# Calculating Infusions of Analgesic and Anesthetic Drugs

Updated: Jan 22

Your patient, Scruffy, is suspected to have pancreatitis. In addition to fluid resuscitation, you want to start her on analgesics as she seems very painful upon abdominal palpation. You want to use an opioid but don’t want her to vomit. In addition, you think that an opioid alone might not be enough and your colleague suggests adding ketamine. You decide to start fentanyl and ketamine infusions. What rate should you use? Do you need a loading dose? Should you just add these to the fluids? Would it be better to use separate syringe pumps? If you do decide to mix them together, how do you calculate the rate of the new solution?

When you give an IV bolus of a drug, plasma concentrations rise sharply and then decrease over time. In fact, the initial plasma concentration may be so high that undesirable side effects can occur. At the tail end, plasma concentrations may decrease below effective levels prior to the next dose. In order to avoid this peak and valley scenario, many analgesic and perioperative drugs are administered as a continuous infusion (often referred to as a Constant Rate Infusion or CRI by veterinary professionals*). Another reason continuous infusion may be employed is for drugs with a very short half life, like dopamine, such that bolus dosing would be logistically difficult.

How about a loading dose? With an infusion, it will take 5 half lives of the drug to get to 97% of the desired plasma concentration. For drugs with long half lives (eg morphine, lidocaine), it can take hours to reach effective plasma concentrations if you don’t administer a loading dose. Unless the half life of the drug is very short, a loading dose will be necessary in order to get to the desired plasma concentration quickly. Often, I use my loading dose as a co-induction agent in order to reduce the amount of IV propofol or alfaxalone and increase plasma concentrations of the drug I want to infuse quickly (for example "ketofol" = 2 mg/kg ketamine and 2 - 3 mg/kg propofol to effect). At the bottom of the post, I have included a table of suggested loading and infusion doses of commonly used perioperative drugs.

You need to make a few decisions when deciding to administer a drug infusion, including dose, dilution if any, and what type of equipment you will use. Syringe pumps are ideal because they allow you to administer a smaller volume with more precision. But what if you don't have a syringe pump? You can administer many infusions in a bag of fluids and use a fluid pump or – cautiously – even free drip while monitoring closely, with a few caveats. First, you may end up wasting more drug in order to get a reasonable concentration in the bag, especially with 1 L IV fluid bags. Diluting a drug into a bag of fluids will mean that the concentration will generally be lower than if you were using a syringe pump and therefore the fluid rate you are giving will be higher. Secondly, if you use the same bag as your main source of crystalloid fluids, you will not be able to bolus those fluids to address hypotension.

If you are piggybacking a drug infusion into a fluid line, whether with a syringe pump or fluid bag dilution, try to place the drug infusion as close to the catheter as possible to get it into the animal in a timely manner and avoid the risk of accidentally bolusing drug that is sitting in the fluid line.

**Now comes the tricky part: the math!**

There are lots of recipes and short cuts available for a variety of analgesic and other drug infusions but anyone administering these drugs should be able to quickly double check themselves and others by doing a little basic math. In addition, you greatly increase your choices for dilution, administration rate, and equipment if you can work your way through dimensional analysis.

The key is cancel out units to get from the dose you want to the volume or rate.

Let’s say you want to run the fentanyl for Scruffy at 3 mcg/kg/hr and the ketamine at 10 mcg/kg/min. You have decided that you will use a syringe pump and you want to mix them together. You decide not to dilute them beyond what you will be by mixing them.

First, figure out what infusion rate of each drug will provide that dose rate.

If you cancel out units that are in the numerator with those in the denominator, you will see that you are left with mL of fentanyl per hour.

You can now practice calculating a ketamine infusion:

Next, you can decide how many hours’ worth of infusion you want to make and mix those volumes together. You will then run the mixture at the combined rate. If you wanted to make 10 hours of the fentanyl/ketamine solution, you would mix 5.4 mL of fentanyl (0.54 mL/hr x 10 hr) with 0.54 mL ketamine (0.054 mL/hr x 10 hr) and run the mixture at 0.59 mL/hr (0.54 mL/hr fentanyl + 0.054 mL/hr ketamine = 0.59 mL/hr of the mixture).

Of course, some syringe pumps will do the math for you if you input the drug concentration and the weight of the animal but they usually aren’t able to handle infusions of multiple drugs in one syringe. If you have multiple syringe pumps, then you can absolutely keep each drug infusion separate.

Let’s calculate the same infusions as above but in a bag of fluids. First, you will need to choose what size bag and the fluid rate. Let’s say you want to use a 250 mL bag of Normosol-R and you have calculated a replacement and maintenance fluid rate of 45 mL/hr.

If you go through and cancel out the units, you see that you are left with mL of fentanyl.

Now that you feel comfortable calculating infusions, here’s a short cut I particularly like.