Power law IVIVC: An application of fractional kinetics for drug release and absorption

Anomalous kinetic study of atenolol release from ATN@DNA a core-shell like structure

The need for more efficient drug delivery strategies with ultraprecision and control over the release of drugs has led to the growth of more sophisticated drug-releasing systems as a promising alternative to conventional clinical therapies. This new seed of strategies has explored an encouraging property to overcome the inherent problems of traditional therapies. One of the major challenges for any drug delivery system is the introduction of a complete view of the delivery system. In this article, we intend to elucidate the theoretical proof of concept of the electrosynthesis ATN@DNA core-shell like structure as a model system. Therefore, we present a fractal kinetic model (non-exponential model) taking into consideration the concept of time-dependent diffusion coefficient, which was developed using a numerical method with the help of COMSOL Multiphysics. In addition to that, we present here a general fractional kinetic model in sense of the tempered fractional operator, which leads to better characterized memory properties of the release process. Also, the fractional model is compared with the fractal kinetic model and both offer a good description of drug release processes that present anomalous kinetics. The solutions of the fractal and fractional kinetic models are also fitted successfully with our real-release results.

Fractal Kinetic Implementation in Population Pharmacokinetic Modeling

Compartment modeling is a widely accepted technique in the field of pharmacokinetic analysis. However, conventional compartment modeling is performed under a homogeneity assumption that is not a naturally occurring condition. Since the assumption lacks physiological considerations, the respective modeling approach has been questioned, as novel drugs are increasingly characterized by physiological or physical features. Alternative approaches have focused on fractal kinetics, but evaluations of their application are lacking. Thus, in this study, a simulation was performed to identify desirable fractal-kinetics applications in conventional modeling. Visible changes in the profiles were then investigated. Five cases of finalized population models were collected for implementation. For model diagnosis, the objective function value (OFV), Akaike's information criterion (AIC), and corrected Akaike's information criterion (AICc) were used as performance metrics, and the goodness of fit (GOF), visual predictive check (VPC), and normalized prediction distribution error (NPDE) were used as visual diagnostics. In most cases, model performance was enhanced by the fractal rate, as shown in a simulation study. The necessary parameters of the fractal rate in the model varied and were successfully estimated between 0 and 1. GOF, VPC, and NPDE diagnostics show that models with the fractal rate described the data well and were robust. In the simulation study, the fractal absorption process was, therefore, chosen for testing. In the estimation study, the rate application yielded improved performance and good prediction-observation agreement in early sampling points, and did not cause a large shift in the original estimation results. Thus, the fractal rate yielded explainable parameters by setting only the heterogeneity exponent, which reflects true physiological behavior well. This approach can be expected to provide useful insights in pharmacological decision making.

Effect of MDI Actuation Timing on Inhalation Dosimetry in a Human Respiratory Tract Model

Accurate knowledge of the delivery of locally acting drug products, such as metered-dose inhaler (MDI) formulations, to large and small airways is essential to develop reliable in vitro/in vivo correlations (IVIVCs). However, challenges exist in modeling MDI delivery, due to the highly transient multiscale spray formation, the large variability in actuation–inhalation coordination, and the complex lung networks. The objective of this study was to develop/validate a computational MDI-releasing-delivery model and to evaluate the device actuation effects on the dose distribution with the newly developed model. An integrated MDI–mouth–lung (G9) geometry was developed. An albuterol MDI with the chlorofluorocarbon propellant was simulated with polydisperse aerosol size distribution measured by laser light scatter and aerosol discharge velocity derived from measurements taken while using a phase Doppler anemometry. The highly transient, multiscale airflow and droplet dynamics were simulated by using large eddy simulation (LES) and Lagrangian tracking with sufficiently fine computation mesh. A high-speed camera imaging of the MDI plume formation was conducted and compared with LES predictions. The aerosol discharge velocity at the MDI orifice was reversely determined to be 40 m/s based on the phase Doppler anemometry (PDA) measurements at two different locations from the mouthpiece. The LES-predicted instantaneous vortex structures and corresponding spray clouds resembled each other. There are three phases of the MDI plume evolution (discharging, dispersion, and dispensing), each with distinct features regardless of the actuation time. Good agreement was achieved between the predicted and measured doses in both the device, mouth–throat, and lung. Concerning the device–patient coordination, delayed MDI actuation increased drug deposition in the mouth and reduced drug delivery to the lung. Firing MDI before inhalation was found to increase drug loss in the device; however, it also reduced mouth–throat loss and increased lung doses in both the central and peripheral regions.

Tailored Pharmacokinetic model to predict drug trapping in long-term anesthesia

Introduction

In long-term induced general anesthesia cases such as those uniquely defined by the ongoing Covid-19 pandemic context, the clearance of hypnotic and analgesic drugs from the body follows anomalous diffusion with afferent drug trapping and escape rates in heterogeneous tissues. Evidence exists that drug molecules have a preference to accumulate in slow acting compartments such as muscle and fat mass volumes. Currently used patient dependent pharmacokinetic models do not take into account anomalous diffusion resulted from heterogeneous drug distribution in the body with time varying clearance rates.

Objectives

This paper proposes a mathematical framework for drug trapping estimation in PK models for estimating optimal drug infusion rates to maintain long-term anesthesia in Covid-19 patients. We also propose a protocol for measuring and calibrating PK models, along with a methodology to minimize blood sample collection.

Methods

We propose a framework enabling calibration of the models during the follow up of Covid-19 patients undergoing anesthesia during their treatment and recovery period in ICU. The proposed model can be easily updated with incoming information from clinical protocols on blood plasma drug concentration profiles. Already available pharmacokinetic and pharmacodynamic models can be then calibrated based on blood plasma concentration measurements.

Results

The proposed calibration methodology allow to minimize risk for potential over-dosing as clearance rates are updated based on direct measurements from the patient.

Conclusions

The proposed methodology will reduce the adverse effects related to over-dosing, which allow further increase of the success rate during the recovery period.

In vivo dissolution of poorly water-soluble drugs: Proof of concept based on fluorescence bioimaging

In vitro‒in vivo correlation (IVIVC) of solid dosage forms should be established basically between in vitro and in vivo dissolution of active pharmaceutical ingredients. Nevertheless, in vivo dissolution profiles have never been accurately portrayed. The current practice of IVIVC has to resort to in vivo absorption fractions (F_a). In this proof-of-concept study, in vivo dissolution of a model poorly water-soluble drug fenofibrate (FNB) was investigated by fluorescence bioimaging. FNB crystals were first labeled by near-infrared fluorophores with aggregation-caused quenching properties. The dyes illuminated FNB crystals but quenched immediately and absolutely once been released into aqueous media, enabling accurate monitoring of residual drug crystals. The linearity established between fluorescence and crystal concentration justified reliable quantification of FNB crystals. In vitro dissolution was first measured following pharmacopoeia monograph protocols with well-documented IVIVC. The synchronicity between fluorescence and in vitro dissolution of FNB supported using fluorescence as a measure for determination of dissolution. In vitro dissolution correlated well with in vivo dissolution, acquired by either live or ex vivo imaging. The newly established IVIVC was further validated by correlating both in vitro and in vivo dissolution with F_a obtained from pharmacokinetic data.

Panos Macheras: a pioneering scientist in pharmaceutical science

Professor Panos Macheras is a pioneering scientist in pharmacokinetics, pharmacodynamics and biopharmaceutics. His many important contributions to pharmaceutical science are reviewed.

On the unphysical hypotheses in pharmacokinetics and oral drug absorption: Time to utilize instantaneous rate coefficients instead of rate constants

This work aims to explore the unphysical assumptions associated with i) the homogeneity of the well mixed compartments of pharmacokinetics and ii) the diffusion limited model of drug dissolution. To this end, we i) tested the homogeneity hypothesis using Monte Carlo simulations for a reaction and a diffusional process that take place in Euclidean and fractal media, ii) re-considered the flip-flop kinetics assuming that the absorption rate for a one-compartment model is governed by an instantaneous rate coefficient instead of a rate constant, and, iii) re-considered the extent of drug absorption as a function of dose using an in vivo reaction limited model of drug dissolution with integer and non-integer stoichiometry values. We found that drug diffusional processes and reactions are slowed down in heterogeneous media and the environmental heterogeneity leads to increased fluctuations of the measurable quantities. Highly variable experimental literature data with measurements in intrathecal space and gastrointestinal fluids were explained accordingly. Next, by applying power law and Weibull input functions to a one-compartment model of disposition we show that the shape of concentration-time curves is highly dependent on the time exponent of the input functions. Realistic examples based on PK data of three compounds known to exhibit flip-flop kinetics are analyzed. The need to use time dependent coefficients instead of rate constants in PBPK modeling and virtual bioequivalence is underlined. Finally, the shape of the fraction absorbed as a function of dose plots, using an in vivo reaction limited model of drug dissolution were found to be dependent on the stoichiometry value and the solubility of drug. Ascending and descending limbs were observed for the higher stoichiometries (2.0 and 1.5) with the low solubility drug. In contrast, for the more soluble drug, a continuous increase of fraction absorbed as a function of dose is observed when the higher stoichiometries are used (2.0 and 1.5). For both drugs, the fraction absorbed for the lower values of stoichiometry (0.7 and 1.0) exhibit a non-dependency on dose profile. Our results give an insight into the complex picture of in vivo drug dissolution since diffusion-limited and reaction-limited processes seem to operate under in vivo conditions concurrently.

Mathematical Models as Tools to Predict the Release Kinetic of Fluorescein from Lyotropic Colloidal Liquid Crystals

In this study, we investigated the release kinetic of fluorescein from colloidal liquid crystals made from monoglyceride and different non-ionic surfactants. The crystals were physicochemically characterized and the release experiments were carried out under the sink conditions, while mathematical models were described as extrapolations from solutions of the diffusion equation, in different initial and boundary conditions imposed by pharmaceutical formulations. The diffusion equation was solved using Laplace and Fourier transformed functions for release kinetics from infinite reservoirs in a semi-infinite medium. Solutions represents a general square root law and can be applied for the release kinetic of fluorescein from lyotropic colloidal liquid crystals. Akaike, Schwartz, and Imbimbo criteria were used to establish the appropriate mathematical model and the hierarchy of the performances of different models applied to the release experiments. The Fisher statistic test was applied to obtain the significance of differences among mathematical models. Differences of mathematical criteria demonstrated that small or no significant statistic differences were carried out between the various applied models and colloidal formulations. Phenomenological models were preferred over the empirical and semi-empirical ones. The general square root model shows that the diffusion-controlled release of fluorescein is the mathematical models extrapolated for lyotropic colloidal liquid crystals.

A reaction limited in vivo dissolution model for the study of drug absorption: Towards a new paradigm for the biopharmaceutic classification of drugs

The aim of this work is to develop a gastrointestinal (GI) drug absorption model based on a reaction limited model of dissolution and consider its impact on the biopharmaceutic classification of drugs. Estimates for the fraction of dose absorbed as a function of dose, solubility, reaction/dissolution rate constant and the stoichiometry of drug-GI fluids reaction/dissolution were derived by numerical solution of the model equations. The undissolved drug dose and the reaction/dissolution rate constant drive the dissolution rate and determine the extent of absorption when high-constant drug permeability throughout the gastrointestinal tract is assumed. Dose is an important element of drug-GI fluids reaction/dissolution while solubility exclusively acts as an upper limit for drug concentrations in the lumen. The 3D plots of fraction of dose absorbed as a function of dose and reaction/dissolution rate constant for highly soluble and low soluble drugs for different "stoichiometries" (0.7, 1.0, 2.0) of the drug-reaction/dissolution with the GI fluids revealed that high extent of absorption was found assuming high drug- reaction/dissolution rate constant and high drug solubility. The model equations were used to simulate in vivo supersaturation and precipitation phenomena. The model developed provides the theoretical basis for the interpretation of the extent of drug's absorption on the basis of the parameters associated with the drug-GI fluids reaction/dissolution. A new paradigm emerges for the biopharmaceutic classification of drugs, namely, a model independent biopharmaceutic classification scheme of four drug categories based on either the fulfillment or not of the current dissolution criteria and the high or low % drug metabolism.

Studies on Core-Shell Nanocapsules of Felodipine: In Vitro-In Vivo Evaluations

The present study aimed for in vitro-in vivo-in silico simulation studies of experimentally designed (3²-factorial) Capmul PG-8-cored, Eudragit RSPO-Lutrol F 127 nanocapsules to ferry felodipine using GastroPlus™. The in silico parameter sensitivity analysis for pharmacokinetic parameters was initially assessed to justify the preparation of felodipine-loaded nanocapsules (FLNs) with enhanced solubility to overcome the bioavailability issues of felodipine. The overall integrated desirability ranged between 0.8187 and 0.9488 for three optimized FLNs when analyzed for mean particle size, zeta potential, encapsulation efficiency, and in vitro dissolution parameters. The morphological evaluation (SEM, TEM, and AFM) demonstrated spherical nanoparticles (200-300 nm). Validated LC-MS/MS analysis demonstrated enhanced relative bioavailability (13.37-fold) of optimized FLN as compared to suspension. The simulated regional absorption of the FLN presented significant absorption from the cecum (26.3%) and ascending colon (20.1%) with overall absorption of 67.4% from the GIT tract. Furthermore, in vitro-in vivo correlation demonstrated the Wagner-Nelson method as the preferred model as compared to mechanistic and numerical deconvolution on the basis of least mean absolute prediction error, least standard error of prediction, least mean absolute error, and maximum correlation coefficient (r ² = 0.920). The study demonstrated enhanced oral absorption of felodipine-loaded nanocapsules, and GastroPlus™ was found to be an efficient simulation tool for in vitro-in vivo-in silico simulations.

Fractional calculus in pharmacokinetics

We are witnessing the birth of a new variety of pharmacokinetics where non-integer-order differential equations are employed to study the time course of drugs in the body: this is dubbed "fractional pharmacokinetics". The presence of fractional kinetics has important clinical implications such as the lack of a half-life, observed, for example with the drug amiodarone and the associated irregular accumulation patterns following constant and multiple-dose administration. Building models that accurately reflect this behaviour is essential for the design of less toxic and more effective drug administration protocols and devices. This article introduces the readers to the theory of fractional pharmacokinetics and the research challenges that arise. After a short introduction to the concepts of fractional calculus, and the main applications that have appeared in literature up to date, we address two important aspects. First, numerical methods that allow us to simulate fractional order systems accurately and second, optimal control methodologies that can be used to design dosing regimens to individuals and populations.

Biopharmaceutic classification of drugs revisited

The biopharmaceutics classification system (BCS) was based on the tube model of the intestinal lumen. This model considers constant drug permeability along the intestines, a plug flow fluid with the suspended drug particles moving with the fluid, and dissolution in the small particle limit. Since then the research work focusing on drug gastrointestinal (GI) absorption phenomena and processes rely on the classical laws of transport, diffusion and kinetics; however, the homogeneous assumptions associated with the well-stirred Euclidean media, where the classical laws of diffusion and kinetics apply, have been questioned in the past. In this work we explore the biopharmaceutic classification of drugs using a heterogeneous pseudo steady-state model of oral drug absorption. The fraction of dose absorbed (F_abs) was expressed as a function of two time-dependent processes where time dependent coefficients govern drug absorption and non-absorption processes. Fundamental drug properties like the absorption potential are correlated with F_abs and allow the biopharmaceutic classification of drugs taking into account the heterogeneous aspects of oral drug absorption. This analysis reveals that for Class I drugs no time dependency is expected for both absorption and non absorption processes since the gastric emptying is controlling the absorption of Class I drugs while the completion of absorption (F_abs>90%) is terminated along the first part of the jejunum. Due to the biopharmaceutical properties of Class II, III and IV drugs, these drugs travel throughout the GI tract and therefore both absorption and non absorption processes will exhibit time dependency. Thus, the calculation of F_abs (<90%) for Class II, III and IV is dependent on the estimates of the time exponents of time dependent coefficients controlling drug absorption e.g. dissolution, uptake or non absorption e.g. precipitation.

Role of chirality and macroring in imprinted polymers with enantiodiscriminative power

Enantioselective discrimination of chiral amines is of great importance as their biological properties often differ. Therefore, here we report the development of synthetic receptors for their enantioselective recognition and pH-sensitive drug release. This paper reports the preparation of three pyridine and two benzene derivatives containing an allyloxy group [(S,S)-5, 6-9] as well as their evaluation as functional monomer anchors for chiral imprinting of amines. The enantiomeric enriching ability and controlled release of the imprinted polymers (IPs) were evaluated using racemic mixture of 1-(1-naphthyl)ethylamine hydrogen perchlorate (1). The effect of the enantiomeric purity of the template on the enantioseparation performance was investigated. Racemic template in combination with enantiomerically pure macrocyclic anchors and vice versa yields IPs with excellent enantiomeric recognition. In vitro drug delivery, enantiomeric enrichment and pH-sensitive release were investigated through kinetic models.

Keeping a critical eye on the science and the regulation of oral drug absorption: a review

This review starts with an introduction on the theoretical aspects of biopharmaceutics and developments in this field from mid-1950s to late 1970s. It critically addresses issues related to fundamental processes in oral drug absorption such as the complex interplay between drugs and the gastrointestinal system. Special emphasis is placed on drug dissolution and permeability phenomena as well as on the mathematical modeling of oral drug absorption. The review ends with regulatory aspects of oral drug absorption focusing on bioequivalence studies and the US Food and Drug Administration and European Medicines Agency guidelines dealing with Biopharmaceutics Classification System and Biopharmaceutic Drug Disposition Classification System.