IV - mg/kg/min

 Adult medications that are dosed by weight include vasopressors & oncology chemotherapeutic agents.  In pediatric medication, dosage by weight is common as is the need to calculate maximum safe dose. Another calculation closely related, are doses based on Body Surface Area (BSA). This page discusses only adult medications.  Although the math is the same with pediatric doses, there are other issues that warrant this a separate topic. I have not provided a BSA example. However,  you can do BSA problems by replace Mg/Kg with Mg/m² in examples below.

Example 1 - 2 step method

Your patient has had poor urinary output (< 30cc/hr) for the second shift in a row.  The patient is able to take PO fluids and has adequate intake. They have stable VS's. You update the managing physician and they want the patient started on dopamine at a renal dose of 4ug/kg/min.  Your patient weights 65kg. Pharmacy supplies the dopamine in a concentration of 400mg/250cc.

We know:
Our ordered dose - 4ug/kg/min
Our available form - 250ml
Our available dose - 400mg
Our Patients weight - 65kg

How do we calculate the IV rate?  The simplest way is to use a two step approach: calculate our dose and then use that dose to calculate the rate. This keeps the arithmetic simple.  We can do this as a single step problem but we end up doing fractional arithmetic. Let's do the 2 step method first.

 

The first thing to calculate is how much drug we need for our ordered dose. The order is for ug, so we start with that:

 

 

Our first factor we'll get from our ordered dose. Since we are only interested in the amount of drug, we will ignore the per minute portion of the order for this. We add the first factor orienting it so the drug weight unit is in the same position as what we want to know:

 

 

 

And then multiply by our patients weight oriented it so the patient weight unit is opposite:

 

 

We can see all units except what we want to know cancel, so solve:

 

 

 

We now replace 4ug/kg in our ordered dose with the calculated dose of 260ug:

Our calculated ordered dose is 260ug/min.  Now we calculate the IV rate. Since we will be programming the IV pump with ml/hr, we start with that:

 

 

Our first factor will be the thing we know that has ml in it oriented so ml is in the same position:

 

 

And multiply by our calculated ordered dose orienting it so the drug's unit of weight is opposite :

 

 

We can see we will need a conversion factor for mg<>ug.  Also, since we have hours on the left of the equation & minutes on the right, we need a conversion factor for hr<>min.  Lets add that one next:

 

 

And then our conversion factor for mg<>ug orienting it so the units are opposite:

 

 

Lets go through and cancel the rest of the units to make sure the only units remaining are the same as what we want to know:

 

 

They are, so we can finish canceling and solve:

 

 

When initiating this drip, the patient should be on a monitor.  And we will need to do frequent vital signs at least until we are sure the patient is stable and tolerating the medication.

When administering this drip, we will need a fractional IV pump. What if we don't have one? Or if the pump only allows specifying 0.1ml increments? What dose would we be giving the patient if we ran the drip at say, 10ml/hr instead of 9.75? Since we have our factor-label hats on, we can easily figure it out.

Example 2 - 1 step method

Let's do the same rate calculation again only this time we will not pre-calculate our dose. We are programming the IV pump, so we begin with ml/hr :

 

 

 

 

 Our first factor will be something we know that has a common unit, oriented in the same position:

 

 

 

 

 Next we multiply by our ordered dose orienting it so the drug unit weight is opposite.

 

 

 

 

Looking at our units, we have a volume and time on the left side of the equation, but we have a volume, a time and TWO weights on the right. We know that mg<>ug will cancel (because we have one on top & one on bottom), but we still have that extra weight to get rid of. Is there any "unused" known that has weight in it?  Yes - the patients weight.  Add that factor, writing it so the units are opposite.

 

 

 

 

 

 

Another look at our factors - we have hours on the left & minutes on the right so we need a conversion factor for hr<>min. Lets add that oriented the units so they are opposite.

 

 

 

 

Lets go through and cancel the units to see if we need anything else remembering we want only the same units on both sides:

 

 

 

 

We still have extra mg & ug on the right side. Since one is a denominator & one is a numerator we can add a conversion factor to get rid of them. Add that orienting so units are opposite.

 

 

 

 

 

Now we can cancel and solve:

 

 

 

 

 

Using the one step method isn't difficult.  Personally,  I prefer to avoid the fractions.

 

©1997-2006 Dale Sampson, RN