CHAPTER 3. PHARMACOKINETIC MODELS. PHARMACOKINETIC MODELING. A Model is a hypothesis using mathematical terms to describe quantitative relationships MODELING REQUIRES: Thorough knowledge of anatomy and physiology Understanding the concepts and limitations
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A Model is a hypothesis using mathematical terms to describe quantitative relationships
Thorough knowledge of anatomy and
Understanding the concepts and limitations
of mathematical models.
Assumptions are made for simplicity
The development of equations to describe drug concentrations in the body as a function of time
By fitting the model to the experimental data known as variables.
A PK function relates an independentvariable to a dependent variable.
1- Route of administration
2- Extent and duration of
distribution into various body
fluids and tissues.
3- The processes of elimination.
4- Intended application of the PK
We Always Choose the SIMPLEST Model
1- Physiologic (Perfusion) Models
2- Compartmental Models
3- Mammillary Models
Models are based on known physiologic
and anatomic data.
Blood flow is responsible for distributing
drug to various parts of the body.
Each tissue volume must be obtained and
its drug conc described.
Predict realistic tissue drug conc
Applied only to animal species and human
data can be extrapolated.
Can study how physiologic factors may change
drug distribution from one animal species to
No data fitting is required
Drug conc in the various tissues are predicted
by organ tissue size, blood flow, and
experimentally determined drug tissue-blood
Pathophysiologic conditions can affect
A compartment is not a real physiologic or
anatomic region, but it is a tissue or group
of tissues having similar blood flow and drug
Within each compartment the drug is considered
to be uniformly distributed.
Drug move in and out of compartments
Compartmental models are based on linear
Rate constants are used to describe drug entry
into and out from the compartment.
The model is an open system since drug is
eliminated from the system.
The amount of drug in the body is the sum
of drug present in the compartments.
Extrapolation from animal data is not
possible because the volume is not a true
volume but is a mathematical concept.
Parameters are kinetically determined from
TimeIntravenous and extravascular Route of Administration
Difference in plasma conc-time curve
The one compartment model offers the simplest way to describe the process of drug distribution and elimination in the body.
When the drug is administered i.v. in a single rapid injection, the process of absorption is bypassed
The one-compartment model does not predict actual drug levels in the tissues, but does imply that changes in the plasma levels of a drug will result in proportional changes in tissue drug levels.
The rate of elimination for most drugs is a
kel is a first-order rate constant with a unit
of inverse time such as hr-1.
Plotting the data
The rate of change of drug plasma conc over time is equal to:
This expression shows that the rate of elimination of drug from the body is a first-order process and depends on kel
Cp = Cp0e-kelt
ln Cp = ln Cp0 kelt
DB = Dose. e-kelt
ln DB = ln Dose kelt
Is the time taken for the drug conc or the amount in the body to fall by one-half, such as Cp = ½ Cp0 or DB = ½ DB0
A plot of Cp vs. time
t1/2 = 3 hr
The fraction of the dose remaining in the body (DB /Dose) varies with time.
The fraction of the dose lost after a time t can be then calculated from:
Is the volume in which the drug is dissolved in the body.
Example: 1 gram of drug is dissolved in an unknown volume of water. Upon assay the conc was found to be 1mg/ml. What is the original volume of the solution?
V = Amount / Conc = 1/1= 1 liter
Also, if the volume and the conc are known, then the original amount dissolved can be calculated
Amount = V X Conc= 1X1= 1 gram
It is called apparent because it does not have any physiological meaning. Drugs that are highly lipid soluble, such as digoxin has a very high Vd (600 liters), drugs which are lipid insoluble remain in the blood and have a low Vd.
For digoxin, if that were a physiological space and I were all water, that would weigh about 1320 lb (599 kg).
Vd is the ratio between the amount of drug in the body (dose given) and the concentration measured in blood or plasma.
Therefore, Vd is calculated from the equation:
Vd = DB / CP
DB= amount of drug in the body
Cp= plasma drug concentration
With rapid IV injection the dose is equal to the amount of drug in the body at zero time (DB).
Where Cp is the intercept obtained by plotting Cp vs. time on a semilog paper.
Since, dDB/dt = -kelD = -kelVdCp
dDB = -kelVdCpdt
dDB = -kelVd Cpdt
Since, Cpdt = AUC
Then, AUC= Dose / kelVd
Drugs can have Vd equal, smaller or greater than
the body mass
Drugs with small Vd are usually confined to the
central compartment or highly bound to plasma
Drugs with large Vd are usually confined in the
Vd can also be expressed as % of body mass and
compared to true anatomic volume
Vd is constant but can change due to pathological
conditions or with age
Example: if the Vd is 3500 ml for a subject weighing 70 kg, the Vd expressed as percent of body weight would be:
The larger the apparent Vd, the greater the amount of drug in the extravascular tissues. Note that the plasma represents about 4.5% of the body weight and total body water about 60% of body weight.
Is the volume of blood that is cleared of drug per unit time (i.e. L/hr).
Cl is a measure of drug elimination from the body without identifying the mechanism or process.
Cl for a first-order elimination process is constant regardless of the drug conc.
A plot of Cp vs. time