Question

A 70 kg calf was given a drug X at a dose of 100 mg/kg body weight. The half-life of the drug X is 10 hours and its initial plasma concentration is 1.9 mg/ml. True statement about drug X is/are
(A). Clearance is around 0.02 litre/hour
(B). Volume of distribution is around 3.68 L
(C). Elimination rate constant is 0.0693
(D). Clearance is around 0.2 litre/hour
Choose the correct answer from the options given below:

• (B) and (C) only.
• (C) and (D) only.
• (A) only.
• (D) only.

Hint:

Always convert units into standard forms first (e.g., converting initial concentration from $1.9 \text{ mg/ml}$ to $1900 \text{ mg/L}$ to match the total dose in mg).
This prevents calculation errors by a factor of 1000.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
To solve this pharmacokinetics problem, we will use basic equations relating dose, initial concentration, half-life, volume of distribution, elimination rate constant, and clearance.
Key Formula or Approach:
The formulas used are:
1. Total Dose ($D$) = $\text{Body Weight} \times \text{Dose rate}$
2. Volume of Distribution ($V_d$) = $\frac{D}{C_0}$
3. Elimination rate constant ($k_{el}$) = $\frac{\ln(2)}{t_{1/2}} \approx \frac{0.693}{t_{1/2}}$
4. Clearance ($Cl$) = $V_d \times k_{el}$

Step 2: Detailed Explanation:
Given values:
- Weight of calf = $70 \text{ kg}$
- Dose rate = $100 \text{ mg/kg}$
- Half-life ($t_{1/2}$) = $10 \text{ hours}$
- Initial concentration ($C_0$) = $1.9 \text{ mg/ml} = 1900 \text{ mg/L}$
Calculate Total Dose ($D$):
\[ D = 70 \text{ kg} \times 100 \text{ mg/kg} = 7000 \text{ mg} \] Calculate Volume of Distribution ($V_d$):
\[ V_d = \frac{7000 \text{ mg}}{1900 \text{ mg/L}} \approx 3.684 \text{ L} \] This confirms Statement (B) is TRUE.
Calculate Elimination Rate Constant ($k_{el}$):
\[ k_{el} = \frac{0.693}{10 \text{ hours}} = 0.0693 \text{ hour}^{-1} \] This confirms Statement (C) is TRUE.
Calculate Clearance ($Cl$):
\[ Cl = V_d \times k_{el} = 3.684 \text{ L} \times 0.0693 \text{ hour}^{-1} \approx 0.255 \text{ L/hour} \] This indicates both Statement (A) ($0.02 \text{ L/hour}$) and Statement (D) ($0.2 \text{ L/hour}$) are FALSE.

Step 3: Final Answer:
Since only statements (B) and (C) are correct, the correct option is (A).