 Definition: The One compartment open model treats the
body as one homogeneous volume in which mixing is
instantaneous. Input and output are from this one volume.
 [full] [icon] Figure: Diagram
of 1COM with terms
 Assumptions:
 Body is one homogeneous compartment  Problems?
Practicalities?
 Instantaneous mixing  Must be instantaneous
"relative to the time scale of
measurement"
 Applicable only to first order processes
 [full] [icon] Figure: Plot of 1COM
plus formula
 [do plot][how?] Plot 1COM
formula and enter various values for A and Ke (actually, elimination halflife) using
a spreadsheet. (NOTE: You must have
Microsoft Excel installed on your machine and your browser
must be appropriately setup for
this to work)
One compartment open
model
Cp(t) = A * e^{(Ke * t)}
(mg/L = mg/L * e^{(frcn/hr * hr)})
Using a calculator

 Cp(t) = concentration in plasma
at defined time interval after the time of known
concentration corresponding to "A"
 A = Known (or estimated)
concentration.
Can be known by actual measurement or estimated
by using Cp(0) = (F * D)/Vd. Could be thought of
as an "anchor" point.
 e = base of natural logarithms
 Ke = elimination rate constant
(Ke is the slope of the line)
 t = selected time after time of anchor
concentration.

 Get the semilog plot you made for miraclemycin in the 70 kg patient in the
volume of distribution discussion.
 Identify the various parts of the 1COM formula on the
graph.
Cp(t) = A * e^{(Ke
* t)} 
 Focus
on the "A" term
 At what time after a drug is given can one make
the best "guestimate" of the value of
"A" if the drug is given IV?
 What does the term Cp_{(0)}
mean?
 How could one estimate Cp_{(0)} given values
for the following and assuming instantaneous
absorption and distribution? Vd, Dose, F
 Understanding the "A" is a
"scaling" factor and that it can be any
place on the time axis where one has a
reasonable ability to know its value will give
one a big boost in understanding simple clinical
pharmacokinetics.
 [do_plot] Exercises
involving "A"  Enter different
numbers for Dose, F, and Vd into spreadsheet to
see the effect on plot of 1COM. (NOTE:Your browser
must be appropriately setup for this to work)
 Does "A" have to be at the
zerotime point on the graph? What if one knows
from measuring drug concentration, the value at 5
hours? Could one estimate the concentration at,
e.g., 10 hours after a dose, given a measured
5hour concentration and a Ke?
The plasma concentration of drugs given by infusion at
constant rate or by repeated dosing at a constant rate will rise
until the concentration high enough that elimination is equal to
input. This is termed "accumulation".
Retrieve or remake graph of Miraclemycin from data in the
lecture on volume of distribution (Vd). [70 Kg data] The data to make
the graph are repeated here.
 70 kg patient given dose of 2,800 mg of
miraclemycin
 Plasma drug concentrations 
Times (hrs) 
2 
4 
6 
8 
Conc (mg/L) 
10 
5 
2.5 
1.25 

 What is the concentration at 8 hr after administering the
drug?
 What was the "zerotime" concentration in that
graph?
 Assuming IV administration and instantaneous
distribution, what would the concentration be if an
identical dose (2800 mg) were given at 4 hours? (Note:
rise in concentration with each dose is 20 mg/L)
 What is the new peak?
 What is the concentration 4 hr after 2nd dose?
 Do this exercise for at least 2 more doses.
 Does the curve keep rising at the same rate?
 Concentrations in this scenario are:
Dose 
First 
Second 
Third 
Fourth 
Peak 
20 
25 
26.25 
26.56 
Trough 
5 
6.25 
6.56 
6.64 
Concentrations are mg/L 
Calculation
 Calculation of accumulation factor for repeated doses
RA
= 1 / [1  e^{(Ke * T)}] 
RA = Accumulation
factor (a ratio)
Ke = elimination rate constant (/hr)
T = dose interval (hr) 
 When T < 5 halflives accumulation will occur
 Examples of relationship between T & Ke on
accumulation
Accumulation Factor: Effect of
Halflife and Dose Interval 
Rates 
Accumulation Factor 
halflife
(h) 
Ke
(frcn/h) 
Dose Interval (h) 
1 
2 
12 
24 
2 
0.3465 
3.4 
2.0 
1.0 
1.0 
50 
0.0139 
72.71 
36.6 
6.5 
3.5 
 Note from the table that given equal dose intervals,
e.g., 24 h, the drug with the longer halflife will
accumulate more. See multiplier 1.0 versus 3.5.
 Changes in halflife: It should be apparent from
this that changes in halflife during therapy can
have tremendous effects on steady state drug
concentrations. Such changes can occur during
disease
 Interindividual variation in halflife: . There
is also a large interindividual variation in
elimination halflife so accumulation may be more
pronounced in one patient than another.
 Examples of some actual concentrations
Peak Concentration at SS vs Initial Peak 
halflife
(h) 
Initial Peak 
Dose Interval (h) 
1 
2 
12 
24 
(mg/L) 
(mg/L) 
(mg/L) 
(mg/L 
mg/L 
2 
20.0 
68.3 
40.0 
20.3 
20.0 
50 
20.0 
1453.0 
731.5 
130.5 
70.7 
On repeated "bolus" administration of drug, the
concentration in the plasma oscillates between the peak
and the trough. The importance of the degree of oscillation is
drug dependent and depends on the dose, dose interval, and
elimination halflife.
 Oscillation can be viewed as a (an) 
 ratio  determined by Dose interval and
halflife
 absolute amount in mg/L (determined by dose
interval, halflife, and (F* dose/Vd))
 Ratio of peak to trough depends on 
 Dose interval
 Elimination halflife
 [Excel] [how?] Use spreadsheet to
see influence of varying T and halflife on the
ratio of peak to trough

Oscillation
ratio = 1/e^{(Ke* T)} 
Ke = elimination rate
constant
T = dose interval 
 Absolute oscillation also includes factor: F*D/Vd
 Ratio: Peak to trough
 At T = halflife, Ratio is 2!, i.e., Peak is
twice the trough
 At T<halflife, Ratio is <2
 At T>halflife, Ratio is >2
 As T increases, Ratio approaches infinity
 As T decreases, Ratio approaches infinitesimal
 Importance of degree of oscillation
 Importance is drug dependent

 The height and shape of the peak on a plot of drug
concentration versus time depends on
 Ka = absorption rate
 Ke = elimination rate
 F*D/Vd
 IV administration gives the sharpest peaks and is
the standard for Ka>>Ke.
Ka >> Ke means absorption is much faster
than elimination so nearly all of the drug is
absorbed before a significant amount is
eliminated.
 PO (per os) and other routes of adminstration and
use of slowly absorbing dose forms may cause
peaks to be much flatter.
 Formulae used below to calculate Peak and Trough
concentrations at steady state and with repeated
doses, assume Ka>>Ke. When this condition
is NOT true, actual peaks will be less and actual
troughs will be higher than predicted by the
formulae.
 [EXCEL] [how?]
Try different values of absorption halflife given a
constant elimination halflife to see the influence of
varying absorption rate on the shape of the curve. Note
the ordinate is in terms of "multiples of the
elimination halflife."
To calculate Peak concentration at steady
state (Css(max))
Css(max)
= (F*D/Vd) * {1 / [1  e(Ke * T)]}
mg/L = (frcn * mg/L) * {1 / [1  e(hr^{1}
* hr)]} 
Css(max) = Peak
concentration at steady state assuming Ka >> Ke
F = bioavailability
D = dose
Vd = volume of distribution
Ke = elimination rate constant
T = dose interval 
 Use of (F*D/Vd) to estimate peak concentration of the first
dose
 Qualifier that Ka >> Ke, i.e., absorption rate must
be much faster than elimination rate. This is true for IV
injections an some intramuscular injections.
 When Ka >> Ke is NOT TRUE, the true peak will be
less than that estimated by this formula. This is a
safety factor in many situations where we use this
formula to estimate the peak concentration.
To calculate Trough concentration at steady
state (Css(min))
Css(min)
= Css(max) * e^{(Ke * T)} 
Css(min)= Trough concentration at steady state (mg/L)
Css(max) = Peak
concentration at steady state as calculated using
appropriate formula (mg/L)
Ke = Elimination rate constant (hr^{1})
T = Dose interval (hr) 
 Note the obvious similarity of this formula to the
standard 1COM formula!
Send suggestions /
questions
Last modified: 04 Sep 1996 14:03 glc