This document discusses the one compartment model for intravenous infusion. It explains that IV infusion maintains a stable drug concentration over a long period by administering the drug at a constant zero-order rate. The key aspects covered include: - Reaching a steady state concentration where the infusion rate equals the elimination rate. - Calculating the steady state concentration, elimination rate constant, and other pharmacokinetic parameters. - The time required to reach steady state being dependent on the drug's half-life, not the infusion rate. - Using a loading dose for drugs with long half-lives to quickly reach the steady state concentration upon starting infusion.

1. One Compartment
Model
IV Infusion
LAKSHMI CHANDRAN
PHARM D
SRM COLLEGE OF PHARMACY

2. Intravenous infusion
When a drug is administered intravenously at a constant rate (zero order) over a long period of time ,
it is known as IV infusion. The duration of the constant rate infusion is much longer than the half life of
the drug. E.g. antibiotics, theophylline, procainamide etc.
Why IV infusion?
•When the drug has potential to precipitate toxicity
•When a stable concentration of the drug is to be maintained for the therapeutic effect.
Advantages
•Ease of control of rate of infusion to fit individual patient needs.
•Prevents fluctuating maxima and minima (peak and valley) plasma level, desired especially when the
drug has a narrow therapeutic index.
•Other drugs, electrolytes and nutrients can be conveniently administered simultaneously by the same
infusion line in critically ill patients.

3. Zero - Order
Kinetics
The rate of change in concentration is expressed as :
𝒅𝑪
𝒅𝒕
= - K . Cn where n is the order of the reaction
for zero order kinetics n=0
𝒅𝑪
𝒅𝒕
= - K0 C0 = - K0 ( zero order rate constant in mg/min)
Rearranging the equation we get:
dC= - K0 t
Integrating both sides
C-C0= - K0 t
C= C0 - K0 t
C0 is conc of drug at t=0
C is conc of drug yet to
Undergo reaction at time t
Zero order processes can be defined
as the one whose rate is independent
of the concentration of drug
undergoing reaction i.e. the rate
cannot be increased further by
increasing the concentration of
reactants.

4. IV Infusion Model
DRUG
BLOOD AND OTHER
BODY TISSUES
ELIMINATION
R0 KE
Zero-order
Infusion rate
R0- Zero order infusion rate
KE- Elimination rate constant

5. At any time during infusion , the rate of change in the amount of drug in the body, dX/dt is the difference between
the zero order rate of drug infusion R0 and first order rate of elimination, -KEX
𝑑𝑋
𝑑𝑡
= R0 – KEX - (1)
Integrating eq.(1) yields
X =
𝑅0
𝐾 𝐸
(1- 𝑒−𝐾𝐸𝑡) - (2)
Since X= Vd.C where Vd is the volume of distribution and C is the Conc. of drug, eq. (2) can be transformed as:
C =
𝑅0
𝐾 𝐸
𝑉 𝑑
(1- 𝑒−𝐾𝐸𝑡 ) =
𝑅0
𝐶𝑙 𝑇
(1- 𝑒−𝐾𝐸𝑡 ) - (3)

6. Plasma concentration – Time profile
1. Initially the drug enters the body at
constant rate
2. The infusion rate R0 > KEX (elimination
rate).
3. As infusion time progresses the rate of
infusion equalizes with the elimination rate
of the drug
4. This stage is called the steady state
concentration /plateau/ infusion
equilibrium. (CSS )
5. At this stage concentration of drug in
plasma approaches a constant value.

7. At steady state , the rate of change of amount of drug in the body is zero, hence the eq. (1) becomes:
𝑑𝑋
𝑑𝑡
= R0 – KEX -(1)
0= R0 – KEXSS
R0 = KEXSS - (4)
Transforming to concentration terms and rearranging the equation:
CSS =
𝑅0
𝐾 𝐸
𝑉 𝑑
=
𝑅0
𝐶𝑙 𝑇
𝑖𝑛𝑓𝑢𝑠𝑖𝑜𝑛 𝑟𝑎𝑡𝑒
𝑐𝑙𝑒𝑎𝑟𝑎𝑛𝑐𝑒
- (5)
KE- Elimination rate constant
CSS- Concentration of the drug at steady state
XSS- Amount of the drug in the body at steady state

8. Calculating KE by using semi logarithmic
plot
Alternative method : During infusion the KE
can be calculated:
𝑅0
𝐶𝑙 𝑇
= CSS -(5)
C= CSS (1-𝑒−𝐾𝐸𝑡) - (6)
[𝐶 𝑆𝑆
−𝐶
𝐶 𝑆𝑆
] = 𝑒−𝐾𝐸𝑡 - (7)
log [𝐶 𝑆𝑆
−𝐶
𝐶 𝑆𝑆
] = −𝐾𝐸𝑡
2.303
- (8)

9. Half life of drug in IV infusion
•The time to reach steady state concentration is
dependent upon the elimination half life and
not on the infusion rate.
•If n is the number of half lives passed since the
start of infusion, the eq. (6) can be written as:
C= CSS {1- ( 𝟏
𝟐) n }
Where C is the concentration of the drug after
nth half life
•The percent of CSS achieved at the end of each
half life is the sum of CSS at previous half life
and the concentration of drug remaining after
a given half life
Half life % remaining % CSS achieved
1 50 50
2 25 50+25=75
3 12.5 75+ 12.5= 87.5
4 6.25 87.5+ 6.25= 93.75
5 3.125 93.75+ 3.125= 96.875
6 1.562 96.875+ 1.562= 98.437
7 0.781 98.437+ 0.781= 99.218
For therapeutic purpose, more than 90% of CSS is desired
which is reached in 3.3 half lives. It takes 6.6 half lives to
reach 99% of CSS. Shorter the half life, sooner the CSS
reached. E.g. Penicillin G with half life of 30 mins.

10. Infusion plus Loading Dose
What is loading dose?
•For drugs having longer half lives, like phenobarbital (5 days), it takes longer time to achieve the
steady state concentration. To overcome the sub therapeutic concentration of these drugs, an IV
loading dose large enough is administered to reach the steady state immediately
•After the loading dose is administered, the IV infusion is given immediately at a rate enough to
maintain this concentration.
Some important drugs that require loading dose:
• Amiodarone- Loading dose of 150 mg IV in 10 minutes slowly, followed by IV infusion of 540 mg over
18 hours.
•Streptokinase- Loading dose of 250,000 IU, followed by IV infusion of 100,000 IU/hr for 72 hours for
recurring pulmonary emboli and DVT.
•Succinylcholine- Loading dose of 0.3-1.1 mg/kg over 30 sec for surgical procedures and a continuous
IV infusion of 0.5-1.0 mg/min for prolonged muscle relaxation.

11. Calculating the loading dose
X= Vd.C
Taking X0,L as the loading dose,
X0,L= CSS. Vd - (9)
Substituting CSS= R0/ KEVd in eq. (9)
X0,L=
𝑹 𝟎
𝑲 𝑬
- (10)
Hence the eq. describing the plasma conc.
Following the IV loading dose and IV infusion
is:
C=
X0,L
Vd
𝒆−𝑲𝑬𝒕 +
𝑹 𝟎
𝑲 𝑬
𝑽 𝒅
(1-𝒆−𝑲𝑬𝒕) - (11)

12. Assessment of Pharmacokinetic
Parameters
•Apparent volume of distribution
Vd =
𝑹 𝟎
𝑲 𝑬
.𝑪𝑺𝑺
•Total systemic clearance
ClT =
𝑹 𝟎
𝑪 𝑺𝑺
•These two parameters can also be calculated from the total area under the curve (AUC) till the
end of infusion:
AUC =
𝑹 𝟎
𝑻
𝑲 𝑬
𝑽 𝒅
=
𝑹 𝟎
𝑻
ClT
= CSS. T
Where T is the infusion time.

13. References:
•Biopharmaceutics and Pharmacokinetics by D. M. Brahmankar and Sunil B. Jaiswal
•Guidance on Drug Doses Loading Doses for Primary Care Health Care Professionals by NHS
http://www.southernhealth.nhs.uk/EasySiteWeb/GatewayLink.aspx?alId=30182