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CHAPTER 3. PHARMACOKINETIC MODELS. 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

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chapter 3

CHAPTER 3

PHARMACOKINETIC MODELS

pharmacokinetic modeling

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

outcome

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 independentvariable to a dependent variable.

fate of drug in the body

Tissues

FATE OF DRUG IN THE BODY

ADME

G.I.

Tract

Oral

Administration

Excretion

Intravenous

Injection

Circulatory

System

Intramuscular

Injection

Metabolic

Sites

Subcutaneous

Injection

complexity of pk model will vary with
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

types of pk models
Types of PK Models

1- Physiologic (Perfusion) Models

2- Compartmental Models

3- Mammillary Models

physilogic pk models

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.

physilogic pk models8

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.

physiological model simulation

Metabolism

Blood

RET

Muscle

Percent of Dose

Lung

Adipose

Time

Physiological Model Simulation

Perfusion Model Simulation of Lidocaine IV Infusion in Man

compartmental models

k12

1

2

k21

1

2

3

COMPARTMENTAL MODELS

The body is represented by a series of compartments that communicate reversibly with each other.

compartmental models11

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.

compartmental models12

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.

mammillary models

ka

kel

1

k12

1

k21

2

2

1

3

MAMMILLARY MODELS

Is the most common compartmental model used in PK. The model consists of one or more compartments connected to a central compartment

intravenous and extravascular route of administration

Cp

Cp

Time

Time

Intravenous and extravascular Route of Administration

Difference in plasma conc-time curve

Intravenous

Administration

Extravascular

Administration

one compartment open model intravenous administration17

kel

i.v.

Blood

(Vd)

Input

Output

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.

When the drug is administered i.v. in a single rapid injection, the process of absorption is bypassed

one compartment open model intravenous administration18

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.

first order kinetics

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.

semi log paper
Semi-logpaper

Plotting the data

integrated equations

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

integrated equations22

INTEGRATED EQUATIONS

Cp = Cp0e-kelt

ln Cp = ln Cp0  kelt

DB = Dose. e-kelt

ln DB = ln Dose kelt

elimination half life t 1 2

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,

estimation of half life from graph

ESTIMATION OF half-life from graph

A plot of Cp vs. time

t1/2 = 3 hr

fraction of the dose remaining

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:

volume of distribution v d

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

apparent v d

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).

apparent v d28

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

for one compartment model with iv administration

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.

calculation of v d from the auc

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

significance of v d

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

apparent v d33

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.

clearance cl

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.

estimation of pk parameters

ESTIMATION OF PK PARAMETERS

Cpo

kel

A plot of Cp vs. time