Determination of the distribution volume that can be used to calculate the intravenous loading dose.

An intravenous loading dose is given to rapidly achieve a desired drug concentration in the blood. A loading dose calculated with the volume of distribution (Vd) at steady state will result in high peak concentrations and possibly serious adverse effects. A loading dose based on the central compartment Vd (Vc) followed by a maintenance infusion may also miss the target drug concentration and cause serious adverse effects. The Vd can be viewed as a time-dependent variable that expands from the Vc immediately after injection, to eventually include the steady-state Vd. If the loading dose is calculated from a Vd determined after the time of peak effect (tmax), then the actual concentration will exceed the target concentration at the tmax. If a loading dose is calculated from a Vd before the peak effect occurs, the actual concentration will be insufficient to achieve the target concentration at tmax. A loading dose based on the Vd at the tmax will accurately achieve the concentration at the tmax without unexpected adverse effects. To determine the Vd at peak effect, it is necessary that an effect can be measured, the peak effect can be detected and the plasma concentrations are sampled frequently enough to quantify the plasma concentrations at the tmax. For drugs that attain an ultra-fast effect (1 to 2 minutes), arterial samples need to be measured. If the onset of effect is intermediate or slow, venous blood can be sampled as the arterial and venous concentrations may be similar at the tmax.

No effect of age on the dose requirement of thiopental in the rat.

With increasing human age (20-80 years), the electroencephalogram (EEG) dose requirement for the intravenous anesthetic thiopental decreases approximately 10% per decade of life. The goal of this study was to compare the dose required to attain isoelectric EEG in young (4-5 month) vs. aged (24-25-month) Fischer 344 rats. One second isoelectricity was found to be an endpoint where minimal cardiorespiratory depression occurred. The effects of age, infusion rate, and repeated administration were examined in nine young and nine old rodents. Thiopental dose requirement increased with increasing infusion rates. Repeated administration at two-day intervals did not demonstrate tolerance to thiopental. No difference in thiopental dose requirement was detected in the young vs. elderly rats. In a separate group of five young and five old rats, thiopental plasma, brain, heart, and CSF concentrations were measured when five seconds of EEG isoelectricity was achieved: no consistent differences were noted. The rat may not be an appropriate model to investigate acute age-related anesthetic effects in humans, because cardiovascular changes with age are dissimilar between species.

Prediction of the disposition of midazolam in surgical patients by a physiologically based pharmacokinetic model.

The aim of this study was to predict the disposition of midazolam in individual surgical patients by physiologically based pharmacokinetic (PBPK) modeling and explore the causes of interindividual variability. Tissue-plasma partition coefficients (k(p)) were scaled from rat to human values by a physiologically realistic four-compartment model for each tissue, incorporating the measured unbound fraction (f(u)) of midazolam in the plasma of each patient. Body composition (lean body mass versus adipose tissue) was then estimated in each patient, and the volume of distribution at steady state (V(dss)) of midazolam was calculated. Total clearance (CL) was calculated from unbound intrinsic CL, f(u), and estimated hepatic blood flow. Curves of midazolam plasma concentration versus time were finally predicted by means of a perfusion-limited PBPK model and compared with measured data. In a first study on 14 young patients undergoing surgery with modest blood loss, V(dss) was predicted with an only 3.4% mean error (range -24-+39%) and a correlation between predicted and measured values of 0.818 (p < 0.001). Scaling of k(p) values by the four-compartment model gave better predictions of V(dss) than scaling using unbound k(p). In the PBPK modeling, the mean +/- standard deviation (SD) prediction error for all data was 9.7 +/- 33%. In a second study with 10 elderly patients undergoing orthopedic surgery, hemodilution and blood loss led to a higher f(u) of midazolam. The PBPK modeling correctly predicted a marked increase in V(dss), a smaller increase in CL, and a prolonged terminal half-life of midazolam, as compared with findings in the first study. Interindividual variation in the disposition of midazolam could thus in part be related to the physiological characteristics of the patients and the f(u) of the drug in their plasma.

Open loop control of multiple drug effects in anesthesia.

Current open-loop computer-controlled infusion pumps do not explicitly control the transient adverse side effects of intravenous drugs during anesthesia. We used optimal control principles to synthesize a single-input multiple-output controller that regulates concentrations at the site of desirable drug effect while penalizing excessive side-effect drug concentrations. The cost function incorporates model-based predictions of future effect-site concentrations, and the capability of the anesthesiologist to anticipate upcoming surgical events. The controller was evaluated and then compared with alternative control strategies through computer simulation of a physiologically based pharmacokinetic model for the intravenous drug alfentanil. Multiple-effect control offers an analytic approach to limit the overshoot in adverse side-effect concentrations at the consequence of increasing the time to achieve the desired drug effect.

The hybrid model: a new pharmacokinetic model for computer-controlled infusion pumps.

Classical pharmacokinetic models used in computer-controlled infusion pumps (CCIPs) assume instantaneous mixing of drug in blood; however, the average recirculation time of blood in man is approximately one minute. To investigate the effects of recirculation dynamics on the transient performance of CCIPs, we propose a hybrid physiologically-based pharmacokinetic model for the narcotic alfentanil. A three-compartment model was derived from the response of the hybrid model to a short infusion and used to compute a CCIP infusion targeting 450 micrograms/l. For this infusion, the hybrid model predicts that the arterial plasma concentration will overshoot the target concentration by 39 percent with an average prediction error of 3 percent. The overshoot and average prediction error increase to 100 and 25 percent respectively when using a three-compartment pharmacokinetic model derived from a bolus. The overshoot can be reduced by decreasing the maximum possible infusion rate, or by increasing the zero-order hold infusion interval.

Closed-loop stability of pharmacokinetic-pharmacodynamic models.

In automatic feedback control of intravenous drug infusions, convergence to the setpoint is an important objective. This paper examines the stability of pharmacokinetic-pharmacodynamic models of patient response regulated with proportional integral feedback. The model consists of three components: linear compartmental pharmacokinetics, a first-order lag, and sigmoidal static pharmacodynamics. The permitted pharmacokinetic models obey the principle of detailed balance and admit drug administration into and sampling from the same compartment. Convergence to the setpoint occurs if the reset time of the controller is greater than the maximum possible time constant of the first-order lag. The convergence analysis uses standard Popov stability theory and takes advantage of the little known fact that many pharmacokinetic models possess poles and zeros that alternate on the negative real axis.

A PC-based graphical simulator for physiological pharmacokinetic models.

Since many intravenous anesthetic drugs alter blood flows, physiologically-based pharmacokinetic models describing drug disposition may be time-varying. Using the commercially available programming software MATLAB, a platform to simulate time-varying physiological pharmacokinetic models was developed. The platform is based upon a library of pharmacokinetic blocks which mimic physiological structure. The blocks can be linked together flexibly to form models for different drugs. Because of MATLAB's additional numerical capabilities (e.g. non-linear optimization), the platform provides a complete graphical microcomputer-based tool for physiologic pharmacokinetic modeling.

The use of modeling and simulation to guide clinical development of olmesartan medoxomil in pediatric subjects.

Modeling and simulation were used extensively in the development of an indication for the use of olmesartan medoxomil in pediatric patients with hypertension. Simulations based on models developed in adult patients indicated that two dose groups were sufficient to estimate a dose-response relationship, thereby reducing by one-third the number of subjects required for the phase III pediatric study. Model-based predictions for blood pressure reduction agreed with the observed results of the subsequent phase III study, showing statistically significant dose-response relationships with respect to both systolic and diastolic blood pressure. Previously established pharmacokinetic and exposure-response relationships in adults, adjusted for the influence of body weight on clearance (wt(0.80)), were confirmed in the pediatric population. Together, these findings support an olmesartan dosing recommendation in pediatric subjects aged 6 to 16 years of 10 mg for subjects weighing <35 kg and 20 mg for those weighing ≥35 kg.

Model-based meta-analysis for comparative efficacy and safety: application in drug development and beyond.

High development cost, low development success, cost-disciplined health-care policies, and intense competition demand an efficient drug development process. New compounds need to bring value to patients by being safe, efficacious, and cost-effective as compared with existing treatment options. Model-based meta-analysis (MBMA) facilitates integration and utilization of summary-level efficacy and safety data, providing a quantitative framework for comparative efficacy and safety assessment. This Commentary discusses the application and limitations of MBMA in drug development.

Pharmacodynamic model for acute tolerance development to the electroencephalographic effects of alfentanil in the rat.

This investigation was carried out to characterize the rate and extent of acute tolerance development to the pharmacodynamics of alfentanil in the rat with the electroencephalogram (EEG) as a measure of alfentanil's effects on the central nervous system. Alfentanil was administered by use of three different drug infusion strategies in order to develop a pharmacokinetic-pharmacodynamic model for acute tolerance: I) intravenous infusion of 0.5 mg/kg in 10 min, achieving peak alfentanil concentrations of 750 ng/ml; II) computer-controlled infusion to rapidly achieve and maintain a constant drug level of 750 ng/ml, followed by washout; III) computer-controlled infusion to step through multiple constant drug levels (up to 1500 ng/ml), followed by washout. Frequent arterial plasma samples were taken and assayed for alfentanil. EEG signals were continuously recorded until effects returned to base-line values. The amplitudes in the 0.5- to 3.5-Hz (delta) frequency band were calculated by aperiodic analysis and used as an EEG effect measure. The pharmacokinetic data were characterized by a three-compartment model with nonlinear clearance. Nonlinear kinetics was apparent from the multiple steady-state protocol III. Clearance values ranged from (S.E.) 49.7 (2.8) ml/min/kg at low alfentanil concentrations to a minimum value of 29.3 (0.8) ml/min/kg at high concentrations. The pharmacodynamic data showed profound acute tolerance development reflected as proteresis in the concentration-effect pairs after protocol I and a rapidly declining effect in the presence of stable alfentanil concentrations after protocols II and III. The effect stabilized within 15 min after a change in target concentration. A physiological tolerance model was developed to characterize the rate and extent of tolerance development to the effects of alfentanil. The models are generally applicable and consider the physiological homeostatic mechanisms responsible for the tolerance development to be an integral part of the pharmacodynamic system. Tolerance was modeled as a negative feedback control of the drug-induced effect with a first-order transfer function. The model required only two tolerance parameters to quantify the rate and extent of tolerance development and allowed for a rebound effect. Maximum tolerance diminished alfentanil's effect by 46% and was achieved with a half-life of 7.0 min.

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 disposition 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)QT)*UDFT(t) where Ca(t) is the arterial concentration, Q tau is the tissue blood flow and * is the convolution operator). The obtained tissue until disposition function (UDF) for each tissue describes the theoretical disposition of a unit amount of drug infected into the tissue in the absence of recirculation. From the UDF, 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 individual UDFs, appropriate submodel selection is driven by relevant information. This paper reports our experience with a piecewise modeling approach for thiopental disposition in the rat.

Application of physiologic models to predict the influence of changes in body composition and blood flows on the pharmacokinetics of fentanyl and alfentanil in patients.

BACKGROUND: The influence of changes in the physiologic state of a patient on the disposition of fentanyl and alfentanil is poorly understood. The aims of this study were to determine whether physiologic pharmacokinetic models for fentanyl and alfentanil, based on data from rats, could predict plasma concentrations of these opioids in humans and to determine how changes in physiology would influence the predictions of their disposition. METHODS: The predictions of the models were tested against plasma concentration data from published pharmacokinetic studies. The influences of changes in body composition, cardiac output, and regional blood flows on the disposition of the opioids were simulated. RESULTS: The models could predict independently measured plasma concentrations of the opioids after short infusions in humans. Simulations then predicted that differences in body composition between men and women would have little influence on the pharmacokinetics of the opioids. Changes in cardiac output would affect drug redistribution, and consequently the early decay of the plasma concentrations, but not markedly influence rates of elimination. Further, the clearance of the opioids would decrease and their volumes of distribution increase with the age of the patient, but this would only marginally affect the early disposition of the drugs. Even large fluctuations in peripheral or hepatic blood flows would have modest effects on arterial plasma concentrations of the opioids, and sudden "postoperative" increases in peripheral blood flows would cause minor secondary plasma concentration peaks. CONCLUSIONS: The ability of the physiologic models to predict plasma concentrations of fentanyl and alfentanil in humans was confirmed. When changes in physiologic condition were simulated, effects on the pharmacokinetics of the opioids with possible implications for dosing were obtained only if cardiac output was varied over a wide range.

Comparative physiological pharmacokinetics of fentanyl and alfentanil in rats and humans based on parametric single-tissue models.

The objectives of this investigation were to characterize the disposition of fentanyl and alfentanil in 14 tissues in the rat, and to create physiological pharmacokinetic models for these opioids that would be scalable to man. We first created a parametric submodel for the disposition of either drug in each tissue and then assembled these submodels into whole-body models. The disposition of fentanyl and alfentanil in the heart and brain and of fentanyl in the lungs could be described by perfusion-limited 1-compartment models. The disposition of both opioids in all other examined tissues was characterized by 2- or 3-compartment models. From these models, the extraction ratios of the opioids in the various tissues could be calculated, confirming the generally lower extraction of alfentanil as compared to fentanyl. Assembly of the single-tissue models resulted in a wholebody model for fentanyl that accurately described its disposition in the rat. A similar assembly of the tissue models for alfentanil revealed non-first-order elimination kinetics that were not apparent in the blood concentration data. Michaelis-Menten parameters for the hepatic metabolism of alfentanil were determined by iterative optimization of the entire model. The parametric models were finally scaled to describe the disposition of fentanyl and alfentanil in humans.

Effects of thiopental on regional blood flows in the rat.

BACKGROUND: The goal of this investigation was to characterize the effects of thiopental on cardia output and regional blood flows in the rat. Blood flows influence thiopental pharmacokinetics. Acquisition of these data may ultimately permit evaluation of the contribution of thiopental-induced alterations in regional blood flows to the disposition and hypnotic effect of this drug. METHODS: Chronically instrumented unrestrained Wistar rats (n=20) aged 3-4 months received either a dose of thiopental sufficient to induce a brief period of unconsciousness (20 mg.kg(-1)) or a larger dose achieving electroencephalographic burst suppression (45 mg.kg(-1)). Cardiac output and blood flows to 14 tissues were determined at 4 times in each rat for a period of 420 min using injections of radioactive microspheres (expressed as mean +/- SD). Mean arterial pressure, heart rate, and blood gas tensions were determined at all measurement times. Arterial plasma concentrations were sampled at postinfusion times. RESULTS: No important changes in systemic cardiovascular measurements were detected after the smaller dose of thiopental. One minute after the larger dose, cardiac output decreased from baseline (123 +/- 14 to 84 +/- ml.min (-1), P< 0.01), flow to muscle and fat decreased, and muscle and fat resistance increased. At 5 min, compared to baseline, no difference in cardiac output was detected (123 +/- vs. 119 +/- ml.min (-1)), intestinal flows increased and intestinal resistances decreased. Cardiac output was again depressed at 30, 90, and 180 min. Brain blood flow decreased 25 +/- 19 % (P< 0.01) from baseline for the duration of the study. CONCLUSIONS: Thiopental acutely decreases cardiac output, and blood flows to muscle and fat tissue. The temporary return of cardiac output to baseline may be related to intestinal vasodilation. These blood flow alterations may influence the pharmacokinetics of thiopental.

The effects of large-dose flumazenil on midazolam-induced ventilatory depression.

Flumazenil, a benzodiazepine antagonist, clearly reverses midazolam-induced sedation; reversal of ventilatory depression has not been as well demonstrated. Thirty-two subjects completed this randomized, double-blind, placebo-controlled study investigating the dose-response relationship and duration of flumazenil's effects on ventilatory depression and hypnosis induced by a continuous midazolam infusion. A computer-controlled infusion of midazolam was used to titrate the predicted midazolam plasma concentration to a level at which subjects were unresponsive to verbal commands and then to maintain that concentration. Measurements of ventilation and hypnosis were repeated at predetermined intervals: before midazolam administration, before test drug (flumazenil [1, 3, or 10 mg] or placebo), and 5, 30, 60, 120, and 180 min after test drug administration. Ventilation and tidal volume were measured during an isocapnic hyperoxia clamp at a PETCO2 of 46 mm Hg (VE46 and VT46, respectively). A pseudo-rebreathing technique was used to measure the hypercapnic ventilatory response (HCVR) slope and ventilation intercept at a PETCO2 of 58 mm Hg (VE58). Midazolam reduced VE46, VT46, and VE58, as well as hypnosis scores, in all test drug groups. The reduction in HCVR slope, however, was significant only when all 32 subjects were considered in aggregate. All three doses of flumazenil reversed hypnosis and also reversed the reduction in VE46 and VT46 within 5 min. The reduction in VE58, however, was reversed less consistently. Flumazenil's effect on VE46 and VT46 lasted at least 30 min after 1 mg and at least 60 min after 3 mg, paralleling the effect of these doses on hypnosis.(ABSTRACT TRUNCATED AT 250 WORDS)

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.

Pharmacodynamics of orally administered sustained- release hydromorphone in humans.

BACKGROUND: The disposition kinetics of hydromorphone generally necessitates oral administration every 4 h of the conventional immediate-release tablet to provide sustained pain relief. This trial examined time course and magnitude of analgesia to experimental pain after administration of sustained-release hydromorphone as compared with that after immediate-release hydromorphone or placebo. METHODS: Using a 4 x 4 Latin square double-blind design, 12 subjects were randomized to receive a single dose of 8, 16, and 32 mg sustained-release hydromorphone and placebo. The same subjects had received 8 mg immediate-release hydromorphone before this study. Using an electrical experimental pain paradigm, analgesic effects were assessed for up to 30 h after administration, and venous hydromorphone plasma concentrations were measured at corresponding times. RESULTS: The hydromorphone plasma concentration peaked significantly later (12.0 h [12.0--18.0] vs. 0.8 h [0.8--1.0]; median and interquartile range) but was maintained significantly longer at greater than 50% of peak concentration (22.7 +/- 8.2 h vs. 1.1 +/- 0.7 h; mean +/- SD) after sustained-release than after immediate-release hydromorphone. Similarly, sustained-release hydromorphone produced analgesic effects that peaked significantly later (9.0 h [9.0--12.0] vs. 1.5 h [1.0--2.0]) but were maintained significantly longer at greater than 50% of peak analgesic effect (13.3 +/- 6.3 h vs. 3.6 +/- 1.7 h). A statistically significant linear relation between the hydromorphone plasma concentration and the analgesic effect on painful stimuli existed. CONCLUSION: A single oral dose of a new sustained-release formulation of hydromorphone provided analgesia to experimental pain beyond 24 h of its administration.

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.