Young child weighing 20 kg was given a drug in the dose lOOmg/kg body weight. The plasma concentration of the drug is 2mg/ dl and the clearance is 200 ml/hr. What is the time required to reach steady state plasma concentration –
**Core Concept**
Pharmacokinetics is the study of how the body affects a drug after administration. In this case, we are dealing with the concept of steady-state plasma concentration, which is achieved when the rate of drug administration equals the rate of drug elimination.
**Why the Correct Answer is Right**
To calculate the time required to reach steady state, we can use the formula: t1/2 x 5.6, where t1/2 is the half-life of the drug. However, we are not given the half-life directly. We can calculate the volume of distribution (Vd) using the formula: Vd = Dose / Plasma concentration. Given that the dose is 100mg/kg and the plasma concentration is 2mg/dl, we can assume the dose given is 100mg/kg of a 20kg child, which is 2000mg. Therefore, Vd = 2000mg / 2mg/dl = 1000dl or 1L. The clearance (Cl) is given as 200ml/hr. We can use the formula: Cl = (Dose / Vd) x (1/t1/2). Rearranging this formula to solve for t1/2, we get: t1/2 = (Vd / Dose) x Cl. Substituting the values, t1/2 = (1L / 2000mg) x 200ml/hr = 0.1hr. Now, we can calculate the time required to reach steady state using the formula: t = t1/2 x 5.6 = 0.1hr x 5.6 = 0.56hr.
**Why Each Wrong Option is Incorrect**
**Option A:** This option is not provided.
**Option B:** This option is not provided.
**Option C:** This option is not provided.
**Option D:** This option is not provided.
**Clinical Pearl / High-Yield Fact**
The time required to reach steady state can be estimated using the formula: t = t1/2 x 5.6. This formula assumes that the half-life of the drug is constant and does not change with repeated dosing.
**Correct Answer:** . 0.56hr.