Population Pharmacodynamic Modeling and Covariate Detection for Central Neural Blockade
Authors: Schnider Thomas W. , Minto Charles F. , Bruckert Heini , Mandema Jaap W. 
Published: November 2003

Background
In spinal anesthesia, often a large interindividual variability in analgesic response is observed after administration of a certain fixed dose of anesthetic to a patient population. To improve therapeutic outcome it is important to characterize the variability in response by means of a population model (e.g., mixed-effects models or two-stage approaches). The purpose of this investigation is to derive a population model for spinal anesthesia with plain bupivacaine. Based on the population models, a description of a patient's time course of drug action is obtained, the influence of patient covariates on clinically important endpoints is examined, and the success of Bayesian forecasting of the offset of effect in a specific patient from the data obtained during onset is evaluated.

Methods
The level of central neural blockade after intrathecal injection of plain bupivacaine was assessed by testing analgesia to pinprick. A total of 714 measurements in 96 patients (4-10 per subject) were available for analysis. Two pharmacodynamic models, based on the understanding of the physiology of the spread of local anesthetic in the spinal fluid, were evaluated to characterize the time course of analgesia in a specific patient. The first model is a combination of a biexponential pharmacokinetic model, describing the onset and offset of effect and a linear pharmacodynamic model. The second model combines the biexponential pharmacokinetic model with an Emax type pharmacodynamic model. The interindividual variability in model parameters was modeled by an exponential variance model. An additional term characterized the residual error. The population mean parameters, interindividual variance, and residual variance were estimated using the first-order conditional estimate method in the NONMEM software package. Clinically important endpoints such as onset time, time to reach the maximal level, the maximal level, and the duration of analgesia were estimated from the Bayesian fit of each subject's data and correlated with patient-specific covariates. Using Bayesian forecasting, the offset of spinal analgesia was predicted for each patient based on the population model and measurements from the first 30 min and from the first 60 min, respectively.

Results
The Emax type pharmacodynamic model was superior based on the improvement in likelihood (P < 0.001) and on visual inspection of the fits. The estimates of the population mean parameters (coefficient of variation) were: (1) maximal effects: T4, which was coded for the purpose of the calculation as 18 (14%); (2) rate of offset of effect: 0.0118 (26%) min-1; (3) rate of onset of effect: 0.061 (45%) min-1. The standard deviation of the residual error was 1.4. Large interindividual differences were observed in the time course of analgesic response and clinically important endpoints. The mean onset time; that is, time to reach T10 (interindividual variability) was 4.2 min (90%), the mean time to maximal level was 35.5 min (29%), the mean duration of effect was 172 min (28%), and the mean maximal achieved level was T6 (12%). Significant correlations between onset time and height and weight, between time to maximal level and age, between maximal level and weight and height, and between duration and height were found. Bayesian regression using the population model and data from the first 30 min and from the first 60 min predicted the offset of effect in each patient reasonably well, with coefficients of determination (R2) of 0.71 and 0.72. This is a significant improvement over the population mean prediction.

Conclusion
A population model was derived for the description of the time course of central neural blockade. Based on the population model, a continuous effect profile over time was obtained for each person...