1. Pharmacokinetics
By: Megan Baird
Faculty Advisor: Dr. Jyoti Champanerkar
(This poster is based on a Capstone project.)
Conclusion
What is the steady-state
level of an infused drug?
Pharmacokinetics is the study of the time course of a specific drug and the
metabolic concentrations of the biological fluids, tissues and excreta.
Metabolism of Everyday Drugs
Introduction
The meaning of Pharmacokinetics is the
application of kinetics to pharmakon,
which is the Greek word for drugs and
poison. Pharmacokinetics is useful to
scientists because it will help predict
future results, which in return would
save money as well as time. To
understand the concepts of
Pharmacokinetics, we study the
mathematical models of Infusions and
Injections.
Injections vs. Infusions
Oral administration of drugs is
considered an injection. Some examples
are:
• Ibuprofen
• Diazepam
• Tetracycline
Injections can be measured by the
formula:
t: time
k: rate constant, related to half-life
Half-Life of Drugs
The half-life of a drug is defined by the duration of time that the drug is
active in the bloodstream. The half-life of a drug is directly correlated
with the rate constant k. In general, if we do not know the rate constant k,
we use the formula
1
2
𝑚0 = 𝑚0 𝑒−𝑘𝑇
, in order to calculate the half-life of a
specific drug.
The Rate Constant
We assume that drugs decay at a rate proportional to the amount of drug that
is present in the body. In general, k depends on a person’s height, weight,
health, etc. If we do not know the rate constant k, we use the formula 𝑚 𝑇 =
1
2
𝑚0, where T is the half-life. We can use the same derived formula for both
injections and infusions.
1
2
𝑚0 = 𝑚0 𝑒−𝑘𝑇 
1
2
= 𝑒−𝑘𝑡 ln(
1
2
) = −𝑘 ∗ 𝑇1 2 
−ln(½)
𝑇1 2
 k =
ln(2)
𝑇1 2
After studying the mathematical
models of two different ways to
administer drugs,
• Injections have a full dose when
it is entered into the bloodstream
but reaches an insignificant
amount over a specific period of
time.
• Infusions begin with 0 mg in the
bloodstream and reaches the
drugs detectable level 2-3 days
after their discharge.
𝑚 𝑡 = 𝑚0 𝑒−𝑘𝑡
for 𝑡 ≥ 0
Intravenous Therapy (IV) is the most
common form of infusion. Tetracycline
is a drug that can be transmitted orally
or intravenously. Infusions can be
measured by the formula:
Assuming no initial drug in the blood,
k: rate constant
A: infusion rate
t: time
𝑚 𝑡 =
𝐴
𝑘
∗ 1 − 𝑒−𝑘𝑡
, 𝑡 ≥ 0
Metabolism of 400 mg Ibuprofen Injection Metabolism of 50 mg/hr IV Antibiotic Infusion
The steady-state level of a drug is
the point of time that the amount of
drug being infused into the
bloodstream is approximately equal
to the amount that is being
naturally eliminated from the
bloodstream. Research shows that
most steady-state levels are
reached within the first 6 half-lives
of the drug.
The steady-state level can be found
using the formula:
lim
𝑡→∞
(
𝐴
𝑘
)(1−𝑒−𝑘𝑡
)
This formula can be simplified to:
lim
𝑡→∞
𝑚(𝑡) =
𝐴
𝑘