Question 1.15: Administration of digitalis to control atrial fibrillation i...
Administration of digitalis to control atrial fibrillation in heart patients must be carefully regulated because even a modest overdose can be fatal. To take differences between patients into account, dosages are sometimes prescribed in micrograms per kilogram of body weight ( \mu g/kg). Thus, two people may differ greatly in weight, but both will receive the proper dosage. At a dosage of 20 \mu g/kg body weight, how many milligrams of digitalis should a 72.6 kg patient receive?
ANALYSIS Knowing the patient’s body weight (in kg) and the recommended dosage (in \mu g/kg), we can calculate the appropriate amount of digitalis.
BALLPARK ESTIMATE At a dosage of 20 \mu g/kg, an 80 kg patient should receive 80 \times 20 \mu g, or about 1600 \mu g of digitalis, or 1.6 mg.
| STEP 1: Identify known information. | Patient weight = 72.6 kg Prescribed dosage = 20 \mu g digitalis/kg body weight |
| STEP 2: Identify answer and units. | Delivered dosage = ?? mg digitalis |
| STEP 3: Identify conversion factors. The correct dose can be determined based on mg digitalis/ kg of body weight. Then, the dosage in \mu g is converted to mg. | 1 mg = (0.001\cancel{ g}) ( \frac {1 \mu g}{ 10^{ – 6}\cancel{g}}) = 1000 \mu g |
| STEP 4: Solve. Use the known information and the conversion factors so that units cancel, obtaining the answer in mg. | 72.6 \cancel {kg} \times \frac {20 \cancel{\mu g} digitalis}{ 1 \cancel{kg} }\times \frac { 1 mg}{1000 \cancel{ \mu g}} = 1.5 mg digitalis (Rounded off) |
BALLPARK CHECK Close to our estimate of 1.6 mg.