Re-writing Oral Pharmacokinetics Using Physiologically Based Finite Time Pharmacokinetic (PBFTPK) Models

Time Scale Calculus: a new approach to multi-dose pharmacokinetic modeling

In this paper, we use Time Scale Calculus (TSC) to formulate and solve pharmacokinetic models exploring multiple dose dynamics. TSC is a mathematical framework that allows the modeling of dynamical systems comprising continuous and discrete processes. This characteristic makes TSC particularly suited for multi-dose pharmacokinetic problems, which inherently feature a blend of continuous processes (such as absorption, metabolization, and elimination) and discrete events (drug intake). We use this toolkit to derive analytical expressions for blood concentration trajectories under various multi-dose regimens across several flagship pharmacokinetic models. We demonstrate that this mathematical framework furnishes an alternative and simplified way to model and retrieve analytical solutions for multi-dose dynamics. For instance, it enables the study of blood concentration responses to arbitrary dose regimens and facilitates the characterization of the long-term behavior of the solutions, such as their steady state.

Application of the Finite Absorption Time (F.A.T.) Concept in the Assessment of Bioequivalence

PURPOSE

Το formulate a methodology for the assessment of bioequivalence using metrics, which are based on the physiologically sound F.A.T.

CONCEPT

METHODS

The equations of the physiologically based finite time pharmacokinetic models for the one-and two-compartment model with one and two input stages of absorption were solved to derive metrics for the extent and rate of absorption. Simulated data were used to study the proper way for the estimation of metrics. A bioequivalence study was analyzed using these metrics.

RESULTS

The rate of drug absorption was found to be equal to the slope of the amount absorbed versus time curve. The amount of drug absorbed at the end of the absorption process, corresponding to the blood concentration at F.A.T. is an indicator of the extent of absorption. The plot of the ratio test/reference of the simulated data for the amount absorbed as a function of time becomes constant beyond the end of drug absorption from the formulation exhibiting the longer absorption. The assessment of the bioequivalence study was based on the slope of the amount absorbed versus time curve for the rate of absorption, while the estimate for the constant ratio test/reference for the amount absorbed was used for the assessment of extent of absorption.

CONCLUSIONS

The assessment of rate in bioequivalence studies can be based on the estimation of slope of the percent absorbed versus time curve while the constant ratio test/reference for the amount of drug absorbed is an indicator of the extent of absorption.

Importance of Considering Fed-State Gastrointestinal Physiology in Predicting the Reabsorption of Enterohepatic Circulation of Drugs

PURPOSE

The purpose of this study was to develop a simulation model for the pharmacokinetics (PK) of drugs undergoing enterohepatic circulation (EHC) with consideration to the environment in the gastrointestinal tract in the fed state in humans. The investigation particularly focused on the necessity of compensating for the permeability rate constant in the reabsorption process in consideration of drug entrapment in bile micelles.

METHODS

Meloxicam and ezetimibe were used as model drugs. The extent of the entrapment of drugs inside bile micelles was evaluated using the solubility ratio of Fed State Simulated Intestinal Fluid version 2 (FeSSIF-V2) to Fasted State Simulated Intestinal Fluid version 2 (FaSSIF-V2). Prediction accuracy was evaluated using the Mean Absolute Percentage Error (MAPE) value, calculated from the observed and predicted oral PK profiles.

RESULTS

The solubilization of ezetimibe by bile micelles was clearly observed while that of meloxicam was not. Assuming that only drugs in the free fraction of micelles permeate through the intestinal membrane, PK simulation for ezetimibe was performed in both scenarios with and without compensation by the permeation rate constant. The MAPE value of Zetia® tablet, containing ezetimibe, was lower with compensation than without compensation. By contrast, Mobic® tablet, containing meloxicam, showed a relatively low MAPE value even without compensation.

CONCLUSION

For drugs which undergo EHC and can be solubilized by bile micelles, compensating for the permeation rate constant in the reabsorption process based on the free fraction ratio appears an important factor in increasing the accuracy of PK profile prediction.

Coupling Drug Dissolution with BCS

PURPOSE

The purpose of this study is to develop a Temporal Biopharmaceutic Classification System (T-BCS), linking Finite Dissolution Time (F.D.T.) and Mean Dissolution Time (M.D.T.) for Class I/III drugs and Mean Dissolution Time for saturation (M.D.T.s.) for Class II/IV drugs.

METHODS

These parameters are estimated graphically or by fitting dissolution models to experimental data and coupled with the dose-to-solubility ratio (q) for each drug normalized in terms of the actual volume of dissolution medium (900 mL).

RESULTS

Class I/III drugs consistently exhibited q values less than 1, aligning with expectations based on their solubility, while some Class II/IV drugs presented a deviation from anticipated q values, with observations of q < 1. This irregularity was rendered to the dissolution volume of 250 mL used for biopharmaceutical classification purposes instead of 900 mL applied as well as the dual classification of some sparingly soluble drugs. Biowaivers were also analyzed in terms of M.D.T., F.D.T. estimates and the regulatory dissolution time limits for rapidly and very-rapidly dissolved drugs.

CONCLUSIONS

The T-BCS is useful for establishing correlations and assessing the magnitude of M.D.T., F.D.T., or M.D.T.s. for inter- and intra-class comparisons of different drugs and provide relationships between these parameters across all the models that were utilized.

IVIVC Revised

PURPOSE

To revise the IVIVC considering the physiologically sound Finite Absorption Time (F.A.T.) and Finite Dissolution Time (F.D.T.) concepts.

METHODS

The estimates τ and τd for F.A.T. and F.D.T., respectively are constrained by the inequality τd ≤ τ; their relative magnitude is dependent on drug's BCS classification. A modified Levy plot, which includes the time estimates for τ and τd was developed. IVIVC were also considered in the light of τ and τd estimates. The modified Levy plot of theophylline, a class I drug, coupled with the rapid (30 min) and very rapid (15 min) dissolution time limits showed that drug dissolution/absorption of Class I drugs takes place in less than an hour. We reanalyzed a carbamazepine (Tegretol) bioequivalence study using PBFTPK models to reveal its complex absorption kinetics with two or three stages.

RESULTS

The modified Levy plot unveiled the short time span (~ 2 h) of the in vitro dissolution data in comparison with the duration of in vivo dissolution/absorption processes (~ 17 h). Similar results were observed with the modified IVIVC plots. Analysis of another set of carbamazepine data, using PBFTPK models, confirmed a three stages absorption process. Analysis of steady-state (Tegretol) data from a paediatric study using PBFTPK models, revealed a single input stage of duration 3.3 h. The corresponding modified Levy and IVIVC plots were found to be nonlinear.

CONCLUSIONS

The consideration of Levy plots and IVIVC in the light of the F.A.T. and F.D.T. concepts allows a better physiological insight of the in vitro and in vivo drug dissolution/absorption processes.

How to use an in vitro approach to characterize the toxicity of airborne compounds

As part of the development of new approach methodologies (NAMs), numerous in vitro methods are being developed to characterize the potential toxicity of inhalable xenobiotics (gases, volatile organic compounds, polycyclic aromatic hydrocarbons, particulate matter, nanoparticles). However, the materials and methods employed are extremely diverse, and no single method is currently in use. Method standardization and validation would raise trust in the results and enable them to be compared. This four-part review lists and compares biological models and exposure methodologies before describing measurable biomarkers of exposure or effect. The first section emphasizes the importance of developing alternative methods to reduce, if not replace, animal testing (3R principle). The biological models presented are mostly to cultures of epithelial cells from the respiratory system, as the lungs are the first organ to come into contact with air pollutants. Monocultures or cocultures of primary cells or cell lines, as well as 3D organotypic cultures such as organoids, spheroids and reconstituted tissues, but also the organ(s) model on a chip are examples. The exposure methods for these biological models applicable to airborne compounds are submerged, intermittent, continuous either static or dynamic. Finally, within the restrictions of these models (i.e. relative tiny quantities, adhering cells), the mechanisms of toxicity and the phenotypic markers most commonly examined in models exposed at the air-liquid interface (ALI) are outlined.

Revamping Biopharmaceutics-Pharmacokinetics with Scientific and Regulatory Implications for Oral Drug Absorption

PURPOSE

The Wagner-Nelson and Loo-Riegelman methods developed in the 1960s and used since for the construction of percent of drug absorbed as a function of time as well as in in vitro in vivo correlations are re-considered in the light of the physiologically sound Finite Absorption Time (F.A.T.) concept developed recently.

METHODS

The classical equations for the percentage of drug absorption as a function of time were modified by taking into account the termination of drug absorption at F.A.T., replacing the parameters associated with the assumption of infinite drug absorption.

RESULTS

Mathematical analysis using the relevant Physiologically Based Pharmacokinetic Finite Time (PBFTK) models assuming one- or two-compartment drug disposition, revealed that the modified %absorbed versus time curves are of bilinear type with an ascending limb intersecting the horizontal line at F.A.T. A computer-based methodology is described for the estimation of F.A.T. from experimental data. More than one linear ascending limb is found when more than one absorption phase is operating. Experimental data were analyzed and the estimates for F.A.T were found to be similar to those derived from nonlinear regression analysis using PBFTPK models.

CONCLUSION

These results place an end to the routinely reported exponential %absorbed versus time curves prevailing in biopharmaceutics-pharmacokinetics since their inception in the'60 s. These findings point to the use of the F.A.T. concept in drug absorption research and regulatory guidelines such as deconvolution techniques for the assessment of drug input rate, stochastic mean absorption time calculations, population analyses, in vitro in vivo correlations and bioequivalence guidelines.

Is the One-Compartment Model with First Order Absorption a Useful Approximation?

PURPOSE

The one-compartment model with first order absorption (ka1C) has been extensively used to fit oral data. But when the disposition parameters of the drug are not available, the bias in the parameter estimates remains unclear. In this paper, the effect of potential misspecification of the area under the curve (AUC) and the mean absorption time (MAT) was evaluated for three relatively slowly absorbed drugs/formulations.

METHODS

Assuming a three-compartment disposition model with an input (absorption) rate described as a sum of two inverse Gaussian functions (2IG3C) as the true model, the deviations of AUC and MAT estimated with simpler models were analyzed. Simpler models, as the ka1C model (Bateman function), the one-compartment model with IG input function (IG1C) and the gamma density function were fitted to the oral data alone, and compared to the fits obtained with the 2IG3C model which also uses the 3C disposition parameters of the drug. Data from pharmacokinetic studies of trospium, propiverine and ketamine in healthy volunteers were analyzed using a population approach.

RESULTS

The Bateman function (ka1C) allowed a robust estimation of the population mean AUC, but the individual estimates were highly biased. It failed in evaluating MAT. The simple alternative models did not improve the situation.

CONCLUSIONS

The Bateman function appears to be useful for estimating the population mean value of AUC after oral administration. The results reemphasize the fact that insight into the absorption process can be only gained when also intravenous reference data are available.

Re-examining Naloxone Pharmacokinetics After Intranasal and Intramuscular Administration Using the Finite Absorption Time Concept

BACKGROUND AND OBJECTIVES

Naloxone for opioid overdose treatment can be administered by intravenous injection, intramuscular injection, or intranasal administration. Published data indicate differences in naloxone pharmacokinetics depending on the route of administration. The aim of this study was to analyze pharmacokinetic data in the same way that we recently successfully applied the concept of the finite absorption time in orally administered drug formulations.

METHODS

Using the model equations already derived, we performed least squares analysis on 24 sets of naloxone concentration in the blood as a function of time.

RESULTS

We found that intramuscular and intranasal administration can be described more accurately when considering zero-order absorption kinetics for finite time compared with classical first order absorption kinetics for infinite time.

CONCLUSIONS

One-compartment models work well for most cases. Two-compartment models provide better details, but have higher parameter uncertainties. The absorption duration can be determined directly from the model parameters and thus allow an easy comparison between the ways of administration. Furthermore, the precise site of injection for intramuscular delivery appears to make a difference in terms of the duration of the drug absorption.

The Finite Absorption Time (FAT) concept en route to PBPK modeling and pharmacometrics

The concept of Finite Absorption Time (FAT) for oral drug administration is set to affect pharmacokinetic analyses, Physiologically-based Pharmacokinetics simulations, and Pharmacometrics.

Physiologically based Pharmacokinetic Models under the Prism of the Finite Absorption Time Concept

To date, mechanistic modeling of oral drug absorption has been achieved via the use of physiologically based pharmacokinetic (PBPK) modeling, and more specifically, physiologically based biopharmaceutics model (PBBM). The concept of finite absorption time (FAT) has been developed recently and the application of the relevant physiologically based finite time pharmacokinetic (PBFTPK) models to experimental data provides explicit evidence that drug absorption terminates at a specific time point. In this manuscript, we explored how PBBM and PBFTPK models compare when applied to the same dataset. A set of six compounds with clinical data from immediate-release formulation were selected. Both models resulted in absorption time estimates within the small intestinal transit time, with PBFTPK models generally providing shorter time estimates. A clear relationship between the absorption rate and the product of permeability and luminal concentration was observed, in concurrence with the fundamental assumptions of PBFTPK models. We propose that future research on the synergy between the two modeling approaches can lead to both improvements in the initial parameterization of PBPK/PBBM models but to also expand mechanistic oral absorption concepts to more traditional pharmacometrics applications.

An Analytical Solution for Saturable Absorption in Pharmacokinetics Models

OBJECTIVE

The first-order absorption is a common model used in Pharmacokinetics. The absorption of some drugs follows carrier mediated transport. It has been proposed that the amount of drug available may saturate the transport mechanism resulting in an absorption slower than the one predicted by the first-order model. Saturable absorption has been modeled at the differential equation level by substituting the constant rate absorption by a Hill kinetics absorption. However, its exact solution is so far unknown. The goal of this is to know the exact solution of different Hill kinetic absorption models.

METHODS

We start defining different absorption models and increasing then their complexity. The simplest case is the first-order absorption model and the most complex will be a generalized Hill kinetic absorption model. The differential equation of each model is integrated.

RESULTS

The complexity of the models their solutions may be not expressed in a close-form, or in term of elementary functions. We obtain and discuss the exact solutions of the different Hill kinetics absorption models. To do that, the solutions are studied according to the possible values of the free parameters of the models. We show the differences between models through simulations.

CONCLUSIONS

The knowledge of closed-form solutions allows to illustrate the differences between the different absorption models and minimizes the errors of numerical integration.

Columbus' egg: Oral drugs are absorbed in finite time

The infinite time of oral drug absorption was conceived from the first day of the birth of pharmacokinetics when H. Dost introduced the term pharmacokinetics in his book published in 1953. He adopted the function developed by H. Bateman back in 1908 for the decay of the nuclei isotopes to describe oral drug absorption as a first-order process. We unveiled this false hypothesis relying on common wisdom i.e. drugs are absorbed in finite time. This false assumption had dramatic effects on the evolution of oral pharmacokinetics but most importantly on the bioavailability and bioequivalence concepts and metrics. This work focuses on the finite absorption time (FAT) concept, the relevant Physiologically Based Finite Time (PBFTPK) models developed and their applications in oral pharmacokinetics, bioavailability and bioequivalence. The crux of the matter is that drug absorption from the gastrointestinal tract takes place under sink conditions because of the high blood flow rate in the vena cava. The termination of oral, pulmonary and intranasal drug absorption at a specific time point, calls for regulatory changes in bioavailability and bioequivalence studies in terms of the study design and metrics used for the bioequivalence assessment.

Effect of Excessive Serotonin on Pharmacokinetics of Cephalexin after Oral Administration: Studies with Serotonin-Excessive Model Rats

PURPOSE

Serotonin (5-HT) is important for gastrointestinal functions, but its role in drug absorption remains to be clarified. Therefore, the pharmacokinetics and oral absorption of cephalexin (CEX) were examined under 5-HT-excessive condition to understand the role of 5-HT.

METHODS

5-HT-excessive rats were prepared by multiple intraperitoneal dosing of 5-HT and clorgyline, an inhibitor for 5-HT metabolism, and utilized to examine the pharmacokinetics, absorption behavior and the intestinal permeability for CEX.

RESULTS

Higher levels of 5-HT in brain, plasma and small intestines were recognized in 5-HT-excessive rats, where the oral bioavailability of CEX was significantly enhanced. The intestinal mucosal transport via passive diffusion of CEX was significantly increased, while its transport via PEPT1 was markedly decreased specifically in the jejunal segment, which was supported by the decrease in PEPT1 expression on brush border membrane (BBM) of intestinal epithelial cells. Since no change in antipyrine permeability and significant increase in FITC dextran-4 permeability were observed in 5-HT-excessive rats, the enhanced permeability for CEX would be attributed to the opening of tight junction, which was supported by the significant decrease in transmucosal electrical resistance. In 5-HT-excessive rats, furthermore, total body clearance of CEX tended to be larger and the decrease in PEPT2 expression on BBM in kidneys was suggested to be one of the reasons for it.

CONCLUSIONS

5-HT-excessive condition enhanced the oral bioavailability of CEX in rats, which would be attributed to the enhanced permeability across the intestinal mucosa via passive diffusion through the paracellular route even though the transport via PEPT1 was decreased.