Development of hysteresis analysis as a model-independent approach to assess temporal dissociation in pharmacokinetics and pharmacodynamics
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Pharmacodynamic hysteresis is a loop, typically anti-clockwise, in the effect-concentration profile, resulting from temporal dissociation between elaboration of effect and changes in drug concentration. Hysteresis behavior impairs recovery of reliable numerical estimates of pharmacodynamic parameters. Existing methods for analyzing data with a hysteresis have focused on integrated pharmacokinetic-pharmacodynamic modeling, which is based on hypothetical constructs and unverifiable assumptions. The work presented herein was aimed at developing and evaluating model-independent metrics to quantify time delays in pharmacokinetic/pharmacodynamic systems. Relationships between various descriptors of hysteresis morphology and parameters associated with distributional (pharmacokinetic) or effect (pharmacodynamic) delays were explored in silico. The ratio of x- versus y-coordinate of the hysteresis centroid was identified through simulation studies as the most useful descriptor in characterizing pharmacokinetic delays. Utility of this metric was demonstrated with mined data examining distribution of methotrexate into human brain, and indicated that hysteresis analysis can provide robust and sensitive results when traditional parametric approaches fail. The utility of hysteresis analysis in pharmacodynamic experiments was examined with simulated data generated from a multiplicity of commonly-encountered pharmacokinetic-pharmacodynamic systems, including systems with delayed distribution to the receptor target (effect-compartment systems) and delayed elaboration of effect after binding of the drug to the target (indirect response systems). In addition, the influence of the shape of the effect-versus concentration relationship (linear, hyperbolic, or sigmoidal) on hysteresis analysis was explored. Results of these experiments indicated that hysteresis analysis is most useful when the effect-concentration relationship is linear. Consistent with observations for nonlinear pharmacokinetic systems, nonlinearities in the effect-concentration profile resulted in nonlinear relationships between hysteresis descriptors and model parameters, with a consequent loss in analytical sensitivity and specificity. Results obtained with simulated data were confirmed with data mined from 12 published reports. Taken together, the results of this project indicate that the hysteresis centroid provides information useful in quantifying delays in pharmacokinetic/pharmacodynamic systems without need for underlying assumptions. In particular, the centroid is useful for hypotheses-testing, rather than descriptive, purposes. As with non-compartmental approaches for pharmacokinetic analysis based on statistical moment theory, hysteresis analysis appears to be useful only for linear systems.