Question

Calculate the dosages as indicated. Use the labels where provided. Dopamine has been ordered to maintain a client's blood pressure; \(400 \mathrm{mg}\) dopamine has been placed in \(500 \mathrm{~mL}\) D5W to infuse at \(35 \mathrm{~mL} / \mathrm{hr}\). How many milligrams are being administered per hour?

Short answer

28 mg/hr of dopamine is administered per hour.

Step-by-step solution

Find the Concentration of Dopamine

First, determine the concentration of dopamine in the solution. We have 400 mg of dopamine in 500 mL of solution. Calculate the concentration using the formula for concentration: \[\text{Concentration} = \frac{\text{Amount of Drug}}{\text{Total Volume}}\]Substitute the values:\[\text{Concentration} = \frac{400 \text{ mg}}{500 \text{ mL}} = 0.8 \text{ mg/mL}\]

Calculate the Dosage per Hour

Now, calculate how many milligrams are administered per hour when the solution is infused at 35 mL/hr. Use the concentration calculated:\[\text{Dosage per Hour} = \text{Infusion Rate} \times \text{Concentration}\]Insert the known values:\[\text{Dosage per Hour} = 35 \text{ mL/hr} \times 0.8 \text{ mg/mL} = 28 \text{ mg/hr}\]

Key concepts

Concentration Calculation

In order to understand how much of a drug is being delivered in a solution, we need to calculate its concentration. This involves determining how much of the drug is present in a given volume of the solution. For example, when 400 mg of dopamine is added to 500 mL of solution, its concentration can be calculated using the formula:\[\text{Concentration} = \frac{\text{Amount of Drug}}{\text{Total Volume}}\] So, \[\text{Concentration} = \frac{400 \text{ mg}}{500 \text{ mL}} = 0.8 \text{ mg/mL}\] This indicates that each milliliter of the solution contains 0.8 mg of dopamine. This concentration value is crucial as it enables healthcare providers to administer the correct dosage over time.

Infusion Rate

The infusion rate refers to the speed at which a medication or fluid is administered into the body through an IV. It's usually measured in mL/hr (milliliters per hour). In the given exercise, the infusion rate is set at 35 mL/hr. This means that every hour, 35 mL of the solution containing dopamine is delivered into the patient's bloodstream. Infusion rate calculations ensure that the patient receives medication at a consistent and safe pace, avoiding overdose or underdose. To determine the dosage being delivered per hour, you'll need to multiply the infusion rate by the concentration you have previously calculated. Substituting the values from the problem gives:\[\text{Dosage per Hour} = 35 \text{ mL/hr} \times 0.8 \text{ mg/mL} = 28 \text{ mg/hr}\]This means the patient receives 28 mg of dopamine each hour.

Pharmacology

Pharmacology is the branch of medicine concerned with the uses, effects, and modes of action of drugs. When calculating dosages and administering drugs like dopamine, a solid understanding of pharmacology helps ensure safe and effective treatment. Medication such as dopamine is used to support blood pressure and cardiac output in critical care settings. Understanding its pharmacokinetics—the way the drug is absorbed, distributed, metabolized, and excreted—helps healthcare providers anticipate the effects on a patient's body. Moreover, pharmacodynamics, which studies how the drug affects the body at the target site, are crucial for managing and adjusting dosages precisely under varying clinical conditions. These principles guide dosage calculations like the one in the exercise.

Medication Administration

Medication administration is the process of providing a patient with a medicine as prescribed. This involves several steps to ensure the right drug is given in the right dosage and at the right time. In our scenario, dopamine needs to be administered carefully to maintain a patient's blood pressure. Proper administration involves verifying the concentration of the drug in the solution, confirming the infusion rate, double-checking calculations, and monitoring the patient's response to the medication. Being vigilant with dosing calculations and continuously assessing the patient's condition allows healthcare providers to make necessary adjustments, ensuring the patient receives optimum care without adverse effects. Overall, thoroughly understanding medication administration principles helps mitigate risks and enhance patient safety.