Comprehending Drug Concentrations and Dilutions
Bonjour! Every year, an unprecedented number of casualties result from errors made by medical staff in administering drugs based on faulty dilutions. Besides human error, a lack of standardized methods for the representation of drug concentrations, contributes significantly to this preventable morbidity and mortality. Today, I will very briefly be discussing, some of the basic rules for calculating drug concentrations & dilutions.
Drug concentrations, when put as percentages (%), either mean weight/weight (w/w %), weight/volume (w/v %), volume/volume (v/v %) or part/part percentages. Furthermore, the denominator in each of these fractions could either stand for the solvent, or the solution as a whole. So, suppose you see a dilution that says 1:1000 (or 1/1000) of 1% lidocaine, which of these fractions apply? To take the complexity up a notch, consider how many milligrams of epinephrine and lidocaine are contained in 50 mL of a 1:100,000 solution obtained by adding 0.1 mL of 1:1000 epinephrine to 10 mL of 1% lidocaine. Understandably, novices find such questions extremely frustrating enigmas.
The key to understanding (i) concentrations & (ii) dilutions, is to engrave in one’s mind the following conventional rules:
- Concentrations:- x % of a drug denotes x grams of the drug (or solute) in 100 milliliters of the solution. Eg. 1% lidocaine contains 1g of lidocaine in 100 mL of solution.
- Dilutions:- Anything represented in an x : y (eg. 1:1000) fashion, is x grams of drug (or solute) divided by y milliliters of solution. Eg. 1:1000 of an epinephrine solution contains 1g of epinephrine in 1000 mL of the solution.
Keeping these cardinal rules in mind, problems such as the above are a piece of cake. With them, you have blissfully attained nirvana! Let us now break down the second sample question:
0.1 mL of 1:1000 epinephrine contains 0.1 mg of epinephrine. 10 mL of 1% lidocaine contains 100 mg of lidocaine. By adding 0.1 mL of 1:1000 of epinephrine to 10 mL of 1% lidocaine, you are in effect adding 0.1 mg of epinephrine to 10 mL of solvent (in this case, lidocaine) with the resultant volume of solution being 10.1 mL. In other words, when you’ve done this, you will have gotten
0.1 mg of epinephrine in 10.1 mL solution
= 0.0001 g of epinephrine in 10.1 mL solution
= 1g of epinephrine in 101000 mL solution
Mathematically, the exact dilution thus obtained would therefore be 1:101000. This is approximately the same as a 1:100000 dilution, that we would’ve obtained had we dropped 0.1 mL from our 10.1 mL final solution volume value. So congratulations, you’ve now successfully made yourself ~ 10 mL of a 1:100000 solution of epinephrine using 1% lidocaine!
Again, because 10 mL of the solution contained 100 mg of lidocaine, 50 mL of such a solution would contain [100 x (50/10)] milligrams of lidocaine = 500 mg lidocaine.
Similarly, because 1:100000 epinephrine solution means 1g of epinephrine in 100000 mL solution, 50 mL such a solution would contain [1 x (50/100000)] grams of epinephrine = [1 x (50/100000) x 1000] milligrams = 0.5 mg of epinephrine.
Seeing how easy this is, you can now dabble around with quirky questions such as:
- How many milligrams of epinephrine are present in 100 mL of a 1:35000 preparation? (Hint:- 1:35000 means 1g of epinephrine in 35000 mL of solution.)
- 5 mL of 1:1000 epinephrine is added to 10 mL of anesthetic solution. What is the resultant dilution of the final preparation? (this is a modification of our sample question)
- Previously, we had a final solution volume of 10.1 mL and neglected the 0.1 mL (arriving at 1:101000 ≈ 1:100000) because it was too minuscule to make a difference. In the present case, the final solution volume comes to (5+10 =) 15 mL, which is significant enough to not ignore. 1:1000 epinephrine contains 1 mg per 1 mL of solution; 5 mL of solution would therefore contain 5 mg of epinephrine. So, this comes to 5 mg of epinephrine in 15 mL of final solution = 1 mg in 3 mL = 0.001 grams per 3 mL = 1:3000. See, it’s peace!
For more on concentrations and dilutions, you might want to look at an article from eMedicine.com here.
As you read your textbooks, you’ll come across drug dosages in some of these forms that ought to be remembered for applying to patients. Before you mindlessly swallow such information, take a step back and check to see if everything adds up. Know whether using an approximation in the calculations is likely to significantly alter your results and if that could affect your treatment. I happened to come across numerous errors from a pediatrics textbook that our school prescribes, namely “Essentials of Pediatrics by O.P. Ghai 6ed” with regard to concentrations & dilutions. As an example, Table 7.2 under ‘Neonatal Resuscitation’ says that 1:10000 epinephrine, which is the concentration that’s needed for neonates, can be prepared by adding 0.5 mL of 1:1000 epinephrine in 5 mL of solvent (in this case water or something similar such as saline). Although this might be due to a typographical error in the book, the approach is clearly flawed. In having done so, what you would’ve gotten would be 0.5 mg of epinephrine in a 5.5 mL preparation = 0.0005 mg in 5.5 mL preparation = 1:11000 dilution. Given a neonate’s low body weight and the average listed dosage as 0.2 mL/kg, this doesn’t affect the final dosage the patient receives much, only reducing it by 0.002 mg/kg. Such an error would’ve been unacceptable had the patient been of a considerably larger body weight, as in a massive adult, so as to cause small decimal errors to add up to significantly larger ones. You could easily have obtained a 1:10000 dilution by adding 0.5 mL of 1:1000 epinephrine to 4.5 mL of solvent in your garden-variety 5 mL syringe.
With that, you’ve come to the end of this post. Readers are welcome to send in their comments. Until my next piece, adieu!!
Just a thought:- Einsteinian physics holds that in the enormous space-time fabric, you, I and everything else in the universe are traveling at the ‘speed’ of light!! Relative to a given frame of reference, that is. Some of this speed goes into our movement in ‘space’ while the rest of it goes into our movement through ‘time’. And because we only have a limited amount of speed (namely ‘c’ or the speed of light), the faster we move through space, the slower our speed through time becomes as seen from that frame of reference and/or observer. If you had to celebrate your birthday with your family in 6 months earth time, but couldn’t physically be with them on earth because you had to attend to a mission on the international space station for the present year, your family would celebrate your birthday later than you would on the station as seen from their frame of reference! To them, your clock ticks slower than theirs. That’s because the ISS & its crew move faster through space than humans on earth. Read more on the time dilation phenomenon here and here.
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