﻿ Pk formulas Pharmacokinetic formulas

Please realize that the drug models are not hard-coded into the Antibiotic Kinetics© program.  The parameters (highlighted below in blue) are found in the drug model database and are fully user-editable.  You may tailor each drug model to fit your patient population, or you may create your own models.  This is the most powerful feature of this program.

For example, there is no consensus on Vancomycin dosing, it is a difficult drug to model and dosing methods vary widely.  The drug model database includes 2 models, named "Vancomycin Kel" and "Vancomycin CL". The CL model calculates a clearance and was derived from the work of Winter. The Kel model calculates an elimination rate constant (Kel), and was derived from the works of Matzke. You may use them as is, modify them to fit your patient population, or add your own Vancomycin model. See the Edit drug models topic for more information on drug model editing.

Also, please see the Vancomycin help topic for important caveats about using a 1-compartment model to dose this drug.

1.   Determine dosing weight (DW)

DW = LBW + ((ABW - LBW) x CF)

where:

ABW = actual weight

CF is a correction factor for obesity:

 • Amikacin, gentamicin  = 0.4
 • Tobramycin = 0.6
 • Vancomycin = 1 (no correction)

2.   Calculate Volume of distribution

Vd = DW x L/kg

where L/kg:

 • Aminoglycosides = 0.27
 • Vancomycin = 0.7

3.   Calculate elimination rate (kel) or Clearance (CL) from Creatinine Clearance:

kel (or CL) = Nonrenal + (CrCl x Renal)

where:

CrCl = creatinine clearance

Aminoglycosides

Nonrenal = 0.01

Renal = 0.0024

Vancomycin Kel model (Calculates Kel)

Nonrenal = 0

Renal = 0.0008

Vancomycin CL model (Calculates CL)

Nonrenal = 0

Renal = 0.065

Since this model calculates clearance, to determine Kel:

Kel = CL / Vd

Vancomycin Adjust CL to IBW model

CL =  [Nonrenal + (NormCrCl x Renal)] x (AdjBW/TBW)

where:

NormCrCl = normalized creatinine clearance

Nonrenal = 0

Renal = 0.065

AdjBW = LBW + (0.4 * (TBW-LBW))

LBW = lean body weight

TBW = total body weight

4.   Determine maintenance dose (MD)

i.   Determine ideal maintenance dose

MD = kel  x  Vd  x  Cpmax  x  tinf  x  (1 - e-kel x tau / 1 - e-kel x tinf)

where:

Cpmax = Target peak

Vd = population volume of distribution

kel = population elimination rate

tinf = length of infusion

ii.   Determine ideal dosing interval (tau)

tau = tinf + [-1 / kel x ln (Cptmin/Cptmax)]

where Cptmin = Target trough

Cptmax = Target peak

iii.   User selects practical dosage and interval

iv.   Calculate expected peak & 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)

Sawchuk and Zaske method

1.  Calculate elimination rate (kel)

kel = (ln Cpmax/Cpmin') / time between samples

where Cpmax = Peak level

Cpmin' = Trough level after the dose

2.  Calculate volume of distribution (Vd)

Vd = [(Dose/tinf) / kel]  x  {(1 - e-kel x  tinf) /  [Cpmax - (Cpmin x e-kel x  t')]}

where

Cpmax = Peak level

Cpmin = Trough level before the dose

tinf = infusion time

t' = hours between time Cpmin drawn and end of infusion

3.  Calculate ideal dosing interval (tau)

tau = tinf + (-1/kel) x  ln (Cptmax/Cptmin)

where Cptmin = Target trough

Cptmax = Target peak

4.  Calculate ideal maintenance dose (IMD)

IMD = kel   x  Vd  x  Cptmax  x  [(1 - e -kel x  tau) / (1 - e -kel x  tinf)]

5.  User selects practical dosage and interval

6.  Calculate expected peak & trough levels

Cpssmax =  [MD / (tinf  x  Vd  kel)]  x  [(1 -  e-kel x  tinf) / (1 -  e-kel x  tau)]

Cpssmin =   Cpssmax * e -kel x (tau - tinf)

Adjust maintenance dose using the 1-compartment Bayesian algorithm

1.   Minimize Bayesian function

The Bayesian method uses population-derived pharmacokinetic parameters (ie., 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. To achieve that end, the least squares method based on the Bayesian algorithm estimates the parameters kel & Vd which minimize the following function: 2.  Calculate ideal dosing interval (tau)

Same as the Sawchuk and Zaske method

3.  Calculate ideal maintenance dose (IMD)

Same as the Sawchuk and Zaske method

4.  User selects practical dosage and interval

5.  Calculate expected peak & trough levels

Same as the Sawchuk and Zaske method

Extended interval method

Initial dose

1.  Calculate dosing weight (DW)

Same as Sawchuk and Zaske's method

2.  Calculate maintenance dose (MD)

MD = DW x QDdose

where QDdose is the daily dose in mg/kg:

Amikacin, kanamycin   = 15 mg/kg

Gentamicin, Tobramycin, Netilmicin = 5 mg/kg

3.  Determine interval

Interval is based on creatinine clearance

 CrCl Interval Over 60 24 hours 40 - 59 36 hours 30 - 39 48 hours Less than 30 Use traditional methods

Extended interval method

1.  Determine interval

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 graphs are decay curves, produced by using a population average 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. The Hartford nomogram is utilized by Kinetics if your model EI dose is 7mg/kg. It is important to note that the Hartford ODA nomogram is only valid for a 7mg/kg dose.  An interval adjustment nomogram for the less aggressive dose of 5mg/kg/day was developed by a consensus panel. For 15mg/kg doses of amikacin multiply the drug-level scale by a factor of three. The consensus nomogram is utilized by Kinetics if your model EI dose is 5mg/kg. 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..

Furthermore, some have questioned the validity of all ODA nomograms because they are based on one-compartment parameters derived from studies of 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.