pharmacokinetics: lecture three

Clearance Concept

Anas Bahnassi PhD RPh

After the completion of this lecture the student should be able to: 1. Define clearance and extraction ratio and describe the relationship

between them. 2. Distinguish clearance from elimination rate and elimination rate

constant. 3. Explain the dependence of elimination half life on apparent

volume of distribution and clearance

4. Calculate area under the plasma drug concentration versus time

curve by use of the trapezoidal rule and by other methods

5. Calculate a patient’s creatinine clearance using the appropriate

equation

6. Calculate dosing adjustments of a renally excreted drug in patients with various degrees of renal impairment (dysfunction).

Lecture Objectives

Heart

(Pump) Clearing Organ

(Kidney/Liver)

The blood exiting the eliminating organ has a lower concentration than the blood entering the organ.

A Physiological Approach to Understand Clearance Concept

The efficiency of Removal is quantified by the Extraction Ratio

[ER].

Site of

Action

Ca

Cv

Extraction Ratio Extraction Ratio can be defined

as the proportion of drug removed during passage through the organ.

𝑬𝑹 =𝑪𝒂 − 𝑪𝒗𝑪𝒂

A proportionality constant describing the relationship between a

substance’s rate of elimination (amount per unit time) at a given time

and its corresponding concentration in an appropriate fluid at that time.

Clearance

The hypothetical volume of blood (plasma or serum) or other

biological fluids from which the drug is totally and irreversibly

removed per unit time.’

Clearance is:

Organ clearance = Blood flow rate X Extraction ratio

𝑪𝒍 = 𝑸. 𝑬𝑹

Types of Clearance

This is the total of every individual organ clearances

that contribute to the elimination of drugs.

However, the organ clearance that can be routinely

determined independently in humans is renal clearance

because this is the only organ for which we can easily

determine an elimination rate.

The clearance of drug (a fraction of total clearance) for a drug that is removed

from the blood (plasma/serum) by the process of renal

excretion.

Renal Clearance

Metabolic Clearance

Hepatic Clearance

𝑪𝒍𝑻𝒐𝒕𝒂𝒍 = 𝑪𝒍𝑹𝒆𝒏𝒂𝒍 + 𝑪𝒍𝑵𝒐𝒏 𝑹𝒆𝒏𝒂𝒍

Clearance is a proportionality constant that relates rate of elimination (rate of excretion in renal clearance) to

Plasma (or serum) concentration at any given time

𝑑𝑥𝑢𝑑𝑡

𝑡= 𝐶𝑙𝑟 𝐶𝑝 𝑡

𝑑𝑥

𝑑𝑡 𝑡= 𝐶𝑙 𝐶𝑝 𝑡

𝐶𝑙 = 𝑘𝑉

𝐶𝑙 = 𝑘𝑉 𝑡½ =0.693

𝑘

𝑡½ =0.693𝑉

𝐶𝑙

Elimination half life is dependent on the volume of distribution and total clearance

Elimination half-life vs. Clearance

IV Bolus

Clearance for the entire dose can be obtained by integrating the right hand side

of the equation from t=0 to t=

Calculating Clearance

𝑑𝑥𝑢𝑑𝑡

𝑡= 𝐶𝑙𝑟 𝐶𝑝 𝑡

𝐶𝑙𝑇 =

𝑑𝑥𝑑𝑡

𝑑𝑡

𝐶. 𝑑𝑡

𝑡=∞

𝑡=0

=𝑇𝑜𝑡𝑎𝑙 𝐸𝑙𝑖𝑚𝑖𝑛𝑎𝑡𝑖𝑒𝑑 (𝐷𝑜𝑠𝑒)

𝑇𝑜𝑡𝑎𝑙 𝐴𝑟𝑒𝑎 𝑢𝑛𝑑𝑒𝑟 𝑡ℎ𝑒 𝑐𝑢𝑟𝑣𝑒

s IV Bolus

Area =𝑎+𝑏 𝑐

2

𝑎 𝑏

𝑐

Calculating AUC

Trapezoidal Rule:

C1 or concentration1


t1 or time1

t2 or time2

Area = ((C1 + C2)/2)(t2 – t1)

Calculating AUC



t1 or time1 t2 or time2

= Area = Sum individual trapezoids

=(((C1 + C2)/2)(t2 – t1))

Trapezoidal Rule:

𝑪.𝒅𝒕

𝒕=∞

𝒕=𝒍𝒂𝒔𝒕

𝑪.𝒅𝒕

𝒕=∞

𝒕=𝟎

Calculating AUC



t1 or time1 t2 or time2

=𝑳𝒂𝒔𝒕 𝑪𝒐𝒏𝒄𝒆𝒏𝒕𝒓𝒂𝒕𝒊𝒐𝒏

𝒌

Trapezoidal Rule:

Calculating AUC

𝑪.𝒅𝒕

𝒕=∞

𝒕=𝒍𝒂𝒔𝒕

𝑪. 𝒅𝒕

𝒕=∞

𝒕=𝟎

𝑨𝑼𝑪𝑳𝒂𝒔𝒕∞

Creatinine Clearance

Creatinine clearance (Clcr) is renal clearance (Clr) applied to endogenous creatinine ( a product of muscles metabolism). It is used to monitor renal function and is a valuable parameter for calculating dosage regimens in elderly patients or those suffering from renal dysfunction. Normal creatinine clearance (Clcr) values are: • Adult males: 120±20mLmin-1

• Adult females: 108 ±20mLmin-1.


𝐶𝑙𝐶𝑟 =

∆𝑥𝑢∆𝑡

(𝐶𝑠)𝐶𝑟

Direct measurement of Creatinine clearance

Rate of Creatinine Excretion

Creatinine Serum Concentration


𝐶𝑙𝐶𝑟 =𝑊𝑒𝑖𝑔ℎ𝑡(𝑘𝑔) × (140 − 𝑎𝑔𝑒 )

72 × 𝐶𝑠 𝐶𝑟(𝑚𝑔%)

Indirect measurement of Creatinine clearance

𝐶𝑙𝐶𝑟 = 0.85𝑊𝑒𝑖𝑔ℎ𝑡(𝑘𝑔) × (140 − 𝑎𝑔𝑒 )

72 × 𝐶𝑠 𝐶𝑟(𝑚𝑔%)

Males:

Females:

Creatinine Clearance The significance of Creatinine clearance

1. Normal Creatinine clearance usually indicates normal kidney function

2. Creatinine clearance changes with age, physiological states, or other medical conditions and dose need to be changed accordingly

3. Dose frequency can be changed instead of changing the dos amount.

4. Changes in Creatinine clearance cause pharmacokinetic parameters to change.

Question 1

The table shows the concentration data vs time for Cinoxacin after IV bolus administration. Plot the data and use the graph to obtain the followings: 1. Elimination half-life (t½) 2. Elimination rate constant (k) 3. Apparent volume of distribution 4. Systemic clearance (Cls) 5. 𝐴𝑈𝐶0

∞ 6. Urine samples over 24 h showed the

percentage of the administered dose recovered unchanged was 50.1%. The rest were metablolites. Determine the renal clearance (Clr), metabolic clearance (Clm), the excretion rate constant (Ku), and the metabolite rate constant (Km).

Time (hr)

Cp (ug/mL)

0.25 11.6±1.3

0.5 8.4±1.0

0.75 7.2±1.1

1 6.1±1.1

1.5 4.2±1.0

2 3.2±0.9

3 1.9±0.7

4 1±0.4

6 0.3±0.2

8 0.09±0.1

0

2

4

6

8

10

12

14

0 1 2 3 4 5 6 7 8 9

Pla

sma

Co

nce

ntr

atio

n (

ug

/mL)

Time (h)

Plasma Concentration vs time Rectilinear Paper

0.01

0.1

1

10

100

0 1 2 3 4 5 6 7 8 9

Pla

sma

Co

nce

ntr

atio

n (

ug

/mL)

Time (h)

Plasma Concentration vs time Semilog Paper

t½=1.2h K=0.577h-1

V=20.833L Cls=12.02L/h AUC=20.797ug/mL Ku=0.298h-1

Km=0.287h-1

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Anas Bahnassi PhD RPh

Pharmacokinetics

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pharmacokinetics: lecture three

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