Chapter 16

Routes of Excretion

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Cpmax/Cpmin Calculations

Another approach is to use the desired Cpmax and Cpmin to define the dosing regimen. The steps to be taken for this approach include:

a. Define Cpmin/Cpmax. From information on the drug with reference to the patient's clinical requirements. For example the normal upper limit for an aminoglycoside peak concentrations might be 6 mg/L, however in case of life-threatening infection higher levels may be approached. Initial calculation might be based on a peak of 6 mg/L and a trough below 1 mg/L. (Use 1 mg/L as the trough and extend the interval when making the adjustment in τ.

b. Determine CLCr. Probably from serum creatinine levels using the Cockcroft-Gault equation.

c. Determine kel. Using the equation kel = km + b • CLCr with km and b values from the literature

d. Calculate Tau. Since and we know Cpmin, Cpmax, and kel we can calculate tau, τ. Typically this will be some uneven time value.

e. Round Tau. A more usual dosing interval should now be chosen. For example a tau of 7.8 or 6.7 hour could be rounded to 8 hours, thus dosing three times a day.

f. Recalculate R. A new value of tau results in a new value of R.

g. Calculate Maintenance Dose. The maintenance dose can be calculated from the minimum or the maximum plasma concentration. Thus

Maintenance dose = Cpmax • V • (1 - R) OR = Cpmin • V • (1 - R)/R

h. Calculate Loading DOSE. The loading dose can be calculated directly (for an IV bolus) by equating Cp0 and the Cpmax value. Thus,

Loading dose = Cpmax • V


A 75 kg, 65 year old male patient, serum creatinine concentration of 2.3 mg/100 ml, is to be given an aminoglycoside IV to achieve a peak plasma concentration of 6 mg/L and trough concentration below 1 mg/L. The apparent volume of distribution is reported to be 0.28 L/kg. From Table 3-9 (Wagner, 1975 p161), km and b values are 0.02 and 0.0028, respectively.

a. Cpmax = 6 mg/L and Cpmin = 1 mg/L

b. CLCr =

c. kel = km + b • CLCr = 0.02 + 0.0028 x 34 = 0.115 hr-1

d. R =

ln (0.1667) = -1.792 = -0.115 x τ

τ = 15.6 hour

e. Since a longer dosing interval is needed to keep the trough level below 1 mg/L use a tau value of 18 hours.

f. New R value. R = e-0.115 x 18 = 0.1262

g. Calculate maintenance dose using Cpmax = 6 mg/L as reference point. Thus

Maintenance dose = Cpmax • V • (1 - R) = 6 x 75 x 0.28 x (1 - 0.1262) = 110 mg

Thus use 100 mg iv every 18 hours

Cpmin = Cpmax • R = 5.45 x 0.1262 = 0.69 mg/L

h. The loading dose can be calculated as:-

Loading dose = Cpmax • V = 6 x 75 x 0.28 = 126 mg. Using 125 mg would give a Cpmax = = 5.95 mg/L.

Thus a loading dose of 125 mg followed by 100 mg every 18 hours should be satisfactory.

Comparison with PDR recommendation.

Usual dose for 75 kg patient is 75 mg q8h. With serum creatinine 2.3 mg/100 ml give 40 percent of 75 mg q8h. That is 30 mg q8h (R = 0.399) giving 2.38 and 0.95 for Cpmax and Cpmin, respectively.

Calculator 16.9.1 Calculator Using Cpmax and Cpmin Criteria

Drug Information

or Enter your own Data

Enter required Cpmax


Enter required Cpmin


Enter V


Enter km or knr value


Enter Dettli slope value

Patient Information

Enter Patient Weight





Male Female

Enter Patient Serum Creatinine level

mg/100 ml

CLCr, kel and Tau

Creatine Clearance


Elimination Rate constant


R is

Exact Tau


Now enter a rounded value of Tau below

Enter Rounded Tau value


Maintenance and Loading Dose

New R value

Maintenance Dose

mg every hr

and Loading Dose


Practice calculating a patient's elimination rate constant from creatinine clearance

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