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A SEMINARON CONCEPTS OF CLEARANCE BY MURALI MANOHAR T Mpharmacy 1st semester(ceutics) St Peters Institute of Pharmaceutical Sciences Hanamkonda, Warangal - 506001




INTRODUCTION Clearance is a parameter that has, perhaps, the greatest potential of any pharmacokinetic parameter for clinical applications. Furthermore, it is the most useful parameter available for the evaluation of the elimination mechanism and of the eliminating organs (kidney and liver). The utility of the clearance measurement lies in its intrinsic model independence. Clearance can also be defined as ‘‘the hypothetical volume of blood (plasma or serum) or other biological fluids from which the drug is totally and irreversibly removed per unit time.’’ The abbreviation ‘‘Cl’’ is used for clearance in mathematical manipulations It is expressed in ml/min


ORGAN CLEARANCE A single, well perfused organ that is capable of drug elimination is taken to understand clearance Rate of elimination = CAQ − CVQ = Q(CA − CV) (1) Fig 1. Flow model for drug clearance by an organ. The term Q denotes blood flow rate through the organ and the terms CA and Cv denote drug concentrations in arterial and venous blood, respectively.

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If one compares the rate of drug elimination with the rate at which drug enters the organ, one obtains a dimensionless quantity that is termed the extraction ratio, ER: we can define the organ clearance of a drug as the product of extraction ratio and flow: It follows that the ratio of clearance to flow is equal to the extraction ratio. (2) (3 )


TOTAL CLEARANCE Total or systemic clearance is the sum of all individual organ clearances that contribute to the overall elimination of a drug. Total or systemic clearance ClS ClS = dx/dt C ClS = D/AUC We can also show that the systemic clearance of a drug is equal to the infusion rate kO divided by the steady-state concentration CSS of drug in blood or plasma after prolonged constant rate intravenous infusion: ClS = K0/CSS (4) (5) (6) (7)


HEPATIC CLEARANCE The difference between systemic clearance and renal clearance is often termed nonrenal clearance. For drugs that are virtually completely metabolized (i .e . , renal clearance is negligible), we can sometimes assume that systemic clearance is equal to hepatic clearance, in this case ClH = QH . ER The relationship between hepatic blood flow and extraction ratio has been derived using a perfusion model which is presented here. Consider the model in Fig.(2) and assume that a bolus of drug is introduced into the reservoir yielding an initial concentration Ci. The principles of mass balance require the following relationships to exist: (8) (9)

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Fig 2. Schematic representation of an isolated perfused organ system consisting of a reservoir and an eliminating organ.

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Solving Eqs. (9) and (10) for Ci and Co in the usual manner, we obtain Since clearance is equal to the ratio of dose to area it follows that (10) (11) (12) (14) (15) (16)

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For many drugs, including antipyrine, most barbiturates, anticonvulsants , hypoglycemic agents, and coumarin anticoagulants, we find that the intrinsic clearance in humans is considerably smaller than hepatic blood flow. If Q » ClI it follows that Eq. (16) reduces to In recent years it has come to light that some drugs, including many analgesics, tricyclic antidepressants, and beta blockers, have intrinsic clearance values in humans that significantly exceed hepatic blood flow. The systemic clearance of such drugs shows a strong dependence on hepatic blood flow. The reason for this is easily demonstrated by considering a second limiting case for Eq. (16) If CII »Q, then (17) (18)


HEPATIC CLEARANCE AND DRUG BINDING IN BLOOD Most drugs are bound to blood constituents, particularly to plasma proteins. To take blood binding into account Eq (16) , must be modified to The drug concentration in blood may be calculated from the drug concentration in plasma by means of the following relationship: (19) (20) (21)

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Fig . 3 Lack of correlation between the systemic clearance of propranolol and fraction of drug in the blood that is unbound. Because of propronolol’s high hepatic clearance ratio, its clearance is largely dependent on hepatic blood flow and relatively independent of drug binding in the blood or hepatic clearance

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Fig . 4 Relationship between extraction ratio and fraction of drug in the blood that is unbound, for a drug (under physiological conditions) with a high extraction ratio (propranolol), one that has a low extraction ratio (warfarin), and a third that has an intermediate extraction ratio (phenytoin), in the isolated perfused rat liver.

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For drugs that show a low extraction ratio (i. e., Fb Cl'I << Q), Eq. ( ) reduces to These drugs are said to be restricted in their hepatic metabolism. Systemic clearance is a function of both binding in the blood and the intrinsic ability of the liver to eliminate the drug. Perturbations that affect plasma protein binding will have a direct effect on the clearance of such drugs (see warfarin and phenytoin in Fig. 5 On the other hand. for drugs that show a high extraction ratio (ie., fBCl'I » Q), Eq. (19) reduces to Eq. (18) (i.e . , the systemic clearance approximates hepatic blood flow). The clearance of these so-called nonrestricted drugs is largely independent of changes in plasma protein binding (see propranolol in Fig. 5) (22)


DRUG BINDING AND FREE DRUG CONCENTRATION Total drug levels in blood after continuous constant rate intravenous infusion to steady state are given by CSS = K0/Cl And free drug levels are given by CSS, free = fB k0/Cl For a restricted drug CSS = K0/fB ClI And CSS,free = k0/ClI For a totally non restricted drug, CSS = K0/Q And that CSSfree = fB k0/Q (23) (24) (25) (26) (27) (28)


HALF LIFE, INTRINSIC CLEARANCE AND BINDING The half-life of a drug is related to its apparent volume of distribution and its systemic clearance: t1/2 = 0.693 V/ClS where V = VB + FB/FT VT and by substituting for Eq. (19) for CIs. to obtain t1/2 = VB + VT (FB/fT) ( 0.693) Q (FB Cl'I)/(Q + FB C'l It follows that for a drug with a high extraction ratio t1/2 = VB + VT (FB/FT) (0.693) Q whereas for a drug with a low extraction ratio t1/2 = VB + VT (FB/FT) (0.693) FB Cl'I (29) (30) (31)


FIRST PASS EFFECT A particularly important characteristic of drugs that show a high hepatic extraction ratio, typified by propranolol or lidocaine, is that on oral administration presystemic or first pass metabolism is significant. The fraction F of an oral dose that reaches the systemic circulation, assuming complete absorption, is given by F = 1 – ER Recognizing that F is simply the ratio of area under the curve after oral adminstration to that after intravenous administration and that ER is a function of intrinsic clearance and blood flow we may rewrite Eq (16), (32)

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AUCoral = 1 - ClI D(Q + ClI) = D = ClORAL Cloral = Q (ClI) (Q + ClI) Q(Q + ClI) The equations presented above indicate that the area under the drug concentration in blood versus time curve after oral administration under conditions of constant hepatic blood flow is a function of administered dose (assuming complete absorption) and intrinsic clearance but is independent of blood flow. However, AUCoral is given by AUCoral = FD ⁄ Cl AUCi.v Q + ClI (Q)AUCi.v AUCoral (33) (34) (35) (36)

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Fig . 5 Drug concentration in plasma after oral administration of a drug with a high hepatic extraction ratio under fasting and nonfasting conditions. The lower curve (labeled fasting) was simulated by maintaining hepatic blood flow constant at 1. 5 liters/min throughout observation period

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Assuming that absorption is complete and elimination occurs solely by hepatic metabolism, the extraction ratio is given by ER = 1 − F Rearranging Eq. (16) we obtain Q = Cl ER Then, F = 1 − ER = 1 - Q . ER = 1 − Cl = D Q Q Q.AUCi.v If we multiply Eq.(39) by AUCoral, we obtain F . AUCoral = AUCoral − FD Q F = Q = Q Q + (D/AUCoral) Q + ClI For partially excreted unchanged drugs in Eq. Cl is replaced by hepatic clearance ClH ClH = Cl − Clr (37) (38) (39) (40) (41) (42)


GUT WALL CLEARANCE Fig .6 Flow model describing the perfusion of the gastrointestinal tract and liver and showing the course of drug given orally and intravenously. After oral administration the drug is potentially subject to first-pass effects in the gut wall and in the liver.

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The systemic availability F of drugs subject to both first-pass hepatic and intestinal mucosa metabolism has also been considered . Under certain conditions (see the model in Fig. ), it can be shown that F is given by F = QHV QPV (QHV + ClHI) (QPV + ClGI In the absence of significant first pass hepatic metabolism (i.e., ClHV << QHV), above Eq(43), reduces to F = QPV QPV + ClGI which can be rearranged to give F = 1 − D AUCi.v . QPV (43) (44) (45)


LUNG CLEARANCE Fig . 7 Schematic representation of the anatomical positions of the potential sites of drug elimination (i.e., the gastrointestinal tract, the liver, and the lung) and of several routes of administration, including oral (p.o.), hepatic portal vein (h.p.v.), intravenous (i.v) , and intra-arterial (i.a.}.

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In the absence of drug metabolism by the lung the systemic availability of a drug is given by the well-known equation Foral = AUCoral AUCi.v when drug clearance by the lung is significant. Under these conditions a more appropriate expression for absolute availability is Foral = AUCoral AUCi.a As shown in Fig.7 , the gastrointestinal mucosa, the liver and the lung are arranged in series, then Foral = fHfL, Fh.p.v = fH fL, Fi.v = fL It follows that fG = AUCoral AUCi.v fH = AUCi.v AUCi.v fL = AUCi.v AUCi.a (46) (47) (48) (49) (50)


RENAL CLEARANCE Renal excretion of a drug is determined by filtration, active secretion, and reabsorption. Renal clearance Clr can be described by the following equation CIr = (CIrf + CIrs )(1 - FR) where Clrf is renal filtration clearance. Clrs is renal secretion clearance and FR is the fraction of drug filtered and secreted that is reabsorbed. The renal filtration clearance (Clrf ) may be expressed as Clrf = fBClcr the renal secretion is given by following equation (51) (52)

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The renal clearance is given by If QK » fBCI'(K). The above equation reduces to Clr = fB(Clcr + Cl'(K) » (1 - FR) (53) (54) (55)

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If tubular reabsorption is prevented FR = 0 On the other hand, if tubular secretion is blocked CI'(K) = 0 CI'(K) can be calculated by rearranging Eq. (55) (56) (57)

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Considering the other limiting case for Eq. [i. e. , fBCl'(K) » QK] we find In this case a plot of renal clearance versus fB should be linear and have a positive intercept. Dividing the slope of a plot of Clr versus fB by its intercept yields (58) (59) (60)


PHYSICAL MODELS OF DRUG CLEARANCE Two models are considered here 1. well stirred model 2. parallel tube model An alternative to the "well-stirred" model is the "parallel tube" model, which envisions that the eliminating organ is composed of a number of identical and parallel tubes with enzymes distributed uniformly along the tubes. Contrary to the assumptions of the well stirred model, the parallel tube model suggests that the concentration of unbound drug in emergent venous blood will be less than the average free drug concentration in the liver, which is given by (C‘a - C‘v)/ln (C‘a/C‘v) The corresponding equation for clearance according to the parallel tube model

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Fig .8 Concentration gradient of a drug across an eliminating organ as envisioned by the well-stirred model (above) and the parallel tube model (below). Ca and Cv denote drug concentrations in arterial and emergent venous blood.

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Cl = Q (1 − e−fB Cl'I ⁄ Q ). It is difficult to prove the validity of either one of these models or even to differentiate experimentally between them. In fact, for drugs with very high or very low extraction ratios, both models predict the same limiting equations for clearance Theoretical analysis of the two models of organ clearance has revealed that the most powerful discriminator between them is the effect of blood flow on either the emergent drug concentration in venous blood (Cout or Cv) of a drug with a very high extraction ratio [which is given by Cin (1 - ER) or Ca(l - ER)] or, in the case of hepatic clearance, the systemic availability F after oral administration of a drug with a very high extraction ratio (which is given by 1 - ER) For a drug with an extraction ratio of 0.95, systemic availability would be expected to increase from 5% to 9.5% upon doubling of hepatic blood flow from 1 to 2 ml/min per gram of liver for the well-stirred model. An increase from 5% to 22.4% would be expected under the same circumstances for the parallel tube model .


CONCLUSION Pharmacokinetic theory of drug elimination has traditionally been based on rate concepts, and the apparent efficiency of elimination processes has usually been described in terms of first-order rate constants or half-lives. This approach has certainly been appropriate and useful for many applications but leads to rather serious problems when one wishes to apply pharmacokinetics in an anatomical/physiological context and to examine drug elimination in a mechanistic sense. So here an alternative approach that has been found to be much more valuable for such applications is the use of clearance parameters to characterize drug disposition is well explained.


REFERENCES Drugs and Pharmaceutical Sciences Volume 15 Pharmacokinetics Second Edition Revised and Expanded by Milo Gibaldi and Donald Perrier Basic Pharmacokinetics by Sunil S Jambhekar and Phillip J Breen Applied Biopharmaceutics and Pharmacokinetics Fifth Edition by Leon Shargel, Sussana Wu-Pong , Andrew. B.C. Yu.

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