Question

Calculate the dosages as indicated. Use the labels where provided. Order: Dopamine \(400 \mathrm{mg}\) in \(500 \mathrm{~mL} 0.9 \% \mathrm{NS}\) to infuse at \(200 \mathrm{mcg} / \mathrm{min} .\) A volumetric pump is being used. Calculate the rate in \(\mathrm{mL} / \mathrm{hr}\).

Short answer

Infuse at 15 mL/hr.

Step-by-step solution

Convert the Ordered Dose to Milligrams per Minute

The order specifies a dose of 200 micrograms, which is equivalent to 0.2 milligrams per minute because there are 1000 micrograms in a milligram.

Calculate the Concentration of Dopamine in the Solution

The solution consists of 400 mg of dopamine in 500 mL of 0.9% Normal Saline. The concentration is therefore \( \frac{400 \, \text{mg}}{500 \, \text{mL}} = 0.8 \, \text{mg/mL} \).

Set Up the Proportion to Find the Infusion Rate

Given the concentration, use the proportion: \( 0.8 \, \text{mg/mL} = \frac{0.2 \, \text{mg}}{X \, \text{mL/min}} \). Solve this to find \( X \).

Solve the Proportion

Cross-multiply to solve for \( X \): \[ X = \frac{0.2}{0.8} = 0.25 \, \text{mL/min}. \]

Convert Milliliters per Minute to Milliliters per Hour

Since the pump requires the rate in mL per hour, multiply the mL/minute rate by 60: \[ 0.25 \, \text{mL/min} \times 60 \, \text{min/hr} = 15 \, \text{mL/hr}. \]

Key concepts

Drug Infusion

Infusing a drug means administering it directly into the bloodstream over a set period. This can be crucial for medications like dopamine, which need to maintain consistent levels for effectiveness. During drug infusion, healthcare providers set a specific rate at which the drug enters the patient's body. This ensures that the medication works as intended without causing harm due to sudden spikes or drops in concentration.

A drug infusion can be continuous, delivering a steady amount of medication, or intermittent, where the drug is given in intervals. The rate of infusion depends on the drug's properties and the patient's needs. In the exercise, dopamine is infused at 200 micrograms per minute. Calculating the mL/hr rate helps ensure that the infusion is safe and effective.

When infusing drugs, consider factors like:

• Correct dosage based on medical order.
• Patient's condition and response to the medication.
• Equipment accuracy and reliability, like using a volumetric pump.

Concentration Calculation

Calculating the concentration of a drug in a solution is a key step in ensuring the correct dosage is administered. Concentration is often expressed as milligrams per milliliter (mg/mL), indicating how much of the drug is present in each mL of solution.

For our exercise, the concentration of dopamine needs to be calculated from the given solution of 400 mg of dopamine in 500 mL of normal saline. This boils down to finding out how concentrated the drug is in the solution:

• Use the formula: \( \text{Concentration} = \frac{\text{Amount of Drug in mg}}{\text{Total Volume in mL}} \)
• Substituting the values: \( \frac{400 \text{ mg}}{500 \text{ mL}} = 0.8 \text{ mg/mL} \).

This concentration helps in setting up the infusion rate, as it gives a precise measurement needed to calculate how much of the solution delivers the required drug dosage.

Proportion Method

The proportion method is a powerful tool in dosage calculations. It helps to solve problems where ratios are involved, especially in determining how much of a solution is needed to meet a certain dosage.

In this exercise, we have the concentration from the previous section and need to find out how many mL per minute will provide the ordered dose of 0.2 mg. Setting up a proportion is straightforward:

• The concentration is \( 0.8 \text{ mg/mL} \).
• The desired dose is \( 0.2 \text{ mg/min} \).

The equation becomes: \( 0.8 \text{ mg/mL} = \frac{0.2 \text{ mg}}{X \text{ mL/min}} \). By cross-multiplying, we find \( X \), the volume needed per minute.

Solving \( X = \frac{0.2}{0.8} \) gives \( X = 0.25 \text{ mL/min} \). This demonstrates how the proportion method converts drug dosage into practical infusion settings.

Volumetric Pump Usage

A volumetric pump is an essential tool for precise drug delivery, permitting healthcare providers to maintain an accurate and continuous infusion rate. When using a volumetric pump, it is vital to set the rate properly to ensure patient safety and medication effectiveness.

In this exercise, you’ve calculated that 0.25 mL/min is the required rate. However, pumps usually require the rate to be input as mL/hr, making conversion necessary:

• Multiply the mL/min rate by 60 to convert to mL/hr: \( 0.25 \text{ mL/min} \times 60 \text{ min/hr} = 15 \text{ mL/hr} \).

This means setting the pump to infuse 15 mL/hr to deliver the exact amount of dopamine required per minute to the patient.

Volumetric pumps offer advantages like:

• Accurate delivery of medication.
• Adjustable settings to meet specific patient needs.
• Ease of monitoring and adjustments.