Pharmaceutical calculations

What is reference of Pharmaceutical calculations.

1-Potency adjustment

2-LOD/Water adjustment

3- Batch calculation regarding quantity of API added in Master formula

Think of these calculations in logical order:

  1. Remove or account for the water
  2. Solve for the API you have left in the remaining chemical
  3. Decide if you need to correct for the salt in the chemical since the formula calls for the base
    

Remembering these three steps in this order will remind you that the salt base conversion is performed with the
molecular weights (MW) of the chemical without the water.
Calculation 1: Water Correction
Water (or LOD) is usually expressed as a percentage on the CofA, such as 7% water. This means that
proportionally every 100 mg of the chemical actually has 7.0 mg of water.
The water correction factor to apply is [(100-Water%)/100] g/g chemical. Let’s apply this formula to a theoretical
lidocaine HCl monohydrate lot we received where the CofA lists a water concentration of 7%. The water
correction factor would be: (100/(100-7.0)) = 1.075.
Even though you could get a pretty good estimate of the water correction factor by using the molecular weight
(MW) for those APIs that are hydrated, there are always small differences between that theoretical number and
an actual determination as reported in the CofA. Using the MW of lidocaine HCl monohydrate, the water factor
formula would look like this (288.81/(288.81-18)) = 1.066 and result in a difference of 0.009
Since USP allows lidocaine HCl monohydrate to have between 5% and 7% water, the most accurate correction
would therefore come from the CofA.
Calculation 2: Assay Correction
Calculate the amount of API in your chemical with the assay correction.
Most assays assigned in the CofA are
done after the water has been removed (on an anhydrous basis). In essence, the API is dried and then a chemical
analysis is performed on the chemical to determine the amount of pure API that is in the particular lot. Most
USP monographs only allow a very narrow band of acceptability, but there are cases where the acceptable range
can be quite large, especially in biologics and antibiotics.
Most of the time, the assay information given on the CofA is listed as a percentage, therefore, making it easier
to calculate. Sticking with the example chemical, lidocaine HCl monohydrate that we used above, let’s say the
actual assay was 98.0% (which is within the USP monograph range o
f 97.5% to 102.5%); this means that the API
has only .98 gm of API per gm of chemical. The correction factor to apply on your compounded preparation
should be (100/98.0) = 1.020.
Calculation 3: The Salt to Base Corrections
First determine what the prescription is requesting. Unfortunately, some prescribers do not take into account the
subtle and not so subtle differences in casual name and exact name of an API. If ever in doubt, always contact
the practitioner first and have the USP monograph on hand when discussing with them. As always make sure
you are labeling the prescription correctly. For example, don’t label a prescription lidocaine 1% if you made it
with 1% of the hydrochloride salt. Instead label it lidocaine HCl 1%.
Once you feel confident that the correct chemical is identified, the next step is to correct for the proper weight of
the chemical. This conversion is obtained by the MWs of the base and salt form of the API. The ratio of these two
MWs will provide the correction factor to apply.
Example using lidocaine HCl monohydrate: use the MW of the lidocaine (MW 234.32 g/mole) and the lidocaine
HCl (MW 270.80 g/mole), not the hydrated lidocaine HCl monohydrate (MW 288.81 g/mole). So if you
have lidocaine HCl monohydrate and need the lidocaine base, the conversion formula for the salt to base is
(270.80/234.32) = 1.156.
ow that you have these three calculations, all generated by your API’s CofA, you can continue on with
other calculations to further ensure the potency of your compounded preparation.
Chemical Weight = Remove Water, Correct for Assay and then Correct for Salt / Base (if needed).
Therefore: Chemical Weight = API Weight x Water Conversion x Assay Conversion x Salt Conversion (if
needed).
For the lidocaine HCl monohydrate to lidocaine base the result using the example above would be:
Weight Lidocaine HCl Monohydrate = Lidocaine API Weight Needed x 1.075 x 1.020 x 1.156 = Lidocaine
Weight Needed x 1.268
Using just the MW for the conversion would give us a theoretical result of:
Weight Lidocaine HCl Monohydrate = Lidocaine Weight Needed x (288.81/234.32) = Lidocaine Weight
Needed x 1.233
Just to further confuse matters, there are preparations that do not require a correction for the salt form or water
content of the chemical. The most notable being morphine sulfate injection, which is made with morphine
sulfate pentahydrate, and the potency of the injection is based on morphine sulfate pentahydrate. The USP
monograph for morphine sulfate injection specifies that it should contain not less then 90% and not more than
110% of morphine sulfate pentahydrate. So when compounding with this API you do not need to adjust for the
water content or the salt form of the chemical. Always consult the USP for the applicable monograph.
Since all these corrections will most likely need to be done for the same preparation, the corrections can be applied
in any order or in one step. However, in most cases you will need to take into account the chemical assay and the
water, either absorbed or in the chemical formula, to get the correct amount of the API in your preparation.

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