Pharmacokinetic formulas

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Drug models
The 1compartment drug models are not hardcoded into the APK program. The parameters (highlighted below in blue) are found in the drug model database and are fully usereditable. You may tailor each drug model to fit your patient population, or you may create your own models. See the drug models section of this help file for further information.
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.
Please see the Vancomycin help topic for important caveats about using a 1compartment model to dose this drug.
Initial dosing adults
Traditional method Onecompartment open model
1. Calculate dosing weight (DW) DW = LBW + [(ABW  LBW) x CF] where: ABW = actual weight LBW = lean body weight CF is a correction factor for obesity:
2. Determine initial maintenance dose (MD)
i. Calculate volume of distribution (Vd)
Vd = DW x L/kg where L/kg:
ii. 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 outlier model (Calculates Kel) Nonrenal = 0 Renal = 0.0008
Vancomycin normal model (Calculates CL) Nonrenal = 0 Renal = 0.06 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 = 0.06 AdjBW = LBW + (0.4 * (TBWLBW)) LBW = lean body weight TBW = total body weight
iii. Calculate ideal maintenance dose
MD = kel x Vd x Cpmax x tinf x (1  ekel x tau / 1  ekel x tinf) where: Cpmax = Target peak Vd = population volume of distribution kel = population elimination rate tinf = length of infusion
iv. Calculate ideal dosing interval (tau)
tau = tinf + [1 / kel x ln (Cpmax/Cpmin)] where Cpmin = Target trough Cpmax = Target peak
v. User selects practical dosage and interval
vi. Calculate expected steadystate peak & trough levels Cpssmax = [MD / (tinf x Vd x kel)] x [(1  ekel x tinf) / 1ekel x tau)]
Cpssmin = Cpssmax * ekel x (tau  tinf)
Extended interval method Pulse dosing nomogram for Aminoglycosides
1. Calculate dosing weight (DW) Same as above
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
Initial dosing pediatrics
Initial pediatric doses are weightbased.
1. Determine maintenance dose (MD)
MD = Weight x mg/kg mg/kg:
2 Determine interval (tau)
tau = model tau
Adjust maintenance dose
Steadystate SawchukZaske method Steadystate peak/trough Trough level prior to dose, then postdose 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  ekel x tinf ) /[ kel x (Cpmax  (Cpmin x ekel x t')] where: Cpmax = Extrapolated peak level Cpmin = Extrapolated trough level t' = time from Cptr drawn to end of infusion
Nonsteadystate SawchukZaske method Non steadystate 3 point Trough level prior to dose, then postdose 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  ekel x tinf ) /[ kel x (Cpmax  (Cpmin x ekel x tinf)] where: Cpmax = Extrapolated peak level Cpmin = Extrapolated trough level tinf = Infusion length
Firstdose SawchukZaske method 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 postdose levels measured: kel = (ln Cp1/Cp3) / tdiff where: Cp1 = Measured peak level Cp2 = Measured midpoint level (optional) Cp3 = Measured trough level tdiff = time between levels Cp1 and Cp3
If 3 postdose 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  ekel x tinf ) /(Cpmax  (Cpmin x ekel x tinf) where: Cpmax = Extrapolated peak level Cpmin = Extrapolated trough level tinf = Infusion length
Steadystate SawchukZaske method Steadystate 2 or 3 point 2 or 3 postdose steadystate measurements
1. Determine elimination rate (Kel) I If 2 postdose levels measured: kel = (ln Cp1/Cp3) / tdiff where: Cp1 = Measured peak level Cp2= Measured midpoint level (optional) Cp3= Measured trough level tdiff = time between levels Cp1 and Cp3
If 3 postdose 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  ekel x tinf ) /[ kel x (Cpmax  (Cpmin x ekel x tinf)] where: Cpmax = Extrapolated peak level Cpmin = Extrapolated trough level tinf = Infusion length
Extended interval method Pulse dosing nomogram for Aminoglycosides
1. Determine interval Obtain a midinterval 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 APK 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 druglevel scale by a factor of three. The consensus nomogram is utilized by APK if your 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 onecompartment 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.

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