# Development of a Novel Simplified PBPK Absorption Model to Explain the Higher Relative Bioavailability of the OROS® Formulation of Oxybutynin

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## Abstract

A new minimal Segmented Transit and Absorption model (mSAT) model has been recently proposed and combined with intrinsic intestinal effective permeability (*P* _{ eff,int }) to predict the regional gastrointestinal (GI) absorption (*f* _{ abs }) of several drugs. Herein, this model was extended and applied for the prediction of oral bioavailability and pharmacokinetics of oxybutynin and its enantiomers to provide a mechanistic explanation of the higher relative bioavailability observed for oxybutynin’s modified-release OROS® formulation compared to its immediate-release (IR) counterpart. The expansion of the model involved the incorporation of mechanistic equations for the prediction of release, transit, dissolution, permeation and first-pass metabolism. The predicted pharmacokinetics of oxybutynin enantiomers after oral administration for both the IR and OROS® formulations were in close agreement with the observed data. The predicted absolute bioavailability for the IR formulation was within 5% of the observed value, and the model adequately predicted the higher relative bioavailability observed for the OROS® formulation *vs.* the IR counterpart. From the model predictions, it can be noticed that the higher bioavailability observed for the OROS® formulation was mainly attributable to differences in the intestinal availability (*F* _{ G }) rather than due to a higher colonic *f* _{ abs }, thus confirming previous hypotheses. The predicted *f* _{ abs } was almost 70% lower for the OROS® formulation compared to the IR formulation, whereas the *F* _{ G } was almost eightfold higher than in the IR formulation. These results provide further support to the hypothesis of an increased *F* _{ G } as the main factor responsible for the higher bioavailability of oxybutynin’s OROS® formulation *vs*. the IR.

## KEY WORDS

CYP3A formulation intestinal metabolism OROS® oxybutynin PBPK model## ABBREVIATIONS

- ACAT
Advanced Compartmental Absorption and Transit

- ADAM
Advanced Dissolution Absorption and Metabolism

- AGP
α

_{1}-Acidglycoprotein- AUC
Area under the curve

- BCS
Biopharmaceutical Classification System

- BW
Body weight

- CES2
Carboxylesterase 2

*C*_{max}Maximum plasma/blood concentration

- CO
Cardiac output

- CPGA
2-Cyclohexyl-2-phenylglycolic acid

- CR
Controlled release

- DEOB
*N*-Desethyloxybutynin*F*Absolute oral bioavailability

*f*_{abs}Fraction of the dose absorbed in the gastrointestinal tract

*F*_{G}Fraction of the dose absorbed that escapes gut wall first-pass metabolism

*F*_{H}Fraction of the dose absorbed that escapes hepatic first-pass metabolism

- FOCE-I
First-order conditional with interaction maximum likelihood estimation method

*F*_{rel}Relative bioavailability

- GI
Gastrointestinal

- HLM
Human liver microsomes

- IR
Immediate release

*IV*or*iv*Intravenous

- LC-MS/MS
Liquid chromatography with tandem mass spectrometry detection

- M&S
Modelling and simulation

- MR
Modified release

- mSAT
Minimal segmented absorption and transit

- OrBiTo
Oral biopharmaceutics tools

- OROS
Osmotic controlled-release oral delivery system

- OXY
Oxybutynin

- PBPK
Physiologically based pharmacokinetic(s)

*P*_{eff}intestinal effective permeability

- SI
Small intestine (al)

- SITT
Small intestinal transit time

## INTRODUCTION

In recent years, there has been an increase in the use of physiologically based pharmacokinetics (PBPK) models in drug development, particularly in the pre-clinical and early clinical stages. Numerous articles coming from academia, industry and regulatory agencies have highlighted the benefits of applying such models in the drug discovery and development arena (1, 2, 3, 4, 5, 6). By incorporating some of the mechanisms driving the pharmacokinetics of a drug, PBPK models allows one to distinguish between drug-related and the physiological factors controlling drug absorption, distribution, metabolism and elimination (ADME). This characteristic enables one to integrate measured *in vitro* or *in silico* drug properties into the model in the so-called *in vitro*–*in vivo* extrapolation (IVIVE) approach, enabling the use of such models in a truly prospective fashion (6). PBPK models have been increasingly applied in oral absorption and biopharmaceutics. This has been partly due to the development and availability of mechanistic absorption models such as the ones included in commercial software packages like SimCYP® (ADAM) (7), GastroPlus™ (ACAT) (8) and PK-Sim® (9,10), as well as some in-house developments coming from academia and industry (11, 12, 13, 14).

Oral absorption and bioavailability are dependent upon numerous physiological and drug-related factors interacting simultaneously. These factors are the key to defining the different steps of the oral absorption process, *i.e.* transit, dissolution, release, permeation, transport and metabolism (15,16). Given the complex nature of these drug–physiology interactions, prospective predictions of oral bioavailability within the PBPK framework are still a challenging task (17, 18, 19). Nevertheless, significant efforts have recently been made in order to improve our understanding of such a complex interplay. For instance, the Innovative Medicines Initiative (IMI) OrBiTo project has amongst its goals to enrich our knowledge of the physiological and biopharmaceutical properties that define *in vivo* drug absorption and to provide new *in vitro* and *in silico* tools that can help to make better predictions of the *in vivo* drug product performance (20).

One of the key biopharmaceutical factors defining oral drug absorption are formulation characteristics. In a recent study, we investigated the impact that modified/controlled release (MR/CR) formulations might have on the oral bioavailability of substrates of the cytochrome P450 (CYP) 3A4 enzymes using a prospective PBPK modelling and simulation (M&S) approach (21). By employing this approach, we were able to evaluate the interplay between drug and physiological-related factors governing intestinal absorption and first-pass metabolism, and in particular to identify the possible scenarios where MR formulations of a CYP3A substrate might display higher relative bioavailability (*F* _{ rel}) compared to its immediate released (IR) counterparts (21). In our previous study, it was shown that highly cleared CYP3A-substrates belonging to Class 1 within the biopharmaceutics classification system (BCS) are more likely to display higher *F* _{ rel } when formulated as MR (21). The mechanism proposed for this phenomenon is an increased intestinal availability (*F* _{ G }) due to a decreased intestinal first-pass metabolism as a result of the lower abundance of CYP3A enzymes in the distal gastrointestinal (GI) tract, where most of the drug contained in the MR formulation is likely to be released and absorbed (21, 22, 23, 24). Another interesting outcome of the study was the observed trend to over predict *f* _{ abs } of MR formulations belonging to BCS Classes 2 and 3 (21,25). This over prediction was attributed to an overestimation of the colonic absorption due to the PBPK approach employed for the study. That is, intestinal effective permeability (*P* _{ eff }) was assumed to be same for all intestinal segments implemented in the absorption model, including the colon (21). In an attempt to address this issue, and given the lack of an implementation of regional intestinal (passive) permeability within in the PBPK framework, two novel approaches to implement regional *P* _{ eff } for prospective PBPK simulations were recently proposed (26). The approaches were based on the translation of regional intestinal variations in the available mucosal surface area (mSA) into segment-dependent permeability and absorption (26). When the approaches were combined with a novel simplified absorption PBPK model, or minimal Segmented Absorption and Transit (mSAT) model, they showed a potential to decrease the observed overestimation of the colonic *f* _{ abs } (26), especially when applying the so-called Method 3 (M3) which was based on the intestinal mSA values derived recently by Helander and Fändriks (26,27).

One of the limitations of the prospective PBPK analysis of the bioavailability differences between IR and MR formulations of CYP3A substrates was the lack of drug-specific simulations necessary to provide stronger support for the prospective modelling and simulation study outcome (21). Therefore, the present work was designed as a continuation of the work performed in the previous studies, with the main aim to provide a drug-specific example to support the hypothesis of a reduced first-pass metabolism as the main driving mechanism of the higher *F* _{ rel } of CYP3A substrates formulated as MR (21).

In particular, this study investigated the bioavailability differences observed for the MR formulation of oxybutynin (OXY). OXY is a highly cleared antimuscarinic drug with anticholinergic, spasmolytic and local anaesthetic properties employed for the treatment of urge urinary incontinency due to over activity of the detrusor muscle (28). OXY is a highly permeable and soluble compound (BCS Class 1) (21). After oral administration, OXY is rapidly absorbed and undergoes extensive first-pass metabolism in both the intestinal wall and the liver, mainly mediated by CYP3A4 (28, 29, 30). When formulated as a once a day (MR) OROS® formulation, the relative bioavailability of OXY was around 153% compared to its IR tablet, while the exposure of its main metabolite, *N*-desethyloxybutynin (DEOB) was reduced by almost 30% (28). This reduction in exposure was translated into an improved safety profile due to a reduction in the incidence of dry mouth episodes, OXY’s main side-effect, which is mainly attributed to its active metabolite, yet keeping the same efficacy (31,32).

In this study, OXY’s bioavailability differences were investigated by means of a PBPK modelling and simulation approach, combining *in vivo*, *in vitro* and *in silico* data together with an extended version of the previously developed mSAT model. The model was expanded to prospectively predict OXY’s oral bioavailability for both IR and MR formulations (26).

## MATERIALS AND METHODS

### PBPK Model Development

The PBPK model employed for the mechanistic pharmacokinetic prediction of OXY was developed using a two-step approach. Firstly, a compound-specific semi-physiological PBPK model was developed and optimized with intravenous (IV) data to describe OXY’s disposition. Secondly, the optimized OXY’s disposition model was coupled with an extended version of the generic mSAT model to predict oral absorption and bioavailability using an *in vitro*–*in vivo* extrapolation (IVIVE) approach. The two-stage approach was chosen as it reduces the confounding issues that can arise when drug’s disposition is not properly considered in the prediction of oral pharmacokinetics, thus providing better information about the predictive performance of the oral absorption model (mSAT). The details of the different steps of the model development are described in the following sections:

### Development of OXY’s Disposition Model

The semi-physiological PBPK model employed to describe OXY’s disposition was developed based on the approach proposed by Cao and Jusko, whereby the model structure represents a hybrid between a whole-body PBPK model and a compartmental or mammillary pharmacokinetic model (33). The advantage of employing such an approach, compared to the use of traditional compartmental models, is that the former allows the use of prior physiological and anatomical knowledge to define the model structure. Therefore, under this approach, the model parameters are constrained between physiologically plausible limits (33). This approach appropriately distinguishes between drug-related and system-specific parameters, as the model can be informed from known drug-related properties, such as plasma protein binding and/or metabolic routes (33). It should be noted however that the model structure was not the product of the reduction of a whole-body PBPK model using formal reduction techniques such as “proper lumping” (34, 35, 36). In contrast, the model development was data driven, whereby the number of tissue compartments was defined based on the best description of the observed clinical data.

*i*th non-eliminating empirical tissue was described by Eq. 1,

*V*

_{tissue,i}represents the tissue volume (L),

*C*

_{tissue,i}is the drug’s concentration in the tissue (mg/L),

*Q*

_{tissue,i}is the tissue blood flow (L/h) and

*K*

_{b,tissue}is an empirical tissue to blood partition coefficient necessary to describe the extent of OXY’s distribution into the tissue compartment. The dynamics in the blood compartment were described by Eq. 2,

*V*

_{blood}is the systemic blood volume (L),

*R*

_{in}is the drug’s infusion rate after IV administration (mg/h),

*Q*

_{HV}is the hepatic vein’s blood flow,

*C*

_{liver}is the concentration in the liver tissue,

*K*

_{ b,liver }is the drug’s liver tissue to blood partition coefficient and

*Q*

_{liver}is the combined hepatic and non-villous splanchnic blood flow (37, 38, 39). The latter parameter was defined the sum of the arterial blood supply to the liver and the non-villous portal blood flow (

*i.e.*oesophagus, stomach, gut tissue, pancreas, upper large intestine, lower large intestine and spleen) (37, 38, 39). Given that the observed clinical data is usually reported as plasma concentrations rather than blood concentrations, the concentration represented by Eq. 2 (blood) was later expressed as plasma concentration by dividing

*C*

_{ blood }by the blood to plasma ratio (BP). OXY’s systemic elimination was assumed to occur exclusively through hepatic metabolism, given that only less than 0.02% of the administered dose was found unchanged in the urine after IV administration (30). The dynamics of the liver compartment were described by Eq. 3,

*Q*

_{ent,n }and

*C*

_{ent,n }are the villous blood flow and concentration entering the liver from the

*n*th enterocyte compartment, respectively (these values were assumed zero for IV administrations),

*f*

_{ up }is the drug’s fraction unbound in plasma and CL

_{liver}is the OXY’s hepatic clearance (L/h). CL

_{liver}was scaled from the drug’s unbound intrinsic microsomal clearance (CL

_{int(u)}, L/h/mg of microsomal protein) using the following equation (40)

*LW*is the liver weight (g) and

*MPPGL*is the amount of microsomal protein per gram of liver (mg/g).

### Disposition Model Parameters and Parameter Estimation

*i.e.*Caucasian male, 70 kg and 1.70 m. The remaining model parameters were obtained by fitting the model shown in Fig. 1a to OXY’s plasma concentration-time profile obtained after a 5 mg IV infusion to four healthy volunteers published by Douchamps and co-workers (30). The data was digitized using GetData Graph Digitizer v2.26 (http://getdata-graph-digitizer.com/). The estimated parameters were

*CL*

_{ int(u) },

*Q*

_{ tissue,i },

*V*

_{ tissue,I }(for tissues 1 to 3) and an empirical unbound tissue to plasma partition coefficient (

*K*

_{ pu,tissue }).

*K*

_{ pu }was assumed to be the same for all the empirical tissues. The

*K*

_{ pu }was converted into a

*K*

_{ b }value, needed for the model equations, using the following equation (41),

*BP*is the OXY’s blood to plasma ratio.

System-Related Parameters Used in the mSAT Model

Parameter [units] | Value | Ref. | ||||

Reference body weight ( | 70 | S3 | ||||

Reference height ( | 1.70 | S3 | ||||

Reference body surface area ( | 1.81 | S3 | ||||

Tissue density ( | 1.040 | S3 | ||||

Cardiac output (CO) [L/h] | 350.37 | S3 | ||||

Blood weight [kg] ( | 5.53 ( | S3 | ||||

Blood volume ( | 5.32 | S3 | ||||

Liver-specific parameters | ||||||

Liver weight [kg] ( | 1.82 ( | S3 | ||||

Liver density ( | 1.080 | S3 | ||||

Liver volume ( | 1.69 | S3 | ||||

Liver blood flow ( | 68.32 ( | S3 | ||||

Hepatic vein blood flow ( | 89.34 ( | S3 | ||||

MPPGL [mg/g] | 40 | S3 | ||||

CYP abundances ( | S3 | |||||

| 137 | S3 | ||||

| 73 | S3 | ||||

| 14 | S3 | ||||

| 8 | S3 | ||||

GI tract parameters | ||||||

Gastric emptying rate constant ( | 4 | S3 | ||||

Mean intestinal transit time ( | 3.32 | S3 | ||||

Ascending colon transit rate constant ( | 0.098 | S3 | ||||

Degrees of flatness coefficient ( | 1.7 | S3 | ||||

Small intestinal length ( | 670.7 | S3 | ||||

Segment | ||||||

Regional intestinal parameters | DUO | JEJ | ILE | COL | ||

Radius ( | 2.37 | 1.75 | 1.5 | 2.42 | S3 | |

Length ( | 53.7 | 248.2 | 368.9 | 16.7 | S3 | |

Fractional length ( | 0.08 | 0.37 | 0.55 | – | S3 | |

Cylindrical volume [mL] | 9.47 × 10 | 2.39 × 10 | 2.61 × 10 | 3.07 × 10 | S3 | |

Mucosal surface area ( | 7.50 × 10 | 5.19 × 10 | 3.86 × 10 | 1.62 × 10 | S3 | |

Surface area scaling factor ratio ( | 0.49 | 1.00 | 0.58 | 0.033 | S3 | |

Enterocyte height [μm] | 32.2 | 32.2 | 32.2 | 35.1 | S3 | |

Enterocyte compartment volume ( | 0.0262 | 0.119 | 0.079 | 8.9 × 10 | S3 | |

Enterocyte compartment blood flow ( | 1.33 (0.0038) | 6.24 (0.0178) | 9.25 (0.0264) | 4.20 (0.012) | S3 | |

Intestinal CYP abundances ( | ||||||

| 9110 | 36,060 | 21,030 | 0 | S3 | |

| 1770 | 7030 | 4100 | 0 | S3 | |

| 210 | 820 | 480 | 0 | S3 | |

| 110 | 440 | 240 | 0 | S3 | |

Segment | ||||||

Regional mSAT luminal parameters | ST | DUO | JEJ | ILE | COL | |

pH | 1.5 | 6.4 | 6.6 | 7.1 | 6.5 | S3 |

Baseline water volume ( | 35 | 6 | 13 | 24 | 5 | S3 |

*Q*

_{ tissue,i }and

*V*

_{ tissue,i }were defined by Eqs. 6 and 7, respectively,

*f*

_{ co,i }and

*f*

_{ BW,i }are the fractions of CO and BW for the

*i*th empirical tissue, respectively,

*f*

_{ CO,liver}is the fraction of the cardiac output corresponding to the blood flow entering the liver (Table I),

*f*

_{ BW,liver }and

*f*

_{ BW,blood }are the fractions of the BW corresponding to the weight of the liver and blood, respectively, and

*ρ*

_{ tissues }is the tissue density (kg/L). The aforementioned fractions were parameterized using a logistic-normal transformation as suggested by Tsamandouras and co-workers (42). An example of this parameterization is shown in Eq. 8,

*θ*

_{ 1 }and

*θ*

_{ 2 }are the parameters needed to be estimated (on the logistic scale). This approach not only constrains the individual fractions to be between 0 and 1 but also imposes the constraint that the sum of the fractions should be equal to 1 (42). The selected parameterization also contributed to the structural identifiability of the model, as the parameters needed to be estimated for the empirical tissues (fractions of volumes and blood flows) were also reduced from six to four. The assumption of a single unique

*K*

_{ pu }to describe the extent of tissue distribution in all the empirical tissues was also based on identifiability grounds, due to the fact that an independent

*K*

_{ pu }for each tissue could not be uniquely identified given the model structure (43,44). The latter was corroborated by performing a model structural identifiability analysis prior to the parameter estimation procedure (43,44). The analysis was done using the “IdentifiabilityAnalysis” package for Mathematica (Wolfram Research, Inc., Champaign, IL, USA) (45,46), where the model was shown to be at least locally identifiable,

*i.e.*there is a finite set of solutions leading to the same input/output relationship (43,45,46). For details on the Identifiability Analysis procedure and the Mathematica Package, readers are referred to (45,46). Finally, the model parameters were estimated in NONMEM version 7.3 (ICON Development Solutions, Hanover, Maryland, USA). The model was implemented using the LSODA differential equation solver (ADVAN13) subroutine in NONMEM (47). The estimation was performed using the first-order conditional estimation with interaction method (FOCE-I), assuming no random effects on the model structural parameters given that only mean data was available for the IV plasma concentration profile (30). For the estimation, both the data and model output were transformed into natural logarithms (transform both sides) and an additive error model (on the log scale) was assumed for the residual unexplained variability (RUV).

*CL*

_{ int(u) }and

*K*

_{ pu,tissues }were also logged for the purposes of parameter estimation. The latter was done to stabilize the estimation and to prevent the model parameters taking negative values in the differential equations (48,49).

### Expansion of the mSAT Model for Mechanistic Bioavailability Predictions

The mSAT model is a multi-compartmental absorption model that has been recently proposed and used for the prediction of the fraction absorbed using different intestinal permeability approaches (26). The model structure was based on the original Compartmental Absorption and Transit (CAT) model developed in the late 1990s by Yu and co-workers (50, 51, 52). The main difference with respect to the CAT model, however, was that the new model describes the small intestine with only three anatomically defined compartments, duodenum, jejunum and ileum, instead of seven in the CAT model. In order to adequately describe the mean small intestinal transit time (SITT) with a reduced number of compartments, the mSAT model was implemented with a Weibull transit function that was optimized based upon the same SITT data used for the development of the CAT model (26,52). As in the first version of the CAT model, the mSAT model structure was kept relatively simple as the initial goal was only to predict the fraction absorbed based on permeability data (26).

For this study, the mSAT model was expanded for the mechanistic prediction of oral absorption and bioavailability following a similar structure to that of the ACAT and ADAM models implemented within GastroPlus™ and the SimCYP® simulator, respectively (8,53).

The expanded mSAT model structure is shown in Fig. 1b. The main segments of the mSAT model are stomach (ST), duodenum (DUO), jejunum (JEJ), ileum (ILE) and ascending colon (COL) (26). For each *n*th GI segment, the drug amount can be modelled either in the solid (*A* _{ solid,n }) state or the dissolved state (*A* _{ diss,n }), where no explicit compartments were implemented for the drug contained in the formulation. The model assumes that all the GI compartments are well mixed (50, 51, 52), only dissolved drug can be absorbed (54), absorption can only occur by means of non-saturable process, no significant absorption can occur from the stomach compartment (50), no drug degradation can occur in the luminal portions of the GI compartments and the lengths of the GI segment are representative of their anatomical lengths (37,55). The model was implemented in MATLAB 2014a (The MathWorks Inc., Natick, MA, USA), and the ordinary differential equations (ODE) were numerically evaluated using the ode15s solver for stiff ODEs. The equations describing the drug’s dynamics within the compartments of the mSAT model are summarized below (Eqs. 9–18), and the model details are given in the following sections.

#### Stomach

#### Duodenum

#### Jejunum and Ileum (*n* = 2, 4)

#### Ascending Colon

#### All the Intestinal Segments

### Drug Transit

Drug mass in the stomach compartment (solid and dissolved) was transferred to the adjacent segment by means of a first-order process controlled by the gastric emptying rate constant, *k* _{GE} (56, 57, 58). In the case of disintegrating solid immediate-release (IR) dosage forms (or suspensions), the initial conditions (at *t* = 0) in the stomach compartment (Eq. 9) were set to the administered dose (*A* _{ solid,st(0) }
*= dose*). However, in the case of non-disintegrating solid dosage forms, the solid drug was transferred to the adjacent segment by means of a discrete process depending upon the mean residence time (MRT) in the stomach (1/k_{GE}); this also applied to the rest of the GI compartments.

For non-disintegrating solid dosage forms, transfer of the solid mass was implemented with a step function (STEP) following the method described by Hénin and co-workers (59). When the STEP function is used, the initial conditions of the stomach compartment are set to zero and an input function (*INPUT(t)*) for the solid mass needs to be used. This *INPUT(t)* function can take any form, for example a zero order input rate, simulated release profile, an *in vitro* release profile, etc. More details about the implementation of the STEP_{ n } function in the mSAT model can be found in Sect. 1 of the Supplementary Material. For the small intestinal compartments, the transit of the drug particles to the adjacent segment (solid and dissolved) was implemented by a time-varying Weibull function, *w(t)* _{ n } (Eq. 15), where *β* and *γ* are dimensionless coefficients with a value of 2.01 and 1.57, respectively (26), *f* _{ LSI,n } is the fractional length of the *n*th small intestinal segment (with respect to the total length of the small intestine, *LSI*), *f* _{ LSI,n } was assumed as 0.08, 0.37 and 0.55 for duodenum, jejunum and ileum, respectively (55). For the ascending colon, the drug transit was assumed as a first-order process depending upon the ascending colon transit rate constant (*k* _{ t,col }). The use of a linear transit model and rate constant for the colon segment was based on the fact that the transit time in the whole colon (from cecum to deciding colon) has been successfully described by using such a model by Bouchoucha and co-workers, where they described transit of markers using three transit compartment, representing ascending, transverse and descending colon or right, left and recto-sigmoid colon, respectively (60,61)

### Dissolution and Solubility

*DR*

_{ n }) can be either inputted from

*in vitro*dissolution studies or predicted using derivations of the Noyes-Withney/Nernst-Brunner equation for drug dissolution (62). Particularly for OXY, the dissolution rate was predicted by using a modification of the model proposed by Wang and Flanagan for spherical particles dissolving over time (53,63,64) as shown in Eq. 19,

*A*

_{ solid(0),n }is the initial amount of solid drug in the given GI segment, this mass was calculated in MATLAB by integrating the cumulative amount of solid drug entering each intestinal segment at each iteration, whereas for the stomach compartment, this mass was assumed equals to the dose,

*D*

_{ aq }is the aqueous diffusion coefficient (cm

^{2}/h),

*r*

_{ 0 }is the initial particle radius (cm),

*ρ*

_{ p }is the particle density (mg/mL),

*S*

_{ n }is the segment-dependent aqueous solubility (mg/mL),

*V*

_{ lum,n }is the segment-dependent luminal fluid volume (mL),

*h*

_{ eff }

*(t)*is the effective diffusion layer thickness (cm) (65,66) and

*r(t)*is the particle radius (cm) at a given time. The main assumptions of Eq. 19 are that the spherical particles are in a well-stirred media, the particles dissolve isotopically, that the total number of particles remains constant across the system, there is an immediate precipitation when the dissolution rate takes positive value (

*i.e.*no super-saturation was allowed in the model) and all the particles have the same initial radius (

*r*

_{ 0 }) (63). The time-varying radius for the dissolving spherical particles was calculated using Eq. 20 (63,64,67). When the particle radius reached a critical value of 10

^{−9}cm, the dissolution was assumed complete and the dissolution rate was assumed to be zero.

*h*

_{ eff }(

*t*), on the other hand, was assumed to be equal to

*r(t)*in the case of particles with radius smaller than 30 μm; otherwise, it was assumed equal to an empirical maximum value of 30 μm (53,66, 67, 68, 69).

OXY’s segmental solubility (*S* _{ n }) was calculated according to its intrinsic solubility (*S* _{ 0 }), pKa and segment-depended pH with the use of the Henderson–Hasselbalch equation for monoprotic bases (70). Details of such calculations can be found in Sect. 4 of the Supplementary Material.

Luminal fluid volumes (*V* _{ lum,n }) were determined using an empirical fluid dynamics model with similar characteristics to the model proposed by Jamei and co-workers (53). The model assumes that fluid movements along the GI tract are driven by gastric emptying and intestinal transit time, taking into account volume fluctuations due to fluid intake, intestinal fluid secretion and reabsorption (53). The empirical nature of the model is due to the fact that the GI fluid secretion and reabsorption parameters were obtained by fitting the model to free intestinal water data (71). This data was obtained by magnetic resonance imaging (MRI) after the intake of 240 mL of water in 12 healthy volunteers under fasting conditions (71). The details of the model and the fitting can be found in Sect. 2 of the Supplementary Material.

### Intestinal Absorption

*k*

_{ a,n }) as shown by Eq. 21

*P*

_{ eff }is the drug’s effective intestinal permeability,

*r*

_{ n }is the radius of the intestinal segment,

*DF*is the degree of flatness coefficient that accounts for changes in surface area to volume ratio due to the elliptical shape of the human intestine (compared to a cylinder) and was assumed to be 1.7 as suggested by Sugano (2009) (72), and

*SAEF*

_{ n }is the ratio between surface area amplification factors of the

*n*th intestinal segment with respect to that of the jejunum, where

*P*

_{ eff }is measured (26,73). This ratio takes into account regional variations in drug absorption due to changes in the available mucosal surface area (mSA), and it is necessary for the implementation or segment-dependent intestinal permeation (26).

*SAEF*

_{ n }differences were implemented using the Method 3 (M3) proposed by Olivares-Morales and co-workers (2015), where

*SAEF*

_{ n }takes values of 0.49, 1.00, 0.58 and 0.033 for the duodenum, jejunum, ileum and ascending colon, respectively, and

*I*

_{ ratio,n }is the ratio between the fraction of unionized drug at the segment’s pH with respect to that in the jejunum (

*I*

_{ ratio,n }=

*f*

_{ unionized,n }/

*f*

_{ unionized,jejunum }). This ratio takes into account regional differences in intestinal permeability due to changes in ionization compared to that of the upper jejunum, where

*P*

_{ eff }is measured (73,74).

*I*

_{ ratio,n }was calculated using the Henderson–Hasselbalch equation based on the segment’s luminal pH and OXY’s pKa (Sect. 4.1 of the Supplementary Material).

### Enterocyte Compartments and Intestinal Metabolism

*C*

_{ ent,n}is the OXY’s concentration in the

*n*th enterocyte compartment (mg/L) and

*V*

_{ ent,n }is the volume of the enterocyte compartment (L). These volumes were calculated by multiplying the

*mSA*

_{ n }of the give intestinal segment by the respective enterocyte height (without accounting for the surface area expansion due to microvilli) (9,27),

*Q*

_{ ent,n }is the villous blood flow of the

*n*th enterocyte compartment (L/h) and CL

_{ ent,n }is the segment-dependent enterocyte clearance. This clearance was calculated according to Eq. 22

*fm*

_{ CYPj }is the fraction of the total intrinsic clearance (

*CL*

_{ int(u) }) associated to the

*j*th CYP isoform. This value was derived from the

*in vitro*data reported by Mizushima and co-workers (75), and the details of such calculations can be found in Sect. 4.2 of the Supplementary Material.

*A*

_{ CYPj(liver) }is the mean liver abundance of the

*j*th CYP isoform (pmol/mg microsomal protein) (76), and

*A*

_{ CYPj(ent),n }is the absolute abundance of the

*j*th CYP isoform in the

*n*th enterocyte compartment (pmol) (22,77,78). Equation 22 assumes that the intrinsic clearances (per pmol of enzyme) are equal in both the liver and the intestinal wall (40,79) and that there is no binding of the drug in the enterocyte compartments (fu

_{gut}= 1) (11,80). All the system-related parameters for the mSAT model were derived from the literature, and they are summarized in Table I.

Finally, the model was implemented with mass balance equations that allowed the estimation of the extent of drug dissolution, absorption (*f* _{ abs }) and availability in the intestine and the liver (*F* _{ G } and *F* _{ H }). The extended model was combined with the disposition model developed in the previous section and implemented together in MATLAB.

### OXY’s Oral PK Simulations and Relative Bioavailability Predictions

*in silico*equations. A summary of the parameters and their values are provided in Table II. More details about the parameter selection and/or calculations can be found in Sect. 4 of the Supplementary Material.

OXY’s Drug-Related Parameters Employed for the Simulations (Racemic Mixture and Isomers)

Parameter [units] | OXY racemic | R-OXY | S-OXY | Ref. | ||

Molecular weight (MW) [g/mol] | 357.5 | – | – | S5 | ||

pKa (base) | 8.04 | – | – | S5 | ||

LogD | 2.98 | – | – | S5 | ||

LogP | 3.71 | – | – | S5 | ||

Intrinsic solubility( | 0.012 | – | – | S5 | ||

Particle density ( | 1.20 × 10 | – | – | S5 | ||

Initial particle radius ( | 1.00 × 10 | – | – | S5 | ||

Aqueous diffusion coefficient ( | 0.025 | – | – | S5 | ||

Blood to plasma ratio ( | 0.686 | 0.71 | 0.682 | S5 | ||

Fraction unbound in plasma ( | 3.40 × 10 | 4.70 × 10 | 2.75 × 10 | S5 | ||

Apparent permeability ( | 21.9 | – | – | S5 | ||

Jejunal effective permeability ( | 4.31 | – | – | S5 | ||

| 1.18 × 10 | 1.00 × 10 | 1.53 × 10 | S5 | ||

| Estimated | – | – | See methods | ||

CL | Estimated | – | – | See methods | ||

| 1 | 0.89 | 1.1 | S5 | ||

fm | 0.80 | 0.79 | 0.81 | S5 | ||

fm | 0.12 | 0.13 | 0.11 | S5 | ||

fm | 0.07 | 0.08 | 0.05 | S5 | ||

fm | 0.01 | 0.00 | 0.03 | S5 | ||

Segment | ||||||

Regional luminal parameters | ST | DUO | JEJ | ILE | COL | |

Segmental solubility ( | 12 | 0.54 | 0.34 | 0.12 | 0.43 | S5 |

Luminal ionization ratio ( | n/a | 0.64 | 1.00 | 2.94 | 0.80 | S5 |

Two different oral pharmacokinetic studies were predicted using the mSAT model. In the first study, the pharmacokinetics of OXY was investigated after the administration of three 5-mg IR tablets (every 5 h) to eight healthy volunteers, four of them participating in the IV study used for the optimization of the disposition model (30). The tablets were administered under fasting conditions together with 100 mL of water, and blood samples were collected up to 15 h post-dose. OXY plasma concentrations were measured using a validated assay (30). This study was simulated with the intention to evaluate the model capacity to mechanistically predict OXY’s oral pharmacokinetic, particularly given the fact that some of the study participants were also part of the IV study used for the development of OXY’s disposition model (30). The model prediction were evaluated graphically and contrasted with observed mean clinical data in terms of accuracy of the prediction of mean pharmacokinetic parameters such as absolute bioavailability (*F*), area under the curve (AUC) and maximum plasma concentration (*C* _{max}).

The second study was a relative bioavailability study between OXY’s IR tablet and its controlled-release (OROS®) formulation. The clinical data of this study was kindly provided by Janssen Pharmaceutica. The study was conducted in 41 healthy volunteers, males and females, where each subject received three 5-mg IR release tablets (every 8 h) and one 10-mg controlled-release (OROS®) formulation in a cross-over fashion. The formulations were administered in the morning under fasted conditions together with a 240-mL glass of water. Blood samples were collected up to 48 h post-dose and were analysed for OXY using a validated LC-MS/MS assay (81). In contrast to the previous study, a stereo-selective assay was employed for the determination of OXY plasma concentrations and the concentrations of OXY enantiomers, *R* and *S*-oxybutynin, were reported (81). It has been shown that OXY enantiomers display stereo-selective pharmacokinetics, mainly attributable to differences in volume of distribution and clearance between the enantiomers (75). To overcome this issue, the aforementioned differences were accommodated into the mSAT model predictions, adapting OXY’s parameters with the observed *in vitro* parameters for each enantiomer (75,82). For instance, changes in volume of distribution between enantiomers were mainly attributed to plasma protein-binding differences (75,82). Hence, stereo-selective plasma protein binding was implemented in the model by employing the reported *f* _{ up } for each enantiomer (Table II). This led to changes in the volume of distribution as the *K* _{ b,tissue } is related to *f* _{ up } by Eq. 5. The clearance differences, on the other hand, were accommodated assuming that the CL_{int,(u)} of the racemic mixture represented an average between the intrinsic clearances of the enantiomers. Thus, the enantiomer-specific CL_{int(u)} was calculated by multiplying the CL_{int(u)} value of the racemic mixture by the CL_{int(u)} ratio between the enantiomers (*R/S* _{ CLint,ratio }). The latter parameter was defined for each enantiomer as the ratio between the observed *in vitro* CL_{int(u)} of the given enantiomer and the average *in vitro* CL_{int(u)} between them. More details on the derivation of the aforementioned parameters can be found in Sect. 4.4 of the Supplementary Material.

For the relative bioavailability predictions, both IR and OROS® formulations were simulated as per the study protocol, whereas an additional IV profile was simulated to estimate the absolute bioavailability of each formulation. The drug was assumed to be administered as a racemic mixture for prediction of the luminal processes (*i.e.* dissolution, release). However, once the drug entered the intestinal wall compartments of the mSAT model, the dose was divided into enantiomer fractions. The compartments within the mSAT model were used to prospectively estimate bioavailability fractions for each formulation (*f* _{ a }, *F* _{ G } and *F* _{ H }). In the case of the OROS® formulation, the observed mean *in vitro* release profile was used as the *INPUT* function (Eq. 9). The *in vitro* release profile was digitized from the literature (81,83). This profile was measured in a USP apparatus VII in different dissolution media such as water, simulated gastric fluid (SGF) and simulated intestinal fluid (SIF) (83). Given the results of the release study, it was assumed that OXY’s release rate from the OROS® formulation was not affected by luminal changes in pH and/or fluid volumes (83). The *INPUT* _{ n } profile can be found in the Sect. 4.3 of the Supplementary Material. Since OXY content in the OROS® is released as a suspension (84,85), the dissolution rate of the suspended drug was calculated using Eq. 19.

Lastly, an additional simulation was conducted for the OROS® formulation using the classical approach for intestinal permeability, *i.e.* Method 1 (M1) in (26), and *SAEF* _{ n } ratio was assumed 1 in all segments. This was done in order to evaluate the benefits of implementing the segment-dependent permeability approach for the prediction of OXY’s pharmacokinetics when administered as an OROS® formulation (26).

## RESULTS

### OXY’s Disposition Parameter Estimation

Estimated OXY Disposition Parameters from the IV Infusion Fit

Parameter | Estimate | RSE (%) |
---|---|---|

CL | 3944 | 5.0% |

| 9.76 (0.0346) | 23% |

| 253 (0.897) | 1.9% |

| 19.4 (0.0688) | 16% |

| 50.8 (0.775) | 3.1% |

| 6.42 (0.098) | 19% |

| 8.33 (0.127) | 8.9% |

| 469 | 10% |

| 6.54 | 35% |

### Mechanistic Prediction of OXY’s Oral Pharmacokinetics

_{0-15h}was 32.5 ng*h/mL, comparable with the reported value (mean ± SEM) of 33.7 ± 7.9 ng*h/mL (30).

*C*

_{max}, on the other hand, was predicted to be 6.24 ng/mL, whereas the reported

*C*

_{max}for the third dose on day 1 was 7.55 ± 2.22 ng/mL (30). The estimated absolute bioavailability for the racemic OXY was 5.94%, whereas the reported absolute bioavailability was 6.2 ± 1.2% (30).

### Relative Bioavailability Between IR and OROS® Formulation

*R*isomer (R-OXY) are shown Fig. 4, whereas the predictions of S-OXY can be found in the Supplementary Material (Fig. S6). Table IV summarizes the observed and predicted relevant pharmacokinetic parameters, stratified by formulation and enantiomers. There was a good agreement between the observed clinical data and the mSAT predictions (Fig. 4a and Fig. S6). Nevertheless, a general trend towards the underestimation of the oral pharmacokinetics of the IR formulation could be observed for both enantiomers (Fig. 4a and Fig. S6A). This underestimation tended to be more prominent for the

*S*enantiomer than for the

*R*enantiomer, both in terms of

*C*

_{max}and AUC

_{0–48}(Table IV). The predicted

*C*

_{max}and AUC

_{0–48}were within ±20% of the observed values for R-OXY, whereas the bias for the

*S*enantiomer was −51 and −37% for

*C*

_{max}and AUC

_{0–48}, respectively. For the OROS® formulations, underestimation of the pharmacokinetic parameters was also observed, though to a lesser extent than for the IR formulation. The latter was particularly observed for the

*R*enantiomer (Fig. 4b) where both AUC

_{0–48}and

*C*

_{max}were within 6% of the observed values

Summary of the mSAT Predicted *vs.* Observed Pharmacokinetic Parameters for OXY Formulations (IR and OROS®)

Isomer | Formulation | Observed values (mean ± SD) | mSAT model predictions | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

| | | | | | C | | | | | | ||

| IR | 21.7 ± 13.0 | 3.28 ± 2.16 | – | n/a | 17.3 | 2.71 | – | n/a | 0.078 | 1.00 | 0.13 | 0.61 |

OROS® | 18.6 ± 10.5 | 0.99 ± 0.59 | 0.65 ± 0.42 | 1.39 ± 0.44 | 19.5 | 0.93 | 0.84 | 1.70 | 0.13 | 0.28 | 0.80 | 0.58 | |

| IR | 31.6 ± 15.8 | 6.58 ± 3.71 | – | n/a | 20.2 | 3.24 | – | n/a | 0.075 | 1.00 | 0.10 | 0.71 |

OROS® | 34.4 ± 17.3 | 1.84 ± 0.97 | 1.18 ± 0.71 | 1.72 ± 0.49 | 27.4 | 1.32 | 1.19 | 2.04 | 0.15 | 0.28 | 0.79 | 0.69 |

The parameters for the *S* enantiomer, on the other hand, showed a bias between 20 and 28% for AUC_{0–48} and *C* _{max}, respectively.

The relative bioavailability (*F* _{ rel }) predictions of the OROS® formulation were consistent with those of the observed values; both enantiomers displayed higher *F* _{ rel } when formulated as OROS® compared to the IR. The *F* _{ rel } predictions tended to be overestimated by a factor of 20%.

*f*

_{ abs }values were close to 1. For the OROS® formulation, this fraction was predicted to be reduced by almost a 70% (Table IV). The predicted intestinal first-pass metabolism for the IR formulation was high (

*F*

_{ G }≤ 0.13), whereas for the OROS® formulations, the

*F*

_{ G }was predicted to be almost eightfold higher. For the IR formulation, the majority of the absorption and intestinal elimination was predicted to occur in the jejunum segment (Fig. 5), while for the OROS® formulation, the absorption was predicted to occur mainly in the distal ileum and ascending colon, with a limited intestinal first-pass only in the ileal segment. The predicted hepatic availability (

*F*

_{ H }) for both formulations was practically the same.

*i.e.*employing the same

*P*

_{ eff }values for all the intestinal segments, a significant overestimation of the distal absorption would have been predicted for OXY. Therefore, the use of the newly proposed regional permeability approach (M3) gives rise to a much more accurate prospective prediction (26), particularly important given the type of nature of the drug (BCS class 1) and the prolonged release from the OROS® formulation (24 h).

## DISCUSSION

The recently proposed mSAT model was successfully expanded and applied to the mechanistic prediction of the oral bioavailability differences between OXY’s IR and OROS® formulation in a purely prospective fashion. The approach employed herein involved several steps that were necessary to appropriately distinguish between OXY’s disposition and absorption processes in the model predictions.

The first step consisted in the development of a disposition model capable of describing OXY’s distribution and elimination processes as well as to mechanistically account for its pre-systemic extraction when combined with the absorption model. Several structures were evaluated for the disposition model, from a three-compartment model with a mechanistic liver compartment to a whole body PBPK model. The chosen model was that of Fig. 1a. This model represents a hybrid between the full PBPK model and the compartmental model, providing the flexibility of the compartmental model for the fitting purposes, yet retaining the mechanistic nature of the PBPK model where it was needed, such as in the liver compartment. As previously described, the model was constrained in terms of the volumes of the empirical tissues and their blood flows following the approach suggested by Cao and Jusko (33). These constraints were implemented during the estimation process in NONMEM with the help of the logistic-normal transformations proposed by Tsamandouras and co-workers (2015). As shown in Fig. 2, the fitted model provided an accurate description of the observed IV infusion data (30) and the model parameters were precisely estimated (Table III). It is worth mentioning that given the model structure and its local identifiability properties (43,45,46), an exchange between the parameters, *Q* _{ tissue,1 } and *Q* _{ tissue,2 }, and *V* _{ tissue,1 } and *V* _{ tissue,2 }, can be made without affecting either fit or the input–output relationship of the model (Table III). The selected modelling approach required the fitting of both the intrinsic microsomal clearance and an empirical *K* _{pu} value. The former could have been informed purely from the reported *in vitro* data, where the unbound *in vitro* formation CL_{int} in HLM has been reported to be 225 and 278 μL/min/mg for R-OXY and S-OXY, respectively (75). However, there were indications that suggested that the use of such *in vitro* value would have led to under-predictions in both the systemic clearance and first-pass metabolism of OXY (21). This underestimation has been previously reported in the literature, particularly for highly cleared and highly protein-bound substrates similar to OXY (86,87). For these reasons, fitting the microsomal clearance to the IV infusion data seemed to be a reasonable choice. This was supported by the estimated CL_{int} of 3944 μL/min/mg for racemic OXY (Table III). However, this estimate assumes that only the CYP-mediated metabolism was responsible for OXY’s elimination, which might not be necessarily true as there is evidence of the formation of an inactive metabolite, 2-cyclohexyl-2-phenylglycolic acid (CPGA), which is mediated by carboxylesterases (mainly CES1) that can be found in both predominantly in the liver and in the intestinal wall to a smaller extent (88,89). Nevertheless, the CPGA formation was assumed to contribute minimally to OXY’s overall elimination, given that the reported *in vitro* CPGA formation CL_{int} in HLM was 5.9 μL/min/mg, a value considerably smaller than the reported formation CL_{int} of OXY’s main metabolite, NDEO (75,89).

The fitted *K* _{pu} value was assumed to be the same for all the empirical tissues. This assumption was mainly based on model structural identifiability grounds that otherwise would have deemed the model as unidentifiable (43,44). The decision to estimate a *K* _{pu} value, instead of directly estimating the *K* _{ b } needed in the model equations, was made to allow for the prediction of the pharmacokinetics of OXY enantiomers. While there is a difference in plasma binding between the two enantiomers, we have assumed that the *K* _{pu} value was the same for both the racemic OXY and its enantiomers (*R* and *S*-OXY). This assumption was based on the fact that OXY, a strong base (pKa > 7), is predominantly bound to α_{1}-acidglycoprotein (AGP), which is mainly located in the circulating plasma. Thus, the impact of OXY’s binding to AGP within tissues was assumed to be minimal (82,90). Consequently, differences in OXY’s volume of distribution can be mainly attributed to plasma protein-binding differences between the enantiomers (and racemic mixture), rather than to tissue binding (75,82,90). These differences were accommodated in the disposition model by using the enantiomer-specific *f* _{ up } value in the calculation of the *K* _{ b }, which in turn affects the volume of distribution (Eq. 5). The latter also highlights the usefulness of the chosen hybrid-PBPK model structure employed in this work, as this extrapolation could have not been possible when using a traditional three-compartment model to describe OXY’s disposition.

The second step in the modelling approach involved the expansion of the mSAT model for the mechanistic prediction of OXY oral bioavailability in a purely prospective manner. As previously described in the “Materials and Methods” section, the model was expanded by incorporating mechanistic equations for the prediction of the most relevant absorption processes using MATLAB: transit, release, dissolution, permeation and intestinal metabolism. Using the expanded mSAT model, the predictions of the oral pharmacokinetic profile of the racemic OXY after the administration of three 5 mg IR tables in the reference individual were in good agreement with the mean observed data (Fig. 3). Similarly, the predicted absolute bioavailability of the racemic OXY was within 5% of the reported mean value of 6.2% for the IR tablets (the oral solution was shown to be bioequivalent with the tablets) (30). Since OXY’s disposition was already accounted by the model in the previous step, the predictions of oral bioavailability were mainly attributed to the mechanistic nature of the mSAT model and the use of the appropriate system-related and drug-specific parameters for such predictions (Tables I and II); the latter provided further support for the use of this model for mechanistic oral absorption predictions (26). Since OXY belongs to Class 1 within the BCS (highly permeable and soluble), there were no major difficulties in terms of the prediction of the dissolution and permeation processes for the IR formulation within the mSAT model (21). These processes were not considered to be the rate-limiting step for OXY’s absorption (30). In contrast, prediction of OXY’s first-pass metabolism was considered the key step for the bioavailability predictions of OXY’s IR formulation. Judging by the outcome of the bioavailability predictions, the expanded mSAT model did a reasonable job for such predictions. The latter also highlights the importance of having good disposition data available for the purpose of judging mechanistic bioavailability predictions, particularly due to the possible confounding issues that can arise from the use of the oral data to calibrate some of the absorption parameters in the model, particularly when the predictions are not in agreement with the observed clinical data. The latter might lead to biased estimates of the absorption parameters due to the fact that the disposition parameters were biased in the first instance (42,91).

Once the ability of the mSAT model to prospectively predict the oral pharmacokinetic profile was established, the third and final step of the modelling approach was the mechanistic investigation of the relative bioavailability between OXY’s IR and OROS® formulations. The pharmacokinetic profiles of both formulations were successfully predicted by the model for the reference individual as shown in Fig. 4 and summarized in Table IV. However, as seen in Fig. 4, there is a large inter-individual variability (IIV) in the observed pharmacokinetic profiles. This IIV was not captured by the mSAT model as it can only provide predictions for the “typical individual”. This is in contrast to available software packages that can include such variability in the model predictions such as SimCYP® and PK-Sim®.

In terms of relative bioavailability, the model predictions were consistent with the observed trend of higher exposure when using the OROS® formulation compared to the IR tablets (Table IV) (28,31). However, the model slightly overestimated the magnitude of the relative bioavailability of the OROS® formulation, mainly due to a 40% underestimation of the exposure of the IR formulations (particularly for the S-OXY). This underestimation could be due to the assumptions made with regard to the intrinsic clearances of each isomer in the model predictions, such as the use of the *in vitro* R/S_{CLint,ratio} to derive the isomer-specific CL_{int(u)} employed in the mSAT model. However, considering that these predictions were based purely on available literature data and no further optimization were made in any of absorption model parameters, this bias was considered acceptable.

From a mechanistic perspective, the model predictions with regard to the bioavailability fractions were consistent with the previous multi-factorial simulation study (21). The predicted *f* _{ abs } of R-OXY and S-OXY were close to the unity, in agreement with the mass balance studies suggesting the complete absorption of the racemic mixture (30). Due to the use of the differential permeability approach employed in the model, the segmental contribution to the overall absorption can be estimated for the different formulations (26). Most of the drug content from the IR formulation was predicted to be absorbed in the upper GI segments (Fig. 5a). Similarly, predictions can be made with regard to the fate of the drug in the enterocyte compartments (Fig. 5b) where most of the drug content was expected to be eliminated by the CYP enzymes located in the upper regions of the GI segments (21, 22, 23, 24). As shown in Table IV, the predicted *F* _{ G } of the IR formulation was approximately 0.13 for both isomers. This value was in close agreement with the observed *F* _{ G } of 0.11 to 0.14, calculated from the reported absolute bioavailability and the *in vivo* clearance using the standard formulae (30,92). The model predicted an *F* _{ H } close to 0.61 and 0.71 for IR formulation of R-OXY and S-OXY, respectively. These values were slightly higher than the estimated *F* _{ H } between 0.44 and 0.58 for the racemic mixture (30,92). The segmented structure of the mSAT model was necessary for the bioavailability predictions of the OXY’s OROS® formulation, particularly when the model structure was combined with the regional permeability approach (M3) (26). Otherwise, the absorption of the OROS® formulation would have been considerably overestimated when using the same *P* _{eff} value for all the segments of the mSAT model, as shown in Fig. 6. This highlights the importance of accounting for the segmental permeability difference in the PBPK framework (26,73,93).

Even though there is no available clinical data regarding to the regional absorption and/or intestinal first-pass metabolism of the OXY’s OROS® formulations. The model outcome can be used to explain the mechanism proposed for the higher relative bioavailability of OXY’s OROS® formulation. It was clear from Fig. 5 and Table IV that the *f* _{ abs } for the OROS® formulation was considerably reduced compared to the IR formulation. However, the predicted *F* _{ G } was almost eight times higher in the OROS® formulation compared to the IR. Since the predicted *F* _{ H } remained almost the same for both formulations (IR and OROS®), the model provided strong support for the hypothesis that the main factor responsible for the higher relative bioavailability observed for OXY’s OROS® formulation was an increased intestinal availability (21,28). This increased availability was mainly due to release of the majority of the drug content from the OROS® formulation in the distal regions of the GI tract, where the abundance of CYP is reduced compared to the upper GI tract (22, 23, 24). This outcome not only corroborates the findings from previous work but also can be seen as a further support to the fact that there is an interesting interplay between absorption and metabolism along the GI that can be explored in formulation development. This phenomenon could be of importance for substrates similar to OXY, where a MR release formulation can be developed to either increase or maintain exposure levels observed with the IR counterparts.

One of the main limitations of this study was the lack of predictions including variability and uncertainty. This variability might be incorporated in the model through the model parameters either from literature sources or estimated from data, and it can be of importance to understand the possible differences in OXY’s *F* _{ G } to its full extent. Another important aspect that was not accounted for in this work was the fate of OXY’s main metabolite, DEOB. This metabolite has clinical implications as it has been associated with the occurrence of OXY’s side effects (28,31,32). However, there was a paucity of data available in the literature regarding the metabolite and did not allow its incorporation in the current model using a “bottom-up” approach. Another aspect that was not considered in this work was the impact that OXY’s anticholinergic activity could have had on gastric emptying and intestinal transit time. This was mainly due to the lack of a pharmacodynamic link for its implementation in the model. However, we did not expect differences in terms of relative bioavailability predictions as this effect is related to OXY’s therapeutic activity (*i.e.* smooth muscle relaxant) which has been shown to be similar between the two formulations (32).

Finally, the results highlighted the usefulness of the newly proposed mSAT model for oral pharmacokinetic predictions. However, these result should be considered carefully as more compounds need to be tested with this particular model.

## CONCLUSION

A newly proposed mechanistic absorption model was expanded and employed for the bottom-up predictions of oral bioavailability of oxybutynin IR and OROS® formulations. The new model was able to capture the bioavailability differences observed between OXY formulations, where the OROS® formulation displayed higher relative bioavailability than its IR counterpart. The model predictions suggest that this higher bioavailability was mainly due to an increased intestinal availability (*F* _{ G }) product of the decreased intestinal first-pass metabolism in the distal regions of the GI tract, where the abundance of the CYP enzymes is decreased.

## Notes

### Acknowledgments

A.O-M. is recipient of a Ph.D. grant awarded by CONICYT Chile, Chilean Ministry of Education and a President’s Doctoral Scholar Award from The University of Manchester. The authors would like to acknowledge Janssen Pharmaceutica for providing the observed clinical data for the relative bioavailability between oxybutynin’s IR and OROS® formulation, as well as Drs. Luca Marciani (University of Nottingham), Deana Mudie (University of Michigan), Prof. Wener Weitschies and Michael Grimm (University of Greifswald) for providing insight on the luminal free water data employed in the development of the fluid dynamics model implemented in the mSAT model. Finally, we would acknowledge the fruitful comments and discussions made with members of the Centre for Applied Pharmacokinetic Research (CAPKR) of The University of Manchester, particularly Thierry Wendling, Nikos Tsamandouras and Aleksandra Galetin. This project is an in-kind contribution from the University of Manchester to the IMI Oral Biopharmaceutics Tools (OrBiTo) project (http://www.imi.europa.eu/content/orbito).

## Supplementary material

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