Question

A 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 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) after a single intravenous (IV) bolus injection of the cephalosporin antibiotic, we can use the following formula:

\[ C_0 = \frac{D}{V_d} \]

where:
- \( C_0 \) = initial plasma concentration (in mg/L)
- \( D \) = dosage administered (in mg)
- \( V_d \) = volume of distribution (in L)

### Step 1: Calculate the Dose (D)
The dosage is given as 5 mg/kg, and the weight of the man is 75 kg. Therefore,

\[
D = 5 \, \text{mg/kg} \times 75 \, \text{kg} = 375 \, \text{mg}
\]

### Step 2: Calculate the Volume of Distribution (V_d)
The apparent volume of distribution is given as 0.28 L/kg. Thus, for a patient weighing 75 kg:

\[
V_d = 0.28 \, \text{L/kg} \times 75 \, \text{kg} = 21 \, \text{L}
\]

### Step 3: Calculate the Initial Plasma Concentration (C₀)

Now we can substitute the values of \( D \) and \( V_d \) into the formula for \( C_0 \):

\[
C_0 = \frac{375 \, \text{mg}}{21 \, \text{L}} \approx 17.86 \, \text{mg/L}
\]

### Final Answer
The initial plasma drug concentration in this patient is approximately **17.86 mg/L**.