# Vancomycin Calculator

## Pharmacokinetic calculator with Bayesian modeling

#### Beta Version Alert!

This is an updated, beta version of ClinCalc's vancomycin calculator. This beta version supports Bayesian modeling, a greater emphasis on AUC:MIC targets, and more advanced modeling for unique patient populations (primarily extreme obesity and critically ill). Because this is a beta version, bugs, errors, and other quirks may be present. If you encounter a problem or have suggestions before this calculator is finalized, please contact us at contact@clincalc.com.

### Patient Parameters

 Body weight: kg lbs Height: in cm Gender: Male Female Patient is critically ill No Yes

Renal function:
Creatinine:
Age:

### Vancomycin Drug Levels

Drug levels available:

Empiric, initial vancomycin dosing will be calculated using population pharmacokinetic parameters. Two vancomycin drug concentrations (such as a peak and trough) should be obtained to optimize therapy. Learn more about the timing of vancomycin drug levels.

Press 'Calculate' to view calculation results.

This vancomycin calculator uses both traditional pharmacokinetic equations (Sawchuk-Zaske method) and Bayesian pharmacokinetic modeling to estimate a vancomycin dosing regimen for an adult patient. Vancomycin regimens are estimated both empirically (without any prior doses) or on the basis of one or two vancomycin levels.

#### How Does This Calculator Work?

This calculator either uses Bayesian modeling (if only one vancomycin level is available) or the Sawchuk-Zaske method (if two vancomycin levels are available) to estimate a patient's volume of distribution (Vd), elimination constant (Kel), and vancomycin clearance (CLvanco). Once these kinetic parameters are determined, one-compartment equations are then used to estimate an anticipated peak concentration, trough concentration, and AUC/MIC ratio.

#### Vancomycin Drug Level Monitoring

The most optimal method of monitoring vancomycin therapy is to obtain two drug levels (such as a peak and trough concentration) during the same dosing interval. These drug levels can either be obtained after the first dose is given (non-steady state) or once steady state is achieved (after the third dose is administered). The use of two drug concentrations allows for patient-specific estimations of all pharmacokinetic parameters using the Sawchuk-Zaske method.

Two drug levels (peak and trough) collected after a single dose (non-steady state)

Two drug levels (peak and trough) collected at steady state (after at least three doses)

Because vancomycin trough levels alone (one drug concentration) has been the standard for so long, some institutions may prefer to monitor drug therapy using a single vancomycin level (typically a trough level). This single drug level may be obtained after the first dose is given (non-steady state) or once steady state is achieved (after the third dose is administered). While a single drug level is less costly and more convenient, it requires Bayesian modeling to estimate pharmacokinetic parameters and may not be as accurate as a two-level approach, particularly in patients with very altered pharmacokinetics (extreme obesity, critically ill, pregnancy, burns, etc.).

One drug level collected after a single dose (non-steady state)

One drug level collected at steady state (after at least three doses)

In selected patients, a loading dose (25-30 mg/kg of total body weight; maximum 3000 mg) may be considered in order to achieve rapid attainment of serum concentrations.1 Patients who should be considered for a loading dose include those who are critically-ill, those receiving renal replacement therapy, or those receiving a continuous infusion of vancomycin. Note that this recommendation is made on the basis of expert opinion and is not supported by clinical trial data.

#### Vancomycin Bayesian Modeling for Kel and Vd

Bayesian modeling can be used to estimate a patient's vancomycin clearance (CLvanco) and volume of distribution (Vd) on the basis of one single vancomycin level either at steady state or even after one single dose. Bayesian modeling is a mathematically complex process that involves the following steps:

1. Identify a publication describing mean and variance of vancomycin clearance and volume of distribution. This publication should include subjects with similar characteristics to the patient who will be receiving vancomycin.
2. One or more vancomycin concentrations are drawn from a patient.
3. An algorithm identifies values for CLvanco and Vd that are most likely (using probability) to explain the patient's serum drug concentrations. These values are optimized based on the original publication's mean and variances of CLvanco and Vd.
4. With a known CLvanco and Vd, an elimination constant (Kel) can be calculated ($$Kel=CL_{vanco}/Vd$$)
5. Once the most likely values of Kel and Vd have been estimated, traditional one-compartment pharmacokinetic equations are used to identify a dose and its associated peak, trough, and AUC/MIC values.

This calculator selects one of three possible Bayesian models to estimate a patient's pharmacokinetic parameters:

• Buelga et. al, 2005:2 Default model for general hospitalized adult patients
• Roberts et. al, 2011:3 Critically ill patient model for ICU patients
• Adane et. al, 2015:4 Extreme obesity model (BMI > 40 kg/m2 and body weight > 120 kg)

There are many models available for Bayesian analysis.5,6 These models were selected based on being generalizable, one-compartment models with reasonable predictive performance in confirmatory publications.

These three models vary significantly between each other given the difference in patient populations modeled, emphasizing the importance that the most representative model is selected for an individual patient. Using an example patient weighing 100 kg with a creatinine clearance of 80 mL/min, the initial pharmacokinetic variables with each model would be:

 Model Intended patient population CLvanco (L/min) Vd (L/kg) Half-life (hr) Buelga 2005 2 General hospitalized 5.184 0.98 13.1 Roberts 2011 3 Critically ill 3.664 1.53 28.9 Adane 2015 4 Extreme obesity 4.186 0.51 8.4

#### Sawchuk-Zaske Method for Kel and Vd

When multiple vancomycin drug concentrations are available, traditional pharmacokinetic equations can be implemented to calculate patient-specific pharmacokinetic parameters. This approach is called the Sawchuk-Zaske method.7 Unlike in Bayesian analysis, this method does not utilize population estimates of kinetic parameters and should provide more reliable results, particularly in patients with very altered pharmacokinetics values.

The Sawchuk-Zaske method uses two post-dose concentrations (regardless of being at steady state) using the following approach:7

##### 1. Determine Kel
$$\\ Cp = Cp^0*e^{-kt} \\ (rewritten\;to\;solve\;for\;k) \\ k = ln(Cp^0/Cp)/t$$
Cp0 is the first (higher) concentration; Cp is the second (lower) concentration; t is the time elapsed between Cp0 and Cp; k is the elimination constant (Kel)
##### 2. Extrapolate to Cmax (peak) and Cmin (trough)

Using the first-order elimination equation ($$Cp = Cp^0*e^{-kt}$$), a true peak (Cmax) can be calculated using the time elapsed between the end of the vancomycin infusion and the first drug concentration (Cp0). Similarly, a true trough (Cmin) can be calculated using the time elapsed between the second drug concentration (Cp) and the when the next dose is due to begin infusing.

##### 3. Calculate volume of distribution (Vd)

A patient-specific Vd can be calculated using Cmax and Cmin from the previous step. If a patient has only received one single dose (thus not at steady state), Cmin is set to 0 (zero).

$$\\ Vd = \frac{Dose/T_{inf}*(1-e^{-k*T_{inf}})}{k*(C_{max} - (C_{min} * e^{-k*T_{inf}}))}$$
Vd is the volume of distribution (in liters); dose is the vancomycin dose (in milligrams); Tinf is the vancomycin infusion time (in hours); k is the elimination constant (Kel, in hr-1); Cmax is the true peak concentration; Cmin is the true trough concentration (if at steady state) or is 0 (zero) if not at steady state
##### 4. Use patient-specific Kel and Vd for additional calculations

Once patient-specific values of Kel and Vd have been determined, traditional one-compartment pharmacokinetic equations are used to identify a dose and its associated peak, trough, and AUC/MIC values.

#### One-Compartment Equations for Peak, Trough, AUC/MIC

##### Peak Estimation

Once a patient-specific Kel and Vd are estimated (Bayesian method) or calculated (Sawchuk-Zaske method), specific vancomycin doses can be inputted into the following equation to estimate the Cpeak (Cmax) concentration at steady state:

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

With a known Cpeak and Kel value, a trough (Ctrough or Cmin) can be estimated using the following equation:

$$\\ Cp=Cp^0*e^{(-kt)} \\ C_{trough} = C_{peak} * e^{(-k * (Tau - T_{inf}))}$$
##### AUC Estimation

There are two methods to estimate the AUC of a given dosing regimen. Method #1 uses a known peak and trough value:

###### AUC Method #1
$$\\ Lin\;trap = \frac{C_{trough}+C_{peak}}{2}*(T_{inf}) \\ Log\;trap = \frac{(C_{peak}-C_{trough})*(Tau-T_{inf})}{\ln(\frac{C_{peak}}{C_{trough}})} \\ AUC_{0-Tau} = (Lin\;trap) + (Log\;trap) \\ AUC_{0-24} = AUC_{0-Tau}*(24/Tau) = AUC\;in\;mcg*h/mL$$
###### AUC Method #2

Method #2 of determining AUC only requires CLvanco and the daily dose:

$$CL_{vanco} = K_{el} * Vd \\ AUC_{0-24}=(Total\;daily\;vancomycin\;dose)/CL_{vanco}$$

#### Inappropriate Populations for This Calculator

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

• Pediatrics (< 18 years)
• Cystic fibrosis
• Severe burn injury

#### Dosing Recommendations for Renal Replacement Therapy (RRT)

Vancomycin dosing in patients receiving renal replacement therapy is complex and usually requires expert clinical judgment in conjunction with assessment of unique patient-specific factors. For example, blood flow rate, filter type, hemodialysis frequency or downtime, effluent rate, and residual renal function are among several factors that influence a patient's vancomycin dosing needs. The following are general considerations and recommendations for this patient population.

##### Intermittent Hemodialysis 1

An initial loading dose of 25 mg/kg is recommended followed by 7.5 to 10 mg/kg after each hemodialysis session. Blood samples may be collected before dialysis (pre-dialysis) or 1-2 hours after dialysis (post-dialysis) and should be used to adjust maintenance dosing to a goal AUC/MIC between 400 to 600 mg*h/L.

##### Sustained Low Efficiency Dialysis (SLED) 1,8

An initial loading dose of 15 to 25 mg/kg is recommended followed by 15 mg/kg after the end of each hybrid hemodialysis session. Blood samples may be collected before hybrid dialysis (pre-dialysis) or 1-2 hours after hybrid dialysis (post-dialysis) and should be used to adjust maintenance dosing to a goal AUC/MIC between 400 to 600 mg*h/L.

##### Continuous Renal Replacement Therapy (CRRT) 9

An initial loading dose of 15 to 25 mg/kg is recommended followed by a maintenance dose based on the CRRT modality (see below). Blood samples should be collected to adjust maintenance dosing to a goal AUC/MIC between 400 to 600 mg*h/L.

• CVVH: 10 to 15 mg/kg every 24-48 hours
• CVVHD: 10 to 15 mg/kg every 24 hours or 7.5 mg/kg every 12 hours
• CVVHDF: 7.5 to 10 mg/kg every 12 hours

1. Rybak MJ, Le J, Lodise TP, et al. Therapeutic monitoring of vancomycin: A revised consensus guideline and review of 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. Draft for comments document available; pending final publication.
2. Buelga DS, del Mar Fernandez de Gatta M, Herrera EV, et al. Population pharmacokinetic analysis of vancomycin in patients with hematological malignancies. Antimicrob Agents Chemother. 2005 Dec;49(12):4934-41. PMID 16304155.
3. Roberts JA, Taccone FS, Udy AA, et al. Vancomycin dosing in critically ill patients: robust methods for improved continuous-infusion regimens. Antimicrob Agents Chemother. 2011 Jun;55(6):2704-9. PMID 21402850.
4. Adane ED, Herald M, Koura F. Pharmacokinetics of vancomycin in extremely obese patients with suspected or confirmed Staphylococcus aureus infections. Pharmacotherapy. 2015 Feb;35(2):127-39. PMID 25644478.
5. Guo T, van Hest RM, Roggeveen LF, et al. External Evaluation of Population Pharmacokinetic Models of Vancomycin in Large Cohorts of Intensive Care Unit Patients. Antimicrob Agents Chemother. 2019 Apr 25;63(5). PMID 30833424.
6. Broeker A, Nardecchia M, Klinker KP, et al. Towards precision dosing of vancomycin: a systematic evaluation of pharmacometric models for Bayesian forecasting. Clin Microbiol Infect. 2019 Mar 11. pii: S1198-743X(19)30097-7. PMID 30872102.
7. Bauer LA. The Aminoglycoside Antibiotics. In: Bauer LA. eds. Applied Clinical Pharmacokinetics. 3rd Ed. New York, NY: 2014.
8. Lewis SJ, Mueller BA. Development of a vancomycin dosing approach for critically ill patients receiving hybrid hemodialysis using Monte Carlo simulation. SAGE Open Med. 2018 May 11;6:2050312118773257. PMID 29780587.
9. Heintz BH, Matzke GR, Dager WE. Antimicrobial dosing concepts and recommendations for critically ill adult patients receiving continuous renal replacement therapy or intermittent hemodialysis. Pharmacotherapy. 2009 May;29(5):562-77. PMID 19397464.