RxKinetics WebApp Formulas

Antibiotic Kinetics©

Lean body weight (LBW)
Devine adult method1
    LBW = 45.5 + [ 2.3 x (60 - Height in inches) ]
    Add 4.5 kg for males

Body surface area (BSA)
Mosteller equation2
    BSA = (HT X WT)2 / 3600
    where
        HT = height in centimeters
        WT = weight in kilograms

Creatinine clearance (CLcr)
In patients 65 years or older who have a serum creatinine less than 0.8, the SrCr is rounded up to 0.8.
 
Cockroft and Gault method3
    CLcr = [Weight x (140 - Age)] / (SCr x 72)
    Decrease by 15% for females
    Weight may be one of the following:
        Lean body weight
        Adjusted body weight
        Total body weight
 
Adjusted body weight for obesity18
    ABW = LBW + [CF x (TBW - LBW)]
    CF = 0.2, 0.3, or 0.4 (user selected)
 
Jelliffe multi-step method5
    1. Estimate urinary creatinine excretion rate (E)
        E Males = LBW x [29.305 - (0.203 x Age)]
        E Females = LBW x [25.3 - (0.18 x Age)]
        where
            LBW = lean body weight in kilograms
    2. Correct E for nonrenal creatinine excretion in chronic renal failure
        E = E x [1.035 - (0.0377 x SCr)]
        where
            SCr is the latest serum creatinine
            OR if SCr is rising, the average SCr
    3. Correct E for rising serum creatinine
        E = E - [4 x LBW x (SCr1 - SCr2)] / D
        where
            SCr1 = the latest serum creatinine
            SCr2 = the earlier serum creatinine
            D = the number of days between
    4. Calculate CLcr
        CLcr = (E x 0.12) / (SrCr x BSA)
        where
            BSA = Body surface area
 
Jelliffe 1973 equation9
    CLcr = 98 - [0.8 x (Age - 20)] / SrCr
        Decrease by 10% for females
 
MDRD method6,7
    CLcr = exp{ 5.228 - [ 1.154 x log(SCr) ] - [ 0.203 x log(Age) ] }
        Decrease by 25.8% for females
        Increase by 121% for African Americans
 
Normalizled CrCl method18
    CLcr = (140 - Age) / SrCr     Decrease by 15% for females
 
Salazar and Corcoran method4
    CLcr Male= { [137 - Age] x [ (0.285 x Wt) + (12.1 x Ht2) ] } / (51 x SCr)
    CLcr Female= { [146 - Age] x [ (0.287 x Wt) + (9.74 x Ht2) ] } / (60 x SCr)
 
Swartz pediatric method8
    CLcr = (c x Ht) / Scr
    where
        Ht = height in cm
        SCr = most recent serum creatinine
        c = 0.45 if age < 1 year
        c = 0.55 if age 1-12 years

Prospective population model
Wagner linear method11
    Kel = Knr + (Kr x CLcr)
    Vd = Vdper x WtKg
    where
        Kel = total elimination rate
        Knr = nonrenal elimination rate constant
        Kr = renal elimination rate
        Vd = apparent volume of distribution in liters
        Vdper = population average Vd in liters per kg
        WtKg = Weight in kg (may be modified for obesity)

Ideal dose calculation
One compartment intermittent infusion11
    tau = tinf + [ (-1 / Kel) x ln (Cpmin / Cpmax)]
    Dose = Kel x Vd x Cpmax x tinf x (1 - e-Kel x tau) / 1-e-Kel x tinf)
    where
        tau = dosage interval in hours
        tinf = infusion time in hours
        Kel = elimination rate constant
        Cpmax= target peak serum level
        Cpmin= target trough serum level
        Dose = dose in mg
        Vd = volume of distribution in liters

Serum level prediction
One compartment intermittent infusion11
    Peak = [Dose / (tinf x Vd x Kel)] x [(1 - e-Kel x tinf) / (1 - e-Kel x tau)]
    Trough = Peak x e-Kel x (tau-tinf)
    where
        Dose = chosen dose in mg
        tau = chosen dosage interval in hours
        tinf = infusion time in hours
        Vd = volume of distribution in liters
        Kel = elimination rate constant

Serum level evaluation
Standard Sawchuk-Zaske Method12
3 or 4 non-steady-state measurements
    Kel = [ln (Cp2 / Cp4)] / tdiff
    Vd = [(Dose / tinf) x (1 - e-Kel x tinf)] / {Kel x [Cp2 - (Cp1 x e-kel x tinf) ] }
    where
        Cp1= trough serum level measured prior to infusion
        Cp2= peak serum level measured after the infusion
        Cp3= mid-point serum level measured after the infusion (optional)
        Cp4= trough serum level measured after the infusion
        tdiff = time between levels in hours
        tau = dosage interval in hours
        tinf = infusion time in hours
        Dose = dose in mg
    Exception: Linear least squares determination of Kel utilized
        if 3 post dose levels measured.
 
Steady-state Sawchuk-Zaske Method13
2 steady-state measurements
    Kel = [ln (Cptr / Cppk)] / (tau - tinf)
    Vd = [(Dose / tinf) x (1 - e-Kel x tinf)] / {Kel x [Cppk - (Cptr x e-kel x tinf) ] }
    where
        Cppk = peak serum level measured after the infusion
        Cptr = trough serum level measured before the infusion
        tau = dosage interval in hours
        tinf = infusion time in hours
        Dose = dose in mg
 
First dose Sawchuk-Zaske Method13
2 or 3 levels drawn after the first dose (no prior drug on board)
    Kel = [ln (Cp1 / Cp3)] / tdiff
    Vd = [ (Dose / tinf) x (1 - e-Kel x tinf) ] / (Cp1 / e-Kel x t1)
    where
        Cp1= peak serum level measured after the infusion
        Cp2= mid-point serum level measured after the infusion (optional)
        Cp3= trough serum level measured after the infusion
        tdiff = time between levels in hours
        t1 = time after infusion peak level drawn in hours
        tinf = infusion time in hours
        Dose = dose in mg
    Exception: Linear least squares determination of Kel utilized
        if 3 post dose levels measured.
 
Linear least squares determination of Kel14
Utilized if 3 post-dose levels measured
    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
 
Bayesian analysis15
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:

TPNassist©

Ideal body weight (IBW)
ASPEN method10
    Pediatric
        IBW = (HtCm2 x 1.76) / 1000
    Adult
        IBW Male= 48 + (2.7 x (HtIn - 60))
        IBW Female= 45 + (2.3 x (HtIn - 60))
    where
        HtCm = height in cm
        HtIn = height in inches

Nutritional dosing weight (NDW)16
    If total weight (TBW) > 120% of IBW:
        NDW = IBW + (0.25 * (TBW - IBW))
    Otherwise:
        NDW = TBW

Basal energy expenditure (BEE)
ASPEN method10
    Age 1 - 2 years
        BEE Male= (60.9 x Weight) - 54
        BEE Female= (61 x Weight) - 51
    Age 3 - 12 years
        BEE Male= (22.7 x Weight) + 495
        BEE Female= (22.5 x Weight) + 499
    Adult
        BEE Male= 66 + (13.7 x Weight) + (5 x Height) - (6.8 x Age)
        BEE Female= 665 + (9.6 x Weight) + (1.7 x Height) - (4.7 x Age)
    where
        Height = height in cm
        Weight = weight in kg
    Weight may be one of the following:
        Total body weight
        Ideal body weight
        Nutritional dosing weight

Body mass index (BMI)
    BMI = WtKg / HtM2
    where
        WtKg = weight in kg
        HtM = height in meters

Nitrogen to Noprotein calorie Ratio (N:NP)
    N:NP = kCal / (Protein / 6.25)
    where
        kCal = total nonprotein calories
        Protein = total protein in grams
            6.25 g protein = 1 g Nitrogen

Ca:Phos solubility product (Ca:Phos)
    Ca:Phos = Ca x Phos
    where
        Ca = total calcium concentration in mEq/L
        Phos = total phosphate concentration in mMol/L

TPN osmolarity10
    Osmol = (AA + Dextrose + Fat + Calcium + OtherLytes) / Volume
    where
        Osmol = approximate osmolarity in mOsmol/L
        AA (amino acids) = 10 mOsmol/g
        Dextrose = 4 mOsmol/g
        Fat = 1.7 mOsmol/g
        Calcium = 1.5 mOsmol/mEq
        Other electrolytes = 1 mOsmol/mEq
        Volume = Total base volume in liters
        Note: does not include volume of micronutrient additives.

References

  1. Devine Ben. Gentamicin therapy. Drug Intell Clin Pharm 1974;8:650-6.
  2. Mosteller RD: Simplified Calculation of Body Surface Area. N Engl J Med 1987 Oct 22;317(17):1098 (letter)
  3. Cockroft D.W., Gault M.H. Prediction of creatinine clearance from serum creatinine. Nephron. 1976;16(1):31-41.
  4. Salazar DE, Corcoran GB. Predicting creatinine clearance and renal drug clearance in obese patients from estimated fat-free body mass. Am J Med. 1988 Jun;84(6):1053-60.
  5. Jelliffe RW, Jelliffe SM. Estimation of creatinine clearance in patients with unstable renal function. (revised). Originally published: A computer program for estimation of creatinine clearance from unstable serum creatinine concentration. Math Biosci. 14:17-24 (June) 1972.
  6. Levey AS, Bosch JP, Lewis JB, Greene T, Rogers N, Roth D: A more accurate method to estimate glomerular filtration rate from serum creatinine: A new prediction equation. Modification of Diet in Renal Disease Study Group. Ann Intern Med 130:461-470, 1999
  7. Levey AS, Greene T, Kusek JW, Beck GJ: A simplified equation to predict glomerular filtration rate from serum creatinine. J Am Soc Nephrol 11:A0828, 2000 (abstr)
  8. Schwartz, GL. A simple estimate of glomerular filtration rate in children Pediatrics 1976:58:259-263.
  9. Jelliffe RW. Creatinine clearance: Bedside estimate. Ann Inter Med. 1973; 79:604.
  10. Gottschlich, MM (Ed). The Science and Practice of Nutritional Support. Dubuque: Kendall/Hunt Publishing, 2001.
  11. Wagner J.G. Fundamentals of Clinical Pharmacokinetics. Hamilton: Drug Intelligence Publications, 1975.
  12. Sawchuk RJ, Zaske DE, et al. Kinetic model for gentamicin dosing. Clin Pharmacol Ther 1977;21;3:362-369.
  13. Bauer, LA. Applied Clinical Pharmacokinetics. New York: McGraw-Hill, 2001.
  14. Bulmer MG. Principles of Statistics. New York: Dover Publications. 1967.
  15. Okamoto MP, Chi A, et al. Comparison of two microcomputer Bayesian pharmacokinetic programs for predicting serum gentamicin concentrations. Clin Pharm 1990 9:708-11.
  16. Krenitsky, J. Evidence to Support the Use of Adjusted Body Weight in Calculating Calorie Requirements. Nutrition in Clinical Practice 2005;20;4:468-473.
  17. Rombeau JL, Rolandeli RH. Clinical Nutrition: Parenteral Nutrition, 3rd ed. Philadelphia: W.B. Saunders Company, 2001. p. 129.
  18. Winter MA, Guhr KN, Berg, GM. Impact of various body weights and serum creatinine concentrations on the bias and accuracy of the Cockcroft-Gault equation. Pharmacotherapy 2012;32(7):604-612.

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