A comparison of numerical integrating algorithms by trapezoidal, Lagrange, and spline approximation

Yeh, Kuang C.; Kwan, K.C.

doi:10.1007/bf01066064

Cited by 394 publications

(147 citation statements)

References 3 publications

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“…According to standard procedures for time series, the remaining specimens were analyzed only once. Areas under the plasma concentration curves (AUC) were calculated for the first (2200 to 0300 hours, for example, 1 h prior to sleep-EEG recording and the first half of sleep-EEG recording time) and for the second part of the night (0300 to 0700 hours, second half of the sleep-EEG recording time) and for the total night (2200 to 0700 hours) by applying the trapezoid rule (Yeh and Kwan, 1978). Maximum concentrations were identified as well.…”

Section: Endocrine Analysismentioning

confidence: 99%

Changes of Sleep Architecture, Spectral Composition of Sleep EEG, the Nocturnal Secretion of Cortisol, ACTH, GH, Prolactin, Melatonin, Ghrelin, and Leptin, and the DEX-CRH Test in Depressed Patients during Treatment with Mirtazapine

Schmid

Wichniak

Uhr

et al. 2005

Neuropsychopharmacol

143

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The noradrenergic and specific serotoninergic antidepressant mirtazapine improves sleep, modulates hormone secretion including blunting of hypothalamic-pituitary-adrenocortical (HPA) activity, and may prompt increased appetite and weight gain. The simultaneous investigation of sleep electroencephalogram (EEG) and hormone secretion during antidepressive treatment helps to further elucidate these effects. We examined sleep EEG (for later conventional and quantitative analyses) and the nocturnal concentrations of cortisol, adrenocorticotropin (ACTH), growth hormone (GH), prolactin, melatonin and the key factors of energy balance, ghrelin, and leptin before and after 28 days of treatment of depressed patients (seven women, three men, mean age 39.974.2 years) with mirtazapine. In addition, a sleep EEG was recorded at day 2 and the dexamethasone-corticotropin-releasing hormone (DEX-CRH) test was performed to assess HPA activity at days À3 and 26. Psychometry and mirtazapine plasma concentrations were measured weekly. Already at day 2, sleep continuity was improved. This effect persisted at day 28, when slow-wave sleep, low-delta, theta and alpha activity, leptin and (0300-0700) melatonin increased, and cortisol and ghrelin decreased. ACTH and prolactin remained unchanged. The first two specimens of GH collected after the start of quantitative EEG analysis were reduced at day 28. The DEX-CRH test showed, at day 26, a blunting of the overshoot of ACTH and cortisol found at day À3. The Hamilton Depression score decreased from 32.177.3 to 15.576.7 between days À1 and 28. A weight gain of approximately 3 kg was observed. This unique profile of changes is compatible with the action of mirtazapine at 5-HT-2 receptors, at presynaptic adrenergic alpha 2 receptors, at the HPA system, and on ghrelin and leptin.

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Section: Endocrine Analysismentioning

confidence: 99%

Changes of Sleep Architecture, Spectral Composition of Sleep EEG, the Nocturnal Secretion of Cortisol, ACTH, GH, Prolactin, Melatonin, Ghrelin, and Leptin, and the DEX-CRH Test in Depressed Patients during Treatment with Mirtazapine

Schmid

Wichniak

Uhr

et al. 2005

Neuropsychopharmacol

143

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“…We focus our attention on estimating the bulk of the area under the concentration-time curve, say for a time interval [0, t max + w] for some w. Then, we suggest that users employ the logarithmic trapezoidal method (Yeh and Kwan, 1978;Chiou, 1978) for estimating AUC. Technically, this focus is justified because when using this method, only the (fixed) final time point after t max + w is required if the PK model is correct and the observations are measured without error.…”

Section: Examplesmentioning

confidence: 99%

Optimal sampling times in bioequivalence studies using a simulated annealing algorithm

2007

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In pharmacokinetic (PK) studies, blood samples are taken over time on subjects after the administration of a drug to measure the time-course of the plasma drug concentrations. In bioequivalence studies, the trapezoidal rule on the sampled time points is often used to estimate the area under the plasma concentration-time curve, a quantity of principle interest. This manuscript investigates the choice of sampling time points to estimate the area under the curve. In particular, we explore the relative merits of several objective functions, those functions which are minimized with respect to the sampling times to obtain an optimal study design. We propose an objective function which overcomes some of the deficits of existing choices. We also present a simulated annealing algorithm to perform the minimization. The main benefits of the simulated annealing algorithm are the ease in which it can handle constraints on the sampling schedules and its ability to accommodate a variety of models and objective functions. The manuscript presents optimal sampling times for some key examples of true underlying models.

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“…The 5-FU AUC was determined by the logarithmic trapezoidal method from 0 to 48 h (midcycle) (Yeh & Kwan, 1978). Systemic clearance was calculated by dividing the total dose administered during 48 h by the AUC (0-48 h) (Gibaldi & Perrier, 1982).…”

Section: Pharmacokinetic Analysismentioning

confidence: 99%

No effect of dose, hepatic function, or nutritional status on 5-FU clearance following continuous (5-day), 5-FU infusion

Fleming

Milano²,

Etienne³

et al. 1992

Br J Cancer

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Summary One hundred and eighty seven patients (155 males, 32 females) with histologically proven and previously untreated head and neck cancer were entered in the study. A total of 222 cycles of therapy were analyzed (cisplatin 100 mg m-2 on day I and 5-day continuous intravenous infusion of 5-FU 550-1069 mg m-2 day-', mean 875.5 mg m-2 day-'). Significant interpatient variability for various 5-FU pharmacokinetic parameters was observed including an almost ten-fold range in 5-FU clearance (5-FU Cl, ml min-m-2 = 791-7769, mean 2820.7).

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A comparison of numerical integrating algorithms by trapezoidal, Lagrange, and spline approximation

Cited by 394 publications

References 3 publications

Changes of Sleep Architecture, Spectral Composition of Sleep EEG, the Nocturnal Secretion of Cortisol, ACTH, GH, Prolactin, Melatonin, Ghrelin, and Leptin, and the DEX-CRH Test in Depressed Patients during Treatment with Mirtazapine

Changes of Sleep Architecture, Spectral Composition of Sleep EEG, the Nocturnal Secretion of Cortisol, ACTH, GH, Prolactin, Melatonin, Ghrelin, and Leptin, and the DEX-CRH Test in Depressed Patients during Treatment with Mirtazapine

Optimal sampling times in bioequivalence studies using a simulated annealing algorithm

No effect of dose, hepatic function, or nutritional status on 5-FU clearance following continuous (5-day), 5-FU infusion

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