A Time-Shared Computer Program for Adaptive Control of Lidocaine

A TIME-SHARED COMPUTER PROGRAM FOR ADAPTIVE CONTROL OF LIDOCAINE THERAPY USING AN OPTIMAL STRATEGY FOR OBTAINING SERUM CONCENTRATIONS

R.W. Jelliffe, D.Z. D'Argenio, J. Rodman, and A. Schumitzky

LABORATORY OF APPLIED PHARMACOKINETICS SCHOOLS OF MEDICINE AND ENGINEERING UNIVERSITY OF SOUTHERN CALIFORNIA, LOS ANGELES, CALIFORNIA ABSTRACT A time-shared computer program previously developed by this laboratory has now been improved to permit adaptive (open-loop feedback) control of lidocaine therapy by fitting a 2-compartment linear model to serum concentrations found on past therapy. It also now includes a module to compute the optimal times to obtain lidocaine serum concentrations to monitor such therapy. The interactive, conversational program accepts data of past dosage, serum data, and cardiac function. An individual model can be fitted, even if cardiac function should be changing. Past serum concentrations are then computed using the fitted model. The desired serum concentration is then entered, and a dosage regimen is computed to achieve it, adjusted to the desired infusion format. Lastly, it computes the optimal times to obtain serum specimens for monitoring the regimen given. The program is available over an international time-sharing facility.

A clinical consequence of such a 2-compartment model, necessary to adequately describe the kinetic behavior of lidocaine, is that in order to achieve and maintain a desired serum concentration, the initial rapid loading infusion which is given to reach the desired concentration must be followed by a tapering infusion protocol thereafter, decreasing in proportion to the buildup of drug in the peripheral compartment. It is simply not possible to achieve and maintain stable serum lidocaine concentrations merely by giving a loading infusion followed by a fixed rate maintenance infusion. This fact may well be responsible for much of the current confusion in lidocaine therapy concerning whether or not one should give "serial boli". The present program utilizes the a priori model and a tapering infusion protocol, and brings the entire system into equilibrium at the earliest possible time consistent with the clinical constraint of achieving but not exceeding the chosen serum concentration.

INTRODUCTION

CLINICAL RESULTS - SERUM LEVELS

A time-shared computer computer program for lidocain therapy previously developed by this laboratory (1) has now been improved to permit adaptive control of lidocaine dosage by fitting a 2-compartment linear pharmacokinetic model to data of serum concentrations found on past therapy. It also includes a module to compute optimal times to obtain lidocaine concentrations for subsequent monitoring.

THE PROGRAM The program employs an a priori 2-compartment linear model based on data from the literature and on previous experience in this laboratory. The rate constants from central to peripheral compartment and return are held fixed. The volume of distribution of the central compartment is linearly proportional to body weight. The rate constant for elimination from the central compartment is related either to measured cardiac index or to clinical estimates of it made as a percent of normal for age. In the latter case, the program first employs the data of Brandfonbrener, et al., (2) to find the normal cardiac index for the patient's age, multiplies it by the clinically estimated percent of normal, and obtains an a priori value for the rate constant for elimination.

0195-4210/80/0000-0975$O0.75

© 1980 IEEE

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Table 1 illustrates the method of estimating cardiac function as a percent of normal for age. Figure 1 illustrates events occurring with a representative patient who received a conventional regimen of serial boli and infusions. At the top of the figure, the initial 75 mg bolus was followed by an infusion of 2.1 mg per minute. Note that neither the predicted serum concentrations (triangles and dashed lines) nor the measured serum concentrations (dots and solid lines) reached the therapeutic range. Because of this, the patient received another 50 mg bolus at 30 minutes, followed by an increase in the infusion rate to 3.0 mg per minute. Both predicted and measured serum concentrations rose slightly, to approximately 2 pg/ml, but it was necessary to give a third bolus of 50 mg at 45 minutes and to increase the infusion rate to 4.4 mg/min before reasonably effective concentrations were achieved. This patient illustrates the common clinical situation in which serial boli are given and the time required to control an arrhythmia often is in the range of 30 to 60 minutes, as shown here. In contrast, Figure 2 shows a representative computer-assisted lidocaine regimen. Here the clinical goal was to achieve and maintain a serum concentration of 4 pg/ml 30 minutes after the

initial 75 mg bolus. Because of this, a regimen was computed in advance and given, consisting of an initial 75 mg bolus, followed by 10 mg/min for 30 minutes, by 6 mg/min for another 30 minutes, by 4 mg/min for one hour, and finally by 3.7 thereafter. This pharmacokinetically oriented tapering infusion protocol achieved the desired goal well, as the measured serum concentrations correspond closely to those predicted for that regimen. Figure 3 illustrates how it is possible to deliver serial tapering infusion protocols of this type to achieve step changes in a patient's serum lidocaine concentrations, permitting rapid evaluation of the patient's clinical response at each step. Use of such tapering infusion protocols has greatly reduced the time required to achieve control of rhythm disturbances, or to discover that the patient actually does not respond to lidocaine. Usually it has required two to three days in the absence of such computer-assisted regimens to come to the conclusion that a patient will not respond to lidocaine. Here, by the use of step changes in serum levels, one can greatly compress this time period into just a few hours. An additional piece of equipment that has been useful in achieving such step changes in serum concentrations has been the programmable infusion pump controller shown in Figure 4 (3). This permits automated delivery of such inftusion protocols without having manually to reset the infusion device. This type of controller has controlled a Harvard Model 2620 infusion device but is adaptable to other devices as well. The accuracy of the predicted serum concentrations found with the a priori pharmacokinetic model is shown in Figure 5. As shown, 192 plasma concentrations in 20 patients were predicted with a standard error of the estimate of + .88 pg/ml, and correlation coefficient of 0.795. Thus if one selects a goal of 3.5 Ag/ml, one is able to be within the therapeutic range of 1.5 to 5.5 Uig/ml well over 95% of the time, using the algorithm in Table 1 to estimate cardiac function as a percent of normal for age. The ability of this program to achieve and maintain effective plasma concentrations early was then evaluated in the coronary care unit of the LAC/USC Medical Center in a random prospective study where 11 patients received a conventional regimen consisting of an initial bolus of 75 mg, followed by 2 mg/min, while 9 computer-assisted patients received regimens to achieve chosen plasma lidocaine concentrations. These clinical goals ranged from 2.5 to 4 pg/ml. As shown in Figure 6, significantly higher and more effective serum lidocaine concentrations were achieved. As shown in the figure, a clear-cut "therapeutic hiatus" was found to be present in the lidocaine concentrations achieved with conventional therapy, as average concentrations over 2 vig/ml were not achieved in the first hour. In contrast, significantly higher and more effective concentrations were achieved during that important first hour with the computer-assisted regimens.

Dr. Earl Kolb (1,4), in the Coronary Care Unit of the Community Hospital of the Monterey Peninsula at Carmel, California. Here a conventional hospital audit was made of the use of these programs from 1974 to July 1976. All patients audited had a recent myocardial infarct and an arrhythmia requiring lidocaine therapy. Patients with pump failure were excluded because they were unevenly distributed between the two groups, as all but one were in the conventional treatment group. Further, some patients in the conventional treatment group received only a bolus but no infusion, or an infusion but no bolus. They were also excluded. Thus two groups of patients were finally developed which had an approximately equal prognosis to allow comparison of the two modes of therapy. Seventy eight conventionally treated patients had 8 episodes of primary ventricular fibrillation, 1 episode of significant cardiac toxicity, and 33 patients required subsequent dosage adjustments. In contrast, the computer-assisted group only had 2 patients with primary ventricular fibrillation. There was also one episode of toxicity that was significantly greater thian paresthesias or mild somnolence, and the two patients with primary ventricular fibrillation were the only patients in the computer-assisted group who required subsequent adjustment of therapy(P .0)01). The use of dosage regimens based on the a priori lidocaine model significantly increased the effectiveness of lidocaine therapy and most suggestively reduced the incidence of primary ventricular fibrillation. ADAPTIVE CONTROL The recent adaptive control feature now permits entry of serum concentrations found on past dosage regimens, permitting an individually fitted pharmacokinetic model to be made. In addition, this fitting is done in a manner that permits cardiac output to change. Other fitting procedures require that the patient remain entirely static from the time the collection of serum concentrations is begun until therapy is completed. This program, in contrast, permits a patient's cardiac index to change even while serum concentrations are being obtained. This is done by identifying the slope of the relationship between the elimination rate constant and cardiac index, however it is perceived, rather than by identifying the rate constant for elimination itself. Thus the individual parameter fitted is the slope of each individual patient's relationship between his perceived cardiac index and the apparent rate constant for elimination of lidocaine. This portion of the program is now ready for clinical use. It is felt that it should permit still further improvements to be made in lidocaine therapy, especially for patients with significant shock, failure, or liver disease. OPTIMAL SAMPLING The module for the optimal sampling strategy was derived from an examination from the times at which lidocaine concentrations minimize the determinant of the asymptotic parameter covariance matrix. This module was then tested as follows.

CLINICAL RESULTS - OUTCOME The largest clinical study of the use of these programs to date has been in collaboration with

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Monte Carlo simulations were performed which represented experience with 400 absolutely identical patients, to compare the accuracy and precision of parameter estimates derived from a conventional sampling strategy versus those derived from an optimal sampling strategy. The test situation employed an initial bolus of 75 mg infused over one minute, followeu by a fixed infusion rate of 1.452 mg/min. The parameter values for that test model were taken from the literature (5), and were: volume of distribution of the central compartment (Vc) = 30 L, apparent rate constant for elimination from the central compartment (Kel) = .0242 min' , apparant rate constant from central to peripheral compartment (Kcp) = .066 min-1, and apparent rate constant from peripheral to central compartment (Kpc) = .038 min-1. The conventional sampling strategy employed 8 samples taken over 12 hours at 5,10,30, 60,120,180,360, and 720 minutes. In contrast, the optimal strategy employed only half the phlebotomies, only 4 phlebotomies, one for each parameter. These were made at 1,10,74, and 720 minutes, with duplicate determinations on each phlebotomy sample to achieve the equal number of 8 data points for comparison. Normally-distributed noise, analogous to laboratory assay error (mean = 0, standard deviation = + .2 pg/ml) was added to the exact model data in a random fashion for each data point. The parameter estimates fo,ind (400 for each strategy) are shown in Figure I a,b,c,d as frequency histograms. They show that the precision of the estimates found with the optimal sampling strategy was visibly better than that found with the conventional strategy. The 95% inclusion intervals for the optimally obtained values of Vc, Kel, Kcp, and Kpc were respectively 21, 6, 21, and 100 percent of those found with the conventional strategy. These results show that the optimal sampling strategy employed in the present lidocaine program permits visibly greater precision in the estimates of each patient's parameter values. This strategy can be used with the a priori pharmacokinetic model to optimally plan the optimal strategy for monitoring initital therapy. It can also be used with the subsequently fitted pharmacokinetic model to optimally monitor the revised lidocaine therapy.

Lastly, based on the patient's fitted model, the optimal sampling strategy to monitor the new regimen is computed and printed. This program is avail-

able for use by hospitals over an internationally accessible time-sharing facility (6). PHIARMACOKINETIC PARAMETERS FOR 20 PATIENTS PARAMETER

MEDIAN

MEAN (+ S.E.M.)

K 10

.0133 min

.0316 min

K12

.0471 minm

.0865 min 1 (+.024)

39.6 Liters

40.3 Liters (+4.6)

(+.015)

12~~~~~~~~~~~~~~~~K21 .0194 min -1 .0315 min 1 (+.009) V1

VDB

207 Liters

244 Liters (+35.9)

VDSS

173 Liters

190 Liters (+2S.5)

Tha

8.3 min

9.9 min (+1.7)

ThE3

274 min

356 min (+39)

Total Body

6.7ml/min/kg

7.81nl/min/kg(+l.3)

Clearance

K10, K12, K21, and V1 described in methods.

are defined in figure 1 and determined as

VDV VDSS' T,ct, T,V

and total body clear-

ance are calculated as described elsewhere (12).

Table 1 - Method of Estimating Cardiac Function as a Percent of Normal for Age.

REFERENCES

1. Jelliffe RW, Rodman J, and Kolb E: Clinical Studies with Computer-Assisted Lidocaine (L) Infusion Regimens. Circulation, 54(2): II-211,

1976. 2. Brandfonbrener M, Landowne M, and Shock NW: Changes in Cardiac Output with Age. Circulation 12: 557-566, 1955. 3. Crone J, Belic J, and Jelliffe RW: A Programmable Infusion Pump Controller. Proceedings of the 30th Annual Conference on Engineering in Medicine and Biology, November 5-9, 1977, Los Angeles, California, p. 95. 4. Jelliffe RW, Schumitzky A, Rodman J, and Crone J: A Package of Time-Shared Computer Programs for Patient Care. Proceedings of the 1st Annual Symposium on Computer Applications in Medical Care, October 3-5, 1977, Washington, D.C., pp. 154-162.

SUMMARY Thus the present program includes a portion for entry of past dosage regimens, the patient's measured or estimated cardiac index or function, and the serum concentrations found. An individualized pharmacokinetic model can be fitted to his data, even if his cardiac index may be rapidly changing. Past peak, trough and end-of-dose interval concentrations are then computed for the entire past therapy, using the individualized model based on his own serum data. Next, the desired serum concentration is entered, along with the present estimated or measured cardiac index or function, and the duration of each desired infusion step. The required, usually tapering, infusion rate to achieve the desired goal is then computed for each infusion step, formatted for the desired amount of lidocaine in the desired syringe or bottle and the drops per ml of the infusion apparatus, if any.

5. Rowland M, Thompson P, Guichard A, and Melmon K: Disposition Kinetics of Lidocaine in Normal Subjects. Ann NY Acad Sci., 179: 383-398, 1971. 6. Comshare, Inc. (The USC*PACK collection) Los Angeles Office 700 South Flower Street Suite 1420 Los Angeles, California 90017 (213) 629-5551

Supportedby US Government Grants MB00146, GM23826, and by a grant from the American Heart Association Greater Los Angeles Affiliate.

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