Which of the following parameters is directly proportional to the elimination rate constant (ke) and inversely proportional to the volume of distribution (Vd)?

Explanation

## Relationship Between Clearance, Elimination Rate Constant, and Volume of Distribution **Key Point:** Clearance (CL) is the fundamental pharmacokinetic parameter that relates elimination rate constant and volume of distribution through the equation: $$CL = k_e \times V_d$$ where: - CL = Total body clearance (mL/min or L/hr) - k_e = Elimination rate constant (hr⁻¹) - V_d = Volume of distribution (L) ### Mathematical Derivation Starting from the elimination rate equation: $$\text{Elimination rate} = k_e \times C_0 \times V_d$$ Clearance is defined as: $$CL = \frac{\text{Elimination rate}}{C_0}$$ Substituting: $$CL = k_e \times V_d$$ **High-Yield:** This relationship is fundamental to understanding drug dosing. Rearranging: - $k_e = \frac{CL}{V_d}$ - $V_d = \frac{CL}{k_e}$ ### Clinical Significance | Parameter | Definition | Clinical Use | |-----------|-----------|---------------| | Clearance (CL) | Volume of plasma cleared of drug per unit time | Determines maintenance dose | | k_e | Fraction of drug eliminated per unit time | Determines dosing interval | | V_d | Theoretical volume in which drug distributes | Determines loading dose | **Mnemonic:** **CL = k_e × V_d** — "Clear Kevin's Volume" — the three pillars of one-compartment kinetics. **Clinical Pearl:** A drug with high clearance and high V_d may have a normal half-life, but will require frequent dosing. Conversely, a drug with low clearance and low V_d will accumulate rapidly with repeated dosing.