Hyderabad following first order kinetics is being administered by constant i.v. infusion at a rate of 10 mg/min. It’s steady state plasma concentration is 2mg/min. If the dose rate is increased to 20mg/do, what will be the new steady state plasma concentration
**Core Concept**
The question is testing the concept of steady-state plasma concentration in the context of first-order kinetics, specifically during constant intravenous infusion. First-order kinetics describe the relationship between the rate of drug elimination and the drug's plasma concentration, where the rate of elimination is directly proportional to the plasma concentration.
**Why the Correct Answer is Right**
At steady state, the rate of drug administration equals the rate of drug elimination. When the dose rate is increased from 10 mg/min to 20 mg/min, the rate of drug administration doubles. Since the drug follows first-order kinetics, the rate of elimination also doubles, but only if the plasma concentration doubles. However, the question states that the steady-state plasma concentration is 2 mg/L when the dose rate is 10 mg/min. To achieve the same rate of elimination (20 mg/min) at the new dose rate of 20 mg/min, the plasma concentration must also double to 4 mg/L.
**Why Each Wrong Option is Incorrect**
**Option A:** This option is incorrect because it suggests that the steady-state plasma concentration remains the same despite a doubling of the dose rate. This contradicts the principles of first-order kinetics, where the rate of elimination is directly proportional to the plasma concentration.
**Option B:** This option is incorrect because it suggests that the steady-state plasma concentration decreases with an increase in the dose rate. This is the opposite of what is expected in first-order kinetics, where an increase in the dose rate should lead to an increase in the plasma concentration.
**Option C:** This option is incorrect because it suggests that the steady-state plasma concentration remains the same despite a doubling of the dose rate. This contradicts the principles of first-order kinetics, where the rate of elimination is directly proportional to the plasma concentration.
**Clinical Pearl / High-Yield Fact**
The key takeaway from this question is that in first-order kinetics, the steady-state plasma concentration is directly proportional to the dose rate. Therefore, when the dose rate is increased, the plasma concentration will also increase, assuming that the rate of elimination remains constant.
**Correct Answer: C. 4 mg/L**