ORIGINAL RESEARCH ARTICLE
Clin. Pharmacokinet. 20 (4): 319-330. 1991 0312-5963/ 91 / 0004-0319/$06.00/0 © Adis International Limited. All rights reserved. CPK1436A
A Computer-Based System for Controlling Plasma Opioid Concentration According to Patient Need for Analgesia Harlan F. Hill, Robert C. Jacobson, Barbara A. Coda and Adam M. Mackie Division of Clinical Research, Fred Hutchinson Cancer Research Center, Seattle, Washington, and Department of Anesthesiology, University of Washington, RN-IO, Seattle, Washington, USA
Summary
Microprocessor-controlled infusion pumps, which allow a patient to self-administer bolus doses of an analgesic to relieve pain, are becoming commonplace. While these patient-controlled analgesia (PCA) systems overcome the large interpatient variations in pharmacokinetics, they do not provide steady relief from pain since they rely on delivering a drug in small, incremental doses. To overcome this problem, the authors developed an algorithm and computer-pump system that allows patients to control their own plasma concentration of analgesic. This approach uses individually predetermined pharmacokinetic parameters to provide steady plasma opioid concentrations that can be increased or decreased by the patient in line with the need for more pain relief or fewer side effects. The control software uses a novel, recursive algorithm to compute the pump rates necessary to maintain constant plasma drug (e.g. morphine) concentrations at desired values and to reach a new steady concentration in response to patient requests. This report describes the mathematical approach to the problem of control of plasma opioid concentration, the application of this new drug delivery system to management of persistent pain in cancer patients undergoing bone marrow transplantation, and the magnitude of pharmacokinetic variability with morphine in this patient population. Results are presented from individual patients using this adjustable drug delivery system continuously for up to 2 weeks to control pain from oral mucositis.
Patient-controlled analgesia (PCA) provides several clear advantages over more traditional means of administering opioids for pain management. Most often used postoperatively, it affords pain relief equal to intramuscular administration, with a lower total drug requirement (Bennett et al. 1982; Hecker & Albert 1988; Robinson et al. 1980). Moreover, patient satisfaction is high (White 1985), and patients may return to normal functional status more quickly (Bennett 1985). When used for longer periods, such as in cancer and burn patients, patient-controlled analgesia maintains these advantages and may decrease the likelihood of tolerance and physical dependence developing, com-
pared with conventional means of opioid administration (Citron et al. 1986; Hill et al. 1986a, 1990a; Sandidge et al. 1987). Much of the advantage of patient-controlled analgesia derives from placing the patient in the central role of deciding when he or she wants additional analgesic medication, and even how much additional drug will be delivered. This minimises the impact of both pharmacokinetic and pharmacodynamic variability in opioid disposition on the analgesic effects in different patients (Hull I 985a). However, current PCA devices still rely on the administration of bolus doses and therefore plasma concentration, central nervous system concentra-
Clin. Pharmacokinet. 20 (4) 1991
320
tion and analgesic effect vary considerably during the interval between doses. Many reports have documented the relationship between plasma opioid concentration and magnitude of pain reduction in cancer patients with hydromorphone and methadone (Inturrisi et al. 1988, 1990), in experimental pain in humans with alfentanil (Hill et al. 1986b) and in postoperative pain with a variety of opioids (Austin et al. 1980; Berkowitz et al. 1975; Nimmo & Todd 1985). In an individual patient there is a plasma opioid concentration below which the analgesic drug produces no pain relief, and above which further increases in concentration produce increasing analgesia. This threshold concentration, the minimum effective analgesic concentration (MEAC), averages about 16 ~g/L for morphine (Dahlstrom et al. 1982; Gourlay et al. 1986), 0.6 ~g/L for fentanyl (Gourlay et al. 1988), 460 ~g/L for pethidine (meperidine) [Austin et al. 1980; Tamsen et al. 1982], and 10 ~g/L for alfentanil (Lehmann 1985). The MEAC for a selected opioid is remarkably consistent for individuals but varies substantially between patients. Theoretically, more consistent analgesic effects could be obtained if the plasma concentration remained constant between patient demands and if the patient could regulate increases or decreases in steady-state opioid concentration instead of merely the frequency of bolus doses (Hill et al. I 990b; Hull 1985b). To allow patients to regulate their own pain control by manipulating the steady-state concentration, we devised a new microprocessor-controlled drug infusion system which uses each patient's own pharmacokinetic profile to reach rapidly and then to maintain a stable initial plasma opioid concentration (e.g. 20 ~g/L for morphine). Thereafter, the patient can operate a hand-held control button to increase or decrease his/her plasma opioid concentration in step changes of preset magnitude in line with increasing need for pain relief or the desire to lessen side effects and perhaps tolerate less pain relief. Several recent reports have shown that morphine-6-glucuronide (M6G) may account for a significant portion of the analgesic effect of morphine
in postsurgical and cancer patients (Osborne et al. 1990; Peterson et al. 1990). However, the relative contributions of morphine and M6G to pain reduction during prolonged morphine infusions is not clear. Consequently, we used the direct approach of developing a means of controlling plasma concentrations of the parent drug only for initial studies of the reliability and effectiveness of this method of analgesic self-administration. Future studies will address the issue of the importance of M6G concentrations in the pharmacokinetic modelling and the beneficial applications of this approach to patient-controlled analgesic administration. Bone marrow transplant patients experience oral mucositis as a result of high dose chemoradiotherapy (Chapko et al. 1989), and the associated pain is severe enough to require parenteral morphine for up to 3 weeks after transplantation. This report describes the hardware and mathematical basis for this new method of patient-controlled analgesia and demonstrates the feasibility of its use in marrow transplant patients controlling their own morphine intake for management of oral mucositis pain. The magnitude of the pharmacokinetic variability with morphine in this patient population is also documented. Although we describe a special case using morphine in bone marrow transplant patients in this report, our pharmacokinetically based patient-controlled infusion system (PKPCA) is designed for the general situation using any opioid which can be modelled for control of painful conditions.
Methods Instrumentation The drug delivery system is composed of a Toshiba 1100+ microcomputer, an Abbott Model 4 variable rate infusion pump and an RS232/RS485 coupler. In addition, the system has a patient-activated control button, a NiCad battery and a speaker for audio feedback of appropriate patientinitiated commands. Components are assembled on a stainless steel cart fitted with 2 IV poles and a lockable Plexiglass cover. The entire assembly is completely mobile and space-conserving.
Kinetically Based Patient-Controlled Analgesia
Software
The operating program for the microcomputer is built around the algorithm described in detail below, and was designed to update the pump with a new drug delivery rate once every 10 seconds when the calculated rate is >50 ml/h and once every 60 seconds at lower pump rates. In addition to frequent calculations of drug delivery requirements and command of the pump, the software includes provisions for presetting a lock-out interval (i.e. the minimum time between allowable plasma change requests), variable allowable increments/decrements in plasma opioid concentration, specification of drug supply concentration and maximum number of increases and decreases allowed per 24h. At the start of the morphine treatment period, we set the initial target concentration at 20 Ilg/L, with lockout at 60 minutes, patient-activated plasma concentration changes at 20% of the prevailing steady concentration and a maximum of 12 increases allowed per day for all patients. For the few patients who were especially sensitive to morphine effects, we reduced the concentration increments to 10% steps as therapy progressed. The program provides for selection of patient control or a steady infusion rate which can be used at night if the patient chooses to do so. Up to 7 days of data on patient demands and pump rates are automatically stored on computer disk for later review. The program has a graphics subroutine for displaying a 24h history of pump operation, including pump rates, estimated plasma concentrations and control events. Finally, we designed the program to allow the patient to be unhooked from the device for periods of up to several hours for any procedure, during which the algorithm continues to model the patient's plasma drug concentration and can automatically restore the previous targeted value by calculating the mass of opioid required to do so and commanding delivery of that dose (bolus plus exponential infusion) when the patient is reconnected to the system.
321
Determination of Individual Pharmacokinetics In our ongoing study using this drug delivery method, we use a patient's unique pharmacokinetic parameters (triexponential coefficients - see below) for an opioid such as morphine, determined from a bolus dose of the drug, as the basis for individually tailoring a subsequent intravenous morphine infusion for oral mucositis pain control. Several days prior to onset of oral mucositis, we administer an intravenous 'tailoring' bolus (75 Ilg/ kg) of morphine sulfate to each patient and draw a series of 15 blood samples over the next 6 to 8h. Plasma morphine concentrations are measured by high performance liquid chromatography (HPLC) [Todd et al. 1982). For each patient, we fit the plasma morphine concentration-time data to biexponential and triexponential models (equation 1 below, Nc = 2 or 3) by nonlinear least squares (RSTRIP, Fox & Lamson; PCNONLIN, Metzler & Weiner 1989), select the model with the smaller sum of squared residuals (Akaike 1969) and use the coefficients and exponents of this individualised function and the bolus dose mass in the control algorithm. Control of Plasma Concentration During Tailored Intravenous Infusions The basic goal of this approach is to operate a continuous intravenous infusion pump at variable rates initially to reach a predetermined plasma opioid concentration rapidly (e.g. within seconds of the initiation of therapy) and thereafter to hold that concentration steady until the patient requests a new one, either higher or lower. On the basis of the MEAC for morphine in postsurgical patients (about 16 Ilg/L; Dahlstrom et al. 1982; Gourlay et al. 1986), we selected an initial target morphine concentration of 20 Ilg/L for the patients in our study to achieve an analgesic effect which was just noticeable at the start of therapy. Rapid attainment of a preselected plasma concentration is straightforward provided that the hypothetical 'volume' to be filled is known. The in-
322
C/in. Pharmacokinet. 20 (4) 1991
dividually derived curves from the tailoring bolus dose could be used to estimate this central compartment volume (V c) from the following relationship: Vc = 0 /
Nc
L: q i=!
where 0 is the mass of the tailoring bolus drug, Nc is the number of compartments assumed in the model and Ci are the pharmacokinetic coefficients (zero-time intercepts, J.LgJL) derived from the tailoring bolus data. Then an intravenous loading dose (CTVc, where CT is the target concentration) will rapidly establish the preselected plasma opioid concentration. Maintaining the target plasma concentration thereafter requires that an exponential loss process (blood-tissue diffusion) and a log linear loss process (elimination) be simultaneously balanced by a specific variable-rate infusion algorithm (KrugerTheimer 1968; Martin et al. 1987; Vaughan & Tucker 1976). These algorithms are suitable to maintain a steady plasma concentration following a step change from a steady-state condition but not for the general case of arbitrary control of plasma concentration. The algorithm described below is more appropriate for the latter case. Mathematical Algorithm In order to obtain equations for the control and maintenance of the plasma opioid concentration, we model the subject's response to drug as a linear system. If a subject is given an intravenous bolus injection of an opioid, the drug will clear from plasma by diffusing into one or more 'compartments' and by elimination (hepatic, renal, etc.). By measuring several plasma concentrations as a function of time following bolus dosing, we can model this diffusion/elimination process with a series of exponential functions (Gibaldi & Perrier 1982). Nc
h(t) =
L:
Cje->'it
(Eq. I)
i=!
where h(t) is the predicted plasma concentration
after the bolus dose. The constants, Ci and Ai (i = I to NC>, can be obtained by a nonlinear least squares fit of plasma concentrations after the drug injection and should be normalised to unit dose. If the diffusion/elimination function derived from the tailoring bolus dose model holds during the later infusion of the drug, the plasma concentration as a function of time [c(t)] can be predicted from the so-called impulse response function [h(t)] and the pump rate [f{t)] from the convolution integral: c(t) = fh(t - t')f{t') dt'
(Eq. 2) o To obtain an expression for the required pump rate f{t), for the attainment of concentration c(t), it is necessary to invert integral equation 2. In principle, inversion can be accomplished by applying the Laplace transform to equation 2, yielding C(s) = H(s)F(s), solving for F(s) and taking the inverse Laplace transformation to obtain f{t). In practice, however, inverse transformations of C(s)/H(s) are obtainable only for simple, predetermined concentration profiles, c(t). Even for the simplest case of a step change, the solution is formidable if Nc is greater than 3 (Kruger-Theimer 1968). In what follows, we cast the above problem in terms of discrete mathematics using difference equations rather than Laplace transforms. Equation 2 becomes manageable, and a simple recursive solution to the inverse problem follows. This recursive method has several advantages over previously employed algorithms based on Laplace transforms (Alvis et al. 1985; Martin et al. 1987; Vaughan & Tucker 1976): (a) the equations are simpler, allowing for any number of 'compartments'; (b) the plasma drug concentration need not be constant (steady-state) at the time of a requested change from one value to another, since the algorithm accommodates to any arbitrary plasma concentration request; (c) the equations are derived assuming stepwise rather than continuously changing pump rates resulting in a more realistic, and hence accurate, model suitable for computer control; (d) the recursive algorithm corrects for inaccuracies due to the limitations of the pump by incorporating the
323
Kinetically Based Patient-Controlled Analgesia
actual pump rate attained, rather than ideal computed rates, in calculating the next commanded rate. If we assume that the pump rate changes in a series of steps, the rate function can be expressed as follows:
where the function u(t) is the unit function: u(t) = { O,t l ,t
<0 ~
Results
0
Using h(t) in equation I , the convolution integral 2 becomes:
where we have defined Cn ~ c(t n), tn O. Evaluating the integral, we obtain:
= t and to =
Nc
E
Cn =
(Eq. 3)
BiUin
i=1 where (Eq. 4)
Uin = e- xitn }:I fk(eXitk+] _ eXitk) k=O
(Eq. 5)
The term Uin represents the state of the ith compartment at time tn. It can be easily shown that Uin satisfies the recursion relation: Uin = e- Xito tnUi(n_l)
+ fn _ 1(1 - e-Xitotn)
(Eq. 6)
where ~tn = tn - tn-I and UiO = O. Inserting Uin in equation 3, reindexing and solving for fn, we have: Nc
Cn+1 -
E
Bie-Xitotn+IUin
i=1 (Eq. 7) Nc
E Bi(l
i=1
Thus, the system will arrive at plasma concentration Cn+1 at the future time tn+l if the pump is commanded to deliver a constant rate, fn, given by equation 7. The present concentration Cn can be calculated from the immediate past compartment states Ui(n-l) and the past pump rate fn-l via equations 3, 4 and 6. In the case of requests for plasma concentration decreases, fn is initially set to zero and then increases as Cn approaches the new target concentration.
- e-Xitotn+l)
Individual Tailoring of Computer-Assisted Patient-Controlled Opioid Infusions for Analgesia In table I, we present pharmacokinetic data from the individual tailoring morphine bolus doses for 15 bone marrow transplant patients who later used the system to suppress oral mucositis pain. In all cases, triexponential models provided the better fit of individual plasma morphine concentration-time data. It should be noted that there was a 3- to 4fold range of values for each pharmacokinetic constant in this group of patients. During the pharmacokinetically based, patientcontrolled opioid infusions, we measured plasma morphine concentration daily. Figure I shows the measured and predicted plasma morphine concentrations for up to 14 days of operation of the system by individual patients having typical or extreme pharmacokinetic profiles for morphine (table II). In each case, the patient regulated the morphine infusion by operating a control button that signalled desired increases or decreases in drug delivery throughout each day. The average number of changes requested was 2.8 per patient per day for the initial 8 days of treatment, with a frequency range of 0 to 17. Note the overall correlation between predicted and measured opioid concentration over the prolonged infusion periods of 6 to 14 days for patients with quite different pharmacokinetic profiles (fig. I) and the strong linear correlation between predicted and measured concentrations in this group of patients, aggregated across study periods (fig. 2).
324
Clin. Pharmacokinet. 20 (4) 1991
_ 100
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80
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40
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0
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a
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4
6
10
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12
0
Time (days)
b
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Time (days)
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80
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Time (days)
Fig. 1. Comparison of predicted (0) and measured (e) plasma morphine concentrations: data for individual patients with (a) lowest central compartment volume (patient No. I), (b) highest central compartment volume (No.7), (c) lowest systemic clearance (No.4), (d) highest clearance (No.6) and (e) values close to the group means (No. 15).
Kinetically Based Patient-Controlled Analgesia
325
Table I. Coefficients of nonlinear least squares fits of bolus dose (75 Itg/kg) concentration-time data in 15 patients receiving tailored morphine infusions. Individual subject data were fitted to equation 1, Nc = 3 (see text)
Patient no.
Weight (kg)
C1 (ltg/L)
C2 (ltg/L)
C3 (ltg/L)
A1 (m-1)
A2 (min- 1)
A3 (min- 1)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
52.0 118.9 75.9 75.5 127.6 83.6 73.0 85.9 55.1 53.1 71.0 87.0 79.4 73.0 78.6
397.9 573.5 245.2 576.3 799.7 326.9 229.7 319.7 348.3 299.7 287.5 366.8 416.9 211.4 276.8
46.47 59.09 41.03 55.62 69.08 71.85 31.80 35.26 38.30 28.50 30.30 84.58 93.96 27.88 42.55
12.78 19.37 11.97 22.87 23.81 9.15 9.55 11.34 8.03 9.12 10.01 19.19 21.49 13.90 12.80
1.0000 0.9362 0.8220 1.5010 1.1398 1.3800 0.5253 0.7448 0.8484 0.7901 0.6177 0.9399 1.4815 0.4717 0.7980
0.1000 0.1021 0.1523 0.1159 0.0956 0.2168 0.0653 0.0955 0.0911 0.0620 0.0517 0.1176 0.1873 0.0696 0.0832
0.0087 0.0073 0.0076 0.0078 0.0062 0.0088 0.0059 0.0037 0.0084 0.0104 0.0065 0.0072 0.0100 0.0081 0.0071
Mean ± SO Range
± 20.35
378.4 ± 154.1 3.8
50.42 ± 20.42 3.4
14.36 ± 5.28 2.9
0.9330 ± 0.3100 3.2
0.1071 ± 0.0448 4.2
0.0076 ± 0.0016 2.9
73.0
Abbreviations: C1, C2, C3 = zero time intercepts; A1, A2,
A3 = slopes.
Inherent Limitations in Maintenance of Constant Concentration Equation 7 is designed to maintain target plasma opioid concentrations at the update times (t n and tn +,). Since the pump rate is constant between updates, we expect some deviation from target concentrations during these intervals. Furthermore, maintaining perfectly constant concentration was impossible, even at the update times, since the infusion pump that we used does not allow for fractional pump rates. This limitation results in an additional error in the targeted concentration. If the actual (integral) pump rate is used for fn-l in equation 6, the calculated concentration Cn (equation 3) will differ from the target concentration. The algorithm will attempt to make a correction (equation 7) on the next update, and the concentration will oscillate about the correct value (fig. 3). We studied the detailed pump rates and concentrations from the stored computer record of a typical patient (No.1, see table I). The error at
each update, due to the limitation of integral pump rates, was computed as the difference between concentrations at the update times and the targeted concentrations, and expressed as a percentage of the target concentration. This error ranged between 1.4 and -1.4% (table III). Between these updates, we computed plasma concentration at 9 additional equally spaced time points from equations 3 and 6 and compared these computed concentrations with those interpolated linearly between updates. We define the interupdate error, due to constant pump rate between updates, as the difference between computed and interpolated concentrations. The interupdate error ranged between a minimum of -1.2% and a maximum of 0.3%.
Discussion We have used the pharmacokinetically based opioid delivery system in studies comparing morphine with other opioids and this method of morphine self-administration to conventional patient-
326
Clin. Pharmacokinet. 20 (4) 1991
Table II. Standard pharmacokinetic measures for the 5 patients represented in fig. 1. Patients with the lowest (No. 1) and highest (No. 7) values for initial dilution (central compartment volume) and the lowest (No.4) and highest (No.6) total body clearance for morphine are included here. The pharmacokinetic profile of patient No. 15 was similar to the group parameters
Patient no.
t'l2.\1
t'l2.\2
(min)
t'l2.\3 (min)
VC
(min)
(L)
CL (L/min)
(L)
4 6 7 15
0.69 0.46 0.50 1.32 0.87
6.9 6.0 3.2 10.6 8.3
80.0 89.0 78.6 116.7 97.3
7.0 7.2 12.6 16.6 14.2
1.37 1.22 3.20 1.77 1.78
103 123 238 195 174
Mean a ± SO
0.83 ± 0.28
7.5 ± 2.7
97.2 ± 28.4
11 .9 ± 3.4
1.78 ± 0.45
168 ± 51
a
Vss
Mean pharmacokinetic parameters for the group of 15 patients.
"2'
Abbreviations: t'l2.\1 ' 3) = half-lives associated with the first (second, third) exponents of a polyexponential equation; Vc = central compartment volume; CL = total body clearance; Vss = volume of distribution at steady-state.
controlled analgesia (Hill et al. 1990c), and found it to be a safe and effective alternative. This approach provides reliable control of plasma morphine concentration and allows the patient to alter the drug concentration in line with the need for increased or decreased pain control and control of side effects. Similar methods for controlling and adjusting plasma opioid concentration intraoperatively, using population pharmacokinetic values, have been reported by Alvis et al. (1985) and Ausems et al.
::r 100
~ <.i
c
80
• •
8 Q)
c
60
E
e-
0
40
~:>
20
E If)
• r = 0.935
as Q)
::!;
00
10
20
30
40
50
60
70
80
90
100
Predicted morphine conc. (I'g/L)
Fig. 2. Relationship between predicted and measured plasma morphine concentrations over the duration of study for the patients shown in fig. I: - = the linear correlation between measured and predicted values; - - - = the line of identity.
(1985). Using alfentanil, the latter reported absolute prediction errors of about 30% of target plasma concentrations during maintenance of anaesthesia. Absolute prediction errors averaged about 15% across the treatment period for the 5 patients in this report using the PKPCA system (fig. I). This relatively high precision is probably the result of using individually determined pharmacokinetics instead of population-based parameters for computing the required infusion rates. There are large interpatient variations in central compartment volumes, volumes of distribution and intercom partmental drug transfer rate and elimination rate constants for morphine and other opioids (Bovill et al. 1982; Reilly et al. 1984; Stanski et al. 1978). We found similar variability in morphine pharmacokinetics with the tailoring bolus doses employed in the cancer patients in this study. The potential impact of this substantial intersubject variability on the rapid and accurate control of plasma opioid concentration can be minimised or nullified by individually tailoring drug delivery to the pharmacokinetics of the selected drug in each patient (Hill 1988; Hill & Chapman 1989; Hill et al. 199Od). In the present study, we found similar, strong correlations between predicted and measured morphine concentrations for patients with extreme pharmacokinetic values (eg. initial dilution volume and
Kinetically Based Patient-Controlled Analgesia
total clearance) and those with pharmacokinetic profiles more typical of the group parameters. This supports our contention that individual pharmacokinetic tailoring of the prolonged morphine infusions effectively minimised the influence of pharmacokinetic variability on the control of plasma morphine concentration during the patientcontrolled infusions. In this research, we chose to base opioid delivery rates on a pharmacokinetic model of morphine distribution and elimination, but alternative approaches do exist. Harrison (1990) has recently described a similar approach to controlling drug input based on effect modelling (e.g. neuromuscular blockade by vecuronium). We believe that, by allowing the patient to control drug input in order to achieve the desired level of pain reduction (variable across patients), the desired goal is reached quite directly. In our studies, bone marrow transplant patients use this system to maintain control of their oral mucositis pain. We find that they regulate their plasma morphine concentrations to between 20 and 80 ~g/L during self-administration, a range that corresponds closely to the MEAC values for morphine in postsurgical patients (Dahlstrom et al. 1982; Gourlay et al. 1986; Lehmann 1990) and to morphine concentrations associated with moderate postsurgical and bum pain relief (Berkowitz et al. 1975; Inturrisi & Colburn 1986). Table III. Update error from subject No.1 (see table I) during a 12h period due to integral pump rates (n = 591) and interupdate error, due to constant pump rates over the finite update interval (n = 6290). The interupdate errors were calculated as differences between concentrations, recomputed and linearly interpolated at 9 additional times between update intervals. Cases in which pump rates were zero or exceeded 20 mlth were considered transitions and were not used in these error statistics All errors are expressed as a percentage of the target concentration Error statistics
Minimum Maximum Median Median of absolute value
Update
Interupdate
(%)
(%)
-1.45 1.4 -0.23 0.67
-1.15 0.28 -0.00042 0.034
327
24
2:Ol
23
..:> u
8 22 Ol
2
"0 ttl
21
E
a:
20 108
112 Time (min.)
116
120
124
128
Fig. 3. Computed plasma morphine concentrations targeted at updates (0) during transition between target morphine concentrations at 20 and 24 I'gfL. Concentrations were recomputed - between these updates, based on constant pump rates. The plot shows small deviations from linearity between updates and larger deviations from target concentrations at the updates due to integral pump rates. Data are selected from a 12h period from patient No. I.
In effect, because the patient directly regulates his/ her own morphine infusion rate over time by activating the computer-pump system to receive more or less morphine according to current need, this opioid delivery system is functionally tailored to pain relief. Using individually determined pharmacokinetic information, the algorithm employed improves further on this by producing rapid, accurate transitions between plasma concentrations (and varying need for pain relief) and maintaining of steady concentrations at desired levels of pain control. Even though our patients use this PKPCA system to self-administer morphine continuously for 2 weeks or longer, they do not develop tolerance to the analgesic effect (Hill et al. I 990c). Plasma morphine concentrations (and morphine intake) reach a peak at about the fourth study day and then remain relatively constant for the remainder of the painful course of oral mucositis (1 to 3 weeks). At the end of morphine therapy, withdrawal symptoms are rarely seen. The apparent absence of tolerance development is similar to our findings with marrow transplant patients using morphine via standard, bolus-dose patient-con-
Clin. Pharmacokinet. 20 (4) 1991
328
trolled analgesia (Hill et al. 1990a) and seems to support the notion that prolonged or repetitious pain inhibits the development of opioid tolerance (Colpaert 1978; Colpaert et al. 1980). On the other hand, this apparent lack of morphine tolerance could be the result of progressive accumulation of M6G (Osborne et al. 1990; Pasternak et al. 1987). During the several days of continuous morphine self-administration, M6G in plasma and at central ~-opioid receptors possibly reached sufficient concentrations to account for some, perhaps most, of the pain relief obtained by patients (Hoskin et al. 1989). The resultant, combined analgesic effects of morphine and M6G might obscure the development of tolerance under these circumstances. A variety of parenteral opioid administration modalities are used for treating postoperative pain, burn pain and pain related to cancer, including intravenous and subcutaneous continuous infusion and conventional, bolus-dose patient-controlled analgesia. While appropriately designed continuous infusions are effective and safe for short and long term use in cancer pain patients (Bauman et al. 1986; Citron et al. 1984; Coyle et al. 1986; Portenoy et al. 1986), dose titration in response to varying analgesic needs can be difficult with this method due to the gradual approach to average steady-state plasma opioid concentrations. Both intravenous and subcutaneous patient-controlled analgesia are also effective and safe for short and long term (up to 225 days) use in cancer pain management (Citron et al. 1986; Kerr et al. 1988). While the conventional system overcomes some of the disadvantages of continuous infusion by allowing rapid dose adjustment and by permitting the patient to balance acceptable analgesia against unwanted side-effects, it still has some limitations. Patients using patient-controlled analgesia characteristically settle for less than total pain relief (Vickers 1985). Furthermore, the use of relatively small doses and short lockout intervals could result in inadequate pain relief while the patient is asleep, although this problem can be offset by combining a 'background' continuous infusion of morphine or similar opioids with bolus doses under patient control (Kerr et al. 1988).
The PKPCA system described in this paper is a further refinement of the concept behind such a combination. We feel that it offers advantages, particularly for the patient with prolonged pain whose analgesic needs vary throughout the day. A pain pattern including exacerbations at certain times during the day and night is typical of bone marrow transplant patients with severe mucositis, but is also common in burn patients who must undergo painful dressing changes once or more daily, and in many cancer patients.
Acknowledgements This research was supported by grants from the National Institute on Drug Abuse (DA 05513) and the National Cancer Institute (CA 38552). The authors wish to thank the marrow transplant nurses at the Fred Hutchinson Cancer Research Center and Swedish Hospital Medical Center for their assistance and support. Abbott Laboratories kindly supplied the Model 4 infusion pumps used in this study.
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Correspondence and reprints: Harlan F. Hill. Division of Clinical Research, AS-122, Fred Hutchinson Cancer Research Center, 1124 Columbia Street, Seattle, WA 98104, USA.
