Question

Cephalosporin antibiotic was given at dose of 5 mg/kg by a single iv bolus injection to a 58 year old man whose weight 75'kg . antibiotic follows the pharmacokinetics of a one compartment model and has an elimination of half life of 2 hr the apparent volume of distribution is 0.28l/kg, and the drug is 35% bound to plasma proteins.what is the initial plasma drug concentration in this patient?

Answer 1

To calculate the initial plasma drug concentration (C₀) for the cephalosporin antibiotic given to the patient, we can use the following formula:

\[ C₀ = \frac{D}{V_d} \]

where:
- \( C₀ \) is the initial plasma drug concentration,
- \( D \) is the dose administered,
- \( V_d \) is the volume of distribution.

1. **Calculate the dose (D)**:
- The dose is given as 5 mg/kg. The patient weighs 75 kg.
\[
D = 5 \, \text{mg/kg} \times 75 \, \text{kg} = 375 \, \text{mg}
\]

2. **Calculate the volume of distribution (V_d)**:
- The apparent volume of distribution is given as 0.28 L/kg.
\[
V_d = 0.28 \, \text{L/kg} \times 75 \, \text{kg} = 21 \, \text{L}
\]

3. **Calculate the initial plasma drug concentration (C₀)**:
\[
C₀ = \frac{D}{V_d} = \frac{375 \, \text{mg}}{21 \, \text{L}} \approx 17.86 \, \text{mg/L}
\]

Thus, the initial plasma drug concentration in this patient is approximately **17.86 mg/L**.