1. CLEARANCE CONCEPTS Text: Applied Biopharm. & PK
L. Shargel, S Wu-Pong & A. Yu;
5th Ed. Chapter 6 (p )
Chapter 11 (p )
Math problems? Call [(10x)(13i)^2]-[sin(xy)/2.362x]

2. 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.

3. Clearance
Def’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 …

4. Can be used to describe drug elimination from either total body (CLT) or from a single organ ( ie. CLH ; CLR ; CLbile ; ).

5. Total Body Clearance (CLT)
Given in Drug Monographs
Mechanism of clearance not identified
Sum total of processes:
CLT = CLM+ CLR+CLBILE +...

6. 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)
100 mg/L
1000 mg Drug
L/hr
10 Litres
Simplest case- a beaker…

7. BODY ke KIDNEY LIVER kbile km URINE DRUG Bile Metabolites
But the body’s not a beaker- multiple systems involved…..
BODY Vd ke
KIDNEY
URINE IV
DRUG
LIVER
kbile km
Bile
Metabolites

8. Calculation of Clearance

9. CLT = K (V) K = km + ke + kbile + …. METHOD 1.
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
Processes
contributing

10. 2 compartment model has distribution & elimination occurring.
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.

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

12. Relationship between CLT and t½
CLT = KV
CLT = *V/ t½
t½ = *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

13. Calculate the CLr, CLT and t ½ for this drug.
Example:
BODY
Ke = 0.147
Vd = 44 L
KIDNEY
URINE IV
DRUG
Kbile = 0.331
LIVER
Km = 0.251
Bile
Metabolites
Calculate the CLr, CLT and t ½ for this drug.

14. Answer:
CLr = ke * V
CLT = K * V
T ½ = 0.693/K

15. 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

16. 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.

17. 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
Slope = CLr
dAe/dt
calculate slope
Plasma Drug Concentration
minimum of 2 determinations are needed

18. 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∞ )

19. Example : Calculating CLr
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
Can be any time period 0-t; t1-t2
 should collect
urine for 5 t½:
*Usually just calculated could also plot intervals

20. Example:
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- = g*hr/L
CLr = ?

21. Answer:
7.5 mg of Drug X was collected in urine during the 12 hour PK study.
Therefore Ae = 7.5 mg
 Have to use AUC 0-12

22. After IV Dose: CLT = DOSEiv/ AUC  * Model independent
Total body clearance can be obtained by integrating this equation from time zero (t0) to infinity (t ). All drug eliminated by t 
dX/dt 0-∞ = DOSE
After IV Dose:
CLT = DOSEiv/ AUC 
Systemic clearance reflects total amount of time that drug resides in the body.
* Model independent

23. What if the patient is given an oral dose of the drug!!
How can I calculate clearance?

24. 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.

25. METHOD 3 CL organ = Q (ER) 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.
NB. Can only be
used for single
organs not CLT

26. 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.
ER = (Cin - Cout )/ Cin
Liver
Blood IN
Blood OUT
Bile

27. Example: The hepatic extraction ratio (ER) for morphine is 0
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)
= L/hr
Will cover in more detail with more examples in hepatic lectures

28. 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.

29. Reporting Clearance 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

30. 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)

31. 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 ?

32. Solution- A.
What is the Half-life?
CLT = Dose/ AUC

33. Solution- B.
What is CLr and CLnr?

34. Solution C.
What is ke ?

35. 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.

36. Sample Problems to work on at home
Applied Biopharm & PK, 5th edition
p 158 # 3, 4, 5, 6, 9
P # 1, 2, 11