Practical Pharmacokinetics September 22, 1998

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

Pharmacokinetic parameters (Katzung) Oral availability (%) Urinary excretion (%) Bound in plasma (%) Clearance (L/h/70 kg) * Volume of distribution (L/70 kg) Half life (h) Effective concentrations (µg/ml, etc.) Toxic concentrations (µg/ml, etc.) *says ‘convert to mL/min by multiplying by 16.6’ (really converts to mL/min/70 kg)

Pharmacokinetic parameters (G&G) Availability (oral) (%) Urinary excretion (%) Bound in plasma (%) Clearance (ml . min-1 . kg-1) Volume of distribution (liters/kg) Half life (hours) Effective concentrations (µg/ml, etc.) Toxic concentrations (µg/ml, etc.)

Dimensional analysis A fancy way of saying. ‘pay attention to the units’ conc =123 ng/ml = 0.123 µg/ml = 123 µg/liter CL = 4.56 liters * min-1 * kg-1 Vd = 78.9 liters …or… Vd = 1.12 liters/kg F = 42% …or… F = 0.42

Drug ADME (absortion, distribution, metabolism & excretion)

The body as a bathtub

Intermittent dosing

First order elimination The rate of elimination is proportional to the concentration of the drug 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)

Elimination rate constant Relationship between the rate of drug elimination and the total amount of drug in the body Quantification: Kelim (h-1) = 0.693/half life (h) 0.693 = natural logarithm of 2

First Order Elimination and Clearance Rate of elimination of the drug is proportional to its concentration. The proportionality is called the clearance (CL) Rate of elimination (mg/h) = CL (liters/h) * conc (mg/liter)

Clearance The sum of all processes that eliminate a drug from the plasma (e.g., CL = CLliver + CLkidney + …) Quantification: 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

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

General determinants of drug distribution

A small volume of distribution

General determinants of drug distribution

A large volume of distribution

Half life Time required for elimination of half of the drug from the body Quantification: half life (h) = (0.693*Vd (liters))/CL (liters/h)

First order elimination Half lives % remaining %eliminated 1 50 50 2 25 75 3 12.5 87.5 4 6.25 93.75 5 3.125 96.875 6 1.5625 98.4375

Vd? Half-life? (2 mg IV, 77 kg subject)

Vd? Half-life? (2 mg IV, 77 kg subject) Half life = 2.001 h (1.823 to 2.217, 95% CI)

Vd? Half-life? (2 mg IV, 77 kg subject) 64 ng/ml = 64 µg/liter = 0.064 mg/liter Vd total = 2 mg/0.064 mg/liter = 31.25 liters Vd = 31.25 liters/77 kg ~ 0.42 liters/kg

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

diazepam, pharmacokinetic parameters Oral availability (%) 100 (N/A) Urinary excretion (%) 1 Bound in plasma (%) 99 Clearance (L/h/70 kg) * 1.62 Volume of distribution (L/70 kg) 77 Half life (h) 43 Effective concentrations (µg/ml, etc.) 300-400 ng/ml Toxic concentrations (µg/ml, etc.) ...

Calculating a bolus IV dose of diazepam for a patient, 100 kg (corrected) Target concentration = 0.35 mg/liter Total Vd = (100 kg) * (77 liters/70 kg) = 110 liters Dose = 110 liters * 0.35 mg/liter = 38.5 mg

Time-concentration curves of diazepam following IV or oral administration of 38.5 mg in 100 kg patient (corrected)

Time-concentration curves of diazepam following IV or oral administration of 38.5 mg in 100 kg patient (corrected)

Zero-order (capacity-limited) elimination 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

Time concentration curve of ethanol in a 70 kg human consuming 3 drinks per hour for 6 hours

Bioavailability Fraction of drug absorbed into the systemic circulation from a given route of administration; usually the oral route. Quantified: F = (AUC)oral/(AUC)IV (May be expressed as a fraction of 1 or as percent)

First pass effect Destruction or elimination of a drug on its first pass by the liver and other absorption pathways Drugs with major first pass effect (bioavailability) imipramine (40) lidocaine (35) morphine (24) propranolol (26) Drug with little or no first pass effect (bioavailability) diazepam (100) clonidine (95) metronidazole (99) sulfamethoxazole (100)

Time-concentration curves of diazepam following IV or oral administration of 28.5 mg in 77 kg patient

Oral vs. I.V., dosing of dicloxacillin, bioavailability ~ 0.5

Time to peak concentration following oral administration of dicloxacillin

Accumulation During repeated dosing the concentration of drug increases until the rate of elimination equals the rate of dosing (depends on half-life and dosing interval) Quantification: accumulation factor# = 1/(1-fraction remaining*) #steady state compared to first dose level *at the end of the dosing interval

Lack of accumulation of dicloxacillin (half-life = 0 Lack of accumulation of dicloxacillin (half-life = 0.7 hours) given at 4 hour intervals

Accumulation of digoxin, 0.3 mg daily (half-life = 39 hours)

Accumulation of digoxin, 0.9 mg daily (half-life = 39 hours) (TOXIC)

digoxin, pharmacokinetic parameters Oral availability (%) 70 Urinary excretion (%) 60 Bound in plasma (%) 25 Clearance (L/h/70 kg) * 7.8 Volume of distribution (L/70 kg) 440 Half life (h) 39 Effective concentrations (µg/ml, etc.) > 0.8 ng/ml Toxic concentrations (µg/ml, etc.) > 2.0 ng/ml

Digitalization (loading dose, 0 Digitalization (loading dose, 0.44 mg) followed by maintenance digoxin, 0.3 mg/day

Approximate accumulation factor of a drug with first order kinetics

Advantages & disadvantages of long half-life Once a day dosage or less Easy to maintain plasma levels in therapeutic window Missed doses are no big deal If toxicity occurs, it is a long wait* *can accelerate removal of some drugs by dialysis

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

Time concentration curve of metoprolol, 25 mg every 6 hours (half life = 3.2 hours), peak/trough ~ 3

Approximate peak/trough ratios for a rapidly absorbed drug with first order kinetics

Time concentration curve of 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 (L/h/70 kg) * 38.4 Volume of distribution (L/70 kg) 77 Half life (h) 1.8 Effective concentrations (µg/ml, etc.) > 1.5-6 mg/L Toxic concentrations (µg/ml, etc.) > 6 mg/L

I. V. infusion of lidocaine (half life 1 I.V. infusion of lidocaine (half life 1.8 h), 100 mg/h without or with a bolus loading dose

Two compartments, initial distribution

Elimination of a drug exhibiting two compartment behavior

Two compartments, equilibrated, in terminal elimination phase

Displacement by sulfisoxazole of bilirubin from plasma protein binding

What is the Vd of quinidine in an 80 kg patient? Katzung: Vd quinidine = 130 L/70 kg 80kg * 130/70 (L/70 kg) = ~ 149 L

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)

Pharmacokinetic model used for simulations