The method of residuals (cont'd):

Example: After a single iv bolus dose of the antiarrhythmic drug bretylium, the following concentrations were obtained:

Time (hr)	Conc (ug/L)	Time (hr)	Conc (ug/L)
0.2	120	4.0	18
0.5	84	6.0	15
1.0	53	8.0	12.5
2.0	29	12.0	8.8

Using the method of residuals determine the equation that describes the plasma conc-time profile at any time.

Plot the concentration versus time on a semilog scale.

slope = -β/2.303

β_{t 1/2}

Identify the best line that represents the drug elimination process

The y-intercept is equal to B. The hybrid elimination rate constant (β) and β-half life can be determined from the line.

slope = -β/2.303

β_{t 1/2}

slope = -α/2.303

α _{t 1/2}

Calculate the residuals during the distribution phase.

Plot the residuals versus time, and draw the best line that goes through the points.

The y-intercept is equal to A. The hybrid distribution rate constant α and a-half life can be determined from the line.

Answer
Graphically :

B = 25 ug/L β = 0.087 hr^-1

A = 120 ug/L α = 1.38 hr^-1

The equation that describe the plasma concentration at any time is:

Cp (ug/L) = 120 e ^{-1.38 t} + 25 e ^{-0.087 t}