# Routes of Excretion

## 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,

Example:

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 mg/L Enter required Cpmin mg/L Enter V L/kg Enter km or knr value hr-1 Enter Dettli slope value min.ml-1.hr-1 Patient Information Enter Patient Weight kg Age years Sex Male Female Enter Patient Serum Creatinine level mg/100 ml CLCr, kel and Tau Creatine Clearance ml/min Elimination Rate constant hr-1 R is Exact Tau hr

### Now enter a rounded value of Tau below

 Enter Rounded Tau value hr Maintenance and Loading Dose New R value Maintenance Dose mg every hr and Loading Dose mg

Practice calculating a patient's elimination rate constant from creatinine clearance
References
• Wagner, J.G. 1975 Fundamentals of Clinical Pharmacokinetics, Drug Intelligence Publications, Inc., Hamilton, IL