Mechanistic pharmacokinetic modelling of ephedrine, norephedrine and caffeine in healthy subjects

AIM

The combination of ephedrine and caffeine has been used in herbal products for weight loss and athletic performance-enhancement, but the pharmacokinetic profiles of these compounds have not been well characterized. This study aimed to develop a mechanistic model describing ephedrine, norephedrine, and caffeine pharmacokinetics and their interactions in healthy subjects.

METHODS

The pharmacokinetic model was developed based on the simultaneous modelling using plasma samples gathered from two clinical trials. The treatments consisted of single-doses of pharmaceutical caffeine and ephedrine, given alone or together, and an herbal formulation containing both caffeine and ephedrine. We used a mixed-effect statistical model and the program NONMEM to take account of intersubject variability.

RESULTS

Three hundred and seventy-nine ephedrine, 352 norephedrine, 417 caffeine plasma concentrations and 40 ephedrine urine concentrations were obtained from 24 subjects. A one-compartment model with first-order absorption described the caffeine data. Caffeine clearance was 0.083 l min(-1) (CV 38%) and decreased to 0.038 l min(-1) in presence of oral contraceptive therapy, its volume of distribution was 38.6 l (CV 20%) and its absorption rate constant was 0.064 l min(-1) (CV 50%). A four-compartment model described the pharmocokinetics of ephedrine and norephedrine. Ephedrine was eliminated mostly renally, with a clearance of 0.34 l min(-1) (CV 11%), and a volume of distribution of 181 l (CV 19%). Nonlinearity in the conversion of ephedrine to norephedrine was observed. Different models showed that the simultaneous administration of caffeine, or the amount of caffeine in the absorption compartment, was associated with a slower rate of absorption of ephedrine. A 32% greater relative bioavailability of herbal compared with pharmaceutical ephedrine administration was observed.

CONCLUSIONS

We describe a mechanistic model for ephedrine, norephedrine and caffeine pharmacokinetics and their interactions. The relative bioavailability of ephedrine differed between the herbal supplement compared with the pharmaceutical formulation. Concomitant ingestion of caffeine slowed the absorption rate of ephedrine, which is mainly related to the amount of the former in the absorption compartment. A saturable process appears to be involved in the metabolism of ephedrine to norephedrine.

Selecting reliable pharmacokinetic data for explanatory analyses of clinical trials in the presence of possible noncompliance

For single-dose concentration-time data collected in clinical trials to be useful for explanatory pharmacokinetic (PK) or pharmacokinetic-pharmacodynamic (PK-PD) analyses, the following two assumptions on the data must hold: (i) the times of the concentration (PK) observations are known, and (ii) the patient's recent past dosing history (times and amounts) is known. If either (or both) of these assumptions does not hold, and data analysis proceeds as if it did, biased estimates may result. Assumption (i) usually does hold as study personnel observe and record PK sampling times. Assumption (ii) is a problem when, as is often the case of outpatient studies, one must rely on patient recall for past dosing history. This paper presents a technique to avoid assumption (ii) by identifying for deletion those PK observation occasions likely exhibiting unreliable preceding dose histories. To so identify occasions, a Bayes objective function (posterior density) for the data is maximized in its parameters for each individual. The likelihood factor of this function is a mixture pharmacostatistical model expressing the likelihood of the observed concentration(s) under three mutually exclusive events: the prescribed dose preceding the occasion was not taken at all (NT), the prescribed dose was taken at the specified time (T), or the prescribed dose was taken at an unspecified time (U). Suspect observations are identified as those whose maximum corresponding likelihood component is other than T. The approach as defined here relies on the following assumptions in addition to (i): (ii) population PK (i.e., the distribution of PK parameters in the population being sampled) is known, at least approximately. (iii) PK samples (at least 1 or 2 per occasion) are available, (iv) doses taken are of the stated magnitude, and (v) the drug has a short half-life. Simulations reveal that especially when more than one PK sample is available per study occasion, the methodology chooses a set of PK observations that should perform better in subsequent explanatory analyses, or as a basis for estimating individual PK parameters, than do other simpler methods.

A Semiparametric Deconvolution Model to Establish In Vivo–In Vitro Correlation Applied to OROS Oxybutynin

In vitro-in vivo correlation (IVIVC) models may be used to predict in vivo drug concentration-time profiles given in vitro release characteristics of a drug. This prediction is accomplished by incorporating in vitro release characteristics as an input function (A(vitro)) to a pharmacokinetics model. This simple approach often results in biased predictions of observed in vivo drug concentrations, and it can result in rejecting IVIVC. To solve this problem we propose a population IVIVC model that incorporates the in vitro information and allows one to quantify possibly changed in vivo release characteristic. The model assumes linear kinetics and describes the in vivo release as a sum of A(vitro) and a nonparametric function (A(d), a spline) representing the difference in release due to in vivo conditions. The function A(vitro) and its variability enter the model as a prior distribution. The function A(d) is estimated together with its intersubject variability. The number of parameters associated with A(d) defines the model: no parameters indicates perfect IVIVC, a large number of parameters indicates poor IVIVC. The number of parameters is determined using statistical model selection criteria. We demonstrate the approach to solve the IVIVC problem of an oral extended release oxybutynin form (OROS), administered in three pharmacokinetic studies. These studies present a particular challenging case; that is, the relative bioavailability for the OROS administration is >100% compared with that of the immediate-release form. The result of our modeling shows that the apparent lack of IVIVC can be overcome: in vivo concentration can be predicted (within or across data sets) based on in vitro release rate together with a simple form of systematic deviation from the in vitro release.

Linear mixed-effect multivariate adaptive regression splines applied to nonlinear pharmacokinetics data

In a frequently performed pharmacokinetics study, different subjects are given different doses of a drug. After each dose is given, drug concentrations are observed according to the same sampling design. The goal of the experiment is to obtain a representation for the pharmacokinetics of the drug, and to determine if drug concentrations observed at different times after a dose are linear in respect to dose. The goal of this paper is to obtain a representation for concentration as a function of time and dose, which (a) makes no assumptions on the underlying pharmacokinetics of the drug; (b) takes into account the repeated measure structure of the data; and (c) detects nonlinearities in respect to dose. To address (a) we use a multivariate adaptive regression splines representation (MARS), which we recast into a linear mixed-effects model, addressing (b). To detect nonlinearity we describe a general algorithm that obtains nested (mixed-effect) MARS representations. In the pharmacokinetics application, the algorithm obtains representations containing time, and time and dose, respectively, with the property that the bases functions of the first representation are a subset of the second. Standard statistical model selection criteria are used to select representations linear or nonlinear in respect to dose. The method can be applied to a variety of pharmacokinetics (and pharmacodynamic) preclinical and phase I-III trials. Examples of applications of the methodology to real and simulated data are reported.

Nasal mucosal versus gastrointestinal absorption of nasally administered cocaine

OBJECTIVE

Several xenobiotics, including cocaine, are dosed by the nasal route for systemic effects. The aim of this study was to estimate and compare cocaine input into the systemic circulation after oral and nasal dosing, and to determine the relevance of local absorption through the nasal mucosa.

METHODS

Cocaine was administered to healthy volunteers through the intravenous, oral, and nasal routes. Cocaine serum concentrations were measured at frequent intervals. From these data, the gastrointestinal, nasal, and nasal mucosa input rate functions were determined using nonparametric, subject-specific population deconvolution.

RESULTS

After oral dosing, cocaine input into systemic circulation increased slowly and peaked around 45 min after ingestion. The median systemic bioavailability after oral dosing was 33%. After nasal dosing, drug input was substantial even during the first minute and showed two peaks at 10 min and 45 min after ingestion. Since the second peak after nasal dosing closely resembled drug input after oral administration, we hypothesized that, after nasal administration, a part of the dose is swallowed and thereafter absorbed gastrointestinally. The data from the sessions with nasal cocaine administration were reanalyzed assuming the same shape for gastrointestinal drug input as after oral dosing. The fraction absorbed through the nasal mucosa was estimated to be 19% (95% CI: 11-26%). The fraction absorbed through the nasal mucosa contributed 31% (95% CI: 23-37%) of total systemic cocaine exposure.

CONCLUSIONS

Our data suggest that the main reason addicts prefer nasal to oral cocaine dosing is faster absorption, enhancing the subjective effects rather than higher bioavailability.

Additive inhibition of nicotinic acetylcholine receptors by corticosteroids and the neuromuscular blocking drug vecuronium

BACKGROUND

Neuromuscular disorders associated with muscular weakness and prolonged paralysis are common in critically ill patients. Acute myopathy has been described in patients receiving a combination therapy of corticosteroids and nondepolarizing neuromuscular blocking drugs for treatment of acute bronchospasm. The cause of this myopathy is not fully established and may involve drug interactions that perturb neuromuscular transmission. To investigate the interaction of corticosteroids with neuromuscular blocking drugs, the authors determined the effects of methylprednisolone and hydrocortisone alone and in combination with vecuronium on fetal (gamma-subunit containing) and adult (epsilon-subunit containing) subtypes of the muscle-type nicotinic acetylcholine receptor.

METHODS

Functional channels were expressed in Xenopus laevis oocytes and activated with 1 microM acetylcholine. The resulting currents were recorded using a whole cell two-electrode voltage clamp technique.

RESULTS

Both forms of the muscle-type acetylcholine receptor were potently inhibited by methylprednisolone and hydrocortisone, with concentrations producing 50% inhibition in the range of 400-600 microM and 1-2 mM, respectively. The corticosteroids produced noncompetitive antagonism of the muscle-type nicotinic acetylcholine receptor at clinical concentrations. Both receptor forms were also inhibited, even more potently, by vecuronium, with a concentration producing 50% inhibition in the range of 1-2 nM. Combined application of vecuronium and methylprednisolone showed additive effects on both receptor forms, which were best described by a two-site model, with each site independent.

CONCLUSIONS

The enhanced neuromuscular blockade produced when corticosteroids are combined with vecuronium may augment pharmacologic denervation and contribute to the pathophysiology of prolonged weakness observed in some critically ill patients.

Down-regulation models and modeling of testosterone production induced by recombinant human choriogonadotropin

Chorionic gonadotropin (CG) is a glycoprotein hormone, whose action is mediated by the luteinizing hormone/CG receptor. Testosterone concentrations from six pituitary-desensitized, healthy male volunteers were obtained after four different administrations of recombinant-human CG (rhCG). We present a modeling study to provide a possible explanation for the observations that increased exposure to rhCG induces higher and then lower testosterone concentrations and that marked rebound effects are observed at the end of repeated administration of rhCG. We used semimechanistic models (in which flexible functions represent unknown parts of the models) to identify the relationship of rhCG concentrations to the testosterone levels. Based on the results obtained with the semimechanistic models, different mechanistic down-regulation models were devised and tested. The final model uses a one-compartment model to describe the endogenous production rate of testosterone; rhCG affects the production rate with a mechanism consistent with a two-site binding site, with effect proportional to one-site bound concentration. The modeling results indicate that when rhCG concentration increases, the testosterone production rate increases to 45 times the baseline value. However, at an rhCG concentration of more than about 30 IU/liter, the production rate decreases. Simulations showed that both dose and dosing interval profoundly influence testosterone response to rhCG.

A general solution for nonparametric control of a linear system using computer-controlled infusion pumps

Investigators have developed algorithms for use in computer-controlled infusion pumps (CCIP's) which dose intravenous drugs assuming multiexponential unit impulse response (UIR) function. However for many UIR multiexponential functions are at best an approximation. For almost all substances the early times after an impulse administration show complex profiles hardly described by multiexponential functions. For many later times also show departures from exponential decline. We derive a general approach for a CCIP which can be used with an arbitrary UIR function. A particular instance of the approach is based on a nonparametric representation of an UIR which uses spline functions. The approach is computationally simple, it can take into account desired constraints (for example no overshoot to avoid toxicity) and presents a solution to control concentrations of substances in a site different from the input site. Examples based on real lodocaine, veralipride, and thiopental data demonstrate the approach.

Characterizing the variability of system kernel and input estimates

The identification of the input to, or kernels of, a system using nonparametric representations and least-squares estimation is becoming increasingly popular. Nonparametric representations avoid making a priori assumptions about the input or having detailed knowledge about the system, and only need to guarantee known general characteristics (for example, positivity), which are obtained through the imposition of constraints on the estimates. An often overlooked problem is how to characterize the variability of the estimates so obtained. This problem is caused by the presence of constraints--and/or the nonlinearities of the estimates, or the complexity of the (regression based) estimation algorithms used--which make standard methods of estimating variability incorrect. In this article we investigate the use of a resampling technique called the "bootstrap" to obtain the desired estimates of variability. We present real data analysis demonstrating the approach, and through simulations we test the performance of a novel bootstrap technique obtaining confidence bands for the estimated functions.

Use of a pharmacokinetic/pharmacodynamic model to design an optimal dose input profile

A model for the pharmacodynamic effect of a drug (designated only X), and the use of the model to explore optimal input is described. The data analyzed here are from a crossover comparison study of the effect of 4 active treatments, yielding distinct concentration vs. time curves, plus placebo in 32 subjects. The model expresses total effect as the sum of placebo effect and (pure) drug effect. The latter allows for possible tolerance (found) and time effects (not found). Random effects allow interindividual differences to be expressed. Conditioning on the fitted model, a population optimal input profile is designed that obeys certain protocol constraints. The profile minimizes the expectation of a sum of squared differences between target effect and the resulting response over a given time interval. The target is a fixed constant, chosen to be either the individuals' maximum effect level in response to a baseline input regimen used in the study or the maximum effect level for the typical individual in the population in response to this regimen, as predicted from the model. The expectation is taken over the estimated nonparametric distribution of the 32 subjects' random effects. As one goal of early clinical studies of drugs may be to provide a basis for designing an optimal delivery profile (with respect to a specified loss function), we suggest this report as an example of a reasonable way to go about finding such a profile.

Importance of chronopharmacokinetics in design and evaluation of transdermal drug delivery systems

Circadian and meal effects on nicotine kinetics determine in part blood nicotine concentrations and in doing so may influence cigarette smoking behavior throughout the day. We have shown previously that nicotine clearance varies by approximately 17% (from peak to through) due to diurnal factors throughout the day and that meals increase nicotine clearance by about 42%. Until now pharmacokinetic analyses of nicotine absorption from patches have assumed a constant clearance of nicotine over 24 hr. Using 11 individual kinetic estimates from a previous study, we analyzed plasma nicotine concentrations vs. time data of two nicotine patch studies, and conducted a set of simulations to determine the extent to which time-varying kinetics would influence the design of transdermal drug delivery systems, intented to maintain a constant plasma nicotine concentration over 24 hr. Not incorporating time-varying kinetics leads to biased estimates of the delivery rate of the nicotine patches, and increases the variability in the delivery rates estimates. The hypothetical transdermal drug delivery systems designed assuming constant nicotine clearance results in a systematical underdosing during the first 12 hr after beginning therapy. The transdermal drug delivery systems obtained assuming the correct time-varying clearance shows three components: 1) an early high delivery rate, followed by 2) a rather constant, but slightly decreasing at night, release rate and 3) transient increases in delivery rate for 2 hr after each meal. The effect of circadian variations in clearance could be compensated for in patch design by decreasing the delivery rate during the night. Transient variations in clearance due to meals would require the corresponding use of rapid drug delivery dosage forms. The methods we devise to predict optimal dosing regimens in presence of chronopharmacokinetics might be useful for other medications in which blood levels need to be precisely controlled.

Passive versus electrotransport-facilitated transdermal absorption of ketorolac

OBJECTIVE

To investigate the bioavailability (extent and rate of absorption) of ketorolac from two cutaneous absorption sources, active electrotransport and passive transdermal, and to examine the enantiomeric selectivity of bioavailability for each source.

METHODS

Based on a crossover study in 12 healthy volunteers, the extent and rate of absorption of ketorolac, delivered by a patch, were found by estimating the input rate function of the drug. For that purpose, deconvolution was used in two steps. First, intravenous data were analyzed to estimate the ketorolac disposition function, and second, postpatch data were deconvolved to estimate the unknown patch input profile given the disposition function estimated in the first step. Because the input rate function curves to be estimated for the patches may be of arbitrary shape, a spline was used to model the patch input function, whereas intravenous data were modeled with use of a sum of exponentials. Differences in the extent of absorption (F) for the four treatment-enantiomer combinations were further examined with a mixed-effect regression model, based on the sets of four individual estimates of bioavailability.

RESULTS

On average, the F value for the active electrotransport treatment, which exhibited the faster absorption rate, was four times greater than the F for the passive transdermal treatment. Further, during the passive treatment, R-ketorolac yielded an average F that is 42% greater than that for S-ketorolac and also exhibited a smaller absorption lag-time. During the active treatment, there was no important enantiomeric difference in either extent or rate of absorption.

Pharmacokinetics of saquinavir, zidovudine, and zalcitabine in combination therapy

We investigated the pharmacokinetics of zidovudine, zalcitabine, and saquinavir in AIDS Clinical Trial Group protocol 229. Patients received either saquinavir, zalcitabine, or a combination of both, together with zidovudine three times a day. Approximately 100 patients were enrolled in each treatment arm, and intensive pharmacokinetic studies were performed on about 25 patients per arm at weeks 1 and 12. We estimated the pharmacokinetic parameters of all three drugs by using parametric and nonparametric methods. The mean values of the pharmacokinetic parameters of zidovudine (clearance [CL]/bioavailability [F], 168 liters/h; volume of distribution [V]/F, 185 liters; half-life, 0.76 h) and zalcitabine (CL/F, 25 liters/h; V/F, 92.2 liters; half-life, 2.7 h) were similar to those reported previously. For saquinavir, the mean pharmacokinetic parameter estimates using parametric methods were as follows: maximum concentration of drug in serum [Cmax], 70.8 ng/ml; time to Cmax, 3.11 h; area under the curve, 809 ng x h/ml; CL/F, 989 liters/h; V/F, 1,503 liters; half-life, 1.38 h. For all three drugs, clearance decreased with age. Weight did not influence the clearance of zidovudine, but the clearance of zalcitabine and saquinavir increased with weight. There were no differences in pharmacokinetic parameters between study weeks and arms, suggesting that there is no change in kinetics with chronic administration and that there are no significant pharmacokinetic interactions among these three drugs.

Exposure-response relationships for saquinavir, zidovudine, and zalcitabine in combination therapy

The relationship of CD4+ cell response, level of RNA in plasma, and quantitative peripheral blood mononuclear cell (PBMC) titer to apparent drug exposure was investigated by using data from AIDS Clinical Trial Group protocol 229, a multicenter randomized study. Patients received either saquinavir, zalcitabine, or a combination of both, along with open-label zidovudine. Approximately 100 patients were enrolled in each arm, and the primary study duration was 24 weeks. Individual drug exposure, the area under the concentration-time curve, was estimated by using population-based pharmacokinetic methods. Response was defined as the maximum increase in CD4+ cell count or the maximum decrease in RNA in plasma or PBMC titer adjusted for baseline CD4+ cell count, RNA in plasma, and PBMC titer, respectively. Regression of responses on exposure demonstrated an exposure effect for saquinavir which was significant for the maximum increase in CD4+ cell count and the decrease in RNA in plasma. For the PBMC titer, no significant relationship could be demonstrated but the results suggested a trend similar to that of the other response variables. For all three response variables, the slope of the saquinavir exposure response was greater with the triple combination (saquinavir, zidovudine, and zalcitabine) than with the combination of saquinavir and zidovudine, suggesting possible synergism between saquinavir and zalcitabine.

Age effects on interrelationships between lung volume and heart rate during standing

To determine the effects of aging and posture on the relationship between respiration and heart rate (HR), we collected 5 min of lung volume and R-R interval data from 7 young (27 +/- 3 yr, mean +/- SD) and 10 old (69 +/- 6 yr) healthy humans during spontaneous breathing while they were supine (SU) and standing (ST). Lung volume and HR power spectra and transfer functions between lung volume and HR were estimated. Age and position effects and age-position interactions were determined by analysis of variance for repeated measures. Older subjects had a lower and more variable respiration rate (P < 0.03, P < 0.04), but both age groups exhibited decreased rate of respiration and increased tidal volume with ST (P < 0.05, P < 0.005). ST decreased lung volume-to-HR transfer function magnitude in both groups (P < 0.07). The more marked age-related differences were in phase angle. Both SU and ST phase angles were greater in older subjects (P < 0.003). ST decreased phase angle in young but increased phase angle in older subjects (P < 0.001). In conclusion, respiration, and respiration-HR interrelationships are altered by aging, with increased time delays between lung volume and HR and altered relationships with ST.

A semiparametric method for describing noisy population pharmacokinetic data

We propose a semiparametric method to estimate model-independent pharmacokinetic (PK) measures such as area under concentration-time, peak concentration and time to peak concentration (Tpeak), for noisy population PK data from a sparsely sampled prospectively designed trial. The method is developed within the mixed-effect model framework, for the single-dose and steady-state case. We describe individual concentration vs. time using a longitudinal spline, consisting of a template spline, common to all individuals, and an individual-specific distortion spline accounting for individual differences. We impose a number of constraints on the longitudinal spline, including (i) it has a decreasing tail, (ii) its typical Tpeak is near the modal Tpeak observed in the population data, and (iii) its value is zero at time zero (single dose), or the same nonzero value at the beginning and end of a dosing interval (steady state). We test our method using simulated data and compare its performance to that of a parametric and a nonparametric method. An actual data example is also shown. The performance of the method is as good or better than that of a standard nonparametric method, and when the analysis model is misspecified, the method is superior to a standard parametric one. Since it is often not apparent that an analysis model is correct, we propose this approach as a general method for analysis.

Pharmacodynamics of acute tolerance to multiple nicotinic effects in humans

Tolerance is an important determinant of addiction as well as therapeutic and/or toxic effects of drugs. The development of acute tolerance to various effects of nicotine was studied in nine healthy smokers who were abstaining from tobacco. Nicotine was infused rapidly to reach a concentration of about 25 ng/ml, followed by a computer-controlled infusion to maintain that concentration. A novel semiparametric model of nicotine effects and tolerance was developed. Tolerance to various effects of nicotine (increases in heart rate, blood pressure, plasma epinephrine and energy expenditure) occurred within the range of nicotine levels found in smokers. However, the rate of tolerance development varied considerably. The half-lives of tolerance ranged from 3.5 min for the increase in energy expenditure to 70 min for systolic blood pressure. There was no apparent tolerance to the effects on free fatty acid concentrations, which reflects lipolysis. Differences in the pharmacodynamics of tolerance may reflect differences in rate of desensitization of various subtypes of nicotinic receptors and/or differences in mechanisms of tolerance for various nicotinic effects.

A pooled analysis of CD4 response to zidovudine and zalcitabine treatment in patients with AIDS and AIDS-related complex

INTRODUCTION

This article reports a meta-analysis focused on the efficacy of zalcitabine and zidovudine alone or in combination as reported by three AIDS Clinical Trial Group trials. We analyzed the log CD4 count (LCD4) response to therapy up to 1 year after the beginning of therapy. One of the purposes of this article was to illustrate a meta-analysis method that permits pooling of original data from trials with different designs.

METHODS

To effectively eliminate obvious differences due to design, we first estimated complete (1 year) individual LCD4 versus time curves using a sophisticated smoothing technique. Then several summary descriptors were computed from the completed LCD4 curves. Those descriptors were corrected for baseline covariate differences, and the corrected values were then related to measures of drug exposure.

RESULTS

Significant baseline covariates were LCD4 baseline count and AIDS-related complex or AIDS diagnosis. The predictor, corrected for baseline covariates, that correlated best with drug exposure was intensity, the initial rate of rise of LCD4, estimated as the slope of LCD4 between pretreatment and peak LCD4.

CONCLUSION

Using intensity as a single response measure, we found weak evidence for synergism of zalcitabine and zidovudine: combination therapy increased response by 20% over that expected from a purely additive interaction.

Modeling a bivariate control system: LH and testosterone response to the GnRH antagonist antide

A pharmacodynamic analysis of the input-response relationship between the gonadotropin-releasing hormone antagonist antide and luteinizing hormone (LH) and testosterone concentrations is presented. A control compartmental model is developed using pharmacokinetic and pharmacodynamic data from experiments in which different short intravenous antide infusions were given to healthy male volunteers. Because of the control interdependence between serum LH and testosterone a separation principle similar to one we have used previously to analyze physiological pharmacokinetic data is used for model exploration: testosterone and LH are first modeled separately, conditioning on the other observed response. This reveals that the LH effect on testosterone depends on previous LH exposure and that LH depends not on current but on previous testosterone exposure, resulting in an LH overshoot after antide-induced suppression. Both submodels are combined into one global model, which in addition includes a model for testosterone circadian variation. This model describes the data well and can be used to predict responses for some nonstudied antide dosages. However, the sensitivity of predictions to model assumptions limits the range of valid extrapolation, and this, too, is illustrated.

Chronopharmacokinetics of nicotine

RATIONALE

For high-clearance drugs such as nicotine, hemodynamic changes throughout the day may be expected to influence the rate of metabolism.

MATERIAL AND METHODS

To assess the effects of meals and diurnal rhythms on nicotine clearance, an intravenous infusion of nicotine bitartrate was administered for 48 hours to 11 subjects. Two models to determine nicotine clearance variation throughout the day are described. Both models were used to estimate the mean effect of meal and diurnal rhythms on nicotine clearance and individual parameters that were regressed against baseline covariates. Clearance was modeled as a function of time [CL(t)] and split it in three components: a (constant) baseline value (theta 1), its circadian (diurnal) variation, and the effect of meal: CL(t) = [theta 1 + circadian(t)] [1 + meal(t)]. A two-compartmental (time-variant) model incorporating CL(t) was then fitted to the data providing estimates of CL(t) conditional on literature values of the time-invariant parameters (volume of distribution and intercompartmental clearances).

RESULTS

The estimated circadian(t) showed a maximum at approximately 11 AM and a flat minimum from 6 PM to 3 AM; the estimated meal(t) showed a sharp increase up to 1 hour (after the meal), at which point clearance is increased 42%, and a slower decrease thereafter, returning to baseline (zero) after 2.8 hours. Individual estimates of baseline clearance are found to have a linear relationship with body weight. No other covariate, sex in particular, effect could be found.

Age and autonomic effects on interrelationships between lung volume and heart rate

To determine effects of aging and autonomic input on interrelationships between respiratory and heart rate variability, we collected 5 min of lung volume of R-R interval data from 7 young [27 +/- 3(SD) yr] and 10 older (69 +/- 6 yr) healthy supine humans before and after double pharmacological autonomic blockade with propranolol (0.2 mg/kg iv) and atropine (0.04 mg/kg iv). Estimates of respiratory and heart rate power spectra and linear transfer functions between the two groups were generated by Fourier analysis. Age, double blockade effects, the age-drug interactions were determined by analysis of variance for repeated measures. Basal R-R intervals were unaffected by age. Double blockade decreased R-R intervals and variability in both age groups (P < 0.0001), but R-R intervals decreased less in older than in young subjects (P < 0.0001). In contrast, basal respiratory intervals and standard deviation were greater in older subjects (P = 0.05) and were unaffected by double blockade in young and older subjects. Lung volume-to-heart rate spectral coherence was highest at frequencies associated with respiration and greater in young than in older subjects (P < 0.07). Double blockade decreased lung volume-to-heart rate variability transfer function magnitude (P < 0.007) and increased phase angle (P < 0.02) without age effects or age-drug interactions. In conclusion, heart rate, respiration, and respiration-heart rate interrelations are altered by aging, and double autonomic pharmacological blockade does not eliminate all age-related differences.

A descriptive tool to characterize nonlinear kinetics, with applications to meperidine and lidocaine

We describe an explorative data analysis tool which can detect and describe the presence of nonlinearities in multiple dose kinetics studies. The method is nonparametric (i.e. not dependent on modeling assumptions), uses regression to estimate the functions representing the kinetics, and makes the detection of nonlinearity a part of the model selection process. Flexible functions (splines) are used to describe the kinetics corresponding to the lowest given dose, and to describe the (possible) departure of the kinetics corresponding to higher doses from the reference kinetics. The estimated kinetics and departures can be examined to offer possible insight into the nature of the nonlinearity. The methodology is applied to the analysis of meperidine and lidocaine kinetics through the lungs and the heart. We find that the lung kinetics of lidocaine and meperidine are linear. However their myocardial kinetics are complex and nonlinear.

Concepts, properties, and applications of linear systems to describe distribution, identify input, and control endogenous substances and drugs in biological systems

The response at time t (R(t)) of a (causal linear time invariant) system to an input A(t) is represented by: [equation: see text] where K(t) is called the unit impulse response function of the system, and the integration on the right side of the equation (above) is called the convolution (from the latin cum volvere: to interwine) of A(t) and K(t). The system described by this equation is at zero (initial conditions) when t = 0. Although it does not even begin to describe the incredible variety of possible responses of biological systems to inputs, this representation has large applicability in biology. One of the most frequently used applications is known as deconvolution: to deinterwine R(t) given a known K(t) (or A(t)) and observations of R(t), to obtain A(t) (or K(t)). In this paper attention is focused on a greater variety of aspects associated with the use of linear systems to describe biological systems. In particular I define causal linear time-invariant systems and their properties and review the most important classes of methods to solve the deconvolution problem, address. The problem of model selection, the problem of obtaining statistics and in particular confidence bands for the estimated A(t) (and K(t)), and the problem of deconvolution in a population context is also addressed, and so is the application of linear system analysis to determine fraction of input absorbed (bioavailability). A general model to do so in a multiinput-site linear system is presented. Finally the application of linear system analysis to control a biological system, and in particular to target a desired response level, is described, and a general method to do so is presented. Applications to simulated, endocrinology, and pharmacokinetics data are reported.

A nonparametric subject-specific population method for deconvolution: II. External validation

A lot of attention has been given in the past to deconvolution and in particular to its nonparametric variants. In a companion paper (1), we present a fully nonparametric deconvolution method in which subject specificity is explicitly taken into account. To do so we use so-called "longitudinal splines." A longitudinal spline is a nonparametric function composed of a template spline, in common to all subjects, and of a distortion spline representing the difference of the subject's function from the template. In this paper we concentrate on testing and documenting the performance of this nonparametric methodology in terms of the approximation of unknown functions. We simulate population data using parametric functions, and use longitudinal splines to recover the unknown functions. We consider different estimation methods including (1) parametric nonlinear mixed effect, (2) least squares, and (3) two-stage. Methods 2-3 are more robust than Method 1, and obtain reliable estimates of the unknown functions. The lack of robustness of Method 1 appears to be due to the misspecifications of the distribution of the subjects' parameters. Results also suggest that in a data-rich situation nonparametric nonlinear mixed-effect models should be preferred.

A nonparametric subject-specific population method for deconvolution: I. Description, internal validation, and real data examples

In a pharmacokinetics context deconvolution facilitates the following: (i) Given data obtained after intravascular (generally intravenous) input one may estimate the disposition function; (ii) given the disposition function and data obtained after extravascular administration one may estimate the extravascular to vascular input rate function. In general if the data can be represented by the convolution of two functions, of which one is unknown, deconvolution allows the estimation of the unknown one. Attention has been given in the past to deconvolution and in particular to its nonparametric variants. However, in a population context (multiple observations collected in each of a group of subjects) the use of nonparametric deconvolution is limited to either analyzing each subject separately or to analyzing the aggregate response from the population without specifying subject-specific characteristics. To our knowledge a fully nonparametric deconvolution method in which subject specificity is explicitly taken into account has not been reported. To do so we use so-called "longitudinal splines." A longitudinal spline is a nonparametric function composed of a template spline, in common to all subjects, and of a distortion spline representing the difference of the subject's function from the template. Using longitudinal splines for input rate or disposition function one obtains a solution to the problem of taking subject specificity into account in a nonparametric deconvolution context. To obtain estimates of longitudinal splines we consider three different methods: (1) parametric nonlinear mixed effect, (2) least squares, and (3) two-stage. Results obtained in one simulated and two real data analyses are shown.

A new method to explore the distribution of interindividual random effects in non-linear mixed effects models

This article presents a new approach for exploring the distribution of interindividual random effects in nonlinear mixed effect models. The approach introduces a spline function, which transforms an assumed normally distributed interindividual random effect to an arbitrary distribution approximating that of the data. The performance of this tool is illustrated using simulated pharmacokinetic data with non-normally distributed random effects. Results of the analyses of two real kinetic data sets are also presented.

Pharmacokinetic-pharmacodynamic (PK-PD) modelling in non-steady-state studies and arterio-venous drug concentration differences

In conducting a non-steady-state pharmacokinetic (PK)-pharmacodynamic (PD) study there is potential for the observed effect (E) vs time, and venous plasma drug concentration (C) vs time, profiles to display temporal displacement with respect to each other. This is most frequently observed when there exists a distributional nonequilibrium across the effect organ giving rise to hysteresis, i.e. observed C preceding E in the time domain, with the resulting potential for a counterclockwise loop to be generated in the observed E vs C plot (when data are connected in time-order). Such temporal displacement does not afford direct prediction of the steady-state E vs C PD relationship. When an arterio-venous (A-V) difference exists across the tissues of the blood sampling compartment (i.e. the arm), and this arises solely from an elimination process then drug concentration in the respective peripheral arterial plasma and venous plasma compartments will be in equilibrium at all times during a non-steady-state PK experiment. If there are no other sources of temporal displacement in the relationship between E and C then the observed E vs C plot will be a direct predictor of the steady-state E vs C PD relationship. In contrast when the A-V difference is of a distributional nature then proteresis, i.e. observed E preceding C in the time domain, will arise with the potential for the generation of a clockwise loop in the observed E vs C relationship. Simulated error-incorporated E vs time, and C vs time, data was analysed by semi-parametric implementation of an effect-compartment link-model that affords accurate steady-state E vs C PD predictions (without the requirement of sampling arterial blood) from data that incorporates the concurrent presence of: (i) distributional nonequilibrium across the effect organ, and (ii) distributional A-V non-equilibrium. Accurate steady-state E vs C PD predictions were achieved irrespective of the comparative magnitudes of the two nonequilibria, i.e. whether the rate of equilibration across the effect organ was faster than, or slower than, the rate of equilibration across the arm (resulting in a clockwise or counterclockwise loop in the observed E vs C plot, respectively), or indeed if one or other of the nonequilibria is essentially absent. When the rate of equilibration across the effect organ is slower than the rate of A-V equilibration (i.e. counterclockwise loop generated in the observed E vs C plot) then the need to model for the underlying A-V nonequilibrium is redundant, i.e. accurate steady-state E vs C PD predictions can be achieved with implementation (strictly incorrectly) of a more simple link parameterised solely to model for distributional nonequilibrium across the effect organ.(ABSTRACT TRUNCATED AT 400 WORDS)

Semiparametric models for antagonistic drug interactions

A new class of models to describe antagonistic drug interactions are presented. They are semiparametric in that they use nonparametric functions (splines) but are forced to obey certain constraints corresponding to reasonable assumptions. We propose the models primarily for exploratory data analysis, but they may also be definitive models for such purposes as predicting future responses. Certain problems that arise in semiparametric modeling, such as model selection, are addressed so that we can propose a relatively automatic and objective approach to model determination. We demonstrate the applicability of the class of models we propose to two real data set examples involving pain relief response to opioid agonists/antagonists. The results suggest that the semiparametric approach is particularly useful when unusual shapes link dose to response.

Estimation and model selection in constrained deconvolution

We analyze in detail the estimation problem associated with the following problem. Given n noisy measurements (yi, i = 1, ..., n) of the response of a system to an input (A(t) where t indicates time), obtain an estimate of A(t) given a known K(t) (the unit impulse response function of the system) under the model: yi = integral of 0(ti) A(s)K(ti - s)ds + epsilon i where epsilon 1, ... ,epsilon n are independent identically distributed random variables with mean zero and common finite variance. In the solution to the problem, the unknown function is represented by a spline function, and the problem is recast in terms of (inequality constrained) linear regression. The main issues addressed are: (a) the comparison of different nonparametric regression methods in this context, and (b) how to do model selection, i.e., given a (finite) set of candidate spline functions, select the (possibly unique) best one using some (statistically based) selection criteria. Different spline candidate sets, and different asymptotic and resampling-based statistical selection criteria are compared by means of simulations. Due to the particular nature of the estimation problem, modifications to the criteria are suggested. Applications to simulated and real pharmacokinetics data are reported.

Two constrained deconvolution methods using spline functions

This paper describes two new methods to solve the following estimation problem. Given n1 noisy measurements (yi1, i = 1,..., n1) of the response of a system to a known input [A1(t) where t indicates time], and n2 noisy measurements (yi2, i = 1,..., n2) of the response of a system to an unknown input [A2(t)], obtain an estimate of A2(t) and K(t) (the unit impulse response function of the system) under the model: [formula: see text] where Eij are independent identically distributed random variables. Both methods use spline functions to represent the unknown functions, and they automatically select the spline functions representing the unknown input and unit impulse response functions. The first method estimates separately the unit impulse response function and the input, recasting the problem in terms of inequality-constrained linear regression. The second method jointly estimates the unit impulse response function and the input function, recasting the problem in terms of inequality-constrained nonlinear regression. Simulated and real data analysis are reported.

Aging effects on stereoselective pharmacokinetics and pharmacodynamics of verapamil

Pharmacokinetics and pharmacodynamics were studied after separate single 15-min infusions of each of verapamil's enantiomers (d, 10-11 mg/kg; l, 0.10-0.11 mg/kg) in 16 healthy non-smoking subjects ranging in age from 24 to 40 (young) and from 63 to 83 years (elderly). Verapamil clearance was found to be decreased in an age-related stereoselective manner, with significant reductions in l-verapamil clearance in older subjects (P < .03), but no age-related change in d-verapamil clearance. Greater l- vs. d-verapamil clearance rates were only seen in younger male subjects. Trends for increased elimination half-lives for both enantiomers were seen with increasing age (for d-, P < .09, l- P = .10). Protein binding was stereoselective, with greater binding of d- vs. l-verapamil in both age groups (P < .0001) with no age-related differences in binding detected. Vd beta was greater for d- vs. l-verapamil (P < .05). l-Verapamil was more potent than d-verapamil (P < .001) for all pharmacodynamic variables measured. Both verapamil enantiomers decreased blood pressure (P < .0001), increased P-R intervals during sinus rhythm (P < .0001) and atrioventricular Wenckebach block cycle lengths (P < .0001) and transiently increased heart rate (P < .0001) in both young and elderly subjects. Age-related differences in responses were seen for blood pressure (greater decreases in systolic pressure in the elderly after d-verapamil, P < .002), heart rate (smaller and only transient increases followed by decreases after d-verapamil) and P-R intervals during sinus rhythm (less prolongation in the elderly after both enantiomers, P < .02).(ABSTRACT TRUNCATED AT 250 WORDS)

Building population pharmacokinetic--pharmacodynamic models. I. Models for covariate effects

One major task in clinical pharmacology is to determine the pharmacokinetic-pharmacodynamic (PK-PD) parameters of a drug in a patient population. NONMEM is a program commonly used to build population PK-PD models, that is, models that characterize the relationship between a patient's PK-PD parameters and other patient specific covariates such as the patient's (patho) physiological condition, concomitant drug therapy, etc. This paper extends a previously described approach to efficiently find the relationships between the PK-PD parameters and covariates. In a first step, individual estimates of the PK-PD parameters are obtained as empirical Bayes estimates, based on a prior NONMEN fit using no covariates. In a second step, the individual PK-PD parameter estimates are regressed on the covariates using a generalized additive model. In a third and final step, NONMEM is used to optimize and finalize the population model. Four real-data examples are used to demonstrate the effectiveness of the approach. The examples show that the generalized additive model for the individual parameter estimates is a good initial guess for the NONMEM population model. In all four examples, the approach successfully selects the most important covariates and their functional representation. The great advantage of this approach is speed. The time required to derive a population model is markedly reduced because the number of necessary NONMEM runs is reduced. Furthermore, the approach provides a nice graphical representation of the relationships between the PK-PD parameters and covariates.

Elderly, conscious patients have an accentuated hypotensive response to nitroglycerin

There is no adequate explanation for the highly variable response of systemic blood pressure to nitroglycerin (glyceryl trinitrate [GTN]). Aging produces cardiovascular changes that should alter the effects of GTN, but elderly patients usually have been excluded from studies of GTN. Accordingly, the authors compared the effects of GTN on systemic blood pressure in elderly and younger patients. Fifty-three patients, aged 49-87 (with 30 patients older than 70), were studied. Before elective vascular surgery, 14 patients received an infusion of placebo; 26, a constant infusion of GTN; and 13, a stepwise increasing infusion of GTN. After a standardized anesthetic induction and the start of surgery, the identical infusion protocols were repeated in each group. Data on GTN infusion rate, arterial blood pressure, and GTN concentrations versus time, age, and other potentially influencing variables were pooled for analysis. Before anesthesia and surgery, GTN more commonly caused excessive hypotension in patients older than 70 yr than in younger patients, but none of the patients had complications. A repeated-measures model analysis indicated that age significantly influenced the effects of GTN on blood pressure. That is, patients who are in their 70s who receive 0.5 micrograms.kg-1.min-1 of GTN are predicted to experience a twofold greater decrease in systolic arterial pressure (approximately 33 mmHg) than patients in their 50s. However, no apparent effect of age on intraoperative GTN responsiveness was discernible nor was a predictable relationship found between the preoperative and intraoperative responsiveness or between arterial concentrations of GTN and blood pressure or age. Therefore, the authors conclude that, in the absence of the effects of anesthesia and surgery, elderly patients have a more pronounced blood pressure response to GTN than younger patients. Furthermore, the authors conclude that preoperative blood pressure responsiveness to GTN is not a reliable predictor of intraoperative responsiveness.

Comparing responses when each response is a curve

We describe, generalize, and demonstrate the application of a method (W. H. Lawton, A. Sylvestre, and M. S. Maggio, Technometrics 14: 513-532, 1972) that can be used to partially analyze population data. The data from each subject consist of a series of responses observed at distinct values of a predictor variable. The method assumes that all subjects' data originate from a common process but differ because the "units" of predictor and response variables differ among subjects. For example, if the predictor variable is time, time can be "faster" or "slower" from subject to subject. We deal with two different problems. In the first one the response at x for the ith subject is of the form beta 1i + beta 2iG[(x - beta 3i)/beta 4i] + epsilon, where G(x) is a mathematical "shape" function (of the predictor variable x) representing the process and epsilon is observation error. The units of observed and predictor variable are then defined by the values of beta 1i, beta 2i and beta 3i, beta 4i, respectively. In particular beta 1i and beta 3i express shifts and beta 2i, beta 4i express scales of the observed and predictor variables, respectively. In the second problem the response at x for the ith subject is of the form beta 1i + beta 2i integral of x0 G[(s - beta 3i)/beta 4i].Hi(x - s) ds + epsilon, where Hi(x) is a known function. In both problems, the method estimates the common "shape" function G(x) nonparametrically and the parameters beta 1i, beta 2i, beta 3i, and beta 4i for each subject.(ABSTRACT TRUNCATED AT 250 WORDS)

Effects of interleukin 3 and interleukin 6 on platelet recovery in mice treated with 5-fluorouracil

We have studied the effects of murine recombinant interleukin 3 (IL-3) and human recombinant interleukin 6 (IL-6) on platelet recovery after administration of 5-fluorouracil (5-FU) to mice. 5-FU at 250 mg/kg body weight was administered as a single i.p. injection, and treatment with IL-3 alone, IL-6 alone, or a combination of IL-3 plus IL-6 was initiated immediately following the 5-FU or after a delay of 2 days. In addition, the effects of the combination of IL-3 plus IL-6 were evaluated following delays in initiation of their administration until 4 or 6 days after 5-FU treatment. In all schedules, the IL-3 and IL-6 treatments were discontinued 8 days following 5-FU. IL-3 and IL-6 were given s.c. three times daily; each injection of IL-3 was 80,000 U, each injection of IL-6 was 5000 U, and the combination comprised separate injections of IL-3 and IL-6 at the same respective doses. The combination of IL-3 and IL-6, initiated immediately or 2 days following 5-FU, diminished the platelet nadir and increased platelet counts on individual days during the recovery phase, thus apparently decreasing the time required for recovery to a normal platelet level. However, using self-modeling nonlinear regression, in order to analyze variability in the duration of thrombocytopenia, statistically significant shortening of the period of thrombocytopenia could not be consistently demonstrated. Neither IL-3 alone nor IL-6 alone had any effect on the above parameters. Recovery of hematocrit values and white blood cell levels was unaffected by administration of either IL-3 or IL-6 alone or the combination of both cytokines. We propose that IL-3 and IL-6 can act synergistically to enhance platelet recovery following 5-FU-mediated thrombocytopenia, but their modification of the response to 5-FU is modest.

Reversal of neuromuscular blockade in humans by neostigmine and edrophonium: a mathematical model

Generalizations of the integrated model describing the interaction of nondepolarizing neuromuscular blocking drugs with reversible anticholinesterase drugs described in Unadkat et al. (1) are reported. The models can deal with possible incomplete reversal (irreversible block) and/or noninstantaneous anticholinesterase kinetics. Experimental data were obtained from 22 human volunteers. Different levels of steady-state vecuronium block were induced in each volunteer (in the range of 50% to 95%), and reversed by short infusions of edrophonium (10 volunteers) or neostigmine (12 volunteers). Edrophonium or neostigmine concentrations and twitch tension (measured as the force of thumb adduction) were measured. The generalized integrated models fit the data well. In the case of neostigmine we find a nondistributional delay in its action. We relate this delay to the slow decarbamylation rate of the (neostigmine-induced) carbamylated anticholinesterase observed in vitro, and are able to model such noninstantaneous anticholinesterase kinetic processes. For both edrophonium and neostigmine we detect an inverse relationship between the (induced) level of initial block and maximal percentage recovery.

Semiparametric analysis of non-steady-state pharmacodynamic data

We present an approach to the analysis of pharmacodynamic (PD) data arising from non-steady-state experiments, meant to be used when only PD data, not pharmacokinetic (PK) data, are available. The approach allows estimation of the steady-state relationship between drug input and effect. The analysis is based on a model describing the time dependence of drug effect (E) on (unobserved) drug concentration (Ce) in an hypothetical effect compartment. The model consists of (i) a known model for the input rate of drug I(t), (ii) a parametric model; L(t, alpha) (a function of time t, and vector of parameters alpha), relating I to an observed variable X, (iii) a nonparametric model relating X to E. Ce is proportional to X. X (t) is given by I(t) * L(t, alpha)/AL, where L(t, alpha) = e-alpha 1t * sigma k m = 1 alpha 2k e-alpha 2k + 1t, sigma k m = 1 alpha 2k = 1, AL = integral of 0 infinity L(t) dt, and * indicates convolution. The nonparametric model relating X to E is a cubic spline, a function of X and a vector of (linear) parameters beta. The values of alpha and beta are chosen to minimize the sum of squared residuals between predicted and observed E. We also describe a similar model, generalizing a previously described one, to analyze PK/PD data. Applications of the approach to different drug-effect relationships (verapamil-PR interval, hydroxazine-wheal and flare, flecainide and/or verapamil-PR, and left ventricular ejection fraction) are reported.

Mean time parameters for generalized physiological flow models (semihomogeneous linear systems)

This note gives expressions for recirculation mean time parameters of the disposition kinetics of particles in a semihomogeneous stationary linear system. In such a system each compartment may have an arbitrary single-pass disposition function, rather than a known parametric (usually monoexponential) one. Such systems provide a generalization of physiological flow models. Given observations of arterial blood concentrations and tissue amounts, and making the additional assumptions that (i) the fraction of total blood flow exiting each tissue that goes to each other tissue is constant and known, and (ii) the fraction of drug entering each tissue that is eliminated to the outside is constant and known, the input to each tissue can be known, and therefore both its total blood flow and its single-pass disposition function can be estimated. Recirculation mean time parameters can be computed from these estimates. Application to real thiopental data is presented as an example.

Comments on two recent deconvolution methods

In a recent paper Vajda et al. presented a deconvolution method based on the assumptions that the response of a system and the input function to a system are described by first-order linear processes. The method is similar to one proposed by Veng-Pedersen, and obtains similar results. In this article a simpler, not new, and now generally available method for this special use is considered to point out potential risks associated with all three deconvolution methods.

Comparative tissue concentration profiles of fentanyl and alfentanil in humans predicted from tissue/blood partition data obtained in rats

The steady-state tissue/blood partition coefficients of fentanyl and alfentanil were determined in 13 organs and tissues in the rat. A 6-h infusion of both drugs was used in order to achieve steady-state. Blood and tissue concentrations of drugs were measured by gas-liquid chromatography. The partition coefficients of fentanyl were two- to 30-fold higher than those of alfentanil. These data were then used in a physiologic pharmacokinetic model describing the disposition of the two opioids in humans. The model predicted the plasma pharmacokinetics of these drugs in humans reasonably well. However, simulation beyond 24 h after a bolus administration showed a terminal half-life of 20 h for fentanyl, i.e., an elimination phase that has not yet been described in actual pharmacokinetic studies. In keeping with this, the volume of distribution of fentanyl in the model was also larger than expected. The simulated tissue concentration curves of fentanyl and alfentanil in humans could be used to explain the propensity of fentanyl to give secondary peaks in plasma concentration curves and the difference in effect kinetics between the two opioids. Physiologic pharmacokinetic modeling, based on measured data in small animals, can generate information that is not obtainable by empirical methods in humans.

Pharmacodynamic modeling of verapamil effects under steady-state and nonsteady-state conditions

Pharmacodynamic models relating the plasma concentration (Cp) of verapamil to the drug's effect (E) on the P-R interval were investigated after single dose infusions of (0.15-0.22 mg/kg) verapamil in 22 normal subjects. Model predictions of the steady-state Cp-E relationship were then compared to results from actual steady-state drug infusions in the same subjects. Two methods of estimating the steady-state concentration response relationship from the single dose data were examined: 1) the relationship of descending limb Cp vs. E and 2) the relationship of estimated effect site concentrations (Ce) vs. E. When compared to experimental steady-state measurements, the absolute errors of predictions from the Ce vs. E method were less than those from the Cp vs. E predictions (6.8 +/- 4.4 vs. 9.6 +/- 6.6, mean +/- S.D.). Similarly, the slope of the linear regression of E on Cp differed more from the observed steady-state slope than the slope of E on Ce. Sigmoid Emax models fit to Cp vs. E. data gave false Emax values even when data immediately following drug infusion were disregarded whereas Ce vs. E plots demonstrated that Emax was not reached (and Ce much less than Cp). Neither the postinfusion (descending limb) Cp vs. E nor Ce vs. E plots allowed analysis of higher concentration vs. effect relationships after usual (0.15-0.22 mg/kg) doses of verapamil. In summary, we have demonstrated that nonsteady-state postdrug infusion effect vs. plasma concentration data for verapamil does not reflect the true steady-state relationship and that use of a model to estimate effect site concentration provides a closer estimate of the true steady-state relationship.

The pharmacokinetics and pharmacodynamics of diltiazem and its metabolites in healthy adults after a single oral dose

A potential complicating factor in the characterization of the pharmacokinetics and pharmacodynamics of diltiazem after an oral dose in the presence of two metabolites, N-demethyldiltiazem and desacetyldiltiazem, in plasma. Both N-demethyldiltiazem and desacetylditiazem have been shown to have pharmacologic activity in animal tissues. It is therefore possible that these metabolites contribute to the pharmacologic effect of diltiazem, but this possibility has not been explored. The purpose of this study was to investigate the pharmacokinetics and pharmacodynamics of diltiazem, N-demethyldiltiazem, and desacetyldiltiazem. Particular attention was paid to the effect of diltiazem on atrioventricular conduction. Six healthy men received a 120 mg oral dose of diltiazem. Concentrations of diltiazem, N-demethyldiltiazem, and desacetyldiltiazem in plasma and urine were measured by a sensitive HPLC method. Measures of pharmacologic response (heart rate, blood pressure, and PR interval) were obtained at each blood sampling time. Mean (+/- SD) peak plasma concentrations of diltiazem, N-demethyldiltiazem, and desacetyldiltiazem were 174.3 +/- 72.7, 42.6 +/- 10.0, and 14.9 +/- 3.3 ng/ml, respectively. The apparent half-lives of diltiazem, N-demethyldiltiazem, and desacetyldiltiazem were 6.5 +/- 1.4 hours, 9.4 +/- 2.2 hours, and 18 +/- 6.2 hours, respectively. Both N-demethyldiltiazem and diltiazem were eliminated by net secretion, whereas the renal clearance of desacetyldiltiazem did not exceed clearance by filtration. Both N-demethyldiltiazem and desacetyldiltiazem are bound to plasma proteins, with unbound fractions of 0.323 +/- 0.035 and 0.230 +/- 0.021. These values are similar to the unbound fraction of diltiazem (0.254 +/- 0.027). No significant effect of diltiazem on blood pressure or heart rate was noted. However, a prolongation of the PR interval was observed in all six subjects. Furthermore, an apparent clockwise hysteresis in the concentration-effect relationship was found in four of the six subjects. These findings suggest that some form of acute tolerance to the electrophysiologic effect of diltiazem develops, but the results of pharmacodynamic modeling suggest that this is not caused by the antagonistic effects the metabolites.

A semiparametric approach to physiological flow models

By regarding sampled tissues in a physiological model as linear subsystems, the usual advantages of flow models are preserved while mitigating two of their disadvantages, (i) the need for assumptions regarding intratissue kinetics, and (ii) the need to simultaneously fit data from several tissues. To apply the linear systems approach, both arterial blood and (interesting) tissue drug concentrations must be measured. The body is modeled as having an arterial compartment (A) distributing drug to different linear subsystems (tissues), connected in a specific way by blood flow. The response (CA, with dimensions of concentration) of A is measured. Tissues receive input from A (and optionally from other tissues), and send output to the outside or to other parts of the body. The response (CT, total amount of drug in the tissue (T) divided by the volume of T) from the T-th one, for example, of such tissues is also observed. From linear systems theory, CT can be expressed as the convolution of CA with a disposition function, F(t) (with dimensions 1/time). The function F(t) depends on the (unknown) structure of T, but has certain other constant properties: The integral integral infinity0 F(t) dt is the steady state ratio of CT to CA, and the point F(0) is the clearance rate of drug from A to T divided by the volume of T. A formula for the clearance rate of drug from T to outside T can be derived. To estimate F(t) empirically, and thus mitigate disadvantage (i), we suggest that, first, a nonparametric (or parametric) function be fitted to CA data yielding predicted values, CA, and, second, the convolution integral of CA with F(t) be fitted to CT data using a deconvolution method. By so doing, each tissue's data are analyzed separately, thus mitigating disadvantage (ii). A method for system simulation is also proposed. The results of applying the approach to simulated data and to real thiopental data are reported.