Question

Round weights and dosages to the nearest tenth as indicated. Acetaminophen (Ofirmev) \(525 \mathrm{mg}\) IV \(\mathrm{q} 4 \mathrm{~h}\) is ordered for a child weighing \(92.4 \mathrm{lb}\). According to The Harriet Lane Handbook, the dosage for a child (age \(2-12\) years) or adolescent/adult weighing less than \(50 \mathrm{~kg}\) is \(15 \mathrm{mg} / \mathrm{kg} /\) dose \(\mathrm{q} 6 \mathrm{~h}\), or \(12.5 \mathrm{mg} / \mathrm{kg} /\) dose q4h IV up to a maximum of \(75 \mathrm{mg} / \mathrm{kg} / 24 \mathrm{hr}\). a. What is the safe dosage for this child? b. Is the dosage ordered safe?

Short answer

The ordered dosage is slightly unsafe for a per-dose and total 24-hour limit.

Step-by-step solution

Convert weight from pounds to kilograms

The child's weight is given in pounds, so we must convert it to kilograms to calculate the dosage accurately, using the conversion factor 1 lb = 0.453592 kg.\[92.4 \text{ lb} \times 0.453592 \text{ kg/lb} = 41.92 \text{ kg}\] Round this to the nearest tenth to get approximately 41.9 kg.

Calculate the maximum safe dosage per dose

The dosage guideline states that a maximum of 12.5 mg/kg/dose q4h is safe. Calculate this dosage using the child's weight in kg.\[12.5 \text{ mg/kg} \times 41.9 \text{ kg} = 523.75 \text{ mg}\] Round this to the nearest tenth for ease of calculation, which gives approximately 523.8 mg per dose.

Calculate the maximum safe dosage for 24 hours

For a maximum safe limit, check the total allowed in 24 hours as per guidelines, which is 75 mg/kg/24 hr.\[75 \text{ mg/kg} \times 41.9 \text{ kg} = 3142.5 \text{ mg}\] Round this value to the nearest tenth, resulting in 3142.5 mg per 24 hours.

Verify if the ordered dosage is safe

The ordered dose is 525 mg every 4 hours. Check if it does not exceed the safe per dose value or the total 24-hour limit. Compare the total given in 24 hours: \[525 \text{ mg} \times 6 \text{ doses} = 3150 \text{ mg in 24 hours}\] The single dose of 525 mg is slightly above the maximum safe per dose amount, but the 24-hour total slightly exceeds the 3142.5 mg 24-hour limit, indicating it's slightly unsafe.

Key concepts

Weight Conversion

When calculating pediatric dosages, it's crucial to convert the weight from pounds (lb) to kilograms (kg) since medicine dosages are typically given in mg per kg. The conversion allows for precise calculations. The standard conversion factor used is 1 lb = 0.453592 kg. You multiply the child's weight in pounds by this factor to find the weight in kilograms.
For example, a child weighing 92.4 lb would be calculated as follows:

• 92.4 lb × 0.453592 = 41.92 kg

We then round this weight to the nearest tenth for easier calculation, giving us approximately 41.9 kg. Without this conversion, dosage calculations would be inaccurate and could either underdose or overdose the child.

Safe Dosage Limits

To ensure a child's safety, it's vital to adhere to safe dosage limits. These guidelines tell us the highest amount of medication that can be safely administered without causing harm. Safe dosage limits are typically provided by trusted medical sources like The Harriet Lane Handbook. They give dosage amounts based on the child's weight in kg, ensuring that each dose is appropriate.
For doses given every 4 hours, the guideline specifies a maximum of 12.5 mg per kg. For the example of a child weighing 41.9 kg, the calculation would be:

• 12.5 mg/kg × 41.9 kg = 523.75 mg per dose

Rounding slightly, this becomes approximately 523.8 mg. This helps healthcare providers avoid overdoses and maintain a safe therapeutic level of medicine in the child's system.

Harriet Lane Handbook

The Harriet Lane Handbook is a trusted resource for healthcare providers. It's specifically designed to assist practitioners in making informed decisions about the care of pediatric patients. It includes up-to-date information on the safe administration of medications, correct dosages, and treatment guidelines for children.
For this particular exercise, the handbook provides the guidelines needed to calculate the appropriate dosing for acetaminophen based on weight in kg. It recommends specific limits for medications, ensuring that both per-dose and 24-hour totals are considered.
This resource helps mitigate the risks of administering incorrect doses, a key aspect of safe and effective pediatric care.

Rounding Numbers

Rounding numbers is an essential step in dosage calculations. It simplifies complex numbers, making them easier to work with. In medicine, especially in pediatric dosing, rounding can ensure that instructions are practical and safe to follow.
In the given exercise, weights and calculated dosages are rounded to the nearest tenth. So, after converting the weight to kg, 41.92 becomes 41.9 kg. The calculated per-dose amount of 523.75 mg also becomes 523.8 mg upon rounding. This little adjustment ensures the numbers are more manageable and measurement tools available in practice align with these approximations.
By rounding, we maintain a balance between accuracy and usability, an important consideration when dealing with sensitive doses in young patients.