Problem 42 - Calculate With Confidence

Question

Calculate the dosages as indicated. Use the labels where provided. Dopamine is ordered at a rate of \(3 \mathrm{mcg} / \mathrm{kg} / \mathrm{min}\) for a client weighing \(95.9 \mathrm{~kg}\). The solution strength is \(400 \mathrm{mg}\) dopamine in \(250 \mathrm{~mL} \mathrm{D}_{5} \mathrm{~W}\). Determine the flow rate for IV pump. Pump capable of delivering in tenths of a mL.

Step-by-Step Solution

Answer

The IV pump should be set to deliver 10.79 mL/hour.

Step 1: Calculate Total Micrograms per Minute

First, determine how many micrograms of dopamine the patient needs per minute. This is calculated using the formula: \( \text{Dosage Rate} (\mathrm{mcg/kg/min}) \times \text{Weight} (\mathrm{kg}) \).ewline\[3 \mathrm{mcg/kg/min} \times 95.9 \mathrm{~kg} = 287.7 \mathrm{~mcg/min}\]

Step 2: Convert Micrograms to Milligrams per Minute

Since 1 mg is equal to 1000 mcg, convert the dosage from micrograms to milligrams to fit with our solution's concentration.ewline\[287.7 \mathrm{~mcg/min} = 0.2877 \mathrm{~mg/min}\]

Step 3: Determine Milligrams per Milliliter in the Solution

To find how many milligrams of dopamine are in each milliliter of the solution, divide the total dosage of dopamine by the total volume of the solution.ewline\[\frac{400 \mathrm{mg}}{250 \mathrm{mL}} = 1.6 \mathrm{mg/mL}\]

Step 4: Calculate Flow Rate in mL/min

With the milligrams per milliliter conversion rate known, calculate the flow rate in mL/min using the formula: \( \frac{\text{required dosage per minute in mg}}{\text{concentration in mg/mL}} \).ewline\[\frac{0.2877 \mathrm{mg/min}}{1.6 \mathrm{mg/mL}} \approx 0.1798 \mathrm{mL/min}\]

Step 5: Convert Flow Rate to mL per Hour

To find out the flow rate in mL per hour, multiply the flow rate per minute by 60.ewline\[0.1798 \mathrm{mL/min} \times 60 \mathrm{~minutes/hour} = 10.79 \mathrm{mL/hour}\]

Key Concepts

Dopamine Dosage

Dopamine is commonly used in medical settings to support blood pressure and cardiac output in patients who require it. The dosage of dopamine is often prescribed based on weight to ensure accuracy and safety. In the given problem, dopamine is ordered at a rate of 3 mcg/kg/min. This unit of measurement is important as it relates to the patient's weight, which in this case is 95.9 kg. Thus, to calculate the total micrograms of dopamine required per minute, you multiply the prescribed dosage (3 mcg/kg/min) by the patient's weight (95.9 kg). This results in 287.7 mcg/min. Understanding how to calculate this dosage ensures that patients receive the correct amount of medication they need to achieve the desired physiologic response.

Micrograms to Milligrams Conversion

Converting between units of measurement is a crucial skill in pharmacy and nursing. It ensures that medications are administered correctly and safely. In the exercise, dopamine dosage must be converted from micrograms (mcg) to milligrams (mg) since the solution's strength is given in milligrams (400 mg in 250 mL of solution). The conversion factor between micrograms and milligrams is 1 mg equals 1000 mcg. To convert 287.7 mcg/min to milligrams per minute, divide by 1000: \[ 287.7 ext{ mcg/min} = 0.2877 ext{ mg/min} \] This conversion is necessary for consistency and precision when working out medication concentrations for intravenous (IV) solutions.

IV Flow Rate Calculation

The calculation of the IV flow rate is vital to ensure the patient receives the correct amount of medication over a specified period. For IV dopamine administration, you need to determine the amount in milliliters per minute or hour that delivers the correct dose. In this exercise, once the dosage is converted to milligrams per minute (0.2877 mg/min), the IV solution concentration is used, which is 1.6 mg/mL (from 400 mg/250 mL). By dividing the required dosage per minute by this concentration: \[ \frac{0.2877 \text{ mg/min}}{1.6 \text{ mg/mL}} \approx 0.1798 \text{ mL/min}\] This flow rate is then multiplied by 60 to convert it to mL/hr: \[ 0.1798 \text{ mL/min} \times 60 \text{ min/hour} = 10.79 \text{ mL/hr} \] This provides the hourly rate at which the medication should be set on the IV pump.

Weight-Based Medication Dosing

Weight-based dosing is crucial especially in critical care settings to tailor the medication dosage to a patient's specific body weight. This method helps in achieving the desired therapeutic effect while minimizing the risk of overdose or underdose. In this problem, dopamine dosage is administered based on the patient's weight (95.9 kg). Each kilogram of body weight corresponds to a certain amount of medication (3 mcg/kg/min). Such dosing requires accurate weight measurement and precise calculation to ensure efficacy and safety in drug delivery. This approach is widely used in drugs like dopamine to ensure accurate blood pressure support based on individual patient needs. Accurate weight-based dosing also takes into account the varying body compositions of different patients, which can significantly affect how drugs are metabolized and respond in the body.