scholarly journals Optimal Design for Estimating Parameters of the 4-Parameter Hill Model

2003 ◽  
Vol 1 (3) ◽  
pp. 154014203902499 ◽  
Author(s):  
Leonid A. Khinkis ◽  
Laurence Levasseur ◽  
Hélène Faessel ◽  
William R. Greco
Keyword(s):  
Laboratory Experiments ◽  
Confidence Region ◽  
Middle Part ◽  
Optimal Designs ◽  
Parameter Estimates ◽  
Hill Model ◽  
Estimated Parameters ◽  
The Hill ◽  
Parameter Values ◽  
True Values

Many drug concentration-effect relationships are described by nonlinear sigmoid models. The 4-parameter Hill model, which belongs to this class, is commonly used. An experimental design is essential to accurately estimate the parameters of the model. In this report we investigate properties of D-optimal designs. D-optimal designs minimize the volume of the confidence region for the parameter estimates or, equivalently, minimize the determinant of the variance-covariance matrix of the estimated parameters. It is assumed that the variance of the random error is proportional to some power of the response. To generate D-optimal designs one needs to assume the values of the parameters. Even when these preliminary guesses about the parameter values are appreciably different from the true values of the parameters, the D-optimal designs produce satisfactory results. This property of D-optimal designs is called robustness. It can be quantified by using D-efficiency. A five-point design consisting of four D-optimal points and an extra fifth point is introduced with the goals to increase robustness and to better characterize the middle part of the Hill curve. Four-point D-optimal designs are then compared to five-point designs and to log-spread designs, both theoretically and practically with laboratory experiments. D-optimal designs proved themselves to be practical and useful when the true underlying model is known, when good prior knowledge of parameters is available, and when experimental units are dear. The goal of this report is to give the practitioner a better understanding for D-optimal designs as a useful tool for the routine planning of laboratory experiments.

Optimized blood sampling protocols and sequential design of kinetic experiments

1981 ◽  
Vol 240 (5) ◽  
pp. R259-R265 ◽  
Author(s):  
J. J. DiStefano
Keyword(s):  
Endocrine System ◽  
Primary Objective ◽  
Blood Sampling ◽  
Optimal Designs ◽  
Parameter Estimates ◽  
Model Parameters ◽  
Reverse T3 ◽  
Model Parameter ◽  
Maximum Accuracy ◽  
Sampling Protocols

Design of optimal blood sampling protocols for kinetic experiments is discussed and evaluated, with the aid of several examples--including an endocrine system case study. The criterion of optimality is maximum accuracy of kinetic model parameter estimates. A simple example illustrates why a sequential experiment approach is required; optimal designs depend on the true model parameter values, knowledge of which is usually a primary objective of the experiment, as well as the structure of the model and the measurement error (e.g., assay) variance. The methodology is evaluated from the results of a series of experiments designed to quantify the dynamics of distribution and metabolism of three iodothyronines, T3, T4, and reverse-T3. This analysis indicates that 1) the sequential optimal experiment approach can be effective and efficient in the laboratory, 2) it works in the presence of reasonably controlled biological variation, producing sufficiently robust sampling protocols, and 3) optimal designs can be highly efficient designs in practice, requiring for maximum accuracy a number of blood samples equal to the number of independently adjustable model parameters, no more or less.

Kinetics and physiological characteristics of autotrophic dentrification by denitrifying sulfur bacteria

2000 ◽  
Vol 42 (3-4) ◽  
pp. 59-68 ◽  
Author(s):  
S.-E. Oh ◽  
K.-S. Kim ◽  
H.-C. Choi ◽  
J. Cho ◽  
I.S. Kim
Keyword(s):  
Gas Production ◽  
Parameter Estimates ◽  
Production Volume ◽  
Autotrophic Denitrification ◽  
Nonlinear Regression Analysis ◽  
Monod Equation ◽  
Sulfur Bacteria ◽  
The Media ◽  
Parameter Values ◽  
Mixotrophic Conditions

To study the kinetics and physiology of autotrophic denitrifying sulfur bacteria, a steady-state anaerobic master culture reactor (MCR) was operated for over six months under a semi-continuous mode and nitrate limiting conditions using nutrient/mineral/buffer (NMB) medium containing thiosulfate and nitrate. Characteristics of the autotropic denitrifier were investigated through the cumulative gas production volume and rate, measured using an anaerobic respirometer, and through the nitrate, nitrite, and sulfate concentrations within the media. The bio-kinetic parameters were obtained based upon the Monod equation using mixed cultures in the MCR. Nonlinear regression analysis was employed using nitrate depletion and biomass production curves. Although this analysis did not yield exact biokinetic parameter estimates, the following ranges for the parameter values were obtained: μmax =0.12-0.2 hr-1; k=0.3-0.4 hr-1; Ks=3-10mg/L; YNO3=0.4-0.5mg Biomass/mg NO3--N. Inhibition of denitrification occurred when the concentrations of NO3--N, and SO42- reached about 660mg/L and 2,000mg/L, respectively. The autotrophic denitrifying sulfur bacteria were observed to be very sensitive to nitrite but relatively tolerant of nitrate, sulfate, and thiosulfate. Under mixotrophic conditions, denitrification by these bacteria occurred autotrophically; even with as high as 2 g COD, autotrophic denitrification was not significantly affected. The optimal pH and temperature for autotrophic denitrification was about 6.5–7.5 and 33–35 °C, respectively.

scholarly journals SENSIBILIDAD DE LA GARRAPATA COMÚN DEL BOVINO Rhipicephalus (Boophilus) microplus A IVERMECTINA ESTIMADA CON EL MODELO SIGMOIDEO DE RESPUESTA MÁXIMA O DE HILL

2021 ◽  
Vol 19 (suplemento) ◽  
Author(s):  
J Torrents
Keyword(s):  
Statistical Analysis ◽  
Boophilus Microplus ◽  
Susceptible Strain ◽  
Maximum Response ◽  
Hill Coefficient ◽  
Concentration Effect ◽  
Hill Model ◽  
Low Concentration ◽  
Immersion Technique ◽  
The Hill

The aim of this study was to obtain pharmacodynamics parameters to detect resistance or susceptibility of R. microplus strains to ivermectin (IVM). Two larvae samples; a susceptible strain (S) and field isolation (T) were treated with increasing concentrations of IVM using the larvae immersion technique the efficacy values measured at 24 hours were analysed with the sigmoidal maximum response so called Hill model as statistical analysis. The results obtained showed that the IVM have an all or nothing response represented by the Hill coefficient value >1 in both samples. Additionally, a low concentration effect was observed as E0 de 12.83% (S) and 9.91% (T). The field isolation larvae were susceptible to IVM in comparison with the susceptible strain by the resistance ratio (RR) which in one case was not significantly greater that one (RR50= 0.756 and RR90=1.009).

scholarly journals Calibrating a global three-dimensional biogeochemical ocean model (MOPS-1.0)

2017 ◽  
Vol 10 (1) ◽  
pp. 127-154 ◽  
Author(s):  
Iris Kriest ◽  
Volkmar Sauerland ◽  
Samar Khatiwala ◽  
Anand Srivastav ◽  
Andreas Oschlies
Keyword(s):  
Large Scale ◽  
Environmental Changes ◽  
Single Species ◽  
Ocean Model ◽  
Biogeochemical Model ◽  
Parameter Estimates ◽  
Spatial And Temporal Scales ◽  
Ocean Models ◽  
Biogeochemical Tracers ◽  
Parameter Values

Abstract. Global biogeochemical ocean models contain a variety of different biogeochemical components and often much simplified representations of complex dynamical interactions, which are described by many ( ≈ 10 to  ≈ 100) parameters. The values of many of these parameters are empirically difficult to constrain, due to the fact that in the models they represent processes for a range of different groups of organisms at the same time, while even for single species parameter values are often difficult to determine in situ. Therefore, these models are subject to a high level of parametric uncertainty. This may be of consequence for their skill with respect to accurately describing the relevant features of the present ocean, as well as their sensitivity to possible environmental changes. We here present a framework for the calibration of global biogeochemical ocean models on short and long timescales. The framework combines an offline approach for transport of biogeochemical tracers with an estimation of distribution algorithm (Covariance Matrix Adaption Evolution Strategy, CMA-ES). We explore the performance and capability of this framework by five different optimizations of six biogeochemical parameters of a global biogeochemical model, simulated over 3000 years. First, a twin experiment explores the feasibility of this approach. Four optimizations against a climatology of observations of annual mean dissolved nutrients and oxygen determine the extent to which different setups of the optimization influence model fit and parameter estimates. Because the misfit function applied focuses on the large-scale distribution of inorganic biogeochemical tracers, parameters that act on large spatial and temporal scales are determined earliest, and with the least spread. Parameters more closely tied to surface biology, which act on shorter timescales, are more difficult to determine. In particular, the search for optimum zooplankton parameters can benefit from a sound knowledge of maximum and minimum parameter values, leading to a more efficient optimization. It is encouraging that, although the misfit function does not contain any direct information about biogeochemical turnover, the optimized models nevertheless provide a better fit to observed global biogeochemical fluxes.

Modeling of respiratory system impedances in dogs

1987 ◽  
Vol 62 (2) ◽  
pp. 414-420 ◽  
Author(s):  
A. C. Jackson ◽  
K. R. Lutchen
Keyword(s):  
Respiratory System ◽  
Element Model ◽  
Parameter Estimates ◽  
Frequency Range ◽  
Nonlinear Regression Analysis ◽  
Entire Frequency Range ◽  
Frequency Dependent ◽  
Impedance Data ◽  
Parameter Values ◽  
Gas Compressibility

Mechanical impedances between 4 and 64 Hz of the respiratory system in dogs have been reported (A.C. Jackson et al. J. Appl. Physiol. 57: 34–39, 1984) previously by this laboratory. It was observed that resistance (the real part of impedance) decreased slightly with frequency between 4 and 22 Hz then increased considerably with frequency above 22 Hz. In the current study, these impedance data were analyzed using nonlinear regression analysis incorporating several different lumped linear element models. The five-element model of Eyles and Pimmel (IEEE Trans. Biomed. Eng. 28: 313–317, 1981) could only fit data where resistance decreased with frequency. However, when the model was applied to these data the returned parameter estimates were not physiologically realistic. Over the entire frequency range, a significantly improved fit was obtained with the six-element model of DuBois et al. (J. Appl. Physiol. 8: 587–594, 1956), since it could follow the predominate frequency-dependent characteristic that was the increase in resistance. The resulting parameter estimates suggested that the shunt compliance represents alveolar gas compressibility, the central branch represents airways, and the peripheral branch represents lung and chest wall tissues. This six-element model could not fit, with the same set of parameter values, both the frequency-dependent decrease in Rrs and the frequency-dependent increase in resistance. A nine-element model recently proposed by Peslin et al. (J. Appl. Physiol. 39: 523–534, 1975) was capable of fitting both the frequency-dependent decrease and the frequency-dependent increase in resistance. However, the data only between 4 and 64 Hz was not sufficient to consistently determine unique values for all nine parameters.

scholarly journals Using Weighted Entropy to Rank Chemicals in Quantitative High-Throughput Screening Experiments

2013 ◽  
Vol 19 (3) ◽  
pp. 344-353 ◽  
Author(s):  
Keith R. Shockley
Keyword(s):  
High Throughput ◽  
High Throughput Screening ◽  
Nonlinear Models ◽  
Hill Equation ◽  
Parameter Estimates ◽  
Chemical Library ◽  
Data Set ◽  
Screening Experiments ◽  
The Hill ◽  
Weighted Entropy

Quantitative high-throughput screening (qHTS) experiments can simultaneously produce concentration-response profiles for thousands of chemicals. In a typical qHTS study, a large chemical library is subjected to a primary screen to identify candidate hits for secondary screening, validation studies, or prediction modeling. Different algorithms, usually based on the Hill equation logistic model, have been used to classify compounds as active or inactive (or inconclusive). However, observed concentration-response activity relationships may not adequately fit a sigmoidal curve. Furthermore, it is unclear how to prioritize chemicals for follow-up studies given the large uncertainties that often accompany parameter estimates from nonlinear models. Weighted Shannon entropy can address these concerns by ranking compounds according to profile-specific statistics derived from estimates of the probability mass distribution of response at the tested concentration levels. This strategy can be used to rank all tested chemicals in the absence of a prespecified model structure, or the approach can complement existing activity call algorithms by ranking the returned candidate hits. The weighted entropy approach was evaluated here using data simulated from the Hill equation model. The procedure was then applied to a chemical genomics profiling data set interrogating compounds for androgen receptor agonist activity.

scholarly journals Escherichia coli O157 infection on Scottish cattle farms: dynamics and control

2010 ◽  
Vol 8 (60) ◽  
pp. 1051-1058 ◽  
Author(s):  
Xu-Sheng Zhang ◽  
Mark E. J. Woolhouse
Keyword(s):  
Escherichia Coli ◽  
Herd Size ◽  
Parameter Estimates ◽  
Control Effort ◽  
Considerable Uncertainty ◽  
Targeted Interventions ◽  
Dynamics And Control ◽  
And Control ◽  
Parameter Values ◽  
Cattle Farms

In this study, we parametrize a stochastic individual-based model of the transmission dynamics of Escherichia coli O157 infection among Scottish cattle farms and use the model to predict the impacts of both targeted and non-targeted interventions. We first generate distributions of model parameter estimates using Markov chain Monte Carlo methods. Despite considerable uncertainty in parameter values, each set of parameter values within the 95th percentile range implies a fairly similar impact of interventions. Interventions that reduce the transmission coefficient and/or increase the recovery rate of infected farms (e.g. via vaccination and biosecurity) are much more effective in reducing the level of infection than reducing cattle movement rates, which improves effectiveness only when the overall control effort is small. Targeted interventions based on farm-level risk factors are more efficient than non-targeted interventions. Herd size is a major determinant of risk of infection, and our simulations confirmed that targeting interventions at farms with the largest herds is almost as effective as targeting based on overall risk. However, because of the striking characteristic that the infection force depends weakly on the number of infected farms, no interventions that are less than 100 per cent effective can eradicate E. coli O157 infection from Scottish cattle farms, implying that eliminating the disease is impractical.

Turbulent Thermal Diffusion Over a Locally-Heated Two-Dimensional Hill

2010 ◽  
Author(s):  
T. Houra ◽  
Y. Nagano ◽  
M. Tagawa
Keyword(s):  
Thermal Diffusion ◽  
Passive Scalar ◽  
Heated Wall ◽  
Windward Side ◽  
Two Dimensional ◽  
Hill Model ◽  
Mean Temperature ◽  
The Mean ◽  
The Hill ◽  
Heated Case

We measure flow and thermal fields over a locally heated two-dimensional hill. The heated sections on the wall are divided into upstream and downstream portions of the hill model. These sections are heated independently, yielding various thermal boundary conditions in contrast to the uniformly heated case. In the separated region formed behind the hill, it is found that the mean temperature profiles in the uniformly heated case are well decomposed into the separately heated cases. This is because the velocity fluctuation produced by the shear layer formed behind the hill is large, so the superposition of a passive scalar in the thermal field can be successfully realized. The rapid increase in the mean temperature near the uniformly heated wall should be due to the heat transfer near the leeward slope of the hill. On the other hand, the mean temperature distributions away from the wall are strongly affected by the turbulent thermal diffusion on the windward side of the hill.

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