Question

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.A client is receiving lidocaine \(2 \mathrm{~g}\) in \(250 \mathrm{~mL}\) D5W. The solution is infusing at \(22 \mathrm{~mL} / \mathrm{hr}\). Calculate the following: a. \(\mathrm{mg} / \mathrm{hr}\) b. \(\mathrm{mg} / \mathrm{min}\)

Short answer

Aminophylline: 100 mg/hr; Lidocaine: 176 mg/hr and 2.93 mg/min.

Step-by-step solution

Understand the First Dosage Requirement

We need to calculate the dosage of aminophylline in mg/hr. Given: 1 g of aminophylline in 1000 mL D5W to infuse over 10 hours.

Convert Grams to Milligrams

Since there are 1000 mg in 1 gram, the total mass of aminophylline is 1000 mg.

Calculate Dosage Rate in mg/hr for Aminophylline

The infusion takes 10 hours, and there are 1000 mg of aminophylline. Therefore, the dosage rate is \( \frac{1000 \text{ mg}}{10 \text{ hours}} = 100 \text{ mg/hr} \).

Understand the Second Dosage Requirement

We need to calculate both the mg/hr and mg/min for lidocaine. Given: 2 g of lidocaine in 250 mL D5W, and the infusion rate is 22 mL/hr.

Convert Grams to Milligrams for Lidocaine

2 grams of lidocaine is equivalent to 2000 mg.

Calculate Concentration of Lidocaine

The concentration of lidocaine in the solution is \( \frac{2000 \text{ mg}}{250 \text{ mL}} \), which is 8 mg/mL.

Calculate Dosage Rate in mg/hr for Lidocaine

With an infusion rate of 22 mL/hr, the dosage in mg/hr is \( 22 \text{ mL/hr} \times 8 \text{ mg/mL} = 176 \text{ mg/hr} \).

Convert mg/hr to mg/min for Lidocaine

To convert 176 mg/hr to mg/min, divide by 60: \( \frac{176 \text{ mg/hr}}{60 \text{ min/hr}} \approx 2.93 \text{ mg/min} \).

Key concepts

Drug Concentration

Understanding drug concentration is crucial in medical dosage calculations. Drug concentration refers to the amount of a specific drug in a given volume of solution. This is often expressed in milligrams per milliliter (mg/mL). Knowing the concentration helps health professionals determine how much of a drug the patient receives per unit of the solution, whether it be a drop, a tablespoon, or an entire intravenous bag.

In our example problem, we find the concentration for lidocaine. We are told there are 2 grams of lidocaine in 250 mL of D5W. First, convert 2 grams to 2000 mg, because medical calculations are typically done in milligrams. The concentration calculation is now straightforward:

- Divide the total drug mass (2000 mg) by the volume of the solution (250 mL) to get the concentration: \[ \ \frac{2000 \text{ mg}}{250 \text{ mL}} = 8 \text{ mg/mL} \]

By knowing this concentration, it's easier to adjust the dosage according to the patient's needs.

Infusion Rate

The infusion rate is a critical factor in administering medication. It is the speed at which a drug is delivered to the patient, often measured in mL per hour. Setting the correct infusion rate impacts how steadily the medicine acts in the body, thereby ensuring its effectiveness while avoiding side effects.

In our scenario with lidocaine, the drug is being infused at 22 mL/hr. With this information and knowing the concentration (8 mg/mL), we proceed to find out how much drug the patient receives per hour.

To determine the amount of medication the patient receives per hour, multiply the infusion rate by the concentration:

• Infusion rate: 22 mL/hr
• Concentration: 8 mg/mL
• Dosage: \[22 \text{ mL/hr} \times 8 \text{ mg/mL} = 176 \text{ mg/hr}\]

This means the patient receives 176 mg of lidocaine every hour thanks to this infusion rate.

Unit Conversion

Unit conversion is often the unsung hero of dosage calculations. It involves changing from one unit of measure to another, such as grams to milligrams, which is a frequent need in pharmacology.

In both parts of the example exercise, converting grams to milligrams is essential. Because we need to talk in milligrams (mg) when figuring out practical doses:

• For the aminophylline case, convert 1 gram to 1000 mg.
• For lidocaine, convert 2 grams to 2000 mg.

The conversion factor here is simple: 1 gram equals 1000 milligrams.

Especially in a healthcare setting, failing to perform accurate conversions can lead to overdoses or inefficacious treatments, so mastering this basic skill is fundamental for safe medication administration.

Medication Administration

Medication administration involves the processes surrounding getting the correct dosage of medication into the patient safely and effectively. It includes calculating the right amount, timing the delivery, and ensuring the patient's treatment is effective.

In this particular exercise, understanding how to correctly set up and interpret results from your calculations means ensuring that the patient receives exactly what they need. Consider the case with lidocaine from the exercise:
- We calculated 176 mg/hr will be administered. To further break it down, we convert it to a smaller time frame:\[\frac{176 \text{ mg/hr}}{60 \text{ min/hr}} \approx 2.93 \text{ mg/min} \]

The smaller unit, mg/min, provides a closer check to make sure no accidental overdose or underdose occurs.

Following these processes and understanding each step in medication administration helps achieve the ultimate goal of patient safety.