The Use of a Sum of Inverse Gaussian Functions to Describe the Absorption Profile of Drugs Exhibiting Complex Absorption

Physiological Dynamics in the Upper Gastrointestinal Tract and the Development of Gastrointestinal Absorption Models for the Immediate-Release Oral Dosage Forms in Healthy Adult Human

This review is a revisit of various oral drug absorption models developed in the past decades, focusing on how to incorporate the physiological dynamics in the upper gastrointestinal (GI) tract. For immediate-release oral drugs, GI absorption is a critical input of drug exposure and subsequent human body response, yet difficult to model largely due to the complex GI environment. One of the biggest hurdles lies at capturing the high within-subject variability (WSV) of bioavailability measures, which can be mechanistically explained by the GI physiological dynamics. A thorough summary of how GI dynamics is handled in the absorption models would promote the development of mechanism-based oral drug absorption models, aid in the design of clinical studies regarding dosing regimens and bioequivalence studies based on WSV, and advance the decision-making on formulation selection.

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.

Dependence of Bioavailability on Mean Absorption Time: What Does It Tell Us?

The extent and rate of bioavailability are fundamental measures to characterize the pharmacokinetics of drugs after oral administration. Together with bioavailability (F), the mean absorption time (MAT) can be used to define the rate of bioavailability, i.e., the rate of drug absorption. Previous results suggest that F may depend on MAT. Estimates of F and MAT were obtained from the input function (sum of two inverse Gaussian functions) used to model the oral absorption process. The estimation was performed by population analysis (nonlinear mixed-effects modeling) based on data from bioavailability studies in healthy volunteers. For trospium and ketamine, F decreased significantly with increasing MAT, while for propiverine, a significant increase was observed. Thus, the interindividual variability in F could be largely attributed to the interindividual variability in MAT. For trospium and propiverine, the relative dispersion (normalized variance) of the absorption time distribution increased significantly with MAT. For trospium and propiverine, the plot of F versus MAT provides information about the effect of gastrointestinal transit on drug absorption. In contrast, an increase in hepatic extraction with increasing MAT is responsible for the dependence of F on MAT. The F versus MAT plot is suggested as a simple diagnostic tool in evaluating the results of bioavailability studies.

Convolution-based approach for modeling the paliperidone extended release and Long-Acting Injectable (LAI) PK of once-, and three-monthly products administration and for optimizing the development of new LAI products

The aim of this paper was to develop a convolution-based modeling approach for describing the paliperidone PK resulting from the administration of extended-release once-a-day oral dose, and once- and three monthly long-acting injectable products and to compare the performances of this approach to the traditional modeling strategy. The results of the analyses indicated that the traditional and convolution-based models showed comparable performances in the characterization of the paliperidone PK. However, the convolution-based approach showed several appealing features that justify the choice of this modeling as a preferred tool for modeling Long Acting Injectable (LAI) products and for deploying an effective model-informed drug development process. In particular, the convolution-based modeling can (a) facilitate the development of in vitro/in vivo correlation, (b) be used to identify formulations with optimal in vivo release properties, and (c) be used for optimizing the clinical benefit of a treatment by supporting the implementation of integrated models connecting in vitro and in vivo drug release, in vivo drug release to PK, and PK to PD and biomarker endpoints. A case study was presented to illustrate the benefits and the flexibility of the convolution-based modeling outcomes. The model was used to evaluate the in vivo drug release properties associated with a hypothetical once-a-year administration of a LAI product with the assumption that the expected paliperidone exposure during a 3-year treatment overlays the exposure expected after repeated administrations of a 3-month LAI product.

Analysis of Complex Absorption After Multiple Dosing: Application to the Interaction Between the P-glycoprotein Substrate Talinolol and Rifampicin

PURPOSE

In order to clarify the effect of rifampicin on the bioavailability of the P-glycoprotein substrate talinolol, its absorption kinetics was modeled after multiple-dose oral administration of talinolol in healthy subjects.

METHODS

A sum of two inverse Gaussian functions was used to calculate the time course of the input rate into the systemic circulation.

RESULTS

The estimated rate of drug entry into the systemic circulation revealed two distinct peaks at 1 and 3.5 h after administration. Rifampicin did not affect bioavailability of talinolol, but did shift the second peak of the input function by 1.3 h to later times. Elimination clearance and one of the intercompartmental distribution clearances increased significantly under rifampicin treatment.

CONCLUSIONS

Rifampicin changes the time course of absorption rate but not the fraction absorbed of talinolol. The model suggests the existence of two intestinal absorption windows for talinolol.

Pharmacokinetics and Dose Optimization Strategies of Para-Aminosalicylic Acid in Children with Rifampicin-Resistant Tuberculosis

Treatment options for children with Rifampicin-resistant tuberculosis (RR-TB) remain limited, and para-aminosalicylic acid (PAS) is still a relevant component of treatment regimens. Prevention of resistance to companion drugs by PAS is dose related, and at higher concentrations, PAS may exhibit significant bactericidal activity in addition to its bacteriostatic properties. The optimal dosing of PAS in children is uncertain, specifically for delayed-release granule preparations, which are the most used. A population pharmacokinetic model was developed describing PAS pharmacokinetics in children receiving routine RR-TB treatment. Model-based simulations evaluated current World Health Organization (WHO) weight-band doses against the adult pharmacokinetic target of 50 to 100 mg/liter for peak concentrations. Of 27 children included, the median (range) age and weight were 3.87 (0.58 to 13.7) years and 13.3 (7.15 to 30.5) kg, respectively; 4 (14.8%) were HIV positive. PAS followed one-compartment kinetics with first-order elimination and transit compartment absorption. The typical clearance in a 13-kg child was 9.79 liters/h. Increased PAS clearance was observed in both pharmacokinetic profiles from the only patient receiving efavirenz. No effect of renal function, sex, ethnicity, nutritional status, HIV status, antiretrovirals (lamivudine, abacavir, and lopinavir-ritonavir), or RR-TB drugs was detected. In simulations, target concentrations were achieved only using the higher WHO dose range of 300 mg/kg once daily. A transit compartment adequately describes absorption for the slow-release PAS formulation. Children should be dosed at the higher range of current WHO-recommended PAS doses and in a once-daily dose to optimize treatment.

Pharmacokinetic Modeling of Ketamine Enantiomers and Their Metabolites After Administration of Prolonged-Release Ketamine With Emphasis on 2,6-Hydroxynorketamines

Modeling of metabolite kinetics after oral administration of ketamine is of special interest because of the higher concentrations of active metabolites because of the hepatic first-pass effect. This holds especially in view of the potential analgesic and antidepressant effects of 2R,6R- and 2S,6S-hydroxynorketamine at low doses of ketamine. Therefore, a 9-compartment model was developed to analyze the pharmacokinetics of ketamine enantiomers and their metabolites after racemic ketamine administered intravenously (5 mg) and as 4 doses (10, 20, 40, and 80 mg) of a prolonged-release formulation (PR-ketamine). Using a population approach, the serum concentration-time data of the enantiomers of ketamine, norketamine, dehydronorketamine, and 2,6-hydroxynorketamine obtained in 15 healthy volunteers could be adequately fitted. The estimated model parameters were used to simulate serum concentration-time profiles; after multiple dosing of PR-ketamine (2 daily doses of 20 mg), the steady-state concentrations of R- and S-ketamine were 1.4 and 1.3 ng/mL, respectively. The steady-state concentration of 2R,6R-hydroxynorketamine exceeded those of R-norketamine (4-fold), R-dehydonorketamine (8-fold), and R-ketamine (46-fold), whereas that of 2S,6S-hydroxynorketamine exceeded that of S-ketamine by 14-fold. The model may be useful for identifying dosing regimens aiming at optimal plasma concentrations of 2,6-hydroxynorketamines.

A Semimechanistic Pharmacokinetic Model for Depot Medroxyprogesterone Acetate and Drug-Drug Interactions With Antiretroviral and Antituberculosis Treatment

Depot medroxyprogesterone acetate is an injectable hormonal contraceptive, widely used by women of childbearing potential living with HIV and/or tuberculosis. As medroxyprogesterone acetate is a cytochrome P450 (CYP3A4) substrate, drug-drug interactions (DDIs) with antiretroviral or antituberculosis treatment may lead to subtherapeutic medroxyprogesterone acetate concentrations (< 0.1 ng/mL), resulting in contraception failure, when depot medroxyprogesterone is dosed at 12-week intervals. A pooled population pharmacokinetic analysis with 744 plasma medroxyprogesterone acetate concentrations from 138 women treated with depot medroxyprogesterone and antiretroviral/antituberculosis treatment across three clinical trials was performed. Monte Carlo simulations were performed to predict the percentage of participants with subtherapeutic medroxyprogesterone acetate concentrations and to derive alternative dosing strategies. Medroxyprogesterone acetate clearance increased by 24.7% with efavirenz coadministration. Efavirenz plus antituberculosis treatment (rifampicin + isoniazid) increased clearance by 52.4%. Conversely, lopinavir/ritonavir and nelfinavir decreased clearance (28.7% and 15.8%, respectively), but lopinavir/ritonavir also accelerated medroxyprogesterone acetate's appearance into the systemic circulation, thus shortening the terminal half-life. A higher risk of subtherapeutic medroxyprogesterone acetate concentrations at Week 12 was predicted on a typical 60-kg woman on efavirenz (4.99%) and efavirenz with antituberculosis treatment (6.08%) when compared with medroxyprogesterone acetate alone (2.91%). This risk increased in women with higher body weight. Simulations show that re-dosing every 8 to 10 weeks circumvents the risk of subtherapeutic medroxyprogesterone acetate exposure associated with these DDIs. Dosing depot medroxyprogesterone every 8 to 10 weeks should eliminate the risk of subtherapeutic medroxyprogesterone acetate exposure caused by coadministered efavirenz and/or antituberculosis treatment, thus reducing the risk of contraceptive failure.

Application of Deep Neural Networks as a Prescreening Tool to Assign Individualized Absorption Models in Pharmacokinetic Analysis

A specific model for drug absorption is necessarily assumed in pharmacokinetic (PK) analyses following extravascular dosing. Unfortunately, an inappropriate absorption model may force other model parameters to be poorly estimated. An added complexity arises in population PK analyses when different individuals appear to have different absorption patterns. The aim of this study is to demonstrate that a deep neural network (DNN) can be used to prescreen data and assign an individualized absorption model consistent with either a first-order, Erlang, or split-peak process. Ten thousand profiles were simulated for each of the three aforementioned shapes and used for training the DNN algorithm with a 30% hold-out validation set. During the training phase, a 99.7% accuracy was attained, with 99.4% accuracy during in the validation process. In testing the algorithm classification performance with external patient data, a 93.7% accuracy was reached. This algorithm was developed to prescreen individual data and assign a particular absorption model prior to a population PK analysis. We envision it being used as an efficient prescreening tool in other situations that involve a model component that appears to be variable across subjects. It has the potential to reduce the time needed to perform a manual visual assignment and eliminate inter-assessor variability and bias in assigning a sub-model.

Physiologically Based Modeling of Food Digestion and Intestinal Microbiota: State of the Art and Future Challenges. An INFOGEST Review

This review focuses on modeling methodologies of the gastrointestinal tract during digestion that have adopted a systems-view approach and, more particularly, on physiologically based compartmental models of food digestion and host-diet-microbiota interactions. This type of modeling appears very promising for integrating the complex stream of mechanisms that must be considered and retrieving a full picture of the digestion process from mouth to colon. We may expect these approaches to become more and more accurate in the future and to serve as a useful means of understanding the physicochemical processes occurring in the gastrointestinaltract, interpreting postprandial in vivo data, making relevant predictions, and designing healthier foods. This review intends to provide a scientific and historical background of this field of research, before discussing the future challenges and potential benefits of the establishment of such a model to study and predict food digestion and absorption in humans.

Two-step in vitro-in vivo correlations: Deconvolution and convolution methods, which one gives the best predictability? Comparison with one-step approach

Finding predictive dissolution tests and valid IVIVCs are essential activities in generic industry, as they can be used as substitutes of human bioequivalence studies. IVIVCs can be developed by two different strategies: a one-step approach or a two-step approach. The objectives of this work were to compare different deconvolution and convolution methods used in the development of two-step level A IVIVCs and to study if the relationship between the in vitro dissolution rate and the in vivo dissolution rate should guide the decision between using a two-step approach or a one-step approach during the development of a new IVIVC. When the in vitro and the in vivo dissolution rates had a linear relationship, valid and biopredictive two-step IVIVCs were obtained, although there was not a combination of deconvolution and convolution methods that could be named as the best one, as long as all the prediction errors for any combination were within the limits. It was not possible to obtain a valid two-step IVIVC when the relationship between dissolution rates was non-linear, but the one-step approach was able to overcome this fact and it gave valid IVIVCs regardless of whether the relationship between dissolution rates was linear or non-linear.

Non-Linear Pharmacokinetics of Oral Roscovitine (Seliciclib) in Cystic Fibrosis Patients Chronically Infected with Pseudomonas aeruginosa: A Study on Population Pharmacokinetics with Monte Carlo Simulations

Roscovitine (Seliciclib), a new protein kinase inhibitor, was administered orally to adult patients with cystic fibrosis for the first time in the ROSCO-CF trial, a dose-escalation, phase IIa, randomized, controlled trial. Extensive pharmacokinetic sampling was performed up to 12 h after the first oral dose. Roscovitine and its main metabolite M3 were quantified by liquid chromatography coupled with tandem mass spectrometry. The pharmacokinetics analyses were performed by non-linear mixed effects modelling. Monte Carlo simulations were performed to assess the impact of dose on the pharmacokinetics of oral roscovitine. Twenty-three patients received oral doses ranging from 200 to 800 mg of roscovitine and 138 data points were available for both roscovitine and M3 concentrations. The pharmacokinetics was best described by a two-compartment parent-metabolite model, with a complex saturable absorption process modelled as the sum of Gaussian inverse density functions. The Monte Carlo simulations showed a dose-dependent and saturable first-pass effect leading to pre-systemic formation of M3. The treatment with proton-pump inhibitors reduced the rate of absorption of oral roscovitine. The pharmacokinetics of oral roscovitine in adult patients with cystic fibrosis was non-linear and showed significant inter-individual variability. A repeat-dose study will be required to assess the inter-occasional variability of its pharmacokinetics.

Trospium chloride is absorbed from two intestinal "absorption windows" with different permeability in healthy subjects

Intestinal P-glycoprotein is regio-selectively expressed and is a high affinity, low capacity efflux carrier for the cationic, poorly permeable trospium. Organic cation transporter 1 (OCT1) provides lower affinity but higher capacity for trospium uptake. To evaluate regional intestinal permeability, absorption profiles after gastric infusion of trospium chloride (30mg/250ml=[I]₂) for 6h and after swallowing 30mg immediate-release tablets in fasted and fed healthy subjects, were evaluated using an inverse Gaussian density function to model input rate and mean absorption time (MAT). Trospium chloride was slowly absorbed (MAT ∼10h) after gastric infusion involving two processes with different input rates, peaking at about 3h and 7h. Input rates and MAT were influenced by dosage form and meal. In conclusion, trospium is absorbed from two "windows" located in the jejunum and cecum/ascending colon, whose uptake capacity might result from local abundance and functional interplay of P-glycoprotein and OCT1.

Input estimation for drug discovery using optimal control and Markov chain Monte Carlo approaches

Input estimation is employed in cases where it is desirable to recover the form of an input function which cannot be directly observed and for which there is no model for the generating process. In pharmacokinetic and pharmacodynamic modelling, input estimation in linear systems (deconvolution) is well established, while the nonlinear case is largely unexplored. In this paper, a rigorous definition of the input-estimation problem is given, and the choices involved in terms of modelling assumptions and estimation algorithms are discussed. In particular, the paper covers Maximum a Posteriori estimates using techniques from optimal control theory, and full Bayesian estimation using Markov Chain Monte Carlo (MCMC) approaches. These techniques are implemented using the optimisation software CasADi, and applied to two example problems: one where the oral absorption rate and bioavailability of the drug eflornithine are estimated using pharmacokinetic data from rats, and one where energy intake is estimated from body-mass measurements of mice exposed to monoclonal antibodies targeting the fibroblast growth factor receptor (FGFR) 1c. The results from the analysis are used to highlight the strengths and weaknesses of the methods used when applied to sparsely sampled data. The presented methods for optimal control are fast and robust, and can be recommended for use in drug discovery. The MCMC-based methods can have long running times and require more expertise from the user. The rigorous definition together with the illustrative examples and suggestions for software serve as a highly promising starting point for application of input-estimation methods to problems in drug discovery.

Incorporation of stochastic variability in mechanistic population pharmacokinetic models: handling the physiological constraints using normal transformations

The utilisation of physiologically-based pharmacokinetic models for the analysis of population data is an approach with progressively increasing impact. However, as we move from empirical to complex mechanistic model structures, incorporation of stochastic variability in model parameters can be challenging due to the physiological constraints that may arise. Here, we investigated the most common types of constraints faced in mechanistic pharmacokinetic modelling and explored techniques for handling them during a population data analysis. An efficient way to impose stochastic variability on the parameters of interest without neglecting the underlying physiological constraints is through the assumption that they follow a distribution with support and properties matching the underlying physiology. It was found that two distributions that arise through transformations of the normal, the logit-normal generalisation and the logistic-normal, are excellent for such an application as not only they can satisfy the physiological constraints but also offer high flexibility during characterisation of the parameters' distribution. The statistical properties and practical advantages/disadvantages of these distributions for such an application were clearly displayed in the context of different modelling examples. Finally, a simulation study clearly illustrated the practical gains of the utilisation of the described techniques, as omission of population variability in physiological systems parameters leads to a biased/misplaced stochastic model with mechanistically incorrect variance structure. The current methodological work aims to facilitate the use of mechanistic/physiologically-based models for the analysis of population pharmacokinetic clinical data.

Model-based evaluation of the impact of formulation and food intake on the complex oral absorption of mavoglurant in healthy subjects

PURPOSE

To compare the pharmacokinetics of intravenous (IV), oral immediate-release (IR) and oral modified-release (MR) formulations of mavoglurant in healthy subjects, and to assess the food effect on the MR formulation's input characteristics.

METHODS

Plasma concentration-time data from two clinical studies in healthy volunteers were pooled and analysed using NONMEM®. Drug entry into the systemic circulation was modelled using a sum of inverse Gaussian (IG) functions as an input rate function, which was estimated specifically for each formulation and food state.

RESULTS

Mavoglurant pharmacokinetics was best described by a two-compartment model with a sum of either two or three IG functions as input function. The mean absolute bioavailability from the MR formulation (0.387) was less than from the IR formulation (0.436). The MR formulation pharmacokinetics were significantly impacted by food: bioavailability was higher (0.508) and the input process was shorter (complete in approximately 36 versus 12 h for the fasted and fed states, respectively).

CONCLUSIONS

Modelling and simulation of mavoglurant pharmacokinetics indicate that the MR formulation might provide a slightly lower steady-state concentration range with lower peaks (possibly better drug tolerance) than the IR formulation, and that the MR formulation's input properties strongly depend on the food conditions at drug administration.

Estimation of parameters for the elimination of an orally administered test substance with unknown absorption

Assessment of the elimination of an oral test dose based on plasma concentration values requires correction for the effect of gastric release and absorption. Irregular uptake processes should be described 'model independently', which requires estimation of a large number of absorption parameters. To limit the associated computational effort a new approach is developed with a reduced number of unknown parameters. A marginalized and regularized absorption approach (MRA) is defined, which uses for the uptake just one parameter to control rigidity of the uptake curve. For validation, elimination and absorption were reproduced using published IVIVC data and a synthetic data set for comparison with approaches using a 'model-free'--staircase function or mechanistic models to describe absorption. MRA performed almost as accurate as well specified mechanistic models, which gave the best reproduction. MRA demonstrated a 50fold increase in computational efficiency compared to other approaches. The absorption estimated for the IVIVC study demonstrated an in vivo-in vitro correlation comparable to published values. The newly developed MRA approach can be used to efficiently and accurately estimate elimination and absorption with a restricted number of adaptive parameters and with automatic adjustment of the complexity of the uptake.

Individualized, discrete event, simulations provide insight into inter- and intra-subject variability of extended-release, drug products

OBJECTIVE

Develop and validate particular, concrete, and abstract yet plausible in silico mechanistic explanations for large intra- and interindividual variability observed for eleven bioequivalence study participants. Do so in the face of considerable uncertainty about mechanisms.

METHODS

We constructed an object-oriented, discrete event model called subject (we use small caps to distinguish computational objects from their biological counterparts). It maps abstractly to a dissolution test system and study subject to whom product was administered orally. A subject comprises four interconnected grid spaces and event mechanisms that map to different physiological features and processes. Drugs move within and between spaces. We followed an established, Iterative Refinement Protocol. Individualized mechanisms were made sufficiently complicated to achieve prespecified Similarity Criteria, but no more so. Within subjects, the dissolution space is linked to both a product-subject Interaction Space and the GI tract. The GI tract and Interaction Space connect to plasma, from which drug is eliminated.

RESULTS

We discovered parameterizations that enabled the eleven subject simulation results to achieve the most stringent Similarity Criteria. Simulated profiles closely resembled those with normal, odd, and double peaks. We observed important subject-by-formulation interactions within subjects.

CONCLUSION

We hypothesize that there were interactions within bioequivalence study participants corresponding to the subject-by-formulation interactions within subjects. Further progress requires methods to transition currently abstract subject mechanisms iteratively and parsimoniously to be more physiologically realistic. As that objective is achieved, the approach presented is expected to become beneficial to drug development (e.g., controlled release) and to a reduction in the number of subjects needed per study plus faster regulatory review.

Implementation of dose superimposition to introduce multiple doses for a mathematical absorption model (transit compartment model)

A mathematical absorption model (e.g. transit compartment model) is useful to describe complex absorption process. However, in such a model, an assumption has to be made to introduce multiple doses that a prior dose has been absorbed nearly completely when the next dose is administered. This is because the drug input cannot be determined from drug depot compartment through integration of the differential equation system and has to be analytically calculated. We propose a method of dose superimposition to introduce multiple doses; thereby eliminating the assumption. The code for implementing the dose superimposition in WinNonlin and NONMEM was provided. For implementation in NONMEM, we discussed a special case (SC) and a general case (GC). In a SC, dose superimposition was implemented solely using NM-TRAN abbreviated code and the maximum number of the doses that can be administered for any subject must be pre-defined. In a GC, a user-supplied function (FUNCA) in FORTRAN code was defined to perform dose superimposition to remove the restriction that the maximum number of doses must be pre-defined.

A note on population analysis of dissolution-absorption models using the inverse Gaussian function

Because conventional absorption models often fail to describe plasma concentration-time profiles following oral administration, empirical input functions such as the inverse Gaussian function have been successfully used. The purpose of this note is to extend this model by adding a first-order absorption process and to demonstrate the application of population analysis using maximum likelihood estimation via the EM algorithm (implemented in ADAPT 5). In one example, the analysis of bioavailability data of an extended-release formulation, as well as the mean dissolution times estimated in vivo and in vitro with the use of the inverse Gaussian function, is well in accordance, suggesting that the inverse Gaussian function indeed accounts for the in vivo dissolution process. In the other example, the kinetics of trapidil in patients with liver disease, the absorption/dissolution parameters are characterized by a high interindividual variability. Adding a first-order absorption process to the inverse Gaussian function improved the fit in both cases.