Table of Contents

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

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):
$$\text{IBW} = 45.5 + 2.3 \times (\text{Height (in)} - 60)$$
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]

eGFR — CKD-EPI 2021 Creatinine-Cystatin C Equation

$$\text{eGFR} = 135 \times \min\!\left(\frac{S_{Cr}}{\kappa},\,1\right)^{\alpha} \times \max\!\left(\frac{S_{Cr}}{\kappa},\,1\right)^{-0.544} \times \min\!\left(\frac{S_{CysC}}{0.8},\,1\right)^{-0.323} \times \max\!\left(\frac{S_{CysC}}{0.8},\,1\right)^{-0.778} \times 0.9961^{\text{Age}}$$
Female: \(\times\; 0.963\)
\(\kappa = 0.7\) (female), \(0.9\) (male)   \(\alpha = -0.219\) (female), \(-0.144\) (male)

Inker LA, Eneanya ND, Coresh J, et al. New creatinine- and cystatin C-based equations to estimate GFR without race. N Engl J Med 2021;385(19):1737–1749. [PubMed]

eGFR — CKD-EPI 2012 Cystatin C Equation

$$\text{eGFR} = 133 \times \min\!\left(\frac{S_{CysC}}{0.8},\,1\right)^{-0.499} \times \max\!\left(\frac{S_{CysC}}{0.8},\,1\right)^{-1.328} \times 0.996^{\text{Age}}$$
Female: \(\times\; 0.932\)

Inker LA, Schmid CH, Tighiouart H, et al. Estimating glomerular filtration rate from serum creatinine and cystatin C. N Engl J Med 2012;367(1):20–29. [PubMed]

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 Binding2%—
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 Binding10%—
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 Binding80%—
Default Infusion Time1 hr—
Default Frequencyq8h—
Cefazolin uses a \(K_e\)-based clearance model rather than a direct CL equation.

Lavillaureix J, Brogard JM, Pinget M, Ledoux F. Dosage adjustments of cefazolin according to the pharmacokinetics of this new cephalosporin. Infection 1975;3(2):105–114. [PubMed]

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 (\(V_1\))7.58 L (at 70 kg)\(V_d = 7.58 \times \left(\dfrac{weight}{70}\right)^{0.575}\) L
Clearance (CL) for CrCL < 100—\(CL\;\text{(L/hr)} = 4.83 \times [1 + 0.00880 \times (CrCL - 100)]\)
Clearance (CL) for CrCL ≥ 100—\(CL\;\text{(L/hr)} = 4.83 \times [1 + 0.00404 \times (CrCL - 100)]\)
Protein Binding58%Primarily to albumin
Half-life (normal renal)2.3–2.8 hrs—
PK/PD Target75% fT>MIC—
Default Infusion Time3 hrs—
Default Frequencyq8h—
Cefiderocol uses a piecewise linear model with different slopes above and below CrCL of 100 mL/min. Weight has minimal clinical impact on Vd (ratio 0.83 at 50 kg, 1.15 at 90 kg vs 70 kg reference).

Katsube T, Wajima T, Ishibashi T, et al. Pharmacokinetic/pharmacodynamic modeling and simulation of cefiderocol for dose adjustment based on renal function. Antimicrob Agents Chemother 2017;61(1):e01381-16. [PubMed]

Katsube T, Echols R, Wajima T. Pharmacokinetic and pharmacodynamic profiles of cefiderocol. Clin Infect Dis 2019;69(Suppl 7):S552-S558. [PubMed]

Sime FB, et al. Clinical pharmacokinetics and pharmacodynamics of cefiderocol. Clin Pharmacokinet 2022;61(2):165-176. [PubMed]

Ceftaroline

ParameterValueFormula / Notes
Clearance (CL)—\(CL\;\text{(L/hr)} = 10.6 \times \left(\dfrac{CrCL}{180}\right)^{0.328}\)
Volume of Distribution (\(V_d\))0.29 L/kg\(V_d = 0.29 \times ABW\)
Protein Binding20%80% unbound fraction
Default Infusion Time1 hr—
Default Frequencyq12h—
PK/PD Target100% fT>MIC—
Non-linear power model from 18 ventilated ICU patients with early-onset pneumonia and augmented renal clearance (CrCL 83–309 mL/min). CL normalized to median CrCL of 180 mL/min.

Chauzy A, Gregoire N, Ferrandiere M, et al. Population pharmacokinetic/pharmacodynamic study suggests continuous infusion of ceftaroline daily dose in ventilated critical care patients with early-onset pneumonia and augmented renal clearance. J Antimicrob Chemother 2022;77(11):3173-3179. [PubMed]

Daptomycin

ParameterValueFormula / Notes
Clearance (CL)—\(CL\;\text{(L/hr)} = 0.272 + 0.00312 \times CrCL\)
Volume of Distribution (\(V_d\))0.1 L/kg\(V_d = 0.1 \times ABW\)
Protein Binding92%—
Default Infusion Time0.5 hr—
Default Frequencyq24h—
PK/PD TargetAUC/MICConcentration-dependent with prolonged PAE
Two-compartment population PK model simplified to one-compartment. CL linearly related to CrCL. Vss ≈ 0.1 L/kg.

Dvorchik BH, Arbeit RD, Chung J, et al. Population pharmacokinetics of daptomycin. Antimicrob Agents Chemother 2004;48(8):2799–2807. [PubMed]

Levofloxacin

ParameterValueFormula / Notes
Clearance (CL)—\(CL\;\text{(L/hr)} = 0.0752 \times CrCL + 1.12\)
Volume of Distribution (\(V_d\))1.1 L/kg\(V_d = 1.1 \times ABW\)
Protein Binding30%—
Default Infusion Time1.5 hr—
Default Frequencyq24h—
PK/PD TargetAUC/MIC ≥ 125Concentration-dependent, AUC-driven
~87% renal elimination. CL linearly related to CrCL.

Roberts JA, Cotta MO, Cojutti P, et al. Does critical illness change levofloxacin pharmacokinetics? Antimicrob Agents Chemother 2016;60(3):1459–1463. [PubMed]

Linezolid

ParameterValueFormula / Notes
Clearance (CL)—\(CL\;\text{(L/hr)} = 2.62 + 4.35 \times \left(\dfrac{CrCL}{44}\right)\)
Volume of Distribution (\(V_{ss}\))45.2 L\(V_{ss} = V_1(16.2) + V_2(29.0)\); not weight-based
Protein Binding30%—
Default Infusion Time1 hr—
Default Frequencyq12h—
PK/PD TargetAUC/MIC 80–120Safety: AUC₄ < 400 (thrombocytopenia risk)
Two-compartment model simplified to one-compartment using Vss. N=40 ICU patients (23 CRRT, 17 preserved renal function). CLnr = 2.62, CLr = 4.35 at CrCL = 44 mL/min.

Soraluce A, Asín-Prieto E, Rodríguez-Gascón A, et al. Novel population pharmacokinetic model for linezolid in critically ill patients and evaluation of the current dosing recommendations. Pharmaceutics 2020;12(1):54. [PubMed]

Imipenem

ParameterValueFormula / Notes
Clearance (CL)—\(CL\;\text{(L/hr)} = 3.243 + 0.113 \times CrCL\)
Volume of Distribution (\(V_d\))0.23 L/kg\(V_d = 0.23 \times ABW\)
Protein Binding20%—
Default Infusion Time1 hr—
Default Frequencyq6h—
PK/PD Target40% fT>MIC—
NONMEM population PK model in critically ill patients. Base CL = 13.3 L/hr adapted to linear CrCL relationship.

Jaruratanasirikul S, Boonpeng A, Nawakitrangsan M, Samaeng M. NONMEM population pharmacokinetics and Monte Carlo dosing simulations of imipenem in critically ill patients. Pharmacotherapy 2021;41(7):572–597. [PubMed]

Fluconazole

ParameterValueFormula / Notes
Volume of Distribution (\(V_d\))0.7 L/kg\(V_d = 0.7 \times ABW\)
Clearance (CL)—\(CL\;\text{(L/hr)} = (0.15 \times CrCL + 3.5) \times 0.06\)
Protein Binding11%—
Default Infusion Time2 hrs—
Default Frequencyq24h—
PK/PD TargetAUC/MIC ≥ 25Concentration-independent, AUC-driven efficacy
Fluconazole is >90% bioavailable orally. ~80% renally eliminated unchanged. Clearance is linearly related to creatinine clearance. The AUC/MIC ratio is the primary pharmacodynamic predictor of efficacy.

Brammer KW, Farrow PR, Faulkner JK. Pharmacokinetics and tissue penetration of fluconazole in humans. Rev Infect Dis 1990;12 Suppl 3:S318-26. [PubMed]

Debruyne D, Ryckelynck JP. Clinical pharmacokinetics of fluconazole. Clin Pharmacokinet 1993;24(1):10-27. [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]