Question

Calculate the dosages as indicated. Use the labels where provided. Order: Dopamine \(400 \mathrm{mg}\) in \(500 \mathrm{~mL}\) D5W to infuse at \(20 \mathrm{~mL} / \mathrm{hr}\). Determine the following: a. \(\mathrm{mg} / \mathrm{min}\) b. \(\mathrm{mcg} / \mathrm{min}\)

Short answer

a. 0.267 mg/min b. 267 mcg/min

Step-by-step solution

Calculate mg/hour

First, calculate how many mg of dopamine are administered per hour. You need to know how much dopamine is present per mL. Since the order is for dopamine 400 mg mixed into 500 mL of D5W, the concentration is \( \frac{400 \, \text{mg}}{500 \, \text{mL}} = 0.8 \, \text{mg/mL}\). At the infusion rate of 20 mL per hour, the drug delivery rate in mg/hour is \(20 \, \text{mL/hr} \times 0.8 \, \text{mg/mL} = 16 \, \text{mg/hr}\).

Convert mg/hour to mg/min

Now, convert the hourly dosage to a per minute dosage. Since there are 60 minutes in an hour, divide the hourly rate by 60: \( \frac{16 \, \text{mg/hr}}{60 \, \text{min/hr}} = 0.2667 \, \text{mg/min}\).

Convert mg/min to mcg/min

To convert milligrams per minute to micrograms per minute, multiply by 1000 (since 1 mg = 1000 mcg). Thus, \(0.2667 \, \text{mg/min} \times 1000 = 266.7 \, \text{mcg/min}\).

Key concepts

Drug Infusion Rate

Understanding drug infusion rates is crucial for healthcare professionals to ensure that patients receive the correct dosage of medication in a controlled manner. The infusion rate refers to the speed at which a drug is administered intravenously over a specific period of time. Medications like dopamine, which require precise dosing, are typically given at a constant rate through an intravenous line. This ensures that the drug maintains its efficacy without causing adverse effects. When calculating the infusion rate, it is important to know the concentration of the medication, which is usually expressed in terms of the amount of drug per volume of solution, such as mg/mL. Knowing the ordered infusion rate (e.g., 20 mL/hr) allows nurses to calculate the actual amount of drug delivered per hour and per minute, which is often necessary for drugs that have a narrow therapeutic range.

Medication Administration

Medication administration involves more than just giving a drug to a patient; it involves understanding the correct method for delivering medication to ensure safety and effectiveness. Healthcare providers must consider the route of administration, such as intravenous, oral, or inhalation, which influences how fast the drug acts and its duration of action. For drugs requiring precise dosing like dopamine, intravenous administration is common due to its quick onset and ability to maintain steady levels of medication in the bloodstream. The five rights of medication administration (right patient, right drug, right dose, right route, right time) are fundamental but understanding the context, like how a drug is diluted or the rate at which it infuses, also plays a significant role. Consistent, accurate dosage calculation ensures patient safety and optimal therapeutic outcomes.

Unit Conversion

Unit conversion is a critical skill in healthcare settings, ensuring that healthcare providers can accurately administer medications. Drugs may be ordered in one unit of measure (such as mg) and need to be converted to another (such as mcg) to align with equipment settings or specific medical protocols. In the context of the dopamine example, conversion from mg to mcg is necessary since the infusion pump settings might require the rate in mcg/min for precision. It’s essential to know the basic conversion factors, such as 1 mg equaling 1000 mcg, and how to apply these appropriately. Unit conversion applies not only to drug doses but also to time, volume, and other physical units associated with medication administration, ensuring calculations are both accurate and actionable.

Nursing Math

Nursing math involves applying basic mathematical skills to solve problems related to medication dosages, IV drip rates, and more. This is a fundamental aspect of nursing practice, ensuring that nurses can provide safe and effective patient care. Nurses use math to calculate the correct dosage based on factors like patient's weight and the concentration of the drug solution. A systematic, problem-solving approach is used in nursing math, particularly for IV drug administration, where calculations determine how much medication a patient receives per minute or hour. In the given example, this involves using formulas to calculate the amount of medication delivered over time, converting between different units, and cross-checking work to avoid errors, ensuring the patient's safety and the treatment's efficacy.