What is the approximate volume of distribution for vancomycin administered to a 70 kg male patient, given his peak plasma concentration of 28.5 mg/L after a 2000 mg loading dose?

To determine the approximate volume of distribution (Vd) for vancomycin in this patient, we can use the formula that relates the dose administered, peak plasma concentration, and volume of distribution:

[ V_d = \frac{D}{C_{peak}} ]

where ( D ) is the dose in mg (2000 mg in this case), and ( C_{peak} ) is the peak plasma concentration (28.5 mg/L).

Now, substituting the values into the formula:

[ V_d = \frac{2000 \text{ mg}}{28.5 \text{ mg/L}} ]

This calculation yields:

[ V_d = 70.175 \text{ L} ]

To convert this volume into a per kilogram basis for the patient, we divide the total volume by the patient's weight:

[ V_d = \frac{70.175 \text{ L}}{70 \text{ kg}} ]

This results in approximately:

[ V_d \approx 1 \text{ L/kg} ]

This calculation indicates that the volume of distribution for vancomycin in this 70 kg male patient is about 1 L/kg, which is consistent with the expected pharmacok