Model-based administration of inhalation anaesthesia. 2. Exploring the system model

Modeling the pharmacokinetics and pharmacodynamics of sevoflurane using compartment models in children and adults

BACKGROUND

Sevoflurane pharmacokinetics have been traditionally described using physiological models, while pharmacodynamics employed the use of minimal alveolar concentration.

AIMS

The integrated pharmacokinetic-pharmacodynamic relationship of sevoflurane in both adults and children was reviewed using compartment models. We wished to delineate age-related changes in both pharmacokinetics and pharmacodynamics.

METHODS

The bispectral index and sevoflurane endtidal concentration were continuously measured in 50 patients, aged 3-71 years, scheduled for minor surgery. During maintenance of anesthesia and after stable bispectral index values of 60-65 were obtained, the inspired concentration of sevoflurane was increased to 5 vol % for 5 minutes or until BIS 40 and then decreased. Data were analyzed using mammillary compartments with nonlinear mixed effects population modeling. The covariate effects of age and size were investigated.

RESULTS

A three-compartment PK model adequately described sevoflurane pharmacokinetics. Size standardization using allometry explained clearance and volume changes with age. The equilibration half-time (1.48 minutes) increased with age, but could be predicted using allometry in those under 40 years. The effect site concentration eliciting half the maximum response at age 40 years was 1.3% (95%CI 1.22, 1.42) decreased with age from 1.6% at 3 years to 1.1% at 70 years.

CONCLUSION

Pharmacokinetic compartment models offer an alternative method to describe inhalation anesthetic drug disposition and effects.

The predictive performance of a pharmacokinetic model for manually adjusted infusion of liquid sevofluorane for use with the Anesthetic-Conserving Device (AnaConDa): a clinical study

BACKGROUND

The Anesthetic-Conserving Device (AnaConDa) can be used to administer inhaled anesthetics using an intensive care unit (ICU) ventilator. We evaluated the predictive performance of a simple manually adjusted pump infusion scheme, for infusion of liquid sevoflurane to the AnaConDa.

METHODS

We studied 50 ICU patients who received sevoflurane via the AnaConDa. They were randomly divided into three groups. A 6-h infusion of liquid anesthetic was adjusted according to the infusion scheme to a target end-tidal sevoflurane concentration of 1% (Group 1%, n = 15) and 1.5% (Group 1.5%, n = 15). The initial rate was adjusted to reach the target concentration in 10 min and then the infusion was reduced to the first hour maintenance rate and readjusted once each hour afterwards. The actual concentrations were measured in the breathing circuit and compared with the target values. In the third group (n = 20) we used the model to increase and decrease the target concentration (+/-0.3%) for 3 h and evaluated the actual change in concentration achieved. The ability of the infusion scheme to provide the target concentration was quantified by calculating the performance error (PE). Infusion scheme performance was evaluated in terms of accuracy (median absolute PE, MDAPE) and bias (median PE, MDPE).

RESULTS

Performance parameters (mean +/- SD, %) were for 1%, 1.5%, increase of concentration by 0.3% and decrease of concentration by 0.3% groups, respectively: MDAPE 5.3 +/- 5.5, 2.6 +/- 4.0, 5.0 +/- 5.6, 5.5 +/- 5.4; MDPE -5.3 +/- 5.5, -2.3 +/- 4.1, -0.1 +/- 7.1, 0.2 +/- 5.4. No significant differences were found between means of all performance parameters when the 1% and 1.5% groups were compared.

CONCLUSIONS

There is an excellent 6-h predictive performance of a simplified pharmacokinetic model for manually adjusted infusion of liquid sevoflurane when using the AnaConDa to deliver sevoflurane to ICU patients.

Applying a physiological model to quantify the delay between changes in end-expired concentrations of sevoflurane and bispectral index

BACKGROUND

The delay between changes in end-expired sevoflurane concentrations and bispectral index (BIS) may be characterized by a 'rate constant' (ke0). A smaller ke0 reflects a longer delay. Values for ke0 vary substantially among studies. The question arises how ke0 depends on experimental conditions, including ventilation and apparatus.

METHODS

Increasing and decreasing sevoflurane concentrations were cyclically delivered to our validated model. First, we quantified theoretical ke0 values for distinct alveolar ventilations, estimating ke0 from sevoflurane tensions in alveolar space and grey matter. Secondly, we investigated the impact of experimental conditions. To predict BIS, the model was extended with a pharmacodynamic section, including ke0. Known values, matching theoretical values, were assigned to this ke0. These were recovered from end-expired concentrations and BIS. Possible determinants of error (difference between assigned and recovered ke0) were varied, that is fraction of dead space gas in end-expired gas (d), and time delays in measuring BIS (tBIS) and end-expired concentrations (tEE).

RESULTS

Theoretical ke0s were 0.7, 0.53, 0.35, and 0.2 min(-1) for an arterial Pco2 of 8, 6.67, 5.33 (normocapnia), and 4 kPa, respectively. For spontaneous ventilation, ke0 = 0.53 min(-1). Recovered ke0s depended on d and Deltat (= tBIS - tEE) and were smaller than assigned values (if Deltat > 0). Errors increased with increasing d and Deltat. For normocapnia, ke0 was between 0.32 and 0.23 min(-1) (d = 0.1; any Deltat = 0-60 s). For spontaneous ventilation, ke0 was between 0.51 and 0.40 min(-1) (d = 0-0.1; Deltat = 5-20 s).

CONCLUSIONS

Published ke0s (0.22-0.53 min(-1)), including our own for sevoflurane-depressed spontaneous ventilation (0.48 min(-1)), are in the ranges dictated by investigation-specific conditions.

Predictive accuracy of a model of volatile anesthetic uptake

A computer program that models anesthetic uptake and distribution has been in use in our department for 20 yr as a teaching tool. New anesthesia machines that electronically measure fresh gas flow rates and vaporizer settings allowed us to assess the performance of this model during clinical anesthesia. Gas flow, vaporizer settings, and end-tidal concentrations were collected from the anesthesia machine (Datex S/5 ADU) at 10-s intervals during 30 elective anesthetics. These were entered into the uptake model. Expired anesthetic vapor concentrations were calculated and compared with actual values as measured by the patient monitor (Datex AS/3). Sevoflurane was used in 16 patients and isoflurane in 14 patients. For all patients, the median performance error was -0.24%, the median absolute performance error was 13.7%, divergence was 2.3%/h, and wobble was 3.1%. There was no significant difference between sevoflurane and isoflurane. This model predicted expired concentrations well in these patients. These results are similar to those seen when comparing calculated and actual propofol concentrations in propofol infusion systems and meet published guidelines for the accuracy of models used in target-controlled anesthesia systems. This model may be useful for predicting responses to changes in fresh gas and vapor settings.

IMPLICATIONS

We compared measured inhaled anesthetic concentrations with those predicted by a model. The method used for comparison has been used to study models of propofol administration. Our model predicts expired isoflurane and sevoflurane concentrations at least as well as common propofol models predict arterial propofol concentrations.

Model-based administration of inhalation anaesthesia. 4. Applying the system model

BACKGROUND

We developed and tested a simple dosing strategy for rapid induction with isoflurane followed by maintenance under minimal-flow conditions, that is 0.5 litre min(-1) total fresh gas flow (FGF). An end-expired concentration was to be achieved within 5 min in a desired therapeutic window, that is 0.8-1.1 vol%, and to be maintained within it for at least 30 min.

METHODS

With our new model we computed a three-stage regimen using one fixed vaporizer setting: 3 vol% isoflurane in a FGF of 3 and 1.5 litre min(-1), each for 3 min, and 0.5 litre min thereafter. The ratio of nitrous oxide:oxygen was, consecutively, 2:1, 2:1, and 2:3. We evaluated this scheme in 58 adult patients (body mass 74 (SD 13) kg), mostly during eye and ear, nose, and throat surgery.

RESULTS

Measured oxygen (33-45 vol%) and nitrous oxide concentrations (66-50 vol%) evolved in accordance with those computed. In five patients with a median of body mass 92 kg (range 76-126 kg), inspired oxygen concentrations decreased to less than 30 vol%. End-expired isoflurane concentration entered the window after 2 min (range 1.0-5.67 min) and attained its maximum, that is 0.96 vol% (0.8-1.2 vol%), after 3.45 min (1.67-6.33 min). The mean end-expired concentration was in the desired window from 3-60 min and an average of 72% of individual measurements were within the window from 3-30 min. The scheme was adapted in six patients (excluded from analysis) because of hypotension.

CONCLUSION

The regimen is easily remembered, reliable, and lends itself to alternative strategies, but must be guided by the monitoring of gas and vapour concentrations and haemodynamic variables.

Predictive performance of a physiological model for enflurane closed-circuit anaesthesia: effects of continuous cardiac output measurements and age-related solubility data

BACKGROUND

The disposition of inhalation anaesthetics is governed by the factors described in the Fick principle.

METHODS

We have recalibrated a previously validated physiological model for enflurane closed-circuit inhalation anaesthesia, using individual continuous cardiac output measurements as well as age-related enflurane solubility coefficients as inputs to the model. Two model versions using 'calculated' (Brody's formula) or 'measured' (thoracic electrical bioimpedance) cardiac output values, and two versions with 'standard' (fixed) or 'age-related' solubility coefficients were formulated.

RESULTS

Data from 62 ophthalmic surgical patients were used to validate the predictive performance of the four model versions. The root mean squared errors (total error) and scatters (error variation) were similar with the extended model versions, but the group biases (systematic error component) were significantly less with the model versions that included age-related solubility compared with the versions using standard solubility coefficients (bias -0.76/-0.78% vs -3.44/-3.60%).

CONCLUSION

The inclusion of age-related solubility coefficients but not of continuous cardiac output measurements improves the predictive performance of the physiological model for closed-circuit inhalation anaesthetic conditions in routine clinical practice.

Model-based administration of inhalation anaesthesia. 3. Validating the system model

BACKGROUND

We quantified the predictive performance of our computer model of the administration of inhalation anaesthesia from a Datex-Ohmeda Modulus CD circle-absorber system.

METHODS

In 50 patients, desflurane anaesthesia was maintained with a fresh-gas flow (FGF) of 0.5 litres min(-1) of both nitrous oxide and oxygen, preceded by fast (n=14) or slow (n=36) induction: FGF greater than total ventilation, Group F; FGF equal to 1.0 litres min(-1), Group S. The two versions of the model studied differed in the size of their inter-tissue diffusion, as 0 (version 1) and 3% (version 2) of the cardiac output was shifted from the viscera to adipose tissue. Model performance was judged by comparing measured and predicted gas concentrations in terms of three variables for each gas concentration in each patient: root mean squared error (rmse=total error), bias (mean predicted - measured) (systematic error), and scatter (error around bias). These variables were then averaged over all patients. These measures were calculated overall, and separately for each group and each stage (1 = induction or 2 = maintenance).

RESULTS

Model predictions were in reasonable to very good agreement with clinically obtained data. Version 2 performed better than version 1. Differences between groups were not demonstrated. The model performed better for stage 2, but only for desflurane. In group S, results (mean (SD); as percentages of the measured values for nitrous oxide, oxygen and desflurane) in the order rmse, bias, and scatter were for end-tidal concentrations of nitrous oxide: 8 (4), 8 (5), 2 (1)%; oxygen: 11 (4), -10 (6), 2 (1.1)%; nitrogen: 0.9 (0.6), -0.8 (0.6), 0.2 (0.1) vol%; carbon dioxide: 1.8 (0.6), 1.8 (0.6), 0.2 (0.1) vol%; desflurane, stage 2: 8 (4), 4 (7), 4 (2)%, vs 15 (6), -10 (8), 9 (4)% for stage 1.

CONCLUSION

Administration of inhalation anaesthesia can be based on version 2 of this model, but must be guided by active monitoring.