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. Streptomycin sulfate $400\mathrm{mg}$ IM daily is ordered for a child weighing $35\mathrm{kg}$. The recommended dosage is 20 to $40\mathrm{mg}/\mathrm{kg}/$ day once daily. a. Is the dosage ordered safe? (Prove mathematically.) b. A $1-g$ vial of streptomycin sulfate is available in powdered form with the following instructions: Dilution with $1.8\mathrm{mL}$ of sterile water will yield $400\mathrm{mg}$ per $\mathrm{mL}$. How many milliliters will you need to administer the ordered dosage? Calculate the dosage if the order is safe.

Short answer

The ordered dosage of 400 mg is not safe; it is below the minimum 700 mg required.

Step-by-step solution

Calculate Minimum Safe Dosage

First, calculate the minimum safe dosage by multiplying the child's weight (35 kg) by the minimum recommended dosage (20 mg/kg/day).$$\text{Minimum Safe Dosage}=35\text{kg}\times 20\text{mg/kg}=700\text{mg/day}$$

Calculate Maximum Safe Dosage

Next, calculate the maximum safe dosage by multiplying the child's weight (35 kg) by the maximum recommended dosage (40 mg/kg/day).$$\text{Maximum Safe Dosage}=35\text{kg}\times 40\text{mg/kg}=1400\text{mg/day}$$

Determine if Ordered Dosage is Safe

The ordered dosage is 400 mg per day. Compare this to the calculated safe dosage range of 700 mg to 1400 mg. Since 400 mg is less than the minimum safe dosage of 700 mg, the ordered dosage is not safe.

Calculate Volume to Administer (Hypothetical)

If the dosage were safe, we would calculate the necessary volume to administer, assuming dilution is correct. Given the dilution instruction, 400 mg is available per 1 mL. Since the prescribed dosage is 400 mg, we would need:$$\text{Volume to Administer}=\frac{400\text{mg}}{400\text{mg/mL}}=1\text{mL}$$

Conclusion

The calculated volume shows how much to administer if the dose were within the safe range. However, as determined in Step 3, the ordered dosage of 400 mg is less than the minimum recommended dosage and is therefore unsafe.

Key concepts

Pediatric Dosage

When it comes to pediatric patients, calculating the correct dosage is crucial. Young bodies are still developing and can react differently to medications compared to adults. To find an appropriate dose, healthcare providers generally use the child's weight in kilograms to determine the right amount. This calculation is essential because children's metabolic rates and body composition vary significantly from adults. By using a weight-based dosage method, we ensure that the drug is both safe and effective for the child's unique physiology. For example, in the case of streptomycin sulfate for a child weighing 35 kg, assessing both minimum and maximum safe dosage ranges allows healthcare providers to spot potential errors before administering the drug. This cautious approach helps protect the child's health and safety.

Medication Safety

Medication safety is a top priority in healthcare, especially for children. Establishing safe dosage limits based on the child's weight, age, and medical history can prevent adverse drug reactions Ensuring safety means carefully calculating the amount, being aware of potential side effects, and understanding the safe dosage range. For streptomycin sulfate, the recommended dosage range from 20 mg to 40 mg per kg per day serves as a guideline. This range helps medical practitioners to decide if the prescribed dose is safe. In the original exercise, the ordered dose of 400 mg was found to be below the safe minimum dose of 700 mg. This highlights why double-checking calculations and prescribed doses is a core part of medication safety practices.

Dosage Calculation Steps

Calculating medication doses involves a systematic approach, ensuring both accuracy and safety. Here we'll break down the steps as shown in the original solution, enhancing your understanding. - **Calculate Minimum Safe Dosage**: Start by multiplying the patient's weight by the lowest recommended dose from the dosage range. In this situation, it's 20 mg/kg. - **Calculate Maximum Safe Dosage**: Next, multiply the child's weight by the highest recommended dose, 40 mg/kg. - **Compare Ordered Dosage**: Assess if the prescribed dose sits within the safe range between the minimum and maximum calculated doses. It's vital to note that if the dose is outside this range, it may be unsafe for the patient. If the dosage were correct, further calculations would determine the exact volume to administer, ensuring the child receives the intended amount of medication safely.