Application of in vitro-in vivo correlations (IVIVC) in setting formulation release specifications

Fexofenadine-loaded chitosan coated solid lipid nanoparticles (SLNs): A potential oral therapy for ulcerative colitis

The targeting and mucoadhesive features of chitosan (CS)-linked solid lipid nanoparticles (SLNs) were exploited to efficiently deliver fexofenadine (FEX) into the colon, forming a novel and potential oral therapeutic option for ulcerative colitis (UC) treatment. Different FEX-CS-SLNs with varied molecular weights of CS were prepared and optimized. Optimized FEX-CS-SLNs exhibited 229 ± 6.08 nm nanometric size, 36.3 ± 3.18 mV zeta potential, 64.9 % EE, and a controlled release profile. FTIR, DSC, and TEM confirmed good drug entrapment and spherical particles. Mucoadhesive properties of FEX-CS-SLNs were investigated through mucin incubation and exhibited considerable mucoadhesion. The protective effect of FEX-pure, FEX-market, and FEX-CS-SLNs against acetic acid-induced ulcerative colitis in rats was examined. Oral administration of FEX-CS-SLNs for 14 days before ulcerative colitis induction reversed UC symptoms and almost restored the intestinal mucosa to normal integrity and inhibited Phosphatidylinositol-3 kinase (73.6 %), protein kinase B (73.28 %), and elevated nuclear factor erythroid 2-related factor 2 (185.9 %) in colonic tissue. Additionally, FEX-CS-SLNs inhibited tumor necrosis factor α (TNF-α) and interleukin 6 (IL-6) to (70.79 % & 72.99 %) in colonic tissue. The ameliorative potential of FEX-CS-SLNs outperformed that of FEX-pure and FEX-market. The exceptional protective effect of FEX-CS-SLNs makes it a potentially effective oral system for managing ulcerative colitis.

Effect of soil particle size and extraction method on the oral bioaccessibility of arsenic

Recent findings indicate that incidental ingestion of soil by humans primarily involves soil particles <150 µm, rather than <250 µm-sized fraction previously used for most oral bioaccessibility and bioavailability studies. It was postulated that a greater soil surface area in the finer fraction (<150 versus <250 µm) might increase oral bioaccessibility of arsenic (As) in soil. Bioaccessibility and concentrations of As were compared in <150 and <250 µm fractions of 18 soil samples from a variety of arsenic-contaminated sites. The two methods used to measure bioaccessibility were compared - EPA Method 1340 and the California Arsenic Bioaccessibility (CAB) method. Arsenic concentrations were nearly the same or higher in the <150 fraction compared with <250 µm. EPA Method 1340 and the CAB method presented significantly different bioaccessibility results, as well as estimated relative oral bioavailability (RBA) based upon algorithms specific to the methods, but there was no marked difference for <150 and <250 µm soil fractions within either method. When compared with RBA determined previously for these soil samples in vivo in non-human primates, EPA Method 1340 was generally more predictive than the CAB method. Data suggest that soil- or site-specific factors control bioaccessibility under either method and that the test method selected is more important than the particle size fraction (<150 or <250) in using these in vitro methods to predict As RBA for use in risk assessment.

Impact of Tablet Shape on Drug Dissolution Rate Through Immediate Released Tablets

Purpose: The aim of this study was to evaluate the influence of the geometric shape on the dissolution rate of the domperidone, a drug model for immediate release dosage form. In this regard, a lack of sufficient information about the effective dissolution rate of the drugs regarding their shapes has made this issue an interesting subject for researchers. Methods: For this purpose, three tablet shapes, namely flat and biconvex both in a round and oblong shapes, with different four sizes were modelled for the preparation of domperidone tablet. In vitro dissolution test was accomplished using a USP dissolution apparatus II. The drug dissolution rate was assessed by calculating various dissolution parameters; e.g., dissolution efficiency (DE), mean dissolution rate (MDR), mean dissolution time (MDT), and difference and similarity factors (f₁ and f₂ ). Results: Regarding the disintegration time, the larger tablets showed a faster disintegration time. When the size of the tablets was smaller, the amount of released drug was significantly decreased. In addition, #9 tablets with a flat or biconvex geometry had obvious effects on the DE values. Generally, biconvex tablets had higher DE percentage than the flat tablets. Conclusion: Noticeable differences in dissolution parameters by considering the different geometric shapes play an important role in the drug release kinetics which makes a significant effect on quick onset of action in oral administration.

An updated overview with simple and practical approach for developing in vitro-in vivo correlation

Preclinical Research & Development An in vitro-in vivo correlation (IVIVC) is as a predictive mathematical model that demonstrates a key role in the development, advancement, evaluation and optimization of extended release, modified release and immediate release pharmaceutical formulations. A validated IVIVC model can serve as a surrogate for bioequivalence studies and subsequently save time, effort and expenditure during pharmaceutical product development. This review discusses about different levels of correlations, general approaches to develop an IVIVC by mathematical modelling, validation, data analysis and various applications. In the current setting, the dearth of success associated with IVIVC is due to complexity of underlying scientific principles as well as the practice of fitting/matching in vivo plasma level-time data with in vitro dissolution profile. Hence, a simple, straightforward practical means to predict plasma drug levels by convolution technique and percentage drug absorbed computed from in vitro dissolution profile based on deconvolution method are illustrated. The bioavailability/bioequivalence assessment and evaluation are frequently validated by the pharmacokinetic parameters such as maximum concentration, time to reach maximum concentration, and area under the curve. The implementation of a quality by design manufacturing based on in vivo bioavailability and clinically relevant dissolution specification are recommended because corresponding design safe space will guarantee that all batches from relevant products are met with sufficient quality and bioperformance. Recently, United States Food and Drug Administration and European Medicines Agency have proposed that in silico/physiologically based pharmacokinetic modelling can be used in decision making during preclinical experiments as well as to recognize the dissolution profiles that can forecast and ensure the desired clinical performance.

Lidocaine Transdermal Patch: Pharmacokinetic Modeling and In Vitro-In Vivo Correlation (IVIVC)

The present study aims to develop the correlation between in vitro and in vivo skin permeation of lidocaine in its transdermal patch. In order to minimize the run-to-run variability during in vitro skin permeation studies, release normalized cumulative percent (%Ct n) was calculated. A suitable polynomial mathematical model was used to establish a correlation between time and %Ct n. Percent in vivo absorbed was calculated by using numerical deconvolution (NDC) and non-compartmental analysis (NCA) methods. Pharmacokinetic (PK) parameters such as AUC last and C max were predicted with the established in vitro-in vivo correlation (IVIVC) models. The minimum prediction errors in NDC method for C max were found to be -30.9 and -25.4% for studies I (in vivo study in human volunteers with one batch of Lidoderm patch; internal validation) and II (in vivo study in human volunteers with another batch of Lidoderm patch; external validation), respectively, whereas minimum prediction errors in NCA method were relatively low (3.9 and 0.03% for studies I and II, respectively) compared to those in NDC method. The prediction errors for AUC last were found to be less than 2% for both methods and studies. The established method in this study could be a potential approach for predicting the bioavailability and/or bioequivalence for transdermal drug delivery systems.

Applications of In Vitro-In Vivo Correlations in Generic Drug Development: Case Studies

In vitro-in vivo correlation (IVIVC) is a predictive mathematical model describing the relationship between an in vitro property and a relevant in vivo response. The main objective of an IVIVC is to serve as a surrogate for human bioequivalence (BE) studies, which may reduce the number of BE studies performed during the initial approval process as well as with certain scale-up and postapproval changes. The US Food and Drug Administration (FDA) published a regulatory guidance related to development, evaluation, and applications of IVIVC for extended-release (ER) oral dosage forms in September 1997. Despite the publication of this guidance, the deficiencies related to IVIVC are still identified by the Division of Bioequivalence in the process of Abbreviated New Drug Application (ANDA) review. Thus, the main objective of this article is to present the most commonly occurring deficiencies associated with IVIVCs via selected case studies from the ANDAs for oral ER drug products only. We searched internal FDA databases from January 1996 to December 2014 to identify the ANDAs for proposed generic oral ER drug products containing IVIVC. Only 14 ANDA submissions had IVIVC data, and most were not acceptable. Only one ANDA submission included adequate information related to IVIVC data enabling the completion of BE review within first review cycle. It is hoped that awareness of the deficiencies presented in our article would help the generic drug applicants to submit complete and appropriate information related to IVIVC data, ultimately, resulting in a more timely approval of ANDAs.

In vitro dissolution similarity factor (f2) and in vivo bioequivalence criteria, how and when do they match? Using a BCS class II drug as a simulation example

The present study examined the agreement between in vitro dissolution f2 similarity and in vivo bioequivalence criteria for BCS class II drugs. Dissolution test profiles were generated using the First-order model with varied dissolution parameters around the standard values of a reference profile. The in vivo curves were derived from in vitro dissolution profiles with the drug's pharmacokinetics parameters by numerical convolution method. The Cmax, Tmax, AUC0-t and AUC0-∞ obtained from in vivo test and reference concentration-time curves were compared, and the CmaxR (Cmax ratio), TmaxDif (Tmax difference), AUC0-tR (AUC0-t ratio) and AUC0-∞R (AUC0-∞ ratio) were determined. The relationships between CmaxR, AUC0-tR, AUC0-∞R, f2 and the First-order model parameters demonstrated that the Similarity Region 1 enclosed by the f2 contour line labeled 50 was completely within the Bioequivalence Region enclosed by the contour lines labeled 0.80 and 1.20 of AUC0-tR, AUC0-∞R, and CmaxR, and the Similarity Region 2 enclosed by the f2 contour line labeled 35 was nearly overlapped with the Bioequivalence Region, but did not exactly match. The results indicate that the public standard for in vitro dissolution f2 similarity criterion (f2⩾50) is probably slightly conservative and may be widened to an appropriate lower critical value.

In vitro- in vivo correlation's dissolution limits setting

PURPOSE

In vitro in vivo correlation (IVIVC) is a biopharmaceutical tool recommended for use in formulation development. When validated, IVIVC can be used to set dissolution limits and, based on the dissolution limits, as a surrogate for an in vivo study. The purpose of this paper is to study the various methods used to fix dissolution limits.

METHODS

Fixing dissolution limits is not a straightforward process; various approaches exist. The classical ±10% of dissolution limits was compared to the recommended ±10% of Cmax and AUC and to an innovative back calculation of the 90% CI. Based on simulated values the influence of the calculation method as well as of the variability of the results and pharmacokinetic processes was investigated.

RESULTS

Depending upon the method, the results are different and their comparison leads to possible rules. It appears that the usage of a back calculation of a 90% CI is an accurate and advantageous method when intra-individual variability associated with the drug is low. Those findings are in accordance with the current practice of IVIVC, which is not recommended for highly variable drugs.

CONCLUSIONS

The approach of using a 90% CI allows the intra-subject variability to be taken into account and fixes limits that ensure a greater chance to show acceptable BE, in case of reasonable intra-subject variability, leading to setting broader in vitro dissolution limits compared to classical solutions.

Prediction of in vivo plasma concentration-time profile from in vitro release data of designed formulations of milnacipran using numerical convolution method

The aim of this study was to predict the in vivo plasma drug level of milnacipran (MIL) from in vitro dissolution data of immediate release (IR 50 mg and IR 100 mg) and matrix based controlled release (CR 100 mg) formulations. Plasma drug concentrations of these formulations were predicted by numerical convolution method. The convolution method uses in vitro dissolution data to derive plasma drug levels using reported pharmacokinetic (PK) parameters of a test product. The bioavailability parameters (Cmax and AUC) predicted from convolution method were found to be 106.90 ng/mL, 1138.96 ng/mL h for IR 50 mg and 209.80 ng/mL, 2280.61 ng/mL h for IR 100 mg which are similar to those reported in the literature. The calculated PK parameters were validated with percentage predication error (% PE). The % PE values for Cmax and AUC were found to be 7.04 and -7.35 for IR 50 mg and 11.10 and -8.21 for IR 100 mg formulations. The Cmax, Tmax, and AUC for CR 100 mg were found to be 120 ng/mL, 10 h and 2112.60 ng/mL h, respectively. Predicted plasma profile of designed CR formulation compared with IR formulations which indicated that CR formulation can prolong the plasma concentration of MIL for 24 h. Thus, this convolution method is very useful for designing and selection of formulation before animal and human studies.

Flip-flop pharmacokinetics--delivering a reversal of disposition: challenges and opportunities during drug development

Flip-flop pharmacokinetics is a phenomenon often encountered with extravascularly administered drugs. Occurrence of flip-flop spans preclinical to human studies. The purpose of this article is to analyze both the pharmacokinetic interpretation errors and opportunities underlying the presence of flip-flop pharmacokinetics during drug development. Flip-flop occurs when the rate of absorption is slower than the rate of elimination. If it is not recognized, it can create difficulties in the acquisition and interpretation of pharmacokinetic parameters. When flip-flop is expected or discovered, a longer duration of sampling may be necessary in order to avoid overestimation of fraction of dose absorbed. Common culprits of flip-flop disposition are modified dosage formulations; however, formulation characteristics such as the drug chemical entities themselves or the incorporated excipients can also cause the phenomenon. Yet another contributing factor is the physiological makeup of the extravascular site of administration. In this article, these causes of flip-flop pharmacokinetics are discussed with incorporation of relevant examples and the implications for drug development outlined.

Preparation and in vitro/in vivo evaluation of microparticle formulations containing meloxicam

In this study, we have formulated chitosan-coated sodium alginate microparticles containing meloxicam (MLX) and aimed to investigate the correlation between in vitro release and in vivo absorbed percentages of meloxicam. The microparticle formulations were prepared by orifice ionic gelation method with two different sodium alginate concentrations, as 1% and 2% (w/v), in order to provide different release rates. Additionally, an oral solution containing 15 mg of meloxicam was administered as the reference solution for evaluation of in vitro/in vivo correlation (ivivc). Following in vitro characterization, plasma levels of MLX and pharmacokinetic parameters [elimination half-life (t(1/2)), maximum plasma concentration (C(max)), time for C(max) (t(max))] after oral administration to New Zealand rabbits were determined. Area under plasma concentration-time curve (AUC(0-∞)) was calculated by using trapezoidal method. A linear regression was investigated between released% (in vitro) and absorbed% (in vivo) with a model-independent deconvolution approach. As a result, increase in sodium alginate content lengthened in vitro release time and in vivo t(max) value. In addition, for ivivc, linear regression equations with r(2) values of 0.8563 and 0.9402 were obtained for microparticles containing 1% and 2% (w/v) sodium alginate, respectively. Lower prediction error for 2% sodium alginate formulations (7.419 ± 4.068) compared to 1% sodium alginate formulations (9.458 ± 5.106) indicated a more precise ivivc for 2% sodium alginate formulation.

Plasma methylphenidate concentrations in youths treated with high-dose osmotic release oral system formulation

BACKGROUND

Children and adolescents are being treated increasingly for attention-deficit/hyperactivity disorder (ADHD) with a variety of stimulants in higher than Food and Drug Administration (FDA)-approved doses and in combination with other medications.

OBJECTIVE

We sought to determine methylphenidate (MPH) concentrations in children and adolescents treated with high-dose, extended-release osmotic release oral system (OROS) MPH plus concomitant medications, and to examine MPH concentrations with respect to the safety and tolerability of treatment.

METHODS

Plasma MPH concentrations were measured by liquid chromatography-mass spectrometry 4-5 hours after administration of medication in a sample of youths diagnosed with ADHD. These youths were treated naturalistically with higher than FDA-approved doses of OROS MPH in addition to their concomitant medications. Markers of safety and tolerability (e.g., measures of blood pressure and heart rate) were also examined.

RESULTS

Among the 17 patients (with a mean age of 16.2 +/- 2 years and a mean number of concurrent medications of 2.23 +/- 0.94), the mean plasma MPH concentration was 28 +/- 9.1 ng/mL, despite a mean daily dose of OROS MPH of 169 +/- 5 mg (3.0 +/- 0.8 mg/kg per day). No patient had a plasma MPH level >or=50 ng/mL or clinical signs of stimulant toxicity. No correlation was found between plasma MPH concentrations and OROS MPH dose or changes in vital signs.

CONCLUSIONS

High-dose OROS MPH, used in combination with other medications, was not associated with either unusually elevated plasma MPH concentrations or with clinically meaningful changes in vital signs. Study limitations include a single time-point sampling of MPH concentrations, a small sample size, and a lack of outcome measures to address treatment effectiveness.

Population in vitro-in vivo correlation model for pramipexole slow-release oral formulations

PURPOSE

To establish an in vitro-in vivo level A correlation (IVIVC) for pramipexole slow-release formulations.

METHODS

The IVIVC was developed based on data from an immediate-release (IR) and three slow-release (SR) formulations of pramipexole; a fourth SR formulation was used for validation purposes. In vitro dissolution profiles were obtained from all SR formulations. Fifteen volunteers received all pramipexole formulations in a randomized cross-over trial. Data were analyzed using the population modelling approach as implemented in NONMEM VI.

RESULTS

Dissolution profiles of the SR formulations were described by the Weibull model. The pharmacokinetics of the IR formulation were described by a two-compartment disposition model with first-order absorption. Difference between the in vivo and in vitro estimates of the release rate constants (k(d)) from the Weibull function suggests the release process occurs faster in vivo. Pharmacokinetic profiles for SR formulations were described based on the in vitro release model with k(d) increased in 0.058 h(-1) and the population pharmacokinetic model developed from the IR formulation.

CONCLUSION

A level A IVIVC was established and evaluated for the pramipexole SR formulations, which can be used in the future as a surrogate to avoid certain bioequivalence studies.

Oral osmotically driven systems: 30 years of development and clinical use

The number of marketed oral osmotically driven systems (OODS) has doubled in the last 10 years. The main clinical benefits of OODS are their ability to improve treatment tolerability and patient compliance. These advantages are mainly driven by the capacity to deliver drugs in a sustained manner, independent of the drug chemical properties, of the patient's physiological factors or concomitant food intake. However, access to these technologies has been restricted by the crowded patent landscape and manufacturing challenges. In this review article, we intend to give an overview of the OODS development in the last 30 years, detailing the technologies, specific products and their clinical use. General guidance on technology selection is described in light of the recent advances in the field. The clinical performance of these technologies is also discussed, with a focus on food effects and the in vivo-in vitro correlation. Special attention is paid to safety given the controversial case study of Osmosin. Overall, oral osmotically driven systems appear to be a promising technology for product life-cycle strategies.

Pharmaceutical applications of AC biosusceptometry

AC Biosusceptometry offers an alternative to investigate noninvasively and without ionizing radiation the behavior of solid dosage forms in vitro and in the human gastrointestinal tract. This versatility allowed applying this technique in a wide field ranging from characterization of the disintegration process to elucidation of how the physiological parameters can interfere with pharmaceutical processes. It is increasingly important to understand how oral solid dosage forms behave in the human gastrointestinal tract. Once labelled, magnetic dosage forms provide an excellent opportunity to investigate complexes' interactions between dosage form and gastrointestinal physiology. In this paper, basic principles of this biomagnetic instrumentation and of the quantification based on magnetic images are reviewed. Also will be presented are some of the most recent applications of AC Biosusceptometry in the pharmaceutical research including oesophageal transit, gastric emptying and transit time of multiparticulate dosage forms, hydrophilic matrices and disintegration of tablets.

Level A in vitro-in vivo Correlation (IVIVC) Model with Bayesian Approach to Formulation Series

In vitro-in vivo correlation (IVIVC) models for formulation series are useful in drug development, but the current models are limited by their inability to include data variability in the predictions. Our goal was to develop a level A IVIVC model that provides predictions with probabilities. The Bayesian approach was used to describe uncertainty related to the model and the data. Three bioavailability studies of levosimendan were used to develop IVIVC model. Dissolution was tested at pH 5.8 with basket. The IVIVC model with Bayesian approach consisted of prior and observed data. All observed data were fitted to the one-compartment model together with prior data. Probability distributions of pharmacokinetic parameters and concentration time profiles were obtained. To test the external predictability of IVIVC model, only dissolution data of formulations E and F were used. The external predictability was good. The possibility to utilize all observed data when constructing IVIVC model, can be considered as a major strength of Bayesian approach. For levosimendan capsule data traditional IVIVC model was not predictable. The usefulness of IVIVC model with Bayesian approach was shown with our data, but the same approach can be used more widely for formulation optimization and for dissolution based biowaivers.

A multi-mechanistic drug release approach in a bead dosage form and in vitro/in vivo correlations

An in vitro/in vivo relationship of a combined multi-mechanistic dosage form has now been established in the literature. In our previous study, we successfully prepared a combination of immediate release, enteric coated, and controlled-release (CR) beads and mathematically modeled in vitro and in vivo drug release characteristics of the combination based on the release profiles of individual beads. The objective of the present study is to develop in vitro/in vivo correlations (IVIVC) for three individual beads and the combination using theophylline as a model drug and the beagle dog as an animal model. In the study, an IVIVC correlation is estimated by two-stage procedures: deconvolution followed by comparison of the fraction of drug absorbed to the fraction of drug dissolved. The Wagner-Nelson mass balance method was used to deconvolute plasma drug concentration-time curves. In vitro, a two-stage medium (0.1 N HCl and pH 6.5 phosphate buffer) was used for the dissolution test; a 2h first stage (acidic) was selected based on the average gastric emptying time in a fasted dog. In vivo, t(lag) was used for the gastric emptying process for enteric coated beads and the combination, which contains enteric coated beads. A time-scaling technique was used to consider the rate difference between in vitro dissolution and in vivo absorption in the process of IVIVC. As shown in the results, a point-to-point correlation was established for each formulation. The linear regression analysis of the correlation was r2>0.99 for all three individual beads and 0.97 for the combined bead dosage form. The results suggest level A IVIVCs indicating an appropriateness for the in vitro and in vivo models used in this study.

Interpretation and Optimization of the Dissolution Specifications for a Modified Release Product with an In Vivo–In Vitro Correlation (IVIVC)

This article considers the in vivo significance attached to in vitro dissolution testing. Almost invariably, the in vitro dissolution test is interpreted in terms of bioequivalence. The literature that describes methods for setting in vitro dissolution specifications is reviewed. The most common interpretation of these specifications is a deterministic one, that is, those batches passing the dissolution specifications would be bioequivalent with the reference if tested in vivo and those failing the dissolution specifications would not be bioequivalent if tested in vivo. Due to random variation, the deterministic interpretation is not appropriate. Instead, we need to consider the conditional probability that a batch that has passed the in vitro dissolution test would demonstrate bioequivalence if tested in vivo, and that a batch known to have failed the in vitro dissolution test would demonstrate bioinequivalence if tested in vivo. One way to estimate these probabilities is by means of a simulated experiment in which the production and testing (in vivo and in vitro) of a large number of batches is computer simulated. Such a simulation can only be performed if the relationship between the in vitro dissolution characteristics and the in vivo performance of the product has been modeled. These models are generally referred to as in vivo-in vitro correlations (IVIVC). The results of one such experiment are described. The above-mentioned conditional probabilities are shown to depend on the choice of dissolution specifications. This result leads to the notion of optimal dissolution specifications. However, both of the conditional probabilities cannot be maximized simultaneously. The probability of making a correct decision on the basis of the in vitro dissolution test is introduced as a possible optimality criterion. This probability is a linear combination of the two conditional probabilities of interest. Using this criterion, the optimal dissolution specifications can be found by searching over the multidimensional space defined by the half width of each interval used in the specifications to find the combination that maximizes this probability. This process is demonstrated using the Nelder-Mead search routine. The choice of dissolution specifications has profound implications for the routine production of the product because if the specifications were very narrow the probability of a batch passing would be low, resulting in a low hit rate. The same computer program used to perform the simulation experiment can be used to estimate the hit rate. Furthermore, it can be used to explore the magnitude of changes required in the parameters describing the test product (particularly variability) to increase a low hit rate to an acceptable level.

Direct, differential-equation-based in-vitro-in-vivo correlation (IVIVC) method

A new, differential equation-based in-vitro-in-vivo correlation (IVIVC) method is proposed that directly relates the time-profiles of in-vitro dissolution rates and in-vivo plasma concentrations by using one- or multi-compartment pharmacokinetic models and a corresponding system of differential equations. The rate of in-vivo input is connected to the rate of in-vitro dissolution through a general functional dependency that allows for time scaling and time shifting. A multiplying factor that accounts for the variability of absorption conditions as the drug moves along is also incorporated. Two data sets incorporating slow-, medium-, and fast-release formulations were used to test the applicability of the method, and predictive powers were assessed with a leave-one-formulation-out approach. All fitted parameters had realistic values, and good or acceptable fits and predictions were obtained as measured by plasma concentration mean squared errors and percent AUC errors. Introduction of step-down functions that account for the transit of the dosage form past the intestinal sites of absorption proved useful. By avoiding the integral transforms used in the existing deconvolution- or convolution-based IVIVC models, the present method can provide increased transparency, improved performance, and greater modelling flexibility.