Problem 18 - Chemistry for Allied Health

Question

Sodium- 24 is used to treat leukemia. A \(36-\mathrm{kg}\) patient is prescribed \(145 \mu \mathrm{Ci} / \mathrm{kg}\) and it is supplied to the hospital in a vial containing \(250 \mu \mathrm{Ci} / \mathrm{mL}\). What volume should be given to the patient?

Step-by-Step Solution

Answer

20.88 mL of the sodium-24 solution should be given to the patient.

Step 1: Calculate Total Dosage

First, determine the total dosage needed for the patient in microcuries \( \mu \mathrm{Ci} \). Multiply the patient's weight by the dosage prescribed per kilogram.\[ \text{Total Dosage} = 36 \, \text{kg} \times 145 \, \mu \mathrm{Ci/kg} = 5220 \, \mu \mathrm{Ci} \]

Step 2: Calculate Volume Required

Using the total dosage calculated and the concentration of the substance in the vial, compute the volume in milliliters. Divide the total dosage by the concentration per milliliter.\[ \text{Volume} = \frac{5220 \, \mu \mathrm{Ci}}{250 \, \mu \mathrm{Ci/mL}} = 20.88 \, \mathrm{mL} \]

Key Concepts

Understanding Radioactive Isotopes in Medicine

Radioactive isotopes, also known as radioisotopes, are atoms that have an unstable nucleus and emit radiation as they decay to a more stable form. In medicine, these isotopes are valuable for both therapeutic and diagnostic purposes. For instance:

• Treatment: Radioisotopes can be used to target and destroy cancerous cells. Sodium-24 and other isotopes are chosen for their ability to deliver precise doses of radiation to affected areas.
• Diagnosis: Radioisotopes can be used to trace the movement of substances within the body, helping to identify issues in organs and blood circulation.

Radioactive isotopes emit three main types of radiation: alpha particles, beta particles, and gamma rays. Each type interacts differently with human tissues. A skilled professional must select the appropriate isotope and radiation type for each unique medical condition. This personalization ensures effective treatment while minimizing potential harm. Utilizing radioisotopes in healthcare requires carefully calculated dosages to ensure safety and efficacy.

The Art of Dosage Calculation

Dosage calculation is a critical step in administering radiopharmaceutical treatments. It's essential to ensure that each patient receives the correct amount of the radioactive substance to effectively treat their condition. The dosage is usually calculated based on the weight of the patient. In our given exercise:

• A patient weighing 36 kg requires a prescription of 145 μCi/kg.
• We calculate the total dosage by multiplying the patient's weight by the prescribed dosage per kilogram: \[ \text{Total Dosage} = 36 \, \text{kg} \times 145 \, μ\mathrm{Ci/kg} = 5220 \, μ\mathrm{Ci} \]

Accurate dosage calculation is important because:

• It ensures enough radiation is delivered to achieve a therapeutic effect.
• It prevents overexposure to radiation, which could be harmful to the patient.

Understanding dosage calculation helps health professionals tailor treatments to individual patient needs effectively.

Exploring Concentration and Volume Relationship

The relationship between concentration and volume is crucial in determining how much of a radioactive solution is required to deliver the correct dosage. Concentration refers to the amount of a substance within a specific volume of a medium. In this exercise, it is expressed as 250 μCi/mL.To find the volume needed to achieve a desired dosage of the radiopharmaceutical preparation, follow this formula:

• Volume (mL) = Total Dosage (μCi) / Concentration (μCi/mL)

In our scenario, the calculation is:\[ \text{Volume} = \frac{5220 \, μ\mathrm{Ci}}{250 \, μ\mathrm{Ci/mL}} = 20.88 \, \mathrm{mL} \]Understanding this relationship allows health practitioners to adjust how much of a solution they will administer. This keeps the treatment both effective and safe. Calculating volume based on concentration and dosage ensures precision in delivering the therapeutic benefits of the isotopes without wasting substances.