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### CHAPTER 3

### PHARMACOKINETIC MODELING

### OUTCOME

### PHYSILOGIC PK MODELS

### PHYSILOGIC PK MODELS

### Physiological Model Simulation

### COMPARTMENTAL MODELS

### COMPARTMENTAL MODELS

### COMPARTMENTAL MODELS

### MAMMILLARY MODELS

### One Compartment Open Model Intravenous Administration

### One Compartment Open Model Intravenous Administration

### FIRST-ORDER KINETICS

### INTEGRATED EQUATIONS

### Elimination Half-Life (t1/2)

### Fraction of the Dose Remaining

### Volume of Distribution (Vd)

### Apparent Vd

### Apparent Vd

### For One Compartment Model with IV Administration:

### Calculation of Vd from the AUC

### Significance of Vd

### Apparent Vd

### CLEARANCE (Cl)

PHARMACOKINETIC MODELS

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

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

ADME

G.I.

Tract

Oral

Administration

Excretion

Intravenous

Injection

Circulatory

System

Intramuscular

Injection

Metabolic

Sites

Subcutaneous

Injection

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

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.

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.

Blood

RET

Muscle

Percent of Dose

Lung

Adipose

Time

Perfusion Model Simulation of Lidocaine IV Infusion in Man

1

2

k21

1

2

3

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

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.

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.

kel

1

k12

1

k21

2

2

1

3

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

Cp

Time

Time

Intravenous and extravascular Route of AdministrationDifference in plasma conc-time curve

Intravenous

Administration

Extravascular

Administration

i.v.

Blood

(Vd)

Input

Output

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

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.

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-logpaper

Plotting the data

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

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,

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:

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

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).

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

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.

Since, dDB/dt = -kelD = -kelVdCp

dDB = -kelVdCpdt

dDB = -kelVd Cpdt

Since, Cpdt = AUC

Then, AUC= Dose / kelVd

Model

Independent

Method

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

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.

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.

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