Clinical Pharmacokinetic
Equations and Calculations
Prof. Henny Lucida, PhD, Apt
Basic equations
• LOADING DOSE:
LD = Css x Vd
• MAINTENANCE DOSE:
MD = Css x Cl
• CLEARANCE:
Cl = ke x Vd
• HALF-LIFE:
t1/2 = 0.693/ke
Intravenous bolus equations
Ct  C0 e
 ket
 ln C1  ln C 2 
ke 
t1  t 2
V D
C0
 V e
C D
t 1  0.693
2
 ket
ke
Intravenous bolus
Continuous iv infusion
Non iv/extravascular
Css av, any route of adm
Problems:
1. A physician wants to give theophylline to a young male
asthmatic patient (age 29, 80 kg). According to the
literature, t1/2 elimination of the drug is 5 hours and
the Vd app is equal to 50% of body weight. The
plasma level of theophylline required to provide
adequate airway ventilation is approximately 10 mg/mL.
a. The physician wants the patient to take medication
every 6 hours around the clock. What dose of
theophylline would you recommend? (F=1)
b. If you were to find that theophylline is available to you
only in 225 mg capsules, what dosage regimen would
you recommend?
Mr JM, a nonsmoking 60 kg patient with
chronic obstructive pulmonary disease, is to be
started on an oral regimen of aminophylline (85%
of which is theophylline). The pharmacokinetic
parameter values for a typical patient population
with this disease are: F = 1 (for theophylline), Vd =
0.5 L/kg and CL = 40 mL/hr/kg. Desain an oral
dosage regimen of aminophylline (100 and 200 mg
tablets are marketed) for this patient to attain and
maintain a plasma conc with ther window 10-20
mg/L. Abs theophylline is complete and rapid
2. The t1/2 elimination of an antibiotic is 3 hours and the
Vd app is 20% of body weight. The therapeutic window
for this drug is from 2 to 10 mg/mL. Adverse toxicity is
often observed at drug concentrations above 15 mg/mL.
The drug will be given by multiple IV bolus injections.
Calculate the dose for an adult male patient (68 yo, 82
kg) with normal renal function to be given every 8 hours.
3. An antibiotic drug is to be given to an
adult male patient (75 kg, 58 years old) by
IV infusion. The drug is supplied in sterile
vials containing 30 mL of the antibiotic
solution at a concentration of 125 mg/mL.
What rate (mL/min) would you infuse this
patient to obtain a Css of 20 mg/mL? What
loading dose would you suggest? Assume:
one-compartment model, Vd = 0.5L/kg and
t1/2 elimination = 3 hours
Equations for iv infusion
C
k0
Vd app  k el
1  e 
Css 
 k el t

C  Css 1  e  k el t

k0
Vd app  k el


k0
k el  t'
k el T
logC  log
1 e

Vd  k el
2.303
Equations for iv infusion
X0 = Css * Vd
R0
Ass 
ke
X  X 0e
 k el t

k0

1  e  k el t
k el
R0
C ss 
CL

4. For prolonged surgical procedures,
succinylcholine chloride is given by iv
infusion for sustained muscle relaxation.A
typical initial dose is 20 mg followed by
continuous infusion of 4 mg/min. The
infusion must be individualized because of
variation in the kinetics of metabolism of
succinylcholine. Estimate the elimination
half-lives of succinylcholine in patients
requiring 0.4 mg/min and 4 mg/min,
respectively, to maintain 20 mg in the
body.
5. Calculate the excretion rate at steady
state for a drug given by iv infusion at a
rate of 30 mg/hr. The Css is 20 mg/mL. If
the rate of infusion were increased to 40
mg/hr, what would be the new Css?
Assume first order elimination kinetics and
a one compartment model.
6. A patient with renal dysfunction received
a dose of vancomycin. Cp were 22 and 15
mg/L at 24 and 48 hours after infusion
respectively. Determine when the
concentration would reach 10 mg/L!
a. 54 hours
b. 72 hours
c. 96 hours
d. 128 hours
7. If the Cp just after a gentamicin dose is 10
mg/L and the patient’s elimination rate
constant is 0.15/hr, predict what the Cp
will be 8 hours later!
a. 6.0 mg/L
b. 3.0 mg/L
c. 1.5 mg/L
d. 1.0 mg/L
8.