Question

Read the dosage information or label given for the following problems. Express body weight conversion to the nearest tenth where indicated and dosages to the nearest tenth. A child weighing 46 lb has an order for ranitidine (Zantac) $20\mathrm{mg}$ IV $\mathrm{q}8\mathrm{h}$. Is the dosage ordered safe? (Prove mathematically.) Available: Pediatric Use: While limited data exist on the administration of IV ranitidine to children, the recommended dose in pediatric patients is for a total daily dose of 2 to $4\mathrm{mg}/\mathrm{kg},$ to be divided and administered every 6 to 8 hours, up to a maximum of 50 mg given every 6 to 8 hours. This recommendation is derived from adult clinical studies and pharmacokinetic data in pediatric patients. Limited data in neonatal patients (less than one month of age) receiving ECMO have shown that a dose of $2\mathrm{mg}/\mathrm{kg}$ is usually sufficient to increase gastric $\mathrm{pH}$ to $>4$ for at least 15 hours. Therefore, doses of $2\mathrm{mg}/\mathrm{kg}$ given every 12 to 24 hours or as a continuous infusion should be considered.

Short answer

Yes, the dosage is safe as 60 mg/day is within the recommended range of 41.4 to 82.8 mg/day.

Step-by-step solution

Convert Weight to Kilograms

Start by converting the child's weight from pounds to kilograms. Since 1 lb is approximately 0.45 kg, calculate:$$46\text{ lb}\times 0.45\text{ kg/lb}=20.7\text{ kg}$$Round to the nearest tenth, the child's weight is 20.7 kg.

Calculate Total Daily Dose Range

The recommended dose range is 2 to 4 mg/kg per day. First, calculate the range:Lower limit:$$2\text{ mg/kg}\times 20.7\text{ kg}=41.4\text{ mg/day}$$Upper limit:$$4\text{ mg/kg}\times 20.7\text{ kg}=82.8\text{ mg/day}$$

Determine Daily Dosage from Prescription

The prescription is for 20 mg every 8 hours, which means the child receives the dosage three times a day:$$20\text{ mg/dose}\times 3\text{ doses/day}=60\text{ mg/day}$$

Assess Prescription Against Recommended Range

Compare the prescribed daily dosage of 60 mg to the calculated safe range of 41.4 to 82.8 mg. Since 60 mg falls within this range, the dosage is safe.

Key concepts

Body Weight Conversion

When calculating pediatric dosages, an essential first step is converting the child's weight from pounds to kilograms. This conversion is crucial because most medication dosages are calculated in milligrams per kilogram. To convert pounds to kilograms, you multiply the number of pounds by the conversion factor 0.45. For example, a child weighing 46 pounds would have their weight calculated in kilograms as follows:$$46\text{ lb}\times 0.45\text{ kg/lb}=20.7\text{ kg}$$Round the result to the nearest tenth to make it easier to use in further calculations, which gives us 20.7 kg. It's important to be accurate in this conversion because even small errors can lead to unsafe dosages for children. Always ensure that the conversion is precise and rounded correctly before moving on to the next steps.

Safe Dosage Range

Once you have the child's weight in kilograms, you can determine the safe dosage range of a medication. Safe dosage ranges are typically given in milligrams per kilogram per day. To find the total safe daily dose, multiply the weight in kilograms by the lower and upper limits of the recommended dose.- **Lower limit:** Multiply the child's weight by the lower end of the dosage range (e.g., 2 mg/kg). For a child weighing 20.7 kg, the lower limit would be:$$2\text{ mg/kg}\times 20.7\text{ kg}=41.4\text{ mg/day}$$- **Upper limit:** Multiply the child's weight by the upper end of the dosage range (e.g., 4 mg/kg). For the same child, the upper limit would be:$$4\text{ mg/kg}\times 20.7\text{ kg}=82.8\text{ mg/day}$$Having this range provides a boundary within which the medication can be safely administered. It helps you to compare the actual prescription against these limits to ensure it is neither too low to be ineffective, nor too high to be potentially harmful.

Medication Administration

After verifying the safe dosage range, it's time to assess the medication prescription. The prescription provides the frequency and amount of medication to be administered. It's essential to accurately calculate the total daily dosage the child will receive based on the prescription details.In this example, the child receives 20 mg of ranitidine three times a day (every 8 hours):- Calculate the total daily dose:$$20\text{ mg/dose}\times 3\text{ doses/day}=60\text{ mg/day}$$Next, compare this calculated daily dose against the previously determined safe dosage range of 41.4 mg to 82.8 mg per day. Since 60 mg falls within this range, the dosage is considered safe and appropriate for the child. Always ensure that the prescribed dosage not only meets the safety criteria but also addresses the medical needs of the patient. Additionally, it's vital to monitor the child for any adverse reactions or side effects after administration.