Text:

Applied Biopharm. & PK

L. Shargel, S Wu-Pong & A. Yu;

5th Ed. Chapter 6 (p131-158)

Chapter 11 (p303-348)

CLEARANCE CONCEPTS

Math problems? Call 1-800-[(10x)(13i)^2]-[sin(xy)/2.362x]

Clearance-Objectives for Today-

Review of methods to calculate total body clearance .

• Understand the relative contribution of specific eliminating pathways on total body clearance.

• Integration of clearance methods for the calculation of specific organ clearances and elimination rates.

ClearanceDef’n: PK term to describe the irreversible

removal of drug from the body (drug elimination)

• Most important PK parameter because it determines Dose & Dosing schedule.– Variable parameter- affected by age, disease,

genetics …

• Can be used to describe drug elimination

from either total body (CLT) or from a

single organ ( ie. CLH ; CLR ; CLbile ; ).

Total Body Clearance (CLT) • Given in Drug Monographs

• Mechanism of clearance not identified

• Sum total of processes:

CLT = CLM+ CLR+CLBILE +...

• Rather than describing in terms of amount of drug removed per unit time, Clearance is described as volume of plasma cleared of drug per unit time (volume/time)

10 Litres

1000 mg Drug

L/hr

100 mg/L

Simplest case- a beaker…

DRUG

URINEke

Metabolites

km

KIDNEY

Bile

kbile

LIVER

BODY

IV

Vd

But the body’s not a beaker- multiple systems involved…..

Calculation of Clearance

Clearance calculated using:

Elimination Rate Constants.

CLT = K (V)

CL r (renal) = ke (V)

CL m (metab) = km (V)

CL bile = kbile (V)

Add all processes & cancel out Volume terms …

K = km + ke + kbile + ….

Beaker- Single Tap Analogy

Processescontributing

METHOD 1.

Model Dependent

• 2 compartment model has distribution & elimination occurring.

K = hybrid value

– Need accurate measurement of K and V

• Assumes First Order Kinetics are followed.

• In many drug monographs – I can only find information on the half-life and distribution. Isn’t this as good as clearance?

Relationship between CLT and t½ CLT = KV

CLT = 0.693 *V/ t½

t½ = 0.693 *V / CLT

• t½ inversely related to CLT

• t½ also dependent on volume of distribution.

• K and t½ are dependent on both CLT &V

Model Dependent

K = 0.693/ t½

DRUGURINE

Ke = 0.147

Metabolites

Km = 0.251

KIDNEY

Bile

Kbile = 0.331LIVER

BODY

IV

Vd = 44 L

Example:

Calculate the CLr, CLT and t ½ for this drug.

CLr = ke * V

CLT = K * V

T ½ = 0.693/K

Answer:

METHOD 2

Clearance calculated using drug concentrations:

CL = (dX/dt) / C

• Clearance is defined as rate of drug loss (from total body or organ) relative to the concentration of drug in plasma.

• Model independent

dX/dt = Rate of drug elimination C = Plasma (or blood) concentration

Rearranging CL = (dX/dt) / C

dX/dt = CL * C

• Clearance can be calculated by plotting elimination rate versus drug concentration.

• Slope will be equal to clearance

• Clearance is a constant.

Example : Calculation CLr Plot of Urinary Excretion Rate (dAe/dt) versus Drug

Conc (mid-point) can be used to calculate CLr

dAe/dt = CLr•C

dAe/dt

Plasma Drug Concentration

Slope = CLr

• minimum of 2 determinations are needed

calculate slope

Rather than plotting, clearance can also be calculated by integrating the equation over time.

- This can be any time period, including time zero (t0) to infinity (t∞ )

Based on previous equation:

dAe/dt = (Clr)C

Integrated to time (t1):

Ae 0-t1 = (Clr) AUC 0-t1

CLr = Ae 0-t / AUC 0-t

Integrated to infinity:

CLr = Ae / AUC

Example : Calculating CLr

should collect urine for 5 t½:

Can be any time period 0-t; t1-t2

*Usually just calculated could also plot intervals

Drug X- administered IV. Plasma and urine collected for 12 hours. A total of 7.5 mg of Drug X was collected in urine during the 12 hour PK study.

Plasma concentrations determined and AUCs calculated:

AUC 0-12 = 2500 g*hr/L

AUC 0- = 3400 g*hr/L

CLr = ?

Example:

7.5 mg of Drug X was collected in urine during the 12 hour PK study.

Therefore Ae 0-12 = 7.5 mg

Have to use AUC 0-12

Answer:

Total body clearance can be obtained by integrating this equation from time zero (t0) to infinity (t ). All drug

eliminated by t

After IV Dose:

CLT = DOSEiv/ AUC

Systemic clearance reflects total amount of time that drug resides in the body.

* Model independent

dX/dt 0-∞ = DOSE

What if the patient is given an oral dose of the drug!!

How can I calculate clearance?

Non-IV (Extravascular) Doses

• ** Need to account for bioavailability

• After Oral dose:

CLT= Fpo * DOSEpo/ AUC

Systemic clearance based on amount of drug which gets into the systemic circulation and residence time of drug in body.

Clearance calculated using:

Physiological parameters of individual organs.

CL organ = Q (ER)

Q = Blood or plasma flow to organ

ER = Extraction Ratio. The efficiency of organ to

clear drug from blood/plasma.

METHOD 3

NB. Can only be used for singleorgans not CLT

ER= 0 – 1. Can be calculated from differences between amount of drug entering and leaving organ. The proportion of drug entering organ that is eliminated/converted upon each pass through the organ.

Liver

Blood IN Blood OUT

Bile

ER = (Cin - Cout )//

Cin

Example: The hepatic extraction ratio (ER) for morphine is 0.65 and has a distribution volume of 4 L/kg. Assuming a hepatic flow rate (Q) of 90 L/hr, what would be the expected hepatic clearance for morphine in a 70 kg man after an IV dose.

CL H = Q (ER)

CL H = 90 L/hr *(0.65)

= 58.5 L/hr

Will cover in more detail with more examples in hepatic lectures

• You will often need to use a combination of these three methods to calculate clearance.

• Look at the information provided and determine which approach you should use for calculations.

• Organ Clearance often reported in different ways.

• Individual processes/ Organ Clearance may be described and calculated from Total body clearance

. – Addition/Subtraction of Clearance Routes– Fraction of Total Body Clearance

Reporting Clearance

To Ilustrate : Renal Clearance (CLr)

Renal Clearance (CLr) is one Component of CLT

• Fraction of drug eliminated renally (fe) describes relationship between Renal Clearance (CLr) and Total Clearance (CLT). Also describes the relationship between ke to total body K

fe = CLr = ke CLT K

fraction excreted in urine = Ae/ DOSEIV

(Ae = Total amount of drug excreted in urine)

Sample Problem. • New Immunosuppressant- Noreject is cleared by

both renal (60%) and non-renal excretion and has a V of 150L. In healthy patients, AUC of 1530 g.hr/L is obtained after a 100 mg IV dose.

a) What is the half-life of Noreject?

b) What is the predicted renal and non-renal clearance of Noreject?

c) What is the urinary elimination rate constant (ke) of Noreject ?

Solution- A. What is the Half-life?

CLT = Dose/ AUC

Solution- B. What is CLr and CLnr?

Solution C.

What is ke ?

Where are we now?

• Can determine clearance based on:– Plasma concentrations (Cp or AUC)– Elimination rate constants– Extraction efficiency of organ

• Can calculate relative contribution of individual clearance routes from total body clearance.

Sample Problems to work on at home

Applied Biopharm & PK, 5th edition

p 158 # 3, 4, 5, 6, 9

P 348-50 # 1, 2, 11