LEADING ARTICLE

Clin Pharmacokinet 2001; 40 (6): 395-403 0312-5963/01/0006-0395/$22.00/0 © Adis International Limited. All rights reserved.

Pharmacokinetic Software for the Health Sciences Choosing the Right Package for Teaching Purposes Bruce G. Charles1,2 and Stephen B. Duffull1 1 School of Pharmacy, The University of Queensland, Brisbane, Queensland, Australia 2 The Australian Centre for Paediatric Pharmacokinetics, The University of Queensland, Brisbane, Queensland, Australia

Abstract

Computer assisted learning has an important role in the teaching of pharmacokinetics to health sciences students because it transfers the emphasis from the purely mathematical domain to an ‘experiential’ domain in which graphical and symbolic representations of actions and their consequences form the major focus for learning. Basic pharmacokinetic concepts can be taught by experimenting with the interplay between dose and dosage interval with drug absorption (e.g. absorption rate, bioavailability), drug distribution (e.g. volume of distribution, protein binding) and drug elimination (e.g. clearance) on drug concentrations using library (‘canned’) pharmacokinetic models. Such ‘what if’ approaches are found in calculator-simulators such as PharmaCalc, Practical Pharmacokinetics and PK Solutions. Others such as SAAM II, ModelMaker, and Stella represent the ‘systems dynamics’ genre, which requires the user to conceptualise a problem and formulate the model on-screen using symbols, icons, and directional arrows. The choice of software should be determined by the aims of the subject/course, the experience and background of the students in pharmacokinetics, and institutional factors including price and networking capabilities of the package(s). Enhanced learning may result if the computer teaching of pharmacokinetics is supported by tutorials, especially where the techniques are applied to solving problems in which the link with healthcare practices is clearly established.

1. Problems with Teaching and Learning Pharmacokinetics Pharmacokinetics is about drug movement. Mathematics provides a convenient tool for describing and predicting drug movement, most often in terms of rate processes such as those associated with absorption and elimination. Not surprisingly, many courses dealing with fundamental and more advanced principles of pharmacokinetic theory have considerable mathematical content. A glance through any of the

pharmacokinetics texts published over the past 30 years leaves but one general impression: pharmacokinetics seems to be concerned mostly with numbers and equations. Worse, many of us provide a disservice to our students by teaching pharmacokinetics in modules which would be more suited to an applied mathematics course. Only very occasionally have we recognised this up-front and made any attempt to ‘de-numerate’ pharmacokinetics.[1] It is hardly surprising, therefore, that since students enrol in health science courses to be health practi-

396

tioners many develop a detached if not hostile attitude towards pharmacokinetics. This hampers any real understanding of clearance and volume of distribution and the application of these most fundamental of kinetic parameters. Half-life, however, is exceptional in that it poses minimal threat to pharmacokinetic cognition, presumably related to its perceived ease of application because it has widespread use in other areas of science. Part of the problem undoubtedly is the inherent ‘dryness’ of the topic, especially if divorced from perceived applications and health outcomes; for practising pharmacists one major outcome is the quality use of medication of which pharmacokinetics is a seemingly unrecognised but vitally important component. In our own experiences with pharmacy students a lesson plan that contains blackboard derivations of pharmacokinetic relationships from first principles, no matter how fundamental, has the kiss of death. How many students genuinely can be excited about a differential equation, let alone deconvolution? The traditional ‘chalk and talk’ approach more often than not results in confusion, disinterest, inattentiveness and absenteeism, culminating in underachievement and poor learning outcomes. Not surprisingly, end of year teaching and subject evaluations by students tend to rank pharmacokinetics lower than many other subjects. 2. A Role for Computer Software In attempting to redress this unsatisfactory situation many have come to recognise that it is often the way pharmacokinetics is taught (the process) which is important, not just plugging in the ‘right’ formula (the content) to answer a given question. The importance in getting the ‘right’balance between process and content is nothing new and has been firmly entrenched at many (but not necessarily all) levels of education. More specifically, the issue for us is to foster a positive learning environment for pharmacokinetic instruction, and to reinforce the relevance and impact of this topic on the broader, day-to-day duties and responsibilities of the health practitioner. © Adis International Limited. All rights reserved.

Charles & Duffull

Recognition of the latter is a very strong motivator to learning. For example, from what pharmacokinetic foundation does one build upon to counsel a patient prescribed drug X (with a half-life of 28 hours) that they should take 2 tablets as the first dose then 1 in the morning thereafter? Why do normal doses of theophylline fail to work sufficiently in a patient who smokes a packet of cigarettes a day? At a broader level, pharmacokinetics is concerned with outcome(s) following some action(s), for example, steady-state trough serum drug concentration resulting from a particular dosage regimen. The prescriber has the power to initiate and alter an action and, therefore, influence the outcome, but so does the system on which the action is imposed (i.e. the biology – what the body does to the drug). This cognition can be tested further by imposing multiple, interacting layers on the actions (e.g. change of dose, formulation, dosage frequency) or on the system (e.g. decrease in renal function, altered gastrointestinal motility, change in liver clearance of a drug via an interaction with a second drug). Education researchers have pointed out that many complex concepts, such as those associated with mathematical processes, may be better taught using multiple, linked representations.[2] In pharmacokinetics, such representations might be plots of serum drug concentrations versus time from various combinations of dose, dosage interval and duration of treatment, or they could include the conceptualisation and on-screen formulation of a model using iconic symbols. The importance of dynamic, interactive media to facilitate cognition of multiple, linked representations was recognised some years ago,[3] but the opportunities to apply this concept have only increased with the introduction of recent generations of computers in combination with software that allows processing of symbolic and graphical data. This brief review compares and contrasts some of the software presently available that use these approaches for teaching pharmacokinetics. We have restricted the scope to packages and programs which are relevant to students in the health sciences, Clin Pharmacokinet 2001; 40 (6)

Software for Teaching Pharmacokinetics

although we recognise that students from other disciplines (e.g. engineering, statistics) also may encounter computer assisted learning of the principles of pharmacokinetics. Wherever possible, pharmacokinetics should be taught in concert with dose-response behaviours of drugs (and their metabolites), namely the pharmacodynamics – what the drug is doing to the body. Sadly, there are few teaching packages which deal adequately with pharmacodynamic principles on their own, let alone the (necessary) integration with the pharmacokinetics. 3. Software for Teaching Pharmacokinetics It seems like everyone has their own concept and implementation of using pharmacokinetics software for teaching purposes, which has resulted in an interesting developmental pathway. This has encompassed the generation of analogue outputs representing plasma drug concentrations over time via manual manipulation of simple electrical circuitry[4] or programming early generations of microprocessors,[5] to very sophisticated, professionally written packages containing pharmacokinetic modules for dosage optimisation. Details of commonly used pharmacokinetic teaching packages are summarised in table I. 3.1 Practical Pharmacokinetics

This popular package won the American Association of Colleges of Pharmacy (AACP) Innovation in Teaching Award in 1996, and is endorsed by the International Association of Therapeutic Drug Monitoring and Clinical Toxicology. It is primarily concerned with the application of pharmacokinetics to serum concentration monitoring and has 2 components, a teaching-tutorial module and a practice module. The teaching functions are enhanced by multiple choice questions. Pharmacokinetic parameter values and dosage recommendations for more than 400 library drugs are calculated based on serum concentration data and patient demographic data and clinical characteristics such as renal and he© Adis International Limited. All rights reserved.

397

patic function. There also is a small database containing data on special populations (e.g. obesity). Some parts of the graphical interface are animated and the user can use the patient database to create a pharmacokinetic consult. However, some elements require updating, for example the aminoglycoside dosage module has only conventional (multiple daily) administration and not once daily, and the recommendations for vancomycin administration are somewhat outdated. The clinical biochemistry units are non-SI which is a considerable limitation for many countries outside the US. This product is available for a networked platform. 3.2 SAAM II

In our opinion this is an excellent package which has evolved over many years and is now widely used in pharmacokinetics teaching and research. There are 2 major modules, the compartmental module and the numerical module. An important learning feature of the compartmental module is that the user initially conceptualises the biological process then links the inputs, transfers and delays in movement between compartments directly onscreen using model-building icons via an excellent graphics interface. The program automatically translates the model into the necessary sets of differential equations following which experimental data can be fitted. The numerical module allows one to fit data to one of a number of predefined models (e.g. sums of exponentials, Michaelis-Menten kinetics, Scatchard analysis for enzyme kinetics) or a nonlibrary model can be defined algebraically. Flexibility is permitted in the modelling environment including simultaneous fitting of multiple experiments to a particular model, a variety of routes and multiple dosage regimens, and alteration in experimental conditions at any time (e.g. deterioration in renal function, altered bioavailability). SAAM II operates from a Windowscompatible workstation and network platform. 3.3 PK Solutions

PK Solutions is an Excel-based program which is used in more than 25 countries. It allows the user Clin Pharmacokinet 2001; 40 (6)

© Adis International Limited. All rights reserved.

ETH Biopharmazie

ETH Biopharmazie

ClinPharm International

Summitt Research Services

Pharsight Corporation

PharmaSim

PharmaCalc

Practical Pharmacokinetics

PK Solutions (2.0)

WinNonlin (3.1)

Algebraic model building.

Library.

Web demonstration.

Via curve-stripping sums of exponentials.

Runs on PC and Mac as an Excel (version 4, or higher) template.

c

d

e

f

http://www.pharsight.com/

http://www.summitpk.com

http://www.clinpharmint.com/

http://aut.ethz.ch/~keller/ pharmacalc.html

http://aut.ethz.ch/~keller/ pharmasim.html

http://www.hps-inc.com/

b

Graphical model design interface.

High Performance Systems, Inc.

Stella (6.0)

a

Bourne, University of Oklahoma

Boomer (2.7.9)

http://www.boomer.org/

http://www.modelkinetix.com/

FamilyGenetix Ltd

ModelMaker (4.0)

http://www.saam.com/ http://www.coacs.com/PCCAL/ products/pccal32.htm

SAAM Institute, Inc

SAAM II (1.2)

Webpage

PCCAL - PharmacoCoAcS Ltd kinetic Simulations (2.0)

Author/distributor

Program

Table I. Summary information on pharmacokinetic teaching software

No

No

No

No

No

Yes

Yes

Yes

No

No

PC/Mac

PC/Mac

Yesb,c

Yesa

PC

Yesb,c Yes

PC/Mac

No

Yese

PC

PC/Mac

No

No

PC/Mac

PC

Yesa,b

No

PC

PC/Mac

Yesa,b,c No

PC/Mac

Modelbuilding

No

No

No

Yes

Yes

Yes

No

Yes

Monte Carlo Curvesimulation fitting

Tutorial

Tutorial

Tutorial

No

Tutorial

Tutorial

Tutorial

Examples

Examples

Examples

Tutorial/ examples

9x/2000/NT

Excelf

3.1/95/98

3.1/95/NT OS7.x/8.x/9.x

3.1/95/NT OSS7.x/8.x/9.x

95/98/NT, OSS7.x/8.x/9.x

DOS, OS7.x/8.x/9.x

95/98/NT

95/98/NT

95/98/NT

Platform

No

Yes

Yes

No

No

Yes

No

Yes

Yesd

Yes

Demo

398 Charles & Duffull

Clin Pharmacokinet 2001; 40 (6)

Software for Teaching Pharmacokinetics

to explore ‘what if’ scenarios in which serum concentration-time curves are simulated from user defined doses, dose intervals and routes of administration. Alternatively, data supplied by the user can be modelled by curve-stripping sums of exponentials and noncompartmental parameter values can be estimated directly. The format is interactive with data entered directly to the screen with instantaneous graphical representation and calculation of kinetic parameter values. The graphical and tabular output is flexible and can be saved and exported. This product is able to be networked. 3.4 ModelMaker

This is a powerful and versatile modelling environment of the same genre as SAAM II and Stella (see section 3.8.1). However, ModelMaker is more akin to Stella in that it is a ‘generic’ program which is capable of being used in areas other than pharmacokinetics. In fact, any process which can be visualised as a system of interacting compartments can be handled by ModelMaker, including continuous, discontinuous, and ‘stiff’ functions. It also can accommodate stochastic processes, notably Monte Carlo simulation which is a recently added feature (Monte Carlo methods allow one to ‘add’ variability to a model by randomly generating parameter values from user defined prior distributions). ModelMaker 4 operates from a Windows-compatible, stand-alone platform. The output from an analysis can be easily saved for reuse, or cut and paste functions allow data, model parameters, graph and tables to be exported to other programs. 3.5 PharmaCalc, PharmaSim

PharmaCalc runs under Windows and functions as a simulator/calculator which uses pre-defined 1-compartment pharmacokinetic models in which the user selects the drug of interest from a large library. Population average (e.g. literature) values of half-life, volume of distribution and, if applicable, absorption rate constant and bioavailability, are automatically loaded after selecting the drug of interest, together with the desired route of admin© Adis International Limited. All rights reserved.

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istration, dose, dosage interval and number of repeat doses. The user can create a new profile for a drug not in the library by entering the appropriate pharmacokinetic data, or the default values of an existing library drug can be altered as required. Appendix I shows an application of PharmaCalc in an undergraduate tutorial exercise based on a clinical problem. PharmaCalc does not have facilities for modelling concentration-time data provided by the user or Monte Carlo simulation. One limitation of PharmaCalc is that it simulates serum or plasma concentrations only, and the graphical output cannot be displayed on a log-scaled axis. Furthermore, the selected pharmacokinetic parameter values and the route cannot be altered once a simulation profile is initiated. For example, it is not possible to display the effects of changing the renal function during a course of treatment, although changes in the dose and dosage interval can be made. PharmaSim is from the same authors as PharmaCalc and generally is similar in concept and function except that at the beginning of a simulation run the pharmacokinetic parameters (e.g. half-life) can be changed dynamically via a slidebar with the display responding instantaneously with the simulated profile. Furthermore, the simulations are integrated with 3 tutorials in a Hypercard type format. The text and pictures in a tutorial are formatted as a script file which can be customised to the user’s requirements using a text editor and a drawing/ artwork program. PharmaCalc and PharmaSim are freeware and can be downloaded from the web. 3.6 PCCAL (Pharmacokinetic Simulations)

Pharmacokinetic Simulations (2.0) is one module in a large suite of computer aided learning packages for the pharmaceutical and life sciences (PCCAL). In keeping with the flavour of PharmaCalc, PharmaSim and PK Solutions, this program is designed to assist the teaching and learning of the fundamentals of pharmacokinetics by providing a ‘what if’ environment under different pharmacokinetic circumstances. In Pharmacokinetic Clin Pharmacokinet 2001; 40 (6)

400

Simulations, this is easily achieved by selecting dose, dosage interval, bioavailability, absorption rate constant, elimination rate constant, volume of distribution, etc., from an analogue slide bar on the left of the screen. The graphical output of the simulation is displayed conveniently on the right of the screen as concentration versus time, or as a semi-logarithmic plot. The library contains models for single and multicompartment linear models, Michaelis-Menten kinetics (including presence of a competitive inhibitor), constant rate and intermittent infusions, intravenous and extravascular routes. Pharmacokinetic Simulations is available as either Windows or Web/Intranet versions. 3.7 WinNonlin (3.1)

This package from the Pharsight company comprises comprehensive software which is widely used by the pharmaceutical industry, regulatory authorities and academia. This product was previously known as PCNonLin. While not specifically designed as a teaching environment WinNonlin has an extensive on-line help and tutorial component to assist the student in the analysis of almost any type of pharmacokinetic or pharmacodynamic model (mixed-effects population modelling is catered for by its sister program, WinNonMix). Besides its reasonably high purchase price, this program is primarily designed for research applications and, therefore, would not be suitable for teaching undergraduates. It is our opinion that the teaching role for WinNonLin would be in advanced or postgraduate pharmacokinetic courses. 3.8 Others 3.8.1 Stella (6.0)

This is a general modelling package which can be adapted to pharmacokinetic applications. It is similar in concept to ModelMaker and SAAM II but has a completely graphical driven interface. 3.8.2 MultiForte/Boomer (2.7.8)

MultiForte/Boomer (2.7.8) is a DOS-based curvefitting program. It can be downloaded free from the web together with a manual which contains instruc© Adis International Limited. All rights reserved.

Charles & Duffull

tions and tutorials on fitting models to data and Monte Carlo simulations. 3.8.3 PHA 5127 Simulations

PHA 5127 Simulations comprises a series of ‘what if’ pharmacokinetic simulation modules (written by Hochhaus and Derendorf, University of Florida, FL, USA) which form part of the coursework at the University of Florida. The simulator can be run on-line via the web (http://cop.ufl.edu/ safezone/pat/ pha5127/) or downloaded free of charge, then subsequently run under Excel. The modules encompass 1- and 2-compartment kinetics, single and multidose administration, and physiological models and drug metabolism. 4. Recommendations and Perspectives There are considerable benefits of computer simulation as an educational tool in the health sciences.[6-12] However, there are a number of factors operating in the teaching environment which need consideration. Some student-related issues include the level of ability and background in general pharmacokinetics,[6] whether the students are undergraduates, postgraduates, postdoctoral or career researchers, the aims and objectives of the subject or course, and the allocated time and workload. Institution-related factors encompass the initial outlay and ongoing licensing costs of the software; this may range from freeware to considerable expense for very comprehensive and highly integrated packages developed and distributed by professional software houses. The physical facilities of the teaching laboratory, especially in relation to the class size, is important. In many institutions large class sizes may require students to work in groups because of insufficient numbers of workstations. This situation may compromise the opportunity for students to learn at an individual level and at their own pace which, for computer-assisted learning of pharmacokinetics, has been shown to be a highlyvalued learning modality.[6] The degree of ongoing maintenance and support is an important consideration when choosing the software package, especially the availability of upgrades in response to evolving teaching pracClin Pharmacokinet 2001; 40 (6)

Software for Teaching Pharmacokinetics

tices and content. Pharmacokinetic software packages which do not keep up with the rapid advances in hardware and software technology, especially with new and powerful multimedia applications, are in danger of extinction. Interestingly, some of the currently-used software is not written to take advantage of the power of a local area network, but this can be circumvented in many cases by physically installing the package on the hard-drive of individual workstations, or by allocation of workstation partitions on a fileserver using an appropriate configuration. For teaching and revising basic pharmacokinetic principles, PharmaCalc and PharmaSim are useful packages and, as downloadable freeware, have distinct advantages if cost is a consideration. They are straightforward in concept and layout and have a shallow learning curve such that most students can familiarise themselves with the program’s features and produce satisfactory results within 15 minutes. We presently use PharmaCalc in a course in the 4th year of the BPharm programme in which students use the simulations as an adjunct to tutorial and assignment tasks which relate to pharmacotherapeutic applications. Many students download the programs from the web and work on the tasks in their own time. Several packages make use of the so-called ‘systems dynamics’ environment in which models are formulated directly on-screen by means of graphical symbols/icons which represent components and functions of some compartmental system typically having an input (e.g. dose), a level or reservoir of some component (e.g. drug concentration), and some output process (e.g. elimination); these usually are linked by directional flow indicators (e.g. arrows). Systems dynamics approaches to computer simulation in teaching have undergone considerable development, particularly the biomedical sciences which are served by packages such as SAAM II, ModelMaker and Stella. Having the student construct the model (as opposed to using a library of fixed models) has the potential to engender a deeper understanding of a particular problem © Adis International Limited. All rights reserved.

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as well as familiarisation with the modelling process itself. On the other hand, if the structural characteristics of a model are known and are straightforward (e.g. 1-compartment model with first-order absorption and elimination) the use of a sophisticated program such as SAAM II may be excessive for the needs of a particular teaching module or course aimed at a basic appreciation of the interplay between maintenance dose and clearance on steady-state serum concentrations. In this instance, a calculatorsimulator such as PharmaCalc, PK Solutions, or PCCAL’s Pharmacokinetic Simulations may be sufficient; however, these programs ignore an important factor, variability, which may be considerable, and it is important for students to appreciate this especially for drugs which have a narrow therapeutic window, for example, phenytoin. Therefore, a teaching module which is concerned with factors that influence pharmacokinetic response may be served better by packages such as ModelMaker or Boomer in which stochastic processes are taken into account in the simulation. We have restricted this review to software which is applicable chiefly to undergraduate teaching, especially where there are considerable numbers of students. However, there are many other very good packages which would be more suited to higher degree students or researchers, perhaps best taught on a one-on-one basis or in small groups. Examples of these programs would be: • RIDO/RIDO PLUS which incorporates pharmacokinetics and pharmacodynamics in clinical pharmacology training and clinical trial simulation modules (http://www.ecpm/ch/html/pg_rido. html) • ADAPT is a package designed for simulation, parameter estimation, and sample schedule design in pharmacokinetics and pharmacodynamics (http://www.usc.edu/dept/biomed/BMSR/ Software/adapt2.html). Packages which can perform population analyses include: • NONMEM ([email protected]) Clin Pharmacokinet 2001; 40 (6)

402

• USC*PACK (http://www.usc.edu/hsc/lab_apk/ index.html) • WinNonMix (http://www.pharsight.com.wnm/ index.htm) • P-PHARM (http://www.InnaPhase.com). In addition, Kinetica 2000 (http://www.InnaPhase. com) is able to perform noncompartmental and advanced pharmacokinetic-pharmacodynamic modelling, but by September 2001 also will support population analyses. Software specifically designed for dose individualisation and clinical decision-making have been reviewed previously in Clinical Pharmacokinetics.[13] MW/PHARM incorporates a pharmacokinetic module for therapeutic drug monitoring applications and is recommended by the Dutch Society of Hospital Pharmacists as the standard program for dosage determination.[14] The list of packages and programs described herein is by no means exhaustive and merely serves as a guide to the features of some of the commonly available software. It is difficult to choose or recommend the ‘right’ software package for teaching pharmacokinetics in the health sciences, a choice made even harder by the fact that there is very little data concerned with a formal evaluation of the educational impact of computer-assisted learning in pharmacokinetics. It is doubtful if many of us have ever made a determined effort to properly assess whether learning outcomes we seek in our students are actually achieved and, more importantly, retained and applied in discharging professional responsibilities. Nonetheless, many good programs have been written which go some way towards serving the specific requirements of a course or a given group of students (e.g. medical, pharmacy, nursing, veterinary or basic science). Whatever software is chosen, more useful and productive learning outcomes might be expected if the computer simulations and modelling are integrated with tutorials, case studies, or other didactic material such as full-scale, simulator-based exercises.[6,8,12] Recently, towards this goal, we began to use PharmaCalc as a tool in clinical problem© Adis International Limited. All rights reserved.

Charles & Duffull

based learning tutorials (see Appendix I). Student feedback has been very positive. The right package is one which achieves the desired teaching objectives and above all, makes students feel more kindly disposed and comfortable with pharmacokinetics than previously. Appendix I. PharmacCalc Undergraduate Tutorial Exercise from the School of Pharmacy, University of Queensland Background

A male patient (age 4 years, bodyweight 36kg, estimated creatinine clearance 140 ml/min) has contracted a nosocomial lower respiratory tract infection and is to be treated with amoxicillin/potassium clavulanate by mouth. The patient cannot take solid dosage forms. You have access to recent data which indicates that more than 80% of isolates from sputum in this hospital were identified as Haemophilus influenzae, and that in vitro sensitivity tests gave minimum inhibitory concentration (MIC) values between 2 and 8 mg/L for amoxicillin-potassium clavulanate (MIC of amoxicillin alone is 64 to 128 mg/L). Task

Prescribe a suitable treatment (product, dose and dosage frequency) which addresses this scenario. In your report, you should provide a graph of the serum concentration-time profile together with the pharmacokinetic values you used. Any assumptions or precautions that apply should be stated and justified. Furthermore, you should provide a pharmacokinetic rationale for selecting your initial regimen of amoxicillin. Process and Desired Learning Outcomes

This case places the pharmacokinetic exercise in a clinical context which involves treatment of a commonly-encountered infection with a widelyused antibacterial and reinforces links with the content of courses taught in the same semester/ year. These include microbiology (MIC, common human pathogens and drug resistance), applied physiology (renal function, via estimated creatinine clearance) and clinical epidemiology (incidence of Clin Pharmacokinet 2001; 40 (6)

Software for Teaching Pharmacokinetics

particular bacterial pathogens). It also includes elements of the pharmacodynamics of antimicrobial action since students are taught that β-lactam antimicrobials are time-dependent in their action such that (unbound) serum concentrations should remain above the MIC of the suspected or confirmed pathogens for between 25 to 50% of the dosage interval; the proportion of the dosage interval, however, can vary with the pathogen involved with shorter times being needed for staphylococci and longer times for streptococci and Gram-negative bacilli. Thus, the dosages recommended by the student should address these requirements. Astute students determined that the population values given in the drug library file are, in fact, adult values and consequently they accessed the literature for paediatric amoxicillin pharmacokinetic parameter values. The task specifically requires a pharmacokinetic rationale for the initial attempt at dosage selection, thus reinforcing basic kinetic principles taught previously:

Css p

=

Dö τ ÷ø CL

æ çF è

⋅

where Css p is plasma concentration at steady state, F is bioavailability, D is dose, τ is dosage interval and CL is total body clearance. This provides a reasonable starting point since it is a requirement that the unbound drug concentrations should remain greater than the MIC for 25 to 50% of the time. Furthermore, PharmaCalc requires values for volume of distribution (Vd) and half-life (t1⁄2), rather than CL, thereby requiring recollection of the relationship between primary and secondary pharmacokinetic parameters. The protein binding of amoxicillin has to be obtained from the literature. The remainder of the exercise requires knowledge of practical pharmacotherapeutics to select a liquid amoxicillin-clavulanate product and to fine-tune the pharmacokinetic simulations to arrive at a (feasible) recommendation on the vol-

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ume of medication and the dosage frequency for a hospitalised child. References 1. Bourne DWA, Triggs EJ, Eadie MJ. Pharmacokinetics for the non-mathematical. Lancaster: MTP Press, 1986 2. Lesh R, Post T, Behr M. Dienes revisited: multiple embodiments in computer environments. In: Wirzup I, Streit R, editors. Development in school mathematics around the world. Reston (VA): National Council of Teachers of Mathematics, 1987: 647-80 3. Kaput JJ. Technology and mathematics education. In: Grouws DA, editor. Handbook of research on mathematics teaching and learning: a project of the National Council of Teachers of Mathematics. New York: Macmillan, 1992 4. Danek A, Poczatek J. A simple electronic circuit for simulation of pharmacokinetic processes. Arzneimettel Forschung (Drug Res) 1976; 26: 321-4 5. Johnson F, Wilson CG. A microprocessor-based simulator for teaching pharmacokinetics [proceedings]. Br J Pharmacol 1979; 67: 502P-3P 6. Aarons L, Foster RW, Hollingsworth M, et al. Computer-assisted learning lessons in drug disposition and pharmacokinetics. J Pharmacol Methods 1988; 20: 109-23 7. Navarro JDS, Alvarez JAT, Ortega FP, et al. A DYNAMO application of microcomputer-based simulation in health sciences teaching. Int J Nurs Stud 1993; 30: 425-36 8. Feldman RD, Schoenwald R, Kane J. Development of a computer-based instructional system in pharmacokinetics: efficacy in clinical pharmacology teaching for senior medical students. J Clin Pharmacol 1989; 29: 158-61 9. Garfield JM, Paskin S, Philip JH. An evaluation of the effectiveness of a computer simulation of anaesthetic uptake and distribution as a teaching tool. Med Educ 1989; 23: 457-62 10. Jean Y, De Traversay J, Lemieux P. Teaching cancer chemotherapy by means of a computer simulation. Int J Biomed Comput 1994; 36: 273-80 11. Le Normand Y, Drugeon HB, Potel G, et al. Teaching individualized antibiotic dosage regimens by means of two computer-assisted learning programs. Int J Biomed Comput 1994; 36: 117-9 12. MacFadyen JC, Brown JE, Schoenwald R, et al. The effectiveness of teaching clinical pharmacokinetics by computer. Clin Pharmacol Ther 1993; 53: 617-21 13. Buffington DE, Lampasona V, Chandler MH. Computers in pharmacokinetics: choosing software for clinical decision making. Clin Pharmacokinet 1993; 25: 205-16 14. Neef C, Proost JH, Meijer DKF. Therapeutic drug monitoring with MW/PHARM. Int J Biomed Comput 1994; 36: 151-2

Correspondence and offprints: Professor Bruce Charles, The Australian Centre for Paediatric Pharmacokinetics, School of Pharmacy, The University of Queensland, QLD 4072, Australia. E-mail: [email protected]

Clin Pharmacokinet 2001; 40 (6)