Clearance Determinations

Arthur G. Roberts

Routes of Elimination

Zero versus First-Order Elimination

Zero Order

First Order

1st Order Elimination

rate of renal excretion = Krenal * [Drug]rate of metabolism = Kmetabolism * [Drug]rate of biliary excretion = Kbiliary * [Drug]rate of other = Kother * [Drug]

Overall elimination = sum of all the ratesOverall elimination = (Krenal+Kmetabolism+Kbiliary+Kother)*[Drug]

Clearance, Elimination and Excretion

• Clearance (Renal) (V/time, L/hr)• Elimination (mass) (a.k.a. Extraction)• Mechanisms for either– biotransformation (e.g. Clint)– excretion

Clearance

• efficiency for kidney or liver removal• L/hour• rapid or slow?– rel. large clearance and small volume distribution– rel. small clearance and large volume distribution

• rate of elimination (extraction) = Clearance * [Drug]plasma

Clearance Terms

[Drug]in (mg/L) [Drug]out (mg/L)

Q (L/h) Q (L/h)

Rate of Drug in = [Drug]in * QRate of Drug out = [Drug]out * QExtraction Rate = ([Drug]in-[Drug]out ) * QExtraction Ratio ([Drug]in-[Drug]out)/[Drug]in)Clearance = E * Q

ArteryVein

Example

Rate Drug in, Rate Drug out, Extraction rate, extraction ratio, Clearance, Elimination Rate

1 L/(kg*hr) 1 L/(kg*hr)

Kidneys

Continuous IV infusion

Clearances

Clearance is additive

sometimes Clh

Elimination Rate Constant and Half Life Versus Clearance

• elimination rate = - K * Drug doseplasma = -Cl * [Drug]plasma

• K = Clearance (Cl)/Volume Distribution (Vd)• T1/2 = (ln 2)/K = (ln 2 * Vd)/Cl

Total Body Clearance[D

rug]

plas

ma

Renal Clearance

Loop of Henle

Proximal Tubule

Distal Tubule

Collecting Duct

Glomerular Filtration

• Glomerulus Q at 1.2 L/min. or 72 L/hour• prefer neutral 4-8 nm• anionic albumin (7 nm) not filtered• insulin (5 kD) filtered• Normal glomerulus filtration rate 10% Q 7.2 L/

hour

Renal Clearance

• Neutral and small drug (< 8 nm)– not bound to plasma proteins• Glomerular Filtration Rate (GFR) = Clearance (ClGF)

– bound to plasma proteins• fraction unbound (fu) * GFR = ClGF

Example:

GFR = 9 L/hourfu = 30%CLGF = ?

Tubular Secretion

Tubular Reabsorption

• Lipophilicity• pKa (acid and base forms)

Renal Clearance

• Renal Clearance (Clr) = ClGF + Clearance from Tubular Secretion (ClTS) – Tubular Reabsorption (TR)

• Clr = fu * GFR + Clts - TR

Renal Clearance Example

Clr = 1.8 L/hr

GFR = 7.2 L/hr

fraction bound = 80%

What are the relative values for active tubular secretion (ClTS) and tubular reabsorption (TR)?

Renal Clearance

[drug]plasma

Clr Example

Period Volume [Drug]urine Period [Drug]plasma

0-1 0.2 15 0.5 0.240

1-3 0.180 19.4 2 0.142

3-5 0.140 12.8 4 0.071

5-10 0.4 3.5 7.5 0.021

Average Excretion Rate (mg/hour) = (Volume * [Drug]urine)/time3 mg/hour = ( 0.2 *15)/1

mg/L mg/Lhours hoursL

Clr Example

Period Avg. Excretion Rate

Period [Drug]plasma

0-1 3 0.5 0.240

1-3 1.746 2 0.142

3-5 0.896 4 0.071

5-10 0.280 7.5 0.021

mg/Lhours hoursmg/hour

slope = (3-0.280)/(0.240-0.21)slope = 2.72/0.219=12.4 L/hour=Clr

Single-Point Determination of Renal Clearance Under Steady-State Conditions

Measurement Amount Normal

Collection Period 24 hours

Volume Urine Collected

1.05 L

Urinary Creatine Concentration

1140 mg/L 400-3000 mg/L

Plasma Creatine Concentration

10 mg/L 6-12 mg/L

55 year old 65 kg female

What is the average Clr?

Hepatic Clearance Mechanisms

• Biotransformation• Excretion

Restrictive and Non-restrictive Clearance

• Non-restrictive Eh > 0.7

• Restrictive Eh < 0.3

Non-Restrictive Hepatic Clearance: High Eh

Restrictive Hepatic Clearance: Low Eh

Blood and Plasma Hepatic Clearance

plasma = protein and water

Example

• Clplasma hepatic = 54 L /hr

• Qhb = 78 L/hr• fu=1• ([drug]plasma/[drug]blood) = 0.3• What is the extraction ratio?• Does the drug undergo restrictive or non-

restrictive clearance?

End of Clearance Determinations