Physiological pharmacokinetic modelling 1245Themeaning ofclearance becomes evident when drug eliminationis placed intophysiological perspective. To be eliminated, a substance must be delivered by theblood to an organ, usually the liver and/or the kidney. Therate of elimination of drugin the liver (dA/dt) is the difference between the rate of presentation in the arterialblood (QHCA) and the rate out in the venous blood (QHCV), where QH is the liverblood flow (i.e. 1-5litrelmin):dAdt - QH(CA-CV)According to its definition (equation (S)), hepatic clearance is:-dA/dtCL, =CACombining equations (15) and (16), hepatic whole blood clearance becomes:where E His the hepatic extraction ratio. Thehepatic extraction ratio is equal to one ifall drug is irreversibly extracted, and zero if no extraction occurs at all. Theextraction concept is valuable since it allows assessment of the effects of changes inblood flow, protein binding or enzyme activity on drug kinetics.One current model for metabolism ofdrugs in the liver assumesthat the unboundconcentrationleavingthe organ (Cu,v)is the concentrationto which the metabolizingenzymes are exposed. Thishas been referred to as the well-stirred model (Nies et al.1976, Pang and Rowland 1977a,b, Rowland 1972, Rowland et al. 1973, Wilkinson1975, Wilkinson and Shand 1975). In this model the rate of metabolism (dM/dt)isdirectly related to the unbound venous concentration:where CLu,intis the intrinsic clearance. Theintrinsic clearancemay be considered asthe sum of all enzymic processes involved in the elimination of the drug. Theextraction ratio may also be expressed in terms of intrinsic clearance (Tozer 1981):E H = cLu, i n t f u ,bQH +cLu, intfu, bThis relationship is extremely important since it allows one to explain how thehepatic clearance is influenced by changes in hepatic blood flow,protein binding andenzymatic activity.The hepatic clearance based on whole blood can also be expressed by:QHCLu, intfu,bCL,= QH -k cLu, intfu, bThis equation shows the dependency of CLb upon the various factors determiningthe hepatic extraction ratio.Xenobiotica Downloaded from informahealthcare.com by Monash University on 10/11/14For personal use only.1246 L. P. Balant and M . Gex-FabrySystemic availability. The fraction of dose reaching the systemic circulation ( F )can be defined as the product of the fraction ofthe dose entering the gut wall ( F J ,thefraction escaping loss on passing through the gut wall (FG)and the fraction escapingloss on passing through the liver (FH):F = FIFGFH (21)The fraction of drug escaping loss across the liver isFH'l-EHAccordingly, for a drugwith a high hepatic extraction ratio, the systemic availabilityis low, whereas for a drugwith a low extraction ratio F tends towards 1. Since E, is afunction of the intrinsic clearance, enzyme induction for example will modify thesystemic availability.Renal clearance.plasma concentration, the following equation may be written:When the rate of excretion of a drug is directly proportional toRenal clearance is usually expressed on the basis of concentrations measured inplasma or plasma water. If protein binding (i.e. f,) is saturable, CL, is not constantbut varies in function of the plasma concentration.The glomerular filtration of a drug may be expressed as a function of theglomerular filtration rate (GFR) and the fraction of drug unbound in plasma. If adrug is only filtered and all filtered drug is excreted into urine, then the rate ofexcretion is the rate of filtration, and the renal clearance based on plasma may beexpressed by:CL, =f,GFR (24)Active secretion and tubular reabsorption are additional phenomena which mayinfluence renal clearance. Depending on their relative importance it may beinteresting to calculate renal clearance values both for plasma and unboundconcentrations of drug. Iff, varies as a function of plasma concentration it may beshown thatthe renal clearance based on Cvaries, but that CLRbased on the unboundplasma concentration (C,) is constant.Influence of plasma protein bindingVolume of distribution. Because the volume of distribution depends on the bindingto plasma proteins (equation (12)), an alteration in binding, as occurs withdrug-drug interactions or in renal and hepatic diseases, produces a change in theapparent volume of distribution. An increase in the fraction unbound would beexpected to increase the volume ofdistribution,but the extent depends on how muchthe drug is usually bound to plasma proteins (figure 1(b)).Hepatic clearance. Binding of drug to plasma proteins inhibits drug removal bymetabolite formation or renal elimination, although different degrees of influence areexpected for highly extracted versus poorly extracted compounds (Wilkinson andShand 1975, Pang and Rowland 1977a,b).
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