William F. Ebling

computer Simulation of the Effects of Alterations in Blood Flows and Body Composition on Thiopental Pharmacokinetics in Humans

Background: Understanding the influence of physiological variables on thiopental pharmacokinetics would enhance the scientific basis for the clinical usage of this anesthetic. Methods: A physiological pharmacokinetic model for thiopental previously developed in rats was scaled to humans by substituting human values for tissue blood flows, tissue masses, and elimination clearance in place of respective rat values. The model was validated with published serum concentration data from 64 subjects. The model was simulated after intravenous thiopental administration, 250 mg, over 1 min, to predict arterial plasma concentrations under conditions of different cardiac outputs, degrees of obesity, gender, or age. Results: The human pharmacokinetic model is characterized by a steady state volume of distribution of 2.2 l/kg, an elimination clearance of 0.22 l/min, and a terminal half‐life of 9 h. Measured thiopental concentrations are predicted with an accuracy of 6 +/‐ 37% (SD). Greater peak arterial concentrations are predicted in subjects with a low versus a high cardiac output (3.1 and 9.4 l/min), and in subjects who are lean versus obese (56 and 135 kg). Acutely, obesity influences concentrations because it affects cardiac output. Prolonged changes are due to differences in fat mass. Changes with gender and age are relatively minor. Conclusions: The physiological pharmacokinetic model developed in rats predicts thiopental pharmacokinetics in humans. Differences in basal cardiac output may explain much of the variability in early thiopental disposition between subjects.

From Piecewise to Full Physiologic Pharmacokinetic Modeling: Applied to Thiopental Disposition in the Rat

Physiologically based pharmacokinetic modeling procedures employ anatomical tissue weight, blood flow, and steady tissue/blood partition data, often obtained from different sources, to construct a system of differential equations that predict blood and tissue concentrations. Because the system of equations and the number of variables optimized is considerable, physiologic modeling frequently remains a simulation activity where fits to the data are adjusted by eye rather than with a computer-driven optimization algorithm. We propose a new approach to physiological modeling in which we characterize drug diposition in each tissue separately using constrained numerical deconvolution. This technique takes advantage of the fact that the drug concentration time course, CT(t), in a given tissue can be described as the convolution of an input function with the unit disposition function (UDFT) of the drug in the tissue, (i.e., CT(t)=(Ca(t)Qr)*UDFr(t) whereCa(t) is the arterial concentration,QT is the tissue blood flow and * is the convolution operator). The obtained tissue unit disposition function (UDF) for each tissue describes the theoretical disposition of a unit amount of drug injected into the tissue in the absence of recirculation. From theUDF, a parametric model for the intratissue disposition of each tissue can be postulated. Using as input the product of arterial concentration and blood flow, this submodel is fit separately utilizing standard nonlinear regression programs. In a separate step, the entire body is characterized by reassembly of the individuals submodels. Unlike classical physiologic modeling the fit for a given tissue is not dependent on the estimates obtained for other tissues in the model. Additionally, because this method permits examination of individualUDFs, appropriate submodel selection is driven by relevant information. This paper reports our experience with a piecewise modeling approach for thiopental disposition in the rat.

Thiopental Pharmacodynamics I. Defining the Pseudo–Steady-state Serum Concentration–EEG Effect Relationship

To assess depth of anesthesia for intravenous anesthetics using clinical stimuli and observed responses, it is necessary to achieve constant serum concentrations of drug that result in constant biophase or central nervous system concentrations. The goal of this investigation was to use a computer-controlled infusion pump (CCIP) to obtain constant serum thiopental concentrations and use the electroencephalogram (EEG) as a measure of thiopentals central nervous system drug effect. The number of waves per second obtained from aperiodic waveform analysis was used as the EEG measure. A CCIP was used in six male volunteers to attain rapidly and then maintain for 6-min time periods the following pseudo-steady-state constant serum thiopental target concentrations: 10, 20, 30, and 40 micrograms/ml. The median performance error (bias) of the CCIP using 149 measurements of thiopental serum concentrations in six subjects was +5%, and the median absolute performance error (accuracy) was 16%. Following the step change in serum thiopental concentration, the EEG number of waves per second stabilized within 2-3 min and the remained constant until the target serum thiopental concentration was changed. When the constant serum thiopental concentration was plotted against the number of waves per second for each subject, a biphasic serum concentration versus EEG effect relationship was seen. This biphasic concentration:response relationship was characterized with a nonparametric pharmacodynamic model. The awake, baseline EEG was 10.6 waves/s; at peak activation the EEG was 19.1 waves/s and occurred at a serum thiopental concentration of 13.3 micrograms/ml. At a serum thiopental concentration of 31.2 micrograms/ml the EEG had slowed to 10.6 waves/s (back to baseline) and at 41.2 micrograms/ml was 50% below the baseline, awake value. Zero waves per second occurred at serum thiopental concentrations greater than 50 micrograms/ml. Using a CCIP it is possible to establish constant serum thiopental concentration rapidly and characterize the concentration versus EEG drug effect relationship.

Quantitation of depth of thiopental anesthesia in the rat

Background In contrast to that of inhalational anesthetics, quantitation of anesthetic depth for intravenous agents has not been well defined. In this study, using rodents, the relationship between the constant plasma thiopental concentrations and the clinical response to multiple nociceptive stimuli were investigated characterizing the anesthetic state from light sedation to deep anesthesia and correlated to the degree of electroencephalogram (EEG) drug effect. Methods Thirty rats were instrumented with chronically implanted EEG electrodes, arterial and venous catheters. A computer-driven infusion pump was used to rapidly attain and then maintain constant, target plasma thiopental concentrations ranging from 7 to 100 micro gram/ml. Three different target plasma thiopental concentrations were achieved in each rat. Electroencephalographic effects were monitored with aperiodic waveform analysis. The following nociceptive stimuli were applied: (1) unprovoked righting reflex, (2) provoked righting reflex, (3) noise stimulus, (4) tail clamping with an alligator clip, (5) constant tail pressure with an analgesia-meter, (6) corneal reflex, and (7) tracheal intubation. For tail clamping, tail pressure, and intubation, either purposeful extremity movement or abdominal muscle contraction response was noted to be present or absent. The clinical responses (present or absent) were modeled using logistic regression to estimate the Cp50, the plasma thiopental concentration with a 50% probability of no response. Results The following mean Cp50 values (95% confidence interval) were obtained: unprovoked righting reflex, 15.9 (15.1-16.6) micro gram/ml; provoked righting reflex, 21.4 (20.2-22.7) micro gram/ml; noise stimuli, 31.3 (29.7-33.0) micro gram/ml; tail clamp and limb movement, 38.3 (36.1-40.4) micro gram/ml, tail pressure and limb movement, 39.2 (37.1-41.3) micro gram/ml; tail pressure and abdominal muscle contraction, 52.5 (50.0-55) micro gram/ml; tail clamping and abdominal muscle contraction, 56.1 (50.0-56.2) micro gram/ml; corneal reflex, 60.0 (56.6-63.4) micro gram/ml; and limb movement or muscle abdominal contraction response to intubation, 67.7 (59.2-76.1) micro gram/ml. At an EEG-effect of 9.1 and 2.2 waves/s, there was a 50% chance of limb movement response to tail clamping and tracheal intubation, respectively. There was a poor relationship between the plasma thiopental concentration and the percent increase of either heart rate or mean arterial blood pressure after applying either tail pressure or tail clamp stimuli. Conclusions A range of nociceptive stimuli and their observed clinical responses can be used to quantitate thiopental anesthetic depth, ranging from light sedation to deep anesthesia (isoelectric EEG and unresponsive to intubation) in the rodent. Clinical response can be mapped to surrogate EEG measures.

Understanding pharmacokinetics and pharmacodynamics through computer simulation. I: The comparative clinical profiles of fentanyl and alfentanil

The authors have used computer simulation to examine the time course of the plasma concentration, estimated effect site concentration, and the intensity of the central nervous system (CNS) effect of fentanyl and alfentanil. The simulations were performed over a range of clinically equivalent doses. Simulations of the changes in the processed electroencephalogram (EEG) was used as a reflection of drug induced CNS effect. The simulations reveal that the rate of equilibration between effect site and plasma concentrations can explain differences in the clinical time course of drug effect between these opioids. The onset of fentanyl EEG drug effect is delayed relative to alfentanil and the duration of action is longer. Pharmacokinetic differences do not explain the disparity seen in the time courses of EEG drug effect. Alfentanil and fentanyl have similar plasma disposition curves during the first 90 min. The concentrations at the effect site are, however, quite different. The simulations illustrate how fentanyls slow blood:brain equilibration can dampen the rate of rise and fall of effect site concentrations. As a mechanism for terminating effect, redistribution of opioid from effect site to other body regions is less relevant for fentanyl compared with that for alfentanil. The evanescent clinical effects of alfentanil can be explained by the rapid blood:brain equilibration. Computer simulation is a useful tool for revealing relevant determinants of the complex relationship between dose and the time course of effect.

Formulation-dependent Brain and Lung Distribution Kinetics of Propofol in Rats

Background Propofol when administered by brief infusion in a lipid-free formulation has a slower onset, prolonged offset and greater potency compared with an emulsion formulation. To understand these findings the authors examined propofol brain and lung distribution kinetics in rats. Methods Rats were infused with equieffective doses of propofol in emulsion (n = 21) or lipid-free formulation (n = 21). Animals were sacrificed at various times to harvest brain and lung. Arterial blood was sampled repeatedly from each animal until sacrifice. Deconvolution and moment analysis were used to calculate the half-life for propofol brain turnover (BT) and brain:plasma partition coefficient (Kp). Lung concentration-time profiles were compared for the two formulations. Results Peak propofol plasma concentrations for the lipid-free formulation were 50% of that observed for emulsion formulation, whereas peak lung concentrations for lipid-free formulation were 300-fold higher than emulsion formulation. Brain Kp calculated from tissue disposition curve and ratio of brain:plasma area under the curves were 8.8 and 13, and 7.2 and 9.1 for emulsion and lipid-free formulations, respectively. BT were 2.4 and 2.5 min for emulsion and lipid-free formulations, respectively. Conclusions Significant pulmonary sequestration and slow release of propofol into arterial circulation when administered in lipid-free vehicle accounts for the lower peak arterial concentration and sluggish arterial kinetics relative to that observed with the emulsion formulation. Higher Kp for the lipid-free formulation could explain the higher potency associated with this formulation. BT were independent of formulation and correlated with values reported for effect-site equilibration half-time consistent with a distribution mechanism for pharmacologic hysteresis.

Tissue distribution of fentanyl and alfentanil in the rat cannot be described by a blood flow limited model

Traditionally, physiological pharmacokinetic models assume that arterial blood flow to tissue is the rate-limiting step in the transfer of drug into tissue parenchyma. When this assumption is made the tissue can be described as a well-stirred single compartment. This study presents the tissue washout concentration curves of the two opioid analgesics fentanyl and alfentanil after simultaneous 1-min iv infusions in the rat and explores the feasibility of characterizing their tissue pharmacokinetics, modeling each of the 12 tissues separately, by means of either a one-compartment model or a unit disposition function. The tissue and blood concentrations of the two opioids were measured by gas-liquid chromatography. The well-stirred one-compartment tissue model could reasonably predict the concentration-time course of fentanyl in the heart, pancreas, testes, muscle, and fat, and of alfentanil in the brain and heart only. In most other tissues, the initial uptake of the opioids was considerably lower than predicted by this model. The unit disposition functions of the opioids in each tissue could be estimated by nonparametric numerical deconvolution, using the arterial concentration times tissue blood flow as the input and measured tissue concentrations as the response function. The observed zero-time intercepts of the unit disposition functions were below the theoretical value of one, and were invariably lower for alfentanil than for fentanyl. These findings can be explained by the existence of diffusion barriers within the tissues and they also indicate that alfentanil is less efficiently extracted by the tissue parenchyma than the more lipophilic compound fentanyl. The individual unit disposition functions obtained for fentanyl and alfentanil in 12 rat tissues provide a starting point for the development of models of intratissue kinetics of these opioids. These submodels can then be assembled into full physiological models of drug disposition.

Pharmacodynamic characterization of the electroencephalographic effects of thiopental in rats.

We have developed a chronically instrumented rat model that uses changes in electroencephalographic waveforms to estimate continuously the degree of central nervous system (CNS) depression induced by thiopental. Such changes were subject to aperiodic signal analysis, a technique that breaks down the complex EEG into a series of discreet neurologic “events” which are then quantitated as waves/sec. We thus obtained a continuous measure of CNS drug effect. In addition we continuously recorded central arterial blood pressure and heart rate and monitored ventilatory status using arterial blood gas determinations. We also determined, with frequent arterial blood sampling, the distribution and elimination of thiopental in individual animals. The time lag occurring in the curve representing arterial concentration of thiopental vs. EEG effect suggests that arterial plasma is not kinetically equivalent to the EEC effect site. Application of semiparametric pharmacodynamic modeling techniques enabled us to estimate equilibration rate constant (Keo for concentrations of thiopental between arterial plasma and the effect site. The half-life for equilibration of thiopental with the EEG (CNS) effect was less than 80 sec. Knowledge of the rate of equilibration permitted characterization of the relationship between the steady state plasma concentrations and CNS effect of thiopental, as measured by activation and slowing of the EEG. At concentrations of thiopental below 5 gmg/ml, EEG activity was 180% higher than during the baseline awake state. Thiopental produced an activated EEG over more than 20% of the concentration-effect relationship. Further increases in the concentration of thiopental at the site of effect depressed EEG activity progressively until complete suppression of the EEG signal occurred (at which time, the concentration was approximately 80 μg/ml). This report describes our model and its application to the assessment of the pharmacodynamics of thiopental as manifested by changes on the EEG.

Plasma Concentration Clamping in the Rat Using a Computer-Controlled Infusion Pump

We have developed a computer-controlled infusion pump to achieve rapidly and then maintain stable plasma thiopental concentrations in rats. Initially we derived the parameters of a triexponential pharma-cokinetic model for thiopental, administered as a brief infusion to 10 rats, using nonlinear regression and standard pharmacokinetic equations. These parameters were incorporated into the pharmacokinetic model of a computer-controlled infusion pump. In a second group of animals this device was used to maintain three consecutive target thiopental concentrations ranging from 5 to 100 µg/ml in a stepwise fashion. Arterial blood gases were kept normal through controlled ventilation when necessary. The plasma thiopental concentrations in this second group of animals were generally higher than the target concentrations. The bias in pump performance (median prediction error) was +25%, and the inaccuracy (median absolute prediction error) was 26%. We fit the parameters of a three-compartment model to the plasma thiopental concentrations observed in the second group of animals. This produced a second set of thiopental pharmacokinetic parameters with the unique characteristic of having been derived from a computer controlled infusion study. These parameters were tested prospectively with a computer-controlled infusion pump in a third group of animals. This second set of thiopental pharmacokinetic parameters performed better, with a median prediction error of 0% and a median absolute prediction error of 15%. This study shows that it is possible to achieve rapidly and maintain steady plasma thiopental concentrations in the rat. Our results suggest that it is feasible to derive robust pharmacokinetic parameters from unusual drug dosing approaches, such as employed by a computer-controlled infusion pump. The ability rapidly to clamp plasma drug concentrations at desired targets in small laboratory animals will facilitate research into the relationship of plasma and tissue concentration to drug effect.

Emulsion formulation reduces propofol's dose requirements and enhances safety

Background: Propofol, a highly lipophilic anesthetic, is formulated in a lipid emulsion for intravenous use. Propofol has brisk onset and offset of effect after rapid administration and retains rapid offset characteristics after long‐term administration. The authors tried to determine whether the emulsion vehicle is requisite for propofols evanescent effect‐time profile. Methods: The time course of sedation and electroencephalographic (EEG) effect after propofol administration was measured in three studies in rats instrumented. In study 1, propofol was infused in either emulsion or lipid‐free vehicle (n = 12), in a repeated measures cross‐over design. In study 2, propofol in lipid‐free vehicle was infused with or without simultaneous infusion of drug‐free lipid emulsion (n = 6) in a repeated measures cross‐over design. In study 3, propofol was infused in either emulsion (n = 5) or lipid‐free vehicle (n = 5) to EEG burst suppression. Results: In study 1, relative to the emulsion formulation, propofol administered at equivalent doses in lipid‐free vehicle resulted in a longer time to effect onset (1.4 +/‐ 0.2 vs. 0.5 +/‐ 0.1 min, EEG) and a trend for delayed anesthetic recovery (26.8 +/‐ 9.4 vs. 17 +/‐ 3.5 min, EEG; 26.1 +/‐ 8.8 vs. 16.8 +/‐ 3.3 min, sleep). In study 2, coadministration of drug‐free emulsion with propofol did not alter the time course of effect. In study 3, more than twice the dose of propofol was required to achieve EEG burst suppression with the lipid‐free formulation. Two animals died after administration of propofol to EEG burst suppression with the lipid‐free formulation; no deaths occurred in the emulsion group. Conclusion: The incorporation of propofol in emulsion reduces dose requirements and produces rapid onset and recovery of anesthetic effect.