13.3 Calculations

Though the label or Master Formulation Record may provide most or all of the calculations for compounding, there may be times when mathematics is required. Many pharmacy software programs automatically print the needed calculations for measurements and dosages of the drugs (the amounts needed to be drawn up or added) on the CSP labels.

However, inside the anteroom, the technician may need to compare the concentration of the dose ordered with the concentration of stock drug on hand and perform calculations to determine the desired volume of each ingredient to add to the LVP or SVP. The IV flow rates are also typically provided on the physician’s medication order. The technician then uses the ordered IV flow rate to calculate the days’ supply for IVs and IVPBs, and the pharmacist verifies the accuracy of the technician’s calculations as a double check. Hospital pharmacy technicians may also serve on cardiopulmonary resuscitation (CPR) or code teams that need to calculate dosages and drip rates for heart medications, prepare IV infusions and tubing, and attach IV sets.

For certain TPN preparations, neonatal (newborn) IVs, and chemotherapy IVs, the process is reversed. For these products, the pharmacist typically performs the first set of calculations, which are then verified by another pharmacist. The pharmacy technician then provides the “third-line check” of these calculations.

The IV technician must always double-check the medication order, labels, and calculations, documenting them all in the Compounding Record.

Common Compounding Calculations

As was demonstrated in Chapter 6 on calculations, numerous calculations may need to be done for different CSPs. The first calculations needed are often ones of measurement conversions, so it is essential to memorize the equivalents and metric conversions provided in Chapter 6. You will also need to know conversions from standard time (clock time) to military time since drug administration times in hospitals and other institutions are generally based on military time. Knowing how to translate temperatures in Fahrenheit to Celsius and back is essential for refrigerator and freezer storage conditions. (These conversions are also explained in Chapter 6.)

Checking and double-checking conversion measurements and IV calculations for children is especially important.

Numerous other calculations are needed, and certain scenarios favor specific formulas and methods for the greatest accuracy. (But you will also have favored methods, based on what you know best.)

• When a measurement is missing in an equation involving equal ratios, proportions, or fractions, the rate and proportion calculation method may be best.

• For multi-stepped problems using conversions, dimensional analysis is usually favored.

• For calculating concentrations based on the body surface area, use the proper equal ratios and proportion formula.

• For addressing dilutions of powders and solutions, a combination of the ratio and proportion method and dimensional analysis can be used.

• For mixing two different concentrations of the same drug, use the alligation method to find the amounts needed of each these solutions.

• For working with milliequivalents for electrolytes and other solutes, there are specialized formulas.

These are not the only calculations needed. In addition, one must know how to handle overfill concerns and calculate drip rates, drop rates, and infusion rates to determine 24-hour IV supply needs. Descriptions of these calculations are to follow.

Overfill Concerns in Admixtures and Dilutions

Although manufactured bags or bottles of medicated solutions are labeled to contain a set number of mL (e.g., 25, 50, 100, 250, 500, or 1,000 mL), the actual volume is greater because the containers include overfill. Overfill is the amount of solution that manufacturers add to make up for the loss of water due to evaporation through plastic. This loss is somewhat dependent on conditions during transport and storage and the ratio of fluid volume to the surface area. The larger the base solution of the IV bag, the greater the potential loss, so the more the manufacturers add overfill to compensate.

Manufacturers are not consistent in their addition of overfill amounts, and they do not always label the overfill percentages they use. (See Table 13.8 for an example of overfill amounts.) Some overwrap their non-PVC (a type of plastic) IV solutions to reduce evaporation. These wraps should stay on until right before compounding or administration.

Overfill Effects on IV Compounding Processes

There are four major ways to create admixtures for IV infusions, each affected by overfill rates to differing degrees:

Small-Volume Medication Addition for a Simple Admixture In this, you add the medication to the manufacturer’s base solution. But before doing so, you may need to reconstitute a powdered medication or dilute a concentrated medication by adding a diluent. These substances increase an IV’s volume. Generally, the SVP IV solution is meant to be infused to a patient until the bag is empty over a short period of time (such as 30 minutes)—as with antibiotics in an IV piggyback. In this situation, there is no need to compensate for overfill because the entire contents will be used and the full dosage will be received. However, the label should list the total amount of the drug and the total estimated amount of solution (including the estimated overfill). The label must also indicate that the CSP is meant for a single dose for a single short-term administration, and the IV tubing should be flushed to ensure that the whole dose is administered.

For example, you may receive a medication order for 20 mL of a drug solute in 100 mL of D5W to be administered over 30 minutes. To prepare the drug, you must add the 20 mL. The estimated overfill of the base solution bag is 7 mL, so the total volume in the SVP is equal to 127 mL. The IV label must read “Infuse entire contents for full dose.”

Volume Withdrawal and Medication Addition Another process is used when adding a large amount of medication to an LVP that is meant to be continuously administered until another IV filled with the same drug follows. Before adding the medication to the IV, a similar volume to that of the drug additive has to be removed first. For example, if you need to add 150 mL of a drug to 1,000 mL of a D5W solution, you must first withdraw 150 mL of the base solution before adding the medication. As with a simple admixture, the label should indicate the total drug amount and the estimated total volume of the solution, which would be the original 1,000 mL plus the overfill of the original base solution.

Larger Volume Withdrawal and Medication Addition When a large volume of an intensely concentrated dose is required, such as with a cancer chemotherapy drug, you may need to remove both the volume (diluent) of the medication to be added plus the estimated amount of the manufacturer’s overfill. That way, when the medication is added to the solution that remains, it will hold the prescribed dosage with no extra overfill solution to dilute it. However, if the overfill amount is not known but is just estimated, then it will still not be a precise dosage. Yet it will be far closer than if the overfill amount was never estimated for some accommodation of the volume. (See overfill calculation Example 1.)

New Container with Solute and Solvent For medications that need to be the most precise, as in chemotherapy, sterile compounding technicians need to work with accurate medication amounts and add them as well as the diluents and base solvent into a new sterile container. This can be done manually or in an automated compounding machine (as with TPN solutions). Using a new container means that there will be no overfill to calculate or estimate.

Overfill Policies

Each hospital and home infusion pharmacy will have written protocols for dealing with overfill calculations when using base solutions that have overfill. Small and large parenteral solutions are the majority of sterile compounded solutions, and normally the overfill amount does not appreciably affect the amount of IV fluids or drug dosages administered. In the case of IV neonatal drugs or cancer chemotherapy drugs that come in premixed solutions that must be reconstituted with a diluent before being transferred into a small or large volume parenteral solution, the combination of the overfill in the IV bag plus the diluent can cause an overdilution of the prescribed dose, especially if the entire contents of the IV solution are not administered. A diluted or less than prescribed dose of a critical drug may adversely affect the disease outcome.

Many pharmacies implement a 10% overfill rule for most medications where overfill issues are encountered. If the total calculated final volume to be administered equals 10% or less additional fluid, it is not necessary to withdraw any of the base solution.

For example, a medication order is received for a doxorubicin 90 mg solution to be added to a 1,000 mL (1 L) NS, with the compounded IV to be infused over six hours. Doxorubicin is available as a 2 mg/mL solution concentration; therefore, a 90 mg dose requires 45 mL of doxorubicin solution to be used.

If the manufacturer offers IV products with overfill amounts like those in Table 13.8, one liter of NS will contain approximately 50 mL of overfill. So 1,000 mL + 45 mL (of the diluent) + 50 mL (of overfill) = 1,095 mL. Ten percent of 1,000 is 100, so an overfill of an additional 10% would total 1,100 mL. Because 1,095 is under the limit of 10% more, no adjustment in the volume of the base solution (NS) would be needed, according to the 10% rule of hospital policy.

When the total calculated final volume to be administered equals more than an additional 10%, it is necessary to withdraw a volume of the base solution equal to the overfill volume plus the diluent of the drug.

Using the same example, if the 90 mg solution (45 mL) was to be added to 500 mL NS instead of 1,000 mL NS, then the final volume would have been 500 mL + 45 mL (volume of doxorubicin) + 30 mL (overfill) for a total of 575 mL. Since this volume is greater than the limit of 10% more of 500 mL (550 mL), the protocol states that 75 mL (45 mL + 30 mL) NS should be withdrawn before adding the medication solution of 90 mg, and 45 mL results in a final (and labeled) concentration of 90 mg of doxorubicin in 500 mL NS.

IN THE REAL WORLD

Determining the Days’ Supply with IV Administration Flow Rates

To determine the correct number of IV bags needed for a 24-hour period and the time when a new IV bag will be needed, technicians at times must calculate the IV administration flow rates based on the size of the IV tubing and on the prescribed infusion rates. These calculations typically address the following questions that affect each other:

• What is the infusion rate in mL/hour?

• What is the size of the tubing and the drip rate (in gtts/min)?

• How long will this bag last?

• How much fluid has the patient received?

• What time will the next bag be needed?

• How many bags will be needed for the patient in a 24-hour period?

To answer these questions, you need to know the total volume of the ordered parenteral solution and either the prescribed infusion rate in milliliters per hour (mL/hr) or the number of hours over which the solution is to be infused. This information can be found in the physician’s medication order or in the Master Formulation Record directions. You then perform a series of IV flow rate calculations using either multiplication or division.

In the most simple sense, the infusion rate (R) is the volume divided by the time it takes (Volume/Time), and the time can be expressed in hours or minutes (and seconds if desired). The volume is expressed in mL.

${\displaystyle \frac{\text{Volume}}{\text{Time}}}=\text{Rate}\left(\text{mL}/\text{hrs}\text{or}\text{min}\right)$

To answer the question, “What is the infusion rate in mL/hr?” you must divide the IV volume in mL by the number of hours (hr) over which the CSP is to be administered (see Example 2, which follows):

$\begin{array}{ccc}{\displaystyle \frac{\text{total}\text{mL}}{\text{total}\text{hours}}}& \text{=}& {\displaystyle \frac{y\text{mL}}{1\text{hr}}}\end{array}$

To answer the question, “How long will this IV bag last (or take to administer)?” you must divide the total mL by the infusion rate (mL/hr) to determine the hours per IV bag (see Example 3):

$\begin{array}{ccc}{\displaystyle \frac{\text{Volume}\left(\text{mL}\right)}{\text{Rate}\left(\text{mL}/\text{hr}\right)}}& \text{=}& \text{Time}\left(\text{hrs}\text{or}\min \text{per}\text{bag}\right)\end{array}$ or z;   z is how long until 1 bag is empty

To answer the question, “What time will the next bag be needed?” you must add this length of time in hours (z) to the standard military time of the last administration of the infusion (see Example 4).

To answer the question, “How many bags will be needed for the patient in a 24-hour period?” you must divide 24 (the number of hours till resupply) by the number of hours calculated (z) that each bag will take to be infused (see Example 5). It is important to practice calculating examples of each equation.

Calculating Infusion Rates in Drops per mL and Drops per Minute

Sometimes it is important to know an even more precise calculation than the infusion rate to figure out how much medication a patient is receiving per drop and per minute. As described in an earlier chapter, the types of IV tubing selected have an influence on the infusion rates because they have a different drop factor, or drops per milliliter.

Macrodrip IV tubing may deliver either 10, 15, or 20 drops per milliliter. (Macro tubing comes in different diameters from manufacturers, resulting in some variance in drop factors.) In contrast, microdrip IV tubing delivers 60 drops per milliliter, so the drops are far smaller than the ones with macrodrip tubing. Macro tubing is generally used when more than 50 mL per hour needs to be administered, while micro tubing is used when fewer milliliters per hour are needed, such as in intensive care, pediatrics, or neonatology, when counting drops is important.

Most simple IV sets, if hung properly, use gravity to force the solution through the IV set to the patient, much as a water tower works to deliver tap water to city residents. However, many hospitals use an IV infusion pump or controller, which automatically adjusts the volume and administration rate of the infusion to fit the desired rate. The infusion pump is often integrated into the electronic medical record (EMR) and bar code point-of-care (BPOC) technologies to improve the accuracy of the IV administration and reduce medication errors.

Nursing personnel simply program the prescribed rate into the electronic infusion pump at the patient’s bedside. The rate can be digitally adjusted, causing the pump’s internal clamp to slow or quicken the rate at which the fluid flows through tubing routed through a chamber in the pump. Pumps can be set to give IV fluids in milliliters per hour or drops per minute.

To determine the rate in drops per minute, when the total volume and infusion time are known, the following formula is used (see Example 6):

${\displaystyle \frac{\text{Volume}\left(\text{mL}\right)}{\text{Time}\left(\min \right)}}\times \text{Drop}\text{factor}\left(\text{gtt}/\text{mL}\right)\text{=}\text{Rate}\text{of}\text{drops}\text{per}\text{minute}\left(\text{gtt}/\text{min}\right)$

Dimensional analysis may also be used to solve this type of equation. Since you cannot administer partial drops, it is common practice to round down answers with partial drops or minutes. For example, if the calculated answer is 20.6 gtts/min, it would typically be rounded down to 20 gtts/min.

An example of an IV set integrated with an infusion pump and bar code software records is the B. Braun Synchronized Intelligence Infusion Platform.

Drop Rate Calculations for Medication Infusion Amounts Occasionally, pharmacy personnel can use drop factor calculations to determine the precise amount of a drug that will be infused per minute. These types of problems are sometimes referred to as IV drip rate calculations and can be solved by using dimensional analysis.