pharm math
Titration: Dosages
spacer spacer Calculating Dosage ("unit of measure"/kg/min):

Key elements:

  • Flow rate must be given.
    • This is expressed as cc or ml/hr.
  • Time is constant (60 min/hr).
  • Weight of the client is expressed in kilograms.
  • Concentration of the infusion.
    • When using a dosage of mcg/kg/min, the end concentration must be expressed in mcg/ml.  (Convert mg to mcg).

      • Rule is: To calculate, one must have like amounts in dose and concentration.
      Rule:  Use the kilogram factor only if kg is in the ordered dose or the drug is reported in mcg/kg/min.  Otherwise, you omit the kg factor from the formula.
Formula to calculate dosage:
       
      Rate (ml/hr) X Concentration ("unit"/ml)
      Time (60 min/hr) X weight in kilograms
Example:

A client is receiving dopamine at 12 ml/hr.  The solution hanging indicates "D5W 250 ml/200 mg dopamine".  The client weighs 133 lbs.  What is the dosage (mcg/kg/min) the client is receiving?

Critical information:
  • Flow rate: 12 ml/hr
  • Solution:  200 mg dopa / 250 cc D5W
  • Client's weight:  133 lbs
Tip
1)  Convert wt to kg.  133 / 2.2 = 60.45 kg
2)  Find concentration of dopamine in 1 cc. 
 
200 mg
250 ml
=
x mg
1 ml
250x
=
200
x
=
0.8

3) Concentration is 0.8 mg/ml.  Convert mg to mcg.

0.8 (mg)  X 1000 (mcg per 1 mg) = 800 mcg /ml

Now that you have gathered all the information, plug it into the formula.

 
12 (ml/hr)   X  800 ("unit"/ml)
(Time) 60 min/hr  X  60.45 (weight in kgs)
=
9600
3627
X
=
2.65
The dosage the client is receiving is 2.65 mcg/kg/min.
.
timing IV Calculating Dosage (amount/hr)

Sometimes you may be asked to calculate how much of a medication the client is receiving per hour via a continuous drip.

Example:

A client is receiving a heparin drip at 22 ml/hr via an infusion pump.  The label on the liter bag of D5W indicates 40,000 U of heparin.  How many units of heparin does the client receive per hour?
Critical information:
  • Flow rate: 22 ml/hr
  • Solution:  L (1000 ml) D5W with 40,000 U heparin
1)  This does not follow the traditional "titration dosage" formula:
  • No weight is involved.
  • This is based on hourly delivery, not minutes, so time constant (60 min/hr) is not required.
2)  Set this up using ratio & proportion.
40,000 U
1000 ml
=
x U
22 ml
1000x
=
880,000
x
=
880
The client is receiving 880 U of heparin per hour.

 

If the problem had asked "How many units per minute is the client receiving?" then you could have used the formula without the kg component.
 

22 (Rate)  X  40 (U/ml)
60 (min/hr)
=
880
60
x
=
14.66 U/min
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01/2003
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