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Multilevel and quasi-Monte Carlo methods for uncertainty quantification in particle travel times through random heterogeneous porous media.

ABSTRACT: In this study, we apply four Monte Carlo simulation methods, namely, Monte Carlo, quasi-Monte Carlo, multilevel Monte Carlo and multilevel quasi-Monte Carlo to the problem of uncertainty quantification in the estimation of the average travel time during the transport of particles through random heterogeneous porous media. We apply the four methodologies to a model problem where the only input parameter, the hydraulic conductivity, is modelled as a log-Gaussian random field by using direct Karhunen-Loéve decompositions. The random terms in such expansions represent the coefficients in the equations. Numerical calculations demonstrating the effectiveness of each of the methods are presented. A comparison of the computational cost incurred by each of the methods for three different tolerances is provided. The accuracy of the approaches is quantified via the mean square error.

SUBMITTER: Crevillen-Garcia D

PROVIDER: S-EPMC5579089 | biostudies-literature | 2017 Aug

REPOSITORIES: biostudies-literature

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Multilevel and quasi-Monte Carlo methods for uncertainty quantification in particle travel times through random heterogeneous porous media.

Crevillén-García D D Power H H

Royal Society open science 20170809 8

In this study, we apply four Monte Carlo simulation methods, namely, Monte Carlo, quasi-Monte Carlo, multilevel Monte Carlo and multilevel quasi-Monte Carlo to the problem of uncertainty quantification in the estimation of the average travel time during the transport of particles through random heterogeneous porous media. We apply the four methodologies to a model problem where the only input parameter, the hydraulic conductivity, is modelled as a log-Gaussian random field by using direct Karhun ...[more]

PMID: 28878974

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Project description:BackgroundFor medication control in several jurisdictions, withdrawal time is the period of refrain from racing after drug administration. It is set by adding a safety period to an experimental detection time. However, there are no reports of statistical analyses of detection time for the determination of withdrawal time in flunixin meglumine-treated horses.ObjectiveTo analyse the population pharmacokinetics of flunixin in horses through the generation of a dataset for detection time statistical analysis and predictions via Monte Carlo simulation.Study designExperimental study.MethodsDrug plasma and urine concentrations following single intravenous administration of flunixin 1.1 mg/kg bodyweight (BW) in 10 horses and multiple administration of q 24 hours for 5 days in 10 horses were measured using liquid chromatography with tandem mass spectrometry (LC-MS/MS). Data were modelled using a nonlinear mixed effect model followed by Monte Carlo simulation. Irrelevant plasma concentration (IPC) and irrelevant urine concentration (IUC) were calculated using the Toutain approach. Detection times were obtained considering the time after the last administration for selected quantiles of 5000 hypothetical horses under the international screening limit (ISL) proposed by the International Federation of Horseracing Authorities (plasma: 1 ng/mL, urine; 100 ng/mL).ResultsFor a regimen of 1.1 mg/kg BW q 24 hours, the IPC and IUC values were 2.0 and 73.0 ng/mL respectively. Detection times in plasma above the ISL for 90% of simulated horses were estimated as 74 hours after a single 1.1 mg/kg dose administration, 149 and 199 hours after multiple doses over 5 days at either 24- or 12-hour intervals respectively. Corresponding detection times in urine were 46, 68 and 104 hours respectively.Main limitationOnly female horses were investigated.ConclusionsStatistical detection times for different flunixin meglumine regimens indicated a delay of detection time in plasma after multiple administrations under ISL.

Dataset Information

Multilevel and quasi-Monte Carlo methods for uncertainty quantification in particle travel times through random heterogeneous porous media.

Publications

Multilevel and quasi-Monte Carlo methods for uncertainty quantification in particle travel times through random heterogeneous porous media.

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