﻿ 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)

Trough level prior to dose, then post-dose peak

1.        Determine elimination rate (Kel)

kel = (ln Cppk/Cptr) / [Interval - (tinf + t' + t")]

where:

Cppk = Measured peak level

Cptr = Measured trough level

tinf = Infusion length

t' = time from Cptr drawn to start of infusion

t" = time from Cppk drawn to end of infusion

2.        Determine Volume of distribution (Vd)

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

where:

Cpmax = Extrapolated peak level

Cpmin = Extrapolated trough level

t' = time from Cptr drawn to end of infusion

Trough level prior to dose, then post-dose peak and trough

1.        Determine elimination rate (Kel)

kel = (ln Cp2/Cp3) / tdiff

where:

Cp2 = Measured peak level

Cp3 = Measured trough level after the infusion

tdiff = time between levels Cp2 and Cp3

2.        Determine Volume of distribution (Vd)

Vd = [(Dose/tinf) x  (1 - e-kel x  tinf ) /[ kel x (Cpmax - (Cpmin x e-kel x tinf)]

where:

Cpmax = Extrapolated peak level

Cpmin = Extrapolated trough level

tinf = Infusion length

First dose 2 or 3 point

2 or 3 levels drawn after the first dose (no prior drug on board)

1.        Determine elimination rate (Kel)

I

If 2 post-dose levels measured:

kel = (ln Cp1/Cp3) / tdiff

where:

Cp1 = Measured peak level

Cp2 = Measured mid-point level (optional)

Cp3 = Measured trough level

tdiff = time between levels Cp1 and Cp3

If 3 post-dose levels measured, linear least squares utilized:

Kel (slope) = [(n * Sxy) - (Sx * Sy)] / [(n * Sxsq) - Sx2]

where

n = number of points

x = hours post infusion

y = natural log of measured serum level

Sx = SUM of x values

Sy = SUM of y values

Sxy = SUM of products (x * y)

Sxsq = SUM of the squares of x values

2.        Determine Volume of distribution (Vd)

Vd = [(Dose/tinf) x  (1 - e-kel x  tinf ) /(Cpmax - (Cpmin x e-kel x tinf)

where:

Cpmax = Extrapolated peak level

Cpmin = Extrapolated trough level

tinf = Infusion length

2 or 3 post-dose steady-state measurements

1.        Determine elimination rate (Kel)

I

If 2 post-dose levels measured:

kel = (ln Cp1/Cp3) / tdiff

where:

Cp1 = Measured peak level

Cp2= Measured mid-point level (optional)

Cp3= Measured trough level

tdiff = time between levels Cp1 and Cp3

If 3 post-dose levels measured, linear least squares utilized:

Kel (slope) = [(n * Sxy) - (Sx * Sy)] / [(n * Sxsq) - Sx2]

where:

n = number of points

x = hours post infusion

y = natural log of measured serum level

Sx = SUM of x values

Sy = SUM of y values

Sxy = SUM of products (x * y)

Sxsq = SUM of the squares of x values

2.        Determine Volume of distribution (Vd)

Vd = [(Dose/tinf) x  (1 - e-kel x  tinf ) /[ kel x (Cpmax - (Cpmin x e-kel x tinf)]

where:

Cpmax = Extrapolated peak level

Cpmin   = Extrapolated trough level

tinf = Infusion length

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.

Area Under the Curve (AUC)

AUC is calculated with the trapezoidal method as illustrated below:

Because the one-compartment model omits the distribution phase, the AUC with this method is under-estimated by approximately 10%.

 • This is a feature not a bug.
 • This assures that the target therapeutic AUC will be achieved with your chosen dose.
 • Conversely if the AUC is near the upper limit it is prudent to decrease the dose.

Targeted AUC Dosing

Targeted AUC dosing takes advantage of the fundamental relationship between clearance, dose and AUC that we all learned in basic pharmacokinetics class:

AUC = Dose (mg/hr) ÷ CL (L/hr)

Simply rearrange this equation to solve for dose:

Dose (mg/hr) = AUC x CL

Since dosing at the half-life is ideal for Vancomycin, the initial interval selected by AbPK is the estimated half-life plus infusion time (rounded to the nearest whole number). The dose then is:

Dose (mg) = Dose (mg/hr) x Interval.

The ideal interval and dose are usually not practical. You must use your clinical judgment to select an appropriate dose.