Question

Calculate the units as indicated by the problem. Use labels where provided to calculate dosages. Order: Heparin 1,500 units/hr IV. Available: 25,000 units of heparin in 500 mL D5W. What rate in \(\mathrm{mL} / \mathrm{hr}\) will deliver 1,500 units/hr?

Short answer

Set the infusion rate to 30 mL/hr.

Step-by-step solution

Determine the Concentration of Heparin

First, we need to calculate concentration of heparin in the solution you have. The total units of heparin available is 25,000 units in 500 mL of D5W. This gives us a concentration of \( \frac{25,000 \text{ units}}{500 \text{ mL}} \).

Simplify the Concentration

Now, simplify the concentration to find out how many units are in 1 mL. Use the ratio: \( \frac{25,000 \text{ units}}{500 \text{ mL}} = \frac{50 \text{ units}}{1 \text{ mL}} \). This means each mL of the solution contains 50 units of heparin.

Calculate the Required Rate in mL/hr

Now that we know there are 50 units of heparin per mL, we can calculate how many mL are needed to deliver 1,500 units per hour. Set up a proportion: \( \frac{1500 \text{ units/hr}}{x \text{ mL/hr}} = \frac{50 \text{ units}}{1 \text{ mL}} \).

Solve for x

To solve for \(x\), multiply both sides by \(x\) and then divide by 50: \[ x = \frac{1500 \text{ units/hr}}{50 \text{ units/mL}} = 30 \text{ mL/hr} \].

Verify the Calculation

Check your calculated rate by substituting back into the problem: 30 mL/hr \(\times\) 50 units/mL should equal 1,500 units/hr, which it does. So the calculation is verified.

Key concepts

Heparin Infusion

Heparin is a medication used to prevent blood clotting. When a doctor prescribes a heparin infusion, they want the medication to be delivered intravenously to ensure it enters the bloodstream directly and quickly. It's crucial to administer the right dosage to maintain its effectiveness while minimizing risks.

Here's why proper heparin infusion is essential:

• Understanding heparin's role in preventing clots helps manage conditions like deep vein thrombosis or pulmonary embolism.
• It ensures continuous blood flow by reducing the risk of clot formation.
• Heparin infusions require careful management to avoid bleeding complications.

Calculating the right infusion rate ensures that heparin is administered safely and effectively. Therefore, always follow dosage instructions as incorrect dosages can lead to severe consequences.

Intravenous Rate Calculation

The calculation of an intravenous (IV) rate involves determining how fast a solution must be administered to a patient. For heparin, it's calculated in milliliters per hour (mL/hr) to achieve the desired dosage effect.

Let's break it down:

• Understand the prescribed dosage: For example, the order might be for 1,500 units of heparin per hour.
• Determine the concentration of the available solution: Knowing how many units are in each milliliter is key.
• Set up the proportions to calculate: This involves equating the dosage required with the concentration.
• Solve the equation to find the IV rate: This is typically straightforward and involves a simple division.

These calculations ensure the right amount administered over time, safeguarding the patient’s treatment plan. Proper calculation prevents over- or under-dosing, which could lead to ineffective treatment or dangerous side effects.

Medication Concentration

Medication concentration refers to how much of a drug is within a given volume of solution. It determines how strongly a drug affects the body and how quickly it works.

For heparin, calculating concentration involves dividing the total amount of heparin by the solution volume:

• Total units in a solution: Start with knowing the total amount of medication available.
• Volume of solution: This is the total fluid volume in which the medication is dissolved.
• Simplify the fraction: Get down to units per milliliter (units/mL) to use in further dosage calculations.

For example, if you have 25,000 units in 500 mL of solution, you divide to find 50 units per mL. This number is vital as it forms the basis for how much medicine the patient will receive per hour when you calculate the intravenous rate. Without knowing the concentration, precise dosing would be remarkably challenging.