Deductive methods
Calculating the dose to be given to a patient can be determined in different ways. Methods include proportion, reasoning, and dosage formula. It is good to verify the correctness of the calculation result with another method of reasoning. In medication calculations, results are always rounded down. This avoids dangerously large medication doses for patients.
Reasoning
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The amount of medication to be given to the patient can be calculated when the prescribed amount of the active ingredient and the amount of the active ingredient in the medication solution or tablet are known. In examples 3 and 4, the amounts of paracetamol tablets and ibuprofen solution to be given to patients were determined.
Formulas for the strength and concentration of the medication can be used to assist in reasoning:
for solid medications:
The text on the side of the medicine package tells you the strength of the medicine in the package (Primaspan 100 mg/tablet, Paracetamol 500 mg/capsule).
for liquid medicine
The concentration of the medicine is written on the side of the bottle (Ibuprofen 100 mg/5 ml).
Example 5.
The patient has been prescribed Elvanse 60 mg in the morning. How many capsules should you give the patient when the capsule strength is 20 mg?
Picture File:Elvanse 20 mg depot capsules finnish packaging.jpg - Wikimedia Commons
Decide on the dose to be given to the patient: multiplying the strength of 20 mg/capsule by three, i.e. 3 x 20 mg, gives 60 mg. So give the patient 3 capsules in the morning.
Picture File:Elvanse 20 mg depot capsules finnish packaging.jpg - Wikimedia Commons
Decide on the dose to be given to the patient: multiplying the strength of 20 mg/capsule by three, i.e. 3 x 20 mg, gives 60 mg. So give the patient 3 capsules in the morning.Example 6.
Anna has been prescribed 2 mg of morphine by injection. How much solution do you put in the syringe when the label on the Morphine bottle says 10 mg/ml?
Now the concentration of the Morphin solution is 10 mg/ml, i.e. the active substance (morphine) is 10 mg in one millilitre of solution. Since the dose prescribed for Anna is less than 10 mg, the volume of solution to be given must also be less than 1 ml.
Reasoning the amount of solution to be injected:
Conclusion: 0.2 ml of solution is taken into the syringe.
| solution (ml) | active substance(mg) | |
| 1 | 10 | |
| 0,5 | 5 | |
| 0,2 | 2 | |
Proportion
There is a direct correlation between the amount of active substance and the number of tablets or drug solution. In other words, the more tablets or drug solution a patient is given, the more active substance the patient will receive. Similarly, the fewer tablets or solution of the drug that is given to the patient, the less active substance the patient will receive.
Since the quantities of tablets or drug solution change in proportion to the amount of the active substance, quantities can be tabulated and compared. Let the unknown (x) denote the dose administered to the patient.
Now let's calculate the amount of morphine given in Example 6 by multiplication. Record the amounts in the table:
The proportion is obtained by writing the columns as fractions. The calculation can be solved by normal equation solving rules (here x cannot be 0, but the dose is of course always greater than 0):
You can also solve the proportion problem by cross-referencing:
1. Multiply the numerator of the first ratio (superscript) by the denominator of the second ratio (subscript), and also the denominator of the first ratio by the numerator of the second ratio. Both inputs give the same value, resulting in a new equation that is the same as the original equation.
2. Divide the equation by the coefficient of the unknown variable.
The result is ml (two tenths of a millilitre) i.e. 0.2 ml. 0.2 ml of morphine solution is therefore injected into the syringe.
It is a good idea to check the result obtained by comparison with some other method of reasoning, for example the reasoning in the previous example.
| solution (ml) | ||
| in the bottle | 10 | 1 | |
| given to the patient | 2 | x |
Dosage formula
The dose to be given can also be calculated using a direct formula. This method of reasoning is called dose formula calculation. The answer to the calculation is the dose to be given to the patient, i.e. the amount of medicine to be taken at one time, either in tablets/capsules or in millilitres of drug solution.
As tablets:
As solution:
Let's calculate the amount of morphine with the dose formula. The amount of active drug prescribed for Anna is now 2 mg and the concentration of the drug solution is 10 mg/ml. Let's place the values in the dosage form :
This means that Anna is given a millilitre dose of the medicine, or 0.2 ml.