# Vancomycin Calculator

### Patient Parameters

 Body weight: kg lbs Volume of distribution (Vd): L/kg Therapeutic goal: Trough 15 to 20 mcg/mL Trough 10 to 15 mcg/mL AUC:MIC ratio > 400 Recommend loading dose: No Yes

### Elimination Constant (Kel)

 Height: in cm CrCl: mL/min Age: years Creatinine: mg/dL µmol/L Gender: Male Female
RESULTS

### Dosing Schedule

Dose
(14.3 mg/kg) Frequency Infusion Time ### Predicted PK

Peak 34.8 mcg/mL
Trough 17 mcg/mL
(goal 15-20 mcg/mL)
AUC:MIC 600 mcg*hr/mL

### PK Parameters

Apparent CrCl 75 mL/min
Vd 73.5 L (0.7 L/kg)
Kel 0.068 hr-1
T1/2 10.2 hrs

This website is intended to be used in conjunction with reasonable clinical judgment. This is not a substitute for clinical experience and expertise. An electronic tool cannot assess the clinical picture and patient-specific factors.

Elimination Constant (Kel) and End of Infusion Peak (EoIP)
$$\\Time = Tau - T_{infusion} - T_{prior\;to\;next\;dose} = 12-1.5- \frac{30min}{60} = 10\;hrs\\ \Delta C = (Peak - Trough) = \frac{Dose}{Vd}*e^{-k*T_{infusion}}\\ End\;of\;infusion\;Peak\;(EoIP) = \frac{Dose}{Vd}*e^{-k*T_{infusion}} + Trough\\ Trough=EoIP*e^{-kt} \rightarrow (\frac{Dose}{Vd}*e^{(-k*T_{infusion})} + Trough)*e^{-kt}\\ 12.5=(\frac{1000}{73.5}*e^{(-k*1.5)} + 12.5)*e^{-k*10} \rightarrow k=0.068\;hr^{-1}\\ EoIP = \frac{Dose}{Vd}*e^{-k*T_{infusion}} + Trough = 13.61*0.9+12.5=24.8\;mcg/mL$$
Volume of Distribution
$$V_d = 0.7 \frac{L}{kg}*105\;kg = 73.5\;L$$
Half-life
$$T\frac{1}{2} = \frac{0.693}{K_{el}} = \frac{0.693}{0.068 hr^{-1}} = 10.2\;hrs$$
Tau
$$\\ Tau = \frac{\ln(\frac{Peak}{Trough})}{K_{el}} + T_{infusion} = \frac{\ln(\frac{40}{15})}{0.068} + 1.5 = 14.4+ 1.5 \;hrs \; \sim = 12\;hrs\;$$
Estimation of Peak
$$\\Dose = \frac{C_{peak}*T_{infusion}*Vd*K_{el}*(1-e^{(-K_{el}*Tau)})}{(1-e^{(-K_{el}*T_{infusion})})}\\ 1500 mg = \frac{C_{peak}*(1.5\;hr)*(73.5 L)*(0.068 hr^{-1})*(1-e^{(-0.068*12)})}{(1-e^{(-0.068*1.5)})} \\ \rightarrow C_{peak}=34.8\;mcg/mL$$
Estimation of Trough
$$\\ Cp=Cp^0*e^{(-kt)}\\ Trough = Peak*e^{(-kt)}\\ Trough = 34.8*e^{(-0.068*(12-1.5))} = 17\;mcg/mL$$
Calculation of AUC:MIC
$$\\\\ Lin\;trap = \frac{Trough+Peak}{2}*(T_{infusion}) = \frac{17+34.8}{2}*1.5\\ \rightarrow Lin\;trap = 38.9mcg*h/mL\\ Log\;trap = \frac{(Peak-Trough)*(Tau-T_{infusion})}{\ln(\frac{Peak}{Trough})}\\ = \frac{(34.8-17)*(12-1.5)}{\ln(\frac{34.8}{17})} \; =261mcg*h/mL\\ AUC_{0-12} = (Lin\;trap) + (Log\;trap) = 38.9 + 261= 299.9\;mcg*h/mL\\ AUC_{0-24} = AUC_{0-12}*2=599.8\;mcg*h/mL\\ AUC_{0-24}:MIC\;ratio = AUC_{0-24} /1=599.8\;mcg*h/mL$$

This vancomycin calculator uses a variety of published pharmacokinetic equations and principles to estimate a vancomycin dosing regimen for a patient. A regimen can be completely empiric, where the vancomycin dose is based on body weight and creatinine clearance, or a regimen may be calculated based on one or more vancomycin levels.

Our vancomycin calculator was specifically designed to help students and clinicians understand the process of calculating a vancomycin regimen. When a vancomycin regimen is calculated, each step in the dosing process is fully enumerated and visible by clicking the "Equations" tab.

In addition to being designed for students, this calculator was also intended with the practicing clinician in mind. All dosing regimens are rounded to the nearest 250 mg with appropriate dosing intervals (eg, Q8hr, Q12hr, Q24hr) to reflect clinical practice. Additionally, after calculating a dosing regimen, a pharmacokinetic progress note template is automatically generated for your convenience. After calculating a dose, click on 'Progress Note' for a pharmacokinetic template or 'Equations' for a step-by-step explanation of the recommended dosing regimen.

### Major Updates to this Calculator

• 2015-06-07 - Drug elimination is accounted for during the infusion time. Read more

#### Inappropriate Populations for This Calculator

This calculator is NOT appropriate for the following patient populations or may require a higher degree of clinical judgment:

• Hemodialysis
• Pediatrics
• Unstable renal function
• Vancomycin MIC ≥ 2 mcg/mL

#### Population Estimate of Kel

Because vancomycin is primarily renally eliminated, the elimination constant (Kel) is directly related to creatinine clearance (CrCl). While several population estimates exist, this calculator uses the Creighton equation 1 to estimate Kel for a given CrCl using the Cockcroft-Gault method:2

$$K_{el} = 0.00083*(CrCl) + 0.0044$$

Importantly, this method relies on an accurate creatinine clearance; therefore, this method may not be appropriate in patients with unstable renal function or other characteristics that make creatinine clearance difficult to estimate (eg, obesity, elderly, amputations, etc.). Furthermore, it should be emphasized that this is merely an estimate of Kel -- there are many other equations to generate an estimate.

#### Estimate of Kel from a Trough Level

This calculator can use a single vancomycin trough to estimate true vancomycin clearance (rather than a population estimate from creatinine clearance). This calculator assumes that the vancomycin trough is drawn at steady state, which occurs prior to the fourth vancomycin dose (assuming a consistent dose and dosing regimen).3

#### Population Estimate of Vd

By default, this calculator suggests a population estimate volume of distribution (Vd) of 0.7 L/kg for vancomycin. There is actually a large variation in the literature, with Vd being described between 0.5 and 1 L/kg.4 There is some evidence that patients with reduced creatinine clearance (CrCl < 60 mL/min) have a larger Vd of 0.83 L/kg, whereas patients with preserved renal function (CrCl ≥ 60 mL/min) have a smaller Vd of 0.57 L/kg.5

#### Actual or Ideal Dosing Body Weight

Although data are limited, it is recommended that vancomycin be initially dosed on actual body weight (not ideal or adjusted weight), even in obese patients.3 Clinically, this dose may be capped at a specific weight (eg, 120 kg) or dose (eg, 2500 mg), although this practice has not been prospectively studied.

While vancomycin is dosed on actual body weight, it should be noted that creatinine clearance (which may be used to empirically estimate Kel) is based on ideal or adjusted body weight. For more information on the appropriate body weight, see Creatinine Clearance - Adjustments for Obesity.

#### Core Pharmacokinetic Equations

This vancomycin calculator uses three "core" clinical pharmacokinetic equations that are well described for intermittent intravenous infusions assuming a one-compartment model.4:

$$Cp=Cp^0*e^{(-kt)}$$

This equation describes how an initial drug concentration (Cp0) declines to a final drug concentration (Cp) over a specified period of time (t) assuming an elimination constant (k).

$$\Delta C = \frac{Dose}{Vd}$$

This equation describes the change in concentration (ΔC = Cfinal - Cinitial) is related to a given dose and volume of distribution (Vd).

$$Dose = \frac{C_{peak}*T_{infusion}*Vd*K_{el}*(1-e^{(-K_{el}*Tau)})}{(1-e^{(-K_{el}*T_{infusion})})}$$

This large equation calculates an appropriate drug dose assuming a goal peak drug level (Cpeak), volume of distribution (Vd), elimination constant (Kel), dosing frequency (Tau), and infusion time (Tinfusion).

#### Therapeutic Targets: Trough Level

Because an AUC:MIC goal value is difficult to calculate, many clinicians continue to use a goal vancomycin trough level as the therapeutic target of choice. As mentioned in guidelines,3 an AUC of 400 may be achieved with a peak of about 40 mcg/mL and a trough of about 15 mcg/mL. This method is often used as an alternative to direct AUC calculations.

Current guidelines make the following suggestions regarding the optimal vancomycin trough level:3

• All patients should achieve a minimum trough level of > 10 mcg/mL
• Patients with complicated infections should have a goal vancomycin trough of 15 to 20 mcg/mL. Complicated infections include:
• Pathogen MIC of 1 mcg/mL
• Bacteremia
• Endocarditis
• Osteomyelitis
• Meningitis
• Hospital-acquired pneumonia caused by Staph aureus

#### Therapeutic Targets: AUC:MIC

Although vancomycin has been on the market since the 1950s, there is still considerable controversy regarding the optimal monitoring parameter to maximize efficacy and minimize toxicity. Current guidelines recommend an AUC:MIC ratio of ≥ 400, although this goal is largely based on weak evidence.3,6,7,8

In order for an AUC:MIC ratio to be calculated, both a peak and trough level must be known. Because only trough levels are drawn clinically, a peak level must be estimated. The following equation is used to estimate vancomycin's area under the curve (AUC):5

$$\\ Lin\;trap = \frac{Trough+Peak}{2}*(T_{infusion}) \\ Log\;trap = \frac{(Peak-Trough)*(Tau-T_{infusion})}{\ln(\frac{Peak}{Trough})} \\ AUC_{0-Tau} = (Lin\;trap) + (Log\;trap) \\ AUC_{0-24} = AUC_{0-Tau}*(24/Tau) = AUC\;in\;mcg*h/mL$$

In seriously ill patients, a loading dose of 25-30 mg/kg (actual body weight) may be considered.3 This practice has a theoretical benefit of attaining therapeutic vancomycin levels earlier, but has not been extensively studied. This approach is not supported by evidence from large clinical trials, therefore, the safety and efficacy of a loading dose practice has not been established.

Regardless, based on expert opinion, the following patient populations may be considered for such a loading dose when MRSA is suspected:9

• Sepsis
• Meningitis
• Pneumonia
• Infective endocarditis
• Severe skin/soft tissue infection

1. Matzke GR, McGory RW, Halstenson CE, Keane WF. Pharmacokinetics of vancomycin in patients with various degrees of renal function. Antimicrob Agents Chemother. 1984 Apr;25(4):433-7. PMID 6732213.
2. Cockcroft DW, Gault MH. Prediction of creatinine clearance from serum creatinine. Nephron. 1976;16(1):31-41. PMID 1244564.
3. Rybak M, Lomaestro B, Rotschafer JC, et al. Therapeutic monitoring of vancomycin in adult patients: a consensus review of the American Society of Health-System Pharmacists, the Infectious Diseases Society of America, and the Society of Infectious Diseases Pharmacists. Am J Health Syst Pharm. 2009;66(1):82-98. PMID 19106348.
4. Bauer LA. Chapter 5. Vancomycin. In: Bauer LA, ed. Applied Clinical Pharmacokinetics. 2nd ed. New York: McGraw-Hill; 2008.
5. DeRyke CA, Alexander DP. Optimizing Vancomycin Dosing Through Pharmacodynamic Assessment Targeting Area Under the Concentration-Time Curve/Minimum Inhibitory Concentration. Hospital Pharmacy. 2009;44(9):751-765. Free Full Text.
6. Craig WA. Basic pharmacodynamics of antibacterials with clinical applications to the use of beta-lactams, glycopeptides, and linezolid. Infect Dis Clin North Am. 2003;17(3):479-501. PMID 14711073.
7. Moise-Broder PA, Forrest A, Birmingham MC, et al. Pharmacodynamics of vancomycin and other antimicrobials in patients with Staphylococcus aureus lower respiratory tract infections. Clin Pharmacokinet. 2004;43(13):925-42. PMID 15509186.
8. Jeffres MN, Isakow W, Doherty JA, et al. Predictors of mortality for methicillin-resistant Staphylococcus aureus health-care-associated pneumonia: specific evaluation of vancomycin pharmacokinetic indices. Chest. 2006;130(4):947-55. PMID 17035423.
9. Liu C, Bayer A, Cosgrove SE, et al. Clinical practice guidelines by the infectious diseases society of america for the treatment of methicillin-resistant Staphylococcus aureus infections in adults and children. Clin Infect Dis. 2011;52(3):e18-55. PMID 21208910.