Cornput. Biol. Med. Vol. 22. No. 3. pp. 155-163. Printed in Great Britain

1991 0

cuHo425/92 s5.00+ .@I 1992 Pergamon Press Lid

MW/PHARM, AN INTEGRATED SOFTWARE PACKAGE FOR DRUG DOSAGE REGIMEN CALCULATION AND THERAPEUTIC DRUG MONITORING JOHANNES H. PROOST

and DIRK K. F. MEIJER

Department of Pharmacology and Therapeutics, University Centre for Pharmacy, University of Groningen, Antonius Deusinglaan 2, 9713 AW Groningen, The Netherlands (Received 29 July 1991; in revised form 20 November 13 December 1991)

1991; received for publication

Abstract-The

pharmacokinetic software package MW/Pharm offers an interactive, userfriendly program which gives rapid answers in clinical practice. It comprises a database with pharmacokinetic parameters of 180 drugs, a medication history database, and procedures for an individual drug dosage regimen calculation. The included curve-fitting facilities allow estimation of pharmacokinetic parameters on the basis of medication history, taking into account a varying status of the patient with respect to body weight and kidney function, optionally using a Bayesian procedure. The module KinBes performs the evaluation of bioavailability studies, including various methods, and an extensive statistical evaluation of bioequivalence. Drug dosing Clinical pharmacokinetics Bayesian parameter estimation Curve-fitting Bioequivalence Bioavailability

Therapeutic drug monitoring Kidney function

INTRODUCTION

For drugs with a small margin of safety a dosage regimen should be chosen carefully in order to obtain a sufficient therapeutic effect at an acceptable risk of side effects. To this purpose knowledge of the pharmacokinetic behaviour of the drug is indispensable, since it forms the link between drug dosing and its pharmacological (therapeutic or toxic) effect. Using this concept the problem of drug dosing can be solved in two steps: First, the aim of achieving a therapeutic effect (which is often difficult to measure adequately for dosing purposes) may be expressed in terms of the concentration of drug in plasma (serum, blood). For many drugs a ‘therapeutic window’ has been established, i.e. minimum and maximum acceptable concentrations of drug in plasma. An appropriate dosing schedule may be defined as a regimen which maintains the drug concentration within the therapeutic window. Second, the relation between dosing regimen and drug concentration in plasma can be predicted on the basis of: (1) Pharmacokinetic population parameters of the drug; (2) Information on the individual patient, e.g. age, sex, body weight, height, creatinine clearance, disease, and co-medication. Because the actual concentration profile in the individual patient is influenced by a variety of unknown factors, it may be necessary to monitor the drug plasma concentration by analyzing blood samples during the period of therapy. On the basis of measured concentrations the dosage regimen can be adjusted in order to maintain the concentration within the therapeutic window. This procedure, called therapeutic drug monitoring (TDM), has proven its value in the treatment with a variety of drugs, including anticonvulsants, antiarrhythmics, digitalis glycosides, theophylline, aminoglycoside antibiotics, antineoplastic agents, and cyclosporine [l-4]. 155

156

J. H. PROOST and D. K. F. MEIJER

Optimal use of pharmacokinetic population data and measured plasma concentrations for calculation of (initial or adjusted) dosage regimens requires reliable software. The application of such a program in practice expands the list of requirements, e.g. with respect to user-friendliness, speed of execution, versatility, and the integration of databases of patients and drug parameters. Recently, a short overview of the currently available programs has been published [5]. In this paper the main features of MW/Pharm are described, and exemplified for the aminoglycoside antibiotic gentamicin (Table 1, Figs 3 and 4) and the anticonvulsant drug phenytoin (Figs 5 and 6). DESCRIPTION In Fig. 1 the main components their interrelation.

OF MW/PHARM

of the program are depicted in a flow chart, showing

Patient registration After entering the personal data of a patient (patient number, name, date of birth, sex, body weight, height, and creatinine clearance), the data can be stored in the patient database, together with the patient medication history and individual pharmacokinetic parameters obtained by curve-fitting (see below). The entries for patient number, name, and date of birth can be used for searching a patient from the database. Patient status From these data the body surface area (BSA), lean body mass (LBM, or ideal body weight), and lean body mass, corrected for drug distribution into fat tissue (LBMc) are calculated (Table 1). The creatinine clearance can be entered by the user, or can be

~................_ DRUG DATABASE

J

PATIENT DATABASE Fig. 1.

Flow chart of MWlPharm

(modules

:

KinFit and KinBes not shown).

An integrated software package

1.57

Table 1. Data used for dosage regimen calculation of gentamicin Therapeutic data

:gentamicin Route of administration:intravenous :l-7mgL-’ Therapeutic window :7 days Duration of therapy Dw

Pharmacokinetic

oomdation

infusion during 0.5 h

data

:O.il’ :0.4 iiat tissue) k,, (metabolic):0.015 k;; (renal) ’ :0.0024 k 12 k 21

L.kg-’ (relative distribution into fat tissue) h-’ * CLc, h-’ :0.030 h-’ :0.0080 h-’

Patient data Age Sex

:55y

:female

:68kg Body weight :162cm Height Serum creatinine concentration: lOO~mol.LDerived patient datu

: 1.73m2 Body surface area (BSA) :54.2 kg Lean body mass (LBM) Lean body mass, corrected (LBMc):59.7 kg :48.2 mL.min-’ (normalized to Creatinine clearance (CL,,)

calculated from creatinine concentration, or by Jelliffe [7,8]. Database of pharmacokinetic

body surfacearea 1.73m2)

using the formulas by Cockcroft and Gault [6],

data of drugs

Pharmacokinetic data of about 180 drugs are available in a database. Among others, the following data are available: (1) Routes of administration: constant intravenous infusion (with or without a bolus loading dose), or repeated administrations as an intravenous bolus, intravenous infusion, oral, or intramuscular. (2) Minimum and maximum effective concentrations, used as the target concentrations in drug regimen calculations; optionally, an average concentration can be used as a target concentration. (3) Pharmacokinetic data from l-, 2-, and/or 3-compartment models (Fig. 2): volume of distribution, metabolic and renal clearance or elimination rate constant (elimination rate constant and clearance are interchangeable), intercompartmental rate constants; for drugs obeying Michaelis-Menten kinetics, the maximum elimination rate V,,,, and the Michaelis-Menten constant K,,,; for extravascular administration absorption rate constant (k,) and bioavailability (F); for extracorporeal clearance the extraction ratio. From these population data the individual pharmacokinetic parameters are calculated. (4) Miscellaneous data: e.g. units, distribution into fat tissue, protein binding, active metabolites. Drug dosage regimen calculation

From these data a ‘theoretical’ dosing regimen is calculated, as shown in Fig. 3 (left value in each column). The theoretical dosing regimen can be modified by the user into a practical applicable dosage regimen, by rounding-off to available doses and practical dosing intervals (Fig. 3, right value in each column). The predicted maximum and minimum concentrations are

J. H. PROOST and D. K. F. MEIJER

158

ADMINISTRATION intravascular

Fig. 2. Compartmental

DOSAGE

REGIMEN

ELIMINATION model used in dosage regimen calculation.

gentamicin

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Fig, 3. Initial dosing advice for gentamicin (calculated using therapeutic, pharmacokinetic and patient data of Table 1). The three columns show the dosing advice for intramuscular, intravenous bolus injection, and intravenous infusion during 0.5 h, respectively. In each column the left number is the “theoretical” dosing advice, i.e. the maximum possible dosing interval, the required maintenance dose corresponding with the maximum dosing interval, the maximum possible loading dose, and the number of doses needed to reach 99% of steady-state. The right number in each column can be entered by the user, in order to design a ‘practical’ dosing advice, based on a practical dosing interval and the available dose strengths. In the lower half the resulting maximum and minimum plasma concentrations, the level expressed as a percentage of the steady-state level, and the time at which the maximum concentration is reached, are glven for each dosing regimen. The bottom line lists the available commands.

h)

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FlCl(Fl]t~+*,PgLtp.PgDn(n = usuory] r =

shouIF;I=patIF8=kinlF9)=doslFZ

159

= comp.2

Fig. 4. Predicted plasma concentration profile following the practical dosing advice (data of Fig. 3, last column). Bottom line lists the available commands (e.g. return to main menu, printing, saving and retrieving of profile). The arrow (lower right corner) can be moved using the arrow keys; the corresponding time and concentration are shown in the upper right corner. The horizontal dashed lines enclose the therapeutic window. Inset: concentration profiles in the peripheral and central compartments; the maximum concentration in the peripheral compartment is 1.4 mg/kg.

recalculated after each modification, facilitating the design of an appropriate schedule. The final dosing advice can be printed by pressing a function key.

dosing

Graphical presentation The dosage regimen can be depicted graphically, allowing a quick inspection of the predicted plasma concentration (Fig. 4). For multi-compartment models the concentration of drug in the peripheral compartment can be viewed in a graphical window, indicating the degree of accumulation in the body (Fig. 4, inset left upper corner). This may be important, e.g. for the aminoglycosides as an indication of the risk of toxicity [9]. Medication history The medication history of each patient can be entered (and stored) in a full-screen editor (Fig. 5). The predicted plasma concentration can be depicted graphically (Fig. 6), taking into account all available data in the medication history table. If body weight changes over time, the corrected lean body mass (LBMc) and, as a result, the volume of distribution, changes continuously. The same applies to a changing creatinine concentration, reflecting a renal clearance changing over time. Moreover, the effect of extracorporeal clearance (dialysis, hemoperfusion) on drug concentration can be taken into account. Bayesian parameter estimation From the graphical presentation of the medication history, a Bayesian parameter estimation (fitting) procedure can be started (Fig. 6) [lo, 111. The procedure searches for a set of pharmacokinetic parameters which fits best to the measured plasma concentrations and (unless the Bayesian option is switched off) to the pharmacokinetic population parameters, i.e. the parameters present in the drug database.

J. H. PROOSTand D. K. F. MEUER

160 date

time

(

dose

DD-MM-YY

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19-01-91 20-01-91 24-01-91 25-01-91 30-01-91 30-01-91

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relative

0

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p=present

dateI+

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Fig. 5. Editor screen for registration of a phenytoin medication history of a 4-year-old boy, body weight 18 kg, height 105 cm. From left to right: date and time of event, administered dose, route of administration (intravascular or extravascular), number of doses, dosing interval (in the case of a multiple dosing regimen), duration of infusion (in the case of intravenous infusion), measured plasma concentration, body weight, measured serum creatinine concentration, and extracorporeal clearance. The three lines at the bottom are reserved for messages and a summary of the available commands.

iteration: pop. init. fit

nn 5.6ew 6.3986

VraX 28.88 22.74

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Fig. 6. Plasma concentration profile following the actual dosing schedule in the medication history (data from Fig. 5), after fitting using the Bayesian procedure. Lower panel depicts the predicted plasma concentration profile using initial parameter estimates (dotted line) and after fitting (solid line), and the measured concentrations (open circles); the horizontal dashed lines enclose the therapeutic window. The upper panel shows the population parameters, initial estimates, and parameter values after fitting (fr is the ratio of renal phenytoin clearance and creatinine clearance). The bottom line lists the available commands. The initial parameter estimates were obtained by a Bayesian fit using only the first plasma measurement; from these estimates a new dosage regimen was calculated (175 mg once a day, see Fig. 5). After 6 days two plasma samples were measured, and the fitting procedure was repeated.

An integrated software package

161

The Bayesian method can be applied with any number of plasma concentration measurements. Using the individualized pharmacokinetic parameters, the optimal dosing regimen can be (re-)calculated as described earlier. If new blood samples are taken, the measured concentrations may be added to the table, and the fitting procedure can be repeated, taking into account the complete history (Fig. 6). KinFit The MW/Pharm package contains also a curve-fitting module for the assessment of pharmacokinetic parameters after a single dose administration, as a quick alternative for the curve-fitting of a complete medication history. The program provides initial estimates using an automated stripping procedure. Kin Bes

A module for the accurate assessment of bioavailability and rate of drug absorption by various methods: numerical deconvolution (including a stabilizing algorithm) [12], a weighted-least-squares reconvolution method [ 121, AUC-ratio and statistical moments, Wagner-Nelson and Loo-Riegelman methods. KinBes allows processing of data of an entire bioavailability or bioequivalence study (number of subjects, number of dosage forms) with respect to calculation in individuals, calculation of mean values, graphics, and statistical evaluation. Bioequivalence data can be evaluated by a wide range of methods, among others, following guidelines of FDA and APV. Hardware requirements

The program runs on IBM personal computers and compatibles (PC/XT/AT) with a minimum of 512 kb RAM. The package can be installed on a hard disk, requiring about 1 Mb disk space. However, the program also runs from one floppy disk drive (minimum 360 kb). MW/Pharm supports CGA, EGA, VGA, Hercules and monochrome graphics adapters. Calculations are performed much faster if the computer is equipped with a 80 x 87 math coprocessor. A drug dosing program for general practice must be as fast as possible, in order to avoid waiting times. Therefore much attention is paid to execution speed of the MW/Pharm dosage regimen calculations and fitting procedures, without significant concessions to accuracy. MW/Pharm is available in English, German, and Dutch versions. Benejit

The aforementioned approaches of drug dosage calculation improve the efficacy of drug therapy, and decrease the risk of side effects and intoxication. Consequently, it may lower the costs of health care by reducing the duration of therapy, by prevention of hospitalization due to improper drug use (under- and overdosing), and also by reducing the number of drug concentration measurements needed for each patient [l-4]. Examples of the use of MW/Pharm can be found in literature, in the evaluation of dosage schedules of thiopental for the treatment of increased intracranial pressure [13], and in forensic toxicology [14]. MW/Pharm has proven its value in hospitals in The Netherlands and Czechoslovakia, and it has been chosen as a standard dosage calculation program by the Dutch Society of Hospital Pharmacists. In a comparison with other programs for therapeutic drug monitoring available in Germany, MW/Pharm was described as the most extensive program, offering unequalled possibilities [5]. SUMMARY The pharmacokinetic software package MW/Pharm offers an interactive, user-friendly program which gives rapid answers in clinical practice. It comprises a database with CM422:3-B

162

J. H. PROOSTand D. K. F. MEIJER

pharmacokinetic parameters of 180 drugs, a medication history database (drug administrations, concentration measurements, and patient status, varying over a period of time), and procedures for a drug dosage regimen calculation based on pharmacokinetic population parameters, and information on the individual patient. The included curvefitting facilities allow estimation of pharmacokinetic parameters (including parameters of multi-compartment and non-linear models) on the basis of medication history, taking into account a varying status of the patient with respect to body weight and kidney function, optionally using a Bayesian procedure. The module KinBes performs the evaluation of bioavailability studies, including calculation of the rate and extent of bioavailability by various methods, and an extensive statistical evaluation of bioequivalence. MW/Pharm has proven its value in hospitals in The Netherlands and Czechoslovakia, and it has been chosen as a standard dosage calculation program by the Dutch Society of Hospital Pharmacists. It is now available in English, German, and Dutch versions. The program runs on any IBM personal computer or compatible (PC/XT/AT) with a minimum of 512 kb RAM, and preferably, but not necessarily, equipped with hard disc and 80 x 87 math coprocessor. REFERENCES 1. C. E. Pippenger, The cost-effectiveness of therapeutic drug monitoring, Ther. Drug Monit. 12,418 (1990). 2. C. J. Destache, S. K. Meyer, M. J. Bittner and K. G. Hermann, Impact of a clinical pharmacokinetic service on patients treated with aminoglycosides: a cost-benefit analysis, Ther. Drug. Monit. 12, 419-426 (1990). 3. C. J. Destache, S. K. Meyer and K. M. Rowley, Does accepting pharmacokinetic recommendations impact hospitalization? A cost-benefit analysis, Ther. Drug Monit. 12, 427-433 (1990). 4. L. D. Ried, J. R. Horn and D. A. McKenna, Therapeutic drug monitoring reduces toxic drug reactions: a meta-analysis, Ther. Drug Monit. 12, 72-78 (1990). 5. B. Illgen and W. Daubenmerkl, Therapeutic drug monitoring. Vorstellung einiger EDV-Programme, Krunkenhauspharmazie 12, 355-357 (1991). 6. D. W. Cockcroft and M. H. Gault, Prediction of creatinine clearance from serum creatinine, Nephron 16, 31-41 (1976). 7. R. W. Jelliffe, Creatinine clearance: bedside estimate, Ann. Int. Med. 79, 604-605 (1973). 8. R. W. Jelliffe and S. M. Jelliffe, A computer program for estimation of creatinine clearance from unstable serum creatinine concentration, Math. Biosci. 14, 17-24 (1972). 9. M. E. De Broe, R. A. Giuliano and G. A. Verpooten, Insights into the renal handling of aminoglycosides: a guideline for prevention of nephrotoxicity, J. Drug Deu. 1 (Suppl. 3). 83-92 (1988). 10. L. B. Sheiner, S. Beal, B. Rosenberg and V. V. Marathe, Forecasting individual pharmacokinetics, Clin. Pharmucol. Ther. 26, 294-305 (1979). 11 L. B. Sheiner and S. L. Beal, Bayesian individualization of pharmacokinetics: simple implementation and comparison with non-Bayesian methods, .I. Phurm. Sci. 71, 1344-1348 (1982). 12 J. H. Proost, Critical evaluation of the determination of bioavailability by numerical deconvolution. Ph.D. Thesis, University of Groningen, Groningen, The Netherlands (1987). 17 __. D. J. Touw, A. A. T. M. M. Vinks and J. T. J. Tans, Toepassing van thiopental bij verhoogde intracraniele druk. Klinische studie en vergelijking van diverse doseerschema’s met computersimulatie, Phurm. Weekbl. 126, 959-966 (1991). 14. D. R. A. Uges and B. Greijdanus, Euthanasia: a challenge for the forensic toxicologist, J. Forensic Sci. 35, 1424-1430 (1990). About the Author-JoHANNEs H. PROOSTreceived the M.Sc. degree in Pharmacy in 1979 and the Ph.D. degree in 1987 from the University of Groningen, The Netherlands. From 1980 to 1987 he worked as a research assistant on the assessment of bioavailability by numerical deconvolution at the Department of Pharmaceutical Technology at the same university. In 1987 Dr Proost joined the staff of the Department of Pharmacology and Therapeutics, Section Pharmacokinetics, at the University Centre for Pharmacy at the University of Groningen. His research interest focuses on the relationship between pharmacokinetics, pharmacodynamics and chemical structure of muscle relaxants, and on the development of computer programs in pharmacokinetics for the clinical pharmacy and fundamental research. Together with Dirk K. F. Meijer he is responsible for the courses in pharmacokinetics for students in pharmacy. About the Authnr-Dmx K. F. MEUER studied pharmacy at the University of Groningen. The Netherlands where he graduated in 1966. In 1972 he received his Ph.D. in Pharmacology from the University of Groningen. He obtained postdoctoral experience in Pharmacology at the Albert Einstein College of Medicine, Department of Pharmacology, New York, U.S.A. (1973-1974). Professor Meijer returned to an appointment as assistant professor at the Department of Pharmacology, Medical Faculty in Groningen and was appointed to the position of Associate

An integrated software package Professor in Pharmacokinetics at the Faculty of Pharmacy of the University of Groningen in 1979. In 1980 he became Professor of Pharmacology and Therapeutics. Professor Meijer is chairman of the National Research Club for ‘Metabolism of Drugs and Toxic Compounds’ and member of that for ‘Liver Research’. He was a committee member of the European Association for Study of the Liver and was involved in the organization of several international meetings. He is a member of the European Association for Study of the Liver (EASL) and the American Association for the Study of Liver Diseases (AASLD). He has initiated the ‘European Study Group for Hepato-biliary Transport’, joining the expertise of sixteen different laboratories in seven countries. He is on the board of several international scientific journals. He is chairman of the recently founded ‘Nederlandse Vereniging voor Farmaceutische Wetenschappen: NVFW’ (Dutch Association for Pharmaceutical Sciences’).

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