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Medical Math for Veterinary Technicians

1 Liter = 10dL = 1000mL      0.001Kg = 1 gram = 1000mg = 1,000,000mg (mcg)

1 tsp = 5mL                            1 tbsp = 15mL                       1Kg = 2.2lbs

At 4^o degrees Celsius, 1 cubic centimeter (cc) of water = 1mL = 1gm

1 ounce is approximately 28gm                        

• Dog – 66mL/kg/day (30mL/lb/day) 
• Cat – 50-60mL/kg/day

• Dog – 90mL/kg 
• Cat – 65mL/kg

• This means the conversion from one unit to another.

• Basically it is a matter of canceling out like units.

• To calculate, divide the amount you want to give (250mg) by the concentration (100mg/ml)
• 250mg Abx ÷ 100mg Abx/mL solution = 2.5mL solution
• or to look at it another way:
• 250mg ABx  X  1mL/100mg = 2.5ml

• To Calculate, divide the amount of KBr (2000mg) by the intended concentration (250mg/ml) to get the volume
• 2000mg KBr ÷ 250mg/ml  KBr = 8mL solution
• or to look at it another way:
• 2000mg KBr X 1mL final solution/250mg KBr = 8mL solution

• 20kg x 66mL/kg/day x 1day/24hours = 55mL/hour
• Step 1- multiple dog's weight (20kg) X maint rate 66ml/kg =
• Step 2- divide total fluids for day by 24 hours to get rate/hr

To convert 5% (gm/dl)  to mg/mL:  5gm/dL x 1000mg/gm x 1dL/100mL = 50mg/mL

•    So a 5% solution = 5gm/dL = 50mg/mL

Problem: Make a 2.5% dextrose solution in a 500mL bag of saline. (Base stock of dextrose is 50%)

• Step 1 – How much dextrose do you need?

                2.5%  = 2.5gm/dL x 1000mg/gm x 1dL/100mL = 25mg dextrose/mL solution x 500mL solution =

12500mg

• Step 2 – How many mL of base stock do you need?

                50% = 50gm/dL x 1000mg/gm x 1dL/100mL = 500mg/mL stock concentration

                12500mg dextrose x 1mL stock/500mg dextrose = 25mL stock solution 

This means to make a 2.5% dextrose solution in a 500mL bag, you need to add 25mL of 50% dextrose.  (Technically you should first remove 25mL of saline out of the 500mL bag before adding the 25mL of dextrose so that your final solution is 500mL and not 525mL.  If you don’t, your solution will be slightly less than 2.5%)

If you have a 15drop/mL set, how many drops/second do you need to run an animal at 30mL/hr?

   Step 1 – How many mL/sec?

                30mL/hr x 1hr/60minutes x 1minute/60seconds = 0.0083mL/sec

   Step 2 – How many drops/second?

                0.0083mL/sec x 15drops/mL = 0.125drops/sec = 1 drop every 8 seconds

• Dosages tend to be given in either mg/kg/day or mg/kg/min (micrograms)

• 1000 mg = 1 mg

CRI Problem #1.

 If you have a vomiting 48kg dog and want to give him the high end dose of metoclopramide in a CRI, how many mL of metoclopramide should you add to a 1L bag of LRS to run the dog at 150mL/hr? (Dose of metoclopramide is 1-2mg/kg/day.  10mg/2mL stock solution.)

    Step 1 – How many mg of metoclopramide do you need per hour?

                48kg x 2mg/kg/day = 96mg/day x 1day/24hours = 4mg/hr

   Step 2 – How many mg metoclopramide do you need per mL of LRS?

                4mg/hour x 1hr/150mL = 0.0267mg metoclopramide/mL LRS

   Step 3 – How many mg metoclopramide per liter of LRS?

                0.0267mg/mL LRS x 1000mL/L = 26.7mg metoclopramide

   Step 4 – How many mL of stock solution do you need?

                26.7mg metoclopramide/L LRS x 2mL stock/10mg metoclopramide = 5.33mL stock /L LRS

If you have a 5kg cat who has a low blood pressure, how much dopamine should you add to a 250mL bag of saline to make a dopamine drip of 5mg/kg/min if you run the fluids at 5mL/hr?  Dopamine dose for blood pressure elevation is 2-10mg/kg/min (up to 15mg/kg/min for shorter duration).  Stock solution is 200mg/5mL.

    Step 1 – How many mg of dopamine do you need per hour?

                5kg cat x 5mg/kg/min x 60min/hour = 1500mg/hr

   Step 2 – How many mg/mL of dopamine do you need?

                1500mg/hr x 1mg/1000mg x 1hr/5mL = 0.3mg dopamine/mL saline

   Step 3 – How many mg dopamine in a 250mL bag?

                0.3mg dopamine/mL saline x 250mL saline = 75mg dopamine

   Step 4 – How many mL of stock solution do you need?

                75mg dopamine x 5mL stock/200mg dopamine = 1.875mL stock solution in a 250mL bag

To sum up: If you add 1.875mL of dopamine to a 250mL bag of saline, you get a dosage of 5mg/kg/min when run at 5mL/hour for a 5kg cat.

(Note: this also means that for this particular bag that every XmL/hr you run the solution at = Xmg/kg/min in a 5kg patient.  So if the blood pressure is still low and you want to increase the dopamine dose to 8mg/kg/min, you don’t have to recalculate the CRI.  You can just increase your fluids to 8mL/hr.)

• To do this, you would calculate an animal’s 24 hour needs and add that to a 240mL bag of fluid.

• Take 10mL out of a 250mL bag to = 240ml.  This way you could run the fluids at 10mL/hr. 

For example, you have a 30kg dog post-op from a splenectomy.  Calculate a CRI of lidocaine for him, using a dose of 50mg/kg/min, to control his ventricular tachycardia.  Your lidocaine is 2%.

    Step 1 – How many mg per minute do you need?

                30kg x 50mg/kg/min = 1500mg/min x 1mg/1000mg = 1.5mg/min

   Step 2 – How many mg per day do you need?

                1.5mg/min x 60min/hour x 24hours/day = 2160mg/day

   Step 3 – How many mL of lidocaine should you add to the 240mL bag to run the bag at 10mL/hr?

                2160mg x 1mL/20mg = 108mL

• This sounds like a lot but you should remove a total of 118mL from a 250mL bag and add 108mL lidocaine (2%) in order to get a total of 240mL final solution.  Then at 10mL/hr the dose is 50mg/kg/min.  To titrate up or down, every 5mL/hr = 25mg/kg/min.

15 x mass of patient (in kg) = # of mg drug to add to a 250mL bag such that when you run that solution at 15mL/hr you are administering a dose of 15mg/kg/min.  (This means that if you want a dose of 10mg/kg/min, change the rate to 10mL/hr.)

A 20kg dog presents to your clinic with a PCV=15%.  How many mL of packed red cells (Assume 100% per volume even though it really is not.) do you need to raise the dog’s hematocrit to 25%?

   Step 1 – What is the dog’s blood volume? (Formula in ‘Conversions’ section)

                20kg x 90mL/kg = 1800mL blood volume

   Step 2 – What is the volume of existing red cells in the dog?

                1800mL x 15%(0.15) = 270mL

   Step 3 – What is the red cell volume desired?

                1800mL x 25%(0.25) = 450mL

   Step 4 – Required red cell mass. (Desired – Existing)

                450mL – 270mL = 180mL

 So if you assume that pRBC’s have a hematocrit = 100% you need 180mL.

A 4kg cat presents to your clinic with a PCV=11%.  How many mL of whole blood (Assume PCV=50%) do you need to raise the cat’s hematocrit to 20%?

   Step 1 – What is the cat’s blood volume? (Formula in ‘Conversions’ section)

                4kg x 65mL/kg = 260mL

   Step 2 – What is the volume of existing red cells in the cat?

                260mL x 11%(0.11) = 28.6mL

   Step 3 – What is the red cell volume desired?

                260mL x 20%(0.20) = 52mL

   Step 4 – Required red cell mass. (Desired – Existing)

                52mL – 28.6mL = 23.4mL

   Step 5 - Required whole blood.

                23.4mL/50%(0.50) = 46.8mL

 In other words, the cat needs 23.4mL of red cells but since whole blood is only ½ red cells you need twice as much, 46.8mL.

1)       You’ve been running a dog on LRS with 20mEq KCl/L at 50mL/hr for 6 hours. (You started with a liter bag)  Now, the doctor asks you to check blood glucose.  BG=60 so he asks you to place the dog on a 5% dextrose drip in LRS.  You don’t want to throw the bag away, so how many mL of 50% dextrose do you need to add to turn the existing bag into a 5% solution? 

2)       Calculate a CRI of Reglan for a dog weighing 66lbs. (Use 2mg/kg/day and a rate of 75mL/hr)

3)       Calculate a CRI of dopamine at 10mg/kg/min for a cat weighing 15.4lbs.  Use a rate of 5mL/hr.

4)       A 50kg dog presents with a PCV=12%.  Calculate a pRBC transfusion (Assume 90%) needed to raise the hematocrit 10 points.

ANSWERS:

1)       70mL (Technically you should remove 70mL from existing bag before adding the dextrose)

2)       6.66mL of Reglan in a one Liter bag

3)       5.25mL of dopamine in a 250mL bag (Note every XmL/hr = 2Xmg/kg/min, so if you run the pump at 4mL/hr you are getting 8mg/kg/min for a 7kg cat.)

4)       500mL of pRBC’s