Pharmacokinetic Reference Guide

Complete Documentation of Formulas, Parameters & Citations

Table of Contents

1 Patient Parameters 2 Core Pharmacokinetic Equations 3 Antibiotic-Specific Parameters 4 CRRT Parameters 5 Vancomycin Two-Level PK Assessment 6 Complete Bibliography

1. Patient Parameters

Body Mass Index (BMI)

$$\text{BMI} = \frac{\text{Weight (kg)}}{\text{Height (m)}^{\,2}}$$

Height is converted from inches: \(\text{Height (m)} = \text{Height (in)} \times 0.0254\)

Ideal Body Weight — Devine (1974)

Males (height ≥ 60 in):
$$\text{IBW} = 50 + 2.3 \times (\text{Height (in)} - 60)$$
Males (height < 60 in):
$$\text{IBW} = 50 - (60 - \text{Height (in)}) \times 0.83$$
Females (height ≥ 60 in):
$$\text{IBW} = 45 + 2.3 \times (\text{Height (in)} - 60)$$
Females (height < 60 in):
$$\text{IBW} = 45.5 - (60 - \text{Height (in)}) \times 0.76$$

Devine BJ. Gentamicin therapy. Drug Intell Clin Pharm 1974;8:650–655.

Adjusted Body Weight (ABW)

$$\text{ABW} = (\text{Actual Weight} - \text{IBW}) \times 0.4 + \text{IBW}$$

Body Surface Area — DuBois & DuBois (1916)

$$\text{BSA (m}^2\text{)} = 0.007184 \times \text{Weight (kg)}^{\,0.425} \times \text{Height (cm)}^{\,0.725}$$

Height is converted from inches: \(\text{Height (cm)} = \text{Height (in)} \times 2.54\)

DuBois D, DuBois EF. A formula to estimate the approximate surface area if height and weight be known. Arch Intern Med 1916;17:863–871.

Creatinine Clearance — Cockcroft-Gault (1976)

$$\text{CrCL (mL/min)} = \frac{(140 - \text{Age}) \times \text{Weight}}{S_{Cr} \times 72}$$
Female adjustment: \(\text{CrCL} \times 0.85\)
Albumin adjustment: If albumin < 3 g/dL, subtract 15 mL/min
Weight selection logic:
  • If Actual Weight < IBW → use Actual Weight
  • If Actual Weight / IBW ≥ 1.4 → use ABW (Adjusted Body Weight)
  • Otherwise → use IBW

Cockcroft DW, Gault MH. Prediction of creatinine clearance from serum creatinine. Nephron 1976;16(1):31–41. [PubMed]

GFR — Grubb Cystatin C Equation (2005)

$$\text{GFR (mL/min/1.73 m}^2\text{)} = 83.93 \times \text{Cystatin C}^{\,-1.676}$$

Grubb A, Nyman U, Bjork J. Simple cystatin C-based prediction equations for glomerular filtration rate. Clin Chem 2005;51(9):1420–1431.

GFR — Larsson Cystatin C Equation (2004)

$$\text{GFR (mL/min/1.73 m}^2\text{)} = 77.239 \times \text{Cystatin C}^{\,-1.2623}$$

Larsson A, Malm J, Grubb A, et al. Calculation of glomerular filtration rate expressed in mL/min from plasma cystatin C values in mg/L. Scand J Clin Lab Invest 2004;64(1):25–30.

GFR — MDRD 6-Variable Equation (1999)

$$\text{GFR} = 170 \times S_{Cr}^{\,-0.999} \times \text{Age}^{\,-0.176} \times \text{BUN}^{\,-0.17} \times \text{Albumin}^{\,0.318}$$
Female: \(\times\; 0.762\)
African American: \(\times\; 1.18\)

Levey AS, Bosch JP, Lewis JB, et al. A more accurate method to estimate glomerular filtration rate from serum creatinine: a new prediction equation. Ann Intern Med 1999;130(6):461–470.

Measured Creatinine Clearance

$$\text{CrCL (mL/min)} = \frac{\text{Urine Cr} \times \text{Urine Volume}}{\text{Serum Cr} \times \text{Collection Time}}$$
BSA-corrected:
$$\text{CrCL}_{BSA} = \text{CrCL} \times \frac{1.73}{\text{BSA}}$$

2. Core Pharmacokinetic Equations

Elimination Rate Constant (\(K_e\))

$$K_e = \frac{CL}{V_d}$$

Half-Life (\(t_{1/2}\))

$$t_{1/2} = \frac{0.693}{K_e}$$

Steady-State Concentration — Continuous Infusion

$$C_{p,SS} = \frac{\text{Dose} \;/\; \tau}{CL}$$

\(\tau\) = dosing interval

Steady-State Peak (\(C_{max,SS}\)) — Intermittent Infusion

$$C_{max,SS} = \frac{\dfrac{\text{Dose}}{t_{inf}} \;\times\; \bigl(1 - e^{-K \cdot t_{inf}}\bigr)}{V_d \times K \times \bigl(1 - e^{-K \cdot \tau}\bigr)}$$

\(t_{inf}\) = infusion duration; \(\tau\) = dosing interval

Steady-State Trough (\(C_{min,SS}\))

$$C_{min,SS} = C_{max,SS} \times e^{-K \cdot (\tau \;-\; t_{inf})}$$

Free (Unbound) Concentration

$$C_{free} = (1 - \text{Protein Binding}) \times C_{total}$$

AUC — Vancomycin (Steady-State Estimate)

$$AUC_{24} = \frac{\text{Dose} \times 24 \;/\; \tau}{CL}$$

3. Antibiotic-Specific Parameters

Cefepime

ParameterValueFormula / Notes
Volume of Distribution (\(V_d\))0.34 L/kgBased on adjusted body weight
Clearance (CL)—\(CL\;\text{(mL/min)} = 10.92 + 0.96 \times CrCL\); convert to L/hr (\(\times\,0.06\))
Protein Binding16%—
Default Infusion Time1 hr—
Default Frequencyq8h—
PK Target\(fT{>}MIC\) 60–70%—

Barbhaiya RH, Knupp CA, Forgue ST, et al. Pharmacokinetics of cefepime in subjects with renal insufficiency. Clin Pharmacol Ther 1990;48:268–76. [PubMed]

Piperacillin/Tazobactam

ParameterValueFormula / Notes
Volume of Distribution (\(V_d\))0.43 L/kgBased on adjusted body weight
Clearance (CL)—\(CL\;\text{(L/hr)} = 16.3 \times \dfrac{CrCL}{100}\)
Protein Binding16%—
Default Infusion Time4 hrsExtended infusion
Default Frequencyq6h—
PK Target\(fT{>}MIC\) 50%Udy Critical Care PK Model

Udy AA, Varghese JM, Altukroni M, et al. Subtherapeutic initial beta-lactam concentrations in select critically ill patients. Chest 2012;142(1):30–39. [PubMed]

Meropenem

ParameterValueFormula / Notes
Volume of Distribution (\(V_d\))0.23 L/kgBased on adjusted body weight
Clearance (CL)—\(CL\;\text{(L/hr)} = 11.3 \times \bigl(1 + 0.00932 \times (CrCL - 80)\bigr)\)
Protein Binding5%—
Default Infusion Time1 hr—
Default Frequencyq8h—
PK Target\(fT{>}MIC\) 40%—

Kees MG, Minichmayr IK, Ganter C, et al. Population pharmacokinetics of meropenem during continuous infusion in surgical ICU patients. J Clin Pharmacol 2016;56(3):307–315. [PubMed]

Ceftazidime

ParameterValueFormula / Notes
Volume of Distribution (\(V_d\))Two-compartment\(V_{SS} = V_1 + V_2\) (Georges Population PK)
\(V_1\) (Central)18.9 L or 9.02 L9.02 L if mechanically ventilated
\(V_2\) (Peripheral)Varies by admissionPolytrauma: 57.1 L; Post-op: 25.7 L; Medical: 13.6 L
Clearance (CL)—\(CL\;\text{(L/hr)} = 2.24 + 0.024 \times CrCL\)
Protein Binding5%—
Default Infusion Time1 hr—
Default Frequencyq8h—
PK Target\(fT{>}MIC\) 60–70%—
Two-compartment model: \(V_1\) depends on mechanical ventilation status; \(V_2\) depends on admission type (polytrauma, post-surgical, or medical).

Georges B, Conil JM, Cougot P, et al. Ceftazidime dosage regimen in intensive care unit patients: from a population pharmacokinetic approach to clinical practice. Br J Clin Pharmacol 2012;73(4):588–596. [PubMed]

Vancomycin

ParameterValueFormula / Notes
Volume of Distribution (\(V_d\))0.57 or 0.83 L/kg0.57 L/kg if \(CrCL \geq 60\); 0.83 L/kg if \(CrCL < 60\)
Clearance (CL)—\(CL\;\text{(mL/min)} = 0.75 \times CrCL\); convert to L/hr (\(\times\,0.06\))
Protein Binding50%—
Default Infusion Time1.5 hrs—
Default Frequencyq24h—
PK TargetAUC/MIC 400–600AUC-guided dosing per 2020 ASHP/IDSA guidelines

Matzke GR, McGory RW, Halstenson CE, et al. Pharmacokinetics of vancomycin in patients with various degrees of renal function. Antimicrob Agents Chemother 1984;25(4):433–437. [PubMed]

Cefazolin

ParameterValueFormula / Notes
Volume of Distribution (\(V_d\))0.21 L/kgBased on adjusted body weight
Clearance (CL)—\(K_e = 0.022 + 0.0028 \times CrCL\), then \(CL = K_e \times V_d\)
Protein Binding5%—
Default Infusion Time1 hr—
Default Frequencyq8h—
Cefazolin uses a \(K_e\)-based clearance model rather than a direct CL equation.

Lavillaureix J, Gravey A, Levy J, et al. Pharmacokinetic study of cefazolin in normal subjects and patients with renal insufficiency. J Clin Pharmacol 1972;12:412–418.

Ampicillin

ParameterValueFormula / Notes
Volume of Distribution (\(V_d\))0.28 L/kgBased on adjusted body weight
Clearance (CL)—\(CL\;\text{(mL/min)} = 2.56 \times CrCL + 29.94\); convert to L/hr (\(\times\,0.06\))
Protein Binding20%—
Default Infusion Time1 hr—
Default Frequencyq6h—

Blum RA, Kohli RK, Harrison NJ, et al. Pharmacokinetics of ampicillin and sulbactam coadministered to subjects with normal and abnormal renal function. Antimicrob Agents Chemother 1989;33(9):1470–1476. [PubMed]

Ceftolozane/Tazobactam

ParameterValueFormula / Notes
Volume of Distribution (\(V_d\))0.22 L/kgBased on adjusted body weight
Clearance (CL)—\(CL\;\text{(L/hr)} = 0.0404 \times CrCL\)
Protein Binding16%—
Default Infusion Time1 hr—
Default Frequencyq8h—

Wooley M, Miller B, Krishna G, et al. Impact of renal function on the pharmacokinetics and safety of ceftolozane-tazobactam. Antimicrob Agents Chemother 2014;58(4):2249–2255. [PubMed]

Penicillin G

ParameterValueFormula / Notes
Volume of Distribution (\(V_d\))0.41 L/kgBased on adjusted body weight
Clearance (CL)—\(CL\;\text{(mL/min)} = 3.35 \times CrCL + 35.5\); convert to L/hr (\(\times\,0.06\))
Protein Binding65%—
Default Infusion Time1 hr—
Default Frequencyq6h—
Conversion1 MU = 625 mgDefault dose: 5 MU (3125 mg)
Penicillin G uses CrCL corrected for BSA: \(\;CrCL_{BSA} = CrCL \times \dfrac{1.73}{BSA}\)

Bryan CS, Stone WJ. Comparable intravascular effects of penicillin G and other antibiotics. J Clin Pharmacol 1975;15:533–535.

Cefiderocol

ParameterValueFormula / Notes
Volume of Distribution (\(V_1\))7.78 LFixed central volume (not weight-based)
Clearance (CL)—\(CL\;\text{(L/hr)} = 4.04 \times \left(\dfrac{\min(CrCL,\,150)}{83}\right)^{0.682} \times 1.08\)
Protein Binding58%—
Default Infusion Time3 hrs—
Default Frequencyq8h—
Cefiderocol uses a fixed \(V_d\) (not weight-based) and caps CrCL at 150 mL/min for clearance calculation.

Kawaguchi N, Katsube T, Echols R, et al. Population pharmacokinetic and pharmacokinetic/pharmacodynamic analyses of cefiderocol. Antimicrob Agents Chemother 2021;65(3):e01437-20. [PubMed]

4. CRRT Parameters

CRRT Clearance Formula

$$CL\;\text{(L/hr)} = SC \times \frac{\text{Effluent Rate (mL/kg/hr)} \times \text{Weight (kg)}}{1000}$$

SC = Sieving Coefficient; \(CL_{nr}\) = Non-Renal Clearance. Total \(CL = CL_{CRRT} + CL_{nr}\) (when available).

Drug Sieving Coefficient (SC) Non-Renal CL (L/hr)
Amikacin0.950.40
Gentamicin0.810.40
Tobramycin0.900.40
Ampicillin0.69—
Piperacillin/Tazobactam0.804.00
Cefepime0.861.10
Ceftazidime0.900.90
Ceftriaxone0.150.49
Imipenem/Cilastatin1.004.65
Meropenem0.954.45
Daptomycin0.200.36
Vancomycin0.702.40
Linezolid0.814.40
Ciprofloxacin0.8913.00
Levofloxacin0.963.95
Cefazolin0.3251.09
Nafcillin0.12519.40
Metronidazole0.84—
Fluconazole0.96—
Amphotericin B0.35—

Sources: Pistolesi V, et al. Blood Purif 2019; FDA Access Data; DailyMed; various PK references.

5. Vancomycin Two-Level PK Assessment

First-Dose Method

Elimination Rate Constant

$$K = \frac{\ln(L_1 \;/\; L_2)}{\Delta t}$$

\(\Delta t\) = time between Level 1 and Level 2 draws (hours)

Peak Concentration (\(C_{max}\))

$$C_{max} = L_1 \times e^{\,K \,\times\, t_1}$$

\(t_1\) = time from end of infusion to Level 1 draw; back-extrapolated to end of infusion

Volume of Distribution

$$V_d = \frac{\dfrac{\text{Dose}}{t_{inf}} \;\times\; \bigl(1 - e^{-K \cdot t_{inf}}\bigr)}{K \times C_{max}}$$

AUC (First Dose — Extrapolation to Infinity)

Linear trapezoid (infusion):
$$AUC_{lin} = \frac{t_{inf} \times (0 + C_{max})}{2}$$
Log trapezoid (elimination):
$$AUC_{log} = \frac{(C_{max} - L_2) \times t_2}{\ln(C_{max} \;/\; L_2)}$$
Terminal extrapolation:
$$AUC_{terminal} = \frac{L_2}{K}$$
Total:
$$AUC_{total} = AUC_{lin} + AUC_{log} + AUC_{terminal}$$

\(t_2\) = time from end of infusion to Level 2 draw

Clearance & Recommended Daily Dose

$$CL = \frac{\text{Dose}}{AUC_{total}}$$ $$\text{Recommended Daily Dose} = 500 \times CL$$

Target \(AUC_{24}/MIC = 400\text{--}600\) (assuming MIC = 1 mg/L, midpoint AUC = 500)

Steady-State Method

Elimination Rate Constant

$$K = \frac{\ln(L_1 \;/\; L_2)}{\Delta t}$$

Trough (\(C_1\)) — Extrapolated to Next Dose

$$C_1 = L_2 \times e^{\,-K \,\times\, t_{L2 \to next}}$$

\(t_{L2 \to next}\) = time from Level 2 draw to next scheduled dose

Peak Concentration (\(C_{max}\))

$$C_{max} = L_1 \times e^{\,K \,\times\, t_1}$$

\(t_1\) = time from end of infusion to Level 1 draw; back-extrapolated to end of infusion

Volume of Distribution (Steady-State)

$$V_d = \frac{\dfrac{\text{Dose}}{t_{inf}} \;\times\; \bigl(1 - e^{-K \cdot t_{inf}}\bigr)}{K \times \bigl(C_{max} - C_1 \cdot e^{-K \cdot t_{inf}}\bigr)}$$

AUC During Dosing Interval

Linear trapezoid (infusion):
$$AUC_{lin} = \frac{t_{inf} \times (C_1 + C_{max})}{2}$$
Concentration at end of interval:
$$C_{end} = C_{max} \times e^{\,-K \cdot (\tau - t_{inf})}$$
Log trapezoid (elimination):
$$AUC_{log} = \frac{(C_{max} - C_{end}) \times (\tau - t_{inf})}{\ln(C_{max} \;/\; C_{end})}$$
Total:
$$AUC_{interval} = AUC_{lin} + AUC_{log}$$

24-Hour AUC & Clearance

$$AUC_{24} = AUC_{interval} \times \frac{24}{\tau}$$ $$CL = \frac{\text{Dose}}{AUC_{interval}}$$

Rybak MJ, Le J, Lodise TP, et al. Therapeutic monitoring of vancomycin for serious methicillin-resistant Staphylococcus aureus infections: a revised consensus guideline and review by the American Society of Health-System Pharmacists, the Infectious Diseases Society of America, the Pediatric Infectious Diseases Society, and the Society of Infectious Diseases Pharmacists. Am J Health Syst Pharm 2020;77(11):835–864. [PubMed]

6. Aminoglycoside Two-Level PK Assessment

First-Dose Method (Gent / Tobra / Amikacin)

Elimination Rate Constant

$$K = \frac{\ln(L_1 \;/\; L_2)}{\Delta t}$$

\(\Delta t\) = time between Level 1 and Level 2 draws (hours)

Peak Concentration (\(C_{max}\))

$$C_{max} = L_1 \times e^{\,K \,\times\, t_1}$$

\(t_1\) = time from end of infusion to Level 1 draw; back-extrapolated to end of infusion

Volume of Distribution

$$V_d = \frac{\dfrac{\text{Dose}}{t_{inf}} \;\times\; \bigl(1 - e^{-K \cdot t_{inf}}\bigr)}{K \times C_{max}}$$

AUC (First Dose — Extrapolation to Infinity)

Linear trapezoid (infusion):
$$AUC_{lin} = \frac{t_{inf} \times (0 + C_{max})}{2}$$
Log trapezoid (elimination):
$$AUC_{log} = \frac{(C_{max} - L_2) \times t_2}{\ln(C_{max} \;/\; L_2)}$$
Terminal extrapolation:
$$AUC_{terminal} = \frac{L_2}{K}$$
Total:
$$AUC_{total} = AUC_{lin} + AUC_{log} + AUC_{terminal}$$

\(t_2\) = time from end of infusion to Level 2 draw

Clearance

$$CL = \frac{\text{Dose}}{AUC_{total}}$$ $$CL_{mL/min} = \frac{CL_{L/hr}}{0.06}$$

Steady-State Method (Gent / Tobra / Amikacin)

Elimination Rate Constant

$$K = \frac{\ln(L_1 \;/\; L_2)}{\Delta t}$$

Trough (\(C_1\)) — Extrapolated to Next Dose

$$C_1 = L_2 \times e^{\,-K \,\times\, t_{L2 \to next}}$$

\(t_{L2 \to next}\) = time from Level 2 draw to next scheduled dose

Peak Concentration (\(C_{max}\))

$$C_{max} = L_1 \times e^{\,K \,\times\, t_1}$$

\(t_1\) = time from end of infusion to Level 1 draw; back-extrapolated to end of infusion

Volume of Distribution (Steady-State)

$$V_d = \frac{\dfrac{\text{Dose}}{t_{inf}} \;\times\; \bigl(1 - e^{-K \cdot t_{inf}}\bigr)}{K \times \bigl(C_{max} - C_1 \cdot e^{-K \cdot t_{inf}}\bigr)}$$

AUC During Dosing Interval

Linear trapezoid (infusion):
$$AUC_{lin} = \frac{t_{inf} \times (C_1 + C_{max})}{2}$$
Log trapezoid (elimination):
$$AUC_{log} = \frac{(C_{max} - C_1) \times (t_{EOI \to next})}{\ln(C_{max} \;/\; C_1)}$$
Total:
$$AUC_{interval} = AUC_{lin} + AUC_{log}$$

24-Hour AUC & Clearance

$$AUC_{24} = AUC_{interval} \times \frac{24}{\tau}$$ $$CL = V_d \times K$$ $$CL_{mL/min} = \frac{CL_{L/hr}}{0.06}$$

Devine BJ. Gentamicin therapy. Drug Intell Clin Pharm 1974;8:650–655.

Nicolau DP, Freeman CD, Belliveau PP, et al. Experience with a once-daily aminoglycoside program administered to 2,184 adult patients. Antimicrob Agents Chemother 1995;39(3):650–655. [PubMed]

7. Complete Bibliography

  1. Barbhaiya RH, Knupp CA, Forgue ST, et al. Pharmacokinetics of cefepime in subjects with renal insufficiency. Clin Pharmacol Ther 1990;48:268–76. [PubMed]
  2. Blum RA, Kohli RK, Harrison NJ, et al. Pharmacokinetics of ampicillin and sulbactam coadministered to subjects with normal and abnormal renal function. Antimicrob Agents Chemother 1989;33(9):1470–1476. [PubMed]
  3. Bryan CS, Stone WJ. Comparable intravascular effects of penicillin G and other antibiotics. J Clin Pharmacol 1975;15:533–535.
  4. Cockcroft DW, Gault MH. Prediction of creatinine clearance from serum creatinine. Nephron 1976;16(1):31–41. [PubMed]
  5. Devine BJ. Gentamicin therapy. Drug Intell Clin Pharm 1974;8:650–655.
  6. DuBois D, DuBois EF. A formula to estimate the approximate surface area if height and weight be known. Arch Intern Med 1916;17:863–871.
  7. Georges B, Conil JM, Cougot P, et al. Ceftazidime dosage regimen in intensive care unit patients: from a population pharmacokinetic approach to clinical practice. Br J Clin Pharmacol 2012;73(4):588–596. [PubMed]
  8. Grubb A, Nyman U, Bjork J. Simple cystatin C-based prediction equations for glomerular filtration rate compared with the modification of diet in renal disease prediction equation. Clin Chem 2005;51(9):1420–1431.
  9. Kawaguchi N, Katsube T, Echols R, et al. Population pharmacokinetic and pharmacokinetic/pharmacodynamic analyses of cefiderocol. Antimicrob Agents Chemother 2021;65(3):e01437-20. [PubMed]
  10. Kees MG, Minichmayr IK, Ganter C, et al. Population pharmacokinetics of meropenem during continuous infusion in surgical ICU patients. J Clin Pharmacol 2016;56(3):307–315. [PubMed]
  11. Larsson A, Malm J, Grubb A, et al. Calculation of glomerular filtration rate expressed in mL/min from plasma cystatin C values in mg/L. Scand J Clin Lab Invest 2004;64(1):25–30.
  12. Lavillaureix J, Gravey A, Levy J, et al. Pharmacokinetic study of cefazolin in normal subjects and patients with renal insufficiency. J Clin Pharmacol 1972;12:412–418.
  13. Levey AS, Bosch JP, Lewis JB, et al. A more accurate method to estimate glomerular filtration rate from serum creatinine: a new prediction equation. Ann Intern Med 1999;130(6):461–470.
  14. Matzke GR, McGory RW, Halstenson CE, et al. Pharmacokinetics of vancomycin in patients with various degrees of renal function. Antimicrob Agents Chemother 1984;25(4):433–437. [PubMed]
  15. Nicolau DP, Freeman CD, Belliveau PP, et al. Experience with a once-daily aminoglycoside program administered to 2,184 adult patients. Antimicrob Agents Chemother 1995;39(3):650–655. [PubMed]
  16. Pistolesi V, Morabito S, Di Mario F, et al. A guide to understanding antimicrobial drug dosing in critically ill patients on renal replacement therapy. Blood Purif 2019;47(4):292–307.
  17. Rybak MJ, Le J, Lodise TP, et al. Therapeutic monitoring of vancomycin for serious methicillin-resistant Staphylococcus aureus infections: a revised consensus guideline. Am J Health Syst Pharm 2020;77(11):835–864. [PubMed]
  18. Udy AA, Varghese JM, Altukroni M, et al. Subtherapeutic initial beta-lactam concentrations in select critically ill patients. Chest 2012;142(1):30–39. [PubMed]
  19. Wooley M, Miller B, Krishna G, et al. Impact of renal function on the pharmacokinetics and safety of ceftolozane-tazobactam. Antimicrob Agents Chemother 2014;58(4):2249–2255. [PubMed]