Pocket Guide: Pharmacokinetics Made Easy - sample

CHAPTER 3
WHAT IS CLEARANCE?
‘Clearance’ describes the efficiency of irreversible elimination of a
drug from the systemic circulation. Elimination in this context refers
to the excretion of the unchanged drug into urine, gut contents,
expired air, sweat, etc., and to the metabolic conversion of the drug
into a different chemical compound, predominantly in the liver, but
also to a small extent in other organs. When the drug has been
metabolised, the parent drug has been cleared or eliminated, even
though the metabolite may still be in the body. Uptake of the drug
into tissues is not clearance if the unchanged drug eventually comes
back out of the tissue, however slowly this occurs.
Clearance is defined as ‘the volume of blood cleared of drug per
unit time’ and the units are thus volume per time, usually litres per
hour or mL per minute. We can refer to clearance by a particular
organ, such as liver or kidney, by a particular metabolic pathway, or
by the whole body. Total body clearance is the sum of all the different
clearance processes occurring for a given drug.
Let’s consider an example. What does it mean if the clearance of a
particular drug by the liver is 60 L/hour and liver blood flow (QH
) is
90 L/hour? It does not mean that 60 L of blood going through the
liver is totally cleared of the drug and the next 30 L is not cleared at
all. Rather, it means that two-thirds (60/90) of the drug entering the
liver in the blood is irreversibly removed by the liver (cleared) in one
pass through the liver. The drug that is extracted from the blood
is metabolised in the liver cell so that the parent compound is
eliminated. The value of two-thirds for this drug is called the
CLEARANCE
CHAPTER 1
1
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2 Pocket Guide: Pharmacokinetics Made Easy
extraction ratio and is simply one minus the ratio of concentration of
drug in blood leaving the liver to that in blood entering the liver.
extraction ratio (EH
) = 1 –
concentration out
concentration in
Equation 1.1
It will be apparent from the above that clearance is determined by
the blood flow to an eliminating organ (QH
in the case of the liver)
and the efficiency of irreversible drug extraction from the blood by
the organ (EH
). This is considered further in Chapter 4.
Obviously, the most drug that could be removed by the liver is all
that enters the organ. In this case, the ‘concentration out’ would be
0.0, extraction ratio would be 1.0 and the hepatic clearance 90 L/hour.
The further significance of the extraction ratio will be discussed in
Chapter 4. For the present, it should be noted that the minimum
clearance by an organ is zero and the maximum clearance by an
organ is the blood flow to the organ.
CLEARANCE AND ELIMINATION
RATE
Another definition of clearance is that it is the constant relating the
concentration of drug in the plasma to the rate at which the drug is
eliminated from the body.
elimination rate = clearance (CL) ∗ plasma drug concentration (C)
(mg/hour) (L/hour) (mg/L)
Equation 1.2
It is apparent that for a given clearance, which is a constant char-
acteristic of a particular drug and a particular patient, the elimination
rate varies directly with the plasma drug concentration.
WHY IS CLEARANCE IMPORTANT?
Clearance is the one parameter that determines the maintenance
dose rate required to achieve a target plasma concentration (and
therefore effect) at steady state. Steady state is defined as the
situation at which the rate of drug administration is equal to the rate
of drug elimination so that the amount of drug in the body, and

Chapter 1 Clearance 3
1
therefore the plasma drug concentration, remains constant. At
steady state,
elimination rate = maintenance dose rate (DR)
Equation 1.3
From Equations 1.2 and 1.3, the maintenance dose rate required to
achieve a target steady state plasma drug concentration can be
calculated as:
maintenance dose rate (DR) = clearance (CL)∗steady state drug
concentration (Css
)
(mg/hour) (L/hour) (mg/L)
Equation 1.4
This is illustrated in Figure 1.1 (following page) for constant rate
intravenous infusions of two drugs, for one of which the clearance is
double that of the other. Note that, with a constant infusion, the
plasma drug concentration rises steadily until it eventually reaches a
plateau or steady state when the rate of drug administration equals
the rate of drug elimination.
The oral dosing situation is slightly more complex because the
drug concentration fluctuates during the dosing interval as the drug
is absorbed and eliminated. Eventually, however, the amount of
drug eliminated during the dosing interval equals the dose admin-
istered, and the drug concentrations then fluctuate over the same
range during each dosing interval; that is, steady state has been
reached. At this point, the average drug concentration over the dosing
interval is the same as the steady state plasma concentration for a
constant intravenous infusion at the same dose rate. From Equation
1.4, it is easy to see that, for a given dose rate, the plasma drug con-
centration is inversely proportional to clearance. For example, if the
clearance is reduced by half, the steady state concentration will
double (see Figure 1.1).
HOW IS CLEARANCE MEASURED?
The classical method of measuring renal clearance (e.g. of creatinine
or drugs) is to measure the rate of excretion in urine, and the
blood concentration at the same time. This is the well-known
CL = U∗V/P relationship where U is urine drug concentration, V is
urine flow rate and P is the plasma (or blood) concentration of a

solute such as creatinine or a drug. This is actually the same as
Equation 1.2, as U∗V is the excretion rate of the solute or drug.
To obtain total body clearance of a drug from the systemic
circulation, we can use Equation 1.4 to obtain clearance from the
steady state drug concentration during a constant intravenous
infusion.
dose rate
clearance =
steady state plasma concentration
CL =
DR
Css
Equation 1.5
Alternatively, we can take frequent blood samples after a single
intravenous dose, measure the drug concentration in each, and
calculate the area under the drug concentration versus time curve
(AUC) (see Figure 1.2 on page 6). Then:
Drugconcentration(mg/L)
Drug A: CL = 5 L/hour
Drug B: CL = 10 L/hour
2.0
1.5
1.0
0.5
0 5 10 15 20 25 30
Time (hours)
Figure 1.1: Effect of clearance on steady state drug concentration time
profile
Clearance determines the plasma drug concentration at steady state. For both
drugs A and B, the dose rate is 10 mg/hour.

1
dose
clearance =
AUCN
(L/hour)
mg
mg∗hour/L
Equation 1.6
From this relationship, it can be seen that the total area under the
plasma concentration time curve after a single intravenous dose is,
like the steady state concentration, only determined by the dose and
the clearance.
PLASMA OR BLOOD DRUG
CONCENTRATIONS?
It is the convention in pharmacokinetics to use plasma concentra-
tions of drugs as this is what is usually measured in the laboratory.
Measuring whole blood concentrations tends to be more difficult due
to the presence of more interfering compounds. Therefore, throughout
this book, pharmacokinetic parameters will be referred to in terms of
plasma drug concentrations. It should be remembered, however, that
the tissues and eliminating organs such as the kidneys and liver are
perfused with blood, not plasma. The plasma concentration of a drug
can be related to the whole blood concentration by the blood:plasma
concentration ratio (λ).
λ =
drug concentration in whole blood
=
Cb
drug concentration in plasma C
Cb
= C∗λ
Equation 1.7
This ratio is usually close to 1.0 as the drug concentrations in the
cellular and plasma components of blood are usually about the same.
The ratio cannot be less than about 0.5 (the haematocrit). It can,
however, be quite large for highly lipophilic drugs like cyclosporin
and chloroquine which are relatively concentrated in the red cells.
In such cases, it is better to express clearance and volume of distribu-
tion in terms of drug concentrations in whole blood rather than
in plasma.

KEY POINTS
Clearance is the fundamental pharmacokinetic parameter that is a•
measure of the efficiency of drug elimination.
Clearance is the volume of blood cleared of drug per unit time and•
is the proportionality constant between plasma drug concentra-
tion and elimination rate.
For a given intravenous maintenance dose rate, clearance is the•
sole parameter determining the steady state drug concentration.
Drugconcentration(mg/L)
Time (hours)
12
10
8
6
4
2 Area under the curve (AUC)
(mg*hour/L)
0 4 8 12 16 20 24
Figure 1.2: Measurement of clearance
Clearance can be determined by measuring plasma drug concentrations at multiple
times after a single intravenous bolus dose. The AUC can be estimated by assum-
ing each pair of drug concentration time observations form a trapezoid. The area of
each trapezoid is calculated then summed.
dose (mg)
CL(L/hour) =
AUC(mg∗hour/L)

1
SELF-TEST QUESTIONS
(Note: There may be multiple correct options.)
1. Elimination of a drug refers to:
excretion of its breakdown products in the urinea)
renal excretion of the unchanged drugb)
uptake of drug from the blood into the liverc)
metabolism of the drug in the liverd)
distribution of the drug into fate)
2. The elimination rate of a drug is:
a constant for a particular drug and patienta)
the extent to which it is excreted in urineb)
directly proportional to the plasma drug concentrationc)
directly proportional to the clearanced)
the extent to which the drug is excreted in the faecese)
3. Clearance:
depends on the elimination ratea)
refers to the efficiency of elimination of drug by an organ orb)
the whole body
cannot be greater than blood flow to an organ (CLc) H
cannot
be greater than QH
but total CL can)
determines the steady state drug concentration duringd)
constant dosing
is determined by the half-lifee)
4. Two definitions of clearance are:
the volume of blood or plasma irreversibly cleared of drug pera)
unit time
the time taken to reduce the plasma concentration by halfb)
the constant relating the rate of elimination of a drug to thec)
plasma drug concentration
the amount of drug metabolised per unit timed)
the amount of drug excreted in urine per unit timee)

Pocket Guide: Pharmacokinetics Made Easy - sample

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Pocket Guide: Pharmacokinetics Made Easy - sample