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.

scholarly journals Mathematical Models for Tumor Growth and the Reduction of Overtreatment

2018 ◽  
Vol 80 (01) ◽  
pp. 072-078 ◽  
Author(s):  
Berdine Heesterman ◽  
John-Melle Bokhorst ◽  
Lisa de Pont ◽  
Berit Verbist ◽  
Jean-Pierre Bayley ◽  
...  
Keyword(s):  
Tumor Growth ◽  
Mathematical Models ◽  
Goodness Of Fit ◽  
Mean Squared Error ◽  
Age At Onset ◽  
Growth Curves ◽  
Magnetic Resonance Images ◽  
Coefficient Of Determination ◽  
Growth Data ◽  
Significant Difference

Background To improve our understanding of the natural course of head and neck paragangliomas (HNPGL) and ultimately differentiate between cases that benefit from early treatment and those that are best left untreated, we studied the growth dynamics of 77 HNPGL managed with primary observation. Methods Using digitally available magnetic resonance images, tumor volume was estimated at three time points. Subsequently, nonlinear least squares regression was used to fit seven mathematical models to the observed growth data. Goodness of fit was assessed with the coefficient of determination (R 2) and root-mean-squared error. The models were compared with Kruskal–Wallis one-way analysis of variance and subsequent post-hoc tests. In addition, the credibility of predictions (age at onset of neoplastic growth and estimated volume at age 90) was evaluated. Results Equations generating sigmoidal-shaped growth curves (Gompertz, logistic, Spratt and Bertalanffy) provided a good fit (median R 2: 0.996–1.00) and better described the observed data compared with the linear, exponential, and Mendelsohn equations (p < 0.001). Although there was no statistically significant difference between the sigmoidal-shaped growth curves regarding the goodness of fit, a realistic age at onset and estimated volume at age 90 were most often predicted by the Bertalanffy model. Conclusions Growth of HNPGL is best described by decelerating tumor growth laws, with a preference for the Bertalanffy model. To the best of our knowledge, this is the first time that this often-neglected model has been successfully fitted to clinically obtained growth data.

scholarly journals Mathematical models to describe the growth curves of white-egg layers

2018 ◽  
Vol 39 (3) ◽  
pp. 1327
Author(s):  
Cleber Franklin Santos de Oliveira ◽  
João Marcos Novais Tavares ◽  
Gerusa Da Silva Salles Corrêa ◽  
Bruno Serpa Vieira ◽  
Silvana Alves Pedrozo Vitalino Barbosa ◽  
...  
Keyword(s):  
Mathematical Models ◽  
Mean Squared Error ◽  
Computer Software ◽  
Logistic Models ◽  
Growth Curves ◽  
Gompertz Model ◽  
Information Criterion ◽  
Coefficient Of Determination ◽  
Population Densities

The aim of this study was to compare mathematical models describing growth curves of white-egg layers at different population densities. To fit the models, 4,000 growing white-egg layers were utilized. The experimental design was completely randomized, with population densities of 71, 68, 65, 62, and 59 birds per cage in the starter phase and 19, 17, 15, 13, and 11 birds per cage in the grower phase, with 10 replicates each. Birds were weighed weekly to determine the average body weight and the weight gain. Gompertz and Logistic models were utilized to estimate their growth. The data analysis was carried out using the PROC NLMIXED procedure of the SAS® statistical computer software to estimate the parameters of the equation because mixed models were employed. The mean squared error, the coefficient of determination, and Akaike’s information criterion were used to evaluate the quality of fit of the models. The studied models converged for the description of the growth of the birds at the different densities studied, showing that they were appropriate for estimating the growth of white-egg layers housed at different population densities. The Gompertz model showed a better fit than the Logistic model.

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.

Growth and Modeling of Staphylococcus aureus in Flour Products under Isothermal and Nonisothermal Conditions

2017 ◽  
Vol 80 (3) ◽  
pp. 523-531
Author(s):  
Hui Cao ◽  
Tingting Wang ◽  
Min Yuan ◽  
Jingsong Yu ◽  
Fei Xu
Keyword(s):  
Staphylococcus Aureus ◽  
Goodness Of Fit ◽  
Storage Temperature ◽  
Growth Curves ◽  
Gompertz Model ◽  
Growth Data ◽  
Safety Standards ◽  
Bias Factor ◽  
Steamed Bread ◽  
Nonisothermal Conditions

ABSTRACT This study was conducted to investigate the growth of Staphylococcus aureus in traditional Chinese flour products under isothermal (10, 15, 20, 25, 30, and 37°C) and nonisothermal (10 to 20, 20 to 30, and 25 to 37°C) conditions. Then, models for the growth of S. aureus in flour products as a function of storage temperature, pH, and water activity (aw) were developed, and the goodness of fit of models was evaluated using the determination coefficient (R2), root mean square error (RMSE), bias factor (Bf), and accuracy factor (Af). Based on the above information, S. aureus growth in steamed bread under nonisothermal conditions was predicted from experiments performed under isothermal conditions. It was shown that different combinations of temperature and aw in flour products have a strong influence on the growth of S. aureus. The modified Gompertz model was found to be more suitable for describing the growth data of S. aureus in flour products, with an R2 of &gt;0.99 and an RMSE of &lt;0.37. The newly developed secondary models were validated, and for the specific growth rate and the lag time, the R2 values were 0.96 and 0.97, Af was 1.12 and 1.06, and Bf was 1.13 and 1.05, respectively. The predicted nonisothermal growth curves of S. aureus were in agreement with the reported experimental ones, with RMSE &lt;0.29, Af value 1.02 to 1.09, and Bf value 0.92 to 0.99. These results indicated that the predictive models provided useful information for the establishment of safety standards and a risk assessment for S. aureus in flour products.

An on-lattice agent-based Monte Carlo model simulating the growth kinetics of multicellular tumor spheroids

2020 ◽  
Vol 77 ◽  
pp. 194-203
Author(s):  
S. Ruiz-Arrebola ◽  
A.M. Tornero-López ◽  
D. Guirado ◽  
M. Villalobos ◽  
A.M. Lallena
Keyword(s):  
Monte Carlo ◽  
Growth Kinetics ◽  
Monte Carlo Model ◽  
Multicellular Tumor Spheroids ◽  
Tumor Spheroids ◽  
Agent Based ◽  
Kinetics Of

scholarly journals Simulating Market Entry Rewards for Antibiotics Development

2018 ◽  
Vol 46 (S1) ◽  
pp. 32-42 ◽  
Author(s):  
Christopher Okhravi ◽  
Simone Callegari ◽  
Steve McKeever ◽  
Carl Kronlid ◽  
Enrico Baraldi ◽  
...  
Keyword(s):  
Sensitivity Analysis ◽  
Monte Carlo ◽  
Research And Development ◽  
Market Entry ◽  
Monte Carlo Model ◽  
Clinical Development ◽  
Policy Intervention ◽  
Venture Capitalists ◽  
Agent Based ◽  
Reducing Costs

We design an agent based Monte Carlo model of antibiotics research and development (R&D) to explore the effects of the policy intervention known as Market Entry Reward (MER) on the likelihood that an antibiotic entering pre-clinical development reaches the market. By means of sensitivity analysis we explore the interaction between the MER and four key parameters: projected net revenues, R&D costs, venture capitalists discount rates, and large pharmaceutical organizations' financial thresholds. We show that improving revenues may be more efficient than reducing costs, and thus confirm that this pull-based policy intervention effectively stimulates antibiotics R&D.

Monte Carlo model for describing charge transfer in irradiated CCDs

1998 ◽  
Author(s):  
Dennis J. Gallagher ◽  
Raymond Demara ◽  
Gary Emerson ◽  
Wayne W. Frame ◽  
Alan W. Delamere
Keyword(s):  
Monte Carlo ◽  
Charge Transfer ◽  
Monte Carlo Model

Monte Carlo model of multi-site adsorption

1985 ◽  
Vol 8 (7) ◽  
pp. 364-365 ◽  
Author(s):  
J. Sedláček ◽  
L. Nondek
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Model
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