Canadian Journal of Anesthesia 48:273-278 (2001)
© Canadian Anesthesiologists' Society, 2001
Regional Anesthesia and Pain
Selective spinal anesthesia for outpatient laparoscopy. IV: Population pharmacodynamic modelling
Himat Vaghadia, MB BS MHSC FCA FRCPC*,
,
Linda Collins, MB BCH BAO FFARCSI*,
Huiying Sun, BSc
and
G.W.E. Mitchell, MB CHB MRCOG FRCS(Ed) FRCSC
* From the Departments of Anesthesia,
Health Care and Epidemiology,
Gynecology and
Statistics, Vancouver General Hospital, University of British Columbia, Vancouver, British Columbia, Canada.
Address correspondence to: Dr. Himat Vaghadia, Department of Anesthesia (Room 3200), Vancouver General Hospital, 3rd Floor - 910 West 10th Ave, Vancouver, British Columbia, V5Z 4E3 Canada. Phone: 604-875-4304; Fax: 604-875-5209; E-mail: hvaghadi{at}vanhosp.bc.ca
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Abstract
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Purpose: To apply a population pharmacodynamic model to small-dose hypobaric spinal anesthesia for outpatient laparoscopy.
Methods: The level of spinal analgesia after spinal blockade with small-dose (20–25 mg) hypobaric lidocaine was assessed by means of pinprick in patients undergoing outpatient laparoscopy. In 57 patients, 385 measurements were available for analysis. We first modelled the data for each patient with a mixed-effects model described by Schnider (Model 1). The population mean parameters, inter-individual variance, and residual variance were estimated. Clinically important endpoints (time to reach T10 (onset), time to maximal level, duration and maximally attained level) of each patient were calculated based on the estimated time course of analgesia level for each patient. The model was used to predict the later data with respect to level of spinal analgesia of each patient from fits based on the observed data in the first 75 min.
Results: The mean ± SD onset time was 8.3 ± 1.9 min, time to maximal level was 20.8 ± 5.3 min, duration of effect was 37.9 ± 13.1 min, and mean maximal level was T5. There was a good correlation (R2=0.90) between the observed levels of analgesia and those predicted from the model. Data from the first 75 min predicted the later observed data for each patient moderately well (R2=0.38).
Conclusion: A population pharmacodynamic model was applied to low-dose hypobaric lidocaine spinal anesthesia. Clinically important endpoints were determined and forecasting of later data with respect to level of spinal analgesia was attempted. Such an approach may be useful in the management of low-dose spinal anesthetic techniques in outpatients.
INCREASINGLY, it is recognized that conventional dose spinal anesthesia may be unsuitable for short to medium duration outpatient procedures because of prolonged motor block and the consequent risk of unplanned admission.1 In our institution, we have achieved success with low-dose techniques that facilitate rapid recovery and discharge after spinal anesthesia for laparoscopy.2–3 However, with the use of low-dose spinal anesthesia, there may be concern that individual variability in response may result in some patients not obtaining adequate anesthesia. One method to resolve this dilemma is to utilize population based pharmacodynamic modelling to characterise individual responses and the variability in response within a defined population.4 Based on such modelling, important clinical endpoints or model specific parameters can be calculated and correlated with patient specific parameters to explain inter-individual variability in response. Such an analysis can be useful in determining the applicability of low-dose spinal anesthetic techniques in the outpatient setting.
The purpose of the present study was to apply a population pharmacodynamic modelling approach to data from a spinal anesthesia study employing low-dose hypobaric lidocaine for outpatient laparoscopy.
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Methods
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The study was approved by the University Ethics Committee and informed consent was obtained from each patient. Patients scheduled for outpatient laparoscopy were assigned to receive spinal anesthesia with 20–25 mg lidocaine 1% (2–2.5 ml, Astra Zeneca, Mississauga, Ontario, Canada), mixed with 10–25 µg fentanyl (0.2–0.5 ml) and sterile water (0.5 ml). Patients were excluded if there was a contraindication to spinal anesthesia or to the spinal drugs. The spinal puncture was performed with a 27-G Whitacre needle with the patient in the sitting position. Spinal puncture was performed at L2–3 or L3–4. The spinal solution was injected rapidly (0.5 ml•sec–1)3 with the needle orifice pointing cephalad. After one minute, patients were placed in reverse Trendelenburg position (15–20) until the level of sensory anesthesia (tested to pinprick) reached T6. Patients were then returned to the horizontal position. Positioning was standardised in all patients. Sensory block was determined by pinprick with an 18-gauge needle at 15 min intervals commencing at 15 min after injection (patients 1–43) and at five minute intervals commencing at five minutes post injection for the first two observations and then at 15 min intervals for the later observations (patients 44–57). Observations were continued for up to 150 min after spinal injection. All assessments were performed by one of the investigators. The dermatome level measurements were expressed in increasing numbers between 1 (S5) and 22 (T1). All observations were discontinued when the patient was ready for discharge and the sensory block had resolved. Fifty-seven subjects with a total of 385 measurements (4–11 per patient) over 5–150 min were available for this analysis.
The structural model used for the analysis was: L(t)=DOSE•CO•(e–1t–e–2t), where L(t) is the level of neural blockade. This model shows that the level of neural blockade is proportional to the dose of injection, equal to zero at t=0 (injection time) and t= (long time from injection), and reaches its maximum some time after injection depending on 1 (the absorption rate) and 2 (the elimination rate). Schnider et al.4 called the model (Model 1 in their paper) a combination of a biexponential pharmacokinetic model, describing the onset and offset of effect and, a linear pharmacodynamic model. Since all patients in the study received a small dose of lidocaine 1% (20–25 mg), we can take DOSE=1, which means that we do not look at dose as a covariate. The volume of injectate and the site of injection were also not looked at as covariates. As in Schnider et al.,4 we assumed that COi, 1i, and 2i, the parameters for the ith patient, were log normally distributed with diagonal covariance matrix having diagonal elements (21, 22, 23).The residual errors for the ith patient are assumed to be independently and identically normally distributed with mean zero and variance 2 (common for all patients). We used NLME in statistical software S-plus to carry out our analysis. Like GLM for generalized linear models in S-plus, NLME is a flexible function for fitting non-linear mixed-effects models which is quite easy to use. Subsequently, clinically important endpoints were derived from the estimated time course of analgesia level for each patient. These were: time to reach T10 (onset time), time to reach maximal level, duration of analgesia (time to analgesia T10), and the maximally attained level. The endpoints were numerically approximated. That is, we calculated the values of the estimated neural blockade level at 165 time points (t=1, 2, ...165) for each patient, then found the approximated endpoints based on the 165 values.
The influence of the covariates height and weight on the clinical endpoints were explored subsequently. Finally, we used information from the onset of effect to predict the later data using the method described by Schnider et al.4
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Results
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Data
A satisfactory block was produced in all patients studied. A scatter plot of observed analgesia levels over time of all 57 patients is shown in Figure 1
. Separate scatter plots of observed analgesia levels of each patient show a peak between zero and 45 min after insertion of the spinal anesthetic. The overall nature of the plots varied considerably from patient to patient. This suggests a nonlinear model to explain analgesia as a function of time but with parameters that vary from patient to patient.
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FIGURE 1 Scatter plot of observed levels of analgesia over time. The measurements for the same patient are connected with lines.
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Model fitting
Following Schnider et al.,4 we first modelled the data for each individual patient using their Model 1:
Table I lists the estimated population parameters for Model 1. Each of the regression parameters is highly significant. On the other hand, the estimated value of ^=2.168 indicates that a considerable amount of the variability in the data is not explained by Model 1. The estimated variance components indicate that there is little variation from patient to patient in the values of COi, but considerable variation in the values of 1i and 2i.
Figure 2 shows the estimated time course of analgesia levels in individual patients. The maximal level in these 57 patients varied between T9 and T1. Figure 3 presents the time course of the best, median and worst predicted profiles, as judged by the sum of squared residuals (per time point) from Model 1. Figure 4 gives the various plots of the residuals. The plot of observed vs fitted values indicates that the model fits the data well; the correlation between the observed and fitted values was 0.95. The plot of residuals vs fitted values does not indicate any extreme departures from the assumptions in the model. The boxplots of the residuals for each individual patient show that, for most patients, the residuals are reasonably symmetrically scattered around zero.
Calculation of clinical endpoints
Based on the estimated time course of analgesia for each patient, we calculated the clinically important endpoints (Table II). The distribution of the different measures across the patient population is shown in Figure 5. The mean time to reach T10 was 8.3 min (median 8 min). A mean level of analgesia of T5 was reached (median T5). The mean duration was 37 min (median 39 min) and the mean time to reach maximal level was 20 min (median 21 min). Height and weight were not found to significantly influence these clinical endpoints.
Forecasting
Model 1 was used to forecast observations beyond 75 min based on all observation times up to 75 min (total 288 observations). Figure 6 shows the plot of observed levels of analgesia (for all times >75 min) vs predicted levels; the correlation between observed and predicted values was 0.62 (R2=0.38).
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FIGURE 6 Observed vs predicted levels of analgesia (for all levels at times >75 min). These predicted levels are based on the individual patient parameters obtained from all the observations in the first 75 min.
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Discussion
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In a study of 57 outpatients who received spinal anesthesia with a small dose of lidocaine 1% (20–25 mg), 385 measurements of analgesia levels were utilized to facilitate population pharmacodynamic modelling with a model previously described by Schnider et al.4 Each of the regression parameters for the model were found to be highly significant. There was a good correlation between observed and fitted values (R2=0.90) indicating that the data fits the model well and there was no apparent extreme departure from the assumptions of the model. Clinically important endpoints calculated were: mean time to reach T10 (onset) of eight minutes, mean time to reach maximal level of 20 min, mean duration of 37 min and the mean maximal level achieved of T5. Forecasting using the model and data up to 75 min predicted the later levels of spinal analgesia only moderately well (R2=0.38, R=62).
The model used in this study was previously described by Schnider et al.4 with intrathecal bupivacaine. It is useful when a different number of data points for each subject are recorded at different points in time and when enough data points are not available in patients to fit each one's analgesic response independently. In the present study, patients received slightly different doses of spinal lidocaine (20–25 mg) and fentanyl (10–25 µg) not unlike the patients in the study by Schnider. An important advantage of collecting observational data from normal clinical practice is that it reflects "real-life" data without controlling the independent variables by selecting a specific dose. The mixed-effects modelling approach used to derive the population model is especially useful when the data is unbalanced. Thus, conclusions, when drawn carefully, can have clinical applicability and relevance. Like Schnider, we treated the data as representing a continuous measurement and assumed that a change in analgesic level from T8 to T7, for example, was the same as a change from S1 to L5.
With intrathecal bupivacaine, Schnider's model was found to be successful with a close correlation (R2=0.7) between observed and predicted levels of analgesia being found with forecasting based on observations in the first 30 min. In our study, with low-dose lidocaine, Schnider's model was found to perform moderately well with correlation of 0.62. Thus, for model fitting, our results were as good as Schnider (R2=0.95 vs R2=0.9). For model forecasting, their results were better than ours (R2=0.7 vs R2=0.38) because we did not have sufficient earlier observations. Another reason for Schnider's results being better than ours could be that we had fewer data (385 observations in 57 subjects) than Schnider (714 observations in 96 subjects). In the present study, we could not forecast offset effects but only the observations later than 75 min because we did not have enough "onset" observations. The model might be used for forecasting offset effect with small-dose spinal anesthesia, if we had more earlier observations. Given the apparent timing of the maximal levels, more frequent measurements right after insertion of spinal anesthetic are required to provide good fits of either of these models for these data. More early observations would also improve the prediction of the offset effect based on early measurements. Schnider also found that inter-individual variability in analgesic levels could be explained in part by covariates such as height and weight. In the present study, very little of the variation in any of the clinical endpoints was explained by height and weight. Other factors such as patient position could also be important in influencing the spread of analgesia and hence contribute to the variability of inter-individual data sets.5 All patients in this study were managed in a standard manner with respect to position change after completion of spinal injection to minimize this source of data imbalance. Because position change was not a part of the model, it would contribute to a deviation between observed and predicted levels of analgesia and become part of the residual error. However, because our data represents actual observational data from "real life" clinical practice, it has the strength of clinical relevance and applicability.
We also explored several other fits to the data. Using the same model, we fitted the data allowing the patient level parameters to be arbitrarily correlated and with the residual errors assumed to be independent and normally distributed with: (a) common variances; (b) variances that vary exponentially with the absolute values of the predicted values. The resulting fitted curves were similar to those illustrated in Figure 2
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Schnider et al.4 used two models, and they indicated that Model 2 provided a better fit to their data than Model 1. Model 2 is presented in the Appendix of their paper as:
With this definition, L2(t) is a decreasing function of t, which means that this model is not suitable for the sensory data. Clearly, this is not the model they used in their paper. It seems likely that the actual model used by Schnider et al.4 as Model 2 was:
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We also fitted our data to the function L2*(t), with the same assumptions on the parameters used by Schnider et al.4 This model seems to be unsuitable for our data set, as the fitted curves reflected very little patient to patient variability. We do not present the results in this paper since we are not sure of the correct definition of their Model 2. Schnider et al.4 do not indicate why they assumed that there was no correlation between the patient-level parameters. Perhaps this was a limitation of the software they employed to perform the fitting. They indicated that the software NONMEM was used to carry out their analysis, we used NLME in S-plus. Like GLM for generalised linear models in S-plus, NLME is a flexible function for fitting non-linear random effects models which is quite easy to use.
In summary, we tested a mixed-effects model for the description of analgesia levels over time after the administration of small-dose lidocaine-fentanyl spinal anesthesia to outpatients undergoing gynecological laparoscopy. Clinically important endpoints were obtained for low-dose lidocaine spinal anesthesia. There was a good correlation between observed and predicted levels of analgesia.
Accepted for publication October 29, 2000.
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References
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1
Vaghadia H. Spinal anaesthesia for outpatients: controversies and new techniques. Can J Anaesth 1998; 45: R64–R70.[Medline]
2
Vaghadia H, McLeod DH, Mitchell GWE, Merrick PM, Chilvers CR. Small-dose hypobaric lidocaine- fentanyl spinal anesthesia for short duration laparoscopy. I. A randomized comparison with conventional dose hyperbaric lidocaine. Anesth Analg 1997; 84: 59–64.[Abstract]
3
Chilvers CR, Vaghadia H, Mitchell GWE, Merrick PM. Small-dose hypobaric lidocaine-fentanyl spinal anesthesia for short duration outpatient laparoscopy. II. Optimal fentanyl dose. Anesth Analg 1997; 84: 65–70.[Abstract]
4
Schnider TW, Minto CF, Bruckert H, Manderna JW. Population pharmacodynamic modeling and covariate detection for central neural blockade. Anesthesiology 1996; 85: 502–12.[Medline]
5
Russell IF. Posture and isobaric subarachnoid anaesthesia. The influence on spread of spinal anesthesia with ‘isobaric’ 0.5% bupivacaine plain. Anaesthesia 1984; 39: 865–7.[Medline]
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Abstract
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