1. Karunya Kandimalla, Ph.D
Principles of Pharmacokinetics Pharmacokinetics of IV Administration, 1-Compartment
Karunya Kandimalla, Ph.D
CP Clarke,L FD/MB

2. Objectives Be able to: To understand the properties of linear models
To understand assumptions associated with first order kinetics and one compartment models
To define and calculate various one compartment model parameters (kel, t½, Vd, AUC and clearance)
To estimate the values of kel, t½, Vd, AUC and clearance from plasma or blood concentrations of a drug following intravenous administration.
CP Clarke,L FD/MB

3. Recommended Readings Chapter 3, p. 47-62 IV route of administration
Elimination rate constant
Apparent volume of distribution
Clearance
CP Clarke,L FD/MB

4. Kinetics From the Blood or Plasma Data
Pharmacokinetics of a drug in plasma or blood
Absorption (Input)
Disposition
Distribution
Elimination
Excretion
Metabolism

5. Disposition Analysis (Dose Linearity)

6. Disposition Analysis (Time Variance)

7. Linear Disposition
The disposition of a drug molecule is not affected by the presence of the other drug molecules
Demonstrated by:
Dose linearity
Saturable hepatic metabolism may result in deviations from the dose linearity
Time invariance
Influence of the drug on its own metabolism and excretion may cause time variance

8. Disposition Modeling A fit adequately describes the experimental data
A model not only describes the experimental data but also makes extrapolations possible from the experimental data
A fit that passes the tests of linearity will be qualified as a model

9. One Compartment Model (IV Bolus)
Schematically, one compartment model can be represented as:
Where Xp is the amount of drug in the body, Vd is the volume in which the drug distributes and kel is the first order elimination rate constant
kel
Drug
Eliminated
Drug in
Body
Xp = Vd • C
The rate of change in systemic drug level is dependent on the balance between the rates of drug absorption and elimination
For both zero and first order processes, the net rate of drug accumulation is equal to the rate of drug absorption minus the rate of drug elimination
The absorption (ka) and elimination (kel) rate constants describe how quickly serum concentrations rise (ka) or decline (kel) after administration.
The elimination rate of a drug can be computed by taking the product of the elimination rate constant (kel) and the amount of drug in the body (Xp)
In general, low molecular weight, high lipid solubility and lack of charge encourage absorption.
CP Clarke,L FD/MB

10. One Compartment Data (Linear Plot)

11. One Compartment Data (Semi-log Plot)

12. Two Compartment Model (IV Bolus)
K 12
Blood, kidneys, liver
Drug in
Central
Compartment
Drug in
Peripheral
Compartment
K 21
kel
Fat, muscle
Drug
Eliminated
For both 1- and 2-compartment models, elimination takes place from central compartment

13. Two Compartment Data (Linear Plot)

14. Two Compartment Data (Semi-log Plot)

15. One Compartment Model-Assumptions
1-Compartment—Intravascular drug is in rapid equilibrium with extravascular drug
Intravascular drug [C] proportional to extravascular [C]
Rapid Mixing—Drug mixes rapidly in blood and plasma
First Order Elimination Kinetics:
Rate of change of [C]  Remaining [C]
Notice here that the log-transformed equation represents the equation of a straight line
CP Clarke,L FD/MB

16. Derivation-One Compartment Model
Bolus IV
Central Compartment (C)
Kel
This is the simplest of the intravascular administration models
The entire dose enters the systemic circulation immediately and the body is depicted as a single homogenous unit
Plasma concentrations are not necessarily equal to tissue concentrations, but they are proportional
The advantage of this model is that it permits calculation of drug concentrations at any time (no absorption phase, no distribution phase)
The disadvantage is that the kinetic parameters do not have physiologic meaning
CP Clarke,L FD/MB

17. Concentration versus time, semilog paper
IV Bolus Injection: Graphical Representation Assuming 1st Order Kinetics
C0 = Initial [C]
C0 is calculated by back-extrapolating the terminal elimination phase to time = 0
C0 = Dose/Vd
C0 = Dose/Vd
Slope = -K/2.303
Slope = -Kel/2.303
Note that half-life can also be read from the graph
Concentration versus time, semilog paper
CP Clarke,L FD/MB

18. Elimination Rate Constant (Kel)
Kel is the first order rate constant describing drug elimination (metabolism + excretion) from the body
Kel is the proportionality constant relating the rate of change of drug concentration and the concentration
The units of Kel are time-1, for example hr-1, min-1 or day-1

19. Half-Life (t1/2)
Time taken for the plasma concentration to reduce to half its original concentration
Drug with low half-life is quickly eliminated from the body
t/t1/2
% drug remaining 1 50 2 25 3
12.5 4
6.25 5
3.125

20. Change in Drug Concentration as a Function of Half-Life

21. Apparent Volume of Distribution (Vd)
Vd is not a physiological volume
Vd is not lower than blood or plasma volume but for some drugs it can be much larger than body volume
Drug with large Vd is extensively distributed to tissues
Vd is expressed in liters and is calculated as:
Distribution equilibrium between drug in tissues to that in plasma should be achieved to calculate Vd

22. Area Under the Curve (AUC)
AUC is not a parameter; changes with Dose
Toxicology: AUC is used as a measure of drug exposure
Pharmacokinetics: AUC is used as a measure of bioavailability and bioequivalence
Bioavailability: criterion of clinical effectiveness
Bioequivalence: relative efficacy of different drug products (e.g. generic vs. brand name products)
AUC has units of concentration  time (mg.hr/L)

23. Calculation of AUC using trapezoidal rule

24. Clearance (Cl)
The most important disposition parameter that describes how quickly drugs are eliminated, metabolized and distributed in the body
Clearance is not the elimination rate
Has the units of flow rate (volume / time)
Clearance can be related to renal or hepatic function
Large clearance will result in low AUC

25. Clearance Concepts Cinitial Cfinal ORGAN
elimination
If Cfinal < Cinitial, then it is a clearing organ

26. Practical Example Time (hr) Plasma Conc. (mg/L) ln (PlasmaConc.) 1
9.46
2.25 2
7.15
1.97 3
5.56
1.71 4
4.74
1.56 6
3.01
1.10 10
1.26
0.23 12
0.83
-0.19
IV bolus administration
Dose = 500 mg
Drug has a linear disposition

27. Linear Plot

28. Natural logarithm Plot
Kel
ln (C0)

29. Half-Life and Volume of Distribution
t1/2 = / Kel = hrs
Vd = Dose / C0 = 500 / = 44.66
ln (C0) =
C0 = Inv ln (2.4155) = mg/L

30. Clearance
Cl = D/AUC
Cl = VdKel
Cl =  = 9.73 L/hr

31. Home Work
Determine AUC and
Calculate clearance from AUC