Knowledge Check: 5 Medical Math Questions for Vet Students

While you may be able to use apps and online calculators for much of the math that you perform on a regular basis, the truth is that both the NAVLE^® and your vet school courses will require you to understand how to perform a variety of calculations without those aids. 

Take this chance to test your knowledge!

1. A 24 kg female spayed Labrador Retriever mix presents for a skin exam. You note that the dog has areas of alopecia and severe pruritus. You perform a skin scrape and are surprised to see a live Sarcoptes scabiei mite in your field of view.
   
   After reviewing the dog’s medical history and the drug options available in your practice, you opt to treat the dog with subcutaneous ivermectin injections at a dose of 0.3 mg/kg.
   You pull the ivermectin bottle from the shelf and see that it has a concentration of 1%. How much ivermectin do you draw up for this patient?
   
   a) 0.2 ml
   b) 0.7 ml
   c) 2.6 ml 
   d) 7.2 ml 

Explanation: 

First, determine how many milligrams of ivermectin you need to administer:  

(24 kg) x (0.3 mg/kg) = 7.2 mg  

Next, determine the volume of ivermectin that is required to deliver 7.2 mg of the drug. Begin by converting the concentration of ivermectin as a % (w/v) to mg/ml:

1% = (1 g) / (100 ml) = (1000 mg ) / (100 ml) = 10 mg/ml 

Now that you’ve found the concentration of ivermectin in mg/ml, you can calculate how much ivermectin to draw up for injection: 

(7.2 mg) / (10 mg/ml) = 0.72 ml

2. You are treating a patient with mild hypoglycemia and you want to ensure that her IV fluids contain 7.5% dextrose. How much 50% dextrose should you add to a 1L fluid bag, in order to create 7.5% dextrose?
   
   a) 50 ml
   b) 100 ml
   c) 150 ml
   d) 200 ml 

Explanation: 

When performing drug dilutions, use the equation C₁V₁ = C₂V₂. In this example, C₁ is the original dextrose concentration (50%), V₁ is the dextrose volume to be added (your unknown), C₂ is the final desired dextrose concentration (7.5%), and V₂ is the final volume of fluid in the bag (1000 ml). 

Plugging the numbers we know into the equation gives us:

(50%) x (ml dextrose) = (7.5%) x (1000 ml)

Divide both sides by 50% to rearrange the equation, then solve:

ml dextrose = (7.5%) x (1000 ml) / (50%) = 150 ml dextrose

Therefore, you will remove 150 ml of LRS from the fluid bag and then add 150 ml of 50% dextrose to the fluid bag. 

3. You are treating an 8 kg dog and would like to administer a ketamine CRI at a dose of 0.5 mg/kg/hr. You will add ketamine to a 1L bag of LRS, which will be delivered at a maintenance rate of 20 ml/hr. How much ketamine (100 mg/ml) should you add to the 1L fluid bag?
   
   a) 0.5 ml
   b) 2.0 ml
   c) 4.0 ml
   d) 6.5 ml  

Explanation: 

Your first goal is to determine how much ketamine (in ml) the dog needs to receive every hour. 

Begin by calculating the dog’s hourly dose in mg:   

(0.5 mg/kg/hr) x (8 kg) = 4.0 mg/hr

Next, determine the volume of ketamine (in ml) that the dog should receive each hour: 

(4.0 mg/hr) / (100 mg/ml) =  0.04 ml/hr 

Now, you need to determine how much ketamine to add to the bag to deliver the ketamine at 0.04 ml/hr. Start by determining how many hours the dog’s bag of IV fluids will last: 

(1000 ml) / (20 ml/hr) = 50 hours

Finally, calculate how much ketamine you need to add to the bag, in order to ensure the dog receives 0.04 ml/hr for 50 hours: 

(0.04 ml/hr) x (50 hrs) = 2.0 ml

You will remove 2.0 ml of fluids from the bag and add 2.0 ml ketamine, to ensure that the dog receives a 0.5 mg/kg/hr ketamine CRI when the fluids are delivered at 20 ml/hr. 

4. While performing an exam on a newly-adopted 5 yo MN Boxer mix, you note that the dog has a BCS of 5/9. The owner says the dog is always hungry, so she is worried she may be underfeeding him and wonders if she needs to increase his food. Bloodwork is within normal limits and a fecal exam shows no evidence of parasites. The dog currently weighs 26.5 kg and his owner reports that he is “a lazy couch potato” at home. Approximately how many calories per day do you recommend feeding this dog?
   
   a) 400 kcal/day
   b) 600 kcal/day
   c) 900 kcal/day
   d) 1200 kcal/day

Explanation: 

To calculate the dog’s caloric requirements, you must first calculate the dog’s Resting Energy Requirement. Use the following equation: 

RER = 70 x (26.5)^0.75 = 70 x 11.7 = 819 kcal/day

The RER should then be multiplied by a multiplication factor of 1.0-1.6, depending on the dog’s reproductive status and activity level. Because this dog is neutered and relatively lazy, you use a multiplication factor of 1.1: 

819 kcal/day x 1.1 = 900.9 kcal/day

Therefore, you recommend that the owner feed approximately 900 kcal (or “calories”) per day. 

5. You are working on a team that is developing a new blood test for feline intestinal lymphoma. You perform the new lymphoma blood test on 100 cats, with 59 of the cats testing positive. Your team then performs surgical biopsies on each cat. Seventy cats were diagnosed with biopsy-confirmed lymphoma; 56 of those cats received positive results on your test and 14 cats received false-negative results on your test. Thirty cats were negative for lymphoma on intestinal biopsies; 27 of those cats tested negative on your test and 3 cats tested positive. What is the sensitivity of your new blood test for feline lymphoma?
   
   a) 59%
   b) 72%
   c) 80%
   d) 85%

Explanation: 

Use the following equation to calculate sensitivity:

Sensitivity = (Number of True Positives) / (Total Number of Affected Animals) x 100

In this case, histopathology is currently regarded as the gold standard for the diagnosis of feline intestinal lymphoma. Therefore, any animal with evidence of lymphoma on biopsy is regarded as an “affected animal.”

Plugging in the numbers obtained in your study results in the following:

Sensitivity = (56 true positives) / (70 cats with lymphoma) x 100 = 80%