Veterinary Medical Math and Dosage Support

Drug dosages are typically provided in mg/kg format, stating how many milligrams of drug a patient should receive for each kg of body weight. In order to determine a patient’s dose, use the following formula:

Patient’s dose (mg) = weight (kg) × dosage (mg/kg)

Example: The veterinarian diagnoses a 23 lb dog with a bacterial skin infection. She asks you to send the dog home with two weeks of cefpodoxime at a dose of 10 mg/kg once daily. What tablet size should you send home, how many tablets should you include, and what should you print on the medication label?

1. First, convert the dog’s weight from pounds to kg:
   (23 lbs) / (2.2 lbs/kg) = 10.5 kg
2. Next, multiply the dog’s weight (in kg) by the medication dosage:
   (10.5 kg) x (10 mg/kg) = 105 mg

Cefpodoxime comes in both 100 mg and 200 mg tablets. You should send the dog home with fourteen 100 mg tablets, with a label that states “Give one tablet by mouth every 24 hours.

The normal maintenance fluid rate for small animal patients is 50-60 ml/kg/day. Intravenous fluid pumps, however, typically require you to enter a fluid rate in terms of milliliters per hour. In order to connect a patient to a fluid pump for the administration of maintenance fluids, you must determine how many mls of fluid the patient needs in a 24-hour period, then divide the daily fluid requirement by 24 (the number of hours in a day) to determine the hourly fluid rate.

If you wanted to create an equation to solve for ml/hr, that equation would look like this:

Maintenance fluid rate (ml/hr) = [patient’s weight (in kg) x 50-60 ml/kg/day] / [24 hrs/day]

In reality, however, it’s probably easier to just think through this problem, instead of writing out a full equation.

Example: A 25 kg dog requires maintenance fluid therapy. What ml/hr rate should be entered into the fluid pump?

1. First, calculate the patient’s 24-hr requirement:
   (25 kg) x (55 ml/kg/day) = 1375 ml/day
2. There are 24 hours in a day, so use this fact to convert ml/day to ml/hr:
   (1375 ml/day) / (24 hrs/day) = 57 ml/hr

Therefore, you should enter a fluid rate of 57 ml/hr into the fluid pump.

In a dehydrated patient, fluid therapy must take into account the patient’s degree of dehydration, in addition to providing for the patient’s maintenance fluid rate. Fluid deficits are typically corrected over a 24-hour period.

Example: The 25 kg dog in the example above is 8% dehydrated. What ml/hr fluid rate should be used for the first 24 hours of IV fluid therapy?

1. As calculated above, the dog’s maintenance fluid rate is 1375 ml/day or 57 ml/hr.
2. Next, calculate the quantity of fluids that must be given to correct dehydration.
   (25 kg) x (0.08 dehydration) = 2 kg water deficit
3. One kg of water is one L of water, therefore:
   2k water deficit = 2L water deficit = 2000 ml water deficit
4. In order to obtain the fluid rate needed to correct dehydration, convert 2000 ml of water per day into ml/hr:
   (2000 ml) / (24 hrs/day) = 83 ml/hr
5. Finally, add the maintenance fluid rate and the rate needed to correct dehydration:
   83 ml/hr + 57 ml/hr = 140 ml/hr

Therefore, a fluid rate of 140 ml/hr will ensure that the dog’s maintenance requirements are met and that the dog’s fluid deficit is corrected within the first 24 hours.

In many cases, dextrose or other substances must be added to IV fluids for a particular patient. The easiest equation to use for this type of calculation is the following:

C1V1 = C2V2

In this equation, C1 and V1 represent the starting concentration and volume, while C2 and V2 represent the final concentration and volume.

Example: A 3 kg hypoglycemic puppy requires a 2.5% dextrose solution for IV fluid administration. You have a 1L bag of LRS and a bottle of 50% dextrose. How much dextrose should you add to the fluid bag?

In this example, C1 is the original dextrose concentration (50%), V1 is the dextrose volume to be added, C2 is the desired dextrose concentration (0.025%), and V2 is the total volume of fluids.

1. Plugging the numbers that we know into the equation gives us:
   (50%) x (ml dextrose) = (2.5%) x (1000 ml)
2. Dividing both sides by 50% to rearrange the equation gives:
   ml dextrose = (2.5%) x (1000 ml) / (50%) = 50 ml dextrose
3. The only tricky thing to remember in this calculation is that you want 50 ml of dextrose in a final volume of 1000 ml. Therefore, you can’t add 50 ml of dextrose directly to the 1L LRS bag.
   First, remove 50 ml of LRS, then replace that 50 ml of LRS with dextrose. This will result in a final volume of 1L in the fluid bag

When calculating a CRI, it’s important to think through the problem in a logical, stepwise fashion. If you know the rate at which you want the patient to receive a particular drug and you know how long the patient’s fluid bag will last, you can determine how much of a particular drug should be added to the fluid bag in order to deliver the drug at your desired rate.

Example: A 10 kg dog requires a ketamine CRI at a dose of 0.5 mg/kg/hr. You would like to add the ketamine to a 1L bag of LRS, which you will administer at a maintenance rate of 23 ml/ hr.

How much ketamine (100 mg/ml) should you add to the fluid bag?

1. First, determine how much ketamine (in mg) the dog needs to receive every hour:
   (0.5 mg/kg/hr) x (10 kg) = 5 mg/hr
2. Next, determine the volume of ketamine (in ml) the dog needs to receive every hour:
   (5 mg/hr) / (100 mg/ml) = 0.05 ml/hr
3. Now, determine how many hours the dog’s bag of IV fluids will last:
   (1000 ml) / (23 ml/hr) = 43.5 hours
4. Finally, calculate how much ketamine needs to be added to the bag of IV fluids, in order to last the entire 43.5 hours?
   (0.05 ml/hr) x (43.5 hrs) = 2.2 ml

Therefore, you should remove 2.2 ml from the bag of fluids and replace it with 2.2 ml ketamine, in order to ensure that the dog receives a 0.5 mg/kg/hr ketamine CRI.

Whether a pet is hospitalized or you are providing an owner with instructions for at-home feeding, there will be times that you need to calculate a pet’s resting energy rate.

The first step to calculating nutritional requirements is to calculate the pet’s resting energy requirement (RER), according to the following equation:

RER = 70 x (body weight in kg)0.75

The RER is then multiplied by 1.0-1.6, depending on the pet’s reproductive status (altered pets < intact pets, lazy pets < active pets).

Example: A 10 kg spayed female dog presents for her annual wellness visit and you note that she has gained some weight since last year. She is not yet overweight, but you want to ensure that she does not gain additional weight. What is a good estimate of how many calories per day her owners should be feeding?

1. First, calculate the dog’s RER:
   RER = 70 x (10)0.75 = 70 x 5.6 = 394 kcal/day

Given that the dog is altered and is prone to gaining weight, the lower end of the multiplication factor range should be used. If the owner is instructed to feed RER x 1.0 to RER x 1.2, a range of 394-472 kcal should be recommended.