Application of Kirchhoff's Laws to pharmacologic and pharmacokinetic analyses.

Abstract

Recently, we introduced a straightforward approach to derive clearance and rate constant equations, without relying on differential equations, utilizing Kirchhoff's Laws, a well known physics methodology used to describe rate-defining processes either in series or parallel. Manuscripts from our laboratory have re-examined published experimental data, demonstrating that the Kirchhoff's Laws methodology can explain data previously considered anomalous, such as the following: (1) all experimental perfused liver clearance data conforming to the equation once thought to represent the unphysiological well stirred model, (2) instances where linear pharmacokinetic systemic bioavailability determinations exceed unity, (3) renal clearance being influenced by drug input processes, (4) statistically significant differences in bioavailability measures between urinary excretion and systemic concentration measurements, and (5) how the long-accepted steady-state clearance approach used in pharmacokinetics for the past half-century leads to unrealistic conclusions about the relationship between liver-to-blood Kp_uu and hepatic availability F_H. These findings demonstrate the potential for errors in pharmacokinetic evaluations that rely on differential equations. The Kirchhoff's Laws approach is applicable to all pharmacokinetic analyses of quality experimental data, both those that align with present pharmacokinetic theory, and those that do not. Although 3 publications have attempted to rebut our position, they fail to address unexplained experimental data, and we detail here why these analyses are invalid. Our discoveries are ongoing. Additionally, we briefly discuss the application of Kirchoff's Laws to saturable nonlinear kinetics, explaining increased pharmacodynamic response for extended vs immediate release dosage forms, as well as the advantages of successfully formulating high hepatic extraction drugs. SIGNIFICANCE STATEMENT: The Kirchhoff's Laws approach to deriving clearance equations for linear systems in parallel or in series, independent of differential equations, successfully describes anomalous published pharmacokinetic data that have previously been unexplained. We review 9 experimental outcomes in humans that are newly explained using the Kirchhoff's Laws approach, including the extension to deriving nonlinear saturable clearance relationships.