Panteleimon D. Mavroudis (1), Kosmas Kosmidis (2,3), Panos Macheras (1,3,4)
(1) School of Pharmacy and Pharmaceutical Sciences, State University of New York at Buffalo, Buffalo, NY, USA (2)Division of Theoretical Physics, Physics Department, Aristotle University of Thessaloniki, Thessaloniki, Greece, (3) Pharmainformatics Unit, Research and Innovation Center “Athena”, Athens, Greece, (4) Department of Pharmacy, National and Kapodistrian University of Athens, Athens, Greece
Objectives: i) examine the homogeneity hypothesis using Monte Carlo simulations for a reaction and a diffusional process, which take place in Euclidean and fractal media ii) re-consider the flip-flop kinetics assuming that an instantaneous rate coefficient and not a rate constant governs the input kinetics for a one-compartment model of drug disposition iii) re-consider the extent of drug absorption using an in vivo reaction limited model of drug dissolution with integer and non-integer stoichiometry values published recently [1].
Methods:
i) Diffusional processes and reactions in homogenous-heterogeneous media.
Diffusional processes were examined in homogeneous and fractal environments. For the homogeneous case a random walker is placed at a randomly chosen lattice site [2, 3] and then performs random walks. For the heterogeneous case, random walks on the percolation fractal were studied. The reaction of type A+B->0 was examined on homogeneous and fractal spaces.
ii) Flip-flop kinetics with time varying absorption rate coefficient.
Kinetics are tested for one compartment model under scenarios where the absorption rate is time-dependent either following a power function or a Weibull distribution function [4].
iii) Classical or fractal kinetics in a reaction-limited in vivo model of drug dissolution.
Simulations were carried out using the in vivo reaction limited model of drug dissolution [1]. Two drugs with different solubilities were considered. The fraction of dose absorbed was calculated as a function of drug dose assuming integer and non-integer values for the stoichiometry of drug dissolution/reaction.
Results:
i) Diffusional processes and reactions in homogenous-heterogeneous media.
We observed straight lines with different slopes when the mean squared displacement of the random walker was plotted relative to time for the homogenous and the fractal case. We further found a profound slowing down of the reactions in fractals as compared to homogeneous spaces. The environmental heterogeneity leads to increased fluctuations of the measurable quantities. At all times the standard deviation for the A+B->0 reaction on a fractal was found to be considerable higher than the homogeneous environment.
ii) Flip-flop kinetics with time varying absorption rate coefficient.
We observed that higher time exponent values of the power-model lead not only to higher Cmax but also to a change of the shape of the curve that retains a steeper drop for higher exponents. Similarly, when Weibull function is used, larger time exponents leads to higher Cmax and a change of the steepness of the C-t curve. The fitting of one compartment model retaining either constant or time-dependent absorption rate coefficients for three compounds known to exhibit flip-flop kinetics [5-7] showed that ka vs ke relationship may be time dependent.
iii) Classical or fractal kinetics in a reaction-limited in vivo model of drug dissolution.
In all cases studied the low values of the fraction absorbed was found to be linked with the backward constant in comparison with the dissolution/rate constant [1]. The fraction of dose absorbed is higher for the stoichiometry integer values. Ascending and descending limbs for the higher stoichiometries were observed. For both drugs, the fraction absorbed for the lower values of stoichiometry exhibit a non-dependency on dose profile.
Conclusions:
Our work revealed that the processes are slowed down in heterogeneous media; besides, the environmental heterogeneity leads to increased fluctuations of the measurable quantities. These findings explain high variability in measurements in understirred biomedia e.g. intrathecal space, gastrointestinal fluids [8,9]. Similarly, incorporation of time-dependent absorption rate coefficients showed that the simulated concentration-time profiles resemble the classical curves but the exact shape of the curve is dependent on the value of the time exponent of the input function. Fitting of PK data further underlined that the rate limiting process is time dependent and as such identification of flip-flop behavior can be misinterpreted. Finally, the profile of the fraction of dose absorbed as a function of dose, assuming different stoichiometries, revealed i) that the shape of the profile is affected by the solubility of drug and the stoichiometry of the dissolution/reaction, and ii) that higher profiles are observed for higher stoichiometries.
References:
[1] Macheras P. Iliadis A. , Melagraki G. A reaction-limited in vivo dissolution model for the study of drug absorption: Towards a new paradigm for the biopharmaceutic classification of drugs. European Journal of Pharmaceutical Sciences. 117, 98-106 (2018)
[2] Bunde,A.,Havlin,S.,2012.Fractals and Disordered Systems.Springer Science & Business Media.
[3] Bunde, A.,Havlin,S.,2013.Fractals in Science. Springer.
[4] Piotrovskii,V.K.,.The use of Weibull distribution to describe the in vivo absorption kinetics. J. Pharmacokinet. Biopharm. 15,681–686 (1987).
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[7] Lin, C.-C., Luu T., Lourenco D., Yeh L.-T., and Lau J.Y., Absorption, pharmacokinetics and excretion of levovirin in rats, dogs and cynomolgus monkeys. Journal of Antimicrobial Chemotherapy,. 51(1), 93-99 (2003).
[8] Clarysse,S., Psachoulias, D. ,Brouwers, J. ,Tack,J. ,Annaert, P., Duchateau,G., Reppas, C. , Augustijns, P. Postprandial changes in solubilizing capacity of human intestinal fluids for BCS class II drugs. Pharm.Res. 26(6),1456–1466 (2009).
[9] Kuttler, A., Dimke, T. , Kern , S. , Helmlinger , G. , Stanski, D. , Finelli , L. A. Understanding pharmacokinetics using realistic computational models of fluid dynamics: biosimulation of drug distribution within the CSF space for intrathecal drugs. J. Pharmacokinet .Pharmacodyn.37(6),629–644 (2010).
Reference: PAGE 28 (2019) Abstr 8915 [www.page-meeting.org/?abstract=8915]
Poster: Drug/Disease Modelling - Absorption & PBPK