# Vancomycin Calculator Update – End of Infusion Peak (EoIP)

We’re releasing a major update to the calculation for our popular vancomycin calculator today. Briefly, the new update implements more advanced calculations when adjusting a vancomycin dose based on a trough level.

## Drug Elimination during Vancomycin Infusion

When adjusting vancomycin based on a trough level, pharmacokinetic textbooks recommend estimating a vancomycin peak level using the following equation:

$$\Delta C = (Trough – Peak) = \frac{Dose}{Vd} \\ t = Tau\;(frequency\;of\;doses)\;-T_{infusion} \\ Trough=Peak*e^{(-kt)}$$

Using these two equations, a known trough and estimated peak can be used to solve for a patient-specific elimination constant (Kel). The problem, though, is that the ‘t’ (time) represents the duration between the end of the infusion and when the trough level is drawn. In other words, these two equations do NOT account for drug elimination during the infusion of vancomycin.

In some cases, drug elimination can actually represent a significant amount of time during the dosing interval. Take the following example of 2 gm IV Q8hr (two-hour infusion):

In cases where vancomycin is dosed frequently (ie, Q8hr or Q6hr) and the vancomycin dose is large enough that the infusion time is significant (ie, 2 or 3 hours), elimination during the vancomycin infusion can actually contribute significantly.

## Pharmacokinetic Textbooks

Interestingly, we have been unable to find a textbook or reference that properly accounts for drug elimination during the infusion period. Popular textbooks like Applied Clinical Pharmacokinetics (Bauer), Basic Clinical Pharmacokinetics (Winter), Applied Pharmacokinetics (Evans), Applied Biopharmaceutics & Pharmacokinetics (Shargel), and Handbook of Basic Pharmacokinetics (Ritschel) just don’t address this phenomenon.

Why wouldn’t these textbooks address elimination during infusion? The most likely reason is that vancomycin is doses very differently today than a decade or two ago. Historically, vancomycin doses and dosing frequencies were much lower. With the ASHP/IDSA/SIDP vancomycin recommendations targeting trough levels of 15-20 mcg/mL and the obesity epidemic, we’re giving larger doses more frequently than ever before.

Because of these larger doses, drug elimination during the infusion actually matters. With lower doses or less frequent administration, accounting for drug elimination during the infusion becomes irrelevant.

## Drug Elimination during Infusion

The amount of drug eliminated during an infusion can be calculated by modifying our equation as follows:

$$\Delta C=\frac{Dose}{Vd}*e^{-k*T_{infusion}}$$

The final expression () provides a decimal value between 0 and 1 describing the fraction of vancomycin remaining after the infusion period. As an example, if this value is 0.7, it means that 30% of the vancomycin was eliminated during the infusion (or that 70% of the vancomycin remains).

## Quantifying Drug Elimination

Consider the following example of a patient with a Kel of 0.0791 hr-1 (CrCl of 90 mL/min) to appreciate the degree of drug elimination as infusion times increase:

 Dose Infusion Time % Eliminated During Infusion 500 mg 0.5 hrs 4% 1,000 mg 1 hr 8% 2,000 mg 2 hr 15% 3,000 mg 3 hr 21%

As demonstrated in the table, accounting for elimination during a large dose (long infusion time) can significantly change this patient’s estimated peak value by about 15-20%. The impact of elimination during infusion is minimized for smaller doses and impaired renal function (smaller Kel).

## End of Infusion Peak (EoIP)

With today’s update to the vancomycin calculator, we are now accounting for drug elimination during the infusion period. Instead of calling this the estimated ‘peak’, we will now be using the term EoIP (end of infusion peak). The EoIP will be used to estimate a patient-specific elimination constant (Kel) when calculating a new vancomycin dose based on a trough level.

## One thought on “Vancomycin Calculator Update – End of Infusion Peak (EoIP)”

1. Ben Devine

A formula for accounting for drug loss during infusion was published by Zaske & Sawchuk in the 70s as applied to gentamicin dosing in burn patients…there are a number of citations. More recently, Rick Tharp @ http://www.rxkinetics.com discusses the effect of infusion time on peak levels in his PK tutorial.