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Practical Pharmacokinetics
September 11, 2007
Frank F. Vincenzi
Learning Objectives
(Fundamental pharmacokinetic concepts)
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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.)
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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 = CLliver + CLkidney + …)
• 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 simpleminded view
of the kidney
nephron
systemic circulation
drug and/or
A simple
minded
view of the
liver
drug and/or
drug
portal
circulation
Gut
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
Plasma
‘Ideal’ 70 kg person 4 L (~5%)
(Total body water = 42 L)
Interstitial
11 L (16%)
Intracellular
28 L(35%)
A small volume of distribution
Isoniazid = 0.067 L/kg
General
determinants of
drug
distribution
Plasma water
~5%
Interstitial water
~16%
Fat
~20%
Intracellular water
~ 35%
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)
0.693 = natural logarithm of 2
First order elimination
• Half lives
0
1
2
3
4
5
6
% remaining
%eliminated
100
50
25
12.5
6.25
3.125
1.5625
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50
75
87.5
93.75
96.875
98.4375
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:
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Oral availability (%)
Urinary excretion (%)
Bound in plasma (%)
Clearance (ml/min/kg)
Volume of distribution
Half life (h)
Effective concentrations (µg/ml, etc.)
Toxic concentrations (µg/ml, etc.)
100 (N/A)
1
99
0.38
1.1 L/kg
43
300-400 ng/ml
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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 10-15 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
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Oral availability (%)
Urinary excretion (%)
Bound in plasma (%)
Clearance (9.2 ml/min/kg)
Volume of distribution (L/kg)
Half life (h)
Effective concentrations (µg/ml, etc.)
Toxic concentrations (µg/ml, etc.)
35
2
70
38.4
1.1
1.8
> 1.5-6 mg/L
> 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)