11 Parenteral solutions and isotonicity
The intravenous (IV) route, when a drug is introduced directly into a vein, is a common method for patients to receive drug therapy. The IV route involves the drug being presented as a sterile aqueous solution. If the volume to be delivered is a few millilitres or less, the solution (normally termed ‘an injection’) is usually administered in one go. If the volume to be delivered is large, it will be administered over a period of time. Such a process is termed ‘intravenous infusion’. In order to deliver an IV infusion at a constant rate, a ‘giving’ or administration device consisting of an electrically driven pump will be used. The administration pump will be set to deliver a chosen number of drops or millilitres (mL) per minute or other unit of time.
With IV infusions, it may be necessary to calculate the volume of solution that is delivered over a period of time or the volume of solution that will deliver a known quantity of drug.
Calculations involving IV infusions may require the determination of the volume of drug solution delivered per period of time. This volume may be expressed as millilitres per minute or hour or the volume converted to drops per minute.
Example 11.1 One litre of 0.9% saline solution is to be given to a patient over a 6-hour period. If 20 drops = 1 mL, how many drops per minute should be administered?
The answer needs to be in minutes, so 6 hours is converted to 360 minutes.
The next stage involves calculating the number of drops in 1 litre, i.e. 1000 mL.
Let the number of drops be x . Setting up proportional sets:
number of drops x 20 volume of solution (mL) 1000 1
Therefore, there will be 20 000 drops in 1000 mL.
The infusion (of 20 000 drops) should take 360 minutes to complete. Let the number of drops per minute be y . Setting up proportional sets:
number of drops 20 000 y number of minutes 360 1
Round up 55.5 to 56
Therefore, the IV administration set should be set for 56 drops per minute.
For some IV solutions a recommended flow rate is given. In which case, it may be necessary to calculate the overall volume to be delivered and the drops per minute.
Example 11.2 The recommended flow rate for drug Y is at a concentration of Drug Y is supplied in 500-mg vials for dilution in glucose 5%. Using one vial of drug Y, what volume of glucose 5% solution should be used and how many drops per minute should be delivered if the flow rate is The IV administration set is calibrated to How long will the infusion take?
It is necessary to calculate the volume of glucose 5% required to produce a solution containing 5 mg of drug Y per mL. A vial of drug Y contains 500 mg.
Let the volume of solution required to contain y mL. Setting up proportional sets:
drug Y (mg) 5 500 volume of solution (mL) 1 y
Therefore, the vial of drug Y should be dissolved in sufficient glucose 5% to produce 100 mL of solution.
Knowing that the IV administration set produces x . Setting up proportional sets:
number of drops x 20 volume (mL) 3 1
3 mL is delivered in 1 minute so the IV infusion set should give a flow rate of 60 drops per minute.
Let the time taken to administer 100 mL of infusion solution be t minutes. Setting up proportional sets:
time (minutes) t 1 volume (mL) 100 3
Therefore, the time taken to deliver 100 mL is 33.3 minutes.
In some situations, two or more injection solutions may be combined and delivered by IV infusion over a known time period. In such cases it is important to remember that the total volume of all the injection solutions should be included in the calculation.
Example 11.3 20 mL of Addiphos solution and 10 mL of multivitamin infusion are added to 500 mL of glucose 5% solution. The resultant solution is to be administered over 4 hours. The administration set is calibrated to Calculate the number of drops per minute to be given if the patient is to receive all of the solution in the specified time.
The total volume of the infusion solution is:
Therefore, 530 mL of solution must be infused over 4 hours.
As we need to calculate the number of drops per minute, we will need to convert the total infusion time to minutes:
The administration set gives x . Setting up proportional sets:
number of drops 20 x volume (mL) 1 530
Therefore, 530 mL is equal to 10 600 drops.
10 600 drops of infusion solution will need to be delivered over 240 minutes.
Let the drops per minute required to deliver the infusion solution be y . Setting up proportional sets:
number of drops y 10 600 time (minutes) 1 240
Therefore, the infusion fluid should be infused at 44 drops per minute.
With some drugs, the IV administration is stated as the amount of drug, rather than the volume, to be infused over a specified time period.
Example 11.4 A 56 kg female patient requires amphotericin by IV infusion at a dose of The concentration of the final solution must not be more than A vial of amphotericin contains 50 mg. Calculate the dose of amphotericin and the volume of IV solution required by the patient if the solution contains the maximum concentration. If the solution has to be delivered in 2.5 hours, what is the rate in If a 50-mg vial is used to prepare the IV solution, what is the total volume of the solution prepared?
First the dose should be calculated.
Let the dose required be x . Setting up proportional sets:
amount of drug (micrograms) 250 x body weight (kg) 1 56
The patient requires a dose of 14 000 micrograms of amphotericin.
If the maximum concentration of amphotericin is
Let the volume required be z . Setting up proportional sets:
volume (mL) 1 z amount of drug (micrograms) 100 14 000
Therefore, the patient will need 140 mL of infusion fluid containing 14 000 micrograms of drug.
If the infusion has to be over 2.5 hours, then the rate of delivery must be calculated. Let the rate of delivery per minute be y . Setting up proportional sets and converting 2.5 hours to 150 minutes:
volume (mL) 140 y delivery time (minutes) 150 1
The delivery rate will be
Amphotericin is available in a vial containing 50 mg. The total volume to contain the amphotericin at a concentration of
Let the total volume be v and convert 50 mg to 50 000 micrograms. Setting up proportional sets:
volume (mL) 1 v drug (micrograms) 100 50 000
Therefore, the 50 mg of amphotericin needs to be dissolved in up to 500 mL of solvent, but only 140 mL will be administered to the patient.
The following example requires the infusion volume to be calculated.
Example 11.5 Phenytoin has a recommended dose of of body weight to be infused at a rate not exceeding Assume that the patient is a woman weighing 56 kg. Phenytoin injection is available in 5-mL ampoules containing The prescriber would like an infusion volume of 100 mL and a dose rate of . Is the prescriber’s request possible and, if so, what is the flow rate per minute?
It is necessary to calculate the recommended dose for the patient.
The patient weighs 56 kg and the dose is
Let the required dose be z . Setting up proportional sets:
dose (mg) 18 z weight (kg) 1 56
