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Summary advanced pharmacokinetics
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Advanced pharmacokineticsLecture 1 Introduction
17/10/2022
Guest lectures are not part of the exam (except Daan Touw), but they will be assessed in
assignments.
PK = fate of drug in the body: what the body does to the drug
PD = effect of drug in the body: what the drug does to the body
You want to understand the relationship between the dose and effect. This is for safer and
more effective treatment of (individual) patients.
Therapeutic window: the range of plasma drug concentration where the therapeutic effect is
adequate and adverse effects are acceptable in a certain number of patients. Above the
window you risk getting adverse effect, below the window the therapy will be ineffective.
ADME:
- Absorption from site of administration to systemic circulation
- Distribution from systemic circulation to tissue, including target
- Metabolism biotransformation to metabolites
- Excretion from systemic circulation to outside the body (in urine, bile/feces)
Qualitative reasoning does not need mathematics. E.g. you can estimate how something
changes, but you cannot determine how much it needs to change. For instance you know
that the dose needs to be increased, but you do not know how much.
Volume of distribution (V): it allows relating the drug plasma concentration (easily
measurable) to the total amount of drug in the body after absorption (not easily measurable).
We define an (apparent) volume of distribution, to be the volume that gives the measured
concentration. V = amount/C
This V is not an actual volume, it can sometimes be larger than a full human. It is just a
relationship that allows us to go from the concentration in plasma to the amount of drug in
the body. V is defined in L of L/kg.
Clearance (CL): the rate of elimination from the total body or a specific organ divided by the
plasma drug concentration. So it is the amount of drug that is eliminated from the body per
unit time (ml/min). Rate of elimination = CL*C
Clearance can also be related to other physiological concepts. CL = EQ, with E being the
fraction eliminated and Q being the volume of fluid entering the organ per unit time.
Elimination rate constant (k): proportionality constant between rate of elimination and drug
amount (assuming first-order elimination) in min-1. Rate of elimination = kA You can also
relate k to the clearance and volume of distribution. k = CL/V
Half-life (t1/2): the amount of time it takes to halve the drug concentration for exponentially
decaying plasma drug concentration (assuming first-order elimination) in min. It is related to
the elimination rate constant. t1/2 = ln2/k
Bioavailability (F): not all of the drug passes into the systemic circulation. It is the amount of
drug that is eventually absorbed divided by the dose. F = Aa/dose
First pass loss: drug must pass through the gut wall and liver before reaching the systemic
circulation proper. Drug can be lost in the gut lumen, gut wall and liver. A drug passes these
,organs before it reaches the systemic circulation proper. If a drug is extensively metabolised
by the liver it will not reach the systemic circulation proper and the drug cannot exert its
effect. F = FFFGFH So FF is what is left after gut lumen, FG is what is left after the gut wall and
FH is what is left after the liver.
Absorption rate constant (ka): proportionality constant between the rate of absorption and
drug amount (assuming first order absorption). It is the rate of absorption (amount of drug
absorbed per unit time) divided by the amount of drug remaining to be absorbed in min-1. So
how quickly does absorption happen. Rate of absorption = kaAa You can also relate ka to the
absorption half-life. t1/2a = ln2/ka
Area under the curve (AUC): the integral of the plasma concentration profile in mg*h/ml.
You can relate it to a specific time range, but when nothing is stated it is from 0 to infinity. It
can be related to other concepts. F*dose = CL*AUC
Trapezoidal rule to measure the AUC: divide the curve into trapezoids. The total AUC is then
the sum of the areas of all trapezoids. The area of a trapezoid is: area = ½(C1+C2)(t2-t1)
When there is exponential decay, it is far easier to calculate the AUC. AUC = C(0)/k with
C(0) being the concentration at the starting point.
The drug plasma concentration time curve of an intravenous bolus
dose: de drug is in the systemic circulation immediately. This typically
gives an exponentially decaying drug plasma concentration time
curve. C(t) = C(0)e-kt
The drug plasma concentration time curve of an extravascular
administration: absorption needs to take place first. Absorption and
elimination happen at the same time. Eventually all drug has been
absorbed and then you only have elimination onwards. You can see
this by an exponential decay developing. A straight line in a
logarithmic curve is an exponential line on the normal curve.
The drug plasma concentration time curve of a continuous
infusion: the drug concentration increases in the beginning when
the drug is entering the patient. Elimination is going on at the
same time. Eventually you reach a steady state (SS) or plateau
where an equal amount of drug is entering the body as is leaving
the body. The concentration in plasma at the steady state is the
infusion rate divided by the clearance. Css = R0/CL The time to
reach the 90% plateau is ~3.3t1/2.
The drug plasma concentration time curve of a repeated administration (extravascular):
same as extravascular administration, but after a while a second pill is taken, so the
concentration will go up again, etc. This is sort of similar to continuous infusion, but the
concentration is not constant. You do reach a kind of plateau, meaning that you see the
same pattern happening again and again after a certain amount of time. They will never be
exactly the same. So there are fluctuations in plasma concentration but these are similar
each addition so this is why we still call it a plateau. This assumes intravenous
, administration. IV administration will have more extreme values, so you know that with the
extravascular administration the maximum and minimum will be less extreme, so there will
be smaller fluctuations. So the predictions are worse than the actual situation.
CL*Css,av = (F*dose)/τ
τ = how often the drug is taken
Ass,max/min = amount of drug in the body at steady state maximum or minimum.
Ass,max = (F*dose)/(1-e-kτ)
Ass,min = Ass,max – F*dose
Css,max = Ass,max/V
Css,min = Ass,min/V
Css,av = dose/τ/CL
Plasma protein binding:
- Albumin especially for drugs with acidic groups. Albumin is very much abundant in
the blood. Albumin levels decrease in case of liver failure (less synthesis) and renal
failure (loss via urine).
- Alpha-1-acid-glycoprotein especially for drugs with basic groups. The levels
increase with inflammation (acute phase protein). The binding to these proteins can
become saturated more easily compared to albumin.
Analysis of an iv bolus dose: For an exponential decaying curve (straight line in the log
scale), the slope of the curve is the elimination rate constant (k). k = -(lnC2-lnC1)/t2-t1
With k you can calculate the t1/2. The next step typically is calculating the AUC using the
trapezoidal rule. With this you can calculate the clearance (dose is known, F = 1) using
F*dose = CL*AUC. With the clearance you can calculate the volume of distribution using k =
CL/V.
Analysis after extravascular administration: use the method of residuals
to find the absorption rate and lag-time. At the end of the curve there
roughly is an exponential decay, so you can find the slope which will be
your elimination rate constant k. The absorption rate constant is more
difficult. Continue the straight line of elimination backwards. Using back-
extrapolations you get to the residuals (the values on the time points of
your actual data, but now at the extrapolated line). Subtract those
concentrations from each other to form the residual line. The slope of this line is the
absorption rate constant. The lag-time is the intersection of the residual line and the
extrapolated line.
Designing dosage regimens:
- The maximum dosing interval is given by Clower = Cuppere-kτmax
- The maximum dose is given by F*dosemax = V(Cupper - Clower)
- The dosing interval and dose need to be adjusted after calculation to get to practical
outcomes. A dosing interval must be adjusted to an even number and it must fit into a
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