Plasma clearance

Introduction

Plasma clearance is the most important of all pharmacokinetic (PK) parameters. It is almost systematically reported in PK papers but is only rarely actually used and almost never interpreted.

This review aims to explain what clearance is, why plasma clearance is the most important PK parameter, how to compute it, how to provide a physiological interpretation to its numerical value in domestic species, and what its main applications are in veterinary pharmacology. An authoritative review on this topic has been written by Wilkinson (1987). The descriptions in veterinary text books by Baggot (1977) and Riviere (1999) also provide good accounts.

The terminology ‘plasma clearance’: a preliminary comment

Plasma clearance is the term generally used, because plasma is the matrix most frequently used to measure circulating drug concentrations. When blood concentration is quantified, a blood clearance is computed. Blood and plasma clearances have the same numerical value as long as whole blood and plasma concentrations are equal. Whenever blood and plasma concentrations are different, attention should be paid to selection of the most appropriate matrix to evaluate the body capacity to eliminate a drug, and on the physiological interpretation of the calculated clearance (vide infra).

The plasma clearance measuring the overall ability of the living organism to eliminate a drug, is also termed total, systemic or body clearance. Unless stated otherwise, we will use all these terms as synonymous.

Why plasma clearance is the most important PK parameter

Plasma clearance is the most important PK parameter because it is one of the three determinants of a dosage rate. Figure 1 gives a pictorial view of the position of plasma clearance in relation to the dosing rate.

Equation 1 expresses formally the relationship between a dosing rate, the plasma clearance, the therapeutic plasma concentration in steady-state conditions and the systemic bioavailability:

()

where ‘Dosing rate’ is the dose per dosing interval (amount/time), ‘Clearance’ is the plasma clearance expressed for the given dosing interval (e.g. per day), ‘therapeutic concentration’ is the average effective target plasma concentration needed to obtain the desired clinical response, and ‘Bioavailability’ is a factor between 0 and 1. Bioavailability × Dose expresses the actual amount of drug that reaches the systemic circulation when a formulation is administered via extra-vascular route.

Inspection of Eqn 1 shows that a dose is not a genuine drug parameter but rather a PK/PD variable, because it is influenced by a PK parameter (plasma clearance), a PK variable (bioavailability for a particular route of administration and a given formulation), and a pharmacodynamic (PD) parameter (target therapeutic concentration) which reflects the in vivo drug potency (for more explanation see Toutain, 2002).

What is plasma clearance?

Plasma clearance is often defined as the plasma volume which is totally cleared of drug per unit of time. Unfortunately, this is not a formal definition of plasma clearance, but rather an operational statement that expresses what is being observed regardless of how it may be interpreted. To be clearly understood, plasma clearance, like any clearance (in vitro, in vivo, total, for a given organ…) should be formally defined as the ratio of two terms: a rate of drug elimination and the corresponding reference concentration (i.e. the driving concentration which ‘supplies’ the eliminatory processes) (Fig. 2). Therefore, any clearance is given by the following general relationship:

()

and in a more compact form:

()

where dx/dt (amount per time) is the rate of drug elimination at a given time t and C(t), the corresponding driving concentration. For plasma clearance, the rate of drug elimination is the total rate of drug body elimination, whilst the driving concentration is the plasma concentration. Therefore, plasma clearance is defined by the following equation:

()

The rationale for scaling (or normalizing) the total rate of drug body elimination by the corresponding plasma concentration is to express the ability of the body to eliminate a drug by a genuine parameter (a constant), rather than by an excretion rate which is a concentration-dependent variable for a drug following a first-order elimination process. If drug clearance does not obey a first-order elimination process, clearance is no longer a parameter but instead becomes a concentration-dependent variable.

Rearrangement of Eqn 4 allows computation of the amount of drug eliminated for a given snapshot plasma concentration:

()

Thus, plasma clearance corresponds to the proportionality constant linked to the rate of drug elimination and a given plasma concentration. The numerical value of body clearance depends on the measured matrix concentration [blood, total plasma or unbound (free) plasma concentration], and the following relationship holds:

()

where Cl_blood, Cl_plasma and Cl_free are the clearances corresponding to the total concentration in blood, total concentration in plasma, and free concentration in plasma. Free plasma clearance can be the relevant parameter to estimate when the binding of the drug to circulating proteins is nonlinear, the total plasma clearance being a concentration-dependent variable, whereas the unbound plasma clearance is a parameter. This is the case for inhibitors of the angiotensin-converting enzyme such as enalaprilat and benazeprilat (Toutain et al., 2000). Blood clearance can be the relevant parameter to estimate for the best physiological interpretation when blood and plasma concentrations are different (vide infra).

How to evaluate plasma clearance

The most frequent technique for estimating plasma (total) clearance (Cl_tot) consists of administering a single dose of the drug by the intravenous (i.v.) route and measuring sequentially plasma concentration until drug concentration in plasma is less than the limit of quantification. Then, the total clearance is derived from:

()

where ‘Dose’ is the administered dose and AUC, the area under the plasma concentration vs. time curve. AUC may be directly evaluated using a trapezoidal rule with or without extrapolation to infinity, or alternatively, by integrating the multiexponential function describing the drug disposition (Fig. 3). Whatever the method used, attention must be paid to the units of AUC which are often wrongly reported. For plasma concentrations measured in μg/mL and for time measured in hours, AUC unit is μg·h·mL⁻¹ (or μg·h/mL) not μg/h/mL!

Equation 7 is easily deduced from the definition of the clearance (Eqn 3). After rearrangement of Eqn 3, the following relationship holds:

()

Integrating both sides in relation to time from t = 0 to infinity, we obtain:

()

When clearance is a parameter, then:

()

and therefore

()

because the term is equal to the total amount of drug ultimately eliminated, i.e. to the administered dose after i.v. and is the total AUC, therefore, Eqn 11 is equal to Eqn 7.

An alternative to Eqn 7 is to measure plasma clearance in steady-state conditions after an intravenous infusion:

()

where K₀ is the infusion rate and C_ss, the plasma concentration at equilibrium (Fig. 3). Equation 12 is a direct application of Eqn 3, K₀, at equilibrium, being by definition, equal to the overall excretion rate. An advantage of intravenous infusion is avoidance of possible side-effects from high plasma concentrations obtained after a single i.v. bolus administration. In addition, plasma clearance at equilibrium can be theoretically obtained using a single snapshot plasma concentration. The limit of the steady-state approach is to ascertain achievement of equilibrium, which can be difficult for drugs having a long terminal half-life.

Regardless of the approach selected, the total dose considered in Eqn 7, or the infusion rate in Eqn 12 should give the amount of drug which actually gains access to the systemic (arterial) circulation. If a fraction of the i.v. dose is destroyed by a first-pass pulmonary effect before reaching the arterial circulation (vide infra), or if the administered agent is a pro-drug (e.g. an ester for corticosteroids) that requires metabolic transformation (e.g. hydrolysis), estimation of total clearance by Eqn 7 or 12 can be very misleading. Figure 4 illustrates the example of methylprednisolone, for which clearance has been calculated by injection of either methylprednisolone itself or methylprednisolone sodium succinate.

How to evaluate plasma clearance when it is not possible to administer the drug by the i.v. route

In some circumstances, the drug cannot be administered by the i.v. route but the estimation of a plasma (total) clearance (Cl_tot) may still be possible if the drug is totally eliminated by a route which is experimentally measurable (e.g. urine, faeces…). Indeed, in most instances, total plasma clearance is the sum of organ clearances, typically:

()

where Cl_renal is the renal clearance, Cl_liver is the hepatic clearance and Cl_other represents collectively all other clearance mechanisms.

Equation 13 expresses that clearances by the liver and the kidneys are additive. Generally, Cl_other is negligible and the plasma clearance is often the sum of renal and hepatic clearance. If Cl_liver is nil, Eqn 13 reduces to:

()

In this situation, the plasma clearance can be measured by injecting the drug by any route of administration (actual bioavailability is not an issue), and providing that the total amount of drug eliminated in urine is actually known (not the administered dose), the following relationship holds (Eqn 15):

()

where AUC is as defined for Eqn 7. The difference between Eqn 7 (Dose/AUC) and Eqn 15 is that the former uses the nominal administered dose, whereas the latter uses a measured eliminated drug amount. Both equations can be used to measure a renal clearance, Eqn 7 being valid only if the drug is given intravenously and is (almost) totally eliminated by the kidney. A clinical application is the measurement of the glomerular filtration rate using as probes, compounds such as iohexol, creatinine or inulin….

In the same circumstance (i.e. when an excretion rate is directly and sequentially measurable), clearance can be evaluated by dividing the average excretion rate (Δx/Δt) by the plasma drug concentration at the time corresponding to the midpoint of the excreta collection period. Indeed, Eqn 3 indicates that clearance is the slope of the regression line linking the drug excretion rate to the plasma concentration. The advantage of this method is that it takes account of possible nonlinearity (Fig. 5).

The physiological interpretation of plasma (blood) clearance

Is a given computed plasma clearance a high, medium or low body clearance? This very relevant question is seldom addressed in veterinary papers because the answer is not straightforward. For instance, a plasma clearance of 20 mL/kg/min should be considered as high in cattle and horses, but rather low in rodents.

The physiological interpretation of plasma clearance needs to have recourse to a model of body clearance. In Fig. 6 the general model of an in vivo clearance is explained, and Eqn 16 shows that in vivo clearance is the product of a blood flow () and an extraction ratio (E):

()

where E is a numerical value between 0 and 1 that can be regarded as the percentage (from 0 to 100%) of the drug which is cleared during a single passage through the clearing organ. Equation 16 corresponds to the minimal physiological model of a clearance and it is not to be confused with Eqn 3 (the definition), and Eqn 7 (the equation for its estimation).

Considering the body as the whole system clearing the drug, Eqn 16 can be used to model the body clearance with cardiac output. Hence,

()

Figure 7 gives supplementary information on derivation and assumption for Eqn 17. Inspection of Eqn 17 shows that body clearance is a hybrid parameter involving cardiac output (which is a specific species property) and E, the overall body extraction ratio being directly related to the properties of the drug under investigation. Thus, the interpretation of body clearance consists of computation and interpretation of E_body, which can be regarded as the percentage of drug being cleared by the entire body during a single passage through the different clearing organs contributing to the body clearance:

()

Cardiac outputs are known for different species or can easily be computed using the following allometric relationship:

()

It should be noted that as cardiac output is a blood flow and not a plasma flow, the interpretation of body clearance using Eqn 19 assumes that plasma clearance and blood clearance are equal (or at least not too different), i.e. the blood and plasma concentrations are equal or similar (vide infra).

The clearance model described by Eqn 17 also indicates that body clearance cannot be higher than the cardiac output (Fig. 8). For a drug exhibiting an extraction ratio equal to 1 (i.e. a total first-pass effect) for both liver and kidney, the expected E_body is equal to about 0.5 due to the fact that the sum of liver and kidney blood flows represents about half of the cardiac output.

If after i.v. administration (e.g. into the jugular vein), body clearance is higher or of the same order of magnitude than the cardiac output (55 mL/kg/min in horse) as reported for acepromazine (46 mL/kg/min) (Marroum et al., 1994) or pentoxyfilline (51 mL/kg/min) (Crisman et al., 1993) in the horse, consideration should be given to a possible pulmonary first-pass effect. Indeed, if the lung is able to eliminate a drug with an extraction ratio higher than 0.5, the body clearance might be greater than the cardiac output because only 50% of the administered dose will be actually available to the systemic circulation (see Chiou, 1982 for further explanation). For PgF2α in sheep, the lung extraction ratio is about 0.9, indicating that 90% of PgF2α is eliminated after a single lung passage (Bonnin et al., 1999). Other possible explanations for a very high body clearance are a direct metabolism of the drug in blood.

Figure 9 shows how to interpret body clearance for four antibiotics in dogs. This figure draws attention to the fact that body clearance and terminal half-life do not convey the same information on drug elimination. Very different terminal half-lives can be observed for drugs having the same body clearances, because terminal half-life is also influenced by drug distribution. Terminal half-life is said to be a hybrid parameter (influenced by both clearance and distribution), and it will be extensively discussed in our companion paper on terminal half-life. Thus, half-life is not an appropriate parameter to assess the intrinsic body capacity to eliminate a drug. For instance, in the horse it was shown for gentamicin in nephrotoxic conditions that terminal half-life was unchanged (192 min vs. 204 min) although plasma clearance was decreased by 40% (Riviere et al., 1983).

The next step in interpreting plasma clearance involves interpreting the body extraction ratio per se by having recourse to some breakpoint values for E_body. Figure 10 explains how to compute these breakpoints. Practically speaking, an E_body of 0.05 or lower is generally desirable to develop a drug for oral administration with a not too high dosage regimen (vide infra). Table 1 gives the breakpoint values for high, medium and low clearances in domestic species.

Application of plasma clearance for computation of a dose

There are many practical uses for plasma clearance, the most relevant application being computing a dose (therapeutic, toxic…) using Eqn 1. For this, the target (therapeutic, toxic…) average plasma concentration must be known (from the literature, from a PK/PD trial, extrapolated from an in vitro assay for example for antibiotics, etc.). For phenylbutazone in the horse, therapeutic concentration was directly estimated by PK/PD modelling (3.6 μg/mL) (Toutain et al., 1994), and considering the plasma clearance (41.3 mL/kg/h), the daily dosage regimen by the i.v. route should be 3.6 mg/kg/day, which is consistent with the recommended dosage regimen. Usually, the plasma clearance is known but this is generally not the case for the plasma concentration of interest (therapeutic, toxic…); compilation of therapeutic and toxic plasma concentrations in man for several hundreds of drugs is given by Schulz and Schmoldt (1997).

For antibiotics, the drug potency is often assessed experimentally by measuring the in vitro minimum inhibitory concentration (MIC) for a given pathogen. In addition, surrogate indices to predict antibiotic efficacy have been proposed such as the area under the inhibitory curve (AUIC) for quinolones (Lees & Shojaee Aliabadi, 2002; Toutain et al., 2002).

Considering the MIC of a given pathogen (e.g. MIC₅₀ or MIC₉₀) and a breakpoint value for AUIC, the dose for a quinolone (or any antibiotic for which AUIC is the relevant surrogate index of efficacy) can be computed with the following relationship:

()

where AUIC (or AUC/MIC) is the targeted endpoint in hours (e.g. 125 h) measured for 24 h, the MIC is for the targeted pathogen, Cl the plasma (total) clearance per hour (not per day), fu the free fraction of drug in plasma (from 0 to 1) and F the bioavailability factor (from 0 to 1). In Eqn 20, AUIC/24 h may be regarded as the desired multiplicative factor for the targeted MIC.

Equation 20 can be simplified by ignoring fu when the free fraction is dominant (e.g. for aminoglycosides) and also F for i.v. route (F = 1). Conversely, for drugs extensively bound in plasma, fu should be taken into account (Hyatt et al., 1995). For further explanation concerning Eqn 20 and its units, see Bousquet-Melou et al. (2002), Toutain et al. (2002) and Toutain (2003).

Estimation of a dose from in vitro data can be carried out for any drug for which an efficacious concentration has been obtained on the basis of an in vitro (or ex vivo) assay. For example, using a membrane feeding system, the IC₉₉ of lufenuron (a compound for control of flea infestation in dog and cat) for Ctenocephalides felis was found to be from 50 to 100 ng/mL. Assuming a lufenuron blood clearance in the cat of about 0.56 L/kg/day, (MacKichan & Hink, 1993) Eqn 1 predicts a minimal lufenuron dose of 0.028–0.056 mg/kg/day (or 5–10 mg/kg per 6 months), which matches the experimentally determined dose of subcutaneously injected lufenuron in cats.

When estimating a dose from in vitro drug potency, it should be remembered that in vitro drug concentrations are generally free drug concentrations (Toutain & Bousquet-Melou, 2002).

The use of plasma clearance to estimate plasma therapeutic and toxic concentrations

The order of magnitude of effective or toxic plasma concentration is required in order to interpret a snapshot plasma concentration in terms of drug efficacy and/or toxicity. If the effective (or toxic) dose is reasonably known for a drug in a given species, the effective plasma concentration (EPC) can easily be estimated by rearranging Eqn 1:

()

where EPC is the average plasma concentration over the dosing interval corresponding to the administration of an efficacious dose. EPC also reflects the drug potency. This approach was subsequently used to determine irrelevant plasma concentration for doping control in the horse (Toutain & Lassourd, 2002a). Table 2 gives the EPC for a selection of drugs in the horse.

The use of plasma clearance to extrapolate a dose from one species to another

When the therapeutic plasma concentration is unknown in a given species (e.g. for minor species), a dose can be tentatively extrapolated from another species (e.g. a major species). One of the best ways to extrapolate a dose from one species to another is to assume that the same overall body exposure (AUC) will produce the same effect in both species (that drug potency is species-independent). The following relation therefore holds:

()

where Cl_species1 and Cl_species2 are plasma clearances for species 1 and 2, respectively.

Therefore, in order to estimate the unknown dose for species 2 from an efficacious dose in species 1, the following equation can be applied:

()

A refinement of Eqn 23 emerges when introducing a bioavailability factor, F, for extra-vascular administration. If plasma protein binding differs widely between the two species, the equation will also need to include an allowance for free fraction, fu, as it is only the free concentration that is responsible for the ultimate effect:

()

where fu₁ and fu₂ are free fractions for species 1 and 2, respectively.

To illustrate the use of Eqn 24, the most likely dose for morphine in the dog and horse can be calculated from the dose recommended in humans, assuming equivalent drug potency between species. The recommended dose in humans is 10 mg in toto (i.e. about 0.17 mg/kg), and plasma clearance is reported to be 14.7 mL/kg/min (Stanski et al., 1978). In the dog, the morphine plasma clearance is higher (85 mL/kg/min) (Barnhart et al., 2000), which leads to an estimated dose of about 1 mg/kg for the dog. In contrast, the morphine plasma clearance in the horse is rather low (8.64 mL/kg/min) (Combie et al., 1983), which implies that a lower dose is needed in horses (0.1 mg/kg). No correction for drug binding to plasma protein is required as the extent of plasma binding is similar across all three species (Baggot & Davis, 1973).

Total clearance and dosage regimen adaptation

Equation 13 indicates that total clearance is the sum of liver and kidney clearances, other clearing mechanisms often being negligible. When measuring simultaneously the total body clearance and renal clearance (with Eqn 15) the hepatic clearance can be determined by the difference, i.e.:

()

By comparing the numerical value of Cl_hepatic and Cl_renal, relevant information is obtained to predict the potential needs for dosage adjustment in animals having liver or kidney disorders. Practically speaking, if the renal clearance mainly contributes to the total clearance (e.g. more than 50% of total body clearance), a significant drug overexposure can be expected in case of renal insufficiency (e.g. renal function is <50% of physiological value), and marketing drug companies should investigate the influence of kidney function on the kinetics of such drugs in animal species prone to renal insufficiency.

Plasma clearance during early development of a new drug entity in order to document the feasibility of an oral route of administration

The plasma clearance concept can be useful in early drug development in order to address some basic questions such as: can the drug be successfully administered as an oral dosage form or conversely, will the drug undergo an extensive hepatic first-pass effect leading to a low and variable systemic bioavailability?

The question can be answered from a single i.v. trial by measuring both total and renal clearance and thus allowing the evaluation by difference of a non-renal clearance, which in the first instance can be attributed to liver clearance.

The liver clearance, as all clearances, is the product of the hepatic blood flow () and the hepatic extraction ratio (E_hepatic), i.e.

()

and

()

As the extraction ratio can be regarded as the percentage of drug which is irreversibly removed during a single (first) passage, the maximal possible bioavailability for a drug cleared by the liver should be:

()

As is known (about 30% of the cardiac output), the F_max can be assessed easily by evaluating only Cl_hepatic, which in turn requires knowledge of both Cl_tot and Cl_renal (Eqn 15). The computed F_max is the real oral bioavailability if the drug is totally absorbed by the digestive tract, i.e. if the loss of drug is only due to the hepatic first-pass effect. Using this approach, the low oral bioavailability of some drugs can easily be predicted. For example, in the dog, propranolol is totally absorbed after oral administration, and is completely eliminated by a high hepatic clearance (41 mL/kg/min). This explains the relatively low measured bioavailability despite total absorption (16 ± 12%) (Bai et al., 1985). Such a low systemic bioavailability was expected because the hepatic clearance of propranolol is of the same order of magnitude as hepatic blood flow.

Blood vs. plasma clearance

The whole blood, rather than plasma, flows throughout the circulating system, and whole blood rather than plasma is generally the more appropriate (but not the most convenient) reference liquid to measure and from which interpret the body clearance. For the sake of simplicity, we have assumed in this review that blood and plasma are equivalent matrices, but this is not true if blood and plasma concentrations are different. For example, if total blood concentration is much higher than plasma concentration, interpretation of plasma clearance in terms of blood flow can be very misleading, and evaluation of blood clearance is preferred. Blood clearance can be directly evaluated by measuring blood concentration vs. time profiles (which is not very convenient but more and more used with analysis by mass spectrometry) or alternatively, by measuring plasma concentration vs. time profiles, and transforming the plasma clearance to the blood clearance using the haematocrit value (H) and the blood-to-plasma (B/P) partition ratio (which can be computed in vitro and is assumed to be constant). Equation 29 allows transformation of a plasma clearance into a blood clearance when a rapid equilibrium exists between plasma and red blood cells:

()

where B/P is the experimental blood-to-plasma concentration ratio for that drug, H is the haematocrit, C_rbc is the red blood cells concentration and C_plasma, the plasma concentration.

For a drug totally excluded from the RBCs (C_rbc = 0), Eqn 29 becomes:

()

Considering a haematocrit value of 0.4, Cl_blood is equal to about 1.66 × Cl_plasma, so that plasma clearance underestimates blood clearance. Therefore, for a drug almost wholly excluded from red blood cells, the maximum possible error when using plasma clearance as a surrogate of blood clearance is no greater than 40%.

In contrast, when a drug accumulates in RBC (e.g. pimobendan, chloroquine, cyclosporin, acetazolamide…), Cl_plasma may considerably overestimate Cl_blood, making the interpretation of plasma clearance incorrect in terms of blood flow. That is why knowledge of the B/P ratio is required very early in drug development, as this will determine whether the appropriate matrix for PK studies is blood or plasma.

The B/P ratio varies between a value of (1 − H) for drugs highly bound to plasma protein or/and poorly partitioned between RBC and plasma, to a possibly large value when drug has a high affinity for RBC (e.g. affinity for haemoglobin…). When B/P is higher than 1, it can be useful to know if the partitioning/departitioning of the drug between plasma and RBC is rapid or not with regard to the transit time through the clearing organ (liver and kidney). Indeed, the presence of drug in RBC is of relevance for PK interpretation only if the exchange between RBC and plasma is sufficiently rapid to participate in the drug clearance process. In other words, if during blood transit throughout the liver (about 10 sec), the kidney cortex (about 2 sec) or the renal medulla (about 30 sec), a drug located in RBC (e.g. the fraction bound to the RBC membrane) can immediately return to plasma to re-equilibrate with plasma which is stripped of the drug during the transit time, the blood concentration and blood clearance are relevant. In contrast, if the departitioning is so sufficiently slow that drug removal from the plasma does not lead to significant re-equilibration during organ transit, plasma concentration becomes the relevant concentration, because then, RBC should be regarded as a peripheral (circulating) tissue compartment and not a central one. This is the case for para-aminohippuric acid (PAH), which is used to assess kidney circulation. PAH undergoes a first-pass effect during its passage throughout the kidney, but only PAH located in plasma is involved. Thus, PAH plasma clearance measures an effective plasma flow and not a blood flow. For further explanation see Hinderling (1997) and Wilkinson (1987).

Arterial versus venous blood sampling: the question of the jugular vein

In veterinary medicine, blood administration and sampling are often carried out at the venous level, which can lead to two possible drawbacks. The first is related to drug administration and to a possible pulmonary first-pass effect, which can reduce the available (systemic) dose by a factor equal to the pulmonary extraction ratio (vide supra). The second difficulty is related to blood sampling from venous vessels and the possibility that the venous plasma concentration may differ from that of arterial plasma. Indeed, for clearance computation, plasma concentration measured at the venous level is assumed to be a surrogate of the simultaneous plasma concentration at the arterial level. This is true only if there is no significant metabolic site between the aorta and the sampling site. This assumption is reasonable when the blood is sampled on the arm in man because the venous blood has only crossed muscles, but it is more debatable for jugular blood which is more often sampled in animals as the blood has crossed the entire head (brain, possible saliva elimination in ruminants, etc.)

Conclusion

Total body clearance is the most important PK parameter and needs to be evaluated in vivo for any drug through an i.v. study. The main use of clearance is to compute or adapt a dosing rate. When interpreted in physiological terms, it provides an understanding of some basic features of drug disposition.