CLEARANCE CONCEPTS Text: Applied Biopharm. & PK L. Shargel, S Wu-Pong & A. Yu; 5th Ed. Chapter 6 (p131-158) Chapter 11 (p303-348) 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.

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 …

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

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

Calculation of Clearance

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

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.

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

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.

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

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

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∞ )

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

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- = 3400 g*hr/L CLr = ?

Answer: 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

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

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.

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

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

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) = 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.

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

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