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<strong>Pharmacokinetics</strong>Single intravenous bolus injection into one compartmentWe re-arrange the standard equation:C t= C 0x e -KtCt / C 0= e -Kt20mg/L / 35mg/L = e -0.045h-1 x t0.57= e -0.045h-1 x t (Take natural logs of both sides)Ln(0.57) = -0.045h -1 x t (Use the Ln button on your calculator to obtain natural log of 0.57)-0.56 = -0.045h -1 x t-0.56 / -0.045h -1 = tt = 12.4hA clinical judgement can now be made as to whether we can wait 12 hours for drug levels to fall spontaneously or whetherartificial means such as hemodialysis are required to speed up the process.5.3 Area Under the Curve (AUC)Having become familiar with concentration versus time graphs, we can introduce a further pharmacokinetic parameter– the Area Under the Curve or AUC. The AUC is quite literally the area under a concentration versus time graph. Seeshaded area in Figure 5.4.Conc (mg/L)321• Area under the concentrationversus time curve• ‘Area Under the Curve’• AUC00 2 4 6 8 10Time (h)Figure 5.4 The Area Under the Curve (AUC)The process of obtaining any area consists essentially of multiplying the height of a figure by its width. The height of thisfigure is measured in concentration units (mass/volume); mg/L in this particular case. The width is in time units; hours inthis case. Hence this AUC would have units of mg.L -1 .h. However, the tidy-minded like to re-arrange the units to mg.h.L -1as it looks prettier. In general, the units of AUC should always be Mass.Time.Vol -1 .Sometimes we want to refer to the area between specific time limits. Figure 5.5 shows a case where we refer to the areabetween 2 and 4 hours. We simply add a subscript to the AUC to indicate the relevant time interval. Any reference to‘AUC’ without time limits can be taken to refer to the full AUC (i.e. between zero and infinity time). Thus AUC is generallyequivalent to AUC 0-∞.52Download free ebooks at bookboon.com
<strong>Pharmacokinetics</strong>Single intravenous bolus injection into one compartmentConc (mg/L)321AUC 2-4h00 2 4 6 8 10Time (h)Figure 5.5 An AUC between specified time limitsAUC will clearly be related to dose, but the efficiency of elimination also has to be accounted for using clearance as theappropriate marker.AUC = F.D / ClThe derivation of this relationship is given in Appendix 2 to this chapter. We will use this relationship in Chapter 9 whendetermining bioavailability.Please click the advert53Download free ebooks at bookboon.com
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