The document discusses various pharmacokinetic models used to describe drug movement in the body. It begins by defining pharmacokinetics and some key parameters. It then describes compartment models, including mammillary and caternary models, and provides an example of a one-compartment open model for intravenous bolus administration. This model assumes rapid distribution and first-order elimination. The document also discusses zero-order and first-order reaction kinetics and how they relate to pharmacokinetic processes. It provides examples of using compartment model equations to calculate drug concentrations over time and dosing requirements.

1. Part II: Clinical pharmacokinetics

2. Definition:
 Pharmacokinetic is defined as the kinetics of drug absorption, distribution,
metabolism and excretion (ADME) and their relationship with the
pharmacologic, therapeutic or toxicologic response in human and animals.
 Pharmacokinetics refers to the way the drug is handled by the body
 Pharmacokinetic measures, such as area under the curve (AUC) and
concentration at the maximum (Cmax) Parameters calculated from those
measures, such as clearance, half-life, and volume of distribution

3. Pharmacokinetics cont…
 A proper understanding of these parameters is required to design an
appropriate drug regimen for a patient;
 Because effectiveness of a dosage regimen is determined by the concentration
of the drug in the body.
 Ideally the concentration of the drug should be measured at the site of action
of the drug; that is, at the receptor.
 However, owing to inaccessibility, the drug concentrations are normally
measured in the whole blood, plasma, urine, saliva, and CSF and considered as
at equilibrium to the site of action

4. Why we study Pharmacokinetics?
 To enhance the safe and effective therapeutic mgt of individual patients
 It tells how much we should dose
 How often we should administer
 What factors affect the response
 Possible drug interactions, disease interactions
 How do we dot it?
– Using pharmacokinetic parameters

5. Some pharmacokinetic parameters
 Bioavailability (F) (Fraction of drug absorbed)
 Volume of distribution .Litres/Kg .
 Half life .Min or hr or day
 Peak conc. ng or mcg or mg per
 Peak time .Min or hr or day
Clearance . ml/min/kg
 AUC. ng hr/ml

7. Rate and order of reaction
 Rate of Reaction
• Reaction rate is the speed at which a reaction takes place. It is “how
quickly” a product is formed in a chemical reaction.
• In the case of multiple step reactions, the slowest step determines the rate of
reaction
Order of Reaction
• The order of reaction is defined as the manner in which the rate of a
reaction varies with the concentration of the reactants Control of speed of
a reaction or process
 Types of Reactions With Respect to their Order
Zero-Order Reaction
First -Order Reaction
Second-Order Reaction

8. Zero order kinetics
 In Zero-Order reaction the reaction rate is independent of the concentration
of the reacting substance or reaction rate depends on the zero power of the
reactant.
 Rate of ADME processes is independent of concentration and rate changes
at a constant rate
e.g . Enzyme present

10. Cont…
where Ko is the zero-order rate constant
• This equation clearly indicates that Y changes at a constant rate,
• The integration of the Eqn. yields the following:
• where Y is amount present at time t and Y0 is amount at time zero.

11. Examples of zero-order process
 administration of a drug as an i.v infusion,
 formulation and administration of controlled release DFs and
 administration of drugs through transdermal drug delivery systems

12. First-Order Reaction
– In first order kinetics ADME rate processes are dependent on concentration
 Elimination of the Drug is directly proportional to its plasma concentration
and on its half life (time dependent).
 First order implies that no matter how much concentration of the drug
you give it will be eliminated 50% by its first half- life (no cumulative
effect).
 Most drugs used in clinical practice at therapeutic dosages will show first
order rates processes

13. First-Order Reaction
 For drugs that show a first order elimination process, as the amount of
drug administered increases, the body is able to eliminate the drug
accordingly and accumulation will not occur.
 However, if we continue to increase the amount of drug administered then
all drugs will change from showing a first order process to a zero order
process,
e.g. overdose situation (non-linear pharmacokinetics)

15. First-order process
where K is the first-order rate constant.
• Upon integration of the above Eqn., we obtain:
Ct = Co* e–ket

16. Applications of first-order process
• It is extremely important in PKs since the majority of
therapeutic drugs are eliminated by this process.
• Conventional tablet
• IM injections

18. Exercise
1. A solution of a drug was freshly prepared at a conc. of 300
mg/mL. After 30 days at 25°C, the drug concentration in the
solution was 75 mg/mL. When will the drug decline to one-half
of the original concentration?
a. Assuming zero-order kinetics, (20days)
b. Assuming first-order kinetics (15days)
1. For a drug that has an initial plasma concentration of 120 mg/L
and a half-life of 3 hours, what would the plasma concentration
be 12 hours later? (assume first order) (7.5mg/L)

19. Exercise
 If C0 = 100 mg/L and K = 0.10 h-1, what is the concentration 6
hours later? (Answer C = 54.9 mg/L)
 If the concentration at 3 hours is 50 mg/L and k = 0.1 h-1, what is
C0?(Answer C0 = 67.5 mg/L)
 If C0 = 100 mg/L and it takes 4 hours to reach a concentration of
10mg/L, what is k? (Answer K = 0.576 h-1)
 How long will it take for concentrations to fall from 100 mg/L to
25 mg/L if K = 0.2 h-1? (Answer t = 6.9 hours)

20. Pharmacokinetic models
 Drug movement within the body is a complex process hence pharmacokinetic
models are necessary to understand them in simple way.
 A model is a hypothesis using mathematical terms to describe quantitative
relationships. And compute meaningful PK Parameters.
 The mathematical model used to calculate absorption, distribution and
elimination are known as pharmacokinetic model.

21. Uses of Pharmacokinetic models
 The pharmacokinetic models express the time course of drug throughout
the body.
 It is also used to predict concentration of drugs in body fluid after
administering dose.
 It is also used to predict the behaviors of drugs in patients.
 to evaluate risk of toxicity

22. TYPE OF PHARMACOKINETICS MODELS
They are of three different types
l. Compartment models
2. Physiological models
3. Non- Compartment models

23. 1. Compartment models
 It is assumed that the body consists of series of compartments.
 Each compartment may exchange material with other compartments.
 A compartment is not real physiologic or anatomic region, but it is
considered as tissues have same blood flow and affinity for drugs.
 The compartment is "well stirred" and distribution of drug is uniform and
rapid within each Compartment.
 The rate of movement of drug within compartments follows first order
kinetic.
 Compartment models are divided into Mammillary and Caternary Model.

24. A. Mammillary Model
 the most common compartment model
used.
 The model consists of central compartment
and peripheral compartments.
 The peripheral Compartments are
connected to central compartment.
 Central Compartment: It comprise of
blood and highly perfuse tissues like liver,
lungs, kidneys, etc. that equilibrate with the
drug rapidly.
 Elimination usually occurs from the central
compartment.
 peripheral compartment: It comprise of
poorly perfuse and slow equilibrating tissues
such as muscles, skin, adipose tissues etc.
B. Caternary Model
It consists of compartments
which are joined to one
another like
compartments of train.
This model is rarely used.

25. Mammillary Model

26. One-compartment open model
 The one-compartment open model is the simplest model which depicts the
body as a single, kinetically homogeneous unit.
 All drugs initially distribute into a central compartment , before
distributing into the peripheral compartment.
 This model thus applies only to those drugs that distribute rapidly though out
the body.
 The concentration of drug in plasma represents the drug concentration in
all body tissues. this does not imply that the drug concentration in plasma
(Cp) is equal to the drug concentration in the tissues.
 The term “open” indicates that the input (availability) and output (elimination)
are unidirectional and that the drug can be eliminated from the body

28. Depending upon the rate of input, several one-compartment open
models can be defined:
 One-compartment open model, i.v. bolus administration
 One-compartment open model, continuous i.v. infusion
 One-compartment open model, e.v. administration, zero-order
absorption
 One-compartment open model, e.v. administration, first-order
absorption

29. One Compartment Model, I.V. bolus
 The plotted curve for plasma concentration versus time data is a straight
line, which clearly indicates the presence of a single pharmacokinetic phase
(namely, the elimination phase).
 Since the drug is administered intravenously, there is no absorption phase.
 The straight line also suggests that distribution is instantaneous; thus the
drug is rapidly distributed in the body

30. One Compartment Model, I.V. bolus cont…
The model can be depicted as follows
The general expression for rate of drug presentation to the body is:
dX/dt = Rate in (availability) - Rate out
(elimination)……………(1)
Since rate in or absorption is absent, the equation becomes: dX/dt =
Rate out ……………2)
If the rate out or elimination follows first-order kinetics, then:
• by employing the following mono-exponential equation C =
C0e-kt , LnC = LnCo -kt

31. One Compartment Model, I.V. bolus cont…
• What IV bolus dose is required to achieve a plasma
concentration of 2.4 mg/L at 6 hours after the dose is
administered. The elimination rate constant, kel, is 0.17 hr-
1) and the apparent volume of distribution, V, is 25 L
(166.4mg)

32. One Compartment Model, I.V. bolus cont…
 What is the concentration of drug 0, 2 and 4 hours after a dose of 500 mg
IV bolus. Known pharmacokinetic parameters are apparent volume of
distribution, V is 30 liter and the elimination rate constant, kel is 0.2 hr-1
 T=0, concentration=16.7mg/L
 T=2, concentration= 11.2mg/L
 T=4, concentration = 7.49mg/L

33. Advantages of compartment model
 The compartment model provides visual presentation of rate processes
involved in drug disposition.
 This model enables to estimate drug concentration time profile in
normal and pathological condition.
 It is also helpful in dosage form development of dosage regimen.
 It helps pharmacokineticist to write differential equation for each of the
rate process to explain drug concentration changes in individual
compartment

34. 2. Physiological models
 In this model the drug concentration profile has drawn from the uptake and
elimination capacity of organs composing the body.
 The distribution of the drug to an organ based on the blood flow to the
organ, the organ size and the partition coefficient of the drug between blood and
the organ.
 The elimination capacities are based on the drug and the organ involved.
 The overall drug concentration profile results from the sum of the Processing
of the drug by different organs. Lungs, liver, brain and kidney are rapidly
equilibrating tissue (RET) and muscles and adipose are considered as slowly
equilibrating tissue (SET)

35. Physiologic models are classification
blood flow rate limited model
membrane permeation rate limited model.
 The blood flow rate limited model are also called perfusion rate limited model.
These models are applicable to low molecular weight, highly lipophilic and
poorly ionized drugs.
 Membrane permeation rate limited model are also called diffusion limited
models.
These models are applicable to highly polar, ionized and charged drugs

36. Advantages of Physiological models
 It is more realistic model.
 The mathematical treatment is straight forward.
 applicable if tissue blood concentration and plasma binding known
 The model provides better picture of drug concentration time profile in
an organ or tissue.
 The extrapolation of animal data in the prediction of human
pharmacokinetics is simple by using this model.

38. 3. Non-Compartment Analysis
 They are also considered as model-independent method because they do not
rely upon assumptions about body compartments. It relies upon algebraic
equations to detect .The blood or plasma samples are collected from study
subjects and analyzed.
 The noncompartmental approach, based on the statistical moment's theory,
involves collection of experimental data following a single dose of drug. The
amount of drug in the body is proportional to the concentration in plasma at all
time points.

39. Estimation of Pharmacokinetic Parameters
 For a drug that follows one-compartment kinetics and administered as
rapid i.v. injection, the decline in plasma drug concentration is only due to
elimination of drug from the body (and not due to distribution), b/c the
body is considered as one the phase being called as elimination phase.
 Elimination phase can be characterized by 3 parameters—
1. Elimination half-life
2.Elimination rate constant
3. Clearance.

40. Elimination half life
• The time required to reduce the plasma concentration to one half its initial
value is defined as the half-life (t1/2).
• And This parameter is very useful for estimating how long it will take for
levels to be reduced by half the original concentration.
Consider
– ln Ct= ln C0- ket
• There will exist a constant relationship between drug concentration in the
plasma C and the amount of drug in the body:
• The proportionality constant V is the apparent volume of distribution.
• X = VC enables the conversion of the amount-time relationship to a
concentration-time relationship

41. Elimination half life
• at time t = 0 Cp = C0. and at time t = t1/2 Cp= C0/ 2
• Let Cp 0 decay to Cp 0/2 and solve for t t1/2:
From equation ; ln Cpt = ln Cp0- ket
• ln(C0/2) = ln C0 - ket1/2
• Hence kt1/2 = ln Cp0 - ln(Cp 0/2)=(ln cp0/cp0/2)
• t1/2 =ln(2)/k
t1/2 =0.693/k

42. Elimination rate constant
The elimination rate constant (k) is the fraction of drug in the body
which is removed per unit time. From the equation t1/2 =0.693/k
K= 0.693/t1/2
• Decay from a toxic level
– Example: patient D has a potentially toxic digoxin level of
4.5g/L. The half-life of digoxin in this patient is 60 h, and
assuming that renal function is stable and absorption is
complete, for how long should the drug be stopped to allow the
level to fall to 1.5g/L?

43. Half-Life and k
To determine Time for decay (t) from Cp1 to Cp2?
First Calculate elimination rate constant (k)?
• t1/2 =0.693/k, K=0.693/60h=0.0116 h-
Then Time for decay (t) from Cp1 to Cp2?
– ln Cpt = ln Cp0- ket formula
LnCPo-lnCP=Kt, t=lnCP1-lnCP2/K=
ln4.5-ln1.5=/0.0116= 94.8h
Time =1.5-0.4/0.0116=94.8

44. Half-Life and k
• If the half-life for decomposition of a drug is 12 hours, how long will
it take for 125 mg of the drug to decompose by 30%? Assume first-
order kinetics. (6.18hr)

45. Practice

46. Basic Parameters
• Useful and fundamental pharmacokinetic parameters
– Volume of distribution
– Elimination half life
– Elimination rate constant
– Systemic clearance