Richard N. Upton

Basic concepts in population modeling, simulation, and model-based drug development-part 2: introduction to pharmacokinetic modeling methods.

Population pharmacokinetic models are used to describe the time course of drug exposure in patients and to investigate sources of variability in patient exposure. They can be used to simulate alternative dose regimens, allowing for informed assessment of dose regimens before study conduct. This paper is the second in a three‐part series, providing an introduction into methods for developing and evaluating population pharmacokinetic models. Example model files are available in the Supplementary Data online.

Basic Concepts in Population Modeling, Simulation, and Model‐Based Drug Development

Modeling is an important tool in drug development; population modeling is a complex process requiring robust underlying procedures for ensuring clean data, appropriate computing platforms, adequate resources, and effective communication. Although requiring an investment in resources, it can save time and money by providing a platform for integrating all information gathered on new therapeutic agents. This article provides a brief overview of aspects of modeling and simulation as applied to many areas in drug development.

Cardiac output is a determinant of the initial concentrations of propofol after short-infusion administration.

UNLABELLED Indicator dilution theory predicts that the first-pass pulmonary and systemic arterial concentrations of a drug will be inversely related to the cardiac output. For high-clearance drugs, these first-pass concentrations may contribute significantly to the measured arterial concentrations, which would therefore also be inversely related to cardiac output. We examined the cardiac output dependence of the initial kinetics of propofol in two separate studies using chronically instrumented sheep in which propofol (100 mg) was infused IV over 2 min. In the first study, steady-state periods of low, medium, and high cardiac output were achieved by altering carbon dioxide tension in six halothane-anesthetized sheep. The initial area under the curve and peak value of the pulmonary artery propofol concentrations were inversely related to cardiac output (R2 = 0.57 and 0.66, respectively). For the systemic arterial concentrations, these R2 values were 0.68 and 0.71, respectively. In our second study, transient reductions in cardiac output were achieved in five conscious sheep by administering a short infusion of metaraminol concurrently with propofol. Cardiac output was lowered by 2.2 L/min, and the area under the curve to 10 min of the arterial concentrations increased to 143% of control. IMPLICATIONS The initial arterial concentrations of propofol after IV administration were shown to be inversely related to cardiac output. This implies that cardiac output may be a determinant of the induction of anesthesia with propofol.

Hemodynamic and central nervous system effects of intravenous bolus doses of lidocaine bupivacaine and ropivacaine in sheep

Lidocaine hydrochloride (HCI) (80–320 mg), bupivacaine HCl (20–80 mg), and ropivacaine HO (30–120 mg) were administered as intravenous bolus doses to conscious sheep (n = 18; average body weight 45 kg) that had previously placed intravascular cannulae for hemodynamic monitoring and for obtaining blood samples. The mean convulsive doses and arterial blood concentrations were ∼110 mg and 40 mg/L, respectively, for lidocaine HCl, 45 mg and 14 mg/L for bupivacaine HCl, and 60 mg and 20 mg/L for ropivacaine HCl. After subconvulsive doses of each agent, there were minimal cardiovascular effects. After convulsive doses, there were marked increases in heart rate, mean arterial pressure, pulmonary artery pressure, cardiac output, systemic vascular resistance, left ventricular end diastolic pressure, and myocardial contractility. Ventricular fibrillation caused death in two sheep after bupivacaine (80 mg) and in two sheep after ropivacaine (90 and 120 mg) administration. With sublethal doses, the hemodynamic responses to these agents were qualitatively and quantitatively similar when compared with their local anesthetic potencies.

Pharmacokinetic Optimisation of Opioid Treatment in Acute Pain Therapy

SummaryTraditionally, opioids have been administered as fixed doses at fixed dose intervals. This approach has been largely ineffective. Patient-controlled analgesia (PCA) and upgraded traditional approaches incorporating flexibility in dose size and dose interval, and titration for an effect in individual patients with the monitoring of pain and sedation scores, can greatly improve the efficacy of opioid administration. Optimising opioid use, therefore, entails optimising the titration process.Opioids have similar pharmacodynamic properties but have widely different kinetic properties. The most important of these is the delay between the blood concentrations of an opioid and its analgesic or other effects, which probably relate to the delay required for blood and brain and spinal cord (CNS) equilibrium. The half-lives of these delays range from approximately 34 minutes for morphine to 1 minute for alfentanil. The titration is influenced by the time needed after an initial dose before it is safe to administer a second dose and the duration of the effects of a single dose, which varies widely between opioids, doses and routes of administration. To compare opioids and routes of administration, we examined the relative CNS concentration profiles of opioids — the CNS concentration expressed as a percentage of its maximum value. The relative onset was the defined as the time the relative CNS concentration first rose to 80% of maximum, while the relative duration was defined as the length of time the concentration was above 80%. For an intravenous bolus dose, the relative onset varies from approximately 1 for alfentanil to 6 minutes for morphine, while their relative durations are approximately 2 and 96 minutes, respectively.Although all of the common opioids, perhaps with the exception of alfentanil, have kinetic and dynamic properties suitable for use in PCA with intravenous bolus doses, the long relative duration of morphine makes it particularly suited to an upgraded traditional approach using staff administered intramuscular or subcutaneous doses. There is a clear kinetic preference for regimens with a rapid onset and short duration (e.g. intravenous PCA) for coping with incident pain. It is shown that, in general, titration is improved by the more frequent administration of smaller doses, but it is important to use additional doses to initially ‘load’ a patient. The titration of opioids should always be accompanied by the monitoring of pain and sedation scores and ventilation.

Pharmacokinetics, Efficacy, and Tolerability of Fentanyl Following Intranasal Versus Intravenous Administration in Adults Undergoing Third-Molar Extraction : A Randomized, Double-Blind, Double-Dummy, Two-Way, Crossover Study

OBJECTIVE The aim of this study was to compare the pharmacokinetic profile, as well as the efficacy and tolerability, of i.n. and i.v. administration of fentanyl in acute, episodic pain in patients undergoing third-molar extraction. METHODS In this randomized, double-blind, double-dummy, 2-way, crossover study, patients were randomized to receive 1 of 4 doses (75, 100, 150, or 200 microg) by both the i.n. and i.v. routes in random order, after each of 2 separate molar extractions (interval, >or=1 week). Venous blood samples were obtained for quantification of plasma fentanyl concentrations before and at 1, 3, 5, 7, 9, 12, 15, 25, 40, 60, 90, 120, and 180 minutes after administration. Pain scores (on an 11-point numeric rating scale) were recorded before and at 15, 30, 45, 60, 75, 90, 105, 120, 150, 180, 210, and 240 minutes. Patients indicated the times at which they perceived meaningful pain relief (onset of action) and at which analgesia ended (duration of effect), after which they were able to use rescue medication (time to rescue medication use). RESULTS A total of 24 patients were enrolled (in all, 47 extractions) (46% male; mean age, 24.1 years; 94% white, 6% Asian). Mean T(max) values were 12.8 and 6.0 minutes (P<0.001), times to onset of analgesia were 7 and 2 minutes (P<0.001), and durations of effect were 56 and 59 minutes after i.n. and i.v. administration (P=NS), respectively. Differences in the onsets and durations of analgesia after i.n. and i.v. administration of single doses were not significantly different, and neither was the difference in overall analgesia, with pain scores returning to near-predose values at statistically similar times after dosing. Duration of effect was directly related to i.n. fentanyl dose, with significantly less use of rescue medication after i.n. than after i.v. administration (P<0.005). The i.n. and i.v. formulations were both well tolerated, with similar numbers of nasally related adverse events recorded for both routes of administration. CONCLUSIONS Onsets and durations of analgesia were not significantly different between single doses of i.n. and i.v. fentanyl in these adults undergoing third-molar extraction. Both i.n. and i.v. administration were generally well tolerated.

The performance of compartmental and physiologically based recirculatory pharmacokinetic models for propofol: a comparison using bolus, continuous, and target-controlled infusion data.

BACKGROUND: With the growing use of pharmacokinetic (PK)-driven drug delivery and/or drug advisory displays, identifying the PK model that best characterizes propofol plasma concentration (Cp) across a variety of dosing conditions would be useful. We tested the accuracy of 3 compartmental models and 1 physiologically based recirculatory PK model for propofol to predict the time course of propofol Cp using concentration-time data originated from studies that used different infusion schemes. METHODS: Three compartmental PK models for propofol, called the “Marsh,” the “Schnider,” and the “Schüttler” models, and 1 physiologically based recirculatory model called the “Upton” model, were used to simulate the time course of propofol Cp. To test the accuracy of the models, we used published measured plasma concentration data that originated from studies of manual (bolus and short infusion) and computer-controlled (target-controlled infusion [TCI] and long infusion) propofol dosing schemes. Measured/predicted (M/P) propofol Cp plots were constructed for each dataset. Bias and inaccuracy of each model were assessed by median prediction error (MDPE) and median absolute prediction error (MDAPE), respectively. RESULTS: The M/P propofol Cp in the 4 PK models revealed bias in all 3 compartmental models during the bolus and short infusion regimens. In the long infusion, a worse M/P propofol Cp at higher concentration was seen for the Marsh and the Schüttler models than for the 2 other models. Less biased M/P propofol Cp was found for all models during TCI. In the bolus group, after 1 min, a clear overprediction was seen for all 3 compartmental models for the entire 5 min; however, this initial error resolved after 4 min in the Schnider model. The Upton model did not predict propofol Cp accurately (major overprediction) during the first minute. During the bolus and short infusion, the Marsh model demonstrated worse MDPE and MDAPE compared with the 3 other models. During short infusion, MDAPE for the Schnider and Schüttler models was better than the Upton and the Marsh models. All models showed similar MDPE and MDAPE during TCI simulations. During long infusion, the Marsh and the Schüttler models underestimated the higher plasma concentrations. CONCLUSION: When combining the performance during various infusion regimens, it seems that the Schnider model, although still not perfect, is the recommended model to be used for TCI and advisory displays.

Pharmacokinetics and Pharmacodynamics of Intranasal Versus Intravenous Fentanyl in Patients with Pain after Oral Surgery

Background: Fentanyl, a short-acting synthetic opioid, has a pharmacokinetic profile suited to fast relief of brief episodic pain. Objective: To characterize the pharmacokinetic-pharmacodynamic correlation of intranasal and intravenous fentanyl in opioid-naïve patients undergoing third molar extraction. Methods: A double-blind, double-dummy, crossover design study was conducted, with patients randomized to receive 1 of 4 fentanyl doses (75,100, 150, or 200 μg) by both the intravenous and intranasal routes. Venous fentanyl concentrations were determined for up to 180 minutes and pain scores were recorded up to 240 minutes postdose. Duration of effect and time to rescue medication were also recorded. Results: The pharmacokinetics of intravenous fentanyl reflected a 2-compartment model with a clearance of approximately 1.5 L/min. There was moderate (<50%) between-subject variability (BSV; %CV [coefficient of variation]) in the systemic kinetics of fentanyl. Bioavailability of intranasal fentanyl was 89%, following first-order absorption, with a lag of approximately 5 minutes and a half-life of approximately 6.5 minutes. Interpatient absorption variability was approximately 30% BSV for all absorption parameters. Intranasal versus intravenous administration led to a delayed mean fentanyl time to maximum concentration (13 vs 6 min) and lower maximum concentration (1.2 vs 2.0 ng/mL). Analgesic effect lagged behind the venous fentanyl concentration, with a half-life of approximately 2.5 minutes as described by a fractional sigmoid maximum drug effect dynamic model. The concentration-analgesia relationship was steep, with a 50% effective concentration of 0.46 ng/mL (Hill coefficient 3.5). Intranasal onset and offset of analgesia were slightly delayed, principally due to the delay and lag in systemic absorption, with slightly lower peak analgesic effect, compared with intravenous fentanyl. Duration of effect was directly related to intranasal fentanyl dose, with pain scores returning to predose values at approximately 120 minutes (75μg) to approximately 240 minutes (200 μg) after a single dose. Conclusions: Intranasal fentanyl showed kinetic and dynamic properties that are desirable for the management of acute, episodic (breakthrough) pain.

A Physiologically Based, Recirculatory Model of the Kinetics and Dynamics of Propofol in Man

Background:The disposition of propofol in man is commonly described using a three-compartment mamillary model. However, these models do not incorporate blood flows as parameters. This complicates the representation of the changes in blood flows that may occur in surgical patients. In contrast, complex physiologically based models are derived from data sets (e.g., tissue:blood partition coefficients) that may not be readily collected in man. Methods:Alternatively, the authors report a recirculatory model of propofol disposition in a “standard” man that incorporates detailed descriptions of the lungs and brain, but with a lumped description of the remainder of the body. The model was parameterized from data in the literature using a “meta-modeling” approach. The first-pass passage of propofol through the venous vasculature and the lungs was a function of the injected drug mixing with cardiac output and passing through a three-“tank in series” model for the lungs. The brain was represented as a two-compartment model defined by cerebral blood flow and a permeability term. The Bispectral Index was a linear function of the mean brain concentration. The remainder of the body was represented by compartment systems for the liver, fast distribution and slow distribution. Results:The model was a good fit of the data and was able to predict other data not used in the development of the model. Conclusions:The model may ultimately find a role in improving the fidelity of patient simulators currently used to train anesthetists and for clinical practice simulation to optimize dosing and management strategies.

Pharmacokinetic‐Pharmacodynamic Modeling of Morphine and Oxycodone Concentrations and Analgesic Effect in a Multimodal Experimental Pain Model

Analgesia from most opioids is mediated by μ receptors located mainly in the central nervous system. Previous studies have shown a different pharmacological profile of oxycodone in respect to visceral analgesia. This study investigated if morphine and oxycodone have different pharmacokinetic/pharmacodynamic profiles, in particular with respect to delay between opioid blood concentration and analgesia. Twenty‐four healthy subjects had oral morphine (30 mg), oxycodone (15 mg), or placebo. Mechanical, thermal, and electrical pain tests were performed in the skin and viscera. Blood samples and pain measurements were taken at baseline and after 15, 30, 60, 90, and 120 minutes. Pharmacokinetic/pharmacodynamic profiles were modeled using a 2‐stage, nonlinear, mixed‐effects approach with an effect compartment to represent the concentration‐analgesia delay. Morphine kinetics was best described by a 2‐compartment model, whereas oxycodone kinetics was best described with a 1‐compartment model. Generally the analgesic effects of morphine were best related to plasma concentration by introducing a delay via an effect compartment. However, for oxycodone, this was only the case for analgesia in the somatic pain measures, whereas the plasma concentration correlated better to the course of the analgesia with no delay in the visceral pain measures. Oxycodone and morphine showed different pharmacodynamic/pharmacokinetic relationships for the visceral analgesia, whereas relationships were alike for somatic analgesia.