Practical Pharmacokinetics September 11, 2007 Frank F. Vincenzi

Learning Objectives (Fundamental pharmacokinetic concepts) Volume of distribution Half life & first order elimination Zero order elimination (capacity-limited) Clearance Bioavailability and area under the curve (AUC) Urinary vs. liver elimination & first pass effect Plasma protein binding Drug accumulation Two compartment behavior

Simplified Table of Pharmacokinetic Parameters (also, Goodman & Gilman, Katzung, etc.) Metabolism Oral availability (%) (or as a fraction, 0.4, etc.) Urinary excretion (%) Plasma binding (%) Volume of distribution (L/kg) (or total liters) Half life (hours) Effective concentrations (µg/mL, etc.) (= mg/L) Toxic concentrations (µg/mL, etc.) pKa - acid or base

Drug ADME (absorption, distribution, metabolism & excretion)

Clearance: a useful way of looking at drug elimination The sum of all processes that eliminate a drug from the plasma (e.g., CL = CL liver + CL kidney + …) Quantification: (For most drugs, the rate of elimination is proportional to the plasma concentration. The proportionality is called the clearance (CL) ) CL (liters/h) = rate of elimination (mg/h)/plasma conc (mg/liter)

A simple- minded view of the kidney nephron

A simple minded view of the liver Gut drug systemic circulation portal circulation drug and/or

Volume of distribution (Vd) Relationship between the total amount of drug in the body and the plasma concentration of the drug Quantification: Vd(liters) = total drug (mg)/plasma conc (mg/liter)

Talk about simple minded! The body as a bathtub

General determinants of drug distribution PlasmaInterstitial Intracellular ‘Ideal’ 70 kg person 4 L (~5%) 11 L(16%) 28 L(35%) (Total body water = 42 L)

A small volume of distribution Isoniazid = L/kg

General determinants of drug distribution Plasma water ~5% Interstitial water ~16% Intracellular water ~ 35% Fat ~20%

A large volume of distribution Loratadine = 120 L/kg

The blood-brain barrier (BBB)

Displacement by sulfisoxazole (91% plasma binding) of bilirubin (normally ~100% plasma binding):

First order elimination (most drugs) The rate of elimination is proportional to the concentration of the drug in the plasma There is a characteristic half life for elimination of the drug Doubling the dosing rate doubles the concentration of the drug in the steady state (linear pharmacokinetics)

Plasma half life (t 1/2 ) of a drug Time required for elimination of half of the drug from the plasma (determined experimentally) Quantification: half life (h) = (0.693*Vd (liters))/CL (liters/h) = natural logarithm of 2

First order elimination Half lives% remaining%eliminated

Drug X, 2 mg IV, 77 kg subject: What is the half-life?

Drug x, 2 mg IV, 77 kg subject: Concentration (log scale) versus time

Drug X, 2 mg IV, 77 kg subject: What is the Vd?

How to calculate a theoretical loading dose (clinical practice may vary) The problem: fill the total volume of distribution with an appropriate initial concentration The solution: loading dose (mg) = Vd (liters) * initial target conc (mg/liter)

Diazepam (Valium®), to be given by rapid IV injection in a patient with status epilepticus Pharmacokinetic Parameters: Oral availability (%) 100 (N/A) Urinary excretion (%)1 Bound in plasma (%)99 Clearance (ml/min/kg)0.38 Volume of distribution1.1 L/kg Half life (h)43 Effective concentrations (µg/ml, etc.) ng/ml Toxic concentrations (µg/ml, etc.)...

Calculating a ‘Vd filling’ IV dose of diazepam for a 70 kg (154 pound) patient Target concentration = 300 ng/ml = 0.30 mg/liter Total Vd = (70 kg) * (1.1 L/kg) = 77 liters Dose = 77 liters * 0.30 mg/liter = 23.1 mg Is this reasonable? PDR Usual Adult Dosage (for status epilepticus): 5-10 mg initially (IV preferred), may be repeated if necessary at min intervals up to a maximum dose of 30 mg - may repeat in 2-4 hrs etc.

Zero-order (capacity-limited) elimination applies to a few drugs Rate of drug elimination is independent of its concentration Elimination process is saturated at plasma concentrations Doubling the dosing rate more than doubles the concentration of drug - steady state not reached (‘non-linear pharmacokinetics’)

Examples of drugs with zero-order or mixed elimination kinetics ethanol phenytoin nifedipine

Ethanol in a 70 kg human consuming 19 ‘drinks’ over 6 hours (~3 drinks/hour)

Time-concentration curve typical of drugs with first order elimination

Bioavailability Fraction of drug absorbed into the systemic circulation from a given route of administration; usually the oral route. Determined by comparing the ‘area under the curve (AUC) of plasma concentration vs. time when taken orally as compared to IV injection. F = (AUC) oral /(AUC) IV

First pass effect: Destruction or elimination of a drug on its first pass by the liver Drugs with little or no first pass effect ( high % bioavailability) diazepam (100) clonidine (95) metronidazole (99) sulfamethoxazole (100) Drugs with major first pass effect (low % bioavailability) imipramine (40) lidocaine (35) morphine (24) propranolol (26) dicloxacillin (50)

Plasma levels during 6 hours following oral or IV dicloxacillin (bioavailability ~ 0.5, t 1/2 = 0.7 h)

Time to peak concentration: absorption = elimination: Plasma concentrations following a single oral dose of dicloxacillin

Drug accumulation depends on half life and dosing interval During repeated dosing the plasma concentration of drug increases until (in the steady state) the rate of elimination equals the rate of dosing Extent of accumulation can be expressed as: accumulation factor # = 1/(1-fraction remaining*) # steady state level compared to first dose level *at the end of the dosing interval (‘trough’)

Lack of accumulation of dicloxacillin (half-life = 0.7 hours) given at 4 hour intervals

Accumulation of digoxin (half-life = 39 hours) during 10 days of dosing 70 kg patient with 0.3 mg daily (THERAPEUTIC)

Long half-life Advantages Once a day dosage or less Easy to maintain plasma levels in therapeutic window Missed doses are no big deal Disadvantages Initial therapeutic effects develop slowly without a loading dose If toxicity occurs, it is a long wait* * can accelerate removal of some drugs by dialysis

Short half-life Advantages Onset of therapeutic effects tends to be rapid Can dynamically titrate effects by I.V. infusion If toxicity occurs, it is not a long wait Disadvantages Missed doses drop plasma levels below therapeutic Difficult to maintain plasma levels in therapeutic window Multiple daily dosage or … May require a slow release dosage form

Time concentration curve during 10 days of treatment with metoproplol, 25 mg every 6 hours (half life = 3.2 hours), peak/trough ~ 4

Time concentration curve during 10 days of treatment with slow release metoprolol, 100 mg every 24 hours (half life = 3.2 h), peak/trough ~ 1.4

I.V. infusion

lidocaine, pharmacokinetic parameters Oral availability (%) 35 Urinary excretion (%)2 Bound in plasma (%)70 Clearance (9.2 ml/min/kg)38.4 Volume of distribution (L/kg)1.1 Half life (h)1.8 Effective concentrations (µg/ml, etc.)> mg/L Toxic concentrations (µg/ml, etc.)> 6 mg/L

I.V. infusion of lidocaine (half life 1.8 h), 100 mg/h without or with a bolus loading dose

Some drugs display two compartment behavior: Initial distribution Potential for initial overdosage

Two compartment behavior, equilibrated, in terminal (or beta) elimination phase

Elimination of a drug exhibiting two compartment behavior

Thiopental: an ultrashort acting, intravenous anesthetic agent whose action is terminated by redistribution, not elimination; 12 minutes of plasma, brain, muscle and fat levels

How to predict steady state plasma concentration Average concentration of drug in the steady state (Css) Quantification: Css (mg/liter) = (dosing rate (mg/h) * bioavailability)/CL (liters/h)

How to calculate dosing rate for a given target steady state plasma concentration Dosing rate (average, may be given in divided doses, be sure to calculate for 24 hours, or etc.) Quantification: (dosing rate (mg/h) = Css (mg/liter) * CL (liters/h)/ bioavailability (F)