1. PHARMACOKINETIC MODELS
CHAPTER 3
PHARMACOKINETIC MODELS

2. 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
of mathematical models.
Assumptions are made for simplicity

3. OUTCOME
The development of equations to describe drug concentrations in the body as a function of time
HOW?
By fitting the model to the experimental data known as variables.
A PK function relates an independent variable to a dependent variable.

4. FATE OF DRUG IN THE BODY ADME Excretion Oral Administration G.I. Tract
Intravenous
Injection
Circulatory
System
Intramuscular
Injection
Tissues
Metabolic
Sites
Subcutaneous
Injection

5. Complexity of PK model will vary with:
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
model.
We Always Choose the SIMPLEST Model

6. Types of PK Models 1- Physiologic (Perfusion) Models
2- Compartmental Models
3- Mammillary Models

7. PHYSILOGIC PK 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.

8. PHYSILOGIC PK MODELS Can study how physiologic factors may change
drug distribution from one animal species to
another
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
ratios.
Pathophysiologic conditions can affect
distribution.

9. Physiological Model Simulation
Perfusion Model Simulation of Lidocaine IV Infusion in Man
Blood
Metabolism
RET
Muscle
Adipose
Lung
Time
Percent of Dose

10. COMPARTMENTAL MODELS
The body is represented by a series of compartments that communicate reversibly with each other. 1 2 3
k12
k21

11. COMPARTMENTAL MODELS 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
affinity.
Within each compartment the drug is considered
to be uniformly distributed.
Drug move in and out of compartments
Compartmental models are based on linear
differential equations.
Rate constants are used to describe drug entry
into and out from the compartment.

12. COMPARTMENTAL MODELS 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
the data.

13. MAMMILLARY MODELS
Is the most common compartmental model used in PK. The model consists of one or more compartments connected to a central compartment 2 1 3 ka
kel
k12
k21

14. Intravenous and Extravascular Administration
IV, IM, SC

15. Intravenous and extravascular Route of Administration
Difference in plasma conc-time curve
Time Cp
Time Cp
Intravenous
Administration
Extravascular
Administration

16. One Compartment Open Model Intravenous Administration

17. One Compartment Open Model Intravenous Administration
The one compartment model offers the simplest way to describe the process of drug distribution and elimination in the body.
Blood
(Vd)
i.v.
Input
kel
Output
When the drug is administered i.v. in a single rapid injection, the process of absorption is bypassed

18. One Compartment Open Model Intravenous Administration
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.

19. FIRST-ORDER KINETICS  The rate of elimination for most drugs is a
first-order process.
 kel is a first-order rate constant with a unit
of inverse time such as hr-1.

20. Semi-log paper
Plotting the data

21. INTEGRATED EQUATIONS
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

22. INTEGRATED EQUATIONS Cp = Cp0e-kelt ln Cp = ln Cp0  kelt
DB = Dose . e-kelt
ln DB = ln Dose  kelt

23. Elimination Half-Life (t1/2)
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
Therefore,

24. ESTIMATION OF half-life from graph
A plot of Cp vs. time
t1/2 = 3 hr

25. Fraction of the Dose Remaining
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:

26. Volume of Distribution (Vd)
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

27. Apparent Vd
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).

28. Apparent Vd
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
where,
DB = amount of drug in the body
Cp = plasma drug concentration

29. For One Compartment Model with IV Administration:
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.

30. For One Compartment Model with IV Administration:
Cpo

31. Calculation of Vd from the AUC
Since, dDB/dt = -kelD = -kelVdCp
dDB = -kelVdCpdt
 dDB = -kelVd  Cpdt
Since,  Cpdt = AUC
Then, AUC = Dose / kelVd
Model
Independent
Method

32. Significance of Vd 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
proteins
Drugs with large Vd are usually confined in the
tissue
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

33. Apparent Vd
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.

34. CLEARANCE (Cl)
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.

35. INTEGRATED EQUATIONS

36. ESTIMATION OF PK PARAMETERS
A plot of Cp vs. time
Cpo
kel