Drugs administered by IV route may either be given at once (as a bolus dose) or by slower IV infusion over a definite time such as Phenytoin which must be given slowly, no greater than 50 mg/min (and preferably 25 mg/min or less) in adults. Such drugs are infused slowly through a vein into the blood at a constant rate (zero order input) which allows precise control of plasma drug concentrations.

2. Introduction
Drugs administered by IV route may either be given at once (as a
bolus dose) or by slower IV infusion over a definite time such as
Phenytoin which must be given slowly, no greater than 50
mg/min (and preferably 25 mg/min or less) in adults. Such
drugs are infused slowly through a vein into the blood at a
constant rate (zero order input) which allows precise control of
plasma drug concentrations.
The following figure represents the plasma-level time curve for a drug
given by constant IV infusion. At time zero, no drug was present in the
body after which the drug level gradually increases until it becomes
constant (plateau or steady-state). Once the drug has reached the
steady-state, the rate of drug leaving the body is equal to the rate of
drug entering the body.

8. (3)

9. 1. A drug has a volume of distribution of 12 L and a K of 0.18 hr . A steady state
concentration (Css) of 12 mg/ml is desired.
(a) What is the infusion rate needed to maintain this concentration ?
(b) How long it takes to achieve 90% and 99% of the Css ?
(c) If the elimination rate constant, K, in a patient with a renal impairment is 0.1 hr-1,
what is the infusion rate required to maintain the same Css in this patient?
Calculation of the plasma drug levels after a single dose IV infusion.
Solution:
(a) Equation 2 can be rewritten as
KO = Css. Vd. K
Therefore:
Infusion rate KO = 12 x 12000 x 0.18
= 25920 mg/hr
= 25.92 g/hr
(b)According to equation 3
C = Css (1- e )
Now, C = 90% of Css,
therefore, we can write,
90% of Css = Css (1_e )
0.9 . Css = Css (1-e )
0.9 = 1 – e
-kt
-kt
-kt
-kt
e = 1 - 0.9 = 0.1
-kt
[OR]
Taking the natural logarithm of both sides –kt = In 0.1
t90% = In 0.1
-K = =
-2.303
-K
-2.303
0.18 = 12.794 hrs
In terms of t1/2 (0.693 / K = 3.85 hrs),
t90% = 12.794
3.85 = 3.32 t1/2
-1
Similarly, t90% = =
In 0.1 In 0.1
K 0.18 =
=
25.58 hrs
6.645 t1/2
(c) The elimination rate constant of the patient is 0.1 hr
The infusion rate for this patient to maintain the steady - state
concentration of 12 mg/ml is
Ko = Css.Vd.K = 12 × 12000×0.1 = 14400 =14.4 mg/hr
When the elimination rate constant decreases, then the infusion rate must
decrease proportionately to maintain the same Css. However, because the
elimination rate constant is smaller (i.e., the elimination half-life is
longer), the time to reach Css will be longer.
The for this patient is 23.02 hrs, and = is 46.05 hrs.
-1
t90% t90%

10. 2) A patient is given an antibiotic having t1/2 of 4 hrs by constant I.V. infusion at
a rate of 3 mg/hr. At the end of 36 hours, the plasma drug concentration is 2.2
mg/L. Calculate the total body clearance, Clt for this antibiotic. What is the
volume of distribution, Vd, of the drug?
Solution: Equation 2 can be rewritten as
Vd.K = = Clt
Css
Ko
The plasma sample is taken after 36 hrs of infusion, which time
represents 9 times t1/2 . Therefore, the plasma drug concentration
approximates the Css.
Clt =
K0
Css
= =
3 mg/hr
2.2 mg/L
=
1.363 L/hr 1363 ml/hr
Volume of distribution,
Vd =
Clt
K
=
1363
(0.693/4)
= 7870.9 ml
= 7.871 Liters

11. Assignment
1. A patient is given an I.V. infusion of an antibiotic at an infusion rate of 26
mg/hr. Blood samples are taken at 10 and 28 hours and plasma drug
concentrations are 10 and 11.9 mg/ml respectively. The antibiotic has an
elimination half-life of 3 to 5 hrs in the general population. Estimate the
elimination half-life of the drug in this patient.
2. A drug whose K = 0.02 hr¹ and Vd =20 liters is infused to a patient at a rate of
3 mg/hr for 8 hrs. What is the concentration of the drug in the body 2 hours
after the cessation of the infusion.
3. What is the concentration of a drug after 8 hours after administration of a
loading dose of 100 mg and simultaneous infusion of 20 mg/hr (the drug has a
t1/2, of 3hrs and a volume of distribution 100 L)?
4. A doctor wants to maintain 2 mg/L of plasma drug level in a patient by
administering a loading dose and simultaneously I.V. infusion to get Css of 2
mg/L. If the drug has an elimination rate constant, K = 0.1 hr and Vd= 15 L,
what is the required loading dose and what is the required infusion rate?
-1

12. 5) An adult male patient (52 years, 70 kg) is to be given an antibiotic
by I.V. infusion. According to this model, the antibiotic has an
elimination half-life of 2 hours, Vd of 0.9 L/Kg, and is effective at a
plasma drug concentration of 10 mg/L. The drug is supplied in 5ml
ampoules containing 200 mg/ml.
6)