LHS-PRCC)) to evaluate model parameters. Results LHS-PRCC analysis of CystiAgent found that the parameters with the greatest impact on model uncertainty were the roaming range of pigs, the infectious duration of human taeniasis, use of latrines, and the set of “tuning” parameters defining the probabilities of infection in humans and pigs given exposure to T. solium. Conclusions CystiAgent is a novel ABM that has the ability to model spatial and behavioral features of T. solium transmission not available in other models. There is a small set of impactful model parameters that contribute uncertainty to the model and may impact the accuracy of model projections. Field and laboratory studies to better understand these key components of transmission may help reduce uncertainty, while current applications of CystiAgent may consider calibration of these parameters to improve model performance. These results will ultimately allow for improved interpretation of model validation results, and usage of the model to compare available control and elimination strategies for T. solium .

Dynamic child growth prediction: A comparative methods approach

2017 ◽  
Vol 17 (6) ◽  
pp. 468-493 ◽  
Author(s):  
Andrada E Ivanescu ◽  
Ciprian M Crainiceanu ◽  
William Checkley
Keyword(s):  
Regression Models ◽  
Prediction Models ◽  
Growth Curves ◽  
Child Growth ◽  
Prediction Performance ◽  
Model Parameters ◽  
Supplementary File ◽  
Functional Regression ◽  
Growth Data ◽  
Missing Data Imputation

Abstract: We introduce a class of dynamic regression models designed to predict the future of growth curves based on their historical dynamics. This class of models incorporates both baseline and time-dependent covariates, start with simple regression models and build up to dynamic function-on-function regressions. We compare the performance of the dynamic prediction models in a variety of signal-to-noise scenarios and provide practical solutions for model selection. We conclude that (a) prediction performance increases substantially when using the entire growth history relative to using only the last and first observation; (b) smoothing incorporated using functional regression approaches increases prediction performance; and (c) the interpretation of model parameters is substantially improved using functional regression approaches. Because many growth curve datasets exhibit missing and noisy data, we propose a bootstrap of subjects approach to account for the variability associated with the missing data imputation and smoothing. Methods are motivated by and applied to the CONTENT dataset, a study that collected monthly child growth data on 197 children from birth until month 15. R code describing the fitting approaches is provided in a supplementary file.

scholarly journals An Agent-Based Model of monocyte differentiation into Tumour-Associated Macrophages in Chronic Lymphocytic Leukemia

2021 ◽  
Author(s):  
Nina Verstraete ◽  
Malvina Marku ◽  
Marcin Domagala ◽  
Julie Bordenave ◽  
H&eacutelène Arduin ◽  
...  
Keyword(s):  
Chronic Lymphocytic Leukemia ◽  
Cancer Cells ◽  
Mononuclear Cells ◽  
Lymphocytic Leukemia ◽  
Leukemic Cells ◽  
Patient Specific ◽  
Model Parameters ◽  
Agent Based Model ◽  
Agent Based ◽  
Monocyte Differentiation

Monocyte-derived macrophages are immune cells which help maintain tissue homeostasis and defend the organism against pathogens. In solid tumours, recent studies have uncovered complex macrophage populations, among which tumour-associated macrophages, supporting tumorigenesis through multiple cancer hallmarks such as immunosuppression, angiogenesis or matrix remodelling. In the case of chronic lymphocytic leukemia, these macrophages are known as nurse-like cells and have been shown to protect leukemic cells from spontaneous apoptosis and contribute to their chemoresistance. We propose an agent-based model of monocytes differentiation into nurse-like cells upon contact with leukemic B cells in-vitro. We studied monocyte differentiation and cancer cells survival dynamics depending on diverse hypotheses on monocytes and cancer cells relative proportions, sensitivity to their surrounding environment and cell-cell interactions. Peripheral blood mononuclear cells from patients were cultured and monitored during 13 days to calibrate the model parameters, such as phagocytosis efficiency, death rates or protective effect from the nurse-like cells. Our model is able to reproduce experimental results and predict cancer cells survival dynamics in a patient-specific manner. Our results shed light on important factors at play in cancer cells survival, highlighting a potentially important role of phagocytosis.

scholarly journals An agent-based model for drug-radiation interactions in the tumour microenvironment: Hypoxia-activated prodrug SN30000 in multicellular tumour spheroids

2018 ◽  
Vol 14 (10) ◽  
pp. e1006469 ◽  
Author(s):  
Xinjian Mao ◽  
Sarah McManaway ◽  
Jagdish K. Jaiswal ◽  
Priyanka B. Patel ◽  
William R. Wilson ◽  
...  
Keyword(s):  
Tumour Microenvironment ◽  
Agent Based Model ◽  
Agent Based ◽  
Tumour Spheroids

scholarly journals Evaluation of Classical Mathematical Models of Tumor Growth Using an On-Lattice Agent-Based Monte Carlo Model

2021 ◽  
Vol 11 (11) ◽  
pp. 5241
Author(s):  
Samuel Ruiz-Arrebola ◽  
Damián Guirado ◽  
Mercedes Villalobos ◽  
Antonio M. Lallena
Keyword(s):  
Monte Carlo ◽  
Mathematical Models ◽  
Monte Carlo Model ◽  
Growth Curves ◽  
Gompertz Model ◽  
Growth Data ◽  
Multicellular Spheroids ◽  
Agent Based ◽  
Simulation Parameters ◽  
Pseudo Data

Purpose:To analyze the capabilities of different classical mathematical models to describe the growth of multicellular spheroids simulated with an on-lattice agent-based Monte Carlo model that has already been validated. Methods: The exponential, Gompertz, logistic, potential, and Bertalanffy models have been fitted in different situations to volume data generated with a Monte Carlo agent-based model that simulates the spheroid growth. Two samples of pseudo-data, obtained by assuming different variability in the simulation parameters, were considered. The mathematical models were fitted to the whole growth curves and also to parts of them, thus permitting to analyze the predictive power (both prospective and retrospective) of the models. Results: The consideration of the data obtained with a larger variability of the simulation parameters increases the width of the χ2 distributions obtained in the fits. The Gompertz model provided the best fits to the whole growth curves, yielding an average value of the χ2 per degree of freedom of 3.2, an order of magnitude smaller than those found for the other models. Gompertz and Bertalanffy models gave a similar retrospective prediction capability. In what refers to prospective prediction power, the Gompertz model showed by far the best performance. Conclusions: The classical mathematical models that have been analyzed show poor prediction capabilities to reproduce the MTS growth data not used to fit them. Within these poor results, the Gompertz model proves to be the one that better describes the growth data simulated. The simulation of the growth of tumors or multicellular spheroids permits to have follow-up periods longer than in the usual experimental studies and with a much larger number of samples: this has permitted performing the type of analysis presented here.

Understanding the dynamics of inter-provincial migration in the Mekong Delta, Vietnam: an agent-based modeling study

SIMULATION ◽  
2021 ◽  
pp. 003754972097512
Author(s):  
Hung Khanh Nguyen ◽  
Raymond Chiong ◽  
Manuel Chica ◽  
Richard H Middleton
Keyword(s):  
Rural Areas ◽  
Large Scale ◽  
Mekong Delta ◽  
Model Parameters ◽  
Migration Behavior ◽  
Agent Based Model ◽  
Contributing Factors ◽  
Factors Affecting ◽  
Agent Based ◽  
Migration Flows

Recent large-scale migration flows from rural areas of the Mekong Delta (MKD) to larger cities in the South-East (SE) region of Vietnam have created the largest migration corridor in the country. This migration trend has further contributed to greater rural–urban disparities and widened the development gap between regions. In this study, our aim is to understand the migration dynamics and determine the most critical factors affecting the behavior of migrants in the MKD region. We present an agent-based model and incorporate the Theory of Planned Behavior to effectively break down migration intention into related components and contributing factors. A genetic algorithm is used for automated calibration and sensitivity analysis of model parameters, in order to validate our agent-based model. We further explore the migration behavior of people in certain demographic groups and delineate migration flows across cities and provinces from the MKD to the SE region.

scholarly journals Remarks on the Behavior of an Agent-Based Model of Spatial Distribution of Species

2021 ◽  
Vol 5 (2) ◽  
pp. 37-49
Author(s):  
João Bioco ◽  
Paula Prata ◽  
Fernando Cánovas ◽  
Paulo Fazendeiro
Keyword(s):  
Complex System ◽  
Spatial Distribution ◽  
Life Cycle ◽  
Point Of View ◽  
Emergent Behavior ◽  
Model Parameters ◽  
Simulation Approach ◽  
Agent Based Model ◽  
Agent Based ◽  
Environment Variables

Agent-based models have gained considerable notoriety in ecological modeling as well as in several other fields yearning for the ability to capture the emergent behavior of a complex system in which individuals interact with each other and with their environment. These models are implemented by applying a bottom-up approach, where the entire behavior of the system emerges from the local interaction between their components (agents or individuals). Usually, these interactions between individuals and their enclosing environment are modeled by very simple local rules. From the conceptual point of view, another appealing characteristic of this simulation approach is that it is well aligned with the reality whenever the system is composed of a multitude of individuals (behavioral units) that can be flexibly combined and placed in the environment. Due to their inherent flexibility, and despite of their simplicity, it is necessary to pay attention to the adjustments in their parameters which may result in unforeseen changes on the overall behavior of these models. In this paper we study the behavior of an agent-based model of spatial distribution of species, by analyzing the effects of the model parameters and the implications of the environment variables (that compose the environment where the species lives) on the models’ output. The presented experiments show that the behavior of the model depends mainly on the conditions of the environment where the species live, and the main parameters presented in life cycle of the species.

scholarly journals Understanding transmission and control of the pork tapeworm with CystiAgent: a spatially explicit agent-based model

2020 ◽  
Author(s):  
Ian Wright Pray ◽  
Wayne Wakeland ◽  
William Pan ◽  
William E. Lambert ◽  
Hector H. Garcia ◽  
...  
Keyword(s):  
Taenia Solium ◽  
Model Performance ◽  
Rank Correlation ◽  
Public Health Problem ◽  
Sensitivity Analyses ◽  
Transmission Model ◽  
Spatially Explicit ◽  
Model Parameters ◽  
Agent Based Model ◽  
Agent Based

Abstract BackgroundThe pork tapeworm (Taenia solium) is a serious public health problem in rural low-resource areas of Latin America, Africa, and Asia, where the associated conditions of nuerocysticercosis (NCC) and porcine cysticercosis cause substantial health and economic harms. An accurate and validated transmission model for T. solium would serve as an important new tool for control and elimination, as it would allow for comparison of available intervention strategies, and prioritization of the most effective strategies for control and elimination efforts. MethodsWe developed a spatially-explicit agent-based model (ABM) for T. solium (“CystiAgent”) that differs from prior T. solium models by including a spatial framework and behavioral parameters such as pig roaming, open human defecation, and human travel. In this article, we introduce the structure and function of the model, describe the data sources used to parameterize the model, and apply sensitivity analyses (Latin hypercube sampling–partial rank correlation coefficient (LHS-PRCC)) to evaluate model parameters. ResultsLHS-PRCC analysis of CystiAgent found that the parameters with the greatest impact on model uncertainty were the roaming range of pigs, the infectious duration of human taeniasis, use of latrines, and the set of “tuning” parameters defining the probabilities of infection in humans and pigs given exposure to T. solium.ConclusionsCystiAgent is a novel ABM that has the ability to model spatial and behavioral features of T. solium transmission not available in other models. There is a small set of impactful model parameters that contribute uncertainty to the model and may impact the accuracy of model projections. Field and laboratory studies to better understand these key components of transmission may help reduce uncertainty, while current applications of CystiAgent may consider calibration of these parameters to improve model performance. These results will ultimately allow for improved interpretation of model validation results, and usage of the model to compare available control and elimination strategies for T. solium.

scholarly journals Agent-based model illustrates the role of the microenvironment in regeneration in healthy and mdx skeletal muscle

2018 ◽  
Vol 125 (5) ◽  
pp. 1424-1439 ◽  
Author(s):  
Kelley M. Virgilio ◽  
Kyle S. Martin ◽  
Shayn M. Peirce ◽  
Silvia S. Blemker
Keyword(s):  
Skeletal Muscle ◽  
Stem Cell ◽  
Muscle Wasting ◽  
Cross Sectional Area ◽  
Model Parameters ◽  
Sectional Area ◽  
Agent Based Model ◽  
Cross Sectional ◽  
Agent Based ◽  
Initial Injury

Duchenne muscular dystrophy (DMD) is a progressive muscle-wasting disease with no effective treatment. Multiple mechanisms are thought to contribute to muscle wasting, including increased susceptibility to contraction-induced damage, chronic inflammation, fibrosis, altered satellite stem cell (SSC) dynamics, and impaired regenerative capacity. The goals of this project were to 1) develop an agent-based model of skeletal muscle that predicts the dynamic regenerative response of muscle cells, fibroblasts, SSCs, and inflammatory cells as a result of contraction-induced injury, 2) calibrate and validate the model parameters based on comparisons with published experimental measurements, and 3) use the model to investigate how changing isolated and combined factors known to be associated with DMD (e.g., altered fibroblast or SSC behaviors) influence muscle regeneration. Our predictions revealed that the percent of injured muscle that recovered 28 days after injury was dependent on the peak SSC counts following injury. In simulations with near-full cross-sectional area recovery (healthy, 4-wk mdx, 3-mo mdx), the SSC counts correlated with the extent of initial injury; however, in simulations with impaired regeneration (9-mo mdx), the peak SSC counts were suppressed relative to initial injury. The differences in SSC counts between these groups were emergent predictions dependent on altered microenvironment factors known to be associated with DMD. Multiple cell types influenced the peak number of SSCs, but no individual parameter predicted the differences in SSC counts. This finding suggests that interventions to target the microenvironment rather than SSCs directly could be an effective method for improving regeneration in impaired muscle. NEW & NOTEWORTHY A computational model predicted that satellite stem cell (SSC) counts are correlated with muscle cross-sectional area (CSA) recovery following injury. In simulations with impaired CSA recovery, SSC counts are suppressed relative to healthy muscle. The suppressed SSC counts were an emergent model prediction, because all simulations had equal initial SSC counts. Fibroblast and anti-inflammatory macrophage counts influenced SSC counts, but no single factor was able to predict the pathological differences in SSC counts that lead to impaired regeneration.

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