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.     

Applications and Simulations of a Discontinuous Oral Absorption Pharmacokinetic Model

Purpose. To illustrate the application of a discontinuous oral absorption model to cimetidine and ranitidine plasma concentration versus time data to demonstrate the use of the model for drugs which display discontinuous oral absorption profiles, and to illustrate the effect of various model parameters on plasma drug concentration versus time profiles and bioavailability. Methods. A discontinuous oral absorption model was used to fit ranitidine and cimetidine serum concentrations following oral and intravenous administration. The model was also used to simulate bioavailability and plasma concentrations versus time profiles for various parameter values. Results. Serum concentrations following administration of ranitidine and cimetidine were well described by the model, and parameter estimates obtained were in agreement with literature values. Simulations demonstrate the effects of various absorption parameters and gastrointestinal tract transit parameters on bioavailability and plasma concentration profiles. Conclusions. This discontinuous oral absorption pharmacokinetic model can be a useful tool in characterizing absorption phases, disposition, and bioavailability of drugs exhibiting two absorption peaks following oral administration.     

Stepwise determination of multicompartment disposition and absorption parameters from extravascular concentration-time data. Application to mesoridazine,flurbiprofen, flunarizine,labetalol, and diazepam

When disposition is monoexponential, extravascular concentrationtime (C, t) data yield both disposition and absorption parameters, the latter via the Wagner-Nelson method or deconvolution which are equivalent. Classically, when disposition is multiexponential, disposition parameters are obtained from intravenous administration and absorption data are obtained from extravascular C, tdata via the Loo-Riegelman or Exact Loo-Riegelman methods or via deconvolution. Thus, in multiexponential disposition one assumes no intrasubject variation in disposition, a hypothesis that has not been proven for most drugs. Based on the classical two and threecompartment open models with central compartment elimination, and using postabsorptive extravascular C, tdata only, we have developed four equations to estimate k₁₀ when disposition is biexponential and two other equations to estimate k₁₀ when disposition is triexponential. The other disposition rate constants are readily obtained without intravenous data. We have analyzed extravascular data of flurbiprofen (12 sets), mesoridazine (20 sets), flunarizine (5 sets), labetalol (9 sets), and diazepam (4 sets). In the case of diazepam intravenous C, tdata were also available for analysis. After disposition parameters had been estimated from the extravascular data the Exact Loo-Riegelman method with the Proost modification was applied to the absorptive extravascular data to obtain A_T/V_p as a function of time. These latter data for each subject and each drug studied were found to befitted by a function indicating either simple firstorder absorption, two consecutive firstorder processes, or zero order absorption. After absorption and disposition parameters had been estimated, for each set of extravascular data analyzed, a reconstruction trend line through the original C, tdata was made. The new methods allow testing of the hypothesis of constancy of disposition with any given drug. There is also a need for new methods of analysis since the majority of drugs have no marketed intravenous formulation, hence the classical methods cannot be applied.     

Empirical models for fitting of oral concentration time curves with and without an intravenous reference

Appropriate model selection is important in fitting oral concentration–time data due to the complex character of the absorption process. When IV reference data are available, the problem is the selection of an empirical input function (absorption model). In the present examples a weighted sum of inverse Gaussian density functions (IG) was found most useful. It is shown that alternative models (gamma and Weibull density) are only valid if the input function is log-concave. Furthermore, it is demonstrated for the first time that the sum of IGs model can be also applied to fit oral data directly (without IV data). In the present examples, a weighted sum of two or three IGs was sufficient. From the parameters of this function, the model-independent measures AUC and mean residence time can be calculated. It turned out that a good fit of the data in the terminal phase is essential to avoid parameter biased estimates. The time course of fractional elimination rate and the concept of log-concavity have proved as useful tools in model selection.     

New method for characterizing dissolution properties of drug powders.

Various multiparticulate dissolution models that assume a log-normal particle-size distribution are fitted by nonlinear least-squares regression to data from the dissolution of micronized glyburide. Estimates of parameters describing the effective initial particle-size distribution are obtained, together with estimates of the specific dissolution rate parameter. A dissolution equation based on an ideal, untruncated, log-normal distribution, with the single particles dissolving according to the Hixson-Crowell cube root law, is the best model. The dissolution behavior of glyburide can be well described by this model in terms of the specific dissolution rate parameter and one other parameter accounting for the distribution effect. The estimation of these two parameters represents a more exact way of describing the dissolution characteristics of drug powders than previous approaches. The method should be of interest in the quality control of drugs that may cause bioavailability problems because of dissolution rate-limited absorption.     

Pharmacokinetic Model of Ascorbic Acid in Healthy Male Volunteers During Depletion and Repletion

Purpose. To develop a new pharmacokinetic model for ascorbic acid (vitamin C) since no previously published model describes ascorbic acid absorption and disposition over a broad physiologic range of doses and plasma concentrations. Methods. A new model was developed through exploratory simulations. The model was fitted to pharmacokinetic data obtained from seven healthy volunteers who underwent ascorbic acid depletion then gradual repletion. Concentrations of ascorbic acid were measured in plasma and urine. Final pharmacokinetic model parameter estimates were obtained using nonlinear regression analysis. Results. The new model included saturable absorption, distribution and renal tubular reabsorption parameters. The model described ascorbic acid concentrations in plasma, cells, and urine during depletion and gradual repletion phases with a residual error less than 15%. Conclusions. The model was useful for obtaining a new understanding of the likely causes for the complex concentration-time profile observed during gradual repletion. At doses of 200 to 2500 mg per day, the plateau in pre-dose concentrations is largely due to apparent saturation of tissue uptake and less a function of oral bioavailability and renal excretion than previously thought.     

Predicting Blood-Brain Transport of Drugs: A Computational Approach

Purpose. This study was conducted to determine the efficacy of using nonempirical parameters in the estimation of blood-brain transport, inferred from central nervous system (CNS) activity, for a set of twenty-eight compounds. Methods. A discriminant function analysis was used to construct three distinct models based on topological indices, a hydrogen-bonding parameter, and logP. Results. These models correctly predict the CNS activity of twenty-seven of the twenty-eight compounds. Conclusions. Nonempirical parameters may be used effectively in the estimation the cerebrovascular penetration for known and newly designed drugs.     

[6]-Shogaol/β-CDs inclusion complex: preparation,characterisation, in vivo pharmacokinetics,and in situ intestinal perfusion study

Abstract

Aims: The aim was to improve the absorption and bioavailability of [6]-shogaol with β-cyclodextrin (β-CD) prior to in vitro and in vivo evaluation.

Methods: [6]-Shogaol/β-CDs inclusion complexes (6-S-β-CDs) were developed using saturated aqueous solution method and characterised with appropriate techniques. The absorption and bioavailability potential of [6]-shogaol was evaluated via in vivo pharmacokinetics and in situ intestinal perfusion.

Results: The results of characterisation showed that 6-S-β-CDs (drug loading, 7.15%) were successfully formulated. In vitro release study indicated significantly improved [6]-shogaol release. Pharmacokinetic parameters such as C_max, AUC_0–36?h, and oral relative bioavailability (about 685.36%) were substantially enhanced. The in situ intestinal perfusion study revealed that [6]-shogaol was markedly absorbed via passive diffusion in the intestinal segments, and duodenum followed by ileum and jejunum.

Conclusions: Cyclodextrin inclusion technology could enhance the intestinal absorption and oral bioavailability of hydrophobic drugs like [6]-shogaol.     

Myo-inositol soft gel capsules may prevent the risk of coffee-induced neural tube defects

Objective: Neural tube defects (NTDs) are classified as folate sensitive (about 70%) and folate resistant (about 30%); although folic acid is able to prevent the former, several data have shown that inositol may prevent the latter. It has recently been proposed that coffee intake might represent a risk factor for NTD, likely by interfering with the inositol signaling. In the present study, we tested the hypothesis that, beside affecting the inositol signaling pathway, coffee also interferes with inositol absorption.

Research design and methods: In order to evaluate coffee possible negative effects on inositol gastrointestinal absorption, a single-dose bioavailability trial was conducted. Pharmacokinetics (PK) parameters of myo-inositol (MI) powder and MI soft gelatin capsules swallowed with water and with a single ‘espresso' were compared. PK profiles were obtained by analysis of MI plasma concentration, and the respective MI bioavailability was compared.

Results: Myo-inositol powder administration was negatively affected by coffee intake, thus suggesting an additional explanation to the interference between inositol deficiency and coffee consumption. On the contrary, the concomitant single ‘espresso' consumption did not affect MI absorption following MI soft gelatin capsules administration. Furthermore, it was observed that MI soft gelatin capsule administration resulted in improved bioavailability compared to the MI powder form.

Conclusions: Myo-inositol soft gelatin capsules should be considered for the preventive treatment of NTDs in folate-resistant subjects due to their higher bioavailability and to the capability to reduce espresso interference.     

Formulation,characterization, in vitro and in vivo evaluation of castor oil based self-nano emulsifying levosulpiride delivery systems

Context: Levosulpiride (LSP) is a hydrophobic benzamide derivative used in the treatment of schizophrenia. SNEDDS were extensively practiced for systemic delivery of poorly aqueous soluble drugs to achieve maximum bioavailability.

Objective: The present study was focussed on the formulation, optimisation and evaluation of LSP SNEDDS using castor oil, for enhancement of drug absorption and bioavailability.

Materials and methods: Pseudo-ternary phase diagram was plotted to identify the range of SNEDDS components. Twenty formulations were designed, prepared and characterised by its particle size, zeta potential, viscosity, and stability. In vitro dissolution data modelling was performed. Microscopy, FTIR and in vivo bioavailability studies were conducted for optimum formulation.

Results, discussion and conclusion: F18 containing castor oil, 0.9?mL; PEG 600, 1.36?mL and Tween 80, 2.74?mL was found to be optimum. The optimised formulation had shown uniform globule size, no interactions of LSP with SNEDDS components and higher pharmacokinetic parameters than that of commercial preparation.     

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

Purpose The aim of this study was to evaluate the utility of a parametric deconvolution method using a sum of inverse Gaussian functions (IG) to characterize the absorption and concentrations vs. time profile of drugs exhibiting complex absorption.Methods For a linear time-invariant system the response, Y(t), following an arbitrary input function I(t), is the convolution of I(t) with the disposition function, H(t), of the system: . The method proposed uses a sum of n inverse Gaussian functions to characterize I(t). The approach was compared with a standard nonparametric method using linear splines. Data were provided from previously published studies on two drugs (hydromorphone and veralipride) showing complex absorption and analyzed with NONMEM®.Results A satisfactory fit for hydromorphone and veralipride data following oral administration was achieved by fitting a sum of two or three IG functions. The predictions of the input functions were very similar to those using linear splines.Conclusions The use of a sum of IG as opposed to nonparametric functions, such as splines, offers a simpler implementation, a more intuitive interpretation of the results, a built-in extrapolation, and an easier implementation in a population context. Disadvantages are an apparent greater sensitivity to initial value estimates (when used with NONMEM®).     

General Moments in Linear Pharmacokinetic Models

Abstract

The communication presents the derivation and application of formulas for estimating the parameters MRT and VRT of the linear or linearised complex time invariant pharmacokinetic system, with or without shunt and time delays, defined on the animal body after any route of drug administration. the derivation is based on the model of the system transfer function and/or the model of the system weighting function. Thus the estimation of the system parameters MRT and VRT according to the formulas presented is not restricted only to using experimental data corresponding to the instantaneous system input. the approach provides feasibility of MRT and VRT estimation and may increase the accuracy of the estimates.     

Selecting oral bioavailability enhancing formulations during drug discovery and development

Introduction: The role of chemical structure, lipophilicity, physico-chemical, absorption, distribution, metabolism, excretion, toxicity (ADMET) and biopharmaceutical properties of compounds including bioavailability are critical in drug discovery and drug dosage forms design.

Areas covered: The authors discuss a number of parameters including computational approaches used for selected chemical structures with biological activity for lead optimization and chemogenomics and preclinical studies for ADMET process development of ligand properties. The authors also look at a number of other parameters including: early drug product formulations with method selection based on the biopharmaceutical classification system (BCS); in vitro–in vivo correlation (IVIVC) and different formulation strategies to enhance solubility; dissolution rate and permeability; bioavailability evaluation and quality by design as an opportunity to develop ‘safe space' regions, where bioavailability is unaffected by pharmaceutical variations.

Expert opinion: The biopharmaceutical requirements for absorption are solubility and permeability. Both are influenced by lipophilicity, but in the opposite way. The genomic methodology, coupled with combinatorial chemistry, high-throughput screening, structure-based design and in silico ADMET would yield parameters as a starting point for the biopharmaceutical properties determination in further preclinical and clinical studies. Consecutive stages in drug discovery and development are irreplaceable, but pharmacokinetics is the critical step. Selection of drug formulations based on the BCS, IVIVC are the principal aspects to enhance the solubility and dissolution rate, while a rationale management of pharmaceutical and technological factors will enhance the bioavailability.     

Biopharmaceutical Approaches for Developing and Assessing Oral Peptide Delivery Strategies and Systems: In Vitro Permeability and In Vivo Oral Absorption of Salmon Calcitonin

Purpose. To evaluate a biopharmaceutical approach for selecting formulation additives and establishing the performance specifications of an oral peptide delivery system using sCT as a model peptide. Methods. The effect of formulation additives on sCT effective permeability and transepithelial electrical resistance (TEER) was evaluated in side-by-side diffusion chambers using rat intestinal segments. Baseline regional oral absorption of sCT was evaluated in an Intestinal and Vascular Access Port (IVAP) dog model by administration directly into the duodenum, ileum, and colon by means of surgically implanted, chronic catheters. The effect of varying the input rate and volume of the administered solution on the extent of sCT absorption was also evaluated. Citric acid (CA) was utilized in all studies to cause a transient reduction in local pH. In vitro samples and plasma samples were analyzed by radioimmunoassay (RIA). Two oral delivery systems were prepared based on the results of the in vitro and IVAP studies, and evaluated in normal dogs. Results. Maximal permeability enhancement of sCT was observed using taurodeoxycholate (TDC) or lauroyl carnitine (LC) in vitro. Ileal absorption of sCT was higher than in other regions of the intestine. Low volume and bolus input of solution formulations was selected as the optimal condition for the IVAP studies since larger volumes or slower input rates resulted in significantly lower sCT bioavailability (BA). Much lower BA of sCT was observed when CA was not used in the formulation. The absolute oral bioavailability (mean ± SD) in dogs for the control (sCT + CA) and two proprietary sCT delivery systems was 0.30% ± 0.05%, 1.10 ± 0.18%, and 1.31 ± 0.56%, respectively. Conclusions. These studies demonstrate the utility of in vitro evaluation and controlled in vivo studies for developing oral peptide delivery strategies. Formulation additives were selected, the optimal intestinal region for delivery identified, and the optimal release kinetics of additives and actives from the delivery system were characterized. These methods were successfully used for devising delivery strategies and fabricating and evaluating oral sCT delivery systems in animals. Based on these studies, sCT delivery systems have been fabricated and tested in humans with favorable results.     

A Heterogeneous Tube Model of Intestinal Drug Absorption Based on Probabilistic Concepts

Purpose. To develop an approach based on computer simulations for the study of intestinal drug absorption. Methods. The drug flow in the gastrointestinal tract was simulated with a biased random walk model in the heterogeneous tube model Pharm. Res. 16, 87-91, 1999), while probability concepts were used to describe the dissolution and absorption processes. An amount of drug was placed into the input end of the tube and allowed to flow, dissolve and absorb along the tube. Various drugs with a diversity in dissolution and permeability characteristics were considered. The fraction of dose absorbed (F _abs ) was monitored as a function of time measured in Monte Carlo steps (MCS). The absorption number An was calculated from the mean intestinal transit time and the absorption rate constant adhering to each of the drugs examined. Results. A correspondence between the probability factor used to simulate drug absorption and the conventional absorption rate constant derived from the analysis of data was established. For freely soluble drugs, the estimates for F _abs derived from simulations using as an intestinal transit time 24500 MCS (equivalent to 4.5 h) were in accord with the corresponding data obtained from literature. For sparingly soluble drugs, a comparison of the normalized concentration profiles in the tube derived from the heterogeneous tube model and the classical macroscopic mass balance approach enabled the estimation of the dissolution probability factor for five drugs examined. The prediction of F _abs can be accomplished using estimates for the absorption and the dissolution probability factors. Conclusions. A fully computerized approach which describes the flow, dissolution and absorption of drug in the gastrointestinal tract in terms of probability concepts was developed. This approach can be used to predict F _abs for drugs with various solubility and permeability characteristics provided that probability factors for dissolution and absorption are available.     

Predictive approaches to increase absorption of compounds during lead optimisation

Introduction: Complex physicochemical and biological processes influence the oral absorption of a drug molecule. Consideration of these processes is an important activity during the optimisation of potential candidate molecules.

Areas covered: The authors review the applications of physicochemical and structural requirements for intestinal absorption. Furthermore, they provide examples of how to aid the lead optimisation process through improvement of solubility and permeability.

Expert opinion: The physicochemical requirements for absorption are solubility and permeability. Both are influenced by lipophilicity, but in the opposite way. The size of the molecule also affects both solubility and permeability. Several models can be used to estimate oral absorption from chemical structure or from measured physicochemical properties. Thus, logD–cMR model, the ‘golden triangle' model, Abraham solvation equations and absorption potential can be used as tools in the lead optimisation process. Measured values of solubility and permeability greatly improve the estimation of in vivo oral absorption of compounds. However, it is important to appreciate that predictions of oral absorption may be confounded by the involvement of active transporters in the gut which may either increase (e.g., active uptake) or decrease (e.g., efflux) the absorption of drug molecules. To evaluate the first-pass metabolism, in vitro clearance measurements using liver microsomes can be used in physiologically based models for the estimation of bioavailability. The general tools discussed in this review are based on the physicochemical property assessment of compound libraries and they help design compounds that occupy desirable property space with increased likelihood of good oral absorption.     

Pharmacokinetic stochastic model with Weibull-distributed residence times of drug molecules in the body

The use of a function to fit blood concentration-time data points is equivalent, under certain assumptions, to specifying a model of the distribution of residence times of the drug molecules in the body (stochastic pharmacokinetic model). An empirical density function of the Weibull type is offered to describe this distribution. The model gives the following disposition function describing the time course of the drug concentrations in blood after an intravenous bolus input: C delta (t) = D/CLs lambda ts-1exp(-lambda ts). It contains only three parameters: lambda is like an 'elimination rate constant' in the single-exponential model into which the Weibull function reduces when the shape parameters becomes equal to unity; CL is the conventional systemic drug clearance, and, D is the dose injected. The Weibull function gives an analytical solution of the convolution integral for zero-order input, thereby permitting use of the model for intravenous infusion data and for extravascular administration, when the absorption may be considered to be zero-order. Using examples from the literature it is shown that in some cases the Weibull function gives a better fit than may be obtained with two- and three-exponential or gamma functions.     

Bioavailability estimation by semisimultaneous drug administration: A Monte Carlo simulation study

The performance of a novel method for determination of drug absorption characteristics was evaluated by Monte Carlo simulations. In bioavailability studies with use of this method, the test and the reference doses are administered within a time interval of hours. Estimates of bioavilability are obtained by fitting an appropriate model to the concentrationtime profile, which in its terminal portion is thus the summed concentration of the two doses. Drugs with different properties, mimicked by varying the kinetic rate constants (k_a, ₁,and ₂),and experimental designs with different sets of conditions regarding the interval between doses, dose ratio, dose order, and duration of sampling, were simulated to determine what factors govern parameter estimation. The absorption characteristics of the simulated drugs could be adequately determined in experiments lasting for 12 hr or less, provided that a proper design was used. Fitting of a simpler or a more complex disposition model produced estimates with similar accuracy and precision to those noted with the true model. For some conditions the use of an improper absorption model resulted in slightly reduced accuracy, but as these fits were poor there was a clear need to try other models. In another set of simulations the use of the proposed method to assess the relative availability of two extravascular doses was evaluated. The relative rate and extent of absorption could be estimated with good precision for two formulations exhibiting a rapid to moderate rate of absorption.     

Development of quantitative structure-metabolism (QSMR) relationships for substituted anilines based on computational chemistry

Abstract

1. A novel stepwise classification approach for predicting the metabolic fate of substituted anilines, based on calculated physicochemical parameters of the parent anilines, was developed. Based on multivariate pattern recognition methods (PLS-DA or soft independent modelling of class analogy [SIMCA]), these models allowed prediction of N-acetylation and subsequent N-oxanilic acid formation. These classification methods provided an improved classification success when compared with existing quantitative structure-metabolism relationship models for substituted anilines.

2. Modelling the physicochemical properties of the N-acetylated compounds was considered as an addition to the stepwise model. Inclusion of parameters describing the N-acetyl moiety had little effect on the predictive ability of a stepwise parent to N-acetyl to N-oxanilic acid PLS-DA model, and had a negative impact on that of SIMCA models. This was attributed to the relatively small contribution to the total parameter variance caused by differences arising as a result of N-acetylation compared to the contribution made by the substituent effects.

3. Calculation of physicochemical properties incorporating the effect of solvation using ab initio methods improved the classification model in terms of both the visual separation in multivariate projections and prediction accuracy.