Fractional dynamics pharmacokinetics–pharmacodynamic models

While an increasing number of fractional order integrals and differential equations applications have been reported in the physics, signal processing, engineering and bioengineering literatures, little attention has been paid to this class of models in the pharmacokinetics–pharmacodynamic (PKPD) literature. One of the reasons is computational: while the analytical solution of fractional differential equations is available in special cases, it this turns out that even the simplest PKPD models that can be constructed using fractional calculus do not allow an analytical solution. In this paper, we first introduce new families of PKPD models incorporating fractional order integrals and differential equations, and, second, exemplify and investigate their qualitative behavior. The families represent extensions of frequently used PK link and PD direct and indirect action models, using the tools of fractional calculus. In addition the PD models can be a function of a variable, the active drug, which can smoothly transition from concentration to exposure, to hyper-exposure, according to a fractional integral transformation. To investigate the behavior of the models we propose, we implement numerical algorithms for fractional integration and for the numerical solution of a system of fractional differential equations. For simplicity, in our investigation we concentrate on the pharmacodynamic side of the models, assuming standard (integer order) pharmacokinetics

Physiologically based pharmacokinetic modeling of arterial – antecubital vein concentration difference

BACKGROUND: Modeling of pharmacokinetic parameters and pharmacodynamic actions requires knowledge of the arterial blood concentration. In most cases, experimental measurements are only available for a peripheral vein (usually antecubital) whose concentration may differ significantly from both arterial and central vein concentration. METHODS: A physiologically based pharmacokinetic (PBPK) model for the tissues drained by the antecubital vein (referred to as "arm") is developed. It is assumed that the "arm" is composed of tissues with identical properties (partition coefficient, blood flow/gm) as the whole body tissues plus a new "tissue" representing skin arteriovenous shunts. The antecubital vein concentration depends on the following parameters: the fraction of "arm" blood flow contributed by muscle, skin, adipose, connective tissue and arteriovenous shunts, and the flow per gram of the arteriovenous shunt. The value of these parameters was investigated using simultaneous experimental measurements of arterial and antecubital concentrations for eight solutes: ethanol, thiopental, (99)Tc(m)-diethylene triamine pentaacetate (DTPA), ketamine, D(2)O, acetone, methylene chloride and toluene. A new procedure is described that can be used to determine the arterial concentration for an arbitrary solute by deconvolution of the antecubital concentration. These procedures are implemented in PKQuest, a general PBPK program that is freely distributed . RESULTS: One set of "standard arm" parameters provides an adequate description of the arterial/antecubital vein concentration for ethanol, DTPA, thiopental and ketamine. A significantly different set of "arm" parameters was required to describe the data for D(2)O, acetone, methylene chloride and toluene – probably because the "arm" is in a different physiological state. CONCLUSIONS: Using the set of "standard arm" parameters, the antecubital vein concentration can be used to determine the whole body PBPK model parameters for an arbitrary solute without any additional adjustable parameters. Also, the antecubital vein concentration can be used to estimate the arterial concentration for an arbitrary input for solutes for which no arterial concentration data is available

Oral heroin in opioid-dependent patients: Pharmacokinetic comparison of immediate and extended release tablets

In diacetylmorphine prescription programs for heavily dependent addicts, diacetylmorphine is usually administered intravenously, but this may not be possible due to venosclerosis or when heroin abuse had occurred via non-intravenous routes. Since up to 25% of patients administer diacetylmorphine orally, we characterised morphine absorption after single oral doses of immediate and extended release diacetylmorphine in 8 opioid addicts. Plasma concentrations were determined by liquid chromatography-mass spectrometry. Non-compartmental methods and deconvolution were applied for data analysis. Mean (+/-S.D.) immediate and extended release doses were 719+/-297 and 956+/-404mg, with high absolute morphine bioavailabilities of 56-61%, respectively. Immediate release diacetylmorphine caused rapid morphine absorption, peaking at 10-15min. Morphine absorption was considerably slower and more sustained for extended release diacetylmorphine, with only approximately 30% of maximal immediate release absorption being reached after 10min and maintained for 3-4h, with no relevant food interaction. The relative extended to immediate release bioavailability was calculated to be 86% by non-compartmental analysis and 93% by deconvolution analysis. Thus, immediate and extended release diacetylmorphine produce the intended morphine exposures. Both are suitable for substitution treatments. Similar doses can be applied if used in combination or sequentially

Population pharmacokinetic modelling of rupatadine solution in 6–11 year olds and optimisation of the experimental design in younger children

AIMS:To optimise a pharmacokinetic (PK) study design of rupatadine for 2-5 year olds by using a population PK model developed with data from a study in 6-11 year olds. The design optimisation was driven by the need to avoid children's discomfort in the study. METHODS:PK data from 6-11 year olds with allergic rhinitis available from a previous study were used to construct a population PK model which we used in simulations to assess the dose to administer in a study in 2-5 year olds. In addition, an optimal design approach was used to determine the most appropriate number of sampling groups, sampling days, total samples and sampling times. RESULTS:A two-compartmental model with first-order absorption and elimination, with clearance dependent on weight adequately described the PK of rupatadine for 6-11 year olds. The dose selected for a trial in 2-5 year olds was 2.5 mg, as it provided a Cmax below the 3 ng/ml threshold. The optimal study design consisted of four groups of children (10 children each), a maximum sampling window of 2 hours in two clinic visits for drawing three samples on day 14 and one on day 28 coinciding with the final examination of the study. CONCLUSIONS:A PK study design was optimised in order to prioritise avoidance of discomfort for enrolled 2-5 year olds by taking only four blood samples from each child and minimising the length of hospital stays