102 trends in analytical chem&try, vol. 5, no. 4, 1986

(1969) 157. 11 A. G. Fogg and A. M. Summan, Analyst (London), 108

(1983) 691, and references cited therein. 12 G. Ali Qureshi, G. Svehla and M. A. Leonard, Analyst

(London), 104 (1979) 705. 13 A. B. P. Lever and P. C. Minor, Inorg. Chem., 20 (1981)

4015, and references cited therein. 14 J. F. C. Boodts, R. Rudnytskij and J. R. Romero, J. Electro-

anal. Chem., 149 (1983) 139, and references therein. 15 M. M. Ghoneim, A. M. Khalil and A. M. Hassanein, Elec-

trochim. Acta, 21 (1979) 623. 16 A. S. N. Murthy and K. S. Reddy, J. Chem. Soc. Faraday

Trans. 1, 80 (1984) 2745. 17 J. Barek, A. Berka and K. Jakubec, Microchem. J., 24

(1979) 484.

18 J. Barek, A. Berka and K. Jakubec, Microchem. J., 25 (1980) 421.

19 D. A. Ben-Efraim, in S. Patai (Editor), The Chemistry of Diazonium and Diazo-Groups, Part 1, Wiley, New York, 1978, p. 149.

20 J. P. Stradins and V. T. Glezer, in A. J. Bard and H. Lund (Editors), Encyclopedia of Electrochemistry of Elements, Vol. 13, Marcel Dekker, New York, p. 197.

P. M. Bersier and J. Bersier are at the Central Analytical Depart- ment and the Central Research Laboratories, respectively, CIBA- GEIGY, Basle, Switserland.

Drug assay in therapeutic monitoring Stephen H. Curry Gainesville, FL, U.S.A.

Biomedical drug analysis has developed in recent years into a major branch of applied analytical chemistry. Data ob- tained are used in characterization of drugs, in optimization of therapy, in reduction of side effects, and in reduction of overall long-term exposure. Methods used commonly exploit instrumental chromatography, particularly high-perform- ance liquid chromatography, but packaged methods, such as those using enzyme multiplied immunoassay techniques, are of major importance. Pharmacokinetic calculations are de- signed to optimize dosing decisions based on limited amounts of data.

Biomedical drug analysis has been important for at least 60 years 1. However, it was post-war escalating interest, first in relation to identification of drug me- tabolites, later in relation to descriptive pharmacoki- netics, and most recently in monitoring as a compo- nent of patient care, that precipitated drug assay to the forefront of applied analytical chemistry 2-5. In an earlier review in this journal 6, it was shown that the objective of drug analysis is production of an ac- curate assessment of the concentration of a partic- ular drug, in biological material such as plasma. Cri- teria for method evaluation are sensitivity, specifici- ty, precision and accuracy. Once an adequate assay becomes available, the pharmacokinetic properties of the drug are commonly characterized by means of multiple-sample studies following single doses in healthy volunteers, and following both single doses and dosing to so-called "steady state" in patients. The typical single dose descriptive concentration growth and decay curve was discussed in the earlier review 6. The present review is concerned with appli- cation of assays, and of the descriptive pharmacoki-

netic data to which assays lead, in monitoring pro- grammes designed to facilitate dosage adjustment. Lithium, theophylline, digoxin, gentamicin and phe- nytoin are considered as examples.

Lithium Lithium is usually assayed by means of flame pho-

tometry, using either atomic absorption spectro- scopy or emission flame photometry. There are no metabolites, and the drug displays first order elimi- nation kinetics with a half-life of 14-33 h. There are usually no dramatic kinetic changes with prolonged treatment, and steady state is reached three to seven days after starting treatment. Lithium is usually measured in serum. At steady state there is fluctua- tion, with serum concentration rises of 15-30% above "trough" (early morning, pre-dose or base- line) levels if doses are given every 8 h. The thera- peutic concentration range is approximately 0.3-1.3 mmol/1, with severe toxicity occurring at concentra- tions above 2.0 mmol/1. In the long term, lithium can cause kidney damage, and when this occurs the half- life of lithium, which is excreted in urine, increases, and if the dose is not reduced, the serum concentra- tion rises, providing a vicious circle of a self-perpetu- ating drug-induced disease problem. Monitoring is usually designed to keep the trough concentration below 1.3 mmol/l, or to maintain lower levels if pos- sible, consistent with good response, so that overall long-term exposure, and hence the risk of renal da- mage, is minimized. In the absence of renal damage, lithium kinetics are predictable, and dose changes produce proportional changes in serum concentra- tions, obviating the need for complex pharmacoki- netic calculations.

0165-9936/86/$02.00. © Elsevier Science Publishers B .V.

trends, in analytical chemistry, vol. 5, no. 4, 1986 103

Theophylline Theophylline has a half-life in the range 4-12 h.

Since 6 h is the shortest practicable dosing interval for a drug given long-term with a need for continu- ous 24-h per day therapy, there is a strong possibility of the fall from peak to trough concentration being more than a 50% reduction. Since the therapeutic range is 10-20 ktg/ml (only a two-fold difference be- tween minimum effective concentration and maxi- mum acceptable level) dosing would appear to inevi- tably cause either toxicity or inadequate treatment in patients in whom the half life is less than 6 h. Titra- tion to the therapeutic range therefore requires monitoring in almost all patients. Monitoring in- volves theophylline measurement in plasma using high-performance liquid chromatography (HPLC) or enzyme multiplied immunoassay (EMIT) tech- niques or equivalent technology, dosage with con- trolled release forms of theophylline to damp down fluctuation and to permit 12-h dosing intervals, and linear adjustment of doses once individual needs are characterized. The usual sampling time is 2-4 h post dosage, approximately at the time of concentration maxima.

Digoxin Like lithium and theophylline, digoxin displays

reasonably predictable kinetics, and plasma level changes are proportional to dosage. The digoxin half-life is approximately 40 h, with a major influ- ence of renal function, which is commonly impaired in the patients who receive digoxin. Monitoring usually involves concentrations late in a chosen do- sage period, or even trough concentrations, as dig- oxin is considered to be a "two-compartment" drug, and its site of action is in the compartment with the slower drug penetration rate. As a result, equilibri- um between the concentrations at the site of action and in plasma is not reached until 4-5 h after each dose. The therapeutic range is approximately 0.9-2.2 ng/ml. Assays can be biological or chemical, but the commonest technique is radioimmunoassay. A particular feature of digoxin is that toxicity (atrial fibrillation) can resemble pathology for which digox- in is sometimes prescribed, such that in a fibrillating patient, a plasma digoxin measurement is needed in order to determine whether dosage should be de- creased or increased.

Gentamicin Gentamicin is different from lithium, theophylline

and digoxin in that fluctuation between peaks and troughs is desirable. It has been shown that therapy requires peaks above 5 /~g/ml, but that toxicity is likely if troughs are not below 2 ~g/ml. Gent~micin is

assayed by HPLC, microbial, radioimmunoassay or EMIT or equivalent methods. An early dose is used for calibration of the patient. The dose is infused for 30-60 min, then a 30-60 min interval elapses before a "peak" concentration is measured. This interval is to allow for distribution equilibrium to be reached between tissues and plasma, as gentamicin is a multi- compartment drug. A second plasma sample is ob- tained just before the next dose, and a two-point half-life is calculated. Simple pharmacokinetic calcu- lations are then performed to adjust the peak to be- tween 5 and 12/~g/ml (depending on the characteris- tics of the infection involved), and the trough to be- low 2/~g/ml. The peak is adjusted by changing the dose; the trough is adjusted by changing the dosage interval. Finally, the dose and dosing interval are fine-tuned to meet the needs of convenience. For ex- ample, dosing intervals need to be simple fractions of 24 h. Fig. 1 shows a typical pattern of devel- opment of an optimum gentamicin dosing regimen. Monitoring is a relatively fast method, compared with observation of response, for optimizing genta- micin therapy.

20

O1

10 9 8 7

6

5

4

i\

1 2 8 14.25 20

24

1'5 3'0 h

Fig. 1. Development o f a gentamicin dosing regimen. The graph shows concentration in plasma (txg/ml) vs. time (h) data following a test dose o f 60 rag, and assays at2 and 8 h after starting the 1-h infusion. A 90-mg dose was proposed, predicting a peak concen- tration o f 7.5 and a trough o f 2.0 at approximately 20 h. A lO0-mg dose was then proposed, giving an acceptable peak, and a trough below 2.0 at a convenient dosing interval o f 24 h.

Phenytoin Phenytoin is unusual among monitored drugs in

that it shows dose dependent pharmacokinetics. The result is non-linear decay of plasma concentrations, relatively long times to steady state with relatively

1 0 4 trends in analytical chemistry, vol. 5, no. 4, 1986

high doses, and relatively large increments in plasma concentration caused by relatively small increases in dose at relatively high levels. Since the therapeutic range is narrow (10-20 ktg/ml), small changes in do- sage can cause dramatic changes in therapy. Also, since phenytoin is given to reduce the incidence of medical crises, the therapeutic end point is difficult to define in the short term.

Phenytoin is assayed by chromatographic or EMIT or equivalent methods. There is little peak to trough fluctuation and so the sampling time is unim- portant. It is possible to calculate a Vma x (dosing rate at which plasma level changes occur at the maximum rate) and an apparent K m (plasma concentration at 0.5 x Vmax) from a two point calibration graph ob- tained by plotting dosing rate against dosing rate/ steady state concentration. Data are collected by dosing to steady state with one regimen, measuring Cps s, then dosing to a new steady state with another regimen, and measuring Cps s again. Up to six weeks are required to reach steady state with each regi- men. Knowing Vma x and K m for the patient, the CPs s predicted to occur with any regimen from 0 to Vma x mg phenytoin per day can be calculated. A regimen giving Cp~ between 10 and 20 ktg/ml can then be de- vised. Fig. 2 shows a g~aph of Cp~ against daily dose for a patient in whom Vma x was 731 mg per day and K m w a s 7 .6 ktg/ml.

30

E ~. 20

==

10

/

200 400 600 Dose (mg per doy)

Fig. 2. Simulated steady state plasma phenytoin (Cpss, ktglml) as a function of daily dose (rag per day) in a patient in whom V,~o~ was 731.25 mg per day and Km was 7.62/~g/ml. This simulation was developed using two data points (5.3/~g/ml at 300 mg per day and 9.2 ¢tg/ml at 400 mg per day). Programs illustrating Figs. 1 and 2 are available for T1-55, EL-512, HP 33C and EC-4004 pocket calculators on request to the author.

General considerations Clinical monitoring, of necessity, involves use of

limited numbers of samples. The guiding principle in this important area of applied analytical chemistry is

the use of top quality, highly specific, assays applied to clinical samples such that the data obtained can be related to basic knowledge of the clinical pharmacol- ogy of the drug in question in the quest for optimized therapy. Because important clinical decisions are based on limited data, assay reliability with coeffi- cient of variation figures no greater than 2% is usual- ly sought. The examples discussed illustrate the ap- plicability of monitoring to cases where: (i) there is potential toxicity with a poorly defined clinical end- point (phenytoin); (ii) the drug has a narrow thera- peutic range (phenytoin, lithium, theophylline and digoxin), (iii) a pharmacokinetic measurement will lead to relatively fast clinical decisions (gentamicin); (iv) unwanted effects of the drug are similar to the illness being treated (digoxin); (v) plasma concen- trations and response are not linearly related to dose (phenytoin); (vi) there may be compliance problems (all examples); and (vii) reduction of overall expo- sure to a minimum reduces the risk of long:term tox- icity (lithium, phenytoin and gentamicin). Drugs other than the five discussed in detail, and some- times monitored, include cephalosporins 4, propra- nolol, lidocaine, procainamide, and quinidine 4, tri- cyclic antidepressants 4,7 and neuroleptics 8.

APPENDIX

Introduction to pharmacokinetics The half-life (tl/2) of a drug is the time for the drug

concentration to fall by 50%. With exponential de- cline, the tl/2 is a constant for given circumstances. It is however much affected by physiological and path- ological influences. The apparent volume of distri- bution of a drug (Vd) is the volume of fluid which the drug would occupy if it was evenly distributed through that volume at the concentration measured in plasma. The first order rate constant of decline of plasma concentration (kel) is defined by:

kel = 0.693/@2 (1)

Clearance (Cl) is defined by:

Cl = Vd.kel (2)

If we measure the area under the curve (AUC) of the graph of concentration against time:

AUC = dose~el (3)

At steady state the mean steady state concentration, Cpss.mean , is defined by:

CPss.mean = ko/Vd" eel (4)

where k 0 is the dosing rate. Hence:

trends in andlytical chemistry, vol. 5, no. 4, 1986 105

A

Cp CPss.meo~

I i I a a, /q

Time

Fig. 3. The relationship between drug plasma concentrations after a single dose (A), and after dosing to a "steady state" in which in- put (dosing rate) is equal to output (daily elimination rate) (B). The two hatched areas are identical.

CPss.mea n oc k 0 oc tl/2

1/Cl ~c l/kel

Provided there are no changes in tl/2 or kel , A U C (first dose) is equal to AUCss (the A U C within one dosage interval at steady state) (Fig. 3). Since:

AUCss = CPss.mean.1- (5)

where r is the dosing interval, much can be learned from a single point assay at steady state, provided that the assay has high precision and accuracy. Note that following an intravenous dose of a drug, if con- centration decay is monoexponential :

Cpt = Cp0 e -kelt (6)

where Cpt is the concentration in plasma measured at any time t, and Cp0 is the theoretical concentration obtained by back extrapolation to t -- 0. V d is then given by:

Vd = dose/CP0 (7)

Taking logarithms:

In Cpt = In Cp0 - kelt (8)

showing that a graph of In Cpt against t is a straight line from which Cpo and kel can be obtained graphi- cally or using a linear regression programme.

At steady state, there is fluctuation between maxi- ma (peaks) and minima (troughs). The extent of fluctuation is governed by the ratio "g/tl/2. Fluctuation is relatively great when this ratio is high. The thera- peutic range is a concentration range between an up- per limit above which unwanted effects occur, and a lower limit below which therapy is inadequate. Corn-

pliance is the phenomenon of patient obedience to prescribing instructions. A pharmacokinet ic com- par tment is a notional body area defined according to drug penetrat ion rate criteria, detected by means of concentration measurements in plasma.

Phenytoin exhibits Michaelis-Menten kinetics. As such, at steady state, when the rate of change of con- centration is plasma is zero, the following equation holds true:

Vmax Css'mean (9)

k 0 = Km + Css.mean

where Vma~ Js the maximum possible elimination rate and K m is the concentration in plasma at half-maxi- mal eliminatl,~n rate. Rearrangement gives:

k0 k 0 = Vma x " g m (10)

Css -nean

such that a graph ot k 0 versus ko/Css.mean is a straight line with intercept on the y axis of Vma x and a slope of - K m. From this:

k0 Km Css mean -- (11)

Vma x - k 0

k 0 indicates the zero-order dosing rate.

R e f e r e n c e s 1 B.B. Brodie, J. Am. Med. Assoc., 13 (1967) 600-603. 2 B.B. Brodie, S. Udenfriend and J.E. Baer, J. Biol. Chem.,

168 (1944) 299-309. 3 M. Rowland and T.N. Tozer, Clinical Pharmacokinetics, Lea

& Febiger, Philadelphia, 1980. 4 W.E. Evans, J.J. Shentag and W.J. Jusko, (Editors), Applied

Pharmacokinetics, Applied Therapeutics, San Francisco, 1980.

5 L.Z. Benet, N. Massoud and J.G. Gambertoglio, Pharmaco- kinetic Basis for Drug Treatment, Raven Press, New York, 1983.

6 R.V. Smith, Trends Anal. Chem., 3 (1984) 178-181. 7 C.L. DeVane, in W.E. Evans, J.J. Shentag and W.J. Jusko

(Editors), Applied Pharmacokinetics, Applied Therapeutics, San Francisco, 1980, pp. 549-585.

8 S.H. Curry, J. Clin. Psychopharmacol., 5 (1985)263-271.

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