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D^

Cl^

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Drug Clearance Models

Lecture#

Drug Clearance Models

Drug

Clearance ● Cl^ may be defined as the rate of drug elimination divided● Cl^ mayT^ T^

be^ defined

as^ the

rate

of^ drug

elimination

divided

by^ the

plasma

drug

concentration.

This

definition

expresses

drug

elimination

in^ terms

of^ the

volume

of

l^

li^ i^

t d^

f d^

it ti

plasma

eliminated

of^ drug

per^

unit^

time.^ ) (^1) ( )(

lim

Cion

concentrat plasma

rate ination e Cl = T^

) (^2) (

min/ / /

)( g^ mLg dtdDC Cl

Cion

concentrat plasmaE T P

P μ=^ μ = ●^ where

D isE^

the^ amount

of^ drug

eliminated

and^

dD^ /E

dt^ is

the^ rate

of^ elimination.

g P

μ

Drug Clearance Models

Drug

Clearance ● A^ first

‐order elimination rate

dD E

/ dt^ is equal to

kD B^

or

●^ A^ first

order

elimination

rate

,^ dD E

/ dt ,^ is

equal

to^ kD

orB

kCV p

.^ BasedD

on^ equation

(1),^ substituting

elimination

rate

for^ kC

V ,^ wepp

get

) (^4) ( D DP P T^

kV VkC C Cl^

=

●^ Equation

(4)^ shows

that

clearance

is^ the

product

of^ V

andD

k ,^ both

of^ which

are^ constant.

As^ the

plasma

drug

concentration

decreases

during

elimination,

the^ rate

of

g^

drug

elimination,

dD /E

dt ,^ decreases

accordingly,

but

clearance

remains

constant.

Clearance

is^ constant

as^ long

as the rate of drug elimination is a first

order process

as^ the

rate

of^ drug

elimination

is^ a^ first

‐order

process

Drug Clearance Models

Example^ ●

Penicillin

has a

Cl of 15 mL/min Calculate the eliminationT^

●^ Penicillin

has^

a^ Cl T^

of^15

mL/min

.^ Calculate

the^ elimination

rate^

for^ penicillin

when

the^

plasma

drug

concentration,

C ,p

is^2 g/mL.

Solution^ ●

Elimination

rate

=^ C p

x^ Cl T

dD^

min/ 30 min/ (^15). / 2

g

mL mLg dDE dt

μ

μ^

=

=

Drug Clearance Models

Example^ ●

Determine the total body clearance for a drug in a 70

‐kg

●^ Determine

the^ total

body

clearance

for^ a

drug

in^ a^

70 kg

male

patient.

The^

drug

follows

the^ kinetics

of^ a^

one‐

compartment

model

and^

has^ an

elimination

half‐

life^ of

h^

ith^

t^ l^

f di t ib ti

f 100

hours

with

an^ apparent

volume

of^ di

stribution

of^100

mL/kg.

Drug Clearance Models

Solution^ ●

First determine the elimination rate constant (

k ) and then

●^ First

determine

the^

elimination

rate

constant

( k )^ and

then

substitute

properly

into

equation

Drug Clearance Models

Physiologic/Organ

Clearance

●^ Clearance may be calculated for any organ involved in the●^ Clearance

may

be^ calculated

for^ any

organ

involved

in^ the

irreversible

removal

of^ drug

from

the^ body.

●^ Many

organs

in^ the

body

have

the^

capacity

for^ drug

elimination,

including

drug

excretion

and

biotransformation. ● The^ kidneys and liver are the most common organs● The^ kidneys

and^

liver^

are^ the

most

common

organs

involved

in^ excretion

and^

metabolism,

respectively.

Physiologic

pharmacokinetic

models

are^ based

on^ drug

clearance

through

individual

organs

or^ tissue

groups.

Drug Clearance Models

Drug Clearance Models

Physiologic/Organ

Clearance

●^ If^ the

drug

concentration

in^ the

blood

( C )^ a

entering

the

g^

(^ )^ a

g

organ

is^ greater

than

the^ drug

concentration

of^ blood

( C )v^

leaving

the^ organ,

then

some

of^ the

drug

has^

been

extracted

by^ the

organ.

The^

ER^ is

C – C a

dividedv

by^ the

y^

g^

a^ v^

y

entering

drug

concentration

( C ).a^ ) (^7) ( ⎞ ⎟⎟ ⎠ ⎛^ ⎜⎜ ⎝

− =^

v CCa C ER ● ER^ is^ a

ratio

with

no^ units.

The^

value

of^ ER

may

range

from

0 (no

drug

removed

by^ the

organ)

to^1

of^ the

drug

is

⎟ ⎠ ⎜ ⎝^ Ca (^

g^

y^

g^ )^

(^

g

removed

by^ the

organ).

An^ ER

of^ 0.

indicates

that

of

the^ incoming

drug

concentration

is^ removed

by^ the

organ

as^ the

drug

passes

through. g p^

g

Drug Clearance Models

Physiologic/Organ

Clearance

●^ Putting

the^ value

of^ ER

into^

equation

(6)^ y

ields

g^

q^

( ) y ) ⎞ ⎟^8 (⎟ ⎠ ⎛^ ⎜⎜ ⎝

−

Cva C a CQ

Clearance ● The^ physiologic

approach

to^ clearance

shows

that

clearance

depends

on^ the

blood

flow

rate

and^

the^ ability

of^ the

organ

to^ eliminate

drug.

g^

g

●^ Physiologic

approach

require

invasive

techniques

to^ obtain

measurements

of^ blood

flow

and^

extraction

ratio.

Th^

l^ i^

l^

h i^ th t

t^ t^

t ti^

f^ ti

●^ Th

e^ classical

approach

is^ th

at^ a^ constant

or^ static

fraction

of^ the

volume

in^ which

the^

drug

is^ contained

is^ removed

per^ unit

time

by^ the

organ.

Drug Clearance Models

Model

‐Independent

Methods

Drug Clearance Models

Model

‐Independent

Methods

●^ Clearance

can be determined directly from the plasma

●^ Clearance

can^

be^ determined

directly

from

the^

plasma

time

concentration

curve

by )

0

∞ D = ∫

Cl ● where

D^ is^0

the^

dose

and^

C ( t )^ is

an^ unknown

function

that

=^ ∫^0

dtt

C

Cl describes

the^ declining

plasma

drug

concentrations.

Drug Clearance Models

Renal

Clearance ● Renal clearance Cl

is defined as the volume of plasmaR

●^ Renal

clearance

,^ Cl,R

is^ defined

as^ the

volume

of^ plasma

that^

is^ cleared

of^ drug

per^ unit

of^ time

through

the^ kidney.

●^ More

simply,

renal

clearance

is^ defined

as^ the

urinary

drug

excretion

rate

(dD^ u

/dt)^ divided

by^ the

plasma

drug

concentration

(Cp).

/ dtu C P

dD

ion

concentrat

plasma

rate

excretion

Cl^

Drug Clearance Models

Comparison

of^ Drug

Excretion

Methods

●^ From a modeling viewpoint renal

clearance may be

●^ From

a^ modeling

viewpoint

,^ renal

clearance

may

be

measured

without

regard

to^ the

physiologic

mechanisms

involved

in^ this

process.

●^ From

a^ physiologic

viewpoint,

however,

renal

clearance

may^

be^ considered

as^ the

ratio

of^ the

sum

of^ the

glomerular filtration and active secretion rates less theglomerular

filtration

and^

active

secretion

rates

less^

the

reabsorption

rate

divided

by^ the

plasma

drug

concentration

b^

i

i

fil^

i^

) (^12) (

sec

P

R^

C

rateon reabsorpti rate retion raten filteratio Cl^

−

=

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