Formulas ¹

General PK

$$C_{ss} = \frac{F(D/\tau)}{CL} \text{ (intermittent)}\\ C_{ss} = \frac{\text{Rate}}{CL} \text{ (infusions)}\\ E = \frac{f_{unbound}CL_{int}}{Q+f_{unbound}CL_{int}}\\ CL = Q \times E\\ CL = k \times V_d\\ V_d = V_{blood} + \frac{f_b}{f_t}V_{tissue}\\ F = \frac{\text{AUC}_{PO}}{\text{Dose}_{PO}} \div \frac{\text{AUC}_{IV}}{\text{Dose}_{IV}} = \frac{D_{IV}\text{AUC}_{PO}}{D_{PO}\text{AUC}_{IV}}$$

1-Compartment Model

$$\tau_{est} = \frac{\ln{(C_{max}} / C_{min})}{k} + t_{inf}\\ MD_{est} = \frac{C_{max} t_{inf} V k \left( 1 - e^{-k\tau} \right)}{\left( 1 - e^{-kt_{inf}} \right)}\\ V = \frac{MD \left( 1 - e^{-kt_{inf}} \right)}{t_{inf}k\left( C_{max} - C_{min}e^{-kt_{inf}} \right)} \\ C_{max} = \frac{MD \left( 1 - e^{-kt_{inf}} \right)}{t_{inf} V k \left( 1 - e^{-k\tau} \right)}\\ C_{pk} = C_{max} e^{-k(t_{pk} - t_{max})}\\ C_{min} = C_{max} e^{-k(\tau - t_{inf})}\\ C_{min} = C_{trough} e^{-k(t_{min} - t_{trough})}\\ C[b] = C[a] e^{-k (a - b)}$$

Vancomycin ^{1, 2, 3, 4}

Peak: 20-40 mg/L

Trough: 10-15 mg/L (minor infections) or 15-20 mg/L (serious infections or lung penetration)

Loading Dose: 25-30 mg/kg (Wt)

NTE 15 mg/min

k ≈ 0.00083 × CrCl + 0.0044

V_d ≈ 0.4-1 L/kg, usually 0.6-0.7 L/kg

$\text{AUC}_{0-24\text{hr}}/\text{MIC} \ge 400$ for appropriate effect

$\text{AUC}_{0-24\text{hr}}/\text{MIC} \le 700$ to prevent toxicity

$$\text{AUC}_{0-\tau} = \frac{C_{max}+C_{min}}{2}t_{inf} + \frac{(C_{max}-C_{min})(\tau-t_{inf})}{\ln(C_{max}/C_{min})}$$ $$\text{AUC}_{0-24\text{hr}} = \text{AUC}_{0-\tau} \frac{24}{\tau}$$

Initial Vanc Dosing Calculator

Level-Based Vanc Dosing Calculator

Aminoglycosides ^{1, 5}

See also: Stanford Aminoglycoside Dosing Guidelines

k ≈ 0.0024 × CrCl + 0.01

V_d ≈ 0.26 L/kg × Wt

V_d may be closer to 0.3-0.35 L/kg in critically ill pts due to fluid overload

Use ABW if Wt/IBW > 130%

Traditional Dosing

Gentamicin / Tobramycin Target Levels ^{1, 6}

Infection	Target Peak (mcg/mL)	Target Trough (mcg/mL)
General	4-10	le; 1
UTI	< 5	≤ 1
Bacteremia	> 5	≤ 1
Pneumonia	> 6	≤ 1
Endocarditis from P. aeruginosa	> 12	≤ 1

Amikacin Target Levels ^{1, 6}

Infection	Target Peak (mcg/mL)	Target Trough (mcg/mL)
General	15-30	4-10
UTI	> 15	4-10
Bacteremia	> 20	4-10
Pneumonia /Serious Infections	> 24	4-10

Target C_pk / MIC > 10 for efficacy Draw levels 1hr after infusion ends Consider target troughs of ≤ 1.5-2 (tob/gent) or ≤ 10 (amikacin) for life-threatening infections. Look up specific trough/peak targets for given infection site.

Initial Aminoglycoside Dosing Calculator

Extended-Interval Dosing

1. Load with 7 mg/kg (15 mg/kg Amikacin)

2. Determine initial dosing frequency from table below

3. Draw level at 6-14hr after 1st or 2nd dose

4. Plot level on Hartford Nomogram (divide level by 2 for Amikacin)

   • If doses other than those above are used, multiplying the level by (expected)/(given) dose can help adjust properly for the nomogram, although this has less evidence

5. Adjust interval per nomogram

6. If borderline, go with longer interval

Hartford Nomogram

Initial Aminoglycoside Interval

CrCl	Interval
≥ 60	Q24H
40-59	Q36H
20-39	Q48H
< 20	Monitor Serial Conc. & Admin when < 1 mcg/mL

References