A drug given intravenously is eliminated from the bloodstream by first-order kinetics,
PHYSICS · Multi-part · Fermi University Physics · Scientific Practice & Experimental Methods · Mathematical Methods for Physics · Data analysis and model fitting in the laboratory
Mathematical Methods for Physics, Ch First-order differential equations and physical modelling
Problem
A drug given intravenously is eliminated from the bloodstream by first-order kinetics, C˙=−C/τ, where C(t) is the plasma concentration and τ is the elimination time constant. The plasma concentration is measured at intervals. Data: C=20.0,15.6,12.1,7.4,4.5,2.7mg/L at t=0,1,2,4,6,8h.
((a)) Using the slope of lnC against t through the first and last readings, estimate the elimination time constant τ, in hours.
((b)) State the elimination half-life, in hours.
((c)) Estimate τ twice more, once from the readings at 0 and 1h alone and once from those at 6 and 8h alone.
((d)) The readings are rounded to 0.1mgL−1. Decide whether the two estimates of part (c) differ by more than that rounding can explain, and say what a clear, systematic difference between early and late estimates would have told you about the model C˙=−C/τ.