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Hill Equation (hill + equation)
Selected AbstractsThe Hill equation: a review of its capabilities in pharmacological modellingFUNDAMENTAL & CLINICAL PHARMACOLOGY, Issue 6 2008Sylvain Goutelle Abstract The Hill equation was first introduced by A.V. Hill to describe the equilibrium relationship between oxygen tension and the saturation of haemoglobin. In pharmacology, the Hill equation has been extensively used to analyse quantitative drug,receptor relationships. Many pharmacokinetic,pharmacodynamic models have used the Hill equation to describe nonlinear drug dose,response relationships. Although the Hill equation is widely used, its many properties are not all well known. This article aims at reviewing the various properties of the Hill equation. The descriptive aspects of the Hill equation, in particular mathematical and graphical properties, are examined, and related to Hill's original work. The mechanistic aspect of the Hill equation, involving a strong connection with the Guldberg and Waage law of mass action, is also described. Finally, a probabilistic view of the Hill equation is examined. Here, we provide some new calculation results, such as Fisher information and Shannon entropy, and we introduce multivariate probabilistic Hill equations. The main features and potential applications of this probabilistic approach are also discussed. Thus, within the same formalism, the Hill equation has many different properties which can be of great interest for those interested in mathematical modelling in pharmacology and biosciences. [source] Pharmacokinetic,pharmacodynamic study of apomorphine's effect on growth hormone secretion in healthy subjectsFUNDAMENTAL & CLINICAL PHARMACOLOGY, Issue 4 2003Guy Aymard Abstract Apomorphine (APO) stimulates growth hormone (GH) release via dopamine D2 receptors (DRD2). There is no specific study assessing the relationship between APO pharmacokinetic (PK) and the pharmacodynamic (PD) response e.g. GH release. The objective of the study is the PK,PD modelling of APO in healthy subjects. This is a randomized crossover study with s.c. administration of 5, 10, and 20 ,g/kg of APO in 18 healthy subjects. APO concentrations were modelled according to both a bi-compartmental model with zero-order absorption and a bi-compartmental model with first-order absorption. PK,PD relationship was modelled in accordance with the Emax Hill equation using plasma concentrations of APO calculated according to the bi-compartmental model with zero-order absorption. Modelled parameters were very similar to the experimental parameters. PK of APO was linear and there was no significant difference between the tested doses for AUC0,, and Cmax (normalised to the dose 1 ,g/kg), t1/2, and t1/2,. These parameters expressed as mean (CV%: SD/mean) were: 17.2 (26.9) ng/mL·min, 0.26 (33.3) ng/mL, 17.1 (54.2) and 45.2 (20.6) min, respectively (n = 53). An anticlockwise hysteresis loop (effect function of APO plasma concentration) appeared for each dose and each subject. The predicted and measured GH concentrations for all subjects and times were similar whatever the dose (P > 0.27). Emax values were 246 (121), 180 (107), 205 (139) ng/mL, respectively, and EC50 were 0.98 (48.1), 1.70 (62.3), 3.67 (65.2) ng/mL, respectively at dose 5, 10, and 20 ,g/kg (P < 10,4). APO and GH concentrations were predicted with good accuracy using bi-compartmental with zero-order absorption PK model and sigmoid Emax PD model, respectively. [source] The effects of obstructive jaundice on the pharmacodynamics of propofol: does the sensitivity of intravenous anesthetics change among icteric patients?ACTA ANAESTHESIOLOGICA SCANDINAVICA, Issue 10 2009J. C. SONG Background Some studies suggest that certain clinical symptoms of cholestasis, such as fatigue and pruritus, result from altered neurotransmission. Patients with obstructive jaundice also have labile blood pressure and heart rate. In the present study, the authors investigated whether obstructive jaundice affects a patient's sensitivity to hypnotics and the haemodynamic profile of propofol. Methods Thirty-six ASA physical status I/II/III patients with serum total bilirubin (TBL) from 7.8 to 362.7 ,mol/l scheduled for bile duct surgery were recruited. A computer-controlled propofol infusion programmed for effect site target was used to rapidly attain and maintain sequential increase of the compartment concentration (from 1 to 3 ,g/ml). Each target-controlled concentration was maintained for about 12 min, and arterial blood samples were drawn for propofol concentration determination. The bispectral index (BIS) and mean arterial pressures (MAP) were used as indices of the propofol effect. The relation between the concentration and the effects was described by the Hill equation. The pharmacodynamic parameters were optimized using a nonlinear mixed-effect model. Results TBL was not a significant covariate of EC50 for the pharmacodynamic model. For BIS and MAP, the parameters of the pharmacodynamic model were Emax=75.77%, EC50=2.34 ,g/ml, and ,=1.82, and Emax=47.83%, EC50=1.49 ,g/ml, and ,=1.88, respectively. Conclusions We demonstrated that obstructive jaundice with serum TBL from 7.8 to 362.7 ,mol/l had no effect on propofol pharmacodynamics observed by BIS and MAP. [source] Dose-response relationship of rocuronium: A comparison of electromyographic vs. acceleromyographic-derived valuesACTA ANAESTHESIOLOGICA SCANDINAVICA, Issue 3 2005A. F. Kopman Background: Acceleromyography (AMG) is being employed with increasing frequency as a research tool. However, there is almost no information available regarding the accuracy of values for drug potency obtained using AMG. This study was an attempt to determine if AMG-derived ED50/95 values are interchangeable with those measured with a more traditional neuromuscular monitor. Methods: Thirty adult patients were studied. Anesthesia was induced and maintained with N20, propofol, and supplementation opioid. Tracheal intubation was accomplished without muscle relaxants. Simultaneous ipsilateral AMG and EMG responses to 0.10 Hz stimulation was recorded. Following instrument calibrations, a single dose of rocuronium was administered. The first patient received a bolus of 0.17 mg kg,1 of rocuronium. Using the Hill equation with a postulated slope of 4.50, the ED50 was calculated. The second subject received a dose which approximated the calculated ED50 for patient no. 1. Successive subjects were given a dose based on the running average of the estimated ED50. Results: The AMG-derived ED50/95 values for rocuronium (0.163 ± 0.055 and 0.314 ± 0.105 mg mg,1) were virtually identical to those established using EMG (0.159 ± 0.043 and 0.306 ± 0.084 mg kg,1). While mean peak twitch depression (,T1) was the same in both groups for individual subjects ,T1 differed by ± 20% (95% confidence interval). Discussion: Acceleromyography-derived twitch heights for individual patients are not necessarily interchangeable with information obtained using electromyography. Nevertheless, acceleromyography appears to be a valid methodology for determining the drug potency when a population rather than an individual subject is being studied. [source] The Hill equation: a review of its capabilities in pharmacological modellingFUNDAMENTAL & CLINICAL PHARMACOLOGY, Issue 6 2008Sylvain Goutelle Abstract The Hill equation was first introduced by A.V. Hill to describe the equilibrium relationship between oxygen tension and the saturation of haemoglobin. In pharmacology, the Hill equation has been extensively used to analyse quantitative drug,receptor relationships. Many pharmacokinetic,pharmacodynamic models have used the Hill equation to describe nonlinear drug dose,response relationships. Although the Hill equation is widely used, its many properties are not all well known. This article aims at reviewing the various properties of the Hill equation. The descriptive aspects of the Hill equation, in particular mathematical and graphical properties, are examined, and related to Hill's original work. The mechanistic aspect of the Hill equation, involving a strong connection with the Guldberg and Waage law of mass action, is also described. Finally, a probabilistic view of the Hill equation is examined. Here, we provide some new calculation results, such as Fisher information and Shannon entropy, and we introduce multivariate probabilistic Hill equations. The main features and potential applications of this probabilistic approach are also discussed. Thus, within the same formalism, the Hill equation has many different properties which can be of great interest for those interested in mathematical modelling in pharmacology and biosciences. [source] An intelligent control concept for formation flying satellitesINTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 2-3 2002S. R. Vadali Abstract This paper deals with the determination of initial conditions and the design of fuel-balancing orbit control laws for a formation of satellites. Hill's equations describe the linearized dynamics of relative motion between two satellites. They admit bounded relative orbit solutions as special cases. Predictably, these bounded solutions break down in the presence of nonlinearities and perturbations. A method for determining the initial conditions that result in quasi-periodic relative orbits over the short term, in the presence of J2 perturbation, is presented. The control acceleration or equivalently, the fuel required to cancel the perturbation on a satellite depends upon its orbital inclination with respect to that of the reference satellite. An intelligent control concept that exploits the physics of the relative motion dynamics is presented. Analysis shows that this concept minimizes the total fuel consumption of the formation and maintains equal, average fuel consumption for each satellite. The concept is implemented using a novel, disturbance accommodating control design process. Numerical simulations and analytical results are in excellent agreement with each other. Copyright © 2002 John Wiley & Sons, Ltd. [source] | ||||||||||