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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)
18.
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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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