How can you estimate the elimination rate constant (ke) and half-life (t1/2) from an IV concentration-time profile?

How can you estimate the elimination rate constant (ke) and half-life (t1/2) from an IV concentration-time profile?

• A. Ke = slope of ln(concentration) vs time; t1/2 = 0.693/ke.
• B. Ke = intercept of ln(concentration) vs time; t1/2 = 0.693/ke.
• C. Ke = slope of concentration vs time; t1/2 = 1/ke.
• D. Ke = slope of log10(concentration) vs time; t1/2 = 0.693/ke.

Answer: (A)

Understanding how elimination shows up in concentration over time is key. If elimination follows first-order kinetics, the drug concentration decays exponentially: C(t) = C0 e^(−k_e t). Taking the natural log gives ln C(t) = ln C0 − k_e t, which is a straight line when you plot ln concentration versus time. The slope of that line is negative and equals −k_e, so the elimination rate constant is the magnitude of that slope (you take the negative slope to obtain a positive ke). Once ke is known, the half-life follows from t1/2 = 0.693/ke, since 0.693 is ln 2. Using natural log keeps the relationship simple; using log base 10 would require adjusting the slope by a factor of 2.303, but the same linear idea applies. For an IV profile, you typically apply this to the terminal linear portion of the plot to get ke and then calculate t1/2 from it.

Understanding how elimination shows up in concentration over time is key. If elimination follows first-order kinetics, the drug concentration decays exponentially: C(t) = C0 e^(−k_e t). Taking the natural log gives ln C(t) = ln C0 − k_e t, which is a straight line when you plot ln concentration versus time. The slope of that line is negative and equals −k_e, so the elimination rate constant is the magnitude of that slope (you take the negative slope to obtain a positive ke). Once ke is known, the half-life follows from t1/2 = 0.693/ke, since 0.693 is ln 2. Using natural log keeps the relationship simple; using log base 10 would require adjusting the slope by a factor of 2.303, but the same linear idea applies. For an IV profile, you typically apply this to the terminal linear portion of the plot to get ke and then calculate t1/2 from it.