Question

A $55$-year-old woman with a history of severe persistent asthma presents to the emergency department with progressively worsening shortness of breath and wheezing over the past $2$ days. She reports taking her prescribed oral theophylline inconsistently over the last week. On examination, she is in mild respiratory distress with diffuse bilateral expiratory wheezes. Her current serum theophylline concentration is measured at $4.0 \text{ mg/L}$. The physician orders an intravenous loading dose of aminophylline to rapidly achieve a target therapeutic theophylline concentration of $12.0 \text{ mg/L}$. The patient weighs $70 \text{ kg}$. The population volume of distribution for theophylline is $0.5 \text{ L/kg}$. Aminophylline is a water-soluble salt complex that contains $80\%$ theophylline by weight (salt factor $S = 0.8$). Assuming complete bioavailability for the intravenous route, what is the appropriate loading dose of intravenous aminophylline required to reach the target concentration?