This document discusses pharmacokinetic models. It begins by covering basic considerations like compartment models, one compartment models for intravenous bolus administration and infusion, and extravascular administration. It also discusses multi-compartment models, non-linear pharmacokinetics including Michaelis-Menten kinetics, and drug interactions. Specific models and concepts covered in more depth include one compartment models, two compartment models, mixed order kinetics, Michaelis-Menten equation, plasma drug concentration profiles, and pharmacodynamic parameters.

1. PHARMACOKINETIC
MODELS
Name: Manjit Kaur
Roll No. 1481311
M. Pharmacy (2nd Sem.)
Department Of Pharmaceutics
Sri Sai College Of Pharmacy

2. PHARMACOKINETIC MODELS
Basic considerations in pharmacokinetics
• Compartment models
• One compartment model
• Assumptions
• Intravenous bolus administration
• Intravenous infusion
• Extravascular administration
(zero order and first order absorption model)
• Multi-compartment model

3. Non linear pharmacokinetics
 Causes
 Michaelis- Menten equation
 Estimation of Kmax and Vmax
Drug interactions

4. BASIC CONSIDERATIONS IN
PHARMACOKINETICS
• Pharmacokinetic parameters
• Pharmacodynamic parameters
• Zero, first order & mixed order kinetic
• Rates and orders of kinetics
• Plasma drug conc. Time profiles
• Compartmental models – physiological model
• Applications of pharmacokinetics
• Non compartment model

5. MIXED ORDER KINETICS
 Kinetics of a pharmacokinetic process changes from First order to
Zero order with increasing dose or chronic medication.
 Deviations from original Linear kinetic profile – Non Linear kinetics.
 Dose dependent kinetics
 Seen when P’kinetic process Carriers / Substrates (Capacity Limited
– get saturated at Higher drug Conc).

6. MICHAELIS – MENTEN KINETICS
 Describes velocity of Capacity limited, enzyme reactions and non
linear pharmacokinetics.
MICHAELIS MENTON EQUATION IS
-DC/DT = VMAX. C / KM + C
KM = Michaelis constant,
Vmax = Theoretical maximum rate of process
 Some examples; Absorption (Vitamin C), Distribution (Naproxen),
and Elimination (Riboflavin)

7. PLASMA DRUG CONCENTRATION
– TIME PROFILE
Effectiveness of Dosage Regimen Concentration of
Drug in the Body Conc. at Site of action Conc. in whole
Blood (Plasma, Serum), Saliva, Urine, PK Parameters
determine drug Conc.
Three important parameters useful in assessing the
bioavailability of a drug from its formulation are:

8. Peak plasma concentration ( cmax ):
The point at which, maximum concentration of drug in plasma.
Units : µg/ml
 Peak conc. Related to the intensity of pharmacological response,
it should be above MEC but less than MSC.
 The peak level depends on administered dose and rate of
absorption and elimination.

9. Time of peak concentration (tmax ):
The time for the drug to reach peak concentration in plasma
(after extra vascular administration).
 Units : hrs
 Useful in estimating onset of action and rate of absorption.
 Important in assessing the efficacy of single dose drugs used to treat acute
conditions (pain, insomnia).

10. Area under curve (AUC):
It represents the total integrated area
under the plasma level-time profile and expresses the
total amount of the drug that comes into systemic
circulation after its administration.
Units : µg/ml x hrs

11. PHARMACODYNAMIC
PARAMETERS
 Minimum effective concentration (MEC): Minimum concentration of drug in
plasma/receptor site required to produce therapeutic effect.
 Antibiotics - MEC 2.
 Maximum safe concentration (MSC): Concentration in plasma above which
adverse or unwanted effects are precipitated.
 Onset time: Time required to start producing pharmacological response. Time for
plasma concentration to reach MEC after administrating drug.

12.  Onset of action: The beginning of pharmacologic response. It occurs when
plasma drug concentration just exceeds the required MEC.
 Duration of action: The time period for which the plasma concentration of
drug remains above MEC level.
 Intensity of action: It is the minimum pharmacologic response produced
by the peak plasma conc. Of drug.
 Therapeutic range: the drug conc. between MEC and MSC.

13. CONCEPT OF “HALF LIFE”
½ Life = how much time it takes for blood levels of drug to
decrease to half of what it was at equilibrium.
There are really two kinds of ½ life.
1. “Distribution” ½ life = when plasma levels fall to half what they
were at equilibrium due to distribution to/storage in body’s tissue
reservoirs.
2. “Elimination” ½ life = when plasma levels fall to half what they
were at equilibrium due to drug being metabolized and eliminated.
It is usually the elimination ½ life that is used to determine dosing
schedules, to decide when it is safe to put patients on a new drug.

14. PHARMACOKINETIC MODELS AND
COMPARTMENTS
Pharmacokinetic Modelling
 Compartment Models:
a. Caternary Model
b. Mamillary Model
 Non-Compartment Models AUC, MRT, MAT, Cl, VSS
 Physiologic Models

15. PHARMACOKINETIC MODELS:
Means of expressing mathematically or quantitatively, time
course of drug through out the body and compute meaningful
pharmacokinetic parameters. Useful in :
Characterize the behaviour of drug in patient.
• Predicting conc. Of drug in various body fluids with dosage
regimen.
 Calculating optimum dosage regimen for individual patient.
 Evaluating bioequivalence between different formulation.
 Explaining drug interaction.

16. Pharmacokinetic models
Pharmacokinetic models are hypothetical structures
that are used to describe the fate of a drug in a
biological system following its administration.
Model is the Mathematical representation of the data
and It is just hypothetical.

17. COMPARTMENTAL MODELS:
A compartment is not a real physiological or anatomic
region but an imaginary or hypothetical one consisting
of tissue/ group of tissues with similar blood flow &
affinity.
Our body is considered as composed of several
compartments connected reversibly with each other.

18. ADVANTAGES:
Gives visual representation of various rate processes
involved in drug disposition.
Possible to derive equations describing drug
concentration changes in each compartment.
One can estimate the amount of drug in any
compartment of the system after drug is introduced
into a given compartment.

19. DISADVANTAGES:
 Drug given by IV route may behave according to single
compartment model but the same drug given by oral route
may show 2 compartment behaviour.
 The type of compartment behaviour i.E. Type of
compartment model may change with the route of
administration.

20.  Central compartment: Blood & highly perfused tissues such
as heart, kidney, lungs, liver, etc.
 Peripheral compartment: Poorly per fused tissues such as fat,
bone, etc.
 MODELS: “OPEN” and “CLOSED” models:
 The term “open” itself mean that, the administered drug dose is
removed from body by an excretory mechanism (for most
drugs, organs of excretion of drug is kidney).
 If the drug is not removed from the body then model refers as
“closed” model.

21. LOADING DOSE:
A drug dose does not show therapeutic activity unless it reaches the
desired steady state.
It takes about 4-5 half-lives to attain it and therefore time taken
will be too long if the drug has a long half-life.
A simple equation for calculating loading dose is :
xo,l = css,av vd / F

22. ASSUMPTIONS
 One compartment: The drug in the blood is in rapid
equilibrium with drug in the extra-vascular tissues. This is
not an exact representation however it is useful for a number
of drugs to a reasonable approximation.
 Rapid mixing: We also need to assume that the drug is
mixed instantaneously in blood or plasma.
 Linear model: We will assume that drug elimination follows
first order kinetics.

23. ONE COMPARTMENT MODEL:
One compartment model can be defined:
a. One com. Open model – i.V. Bolus.
b. One com. Open model - cont. Intravenous infusion.
c. One com. Open model - extra vas. Administration (zero-order
absorption)
d. One com. Open model - extra vas. Administration (First-order
absorption)

24. INTRAVENOUS (IV) BOLUS
ADMINISTRATION
 INTRAVENOUS (IV) BOLUS ADMINISTRATION RATE OF DRUG
PRESENTATION TO BODY IS:
If rate out or elimination follows first order kinetic
Dx/dt = -kex ----------------(1)
 ELIMINATION PHASE:
 Elimination phase has three parameters:
 Elimination rate constant,
 Elimination half- life,
 Clearance
 ELIMINATION RATE CONSTANT: Integration of equation (1)
In x = ln xo – ke t -----------(eq.2)

25. Elimination half -life can be readily obtained from the
graph of log c versus t.
Half-life is a secondary parameter that depends upon
the primary parameters such as clearance and volume
of distribution.
T1/2 = 0.693 Vd / ClT

26.  APPARENT VOLUME OF DISTRIBUTION:
defined as volume of fluid in which drug appears to be distributed. Vd =
amount of drug in the body (x) / Plasma drug concentration (C)
 CLEARANCE: rate of elimination / Plasma drug conc..
 ORGAN CLEARANCE: Rate of elimination by organ= rate of presentation to
the organ – rate of exit from the organ.
Clorgan= Q.Er …………….(eq 22)
Extraction ratio: ER= (Cin- Cout)/ Cin

27. ONE COMPARTMENT MODEL: EXTRA VASCULAR
ADMINISTRATION (ZERO ORDER ABSORPTION)
 This model is similar to that for constant rate infusion. Rate
of drug absorption as in case of CDDS , is constant and
continues until the amount of drug at the absorption site (Ex.
GIT) is depleted.
 All equations for plasma drug conc. Profile for constant rate
I.V. Infusion are also applicable to this model.

28. ONE COMPARTMENT MODEL: EXTRA VASCULAR
ADMINISTRATION (FIRST ORDER ABSORPTION):
 Drug that enters the body by first order absorption process gets
distributed in the body according to one compartment kinetic and
is eliminated by first order process. The model can be depicted as
follows and final equation is as follows Blood & other Body
tissues
C=Ka F Xo /Vd (Ka -KE ) [e -Ket -e -Kat]

29. MULTI- COMPARTMENT MODELS:
 Ideally a true pharmacokinetic model should be the one with a rate constant for
each tissue undergoing equilibrium.
 Therefore, best approach is to pool together tissues on the basis of similarity in
their distribution characteristics. The drug disposition occurs by first order.
 Multi-compartment characteristics are best described by administration as i.v
bolus and observing the manner in which the plasma concentration declines with
time.
 The no. Of exponentials required to describe such a plasma level-time profile
determines the no. Of kinetically homogeneous compartments into which a drug
will distribute.

30. The simplest and commonest is the two compartment
model which classifies the body tissues in two
categories :
1. Central compartment or compartment
2. Peripheral or tissue compartment or compartment

31. TWO COMPARTMENT OPEN MODEL-IV
BOLUS ADMINISTRATION:
Elimination from central compartment
• After the iv bolus of a drug the decline in the plasma conc. Is bi-
exponential.
• Two disposition processes- distribution and elimination.
• These two processes are only evident when a semi log plot of C vs. T
is made.
• Initially, the conc. Of drug in the central compartment declines rapidly,
due to the distribution of drug from the central compartment to the
peripheral compartment. This is called distributive phase.

32. TWO-COMPARTMENT OPEN
MODELEXTRAVASCULAR ADMINISTRATION:
First - order absorption:
For a drug that enters the body by a first-order
absorption process and distributed according to two
compartment model, the rate of change in drug conc.
in the central compartment is described by three
exponents:
An absorption exponent, and the two usual exponents
that describe drug disposition.

33.  The plasma conc. at any time t is
 C = n e-kat + l e-at + m e-bt C = absorption + distribution
+ elimination exponent
 Besides the method of residuals, ka can also be found by loo-
riegelman method for drug that follows two-compartment
characteristics.
 Despite its complexity, the method can be applied to drugs that
distribute in any number of compartments.

34. NONLINEAR PHARMACOKINETICS
 The rate process of drug’s ADME are depend upon carrier or enzymes that
are substrate specific, have definite capacities and are susceptible to
saturation at a high drug concentration.
 In such cases, an essentially first-order kinetics transform into a mixture of
first-order and zero-order rate processes and the pharmacokinetic
parameters are changed with the size of the administered dose.
 Pharmacokinetics of such drugs are said to be dose dependent. Terms
synonymous with it are mixed-order, nonlinear and capacity-limited
kinetics.

35. DETECTION OF NON-LINEARITY IN
PHARMACOKINETICS:
 There are several tests to detect non –linearity in
pharmacokinetics but the simplest ones are:
 First test:- Determination of steady state plasma concentration
at different doses.
 Second test:- Determination of some important pharmacokinetic
parameters such as fraction bioavailability, elimination half -life
or total systemic clearance at different doses of drug.
 Any change in these parameters is indicative to non-linearity
which are usually constant.

36. CAUSES OF NON-LINEARITY
 DRUG ABSORPTION
 Three causes:-
I) Solubility / dissolution of drug is rate-limited; Griseofulvin - at high concentration in
intestine.
II) Carrier - mediated transport system; Ascorbic acid - saturation of transport system.
III) Pre-systemic gut wall / hepatic metabolism attains saturation; Propranolol.
 These parameters affected F, Ka , Cmax and AUC.
• A decrease in these parameters is observed in former two causes and an increase in
latter cause.

37. DRUG DISTRIBUTION
 At high doses non-linearity due to two causes: -
I) Binding sites on plasma proteins get saturated; Phenylbutazone.
II) Tissue binding sites get saturated.
 In both cases there is increase in plasma drug concentration.
 Increase in Vd only in (I).
 Clearance with high ER get increased due to saturation of binding sites.

38. DRUG METABOLISM
 Non-linearity occurs due to :
 capacity limited metabolism
 small changes in dose administration
 large variations in plasma concentration at steady state

39. Two imp causes: -
I) Capacity - limited metabolism - enzyme &/
cofactor saturation; Phenytoin, Alcohol.
II) Enzyme induction - decrease in plasma
concentration; Carbamazepine.

40. DRUG EXCRETION
 Two active processes which are saturable : -
 Active tubular secretion - Penicillin G
 Active tubular reabsorption - Water soluble vitamins & Glucose.
Saturation of carrier systems - decrease in renal clearance in case of I
& increase in II. Half-life also increases.
 Other reasons like forced diuresis, change in urine pH, nephrotoxicity
& saturation of binding sites.
 In case of biliary excretion non - linearity due to saturation -
Tetracycline & Indomethacin.

41. MICHAELIS MENTEN ENZYME KINETICS
It is also called as Capacity-limited metabolism or Mixed order
kinetics.
E + D = EDE + M
Enzymes usually react with the substrate to form enzyme substrate
complexes; then the product is formed. The enzyme can go back to
react with another substrate to form another molecule of the
product.

42. MICHAELIS MENTEN EQUATION
 The kinetics of capacity limited or saturable processes is best described
by Michaelis-Menten equation.
-DC/DT = VMAX. C / KM + C ----------------(Eq.1)
 Where, -dC/dt = rate of decline of drug conc. with time
 Vmax = theoretical maximum rate of the process
 KM = Michaelis constant.

43.  Three situation can now be considered depending upon the value
of Km and C.
 when KM = C : -
 under this situation, eq I reduces to,
-dC/dt = Vmax/2...................II
 The rate of process is equal to half of its maximum rate.
 This process is represented in the plot of dc/dt vs. C.

44.  If a drug at low conc. undergoes a saturable biotransformation
then
KM>>C
 KM +C =KM and eq. I reduces to,
-dC/dt =Vmax C /KM………………III
above eq. is identical to the one that describe first order elimination
of drug,
where Vmax/KM= KE.

45. DRUG INTERACTIONS LINKED
TRANSPORTS:
INTRODUCTION:
 On its journey through the body, a drug needs to cross different
biological barriers.
 These barriers can be - A single layer of cells (e.g. the intestinal
epithelium), - Several layers of cells (e.g. in the skin), - Or the cell
membrane itself (e.g. to reach an intracellular receptor).
 A drug can cross a cell layer either by traveling through the cells
(transcellular drug transport) or through gaps between the cells
(paracellular drug transport).

46. Transcellular drug transport
 In order to travel through a cell or to reach a target inside a cell, a
drug molecule must be able to transverse the cell membrane.
 Although cell membranes largely vary in their permeability
characteristics depending on the tissue, the main mechanisms of
drugs passing through the cell membrane are passive diffusion,
carrier-mediated processes and vesicular transport.

47. The 3 steps involved in transcellular transport of drugs are
i. Permeation of GI epithelial cell membrane, a lipoidal
barrier- this is the major obstacle to drug absorption.
ii. Movement across the intracellular space (cytosol).
iii. Permeation of the lateral or basolateral membrane- this is
of secondary importance.

48. a. Passive Transport:
 Passive diffusion is the process by which molecules spontaneously diffuse from a
region of higher concentration (e.g. outside of the cell) to a region of lower
concentration (e.g. inside the cell), and it is the main mechanism for passage of drugs
through membranes.
b. Carrier-mediated processes
 Many cell membranes possess specialized transport mechanisms that regulate entry and
exit of physiologically important molecules and drugs.
 Such transport systems involve a carrier molecule, that is, a trans membrane protein
that binds one or more molecules and releases them on the other side of the membrane.

49. c. Ion-Pair Transport
Mechanism that explains the absorption of drugs like quaternary
ammonium compounds and sulphonic acids, which ionize under all
pH conditions, is ion-pair transport.
d. Pore transport
It is also known as Convective transport, bulk flow or filtration.
This mechanism is responsible for transport of molecules into the
cell through the protein channels present in the cell membrane.

50. Paracellular transport/Intercellular transport
Drugs can also cross a cell layer through the small aqueous
contact points (cell junctions) between cells.
This paracellular drug transport can be initiated by a
concentration gradient over the cell layer (passive diffusion), or
By a hydrostatic pressure gradient across the cell layer
(filtration).

51. Vesicular or Corpuscular Transport
(Endocytosis)
During vesicular transport the cell membrane forms a
small cavity that gradually surrounds particles or
macromolecules, thereby internalizing them into the cell
in the form of a vesicle or vacuole.

52. CYTOCHROME P450 DRUG
INTERACTION
 Humans constantly exposed to xenobiotics(usually non polar) that can cause harmful effect if not
eliminated. 
 Biotransformation convert non polar compounds to polar and helps in their elimination. 
 Biotransformation occurs in 2 phases(phase1 &phase 2). 
 Cytochrome p-450 is a superfamily of enzymes that catalyse most of the oxidation reactions of
phase 1. 
 Require both molecular oxygen and NADPH to effect reaction.  Also called mixed function
oxidases and mono-oxygenases.

53. CYTOCHROME P450 ISOFORMS:
 Isoforms mean same enzyme that belong to cyp450 enzyme and which
having ability to metabolized drug. 
 There are several isoforms of enzyme which is given below:-
1. CYP1A2
2. CYP2C9
3. CYP2C19
4. CYP2D6
5. CYP2E1 etc.

54. CYP1A2…  Metabolize the chemical and environmental
chemicals.  13% total hepatic content of isoenzyme. 
 Drug substrate E.g- caffein, theophylline, propanolol. 
 Drug inhibitor E.g- ciprofloxacin, cimetidine, erythromycin. 
 Drug inducer E.g- hydrocarbon, phenobarbital, rifampicin.
CYP2C9…  Responsible for metabolism of ibuprofen,
tolbutamide, torsemide.  Warfarin is mainly metabolized by this
isoforms. 9  Inhibitor of warfarin
 E.g- fluconazole, metronidazole, amiodarone.

55.  CYP2C19...  Responsible for metabolism of
diazepam, omeprazole, lansoprazole. Poor
metabolizers.
CYP2D6...  Enzyme not inducible by drug.  Most
drug use in clinical evaluation metabolized by this
isoforms.

56. INDUCTION AND INHIBITION OF
CYP450:
 Induction of drug metabolism can lead to unexpected drops in drug
concentration or the build-up of metabolites.
 The reverse can occur when there is inhibition of drug metabolism.
 The major organ involved in metabolism is liver and the major
enzyme system involved in drug metabolism is CYP 450, the well-
known family of oxidative hemoproteins.
 Induction CYP 450 enzymes at the liver is responsible for
induction of metabolism of many drugs.

57. INHIBITION OF CYP450:
Decrease in the drug metabolism ability of enzyme by
drug is called enzyme inhibition.  inhibition of CYP
enzymes can be classified :
1.Reversible inhibition.
2.Irreversible inhibition.

58.  Reversible inhibition... 
 Direct competition for binding site between substrate and inhibitor.  determination of
potency of inhibitor. 
 for example:- cimetidine H2 receptor antagonist. 16
 Irreversible inhibition... 
 It is occur by reactive metabolites generation.  first type of irreversible inhibition
involves the formation of metabolic intermediate complexes.  inhibition of CYP3A by
erythromycin. 
 Transformation reactions such as N-hydroxylation, N-demethylation, N-oxidation
catalyzed by CYP3A.

59. THANK
YOU