Section 2 - Applied Pharmacokinetics

### Aminoglycoside dosage calculation

A one-compartment model provides a clinically useful framework for estimating the serum level time curve of aminoglycosides. Two parameters are required for this model, apparent volume of distribution (Vd) and elimination rate (Kel).

Initial dosing

1. Determine elimination rate (Kel)
For initial dosing, before serum level data are available, the elimination rate is estimated from a Dettli plot of CLcr versus Kel:

Kel = 0.01 + (CLcr x 0.0024)

where

CLcr = creatinine clearance

2. Determine Volume of distribution (Vd)
The apparent volume of distribution is estimated by multiplying a population average by the patient's weight. Please note however, that Vd varies considerably between patients, and this variability has a substantial effect on serum concentrations and dosage requirements.

Vd = DW x Vdperkg

where

DW = dosing weight
Vdperkg = 0.30 liters/kg if age>=65
Vdperkg = 0.27 liters/kg if age<65

Serum level analysis

Sawchuk and Zaske's method provides a simple way of calculating individualized pk parameters for the one-compartment model based on peak and trough levels.
1. Determine elimination rate (Kel)

Kel = (ln Cpmax/Cpmin') / t"

where

Cpmax = Peak level
Cpmin'= Trough after dose
t" = time between samples

2. Determine Volume of distribution (Vd)

VD = [(Dose/tinf) / Kel] x (1- e-Kel x tinf) / Cpmax - (Cpmin x e-Kel x t' )

where

tinf = length of infusion
Cpmax = Peak level
Cpmin = Trough before the dose
t' = hours between time Cpmin drawn and end of infusion

Bayesian analysis

Bayesian analysis is automatically utilized when only one serum level is entered into Kinetics, it is optional when two or more SDC's are available.

The Bayesian method uses the population-derived pharmacokinetic parameters, Vd and Kel, as a starting point and then adjusts those parameters based on the serum level results taking into consideration the variability of the population-derived parameters and the variability of the drug assay procedure.

The appeal of this approach is that it mimics human thinking. That is, SDC's are interpreted in light of both our expectations from the population model and our knowledge of the variability of the test itself.

The main advantage of Bayesian analysis is that only one steady-state SDC, preferably a trough, is required to perform an accurate analysis.

Determine ideal dose

After calculating the model parameters from either the population model, the serum level data, or both (as in the case of Bayesian method), the next step is to determine the ideal dose and interval.
1. Determine ideal dosing interval (tau)
The ideal interval is determined by calculating the time it takes for our target peak to diminish to our target trough:

tau = tinf + [ln(Cptmax / Cptmin) / Kel]

where

tinf = infusion length
Cptmin = Target trough
Cptmax = Target peak

2. Determine ideal maintenance dose
Note that the target peak level drives the dose in this equation. This meshes perfectly with the concentration-dependent killing property of aminoglycosides where our goal is to target a peak level which is 8 to 10 times the MIC.

MD = Kel x Vd x Cptmax x (1 - e-Kel x tau / 1 - e-Kel x tinf)

where

tinf = infusion length
Cptmax = Target peak
tau = ideal dosing interval

3. Select a practical dosage and interval
• Choose practical, convenient doses and administration schedules.
• A general rule of thumb is to round the dose off:
• Gent and tobra round to the nearest 10mg
• Amikacin round to the nearest 50mg

4. Calculate steady-state peak and trough levels

Cpssmax = (MD / tinf x Vd x Kel ) x (1 - e-Kel x tinf /1 - e-Kel x tau )
Cpssmin = Cpssmax * e-Kel x (tau - tinf)

where

tinf = length of infusion

Extended interval method
Extended-interval (aka "once-daily" or "pulse") aminoglycoside dosing has gained popularity in recent years. This simplified dosing method is appropriate in young, otherwise healthy patients with sepsis. Keep in mind however, there are many patient groups who are not candidates for EI dosing. For detailed information please read the following 1997 consensus statement:

Initial dose

1. Determine maintenance dose (MD)

MD = DW x QD-dose

where QD-dose is:

• Amikacin, kanamycin = 15 mg/kg
• Gentamicin, Tobramycin, Netilmicin = 5 mg/kg

2. Determine interval based on creatinine clearance

CLcr Interval
Over 60 24 hours
40-59 36 hours
30-39 48 hours
Less than 30 Use traditional dosing method
Obtain a mid-interval drug level 6 to 16 hours after the initial dose, then evaluate the interval based on the dosage adjustment nomogram.

If the 6 to 16 hour level is undetectable and the infection is not responding, consider changing to a traditional dosing method.

The three interval break points on the Hartford interval adjustment nomogram are the approximate decay curves from a 7mg/kg gentamicin dose. These decay curves were calculated using a one compartment model with a volume of distribution of 0.25 L/kg and an elimination rate calculated from creatinine clearances of 25, 40, and 60 ml/min for 48, 36, and 24 hour intervals respectively. The authors of the Hartford nomogram then flattened these decay curves to simplify the nomogram.5

It is important to note that the Hartford interval adjustment nomogram is only valid for a 7mg/kg dose. A nomogram for the less aggressive dose of 5mg/kg/day was developed by a consensus panel.23 For 15mg/kg doses of amikacin multiply the drug-level scale by a factor of three. This same consensus panel argues that the 48 hour interval should be abandoned, that patients with a CrCl < 40ml/min should be dosed by traditional pharmacokinetic methods.

The consensus panel also suggests that younger patients with excellent renal function may require Q 12 hour dosing. A dosing algorithm for this subpopulation has been proposed by Urban and Craig.24

Some have questioned the validity of all ODA nomograms because they are based on one-compartment parameters derived from traditional dosing methods. Some pk studies have shown that the pharmacokinetics of aminoglycosides at high doses differ significantly from those at traditional doses. Therefore, it is argued that nomograms based on an assumption of similar kinetics are invalid. 25

Section 2 - Applied Pharmacokinetics

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