2 Principles of Pharmacology - Summary of Pharmacokinetic Calculations
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Course
Pharmacology
Institution
Pharmacology
The object of the course is to teach students an approach to the study of pharmacologic agents. It is not intended to be a review of the pharmacopoeia. The focus is on the basic principles of biophysics, biochemistry, and physiology as to the mechanisms of drug action, biodistribution and metabolis...
Harvard-MIT Division of Health Sciences and Technology
HST.151: Principles of Pharmocology
Instructor: Dr. Carl Rosow
1
Summary of Pharmacokinetic Calculations
The following list was extracted from pharmacology lecture notes provided by Dr. Steven
Shafer. It summarizes and embellishes the pharmacokinetic concepts presented:
1. The rate of change (decrease) when drug is injected into a 1 compartment model is
dX
= −kX (first order process)
dt
2. The concentration following that injection is
C(t) = C0 e −kt where C0 is the initial concentration
3. The half-life, t½ (time required for a 50% decrease), is
0.693
t1 =
2 k
4. If you know the time required for a 50% decrease, the rate constant, k, is
0.693
k=
t1
2
5. The definition of concentration is
X
C= , where X is amount and V is volume
V
6. The concentration at time t following a bolus injection will be
X 0 − kt X
C(t) = e where 0 is the initial concentration
V V
7. If ClT is the total clearance (or flow) from a 1 compartment model, the rate at which
drug leaves can be calculated
dX
= C(Cl T )
dt
8. Since item 1 and item 7 are the same rate, it follows (after substituting X/V for C)
that
, 2
Cl T
k=
V
Substituting in equation 3, we get this important relationship
0.693(V)
t1 =
2 Cl T
So, as clearance (ClT) increases, k increases, and the half-life decreases. As volume
(V) increases, k decreases, and half-life increases.
9. During an infusion at rate k0, the concentrations are described by the equation
C(t) = C ss (1 − e −kt ) where Css is the concentration at steady-state.
10. The steady-state concentration can be calculated from infusion rate and clearance
k0
Css =
Cl T
11. Half-lives describe the time for a 50% decrease in concentration following a bolus,
and they also describe the time required to reach 50% of the steady-state
concentration during an infusion. Following a bolus, the concentrations will be at
25%, 13%, 6%, and 3% of the initial concentration following 2, 3, 4, and 5 half-lives,
respectively. During a constant-rate infusion, the concentration will reach 75%, 88%,
94%, and 97% of the steady-state concentration in 2, 3, 4, and 5 half-lives,
respectively.
What do you do with this? Well:
1. If you know the amount of drug injected (X0), and the concentration at time 0 (C0),
you can calculate the volume
X0
V=
C0
2. If you know X0, V, and k, then you can calculate the concentration at any given time t
X 0 − kt
C(t) = e
V
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