Keith M. Gregg

Response surface model for anesthetic drug interactions

Background Anesthetic drug interactions traditionally have been characterized using isobolographic analysis or multiple logistic regression. Both approaches have significant limitations. The authors propose a model based on response-surface methodology. This model can characterize the entire dose–response relation between combinations of anesthetic drugs and is mathematically consistent with models of the concentration–response relation of single drugs. Methods The authors defined a parameter, &thgr;, that describes the concentration ratio of two potentially interacting drugs. The classic sigmoid Emax model was extended by making the model parameters dependent on &thgr;. A computer program was used to estimate response surfaces for the hypnotic interaction between midazolam, propofol, and alfentanil, based on previously published data. The predicted time course of effect was simulated after maximally synergistic bolus dose combinations. Results The parameters of the response surface were identifiable. With the test data, each of the paired combinations showed significant synergy. Computer simulations based on interactions at the effect site predicted that the maximally synergistic three-drug combination tripled the duration of effect compared with propofol alone. Conclusions Response surfaces can describe anesthetic interactions, even those between agonists, partial agonists, competitive antagonists, and inverse agonists. Application of response-surface methodology permits characterization of the full concentration–response relation and therefore can be used to develop practical guidelines for optimal drug dosing.

Algorithms to rapidly achieve and maintain stable drug concentrations at the site of drug effect with a computer-controlled infusion pump

Computer-controlled infusion pumps incorporating an internal model of drug pharmacokinetics can rapidly achieve and maintain constant drug concentrations in the plasma. Although these pumps offer more accurate titration of intravenous drugs than is possible with simple boluses or constant rate infusions, the choice of the plasma as the target site is arbitrary. The plasma is not the site of drug effect for most drugs. This manuscript describes two algorithms for calculation of the infusion rates necessary for a computer-controlled infusion pump to rapidly achieve, and then maintain, the desired target concentration at the site of drug effect rather than in the plasma.

Using the time of maximum effect site concentration to combine pharmacokinetics and pharmacodynamics.

Background To simulate the time course of drug effect, it is sometimes necessary to combine the pharmacodynamic parameters from an integrated pharmacodynamic–pharmacodynamic study (e.g., volumes, clearances, ke0 [the effect site equilibration rate constant], C50 [the steady state plasma concentration associated with 50% maximum effect], and the Hill coefficient) with pharmacokinetic parameters from a different study (e.g., a study examining a different age group or sampling over longer periods of time). Pharmacokinetic–pharmacodynamic parameters form an interlocked vector that describes the relationship between input (dose) and output (effect). Unintended consequences may result if individual elements of this vector (e.g., ke0) are combined with pharmacokinetic parameters from a different study. The authors propose an alternative methodology to rationally combine the results of separate pharmacokinetic and pharmacodynamic studies, based on tpeak, the time of peak effect after bolus injection. Methods The naive approach to combining separate pharmacokinetic and pharmacodynamic studies is to simply take the ke0 from the pharmacodynamic study and apply it naively to the pharmacokinetic study of interest. In the tpeak approach, ke0 is recalculated using the pharmacokinetics of interest to yield the correct time of peak effect. The authors proposed that the tpeak method would yield better predictions of the time course of drug effect than the naive approach. They tested this hypothesis in three simulations: thiopental, remifentanil, and propofol. Results In each set of simulations, the tpeak method better approximated the postulated “true” time course of drug effect than the naive method. Conclusions Tpeak is a useful pharmacodynamic parameter and can be used to link separate pharmacokinetic and pharmacodynamic studies. This addresses a common difficulty in clinical pharmacology simulation and control problems, where there is usually a wide choice of pharmacokinetic models but only one or two published pharmacokinetic–pharmacodynamic models. The results will be immediately applicable to target-controlled anesthetic infusion systems, where linkage of separate pharmacokinetic and pharmacodynamic parameters into a single model is inherent in several target-controlled infusion designs.

Validation of the Alfentanil Canonical Univariate Parameter as a Measure of Opioid Effect on the Electroencephalogram

Background Several parameters derived from the multivariate electroencephalographic (EEG) signal have been used to characterize the effects of opioids on the central nervous system. These parameters were formulated on an empirical basis. A new statistical method, semilinear canonical correlation, has been used to construct a new EEG parameter (a certain combination of the powers in the EEG power spectrum) that correlates maximally with the concentration of alfentanil at the effect site. To date, this new canonical univariate parameter (CUP) has been tested only in a small sample of subjects receiving alfentanil.

Derivation and cross-validation of pharmacokinetic parameters for computer-controlled infusion of lidocaine in pain therapy

Background Lidocaine administered intravenously is efficacious in treating neuropathic pain at doses that do not cause sedation or other side effects. Using a computer-controlled infusion pump (CCIP), it is possible to maintain the plasma lidocaine concentration to allow drug equilibration between the plasma and the site of drug effect. Pharmacokinetic parameters were derived for CCIP administration of lidocaine in patients with chronic pain. Methods Thirteen patients (mean age 45 yr, mean weight 66 kg) were studied. Eight subjects received a computer-controlled infusion, targeting four increasing lidocaine concentrations (1-7 micro gram *symbol* ml sup -1) for 30 min each, based on published kinetic parameters in which venous samples were obtained infrequently after bolus administration. From the observations in these eight patients, new lidocaine pharmacokinetic parameters were estimated. These were prospectively tested in five additional patients. From the complete data set (13 patients), final structural parameters were estimated using a pooled analysis approach. The interindividual variability was determined with a mixed-effects model, with the structural model parameters fixed at the values obtained from the pooled analysis. Internal cross-validation was used to estimate the residual error in the final pharmacokinetic model. Results The lidocaine administration based on the published parameters consistently produced higher concentrations than desired, resulting in acute lidocaine toxicity in most of the first eight patients. The highest measured plasma concentration was 15.3 micro gram *symbol* ml sup -1. The pharmacokinetic parameters estimated from these eight patients differed from the initial estimates and included a central volume one-sixth of the initial estimate. In the subsequent prospective test in five subjects, the new parameters resulted in concentrations evenly distributed around the target concentration. None of the second group of subjects had evidence of acute lidocaine toxicity. The final parameters (+/-population variability expressed as %CV) were estimated as follows: V1 0.101+/-53% 1 *symbol* kg sup -1, V2 0.452 +/-33% l *symbol* kg sup -1, Cl1 0.0215+/-25% l *symbol* kg sup -1 *symbol* min sup -1, and Cl2 0.0589+/-35% l *symbol* kg sup -1 *symbol* min sup -1. The median error measured by internal cross-validation was +1.9%, and the median absolute error was 14%. Conclusions Pharmacokinetic parameters for lidocaine were derived and administration was prospectively tested via computer-controlled infusion pumps for patients with chronic neuropathic pain. The estimated parameters performed well when tested prospectively. A second estimation step further refined the parameters and improved performance, as measured using internal cross-validation.

Application of semilinear canonical correlation to the measurement of opioid drug effect

To examine the relationship between the electroencephalograph (EEG) and plasma opioid concentration, one would like to collapse the high-dimensional EEG signal into a univariate quantity. Such a simplification of the EEG is desirable because a univariate quantity can be modeled using standard nonlinear regression techniques, and because most of the information in the EEG is redundant or unrelated to drug concentration. In previous studies of the EEG response to opioids, the manner in which a univariate component was extracted from the EEG was ad hoc.In this paper, this extraction was performed optimally using a new statistical technique, semilinear canonical correlation. Data from 15 patients who received an intravenous infusion of the semisynthetic opioid alfentanil were analyzed. The components of the EEG that were nearly maximally correlated with plasma drug concentration were found, based on a standard pharmacokinetic-pharmacodynamic model. Two new EEG components were produced from the powers in the frequency spectrum of the EEG: a weighted sum of the logarithms of the powers, and a weighted sum of the powers expressed as percentages of the total power. These components both had a median R2of 0.84, compared to median R2sranging from 0.37 to 0.83 for five commonly used ad hocEEG components. The new components also had less variability in R2between subjects.

Role of serotonergic neurotransmission in the hypnotic response to dexmedetomidine, an α2-adrenoceptor agonist

The role of serotonergic pathways in the hypnotic response to dexmedetomidine was examined in neurochemical and behavioral studies. Following acute administration of dexmedetomidine, loss of righting reflex and changes in serotonin (5-hydroxytryptamine, 5-HT) and norepinephrine turnover in different brain regions (locus coeruleus and hippocampus) were assessed. In separate experiments, the effect of dexmedetomidine on 5-HT turnover was measured in rats rendered tolerant to the hypnotic effects of dexmedetomidine. These neurochemical data were complemented by a study of dexmedetomidine-induced hypnotic response in the presence of a 5-HT2 receptor agonist and antagonist, 1-(2,5-dimethoxy-4-iodophenyl)-2-aminopropane (DOI) and ritanserin, respectively. Dexmedetomidine (1-500 micrograms.kg-1) dose dependently reduced 5-HT and norepinephrine turnover in both the locus coeruleus and hippocampus. The decrease in 5-HT turnover more closely correlated with the dose-response curve for loss of righting reflex, a behavioral measure of hypnosis, than did the norepinephrine turnover. In previous studies with chronic administration of dexmedetomidine (3 micrograms.kg-1.h-1 for 7 days), the norepinephrine turnover effect of acute dexmedetomidine (30 micrograms.kg-1) persisted while the hypnotic effect was blunted. Following the same regimen, the drugs ability to diminish 5-HT turnover was also blunted. This biochemical evidence for the role of 5-HT in sleep was supported by the behavioral evidence that dexmedetomidine (100 micrograms.kg-1 i.p. or 7 micrograms.0.2 microliter-1 locus coeruleus)-induced hypnosis was dose dependently blocked by DOI (0.08-0.32 mg.kg-1 i.p.). The selectivity of this effect was demonstrated by the finding that ritanserin (0.16 mg.kg-1 i.p.) pretreatment blocked the effects of DOI (0.16 mg.kg-1 i.p.) on dexmedetomidine (100 micrograms.kg-1 i.p. or 7 micrograms.0.2 microliter-1 locus coeruleus)-induced loss of righting reflex. In conclusion, these findings suggest that the hypnotic effect of the alpha 2-adrenoceptor agonist, dexmedetomidine, is not mediated solely by changes in noradrenergic neurtransmission, but instead is strongly associated with a decrease in serotonergic neurotransmission and correspondingly diminished by stimulation of 5-HT2 receptors.

A technique for population pharmacodynamic analysis of concentration-binary response data.

Background: Pharmacodynamic data frequently consist of the binary assessment (a “yes” or “no” answer) of the response to a defined stimulus (verbal stimulus, intubation, skin incision, and so on) for multiple patients. The concentration‐effect relation is usually reported in terms of C50, the drug concentration associated with a 50% probability of drug effect, and a parameter the authors denote gamma, which determines the shape of the concentration‐probability of effect curve. Accurate estimation of gamma, a parameter describing the entire curve, is as important as the estimation of C50, a single point on this curve. Pharmacodynamic data usually are analyzed without accounting for interpatient variability. The authors postulated that accounting for interpatient variability would improve the accuracy of estimation of gamma and allow the estimation of C50 variability. Methods: A probit‐based model for the individual concentration‐response relation was assumed, characterized by two parameters, C50 and gamma. This assumption was validated by comparing probit regression with the more commonly used logistic regression of data from individual patients found in the anesthesiology literature. The model was then extended to analysis of population data by assuming that C50 has a log‐normal distribution. Population data were analyzed in terms of three parameters, (C5‐0>, the mean value of C50 in the population; omega, the standard deviation of the distribution of the logarithm of C50; and 3. The statistical characteristics of the technique were assessed using simulated data. The data were generated for a range of gamma and omega values, assuming that C50 and had a log‐normal distribution. Results: The probit‐based model describes data from individual patients and logistic regression does. Population analysis using the extended probit model accurately estimated , gamma, and omega for a range of values, despite the fact that the technique accounts for C sub 50 variability but not gamma variability. Conclusion: A probit‐based method of pharmacodynamic analysis of pooled population data facilitates accurate estimation of the concentration‐response curve.