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Or, solving by dimensional analysis:
Or, solving by the equation:
Using an infusion rate table
An infusion rate table, as exemplified by Table 13.2, may accompany a commercial product to facilitate dosing. The composition of the example table is based on the concentration of the infusion solution to be used, the desired dose of the drug, and the patient’s weight. Other tables may be designed differently; for example, rather than the patient’s weight, the patient’s body surface area, in square meters, may be used. In each case, however, the table provides guidelines for the delivery rate of an infusion.
Table 13.2 is used by matching the column of the desired drug delivery rate
against the patient’s weight to yield the infusion delivery rate in mL/h.
TABLE 13.2 INFUSION RATE OF A HYPOTHETICAL DRUG FOR A CONCENTRATION OF 0.2 mg/mL
1. Using Table 13.2, determine the delivery rate, in mL/h, for a drug to be administered at 10 mcg/kg/min to a patient weighing 65 kg.
2. If the infusion pump used in the previous example delivers 60 microdrops/milliliter, how many microdrops would be administered to the patient per minute?
3. Calculate the entry shown in Table 13.2 for the infusion delivery rate as determined in the first example problem (i.e., 195 mL/h).
A different type of flow rate table is shown in Table 13.3. This type of table is used for determining flow rates for different doses when using a specific drug concentration. The data in the table are calculated as by the following illustration:
TABLE 13.3 EXAMPLE OF A FLOW RATE TABLE FOR AN INFUSION CONTAINING DRUG IN A
CONCENTRATION OF 200 μg/mL
a
a
After finding the desired dose in μg/min in the top column, the rate of flow in mL/h is found by the number below. The table may be extrapolated; for example, a dose of 80 μg/min would translate into a rate of 24 mL/h. Also, the table may be changed for a different drug concentration; for example, a drug concentration of 100 μg/mL and a dose of 5 μg/min would necessitate a flow rate of 3 mL/h.
1. Use Table 13.3 to determine the infusion administration rate, in mL/h, to
deliver drug at 16 μg/min.
For 8 μg/min, the rate is 2.4 mL/h Thus, for 16 μg/min, the rate would be double or 4.8 mL/h Proof: The infusion contains 200 μg/mL
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Or, note from the table that the rate in mL/h for each dose may be determined by multiplying by the factor 0.3. Thus, 16 μg/min × 0.3 = 4.8
mL/h
CALCULATIONS CAPSULE
Intravenous Infusions
In certain calculations, the following equations find application.
To calculate infusion time:
To calculate flow rate in drops/minute:
CASE IN POINT 13.1
A physician prescribes amiodarone HCl IV for a patient with ventricular fibrillation. The prescribing information is:
Loading infusions:
Maintenance infusion:
Amiodarone HCl IV is available in 3-mL vials containing 50 mg/mL.
The pharmacist uses a 100-mL bag of D5W for the rapid infusion and
250-mL bottles of D5W for the slow infusions.
a. How many milliliters from an amiodarone HCl IV vial should be
placed in the 100-mL bag for the rapid infusion? b. What is the drug concentration in the rapid infusion, in mg/mL? c. If the pharmacist added the contents of 3 vials to each 250-mL
bottle of D5W needed for the slow infusions, calculate the drug
concentration in mg/mL.
d. What rate of administration, in mL/h, should the pharmacist
recommend during the 6-hour infusion segment? e. Calculate the rate of administration in (d) in drops/minute with an
administration set that delivers 15 drops/mL. f. Calculate the milligrams of drug administered by slow infusion
over the 6-hour segment. g. Make the same calculation as that in (f) but over the 18-hour
segment.
Monoclonal antibodies (mAbs) infusion calculations
Monoclonal antibodies (mAbs) are used in the diagnosis and treatment of various diseases. In general, mAbs are dosed on the basis of body weight or body surface area and are administered by injection or infusion. Table 13.4 presents some examples of mAb infusions.
TABLE 13.4 EXAMPLES OF MONOCLONAL ANTIBODIES (mAbs) ADMINISTERED BY INTRAVENOUS INFUSION
a
Stated usual doses/rates are for illustration; actual clinical doses/rates are
determined based on individual patient parameters.
1. In preparing an infusion of the drug trastuzumab, a pharmacist adds 20
mL of bacteriostatic water for injection to a vial containing 420 mg of the mAb. The resulting solution contains trastuzumab, 21 mg/mL. Using the information from Table 13.4, (a) calculate the milliliters of solution required for the loading dose for a 165-lb patient. The pharmacist then transfers the calculated volume into an infusion bag containing 250 mL of sodium chloride injection. Calculate (b) the quantity of trastuzumab administered in mg/min and (c) the drip rate, in drops/minute, using an administration set that delivers 20 drops/mL.
a. Weight of patient: 165 lb × 1 kg/2.2 lb = 75 kg
Loading dose in mg: 75 kg × 4 mg/kg = 300 mg
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b. 300 mg/90 min = 3.33 mg/min c. Volume of infusion: 250 mL + 14.29 mL = 264.29 mL
Example calculations derived from a product label
The following calculations are derived from the product label for CLEOCIN PHOSPHATE, shown in Figure 13.6.
FIGURE 13.6 Label of product used in intramuscular and intravenous solutions. (Source: https://dailymed.nlm.nih.gov/dailymed/drugInfo.cfm? setid=05a75685-0af5-407c-ac57-e380c882b49d. Courtesy of Pfizer, Inc.)
1. According to the package insert, a solution of clindamycin for
intravenous infusion should not exceed a concentration of 18 mg/mL. On this basis, calculate the minimal volume of infusion, which may be prepared from the entire contents of the vial.
2. If the contents of the vial are added to 50 mL of D5W and an infusion
administered over a 20-minute period of time, calculate the clindamycin administered in (a) mg/mL and (b) mg/min.
a. 4 mL (vial) + 50 mL D5W = 54 mL, total volume
600 mg/54 mL = 11.11 mg/mL
b. 600 mg/20 min = 30 mg/min
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3. If a pediatric patient weighing 12 lb is to receive clindamycin at the rate
of 20 mg/kg/day in three equally divided doses, calculate the contents of the vial, in milliliters, which may be used as an additive for a single dose.
PRACTICE PROBLEMS
Calculations of Basic Intravenous Infusion Solutions
How many grams each of sodium chloride and dextrose are present in a 1000-mL IV bag of 0.18% w/v sodium chloride and 4% w/v dextrose?
A medication calls for 1000 mL of D5W½NSS to be administered over 8 hours. Calculate the quantity, in grams, each of dextrose and sodium chloride administered in a 20-minute period.
Calculations of Infusion Time
If a standard microdrop infusion set is used to administer 100 mL of an infusion over a 2-hour period, calculate the rate of delivery, in drops/min.
A patient was administered 150 mL of D5W at a rate of 25 mL/h. If the infusion was begun at 8 AM, at what time was it completed?
A patient received 500 mL of D5W½NS at a rate of 15 drops/min. If the administration set used delivered 15 drops/mL, calculate the
infusion time in hours, minutes. A pediatric patient received 50 mL of an infusion at 10 drops/min
with an administration set that delivered 60 drops/mL. Calculate the duration of the infusion in minutes.
An intravenous drip contains 2 g of lidocaine HCl (XYLOCAINE) and is administered at a rate of 4 mg/min. Calculate the total time, in minutes, for the complete infusion.
Calculations of Intravenous Infusions with Additives
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Daptomycin (CUBICIN), 4 mg/kg, is recommended for administration over a 30-minute period by intravenous infusion in
0.9% sodium chloride. How many milliliters of a vial containing 500 mg of daptomycin in 10 mL should be added to a 100-mL bag of normal saline in treating a 165-lb patient?
An emergency syringe contains lidocaine, 1 g/5 mL. How many milliliters should be used in preparing 250 mL of an infusion to contain 4 mg/mL of lidocaine in D5W?
A fluconazole injection contains 400 mg of fluconazole in 200 mL of normal saline injection for infusion. Calculate the concentration of fluconazole in mg/mL.
Intravenous immunoglobulin (IVIG) has been administered in the pretransplantation of organs at a rate of 0.08 mL/kg/min. Calculate the number of milliliters administered to a 154-lb patient over a period of 4 hours.
If 200 mg of dopamine in 250 mL D5W is administered to a 145-lb patient, at 15 mL/h, how many mcg/kg/min is the patient receiving?
A pharmacist receives a medication order for 300,000 units of penicillin G potassium to be added to 500 mL of D5W. The directions on the 1,000,000-unit vial state that if 1.6 mL of solvent is added, the solution will measure 2 mL. How many milliliters of the solution must be withdrawn and added to the D5W?
A physician orders 2 g of an antibiotic to be placed in 1000 mL of D5W. Using an injection that contains 300 mg of the antibiotic per 2 mL, how many milliliters should be added to the dextrose injection in preparing the medication order?
An intravenous infusion for a patient weighing 132 lb calls for 7.5 mg of amikacin sulfate per kilogram of body weight to be added to 250 mL of 5% dextrose injection. How many milliliters of an amikacin sulfate injection containing 500 mg/2 mL should be used in preparing the infusion?
Lidocaine injection may be administered by continuous intravenous infusion to treat cardiac arrhythmias at a dose of 2 mg/min. Solutions for intravenous infusion may be prepared by the addition of 1 g of lidocaine hydrochloride to 1 L of 5% dextrose in water. Calculate the maximum duration of this infusion in minutes.
A medication order calls for acyclovir, 355 mg, to be administered by intravenous infusion over 60 minutes. A 500-mg vial of acyclovir is available that must be mixed with sterile water for injection to prepare 10 mL of injection. The proper amount is then admixed with 100 mL of normal saline solution. Calculate (a) the volume to be taken from the vial of mixed acyclovir, (b) the rate of infusion in mL/min, and (c)
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the drops/minute if using an intravenous set that delivers 20 drops/mL.
A medication order for a 20-lb pediatric patient calls for vancomycin, 10 mg/kg, to be administered by intravenous infusion. The pharmacy has a 10-mL injection containing 500 mg of vancomycin. The pharmacist adds the correct amount to a 100-mL bag of normal saline solution. (a) How many milliliters of the injection were added and (b) what is the content of vancomycin in the infusion, in mg/mL?
Various Calculations of Infusions Including Drip Rates
A medication order calls for a dopamine drip at 5 μg/kg/min for a 185-lb patient. The pharmacy adds 400 mg dopamine in 250 mL of D5W. Calculate the drip rates per minute when using administration sets delivering (a) 15 drops/mL, (b) 20 drops/mL, and (c) 60 drops/mL.
A physician orders 4 L of intravenous fluids for a dehydrated patient to be administered over a period of 24 hours using an intravenous set that delivers 15 drops/mL. Calculate the drip rate in (a) drops per minute and in (b) milliliters per hour.
How many milliliters of an injection containing 1 g of drug in 4 mL should be used in filling a medication order requiring 275 mg of the drug to be added to 500 mL of D5W solution? If the solution is administered at the rate of 1.6 mL/min, how many milligrams of the drug will the patient receive in 1 hour?
A physician orders a 2-g vial of a drug to be added to 500 mL of D5W. If the administration rate is 125 mL/h, how many milligrams of the drug will a patient receive per minute?
The drug labetalol has a dose of 300 mg and is administered in 300 mL of an intravenous infusion at a rate of 2 mg/min. Using an infusion set that delivers 20 drops/mL, calculate the required drip rate in drops/minute.
A physician orders 35 mg of amphotericin B and 25 units of heparin to be administered intravenously in 1000 mL of D5W over an 8-hour period. In filling the medication order, the available sources of the additives are a vial containing 50 mg of amphotericin B in 10 mL and a syringe containing 10 units of heparin per milliliter.
a. How many milliliters of each additive should be used in filling the
medication order?
b. How many milliliters of the intravenous fluid per minute should the
patient receive?
A solution containing 500,000 units of polymyxin B sulfate in 10 mL of sterile water for injection is added to 250 mL of 5% dextrose injection. The infusion is to be administered over 2 hours. If the
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administration set delivers 15 drops/mL, at what rate, in drops per minute, should the flow be adjusted to administer the infusion over the designated time interval?
Five hundred milliliters of a 2% sterile solution of a drug are to be administered by intravenous infusion over a period of 4 hours. If the administration set delivers 20 drops/mL, at what rate, in drops per minute, should the infusion flow? Solve the problem by calculation and by using the nomogram in this chapter.
An 8-kg infant requires a continuous infusion of a drug to run at 1 mL/h to deliver 4 mcg of drug/kg/min. Calculate the milligrams of drug that must be added to a 100-mL intravenous infusion solution.
At 8:30 AM a patient begins receiving 1000 mL of D5NS solution containing 25 mEq of sodium lactate at a rate of 60 mL/h. At 1:00 PM an order is received in the hospital pharmacy instructing to increase IV fluids to 85 mL/h. At what time exactly should the next container of solution be started, assuming that the rate on the existing container was changed at 1:00 PM?
A hospital pharmacist prepared thirty 100-mL epidural bags containing 0.125% of bupivacaine hydrochloride and 1 μg/mL of fentanyl citrate in 0.9% sodium chloride injection. How many (a) 30­mL vials of 0.5% bupivacaine hydrochloride, (b) 20-mL vials of 50 μg/mL of fentanyl citrate, and (c) 1-L bags of 0.9% sodium chloride were required?
An intravenous fluid of 1000 mL of lactated Ringer’s injection was started in a patient at 8 AM and was scheduled to run for 12 hours. At 3 PM, 800 mL of the fluid remained in the bottle. At what rate of flow should the remaining fluid be regulated using an IV set that delivers 15 drops/mL to complete the administration of the fluid in the scheduled time?
If a physician orders 5 units of insulin to be added to a 1-L intravenous solution of D5W to be administered over 8 hours, (a) how many drops per minute should be administered using an IV set that delivers 15 drops/mL, and (b) how many units of insulin would be administered in each 30-minute period?
A patient is to receive 3 μg/kg/min of nitroglycerin from a solution containing 100 mg of the drug in 500 mL of D5W. If the patient weighs 176 lb and the infusion set delivers 60 drops/mL, (a) how many milligrams of nitroglycerin would be delivered per hour, and (b) how many drops per minute would be delivered?
Using the nomogram in Figure 13.5, determine the approximate rate of infusion delivery, in drops per minute, based on 1.5 liters of fluid to be used over a period of 8 hours with an infusion set calibrated to deliver 16 drops/mL.
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The drug alfentanil hydrochloride is administered by infusion at the rate of 2 μg/kg/min for anesthesia induction. If a total of 0.35 mg of the drug is to be administered to a 110-lb patient, how long should be the duration of the infusion?
The recommended maintenance dose of aminophylline for children 1 to 8 years old is 1.01 mg/kg/h by IV infusion. If 10 mL of a 25­mg/mL solution of aminophylline is added to a 100-mL bottle of dextrose injection, what should be the rate of delivery, in milliliters per hour, for a 40-lb child?
A patient is to receive an infusion of a drug at the rate of 5 mg/h for 8 hours. The drug is available in 10-mL vials containing 8 mg of drug per milliliter. If a 250-mL bottle of D5W is used as the vehicle, (a) how many milliliters of the drug solution should be added, and (b) what should be the flow rate in milliliters per minute?
A patient is receiving 500 mL of an intravenous drip containing 25,000 units of sodium heparin in sodium chloride injection. Calculate (a) the administration rate, in mL/h, to deliver 1200 units of sodium heparin per hour and (b) the administration rate, in drops/minute, with an IV set that delivers 15 drops/mL.
A 50-mL vial containing 1 mg/mL of the drug alteplase is added to 100 mL of D5W and administered intravenously. How many milliliters per hour should be given to administer 25 mg of the drug per hour?
If the loading dose of phenytoin in children is 20 mg/kg of body weight to be infused at a rate of 0.5 mg/kg/min, over how many minutes should the dose be administered to a 32-lb child?
A pharmacist prepares an intravenous infusion containing 1 g dobutamine in 250 mL of D5W. An IV pump is programmed to deliver 10 mcg/kg/min to a 209-lb patient. Calculate the flow rate in mL/h.
If a medication order calls for a dobutamine drip, 5 μg/kg/min, for a patient weighing 232 lb, what should be the drip rate, in drops per minute, if the 125-mL infusion bag contains 250 mg of dobutamine and a microdrip chamber is used that delivers 60 drops/mL?
At what rate, in milliliters per hour, should a dose of 20 μg/kg/min of dopamine be administered to a 65-kg patient using a solution containing dopamine, 1.2 mg/mL?
A pharmacist places 5 mg/mL of acyclovir sodium in 250 mL of D5W for parenteral infusion into a pediatric patient. If the infusion is
to run for 1 hour and the patient is to receive 500 mg/m2 BSA, what would be the rate of flow in milliliters per minute for a patient measuring 55 cm in height and weighing 10 kg?
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