1420
Regular Article
Biol. Pharm. Bull. 36(9) 1420–1427 (2013)
Vol. 36, No. 9
Estimating the Plasma Effect-Site Equilibrium Rate Constant (Ke0) of
Propofol by Fitting Time of Loss and Recovery of Consciousness
Qi Wu, Baozhu Sun, Shuqin Wang, Lianying Zhao, and Feng Qi*
Department of Anesthesiology, Qilu Hospital of Shandong University; 107 Wenhuaxi Road, Jinan 250012, China.
Received December 20, 2012; accepted June 13, 2013; advance publication released online June 27, 2013
The present paper proposes a new approach for fitting the plasma effect-site equilibrium rate constant
(Ke0) of propofol to satisfy the condition that the effect-site concentration (Ce) is equal at the time of loss of
consciousness (LOC) and recovery of consciousness (ROC). Forty patients receiving intravenous anesthesia
were divided into 4 groups and injected propofol 1.4, 1.6, 1.8, or 2 mg/kg at 1200 mL/h. Durations from the
start of injection to LOC and to ROC were recorded. LOC and ROC were defined as an observer’s assessment of alertness and sedation scale change from 3 to 2 and from 2 to 3, respectively. Software utilizing bisection method iteration algorithms was built. Then, Ke0 satisfying the CeLOC=CeROC condition was estimated.
The accuracy of the Ke0 estimated by our method was compared with the Diprifusor TCI Pump built-in Ke0
(0.26 min−1), and the Orchestra Workstation built-in Ke0 (1.21 min−1) in another group of 21 patients who were
injected propofol 1.4 to 2 mg/kg. Our results show that the population Ke0 of propofol was 0.53±0.18 min−1.
The regression equation for adjustment by dose (mg/kg) and age was Ke0=1.42–0.30×dose–0.0074×age. Only
Ke0 adjusted by dose and age achieved the level of accuracy required for clinical applications. We conclude
that the Ke0 estimated based on clinical signs and the two-point fitting method significantly improved the
ability of CeLOC to predict CeROC. However, only the Ke0 adjusted by dose and age and not a fixed Ke0 value can
meet clinical requirements of accuracy.
Key words
algorithm; anesthetic; intravenous; pharmacokinetics; propofol
Propofol is a routine intravenous anesthesia, used for induction and maintenance of anesthesia. Target-controlled infusion
(TCI) has been developed as a standardized infusion method
for the administration of propofol. The first generation of TCI
devices, which is based on the classic multi-compartment
pharmacokinetics (PK) model, only calculated and maintained
plasma concentration (Cp).1) Drug effects and concentrations
in drug effect-sites are highly correlated. Considering that
the effect-site of propofol is not in the plasma, the effects of
propofol lag behind plasma concentrations. Therefore, a pharmacokinetic–pharmacodynamic (PK–PD) model, in which a
pharmacodynamic (PD) compartment was added to the PK
model was utilized,2) was employed to control drug concentrations at effect-sites. The critical parameter of the PD model is
equilibrium rate constant (Ke0) between the plasma and effectsite concentrations (Ce). Ke0 has a significant influence on the
output regimen of syringe pumps.3)
Three currently used methods for deriving Ke0 include the
time to peak effect (Tpeak), non-parametric, and parametric
approaches.4–9) The Tpeak approach measures the time required for the effect to peak through effect indicators. The Ke0
value is obtained if it satisfies the condition that the calculated
Ce is maximal at Tpeak.5) The non-parametric approach calculates the Cp trend using the PK model. It draws the Ce trend
curve using the assumed Ke0 and the effect trend curve based
on the effect indicators. The Ke0 value that minimizes the lag
ring between the two curves is the optimal Ke0.6,7) The parametric approach parameterizes Ce and effect indicators using
the classic Sigmoid Emax model, collects the time process
of effect indicators, and estimates Ke0 using WinNonlin or
NONMEM software.8,9)
Optimized target-controlled infusion (OTCI) targets concentrations according to individual Ce upon loss of consciousThe authors declare no conflict of interest.
ness (LOC). Simultaneously, the individual minimum Ce at
loss of consciousness (MECLOC) is locked.10) The feasibility
of OTCI is based on the condition that Ce is equal at times of
LOC (CeLOC) and recovery of consciousness (ROC) (CeROC),
but the calculated CeLOC and CeROC are not equal if Ke0 is not
appropriate. Iwakiri et al. revealed a CeLOC value higher than
CeROC by 1.8±0.7 µg/mL.11) Simoni et al. found that CeLOC and
CeROC vary greatly under different Ke0.12) So OTCI can be a
good way of verifying the PD model by comparing the CeLOC
and CeROC, and the optimum Ke0 can be fitted by the verified
process.
Studies published to date have generally used electroencephalogram (EEG) derived parameters, such as the
bispectral index (BIS) and the acoustic evoked potential index
(AAI), as effect indicators. Obtaining EEG-derived parameters is time-consuming, requires considerable data for analysis
or average superposition, does not provide real-time results. In
the Tpeak approach, the peak cannot be clearly identified because the shape of the effect curve resembles a flat deck roof.
Here, we propose a new approach for estimating Ke0 based
on the Principle of OTCI and employing clinical signs as
effect indicators. Since clinical signs can be obtained in real
time, flaws in EEG-derived parameters can be avoided using
this approach.
MATERIALS AND METHODS
After obtaining approval from the Institutional Ethics Committee (Qilu Hospital of Shandong University, Jinan, Shandong, China) and informed consent from participants, 40 adult
patients scheduled for surgery under general anaesthesia were
studied. All patients were American Society of Anesthesiologist physical status I or II and did not receive premedication.
Exclusion criteria included obesity (body mass index >30),
neurological disorders, heart, lung, liver, and kidney dysfunc-
To whom correspondence should be addressed. e-mail: [email protected]
* © 2013 The Pharmaceutical Society of Japan
September 20131421
Fig. 1.
A 60 kg Subject’s Concentrations Trend after Administration of 1.8 mg/kg Propofol Bolus
This typical subject’s times to LOC and to ROC are 61 and 458 s, respectively. The two black vertical lines represent LOC and ROC time marks. The concentrations are
calculated from the established software. The solid curve represents Cp. The dash curve represents Ce under fitted Ke0 (this case is 0.46 min−1); where the CeLOC=CeROC. The
dash dot curve represents Ce under freely inputted Ke0 (this case is 1.21 min−1), where the CeLOC ≠ CeROC. In the dash curve, with the Tpeak approach, the Tpeak appeared
184 s after drug infusion but the Ce was at more than 95% of the peak value between 135 s and 249 s, determining the 5% change over the 114 s duration using EEG-derived
parameters is difficult. With the two-point approach proposed by this study, the time to LOC was 61 s, and the ±5% change near LOC was just 6 s, the time to ROC was
458 s, and the ±5% change near ROC was 35 s. Accurately identifying the time to LOC and to ROC is easier than the time to Tpeak.
tion, and auditory dysfunction. After overnight fasting, the
patients were brought to a quiet operating room. A cannula
was inserted into an antecubital vein for propofol and fluid
injection. Oxygen was supplied at 2 L/min and routine noninvasive monitoring of arterial pressure, electrocardiogram,
and pulse oximetry was initiated. The head pillow was moved
away to maintain an open airway. Propofol (1%, AstraZeneca,
Batch Number: X11209A) bolus was injected at 1200 mL/h
using a Pilot Anesthesia 2 syringe pump (Fresenius SE & Co.,
61346 Bad Homburg KgaA, Germany). Patients were divided
randomly into four groups of 10 participants each based on
the bolus dose of propofol: P1 group (1.4 mg/kg), P2 group
(1.6 mg/kg), P3 group (1.8 mg/kg), P4 group (2.0 mg/kg). The
verbal stimulation “open your eyes” was recorded in advance
using an MP3 player with recording capabilities. The verbal
stimulation was played looped for 3 s at a fixed loud volume
after propofol injection. Times from the start of injection to
LOC and ROC were recorded with a stopwatch. Within the
study period, if pulse oximetry reading fell below 90%, artificial ventilation was given through the pressurized mask. Once
pulse oximetry reading rose to 96%, the artificial ventilation
was stopped. Induction of general anaesthesia was continued
after time to ROC was recorded.
In order to validate Ke0, the additional group Px was participated: 21 patients received seven graded doses 1.4, 1.5, 1.6,
1.7, 1.8, 1.9 or 2.0 mg/kg, each grade included 3 patients. The
times to LOC and to ROC in these patients were recorded
using the above-mentioned method.
Determination of LOC and ROC LOC is defined as loss
of the patient’s reaction to verbal stimulation, equivalent to an
observer’s assessment of alertness and sedation (OAA/S) scale
change from 3 to 2. ROC is defined as appearance of reaction
in the patient to verbal stimulation, equivalent to an OAA/S
Table 1.
scale change from 2 to 3.11–15) The times elapsed from propofol
injection to these two time points was recorded with a stopwatch as the time to LOC and to ROC, respectively.
Authoring Software The Ke0 -fitting software was custom-built using the Microsoft Visual Studio 2010 programming environment and the C# language. The software was
used as follows:
1. Marsh’s PK model16) and TCI calculative method17) were
set up following the calculation method described previously.
The specific parameters of the Marsh PK model are listed in
Table 1.
2. The time process of Cp after bolus injection was calculated and used as the basis to calculate Ce. The Ke0 satisfying
the condition of CeLOC equals CeROC was fitted using the bisection method iteration (details shown in Appendix).
3. The software could also input free Ke0 to calculate and
display the corresponding Ce trend graph in order to observe
CeLOC and CeROC changes under different Ke0.
4. Trend graphs for the calculated Cp, fitted Ce, and observed Ce were simultaneously displayed at the bottom of the
software interface to facilitate comparison.
Statistical Analysis All variables are expressed as mean±
S.D. or median and interquartile ranges (25 to 75%) based on
the results of the Shapiro-Wilk test for normality. Paired,
unpaired t-tests for variables were performed where appropriate. Individual Ke0, CeLOC, and CeROC values were fitted to 40
patients in groups P1 to P4. The mean Ke0 was considered the
population Ke0, and the Ke0 were multiple linear regressed by
dose and age to obtain the adjusted population Ke0.
The population Ke0, population Ke0 adjusted by dose and
age, Diprifusor TCI Pump built-in Ke0 (0.26 min−1), and Orchestra Workstation built-in Ke0 (1.21 min−1) were entered on
the software. Individual CeLOC and CeROC values of group Px
Parameters of Marsh’s PK Model
V1 (L)
K10 (min−1)
K12 (min−1)
K21 (min−1)
K13 (min−1)
K31 (min−1)
0.228×Weight (kg)
0.119
0.112
0.055
0.0419
0.0033
1422
Vol. 36, No. 9
were calculated according to the actual LOC and ROC times
acquired. The approach to evaluate the performance of the
TCI system was used to evaluate the ability of CeLOC to predict CeROC.18) The formula used to calculate the performance
error (PE) of individual CeLOC to predict CeROC is as follows:
PE(%) =
CeLOC − CeROC
×100(%)
CeROC
Using the median of PE (MDPE) as a bias index and the
median of absolute PE (MDAPE) as an accuracy index, the
performance of CeLOC to predict CeROC under the four Ke0
values was evaluated. A paired t-test was carried out between
CeLOC and CeROC under four Ke0. p<0.05 was considered
statistically significant, and p<0.01 was considered highly
statistically significant. Linear regression was also performed
to derive the regression equation of CeROC from CeLOC under
different Ke0.
All statistical analyses were done using SAS 9.1.3.
RESULTS
The characteristics of the five groups studied are shown in
Table 2.
Ke0 fitting was successful for all patients in groups P1 to
P4. The results showed a normal distribution in all groups
(Table 3). The population Ke0 (mean±S.D.) of all 40 patients in
groups P1 to P4 was 0.53±0.18 min−1. Detailed Ke0 of groups
P1 to P4 were 0.62±0.15, 0.55±0.16, 0.50±0.22 and 0.45±
0.17 min−1, respectively. Ke0 declined as dose increased, as
shown in Fig. 2. Consistent with the results of Schnider et
al.,19) Ke0 also declined as age increased, as shown in Fig. 3.
The Ke0 regression equation adjusted by dose (mg/kg) and age
was Ke0=1.42−0.30×Dose−0.0074×Age, R 2=0.33.
The population Ke0 before and after dose and age adjustment, the Diprifusor TCI Pump built-in Ke0 (0.26 min−1), and
Orchestra Workstation built-in Ke0 (1.21 min−1) were used to
calculate the patients’ CeLOC and CeROC in the Px group (Table
4). The bar graphs and linear regression graphs are shown in
Fig. 4.
Under population Ke0 before adjustment by dose and age
(0.53 min−1), the MDPE of CeLOC to predict CeROC was 9.5%
(−20.3 to 67.5%), and the MDAPE was 35.8% (9.1 to 60.0%).
According to the common opinion that the MDPE of the TCI
system should be less than 15% and that MDAPE should be
less than 30%,20) the bias satisfied the clinical requirement
but the accuracy was insufficient. Paired t-test indicated that
CeLOC and CeROC were not significantly different, and the regression expression obtained was CeROC=0.84×CeLOC. These
results show that the performance of CeLOC to predict CeROC
is unacceptable using the population Ke0 before adjustment by
dose and age.
Using the population Ke0 after adjustment by dose and age,
on the other hand, the MDPE of CeLOC to predict CeROC was
Table 2.
Fig. 2.
Relationship between Ke0 and Dosage
1.5% (−16.7 to 59.8%), and the MDAPE was 24.2% (9.4 to
59.8%). Referencing the aforementioned standards, the bias
and accuracy both satisfied clinical requirements. Paired ttest indicated that CeLOC and CeROC were still not significantly
different, and the corresponding regression expression was
CeROC=0.89×CeLOC. Thus, the performance of CeLOC to predict
CeROC is acceptable under the population Ke0 after adjustment
by dose and age.
Using the Diprifusor TCI Pump built-in Ke0 (0.26 min−1),
the MDPE of CeLOC to predict CeROC was −43.2% (−49.3 to
−23.7%), and the MDAPE was 43.2% (23.7 to 49.3%). Referencing the aforementioned standards, the bias and accuracy
did not satisfy clinical requirements. Paired t-tests revealed
that CeLOC and CeROC were significantly different (p<0.01), and
the regression expression was CeROC=1.60×CeLOC. Thus, the
performance of the CeLOC to predict CeROC was unacceptable
under the Diprifusor TCI Pump built-in Ke0. The CeLOC was
smaller than CeROC in almost all patients.
Using the Orchestra Workstation built-in Ke0 (1.21 min−1),
the MDPE of CeLOC to predict CeROC was 146% (58.8 to 284%),
and the MDAPE was 146% (58.8 to 284%). Referencing the
aforementioned standards, the bias and accuracy did not satisfy clinical requirements. Paired t-test results indicated that
CeLOC and CeROC were significantly different (p<0.01), and the
corresponding regression expression was CeROC=0.40×CeLOC.
The performance of CeLOC to predict CeROC was thus unacceptable under the Orchestra Workstation built-in Ke0. The
CeLOC was larger than the CeROC in all patients.
DISCUSSION
There is substantial variation in propofol Ke0 values reported
in previous studies. For example, Billard et al. and Schnider et
al. reported Ke0 values of 0.291 min−1 and 0.456 min−1, respectively.8,19) The Diprifusor TCI Pump and Orchestra Workstation were built on the same Marsh PK model but have the
default Ke0 values of 0.26 min−1 and 1.21 min−1, respectively.
Patient Characteristics
Group
Gender (m/f)
Age (years old)
Weight (kg)
P1 (n=10)
P2 (n=10)
P3 (n=10)
P4 (n=10)
Px (n=21)
6/4
51.3±9.6
64.5±10.8
5/5
51.8±13.0
63.2±10.1
6/4
48.0±10.1
67.4±8.6
6/4
51.2±12.0
68.0±8.0
13/8
50.0±12.9
63.0±13.0
Data are expressed as numbers or mean±S.D.
September 20131423
Fig. 3.
Relationship between Ke0 and Age
A: Relationship between Ke0 and age in group P1. B: Relationship between Ke0 and age in group P2. C: Relationship between Ke0 and age in group P3. D: Relationship
between Ke0 and age in group P4. E: Relationship between Ke0 and age in groups P1 to P4.
Table 3.
Time to LOC, ROC and Fitting Results of Ke0 in Groups P1 to P4
Group
Time to LOC (s)
Time to ROC (s)
Ke0 (min−1)
P1
P2
P3
P4
63.4±11.7
351±84.5
0.62±0.15
63.6±9.4
402±95.5
0.55±0.16
61.7±8.6
501±154
0.50±0.22
60.9±8.4
564±186
0.45±0.17
Data are expressed as numbers or mean±S.D.
Zhang determined the effects of propofol using AAI and BIS
on the same population and obtained Ke0 values of 0.64 and
1.87 min−1, respectively.21)
Four factors could lead to such differences in Ke0. First,
commonly used EEG-derived parameters cannot simultaneously reflect the effects of drugs.22–26) The acquisition of BIS
and AAI requires the collection of sufficient data or average
superposition operations. In addition, the synchrony between
change in consciousness and raw EEG is not clear yet. Pilge
et al. studied the delay between raw EEG and EEG-derived
parameters using artificially generated and perioperatively recorded EEG data and found that the delays were inconstantly
15–64 s and were different for ascending and descending
values. They believed that the results of PD studies might be
influenced by this phenomenon.22,23) Baker et al. observed the
BIS to lag about 60 s behind the clinical sign.24) Chen and Rex
1424
Fig. 4.
Vol. 36, No. 9
Calculated CeLOC and CeROC Column Chart (Left Column) and Linear Regression (Right Column) in Group Px under Different Ke0
A and B: CeLOC is approximately equal to CeROC under the population Ke0 value 0.53 min−1 proposed by this research. C and D: Further improvements in similarity
between CeLOC and CeROC under population Ke0 adjusted by dose and age. CeLOC predicted CeROC more accurately. E and F: CeLOC is obviously less than CeROC using the
Diprifusor TCI Pump built-in Ke0 of 0.26 min−1. CeLOC cannot predict CeROC. G and H: CeLOC is obviously higher than CeROC using the Orchestra Workstation built-in Ke0 of
1.21 min−1. CeLOC cannot predict CeROC.
September 20131425
Table 4. CeLOC and CeROC under Different Ke0 in Group Px
No.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
Mean±S.D.
Ke0=0.53 (min−1)
Ke0=0.26 (min−1)
Ke0 Adjusted by dose and age
Ke0=1.21 (min−1)
CeLOC (µg/mL) CeROC (µg/mL) CeLOC (µg/mL) CeROC (µg/mL) CeLOC (µg/mL) CeROC (µg/mL) CeLOC (µg/mL) CeROC (µg/mL)
1.67
2.31
2.26
2.25
1.80
2.30
1.77
2.12
2.21
2.32
2.61
2.18
2.56
2.48
1.76
2.28
2.51
2.14
2.35
2.15
3.07
2.95
2.31
1.38
2.79
2.42
1.15
2.75
1.95
2.81
2.29
1.72
2.20
0.88
1.59
3.01
1.84
2.29
1.25
1.13
1.41
1.28
2.37
2.58
2.38
2.31
2.20
2.49
1.77
2.12
2.79
2.11
1.92
2.18
1.96
2.33
2.30
2.31
2.04
2.41
2.73
1.39
2.05
3.13
2.28
1.35
2.80
2.34
1.10
2.75
1.95
2.75
2.34
1.92
2.20
1.03
1.63
2.90
1.83
2.43
1.18
1.05
2.19
1.59
2.24±0.32*
1.97±0.67*
2.23±0.32#
2.04±0.65#
0.90
1.31
1.28
1.25
0.97
1.28
0.94
1.16
1.22
1.27
1.46
1.19
1.41
1.36
0.94
1.23
1.37
1.15
1.26
1.15
1.72
2.20
2.11
1.61
2.35
2.25
1.46
2.45
2.09
2.47
2.34
1.99
2.28
1.22
1.93
2.72
2.16
2.47
1.65
1.54
1.84
1.71
3.08
3.78
3.73
3.82
3.31
3.88
3.30
3.76
3.89
4.09
4.42
3.89
4.46
4.36
3.35
4.15
4.45
3.98
4.34
4.04
5.17
1.23±0.19†
2.04±0.39†
3.96±0.48‡
#
3.08
1.99
1.07
2.56
2.05
0.90
2.40
1.55
2.49
1.85
1.34
1.76
0.73
1.23
2.60
1.43
1.81
0.99
0.91
1.11
1.02
1.66±0.68‡
†
Data are expressed as numbers or mean±S.D. * p>0.05, compared with each other within pairs. p>0.05, compared with each other within pairs. p<0.01, compared with
each other within pairs. ‡ p<0.01, compared with each other within pairs.
used the OAA/S scale as clinical sign and observed that the
lag time of BIS was 117.4 s during the onset of propofol.25)
According to the above results, the time delay between consciousness and EEG-derived parameters is dozens of seconds,
however, the peak effect of propofol bolus injection is obtained after hundreds of seconds, a considerable deviation of
Ke0 is observed. A computer simulation displayed that 15 s
time delay resulted in a −13.2% error of Ke0. Because the time
delay is inconstant, artificially correcting the unpredictable
delays adds subjective errors. Second, the Ce peak curve was
shaped like a flat deck roof. Figure 1 shows a typical subject’s
Ce trend, the Tpeak appeared 184 s after drug infusion, but
the Ce was in the 95 to 100% of the peak between 135 s and
249 s, determining the 5% change over the 114 s duration by
using the EEG-derived parameters was difficult. A computer
simulation showed that the Ke0 values 0.81 and 0.25 fit when
the peak effect appeared 135 s and 249 s after drug infusion,
respectively; thus, the ambiguity of the peak resulted in the
deviation of Ke0 from +82 to −46%. Third, considering the
unavoidable disturbance of EEG-derived parameters, the
bottom of the BIS curve reflected the effect peak is difficult
to determine. The full or no phenomena in AAI illustrates the
AAI trend graph as a flat basin, thus, the real bottom based
on the AAI minimum is difficult to confirm. Zhang et al. reported that AAI or BIS values could not provide evident minimum recordings in some patients because of disturbances.21)
Finally, the Tpeak approach can only fit one dataset because
of the three reasons discussed above. If the unique data are
inaccurate, the values of Ke0 are unreliable. The calculated Ke0
matches the effect indicators from baseline to the maximum
effect in parametric and non-parametric approaches. However,
the weights of data at the time of LOC and ROC are dis-
persed, Ke0 cannot optimally predict the Ce at LOC and ROC,
which is of great concern in clinical works.
Most published studies do not provide validation of Ke0.
This study proposes an approach for Ke0 validation which involves comparing CeLOC and CeROC. Currently, the most widely
used Ke0 values are the Diprifusor TCI Pump built-in value
of 0.26 min−1 and the Orchestra Workstation built-in value of
1.21 min−1. We verified these two Ke0 values using the method
we have described here.
In view of the shortcomings of previous studies, this study
proposed a two-point fitting method based on clinical signs.
According to the principle of OTCI, a suitable Ke0 should
satisfy the condition CeLOC=CeROC. Thus, the bisection method
iteration can fit the best Ke0. This method is a variation of the
non-parametric approach.
The proposed approach has 4 advantages. First, real-time
clinical signs are used, which are based on OAA/S, and the
error due to the 3-s interval for verbal stimulation is minor.
A computer simulation showed that the worst situation was
a 5.4% error when 3-s earlier LOC and 3-s delayed ROC
happened simultaneously. This error was less than that obtained from acquisition calculation delay of the Tpeak method.
Second, drug effects at LOC and ROC rapidly fluctuate
relative to those at Tpeak, as shown in Fig. 1. In a typical
subject, the time to LOC was 61 s, and the ±5% change near
LOC was just 6 s. The time to ROC recorded was 458 s, and
the ±5% change near ROC was 35 s. Accurately identifying the time to LOC and to ROC is easier than the time to
Tpeak. Third, non-parametric or parametric approaches fit
data collected from baseline to the maximum effect, the
weights of data are dispersed. Our new approach only fits
data collected from LOC and ROC, hence, the data at time of
1426
LOC and ROC, which is more concerned in clinical, occupied
all weights in fitting. The fitted result can predict CeLOC and
CeROC more accurately, as revealed from this study, so the capability of OTCI-locked MECLOC was improved. Fourth, the
target of routine anaesthesia is slightly higher than MECLOC,
because the Ke0 proposed in this study is the best value for
predicting concentrations near MECLOC. Therefore, this new
Ke0 is most suitable for routine anaesthesia.
The MECLOC locked capability in OTCI depends on two
aspects: PK and PD. Similar to three previous approaches for
estimating Ke0, our new approach is based on a particular PK
model because the Cp used for fitting is not the real value but
that predicted by the PK model. The fitted Ke0 changes follow
the PK model. Thus, the Ke0 cannot cross link with other PK
models outside its basic model.
The ideal control target of most drugs is to maintain the
effect at slightly more than the onset level to reduce its side
effects. The onset and offset concentrations of most drugs
are equal in theory. If there are monitoring signs reflected
the onset and offset, the approach proposed in this study can
fit the optimal Ke0. Thus, the proposed fitting method can be
used not only for anesthetics but also for other drugs.
The classic approach to measure predictive performance is
the root mean square error (RMSE).27) Perhaps due to errors
derived from the PK model, the CeROC of the groups P1 to P4
are not identical. Because the difference between CeLOC and
CeROC, which belong to absolute error, can be affected by the
size of CeROC, the PE, which divided by the predicted value,
belong to relative error, is more reasonable. In addition, consistent with the results of Varvel et al., the PE under Ke0=0.53
and dose and age adjusted population Ke0 did not pass the normality distribution test.18) Therefore, instead of using RMSE,
we followed the Shafer’s approach, using MDPE as bias index
and MDAPE as accuracy index of CeLOC to predict CeROC.
The accuracy of CeLOC to predict CeROC in the present study
demonstrates that all three fixed Ke0 do not achieve CeROC
to be predicted accurately by CeLOC. Performance of OTCI
using currently available commercial TCI equipment is not
satisfactory, and only the Ke0 values adjusted by dose and age
satisfied the accuracy requirements of clinical applications.
However, with the adjusted Ke0, the regression expression of
the validation group was CeROC=0.89×CeLOC; the calculated
CeROC and CeLOC still differed. The populations included for
the fitting or validation of Ke0 were different, and this was the
reason for the difference in the calculated CeROC and CeLOC.
Furthermore, common inaccessible factors, such as cardiac
output and permeability of the blood–brain barrier, which
have a significant impact on Ke0 theoretically, were not considered in this study. Moreover, the fitting and validation of
Ke0 was based on a fixed PK model derived from a population
included in another study, which did not accurately represent
the population in the present study. These are the other reasons for the difference between CeROC and CeLOC. Because the
PK and PD parameters between individuals are substantially
different, the present study shows a huge difficulty to improve
the performance of TCI technique.
Acknowledgments This work was supported by the Development Plan of Science and Technology of Shandong Province, China (No. 2009GG10002028 and 2007GG3WZ 02057
to Q. W.).
Vol. 36, No. 9
APPENDIX
Bisection Method Iteration for Fitting Ke0: in Detail
Marsh’s PK parameters (shown in Table 1) are set up in software program for this study. The propofol Cp-time trend graph
(solid curve shown in Fig. 1) is then calculated under the
said PK parameters. The individual LOC time and ROC time
clinically collected are inputted to fit the individual Ke0 to
meet individual CeLOC=CeROC conditions. This fitting method
is classic bisection method iteration. In the bisection method
iteration, the search space of the variable is bisected gradually
and the variable approach to the real value gradually to obtain
an approximation with adequate precision. First, the minimum
Ke0 minimum (Ke0min) is set at 0.052, which is one fifth of the
Diprifusor TCI Pump built-in Ke0 of 0.26. The maximum Ke0
(Ke0max) is set at 6.05, which is a quintuple of the Orchestra
Workstation built-in Ke0 of 1.21. The initial Ke0 search space is
defined between Ke0min and Ke0max. The Ke0 is hypothesized as
Ke0(1)=(Ke0min+Ke0max)÷2. The CeLOC and CeROC are calculated
using the PK–PD equation.16) The value of CeLOC–CeROC is
then obtained. If this value is positive, the real value should be
determined less than the current hypothetic Ke0. Ke0(1) should
be the new Ke0max. In contrast, if the value obtained is negative, the real value should be certified larger than the current
hypothetic Ke0. Ke0(1) should then be the new Ke0min. The
Ke0 space is reduced according to the new Ke0max or Ke0min.
Then, the CeLOC and CeROC under Ke0 (2)=(Ke0min+Ke0max)÷2
is calculated, and so on. The terminal condition of the iterative is |Ke0(n)−Ke0(n−1)|<0.0005. The terminal result is
Ke0=(Ke0(n−1)+Ke0(n))÷2. The computer program was written
according to the above process using C# language. The program displays the Ce trend graph using dash curve after every
iteration, demonstrating the approach of CeLOC and CeROC stepby-step in animated form.
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