Medical Math - Constant Rate Infusion

A Constant Rate Infusion (CRI) is utilized to administer a continuous dose of drug in intravenous fluids. Review specific calculations and examples from Megan Brashear, CVT, VTS (ECC)   for administering multiple drugs in intravenous fluids.

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A Constant Rate Infusion (CRI) is utilized to administer a continuous dose of drug in intravenous fluids. We are most used to CRIs for pain management, as in this form the drug can be maintained at effective plasma concentrations for the duration of treatment and avoid pain peaks and valleys. CRIs are also utilized for blood pressure management medications, electrolyte supplementation, GI motility medications, anesthesia, and insulin administration. Drugs can be administered without dilution, calculated to be mixed in to IV fluids running at a pre-determined rate, or prepared to be titrated to different rates depending on patient needs.

Calculations for Fluids Running at a Pre-Set Rate

If the drug is to be added to fluids running at a set rate, you will need to know:

  • The dose for the CRI (like mg/kg/day)
  • The concentration of the drug
  • The hourly fluid rate

For example, a 17 kg dog has fluids running at 65 ml/hr. You are asked to make a metoclopramide (5 mg/ml) CRI at a dose of 1 mg/kg/day. How many ml of metoclopramide do you add to a liter of fluids that will run at 65 ml/hr?

17 kg x 1 mg/kg/day = 17 mg metoclopramide/day

(1mg/kg/day means the dog needs 17mg/day (24 hours) of metoclopramide)

 

17 mg/day ÷ 24 hr/day = 0.7 mg metoclopramide/hr

 

1000 ml/L ÷ 65 ml/hr = 15.4 hr/L

(1000ml in a liter ÷ hourly fluid rate = hours of fluids in liter)

 

15.4 hr/L x 0.7 mg metoclopramide/hr = 10.8 mg metoclopramide/L

(hours of fluids in liter x drug dose per hour = medication needed per liter of fluids)

 

10.8 mg metoclopramide/L ÷ 5 mg metoclopramide/ml = 2.16 ml metoclopramide

(drug dose ÷ drug concentration = drug dose needed in total fluids)

 

If you add 10.8 mg metoclopramide (5mg/ml) to 1 liter of fluids running at 65 ml/hr, a 17 kg dog will receive 1 mg/kg/day of metoclopramide

 

This calculation should be taken one step further to determine how many milligrams of metoclopramide are in each milliliter of fluid so if the fluid rate changes the dose is known. If the dog’s fluid rate is changed to 75 ml/hr, how much metoclopramide is the dog receiving?

10.8 mg metoclopramide ÷ 1000 ml = 0.0108 mg metoclopramide/ml

(mg of medication added  ÷  ml of fluid it is added to = dose per ml of fluid)

 

0.0108 mg metoclopramide/ml x 75 ml/hr = 0.81 mg metoclopramide/hr

(mg of medication needed per ml of fluid x fluid rate = dose per hour)

 

0.81 mg metoclopramide/hr x 24 hr/day = 19.44 mg metoclopramide/day

(dose per hour x hours in a day = dose per day)

 

19.44 mg metoclopramide/day ÷ 17 kg = 1.14 mg metoclopramide/kg/day

(dose per day ÷ patient weight in kg = dose for patient weight in kg per day)

 

This new dose of 1.14 mg metoclopramide/kg/day can be compared to the therapeutic dose for metoclopramide and steps taken as needed to ensure patient safety.

 

Calculations for Titratable CRIs

Some CRIs are calculated to be titratable, meaning the dose of drugs is changed by adjusting the fluid rate until the appropriate response from the patient is reached. There is often a dose range as opposed to a set dose per hour. These CRIs will be created and managed separate from the IV fluids as the rate may need to be changed frequently. A simple way to approach these calculations is to make the CRI so that if it runs at 1 ml/hr, the patient receives 1 mcg/kg/hr (or 1 mcg/kg/min, depending on the drug dosage). If this is how the CRI is calculated, the math is done prior to the rate change and adjustments can be made quickly. Because 1 ml/hr = 1 mcg/kg/hr, a fluid rate of 4 ml/hr will deliver 4 mcg/kg/hr. A fluid rate of 9 ml/hr will deliver 9 mcg/kg/hr. Doses can be quickly changed without needing to perform more math equations. For example:

A 21 kg dog has been hit by a car and needs pain management administered as a CRI. You are asked to calculate a fentanyl (50 mcg/ml) CRI and place the patient at 3 mcg/kg/hr of fentanyl with the ability to titrate the dose as needed. You plan on making this CRI in a 60 ml syringe of NaCl and delivering it on a syringe pump.

 

1ml/hr needs to = 21 mcg fentanyl/hr (the patient weighs 21kg, so you want 1ml/hr to deliver 21mcg/hr)

 

60 ml x 1 ml/hr = 60 hr

(amount of total fluids x hourly fluid rate = hours of CRI)

 

21 mcg fentanyl/hr x 60 hr = 1260 mcg fentanyl

(hourly dose x hours of CRI = drug dose)

 

1260 mcg fentanyl ÷ 50 mcg fentanyl/ml = 25.2 ml fentanyl

(drug dose ÷ drug concentration = drug dose needed in total fluids)

 

Run the CRI at 3 ml/hr to deliver 3 mcg/kg/hr to the 21kg dog

 

Because the equation used 60 ml as the total amount of fluids in the CRI (including the drug you are adding), the total amount of fluids and drug in the syringe must be 60 ml. Prior to adding any drug, you must remove an equal amount of fluid from the syringe or bag of fluids. In this case, 25.2 ml of fentanyl is added to 34.8 ml of NaCl equaling a total volume of 60 ml. The label on the syringe should read:

Fentanyl 1260 mcg qs 60 ml NaCL

(The “qs” means quantity sufficient, meaning the entire volume of drug and NaCl is 60 ml)

 

Some drugs are dosed as mcg/kg/min. Dobutamine is one such drug. The dose needed is titrated up depending on patient response and weaned down as improvement is seen. Having this CRI calculated so that 1 ml/hr = 1 mcg/kg/min will make frequent dose changes a simple process and prevent complicated math each time the dose is changed.

A 4.5 kg cat has been battling hypotension and you are asked to calculate a dobutamine (12.5 mg/ml) CRI and then start administering 2 mcg dobutamine/kg/min to the cat. For ease of titrating, you will make the CRI so that 1 ml/hr = 1 mcg/kg/min. You will be making the CRI in a 100 ml bag of NaCl.

1 ml/hr needs to = 4.5 mcg/min (the patient weighs 4.5 kg, you want 1 ml/hr to deliver 4.5 mcg/min)

 

4.5 mcg/min x 60 min/hr = 270 mcg/hr

(because your fluid rate is in ml/hr, you must convert your dose into mcg/hr)

 

270 mcg /hr  ÷ 1000 mcg/mg  = 0.27 mg /hr

(because your drug concentration is in mg/ml, you must convert mcg /hr to mg /hr)

 

100 ml ÷ 1 ml/hr = 100 hr

(total fluid bag ÷ hourly fluid rate = hours per fluid bag)

 

0.27 mg dobutamine/hr  x 100 hr = 27 mg dobutamine/100 ml

(hourly dose x hours per fluid bag = drug dose)

 

27 mg dobutamine ÷ 12.5 mg/ml = 2.16ml dobutamine needed

(drug dose ÷ drug concentration = dose of drug to be in total fluids)

 

Run the CRI at 2 ml/hr to deliver 2 mcg dobutamine/kg/min to the cat

 

The equation used 100 ml as the total amount of fluids needed including the drug we are adding. From the 100 ml bag, remove 2.16 ml of NaCl then add 2.16 ml of dobutamine. Label the bag:

Dobutamine 0.27 mg qs 100ml NaCl

 

With small patients or those that cannot tolerate high rates of intravenous fluids, it may not be appropriate to run a CRI at 10 or 15 ml/hr. In those patients it may be better to calculate their CRI so that 1 ml/hr = 10 mcg/kg/min, or 1 ml/hr = 5 mcg/kg/hr. The remainder of the math remains the same.

Calculating CRIs can seem intimidating, and these preparations need special care and attention paid, but the benefit to the patient makes it worth the work. It is important when administering a CRI to ensure that all medications going through the fluid line (including any that are injected separately, like bolus pain management or antibiotics) are compatible. Drugs like metoclopramide, lidocaine, and morphine will need to be protected from light if they are to be hung for more than 24 hours. Constant Rate Infusions must be labeled with the drug name, the drug dose per milliliter, the time and date the CRI was mixed, and the initials of the person who created the CRI. The fluid bag must be labeled as well as noting the dose and calculation in the medical record. It is vital that CRIs are calculated correctly, as incorrect doses administered over multiple hours can be detrimental and even deadly to patients. Once a CRI is utilized, the fluid rate should be checked at least every four hours and matched to the dose ordered by the medical record.

When in doubt, double check your calculations and always clearly label all CRIs. Practice makes perfect; use the following CRI orders to practice your new found skills in CRI calculations.

 

Test Your Knowledge:

  1. You are asked to make a 1 mg/kg/day metoclopramide (5 mg/ml) CRI for a patient that weighs 12 kg. The fluids are running at 45 ml/hr. How many milliliters of metoclopramide will you add to a full liter of fluids for this patient?
  2. You are asked to make a 1.5 mg/kg/day metoclopramide (5 mg/ml) CRI for a patient that weighs 5.5 kg. Their fluid rate is 15 ml/hr. How many milliliters of metoclopramide will you add to a full liter of fluids for this patient? If their fluid rate is increased to 20 ml/hr how many mg/kg/day of metoclopramide will they be receiving?
  3. You are asked to make a dopamine (40 mg/ml) CRI for a 24 kg dog. For ease of dosing, you need to make the CRI so that 1 ml/hr = 1 mcg/kg/min. You will be making the CRI in 250 ml NaCl. How many milligrams of dopamine will you qs to 250 ml NaCl?
  4. You are asked to make a fentanyl (50 mcg/ml) CRI for a 7 kg cat. For ease of dosing, you need to make the CRI so that 1 ml/hr = 1 mcg/kg/hr. You will be making the CRI in 100 ml NaCl. How many micrograms of fentanyl will you qs to 100 ml NaCl?

Answers:

  1.   2.2 ml
  2.   4.53 ml added to the liter, 1.97 mg/kg/day metoclopramide
  3.   360 mg (9ml)
  4.   700 mcg (14ml)

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