Download Introduction to Clinical Pharmacokinetics

Introduction to Clinical Pharmacokinetics
Module contents
The objectives are as follows.
 To provide an introduction to the concepts of clinical pharmacokinetics and
therapeutic drug monitoring.
 To provide an understanding of fundamental parameters, specifically; Volume of
Distribution, Clearance, Elimination Rate constant (K) and Half Life.
 To provide an understanding of how these parameters are related.
 To provide you with the tools and knowledge to perform simple pharmacokinetic
calculations
 To provide skills required to interpret drug plasma concentrations and apply the
results of these in clinical practice
 For all of the above; to identify more advanced learning objectives.
Resources and Readings
Interactive Clinical Pharmacology
This is not part of this course but you may refer to it for personal use to help in the
explanation of some of the concepts. Readings have also been emailed to participants.
This introduction will also supplement these and others that will be available on the
course web site.
Powerpoint Presentation.
You can download this for future reference
Course Text
Summary
Pharmacokinetics is what the body does to the drug, i.e. how it handles the drug once it is
in the body. This involves Absorption, Distribution and Elimination (Metabolism and
Excretion).
Clinical pharmacokinetics is the study of the relationships between drug dose regimens
and drug concentration time profiles. Three basic parameters control these relationships,
these are; Clearance (CL) – the volume of fluid which is completely cleared of drug per
unit time; Volume of Distribution (VD) – the apparent volume in to which the drug is
distributed to produce the measured concentration; and Elimination half-life- the time
taken for the drug concentration to decrease by 50%.
The VD can be used to calculate loading doses in order to reach a target concentration
quickly. The usual units of VD are L or L/kg.
CL is sued to calculate the dose required to maintain a desired target drug concentration
(maintenance dose). The usual units of CL are L/hr or L/hr/kg.
The elimination half-life gives an indication of how long it takes for steady state drug
concentrations to be reached on multiple dosing (about four to five half-lives) and how
long it will take for drug concentrations to decline if the drug is stopped. Half-life is
usually expressed in hours and the related elimination rate constant (k) in hr -1
Introduction
In clinical pharmacy practice the principles of pharmacokinetics are used to relate drug
doses with concentration time profiles. If there is a close relationship between drug
concentration and clinical effect and toxicity therapeutic drug monitoring (TDM) can be
used to optimize clinical effect and minimize toxicity. There is great variability in drug
handling between individuals so the application of the principles of clinical
pharmacokinetics and TDM are very important to individualise drug therapy, especially if
the margin between drug effectiveness and toxicity is narrow. Examples of drugs with
such a narrow therapeutic range include digoxin, lithium, theophylline and phenytoin.
While it may be important to attain drug concentrations that are within a certain target
range (therapeutic range) the shape of the drug concentration-time profile may be
important for some drugs. For example high peak concentration of carbamazepine may
produce toxicity but low troughs may lead to loss of clinical effect. The target profile is
therefore flat with little fluctuation between doses. Conversely, with an aminoglycoside
such as gentamicin high peaks are associated with greater antimicrobial effects and low
troughs reduce toxicity, so large swings in drug concentrations are desired.
The application of the principles of clinical pharmacokinetics allows the calculation or
estimation of dosage regimens to give the ideal concentration-time profile for individual
patients.
Drug Absorption
The bioavailability of a drug formulation F is the fraction of the dose administered which
is absorbed and reaches the systemic circulation. A drug given intravenously usually has
a bioavailability of 100% or 1. The same drug given orally has to cross barriers in the gut
mucosa and first pass metabolism in the liver so the bioavailability may be reduced, for
example F of oral digoxin is 0.7 – 0.8 depending on the formulation.
Factors which may affect bioavailability include:
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Physicochemical properties of the drug and its formulation
Extent of metabolism in the gut wall. There are drug metabolizing enzymes
(CYPs) in the gut wall.
Extent of first pass metabolism in the liver.
Drug interactions. For example itraconazole can increase the bioavailability of
simvastatin by reducing first pass metabolism.
Blood flow and gut motility.
Diarrhoea and vomiting
Volume of Distribution (VD)
The Volume of distribution (VD) relates the amount of drug in the body to the measured
plasma drug concentration. Usually the VD does not represent a physiological volume
but the apparent volume into which the drug is distributed. If we view the body
simplistically as a single compartment with a volume of 100 L a dose of 100 mg instantly
distributed will give a drug concentration of 1 mg/L. The body however comprises many
compartments and tissues types and drugs are not confined to the vascular or fluid
compartments. Let’s say our drug distributes in to skeletal muscle and 90 mg of the dose
is tightly bound to these tissues, leaving only 10 mg of drug in our compartment. In this
case our measured drug concentration will only be 0.1 mg/L giving an apparent volume
of distribution of 1000 L. When the drug is fully distributed in to the tissues there is an
equilibrium between the tissues and the plasma. The plasma can be viewed as the
measurable compartment and indicates the apparent volume in to which the drug is
distributed. In order to get the desired plasma concentration (which usually relates to
clinical effect) we have to give a dose will give this concentration in our apparent
volume. If we need to attain these concentrations quickly then a loading dose is given
which is a relatively large dose sufficient to give the required plasma concentration
rapidly. This the VD is the parameter required to calculate the loading dose.
Loading doses are sometimes given with digoxin (if rapid control of heart rate is
required) or some anticonvulsants.
The Loading Dose is calculated from the following equation;
D (loading) = VD (L) x Plasma Concentration (Desired)
For some drugs the VD is expressed as L per kg so this value needs to be multiplied by
the patient’s weight.
Suggested Exercises
1.Find values of VD for some commonly used drugs such as digoxin, gentamicin and
lithium.
2. Drug A has a VD of 0.25 L/kg what IV loading dose is required to give a plasma
concentration of 10 mg/L ?
Clearance (CL)
In one of our examples above we had 100 mg of drug distributed in a VD of 100L and
drug concentration of 1 mg/L. Obviously drug will start to be removed almost
immediately and unless removed drug is replaced the drug concentration will start to
decline.
Clearance represents the irreversible removal of drug from the body and determines the
average steady state drug concentration with a regular maintenance dose. The clearance
can be defined as the volume of fluid which is completely cleared of drug per unit time.
The units of CL are expressed as L/hr, ie Litres of fluid cleared of drug per hour.
If we go back to our example; draw a rectangle and assign it a volume of 100 L. Now
place an arrow above the rectangle indicating that a dose of 100 mg was given and
assume simple distribution in to one compartment of 100 L. Next draw another rectangle
within the first one which corresponds to a volume of 10 L and imagine that this is
completely cleared of drug each hour. This is the clearance, 10 L of fluid is completely
cleared of drug each hour and this corresponds to the removal of 10 mg of drug. The
resulting drug concentration will now be 0.9 mg/L. In order to maintain the drug
concentration at 1 m/L we need to replace the drug removed. Obviously this is a very
simple example but hopefully you can see how CL will determine the maintenance dose
required to keep the drug concentration at our target.
Maintenance Dose = Target average drug concentration at steady state X CL
The are a couple of important things to note about this equation. Firstly the units must
balance on each side. The target drug concentration will be in mg/L and the CL in L/hr,
so mg/L x L/hr gives a dose in mg/hr. This is actually a dose rate so it must me multiplied
by 24 to give the total daily dose. Secondly, equation is used to calculate an average drug
concentration at Steady State (SS). Steady state is reached when the rate of drug
administration is equal to rate of drug eliminated from the body, i.e. Rate in = Rate Out.
SS is not reached after the first dose and it will take time for the target drug concentration
to be reached (see below). That is why a loading dose may be given in some situations if
therapeutic drug concentrations are required quickly.
Now a good test of you understanding of CL. Refer back to your rectangle as the example
above. That is a 100L volume with 100 mg of drug evenly distributed in it and a
representative CL of 10 L/hr. What will to the CL if the VD increase to 120 L ?
The CL will stay the same i.e. 10 L/hr but the corresponding amount of drug removed
will be reduced as the drug is distributed in to a larger volume.
Work out how much drug will be removed if the VD increase by 20 L.
This example demonstrates that CL is usually a constant and its value is not affected by
the concentration of drug in the plasma. CL is often incorrectly described as the amount
of drug removed from the body but it is the VOLUME cleared and the amount cleared
will depend on the drug’s concentration.
Suggested exercises
What factors can change reduce the clearance of lithium ?
What factors can increase or decrease the clearance of Theophylline ?
What factors can increase or decrease the clearance of digoxin ?
Calculate the maintenance dose for drug B for a patient who weighs 70 k, required to
give a SS concentration of 10 mg/L. The drug’s clearance is 0.5 L/hr/kg
Half-Life (t½ and Elimination Rate Constant (k)
When a drug is administered at a constant rate, e.g. as an intravenous infusion the drug
concentration gradually increases until the concentration-time profile flattens out. At this
point the Rate in = Rate out and the steady state drug concentration is reached.
If the drug is given by IV bolus at regular intervals plasma drug concentration will
fluctuate between peaks and troughs. The difference between the peak and trough will
depend on how often the drug is given (dosage interval) and the rate of drug elimination.
When oral doses are given there will be similar fluctuations between peaks and troughs
but the concentration-time curve will be influenced by addition factors such as
absorption. With drugs given at regular intervals a steady state average concentration is
eventually reached so a line drawn through the mid point of the peak and trough will be
straight.
For the majority of drugs the rate of drug elimination from the body is proportional to the
amount of drug present. Consequently a constant fraction of drug is removed per unit
time, e.g. 20% of the drug remaining in the body is removed each hour. This gives an
Elimination Rate Constant of 0.2 hr-1 . The shape of the decline in drug concentration is
therefore exponential.
The value of k depends on two parameters the VD and the CL.
k = VD (L/hr) divided by CL (L);
k = VD/CL
Also CL = kVD
The half-life is related to k and is defined as the time it takes for the drug concentration to
fall to half its original value. Therefore 50% of the dose will be eliminated in one halflife, 75% in two half-lives and 97% in 5 half-lives.
The decline in drug concentrations is exponential as expressed as follows;
Cp2 = Cp1 e-kt
Where Cp1 is the initial drug concentration; Cp2 is a second concentration serrated by
time t and k is the elimination rate constant.
If we take the natural logarithm of both sides of this equation we obtain the well known
equation for calculating half-life.
t½ = 0.693/k
The time taken to reach steady state (SS) with multiple dosing depends on the half-life, so
50% of SS is reached in one half-life and 97% of SS is reached after 5 half-lives.
Therefore is a drug concentration is measured after one half-life it will not give a true
indication of the eventual SS drug concentration. The sample should be taken at a time
that corresponds to estimated SS. This is a very important principle when interpreting
drug concentrations in TDM
We have just described linear pharmacokinetics and most drugs behave this way within
their therapeutic range. In linear pharmacokinetics the CL is constant as k. The SS drug
concentration is directly proportional to the dose. For example, if a dose gives a SS
concentration of 10 mg/L, doubling the dose will give a new SS concentration of 20
mg/L. It follows that if we know a drug concentration represents SS we can make empiric
a dose alterations by simple proportion. However we must be sure that the sampling time
is correct, the assay is accurate and the patient is compliant or this will affect the
accuracy of the estimation.
Some drugs, in particular phenytoin exhibit non-linear pharmacokinetics, in this case due
to saturable hepatic metabolism. In this case dose increase will produce disproportionate
increase in drug concentration and may even lead to toxicity. With phenytoin, very small
dose increase are made with repeat monitoring of the plasma drug concentration.