Problem 17 - Calculate With Confidence

Question

Calculate the dosages as indicated. Use the labels where provided. Order: \(1 \mathrm{~g}\) of aminophylline in \(1,000 \mathrm{~mL}\) D5W to infuse over \(10 \mathrm{hr}\). Calculate the dosage in \(\mathrm{mg} / \mathrm{hr}\) the client will receive.

Step-by-Step Solution

Answer

The client will receive 100 mg/hr of aminophylline.

Step 1: Convert grams to milligrams

The order is to infuse 1 gram of aminophylline over 10 hours. Since dosage is usually measured in milligrams, first convert 1 gram to milligrams. Since 1 gram equals 1,000 milligrams, you have 1,000 mg of aminophylline.

Step 2: Determine the infusion rate per hour

To find out how much aminophylline is infused per hour, divide the total amount of aminophylline by the total infusion time in hours. This is done by the calculation: \(\frac{1,000 \, \text{mg}}{10 \, \text{hours}} = 100 \, \text{mg/hr}.\)

Step 3: Conclude the dosage

The calculated dosage is the infusion rate at which the client will receive aminophylline over the duration of the infusion.

Key Concepts

Understanding Aminophylline

Aminophylline is a medicine used in medical settings primarily to help breathing. It's a derivative of theophylline, which is a bronchodilator that helps to relax and open air passages in the lungs, making it easier for patients to breathe. This is why aminophylline is often used in cases where patients are experiencing symptoms like asthma attacks or chronic obstructive pulmonary disease (COPD).

In the exercise, aminophylline is administered to a patient through an intravenous (IV) infusion, ensuring the drug is delivered directly into the bloodstream for immediate effect. It's important for healthcare providers to calculate the correct dosage to ensure effectiveness while minimizing potential side effects. Hence, accurate dosage calculations, like converting measurements and determining infusion rates, are key skills in administering aminophylline safely.

Calculating the Infusion Rate

The infusion rate is fundamental in medical settings as it helps determine how much medication a patient receives over a specific period. Wondering why it's crucial to calculate this rate accurately? It ensures that the patient gets the correct dosage continuously without any risk of under or overdose which can be harmful.

In our example, the aim is to administer 1,000 mg of aminophylline over 10 hours. To find out how much the patient receives each hour, divide the total milligrams by the total hours of the infusion:

• Infusion formula: \[\frac{\text{Total milligrams}}{\text{Total hours}} = \text{Infusion Rate} \]
• For aminophylline: \[\frac{1,000 \, \text{mg}}{10 \, \text{hours}} = 100 \, \text{mg/hr}\]

So, the patient receives 100 mg of aminophylline each hour during the 10-hour infusion period.

Mastering Unit Conversions

Unit conversions are essential in calculating dosages in medical practice. Medications are often distributed and measured in different units, making conversion skills necessary to ensure accuracy.

In the given exercise, the dosage of aminophylline is originally prescribed in grams, but medical doses are more commonly calculated in milligrams, particularly when determining rates like mg/hr. Knowing that

• 1 gram = 1,000 milligrams

helps to make these calculations straightforward.

It's vital to be comfortable with multiplying and dividing to switch between different units of measurement. Practicing these conversions can prevent errors, ensuring patients receive the appropriate amount of medication, which is crucial for their treatment success.