Question

Calculate the hourly dosage of heparin (units/hr). Order: 30,000 units of heparin in \(500 \mathrm{~mL}\) of D5W to infuse at \(25 \mathrm{~mL} / \mathrm{hr}\).

Short answer

1500 units/hr

Step-by-step solution

Understanding the problem

We need to find out how many units of heparin are administered per hour when the solution is infused at a rate of \(25 \, \mathrm{mL/hr}\). The total solution contains \(30,000\) units of heparin in \(500 \, \mathrm{mL}\) of D5W.

Calculate the concentration of heparin

First, find out how many units of heparin are in one milliliter of the solution. Since we have \(30,000\) units in \(500 \, \mathrm{mL}\), divide \(30,000\) by \(500\) to find units per \(\mathrm{mL}\):\[\text{Units per } \mathrm{mL} = \frac{30,000}{500} = 60 \text{ units/mL}\]

Determine the hourly dosage

Next, multiply the units per \(\mathrm{mL}\) by the infusion rate to calculate how many units are administered per hour. Using the infusion rate of \(25 \, \mathrm{mL/hr}\), calculate the hourly dosage:\[\text{Hourly dosage} = 60 \text{ units/mL} \times 25 \text{ mL/hr} = 1500 \text{ units/hr} \]

Key concepts

Understanding Heparin Dosage

Heparin is a medication used to prevent and treat blood clots. Calculating the correct dosage is crucial, as it ensures therapeutic efficacy and reduces the risk of bleeding. Dosage calculation in pharmacology often requires a clear understanding of the prescription details and the concentration of the drug in a solution.
In our exercise, we were given a prescription indicating that 30,000 units of heparin are diluted in 500 mL of D5W (a glucose solution), and the infusion is set to run at a rate of 25 mL per hour.
Properly calculating the heparin dose involves determining how much of this medication is delivered to the patient each hour. This ensures the treatment aligns with the prescribed therapeutic levels.

Calculating Infusion Rate

Infusion rate refers to the speed at which a drug solution is administered to a patient, typically measured in mL per hour. It is a critical factor in pharmacological treatments, as it affects how quickly the medication achieves its desired effect.
In our problem, the infusion rate is specified as 25 mL per hour. Knowing the infusion rate helps us determine how much of the heparin solution reaches the patient over a given time period. By controlling the infusion rate, healthcare providers can ensure the medication is given consistently and safely.

Heparin Concentration Calculation

Concentration calculation involves finding out the amount of active drug present in a specific volume of solution. This is fundamental in medication dosing, as it helps to understand how much of the drug is administered at once.
To calculate concentration, divide the total amount of heparin (30,000 units) by the total volume of the solution (500 mL). This provides the concentration in units per milliliter:

• \( \frac{30,000 \text{ units}}{500 \text{ mL}} = 60 \text{ units/mL} \)

This tells us each milliliter of the solution contains 60 units of heparin, which is vital for calculating the rate at which the drug is administered over time.

Mastering Medical Mathematics

Medical mathematics involves applying fundamental math skills to solve real-world medical problems. This includes interpreting prescriptions, adjusting drug concentrations, and calculating dosages.
To solve pharmacological problems like our heparin dose calculation, one needs to harness skills like division (to find concentrations) and multiplication (to determine dosages).
Medical professionals rely on these calculations to provide safe and effective treatments. A solid grasp of medical mathematics ensures precise medication delivery, which is crucial for patient safety and treatment success. Understanding the mathematical relationship between drug concentration, solution volume, and infusion rate plays a pivotal role in daily medical practice.