Section 2 - Applied Pharmacokinetics

### Vancomycin dosage calculation

Choosing a model

Vancomycin has a relatively long distribution phase and is best characterized with a 2-compartment model. However, after the 1 to 2 hour distribution phase, it collapses to a 1-compartment model. Therefore, if peak serum levels are drawn and targeted for at least one hour after the infusion, a 1-compartment model is sufficient.

The 2-compartment vancomycin model utilized by Kinetics is based on Lake and Peterson's data and is meant to approximate their published nomogram. L&P's method, which is the only published vancomycin dosing method to be independently verified, achieves target peaks of 20 to 30 mcg/ml and target troughs of 5 to 10 mcg/ml in 80% of patients.

Initial dosing

If a one-compartment model is utilized, the methodology is identical to that used for aminoglycoside dosing. But because we are attempting to fit a 2-compartment drug into a 1-compartment model, it is akin to forcing a square peg into a round hole. As a result, hybrids values are utilized for the pk parameters, hence they don't match up exactly with what you may read in the published literature.

1. Determine elimination rate (Kel)

Kel = 0.009 + (CLcr x 0.0022)

where

CLcr = creatinine clearance

2. Determine Volume of distribution (Vd)
Vd varies considerably between patients, the "normal" range is 0.4 to 0.9 L/kg. This disparity in reported Vd is the main reason why vancomycin serum concentrations and dosage requirements are so unpredictable.

Vd = DW x Vdperkg

where

DW = dosing weight
Vdperkg = 0.5 liters/kg

3. Determine ideal dosing interval (tau)

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

where

tinf = infusion length
Cptmax = Target peak, 30 mcg/ml.
Cptmin = Target trough, 5 mcg/ml.

4. Determine ideal maintenance doses

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

5. Select a practical dosage and interval
• Choose practical, convenient doses and administration schedules.
• A general rule of thumb is to round Vancomycin doses to the nearest 250mg.

Two-compartment equations are quite complex and are presented here only for completeness. As stated earlier, this model is based on Lake and Peterson's data and works well if you give small doses, more frequently. However, if your practice standard is to give large doses less often, then the 1-compartment model may be a better choice.

1. Determine clearance (CL)
Clearance is estimated from a Dettli plot of CLcr vs Vanco CL. Because Clearance includes a volume term, it must be normalized to a population average weight.

CL = [0.17 + (CLcr x 0.06)] x (DW / 70)

where

CLcr = creatinine clearance

2. Determine dosing interval (tau)
The drawback to a 2-compartment model is that it does not provide a ready means of calculating a dosing interval. The equation below approximates the intervals recommended by Lake and Peterson's nomogram:

 Creatinine Clearance Dosing interval >90 6 hours 70-89 8 hours 46-69 12 hours 30-45 16 hours 15-29 24 hours

tau = 6 x (72 / [(10 * CL) + 1.9])

3. Determine ideal maintenance dose (k0)
Note that in this 2-compartment equation, the target trough level drives the dose. This meshes perfectly with the concentration-independent killing property of vancomycin where our goal is to target a trough level which remains above the MIC.

k0 = 1/{[(k12-kd) (1 - ekd x tinf) ekd x t)] / [Vc x kd (kd-kel) (1 - ekd x tau)] +
[(kel-k21) (1 - ekel x tinf) ekel x t)] / [Vc x kel (kd-kel) (1 - ekel x tau)]} / 1/CPtarget

where

• k0 = infusion rate (mg/hour)
• tau = dosing interval (hours)
• tinf = infusion time (hours)
• t = time at which to predict serum concentration
• k12 = rate constant for distribution from central to peripheral compartment (1.12 hr -1)
• k21 = rate constant for distribution from peripheral to central compartment (.42 hr -1)
• Vc = Volume of central compartment (.205 L/kg)
• kd (hybrid distribution rate constant) = (k21 x k10)/kel
where
k10 = CL/Vc
• kel (hybrid elimination rate constant) = CL/Vd
where
Vd = .65 L/kg
• CPtarget = Target trough level

1-compartment serum level analysis

For 1-compartment serum level analysis, Sawchuk and Zaske's method provides a simple way of calculating individualized pk parameters based on peak and trough levels. This is the same method utilized for aminoglycosides.

Important: the one caveat when using a 1-compartment model for Vancomycin serum level analysis is that you must ensure that SDC's are drawn during the post-distribution elimination phase.

Bayesian analysis

Bayesian analysis is always utilized to analyze serum levels when using the 2-compartment model, it is optional for the 1-compartment model.

The Bayesian method uses population-derived pharmacokinetic parameters, Vd and CL, 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.

 Section 2 - Applied Pharmacokinetics