INTRODUCTION TO PHARMACOKINETIC MODELS, ONE COMPARTMENT OPEN MODEL IV BOLUS, IV INFUSION, EXTRAVASCULAR ADMINISTRATION, WAGNER NELSON METHOD, METHOD OF RESIDUALS

1. RATNAM INSTITUTE OF PHARMACY
PHARMACOKINETIC MODELS
By,
MR. CH.PRAVEEN KUMAR M.Pharm., (Ph.D)
ASSOCIATE PROFESSOR
DEPARTMENT OF PHARMACEUTICS

2. Drug movement within the body is a complex process. The major objective is
therefore to develop a generalized and simple approach to describe, analyse
and interpret the data obtained during in vivo drug disposition studies.
The two major approaches in the quantitative study of various kinetic
process of drug disposition in the body are-
1. Model approach
2. Model independent approach
INTRODUCTION
Pharmacokinetic
Models
2

3. 1. MODEL-
A Model is a hypothesis that employ mathematical terms to concisely
describe quantitative relationship.
2. PHARMACOKINETIC MODEL-
It provide concise means of expressing mathematically or quantitatively, the
time course of drug(s) throughout the body and compute meaningful
pharmacokinetic parameters.
Pharmacokinetic Model Approach
3
Pharmacokinetic
Models

4. Pharmacokinetic models are useful in-
Characterizing the behavior of drugs in patients.
Predicting the conc. of drug in various body fluids with any dosage regimen.
Predicting the multiple dose concentration curves from single dose
experiment.
Calculating the optimum dosage regimen for individual patients.
Correlating plasma drug concentration with pharmacological response.
Determination of altered ADME level in specific disease condition.
Predicting the possibility of drug interaction.
Applications
4
Pharmacokinetic
Models

5. 5
Methods for analysis of Pharmacokinetic Data
Pharmacokinetic
Models

6. It is a hypothetical model and this model simply interpolate the experimental
data and helps to estimate the kinetics of a particular drug by using simple
formula.
Since it is hypothetical approach it is based on certain assumptions:-
The body is represented as a series of compartment arranged either in series
or parallel to each other, which communicate reversibly with each other.
Each compartment is not a real physiological or anatomical region but of a
fictitious or virtual one and considered as a tissue or group of tissue that have a
similar drug distribution characteristics.
 Within each compartment the drug is considered to be rapidly and uniformly
distributed.
Compartment Models
6
Pharmacokinetic
Models

7. The rate of drug movement between two compartment is described by first
order kinetics.
Rate constants are used to represent rate of entry and exit from the
compartment.
Mamillary Model Catenary Model
Compartment Models
7
Pharmacokinetic
Models

8. This is the most common model used in pharmacokinetics.
The model consists of one or more peripheral compartments connected to a
central compartment.
 The central compartment consists of plasma and highly perfused tissues in
which drug distributes rapidly.
The peripheral compartments or tissues compartments (denoted by numbers
2,3,etc.) are those with low vascularity and poor perfusion.
 The no. of rate constant which will appear in a particular compartment model
is given by R.
For intravenous admin. R = 2n-1 for extravascular admin. R = 2n
where n is no. of compartments.
Compartment Model- Mamillary Model
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Pharmacokinetic
Models

9. In this model, the compartment are joined to one another in a series like
compartments of a train.
This is however not observable physiologically/anatomically as the various
organs are directly linked to the blood compartment.
Rarely used.
Compartment Model- Catenary Model
9
Pharmacokinetic
Models

10. It is a simple and flexible approach and thus widely used.
It give a visual representation of various rate processes involved in drug
disposition and also give data.
 It enables monitoring of drug concentration change with time with a limited
amount of data.
 It is useful in predicting drug concentration time profile in both normal
physiological and in pathological condition.
 It is useful in the development of dosage regimens.
 Its allow the easy tabulation of parameters such as volume of distribution, half
life etc.
Compartment Model- Applications
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Pharmacokinetic
Models

11.  The compartments and parameters bear no relationship with the
physiological functions or anatomical structure of species.
 Extensive efforts are required in the development of exact model that predict
or describe the ADME of a certain drug.
 The model is based on curve fitting of plasma conc. with complex multi
exponential mathematical equations.
 The approach can be applied only to a specific drug under study.
 Owing to its simplicity, compartment models are often misunderstood.
Compartment Model- Disadvantages
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Pharmacokinetic
Models

12.  Also called as physiologically based pharmacokinetic models (PB-PK)
 They are drawn based on anatomic and physiological data
 Provides realistic picture of drug disposition in various tissues and organs.
 No. of compartments depends on drug disposition.
 Organs with no drug penetration is excluded (ex: Bones)
 More complex mathematical equations and all the organs are grouped as RET
(Rapidly Equilibrated Tissues) and SET (Slowly Equilibrated Tissues).
 Drug uptake by tissue depends on
a) Rate of blood flow to organ
b) Tissue/blood partition co-efficient
Physiological Model
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Pharmacokinetic
Models

13. Physiological Model
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Representation of physiological pharmacokinetic model
Pharmacokinetic
Models

14. Mathematical treatment is straight forward.
Data fitting is not required.
 Gives exact description of drug concentration time profile in any organ or
tissue.
 Influence of altered physiology or pathology on drug disposition can be easily
predicted.
 Model is frequently used in animals to collect the tissue samples easily using
invasive methods.
 Data can be correlated in various animals and species and data can be
extrapolated to humans.
 Pharmacokinetics of drug can be easily explained.
Physiological Model- Applications
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Pharmacokinetic
Models

15.  Obtaining experimental data and monitoring drug concentration in body is an
exhaustive process.
 Predicting the individualized dosing is difficult due to the assumption of
average blood flow for individual subjects.
 Data points are less and makes difficult to asses the pharmacokinetic
parameters.
Physiological Model- Disadvantages
15
Pharmacokinetic
Models

16.  Obtaining experimental data and monitoring drug concentration in body is an
exhaustive process.
 Predicting the individualized dosing is difficult due to the assumption of
average blood flow for individual subjects.
 Data points are less and makes difficult to asses the pharmacokinetic
parameters.
Physiological Model- Disadvantages
16
Pharmacokinetic
Models

17. Time course of drug concentration in the body can be satisfactorily explained by
assuming the body as single well mixed compartment with first order
disposition process.
Assumptions:
 The body is considered as a single, kinetically homogenous unit.
Drugs move dynamically, in (absorption) and out (elimination) of this
compartment.
Final distribution equib. between drug in plasma and other body fluid is
attained instantaneously.
Elimination is a first order (monoexponential) process.
Rate of input (absorption) > rate of output (elimination).
One Compartment Open Model
(Instantaneous distribution model)
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Pharmacokinetic
Models

18. Assumptions:
 Reference compartment is plasma and it is the representation of drug
concentration in all the body tissues.
However, the model doesn’t assume that the drug concentration in plasma is
equal to that in other body tissues.
The term “Open” indicates that input (absorption) and output (elimination) are
unidirectional and that the drug can be eliminated from the body.
One Compartment Open Model
(Instantaneous distribution model)
18
Pharmacokinetic
Models
Representation of one compartment open model

19. Depending on rate of input:
Several one compartment models are defined as
1. One-compartment open model – IV Bolus administration
2. One-compartment open model – IV Infusion
3. One-compartment open model – Extravascular administration – Zero order
4. One-compartment open model – Extravascular administration – First order
One Compartment Open Model
(Instantaneous distribution model)
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Pharmacokinetic
Models

20. When the drug is given in the form of rapid intravenous injection, it takes a
maximum of three minutes for complete circulation, therefore rate of
absorption is neglected in the calculations.
One Compartment Open Model –
IV Bolus administration
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Pharmacokinetic
Models
Representation of one compartment open model – IV Bolus

21. One Compartment Open Model –
IV Bolus administration
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Pharmacokinetic
Models

22. Estimation of pharmacokinetic parameters: - IV bolus
Drug that follows one compartment kinetics when the drug is given as IV bolus,
the decline in plasma concentration is due to elimination from the body.
The elimination phase can be characterized by 3 parameters
1. Elimination rate constant (KE)
2. Elimination Half-life (t1/2)
3. Clearance (CL)
One Compartment Open Model –
IV Bolus administration
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Pharmacokinetic
Models

23. Elimination rate constant (KE): -
One Compartment Open Model –
IV Bolus administration
23
Pharmacokinetic
Models

24. Elimination rate constant (KE): -
One Compartment Open Model –
IV Bolus administration
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Pharmacokinetic
Models

25. Elimination rate constant (KE): -
One Compartment Open Model –
IV Bolus administration
25
Pharmacokinetic
Models
To find elimination rate constant KE = slope x 2.303

26. Half-Life (t1/2): -
t1/2 = 0.693/KE
Volume of distribution (Vd): -
X = VdC
Vd = X/C
Vd = X/(KE . AUC) (If non-compartment model)
Clearance (CL): -
CLT = KE . Vd
KE = CLT /Vd Substituting this eq. in t1/2 = 0.693/KE
we get - t1/2 = (0.693. Vd) / CLT
One Compartment Open Model –
IV Bolus administration
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Pharmacokinetic
Models

27. Clearance (CL): -
CLT can be written as
CLT = Rate of elimination/ Plasma drug concentration
CLT = (dx/dt)/ C
Since dx/dt = KE . X
CLT = KE . X /C
(Since Vd = X/C)
Eq. can be written as CLT = KE . Vd
Renal clearance : CLR= Ke . Vd
Hepatic clearance : CLH= Km . Vd
Total systemic clearance is given as CLT = CLR+ CLH+ CL Others …………..
One Compartment Open Model –
IV Bolus administration
27
Pharmacokinetic
Models

28. If a drug has a potential to precipitate toxicity, it is unsuitable as rapid IV
injection.
Steady state kinetics can be attained using infusion.
Several antibiotics, theophylline, procainamide is administered at a constant
rate (zero order) by IV infusion.
Duration of constant rate infusion is much longer than the half-life of the drug.
Advantages:
Ease of control of rate of infusion to fit the individual patients.
Prevents fluctuating maxima and minima when the drug has narrow
therapeutic index.
Electrolytes and nutrients can be simultaneously administered.
One Compartment Open Model –
IV Infusion
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Pharmacokinetic
Models

29. One Compartment Open Model –
IV Infusion
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Pharmacokinetic
Models
Representation of one compartment open model – IV Infusion
At ant time of infusion, the rate of change in the amount of drug in the body
(dx/dt) is the difference between zero order infusion (R0) and first order
elimination (– KE X)
dX/dt = R0 – KE X

30. One Compartment Open Model –
IV Infusion
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Pharmacokinetic
Models

31. Initially the amount of drug in the body is zero and hence no elimination
As time passes the amount of drug in the body gradually rises until rate of
elimination is equals to rate of infusion (steady state/plateau/infusion
equilibrium)
One Compartment Open Model –
IV Infusion
31
Pharmacokinetic
Models

32. At steady state:
Rate of change in the amount of drug is zero and the eq. becomes
One Compartment Open Model –
IV Infusion
32
Pharmacokinetic
Models

33. One Compartment Open Model –
IV Infusion
33
Pharmacokinetic
Models
Elimination rate constant (KE): -

34. One Compartment Open Model –
IV Infusion
34
Pharmacokinetic
Models
Elimination rate constant (KE): -
To find elimination rate constant KE = slope x 2.303

35. One Compartment Open Model –
IV Infusion
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Pharmacokinetic
Models
Infusion plus Loading dose-
Drugs having longer half-lives takes very long time to reach steady
state/plateau (eg: Phenobarbital – 5 days). Thus initially these type of drugs
have subtherapeutic concentrations and can be overcome by administering an
IV loading dose large enough to yield the steady state immediately following IV
infusion.

36. One Compartment Open Model –
IV Infusion
36
Pharmacokinetic
Models
Infusion plus Loading dose-

37. One Compartment Open Model –
IV Infusion
37
Pharmacokinetic
Models
Infusion plus Loading dose-

38. One Compartment Open Model –
IV Infusion
38
Pharmacokinetic
Models
Infusion plus Loading dose-

39. One Compartment Open Model –
Extravascular Administration
39
Pharmacokinetic
Models
When a drug is administered through extravascular route, absorption is the
prerequisite for its therapeutic activity.
Rate of absorption may be zero order or first order.
Zero order absorption model:
All equations that explain constant rate IV infusion is applicable to this model.

40. One Compartment Open Model –
Extravascular Administration
40
Pharmacokinetic
Models
First order absorption model:

41. One Compartment Open Model –
Extravascular Administration
41
Pharmacokinetic
Models
First order absorption model:

42. One Compartment Open Model –
Extravascular Administration
42
Pharmacokinetic
Models
First order absorption model:

43. One Compartment Open Model –
Extravascular Administration
43
Pharmacokinetic
Models
First order absorption model:

44. One Compartment Open Model –
Extravascular Administration
44
Pharmacokinetic
Models
First order absorption model: Estimation of Ka and KE
Method of Residuals (Feathering/Peeling/Stripping) –
Commonly used in pharmacokinetics to resolve a multiexponential curve to its
individual components.
So, the biexponential equation when the drug is administered through
extravascular site is

45. One Compartment Open Model –
Extravascular Administration
45
Pharmacokinetic
Models
First order absorption model: Estimation of Ka and KE
Method of Residuals (Feathering/Peeling/Stripping) –

46. One Compartment Open Model –
Extravascular Administration
46
Pharmacokinetic
Models
First order absorption model: Estimation of Ka and KE
Method of Residuals (Feathering/Peeling/Stripping) –

47. One Compartment Open Model –
Extravascular Administration
47
Pharmacokinetic
Models
First order absorption model: Estimation of Ka and KE
Method of Residuals (Feathering/Peeling/Stripping) –

48. One Compartment Open Model –
Extravascular Administration
48
Pharmacokinetic
Models
First order absorption model: Estimation of Ka and KE
Method of Residuals (Feathering/Peeling/Stripping) –

49. One Compartment Open Model –
Extravascular Administration
49
Pharmacokinetic
Models
First order absorption model: Estimation of Ka and KE
Wagner Nelson Method –
This method determines Ka from percent unabsorbed – time plots and doesn’t
require the assumption of zero or first order.
After oral administration of a single dose, at any given point of time, the amount
of drug absorbed into systemic circulation XA is the sum of amount of drug in
the body X and amount of drug eliminated from the body XE, Then
XA = X+XE

50. One Compartment Open Model –
Extravascular Administration
50
Pharmacokinetic
Models
First order absorption model: Estimation of Ka and KE
Wagner Nelson Method –

51. One Compartment Open Model –
Extravascular Administration
51
Pharmacokinetic
Models
First order absorption model: Estimation of Ka and KE
Wagner Nelson Method –

52. One Compartment Open Model –
Extravascular Administration
52
Pharmacokinetic
Models
First order absorption model: Estimation of Ka and KE
Wagner Nelson Method –

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REFERENCES
 Biopharmaceutics and pharmacokinetics – A Treatise , D. M. Brahmankar, Sunil
B.Jaiswal. Vallabh prakashan IInd edition, pp- 315-366.
 Basics of Pharmaokinetics, Leon Shargel, fifth edition, willeypu blications, pp- 453-
490.
 Shargel L., Andrew B.C., Fourth edition “Physiologic factors related to drug
absorption” Applied Biopharmaceutics and Pharmacokinetics, Prentice Hall
International, INC., Stanford 1999. Page No. 99-128.
 Internet sources.
Pharmacokinetic
Models

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