Problem 72 - Chemistry

Question

Administration of digitalis, a drug used to control atrial fibrillation in heart patients, must be carefully controlled because even a modest overdose can be fatal. To take differences between patients into account, drug dosages are prescribed in terms of \(\mathrm{mg} / \mathrm{kg}\) body weight. Thus, a child and an adult differ greatly in weight, but both receive the same dosage per kilogram of body weight. At a dosage of \(20 \mu \mathrm{g} / \mathrm{kg}\) body weight, how many milligrams of digitalis should a \(160 \mathrm{lb}\) patient receive?

Step-by-Step Solution

Answer

A 160 lb patient should receive approximately 1.45 mg of digitalis.

Step 1: Convert Pounds to Kilograms

The first step is to convert the patient's weight from pounds to kilograms since the dosage is given in micrograms per kilogram. We use the conversion factor: \(1 \text{ pound} = 0.453592 \text{ kilograms}\). So, \(160 \text{ pounds} \times 0.453592 = 72.57472 \text{ kilograms}\).

Step 2: Calculate Dosage in Micrograms

With the patient's weight in kilograms, we can now calculate the dosage in micrograms. The dosage is \(20 \mu \text{g/kg}\) body weight, so multiplying by the weight in kilograms gives us: \(20 \mu \text{g/kg} \times 72.57472 \text{ kg} = 1451.4944 \mu \text{g}\).

Step 3: Convert Micrograms to Milligrams

The final step is to convert the dosage from micrograms to milligrams. Since \(1 \text{ milligram} = 1000 \text{ micrograms}\), we need to divide the dosage in micrograms by 1000: \(\frac{1451.4944 \mu\text{g}}{1000} = 1.4514944 \text{ mg}\).

Step 4: Round to Appropriate Precision

Typically, medication dosages are rounded to an appropriate level of precision, often to the nearest hundredth for milligrams. Therefore, \(1.4514944 \text{ mg}\) rounds to \(1.45 \text{ mg}\).

Key Concepts

Unit Conversion

Unit conversion is essential when working with measurements, especially in medical calculations. It allows us to convert measurements from one unit to another to match the desired output format. This process involves simple arithmetic using well-known conversion factors.
For instance, converting a patient's weight from pounds to kilograms requires the knowledge of the conversion factor:

• 1 pound is equal to 0.453592 kilograms

To convert a weight in pounds to kilograms, multiply the number of pounds by the conversion factor. This adjustment ensures the weight is in the correct units for dosage calculations, which often require measurements in the metric system.
Understanding and mastering unit conversion is crucial for accurate calculations in science, especially in medicine, where precise measurements can significantly impact treatment outcomes.

Micrograms to Milligrams

Micrograms and milligrams are both metric units of mass used to express very small quantities. A microgram is one-millionth of a gram, and a milligram is one-thousandth of a gram. Converting between these two units is a common task in pharmaceutical calculations.
The conversion factor here is:

• 1 milligram equals 1000 micrograms.

To convert a microgram dosage to milligrams, divide the number of micrograms by 1000. This conversion is critical because medicine dosages are often provided and administered in milligrams, requiring any necessary conversion from micrograms, especially when prescribing medications like digitalis. Being adept at making this conversion ensures accurate and safe dosage calculation.

Dosage Per Kilogram

Dosage per kilogram is a method used to tailor medication doses based on a patient's body weight. This approach is particularly useful for medications that have narrow therapeutic windows, like digitalis, where precise dosing is crucial.
The process involves:

• Multiplying the prescribed dosage (e.g., micrograms per kilogram) by the patient's weight in kilograms.

This ensures each patient receives the correct dose adjusted for their weight, providing a fair and equitable approach and reducing the risk of overdose, especially important when dosing children compared to adults. Understanding this method can help prevent miscalculations and ensure the treatment is both effective and safe.

Pounds to Kilograms Conversion

Converting pounds to kilograms is a common necessity in medical settings, as the metric system (kilograms) is often used for precise dosing calculations. Knowing how to quickly and accurately make this conversion is vital for healthcare professionals.
The key conversion factor is:

• 1 pound equals 0.453592 kilograms.

By multiplying the weight in pounds by 0.453592, you convert it to kilograms. This step is critical for dosage calculations that use the metric system. Since medication dosages are calculated per kilogram, accurately converting weight measurements ensures that patients receive the correct amount, enhancing the safety and effectiveness of their treatment.