Question

Calculate the dosages as indicated. Use the labels where provided. Infuse Dobutamine \(250 \mathrm{mg}\) in \(500 \mathrm{~mL} \mathrm{D}_{5} \mathrm{~W}\) at \(5 \mathrm{mcg} / \mathrm{kg} / \mathrm{min}\). The client weighs 143 lb. Concentration of solution is \(500 \mathrm{mcg}\) per mL. How many meg of dobutamine will be infused per minute? ______ Per hour? _______

Short answer

325 mcg/min; 19,500 mcg/h.

Step-by-step solution

Convert Weight from Pounds to Kilograms

The client's weight is given in pounds (143 lb). To convert this into kilograms, use the conversion factor: 1 kg = 2.2 lb. So, divide 143 by 2.2 to get the weight in kilograms.\[\text{Weight in kg} = \frac{143}{2.2} \approx 65 \text{ kg}.\]

Calculate the Infusion Rate in mcg/min

The order is to infuse at 5 mcg/kg/min. Multiply the client's weight in kilograms by this rate to find the total dosage in mcg/min.\[\text{Dosage} = 65 \text{ kg} \times 5 \text{ mcg/kg/min} = 325 \text{ mcg/min}.\]

Determine the Concentration of the Solution

The concentration of the Dobutamine solution is given as 500 mcg/mL. This tells us how many micrograms of Dobutamine are in each milliliter of the solution.

Calculate the Volume Infused per Minute

Divide the dosage in mcg/min by the concentration (mcg/mL) to find the volume in mL that needs to be infused per minute.\[\text{Volume per min} = \frac{325 \text{ mcg/min}}{500 \text{ mcg/mL}} = 0.65 \text{ mL/min}.\]

Calculate the Volume Infused per Hour

Multiply the volume infused per minute by the number of minutes in an hour (60) to find the amount infused per hour.\[\text{Volume per hour} = 0.65 \text{ mL/min} \times 60 \text{ min/h} = 39 \text{ mL/h}.\]

Calculate the mcg Infused per Hour

Finally, convert the hourly infusion volume back to mcg using the solution concentration.\[\text{mcg per hour} = 39 \text{ mL/h} \times 500 \text{ mcg/mL} = 19,500 \text{ mcg/h}.\]

Key concepts

Weight Conversion

When it comes to medical dosage calculations, accurately converting weight from one unit to another is crucial. Often, medication dosages are based on a patient's weight in kilograms, while in some regions, weight is commonly reported in pounds. This requires a seamless conversion between these units. For conversions between pounds and kilograms, the factor used is:

• 1 kg = 2.2 lb

To convert pounds to kilograms, you divide the weight in pounds by 2.2. For example, if a patient weighs 143 pounds, the conversion to kilograms would be:\[ \text{Weight in kg} = \frac{143}{2.2} \approx 65 \text{ kg} \]Accurately converting weight ensures the correct dosage is administered, as the rate of medication is often given in micrograms per kilogram per minute (mcg/kg/min). Getting this right is essential for patient safety.

Infusion Rate Calculation

Infusion rate calculation is a specific type of dosage calculation, important when you need to know how fast a medication should be delivered. The rate of infusion is typically calculated based on a per minute basis and then can be extended to an hourly rate. You start by calculating the exact dosage per minute. This involves:

• Using the weight in kg
• Multiplying by the prescribed rate (e.g., mcg/kg/min)

For our example where the patient weighs 65 kg and requires 5 mcg/kg/min, the infusion rate is:\[ \text{Dosage per minute} = 65 \text{ kg} \times 5 \text{ mcg/kg/min} = 325 \text{ mcg/min} \]This simplifies the process of determining the correct flow rate, ensuring the patient receives the optimal therapeutic benefit without adverse effects.
To find out the volume that needs to be infused, knowing the solution concentration in mcg/mL is required.

Concentration Determination

Understanding the concentration of a solution is fundamental in calculating both how much solution to administer and the efficacy of the treatment. Concentration in medication indicates how much of the active ingredient is present per unit of the solution, usually in terms of mcg/mL or mg/mL. For example, if a solution is labeled as 500 mcg/mL, this means each milliliter of the solution contains 500 micrograms of the medication.
Knowing the concentration allows you to determine how much volume of solution is needed per minute. If you need to administer 325 mcg per minute, use the following equation:\[ \text{Volume per min} = \frac{325 \text{ mcg/min}}{500 \text{ mcg/mL}} = 0.65 \text{ mL/min} \]Understanding concentration helps ensure that calculations are precise, making it a vital part of ensuring appropriate patient care.

Unit Conversion

Unit conversion is a basic yet critical skill in the realm of medical dosages. This often involves converting quantities from one unit of measurement to another, ensuring that calculations are consistently accurate. In infusion therapy, you've seen conversions such as mcg to mg, mL to L, or minutes to hours used.

• To convert mcg to mg, recall that 1 mg = 1000 mcg.
• To transition time, remember 1 hour = 60 minutes.

In transporting the daily infusion volume to an hourly context, you'll scale up by converting time. For example, if you have 0.65 mL per minute, you need to calculate the amount for one-hour:\[ \text{Volume per hour} = 0.65 \text{ mL/min} \times 60 \text{ min/h} = 39 \text{ mL/h} \]Thoroughly conducted conversions support precise dosage administration, which is essential for effective treatment outcomes and patient safety.