Nonlinear pharmacokinetics of mibefradil in the dog

Fractal michaelis-menten kinetics under steady state conditions: Application to mibefradil

PURPOSE

To provide the first application of fractal kinetics under steady state conditions to pharmacokinetics as a model for the enzymatic elimination of a drug from the body.

MATERIALS AND METHODS

A one-compartment model following fractal Michaelis-Menten kinetics under a steady state is developed and applied to concentration-time data for the cardiac drug mibefradil in dogs. The model predicts a fractal reaction order and a power law asymptotic time-dependence of the drug concentration, therefore a mathematical relationship between the fractal reaction order and the power law exponent is derived. The goodness-of-fit of the model is assessed and compared to that of four other models suggested in the literature.

RESULTS

The proposed model provided the best fit to the data. In addition, it correctly predicted the power law shape of the tail of the concentration-time curve.

CONCLUSION

A simple one-compartment model with steady state fractal Michaelis-Menten kinetics describing drug elimination from the body most accurately describes the pharmacokinetics of mibefradil in dogs. The new fractal reaction order can be explained in terms of the complex geometry of the liver, the organ responsible for eliminating the drug.

Asymptotic time dependence in the fractal pharmacokinetics of a two-compartment model

We further investigate, both analytically and numerically, the properties of the fractal two-compartment model introduced by Fuite [J. Fuite, R. Marsh, and J. Tuszynski, Phys. Rev. E 66, 021904 (2002)]. Specifically, we look at the effects of the fractal exponent of the elimination rate coefficient on the long-time behavior of the pharmacokinetic clearance tail. For small exponent values, the tail exhibits exponential behavior, while for larger values, there is a transition to a power law. The theory is applied to seven data sets simulating drugs taken from the pharmacological literature.

Michaelis-Menten kinetics under spatially constrained conditions: application to mibefradil pharmacokinetics

Two different approaches were used to study the kinetics of the enzymatic reaction under heterogeneous conditions to interpret the unusual nonlinear pharmacokinetics of mibefradil. Firstly, a detailed model based on the kinetic differential equations is proposed to study the enzymatic reaction under spatial constraints and in vivo conditions. Secondly, Monte Carlo simulations of the enzyme reaction in a two-dimensional square lattice, placing special emphasis on the input and output of the substrate were applied to mimic in vivo conditions. Both the mathematical model and the Monte Carlo simulations for the enzymatic reaction reproduced the classical Michaelis-Menten (MM) kinetics in homogeneous media and unusual kinetics in fractal media. Based on these findings, a time-dependent version of the classic MM equation was developed for the rate of change of the substrate concentration in disordered media and was successfully used to describe the experimental plasma concentration-time data of mibefradil and derive estimates for the model parameters. The unusual nonlinear pharmacokinetics of mibefradil originates from the heterogeneous conditions in the reaction space of the enzymatic reaction. The modified MM equation can describe the pharmacokinetics of mibefradil as it is able to capture the heterogeneity of the enzymatic reaction in disordered media.

Fractal pharmacokinetics of the drug mibefradil in the liver

We explore the ramifications of the fractal geometry of the key organ for drug elimination, the liver, on pharmacokinetic data analysis. A formalism is developed for the use of a combination of well-stirred Euclidean and fractal compartments in the body. Perturbation analysis is carried out to obtain analytical solutions for the drug concentration time evolution. These results are then fitted to experimental data collected from clinically instrumented dogs [see, A. Skerjanec et al., J. Pharm. Sci. 85, 189 (1995)] using the drug mibefradil. The thus obtained spectral fractal dimension has a range of values that is consistent with the value found in independently performed ultrasound experiments on the liver.

Comparison of the efficacy and safety of losartan (50-100 mg) with the T-type calcium channel blocker mibefradil (50-100 mg) in mild to moderate hypertension

The objective of this study was to compare the antihypertensive efficacy and safety of losartan and mibefradil. 324 outpatients (57 +/- 9.2 years) with mild to moderate hypertension were randomly allocated in a double-blind fashion to receive 50 mg of losartan or mibefradil once daily p.o. for 6 weeks after 2 weeks of placebo run-in. Titration was then forced to 100 mg of losartan or mibefradil for an additional 6 weeks. Patients were assessed at baseline, 6 and 12 weeks. The primary efficacy variable was change in predose sitting diastolic (SDBP) and systolic (SSBP) blood pressure at 12 weeks. Secondary variables included change in mean 24-hour ambulatory blood pressure and comparison of safety and tolerability. Both treatments lowered SSBP and SDBP at 6 and 12 weeks (week 6: mibefradil -14/-9 mm Hg; losartan -12/-7 mm Hg) (P <0.001). The primary objective, a difference between treatments in reduction of SSBP and SDBP at week 12 could be demonstrated (mibefradil -22/-16 mm Hg; losartan -16/-10 mm Hg) (P=0.003 and P=0.001, respectively). Twenty-four-hour SBP and 24-hour DBP were reduced (P<0.001) within each treatment group at weeks 6 and 12. The secondary objective, a difference between treatments in reduction of 24-hour blood pressure at week 12 could be demonstrated (P<0.001). Twenty-four-hour heart rate was lowered in the mibefradil group at weeks 6 and 12 (P < 0.001). Responder rates at 6 and 12 weeks were 56.2% and 78.5% for mibefradil versus 56.1% and 55.3% for losartan (P = 0.001). Both treatments were equally well tolerated. This study demonstrates that 50 mg losartan is comparably effective to 50 mg mibefradil in the treatment of mild to moderate hypertension with 100 mg mibefradil being more potent than losartan.