A Population-based PBPK Model for the Prediction of Time-Variant Bile Salt Disposition within GI Luminal Fluids.

In vivo studies have shown cyclic bile salt (BS) outputs during fasting whereas higher amounts have been observed in fed states. This leads to fluctuations of intestinal BS concentrations ([BS]) that can affect the rate and extent of ab-sorption of lipophilic drugs in particular. However, most PBPK models use fixed values of [BS] in fasted and fed states albeit with different values in different regions of the GI tract. During fasting, there is a relationship between gallblad-der volume (GBV) and the phase of the Interdigestive Migrating Motor Complex cycle (IMMCc), showing cyclic GBV changes with periodic filling and emptying. This relationship is also affected by the origin of the IMMCc (antral or du-odenal). In fed states, meta-analysis indicated that GB residual volume (% of fasting maximum) was 46.4 ±27 %CV and 30.7 ±48 %CV for low- and high-fat meals respectively. The corresponding values for the duration of the emptying phase were for low fat meals 0.72h ±1%CV and for high fat meals 1.17h ±37%CV. The model, the Advanced Dynamic Bile Salt Model (ADBSM), was built bottom-up and its parameters were not fitted against in vivo measurements of [BS]. It involved update of the dynamic luminal fluid volumes model based on meta-analysis of available imaging data. The ADBSM is incorporated into the Simcyp® (v18r2) PBPK simulator. The model predictivity was good (within 1.25 fold error for 11/20 of the clinical studies) and was assessed against clinical studies of luminal [BS] that provide only the type of meal (i.e., low- or high-fat), the timing of the meal and/or water intake events, and the number and age range of the study participants. The model is also an important component of models capturing enterohepatic recirculation of drug and metabolite.


INTRODUCTION
Along with other parameters, such as stability, permeability and first-pass metabolism, solubility in luminal fluids is considered to be a key factor for the prediction of oral drug bioavailability. Bile salts (BS) play a crucial role in the solubilisation and absorption of lipophilic and poorly soluble compounds. [25][26][27] Several studies have been conducted in the past to characterize fasting and fed duodenal, jejunal and colonic aspirates in healthy 2, 27-31 and non-healthy (e.g., with ulcerative colitis) 32 subjects. These studies have been used to design simulated biorelevant media (FaSSIF, FeSSIF) enabling in vivo prediction of drug solubility. 33 Similarly, this information has been implemented in in-silico platforms; e.g., SimCYP, as a part of the Advanced Dissolution Absorption and Metabolism (ADAM) model 34 , GastroPlus and GI-SIM. 35 However, BS concentrations ([BS]) used in in vitro dissolution experiments and in PBPK modelling are fixed and represent a snapshot of the dynamically changing in vivo environment. Furthermore, the in vivo information on [BS] integrated into in vitro and in-silico models, doesn't currently take into account biliary motility when aspirating duodenal and/or jejunal fluids. For instance, [BS] varies significantly within the GI tract due to a number of factors such as cyclic motility patterns of the gallbladder (GB) linked to the phase of the IMMCc, 13,36,37 dynamic intestinal water volumes changes 38,39 and postprandial strong GB contractions emptying a significant amount of BS. 5,19 Furthermore, several studies have shown that in the fed state, the GB ejects 30 -70% of its content within 20 -30 mins, depending on meal composition. 4,8,39,40 Effort has been put into the development of mechanistic models incorporating biliary motility with the main focus on the GB. Guiastrennec et al., 41 developed a mechanistic model of GB emptying in response to calorie intake with the intention to use it for predicting postprandial changes in drug absorption. However, the Guiastrennec et al., 41 mechanistic model describes GB motility only in the fed state and is based on a single in vivo study. 40 A different approach for mechanistically modelling GB motility is to link it to the secondary peaks appearing in the plasma concentration profile of drugs undergoing enterohepatic circulation (EHC). Abbiati and Manca 42 developed a PBPK model which links the GB emptying period with the onset time of secondary peaks in plasma concentration of sorafenib. However, this approach is essentially fitting the GB motility to reproduce the observed secondary peaks and does not take into account the different factors affecting/controlling GB motility. In other words, it may not be appropriate to link GB motility exclusively to the onset time of a secondary peak in the drug's plasma concentration profile; secondary peaks have appeared in cholecystectomized patients as well as in rats which do not have a gallbladder. The same approach has been taken by Jain et al. 43 A more physiologically relevant mechanistic model of EHC has been developed by Lehr et al 44 with the introduction of a clock time function as a control element of a trigonometric GB release function mimicking an ultradian rhythm. However, interindividual variability was applied only to the clearance and the distribution volume of the targeted drug (tesofensine). MRI and ultrasound measurements of fasting GB volume indicate high inter-subject variability. 19 Furthermore, the GB volume changes linked to the IMMC are too complex 22 to be described by a simple sine function. 44 Another limitation of the Lehr et al 44 approach is that the ultradian rhythm of the GB is linked to (i.e., starts at) the time of dose administration. However, dose can be administered randomly with respect to filling-emptying cycles of the GB which means, for example, that the GB won't necessarily enter an emptying phase due to drug administration. So, in order to be able to adequately predict the duodenal [BS] in fasted and fed states, GB motility ideally should be directly modelled based on the physiological parameters affecting it.
Thus, the present study aims to develop a more generalized mechanistic model of biliary system motility with the main focus on the GB, reflecting current knowledge obtained by a systematic literature review and meta-analysis. Thus, specific relationships between GB motility, residual volumes, bile secretion rates and gut motility in the fasting and fed states, are defined in order to build the mechanistic model. A general aim of the proposed mechanistic model is for it to be as flexible as possible in order to be easily coupled to EHC of different drugs and their primary and secondary metabolites. Furthermore, the proposed mechanistic model is coupled with the previously developed and recently updated Dynamic Fluid Volume model, as part of ADAM platform in SimCYP, to account the time-dependent intestinal [BS]. It is essential to use as accurate as possible luminal fluid volumes in order to simulate accurate [BS]. METHODS Prior to model development, a systematic literature review and meta-analysis of the selected articles was conducted using PubMed and Scopus search engines. Reviews focused on th biliary system 37,[45][46][47] were screened first to gain a general idea about biliary motility and the factors affecting its functionality in fasting and fed conditions. Useful articles were manually extracted from those reviews and screened for eligibility. Then, the literature review focused first on GB motility and its relationship to gastroduodenal motility in the fasted state and thereafter to postprandial periods. The terms, "gallbladder", "gallbladder emptying", "gallbladder volume" and "Interdigestive Migrating Motor Complex" (IMMC) were used for the fasting state whereas "postprandial gallbladder motility" and "postprandial gallbladder volume" were used for the fed state. Search results were restricted to full text articles written in the English language, including healthy human subjects, of adult Caucasians. Additional articles were found through the manual search of included studies' references. Apart from the general criteria, the analytical methods used to monitor gallbladder motility in fasting and fed were critically evaluated and used as an inclusion or exclusion criterion, considering the opinion of the experts in the field, as it has been reported in the literature. 6,48  groups were further divided into two subgroups: fasted-GB (7 articles), fasted-BS (3 articles), fed-GB (10 articles) and fed-BS (3 articles).

Fasting
Various studies have shown strong correlation between the cyclic GB motility (i.e., repeating emptying and filling phases) and the IMMC 13,22 . Unlike the filling phase, the residual GB volume and the duration of the emptying phase depend on the origin of the IMMCc (gastric or duodenal). In particular, GB filling starts at phase I of the IMMCc with the GB reaching its maximum volume at 30% of the IMMCc cycle 13,22 . Thereafter emptying takes place which ends at 90% of the IMMCc, where phase III starts is of antral origin, or at 60% when phase III is of duodenal origin. 13 Thereafter, a steady period, i.e. no further decrease or significant increase in the GB volume, takes place. Converting the GB fraction vs IMMC fraction relationship to actual GB volume (mL) and IMMC duration time (h), individual fasting GB volume change profiles can be generated with both intra-and inter-subject variability. This means that each Filling-Emptying (F-E) cycle is not the same within an individual's GBV profile. The generation of an individual 24 h GB profile is performed as follows: 1) Individual maximum GB volume (mGBv): in order to calculate GBV fraction at each IMMC time point, the mGBv per individual is needed. The mGBv (mL), which is taken to represent the maximum anatomical GB volume, is considered the maximum volume reported in the studies used in the meta-analysis. Normally fasting GB volume is measured 5, 10, 15 min or more before meal. For those studies which provide only the mean value of those measurements per individual is used as "the anatomical GB volume". However, for those studies reporting all the measurements, only the maximum value is selected. To generate an individual mGBv, random sampling is performed from a normal distribution with mean=18.8 mL, %CV= 53, and range= 4.0 -93.0 mL (Table 1).
2) Number and duration of IMMC events per individual: now the %IMMC time points need to be converted to actual time (h). First it should be pointed out that the number (N) of F-E cycles and the duration of each N th cycle should be linked to the number of IMMC events observed in an individual within a 24h period time as well as to the duration of each IMMC. Furthermore, the duration of each IMMC depends on the origin (i.e. antrum or duodenum). Although, IMMC can start from other origins, i.e. esophagus, jejunum 49 , however, limited info was found with regards to fasting GB volume vs IMMC profile, in particular in jejunum. 50 Hence, the meta-analysis was focused on IMMC events started from antrum and duodenum. So, the percentage (i.e. the probability) of the IMMC events started from antrum was obtained by dividing the number of IMMC events commencing for example in the antrum with the total number of IMMC events commencing in both regions, antrum and duodenum. Thus, the probability of the IMMC starting from the antrum is 60% and 40% from duodenum. Then, a random number between 0-1 is generated from a uniformly distributed random numbers. If this number is <0.6, then the first IMMC event is assigned to antrum and hence the duration (h) of this IMMC event is randomly generated from normal distributed data with mean=2.6, %CV= 30.2, and range=0.9 -4.3 (Table 1). Otherwise the IMMC is assigned to duodenum with mean=1.3, %CV=60.3 and range=0.5 -3.4. The same procedure was repeated for the next IMMC and until the cumulative sum of the duration of the IMMC events is in total ≤24 h for every individual. 3) Obtaining filling and emptying rate constants for each F-E cycle of each individual: knowing the individual mGBv and the duration of each IMMC, the corresponding GB volumes at 60 and 90% of each IMMC can be obtained. In particular, a random %GBV value is generated from normal distributed data with mean= 74.0, %CV= 10, and range=70 -100, in case where the IMMC starts from antrum, and mean= 80.7, %CV= 17, and range= 70 -100, if IMMC starts from duodenum. This %GBV is the %residual GB volume at 90% of IMMC or at 60% of IMMC, according to the origin. In addition, this first generated %GBV value is used as the initial condition (t=0) for generating the individual 24 h fasting GB volume changes profiles. As mentioned above the mGBv is normally observed at 30% of the IMMCc. Thus, it is assumed that the GB volume at 30% of each IMMCc, always corresponds to the mGBv. This is in accordance with the observed data where the GB's filling phase continues, unless meal is given, until the mGBv has been reached and thereafter a new emptying phase will occur. 22,51 It is also assumed that the filling phase takes place is zero order (IMMCc= 0 -30%), whereas the emptying phase under first order kinetics 52 followed by a constant volume. The filling (Eqs. 1-2) and emptying (Eqs. 3-4) rate constants used to generate the individualized 24 h GBV fasting profile are showed below.
Where the letters 'a' and 'd' denote the origin of the IMMCc ('a'=antral and 'd'=duodenal) whereas DurIMMC denotes the actual duration of the N th IMMC (h). After obtaining the F-E constants for 1 st , 2 nd , …, N th IMMC assigned to 1 st , 2 nd , …, i th individual, the following equations were used for the filling (Eq. 5), emptying (Eq. 6) and steady period (Eq. 7) to obtain all the data points for the 24h fasting profile of GBV.
= 0 (7) Fig. 2 shows how the observed relationship between %GBV and %IMMC is converted to individual GBV (mL) vs IMMC (h) profile using Eqs. 1 -7 after random generation of mGBv, origin and duration A B C of each IMMC per individual and %GBV at t=0 (only once per individual), 60% or 90% depending on the origin of each IMMC. Fig. 2C shows clearly the difference between E-F cycles which associated with IMMCc of duodenal and antral origins, in terms of decrement of GBV and duration of emptying phase. Fig. 2. Generation of 24h individual fasting GBV profiles. A) Relationship between %GBV and %IMMC with respect to the origin of the IMMC. The horizontal solid bars indicate the different GB F-E phases with respect to the IMMC for both origins, D:duodenal and A:antralm (modified from Stolk et al 1993 13 ); B) An example showing how a %GBV vs. %IMMC profile is created for one IMMC cycle from in vivo data (A) after generating random %GBV numbers sampled within the specific range of the normal distribution curves at 60% of IMMC for those IMMCs originating in the duodenum and at 90% of IMMC for those IMMCs of antral origin; at t=0, random sampling performed only once per individual; C) An example of a 24h fasting GBV profile of a representative (average) individual with mGBV= 18.8 (mL), 12 IMMC events where 7 starting from antrum and 5 from duodenum with a sequence as followed:

Fed
Strong contractions of the GB occur upon stimuli such as after meal ingestion. Depending on the strength of the stimulus, e.g. fat content of the meal, the residual GBV and the duration of the emptying phase vary significantly. Clinical studies passing the inclusion criteria were split to two groups based on the %fat caloric content contributing to the total kcal of the meal. Thus, a high-fat meal is defined when the %kcal coming from fat is ≥40%. Meta-analysis showed that the duration of the GB emptying phase is for 0.72 ±30 (%CV) h (range: 0.5 -0.73 h) and 1.17 ±37 (%CV) h (range: 0.33 -2.08 h) for low-and high -fat meals respectively (p<0.05). After the emptying period, the GB enters the refilling phase, treated as zero order as indicated previously, until reaching the maximum ('anatomical') volume, 5 unless interrupted by further food intake. 53 Based on our knowledge and the available data in the public domain, there are not enough prolonged recordings of the GB motility to show if the GB enters the fasting F-E cycling profile exactly after the postprandial refilling period. Thus, it's assumed that after GB reaches the maximum volume, a new fasting F-E cycling pattern is followed which continuous until the next meal. Furthermore, the common practice to investigate GBV changes and duodenal [BS] under multiple meals is to administer food every 4, 5 and/or 6 h. 1, 53-55 However, it was not where possible to find information indicating how the GB behaves with shorter time intervals between the meals (e.g. every 1, 2, 3 h etc.). Nevertheless, 1 or 2 h time interval between meals might be too short reflecting a situation where the GB would be physiologically inactive due to continuous feeding. 54 Thus, the proposed model allow the GB to enter a fed state only if the next meal is 4 h after the previous one, otherwise the GB's refilling phase continues until mGBv has been reached.
Generation of the individual fed GBV profile is performed as follows: A meal can be given at random time point during an individual IMMCc and thus at a random point dur-ing the GB cyclic fasting profile; the meal, of course, interrupts the fasting profile. Thus, the fasting GBV (taken from the pre-generated fasted GBV profile) at the time of interruption ( 1 ) is used as the starting point for the emptying phase of the GB in the fed state ( @ 1 ). Fed state GB emptying is characterized by a first order process (Eq. 8).
To generate individual fed GBV profiles, a transition from the emptying to refilling phase is needed. Meta-analysis showed that there is a linear correlation (R 2 =0.6, SF12) between the emptying rate constant (h -1 ) (Eq. 9) and the refilling rate (mL/h), regardless of the fat content of the meal. Linear regression of the data gave Eq. 10 which was used in Eq. 11 to obtain the GB refilling profile. Thus, after obtaining , Eq. 10 is used to calculate . Then Eq. 8 (t1 ≤ t < t2) and Eq. 11 (GBV@t2-i ≤ GBV < mGBv, i= lf or hf for a low fat or high fat meal respectively) are used to generate the fed GBV profile. Fig. 3 shows an example of a fasting-fed-fasting GBV profile for low-and high-fat meals. The GBV fasting profile prior to the meal corresponds to the fasting GBV profile as showed in Fig. 2C. After the end of refilling phase the GB enters the fasting profile which is re-generated as described in the fasted section for the remaining time period. This example illustrates the effect of a high-fat meal compared to a low-fat meal where normally a higher fraction of the stored bile is ejected from the GB into the duodenum and the duration of the refilling phase is longer; ~3 h compared to ~1.5 h for a low-fat meal. Fig. 3. Example of fasting -fed -fasting transitions; a scenario where meal is given at a random time point of the 24 h GB volume profile; GBV@t2-lf: residual GBV after low-fat (lf) meal ingestion; GBV@t2-hf: residual GBV after high-fat (hf) meal ingestion; t1: random time-point of meal administration; t2-lf: time point at which the emptying phase ends after low-fat meal; t2-hf: time point at which emptying phase ends after high-fat meal.

Bile Salt Disposition within GI Luminal segments
Knowing the GBV profile, either fasting and/or fasting-fed-fasting, the fluctuating duodenal, jejunal, ileal and colonic bile salts -times concentrations profiles-(mM) can be obtained. However, it is also important to know hepatic bile salt secretions in the fasted and fed states, time-dependent water volume distribution and absorption kinetics within the different GI tract segments. The ADAM model in Simcyp simulator (v18r2) provides nine luminal segments (stomach, duodenum, jejunum 1-2, ileum 1-4 and colon) with a dynamic water volume distribution in each segment, transit rate constants, dynamic (i.e., time varying) secretions (saliva, gastric and intestinal secretions such as from the Brunner's glands) as well as absorption rate constants for water. Furthermore, within this work, passive and active absorption of bile salts in the different ADAM GI tract segments was modelled based on absorption kinetics derived from human perfusion studies. 23,24 Based on the available data, passive absorption of BA predominates in jejunum 1-2 and the colon whereas active absorption predominates in the ileal segments. For the passive component in jejunum 1-2, glycochenodeoxycholic acid (GCDC) was used as reference 23 and chenodeoxycholate (CDCA) in colon 24 whereas taurocholate (TA) was used as reference for active absorption in the ileal segments. 23 However, TA, GCDC and CDCA are only a fraction of the total BA present in luminal fluids, hence the fraction available for passive absorption in the jejunum and colon as well as active absorption in ileum, should be assigned to the fraction of TA, GCDC and CDCA present in lumen aspirates. 2,27 However, differences in the luminal bile salts compositions have been found between studies, which can be attributed population differences. 2 In this work, the bile salt composition, as published by Riethorst et al (2016), 2 was used as a case study based on which fractions of GCDC and TA were found to be 30% and 10%, respectively. Thus, for the passive component the fraction available was set to 0.15 for each jejunal segment. The active component was set to 0.05 for ileum 3 & 4 and zero for ileum 1 & 2, since the perfusions studies have been conducted mainly within the terminal ileum (i.e. within 30 cm of the ileocecal valve). The passive component was set to zero for all ileal segments, as active absorption takes place mainly within this region.
Eqs 12 -18 were used to obtain the time-dependent biliary secretions following the F-E phases of the pre-generated GBV profile: -Filling period of GB o Hepatic bile secretions (Hsr, mL/h) are back-calculated from the filling rate constant of the GB. This is based on the fact that the liver is the only source of bile flow during the closure of the sphincter of Oddi and relaxation of the GB muscle tissue. Thus the GB filling rate should reflect the hepatic secretion rate, accounting also for the fraction of the bile entering the GB.
where is derived from Eqs 1 and 2 and is the % of Hepatic Bile Entering Gallbladder (Table 1).
o Bile flow rate to duodenum (BfD) mL/h: o Rate of bile salt entering the duodenum (BSenDuo): where is the hepatic bile salt mass rate, mmol/h (Table 1) and c = 'fasted' or 'fed'.
-Emptying period of GB o Hsr, according to Eq. 12 o BfD where k is the emptying rate constant (h -1 ) in fasted or fed state and switches from one state to another according to the GBV profile.
o BSenDuo where HBSmassrate and k have the same function as described in Eqs. 14 and 15, respectively.
-Steady period of GB This period is only applied during the fasted state.
o Hsr, according to Eq. 12 o BfD Eqs. 19 -21 were used to obtain time-variant luminal bile salt concentrations within the ADAM GI tract segments; bile salts concentration in stomach is static for healthy humans albeit with inter-subject variability.
where i indexes the duodenum, jejunum 1… colon, BSm is the bile salt mass (mmol) in each segment, KAbs is the absorption rate constant of bile salts.  Table 1.
Eq. 21 shows that the passive and active absorption component is available for all ADAM segments but since, for example the passive component is considered to be zero in the ileum segment the first term of KAbs will be zero and hence only the second (i.e., active uptake) will contribute to the total [BS] in ileum. However, this gives flexibility to apply both or only one absorption component according to new findings or data available for bile salt absorption in GI tract. The terms � ( ) − _ � and � where Vi(t) is the time-dependent fluid volume in the fasted or fed state in the i th ADAM GI tract segment (as discussed below, first-order transit rate constants are used).

DISCUSSION
After constructing all the equations describing the time-variant EHC of bile salts coupled to time-dependent luminal fluid volumes, simulated luminal [BS] were obtained and compared to the observed data. The ADBSM was tested for its predictiveness with informing Simcyp® (v18r2) simulator only with the type of meal (i.e. low-or high-fat), the time of the meal intake and/or water intake events (using the Food Staggering Custom Dosing tool), the number, gender and age-range of the participants in each study. Thus, the ADBSM was not adjusted, optimized or tested against a single study. Moreover, it should be pointed out that none of the clinical studies selected for the performance verification (PV) provided information about GB volumes, transit rates, IMMC events and their duration, fluid volumes etc. In total 12 clinical studies were used for PV of the model (Table S1) , where no significant differences were found between observed and simulated profiles (p=0.1, t-test), the values of the [BS] after ~5h were higher in observed data without showing further decline; see especially Individual 1 (Fig. 4Aa') and 2 and (Fig.4Ab'). If it's assumed that these steady state concentrations are related to the fasted [BS] period for those individuals, perhaps the main reason for higher fasted [BS] in some individuals, might be the baseline fluid volumes differences between the virtual populations and the healthy volunteers. In these studies the average profile was within the predicted range of 5%-95% confident intervals. In fig.4B the maximum [BS] was 7.7 mM at 4.5h and 9.8mM at 4.9h for observed and simulated data, respectively (p=0.24). In observed data, fasted [BS] values were restored 1.5h from meal ingestion without further change after 2h. In the simulated profiles there was a deeper decrease in [BS] whereas steady state fasted [BS] values were restored 7h after a meal reaching similar values with the observed data. However the duration of the study is not long enough to know the evolution of [BS]. In fig.4C the fasting values of [BS], i.e. before meal (2.5-3.8 h), were 4.7 ±1.05 mM and 5.13 ±3.9 mM for observed and predicted data (p=0.12), respectively. In the fed period, i.e , almost instantaneously upon meal ingestion. This is because, based on the model design, the GB responds immediately to a meal. However, it has been shown that there is a lag time between meal ingestion and GB emptying linked to the phase of IMMCc at which meal was given. 58 However, there is only one study showing this and to the best of the current authors knowledge there is no other study investigating this phenomenon. It seems unlikely, although motility was not recorded in the Riethorst et al study, that in all subjects the meal was given at the same IMMCc phase something which could explain the delayed response of the GB and hence a shift to the maximum peak upon GB contraction. Although, there is no information for the first 30 minutes in the Riethorst et al study, it seems that this is the only study where duodenal [BS] are so high. Most of the studies (Figs. A, D, E and F) used for PV showed sharp increase and decrease of [BS] following the simulated profiles. This can be attributed to differences in the sampling time intervals and sample volume and hence how extensively the EHC has been interrupted, population differences in biliary secretions, fluid volumes, 59 GI tract motility and so on. With regard to the multiple peaks in the observed profiles, SFig. 9B shows three characteristic simulated profiles with one close to the observed [BS] duodenal profile. According to the selected virtual profiles, the subjects with the elevated multiple peaks should have GB kinetics which combine a deep decrease in GB volume upon meal ingestion followed by a more than 25% reduction of the maximum anatomical volume in the first fasting emptying phase appearing once the prolonged refilling phase in the fed state has been completed (SFig.9C, virtual individual162-Trial1). These GB kinetics lead to no significant accumulation of BS in the GB (SFig.9D). In addition, the subjects are expected to have relatively low duodenal fluid volumes (SFig.9E) combined with low fluid transit times (see supplementary materials), resulting in elevated duodenal [BS]. However, these conditions are for an average subject whereas individual profiles, if available, may tell a different story.
Prolonged measurements of duodenal [BS] as in the Clarysse et al 2009 study (Fig.4F (a'-d')) showed multiple peaks appearing in [BS] several hours after a meal. There may be several reasons for these secondary peaks. It may be due to the GB fasting emptying-filling cycle which may appear sooner than the simulated profile. However, this cannot be absolutely true because it takes several hours for the GB to enter its fasting profile as a prolonged refilling phase take places after the strong GB contraction of due to meal ingestion. 60 This can be also seen from the mean simulated profile (Fig. 4F) where a rise of the [BS] and the following peaks were observed several hours after a meal. This deep drop in [BS] after the high peak (between ~5 -7.4h) is related mainly to GB kinetics where the GB enters the refilling phase, hepatic secretions are lower (i.e. back to fasting secretion rates) and to the dilution of the duodenal contents due to elevated fluid volumes. Another possible reason that is not known to have been explored and/or utilized in PBPK modelling is the "to and fro" fluid motion across intestine which might cause these secondary peaks. 61 A further possibility gastric emptying which is known to occur as a sequence of spurts. 62 However, the remaining food in the stomach might not be sufficient to trigger repeated GB emptying and/or elevated hepatic secretions. This is because in vivo studies have shown no evidence of high biliary secretions in duodenal aspirates, expect from the initial high peak in [BS] due to GB emptying, after continuous or intermittent feeding with the [BS] equal to the fasted values on average. 54 This might related to the feedback mechanism controlling GB contractions. 63 The model doesn't allow the GB to contract before five gastric emptying half-life (~4h) have been completed. This is also in accordance with the available experimental information where the shortest time intervals between meals is 4h showing repeating GB contractions without the GB reaching its maximum volume and then entering to the fasting filling-emptying cycles. It should be also pointed out that the model was able to capture the drop and rise of [BS] in fasting periods when only water is provided; see Fig.4F and individual profiles Fig4F(a'-d') between 4.5 -6.5h.   Fig.5 D). In the Fields & Duthue study, sampling was conducted in different segments of the small intestine. The model picks up the range in most of the observed data, including variability (see Fig. 5A, Fig. 5B and Fig. 5C). However, in the case of jejunum II (Fig. 5D), the maximum [BS] appeared sooner compared to the simulated profile. Looking at the simulated individual profiles this could be because of differences in the transit times used in the model and those of the participants in the Fields & Duthue study. However, this information is not directly available from the in vivo study, but perhaps the transit times are more rapid compared to the values in Simcyp® library. Thus, the model doesn't capture the Tmax for this study, but this could be improved by adjusting the transit time rate constant. In this simulation only 3 virtual individuals were found to have sufficiently rapid transit times after a meal. The majority of the simulated profiles had Tmax > 0.5h with mean=1.2 ±1.5h after a meal. This reflects the physiology of the selected virtual population (Healthy Volunteers). The fact that the model can capture the observed data for most of the studies, shows that the built-in distribution of the transit times reflects actual population distribution here. The physiological parameters provided by Simcyp®, in this case fluid transit times, is based on an extensive meta-analysis covering separately different populations and different moieties, i.e. fluids, tablets, fine particles and so on. So, in this work the fluid transit times reflect BS transit times. However, the transit times used in publications, where a bile salt model was built to capture the time-dependent concentration profiles of BS, have been derived from mixed populations 64 whereas in other models covering different aspects, e.g. bile salt metabolism, the same authors may have used different intestinal transit times. 65 Looking into the literature, it was found that this is the case for most of the developed, reported EHC models 66 while in some cases calibration of the model with respect to intestinal fluid transit times has been performed based on values for non-disintegrating tablets 67 which are not expected to match fluid transit. 68 2 mM (fig. 5B). Based on model structure, [BS] cannot go below the baseline concentration assigned to an individual. This can be improved by either increasing %CV or decreasing the mean baseline [BS] or increase the passive absorption rate (Pappcoef, Table 3). In the first case, the range of the confidence intervals will be wider, allowing the observed data to be within this range, whereas in the second and third cases the simulated curves would shift toward lower [BS]. In any case any change should be justified from meta-analysis of the available data in the public domain.   Both absorption kinetics and transit times are not easy to appropriately-mechanistically reproduce. There are limited perfusion studies in humans for bile salt absorption in different regions of the GI tract. Absorption is more complex when a mixture of bile salts is perfused compared to a single bile salt. 23 Furthermore, the available perfusion studies have been conducted for specific bile salts and hence the absorption kinetics in the current model are applied to a fraction of the total [BS], reflecting the fraction of that specific BS.
However, the composition of bile salts is not the same between populations 2 and not all the studies provide this information. With respect to the transit times (residence times), used in the ADAM model these are derived only from scintigraphy and/or MRI studies which give the total and not the regional (segmental) transit times in the small intestine. The regional transit values used in the ADAM model assume residence time is proportional to anatomical length -population variability in regional residence times is derived from population variability in these lengths. To the authors knowledge even where regional transit has been assessed for a particular GI tract region 69 there is a lack of information on total small intestinal transit time in the same subjects. However, a priori it seems reasonable that slow or fast transit times can occur within the same and/or different regions, even of the same length due to different motility patterns, e.g. forward or backward propagating waves. 61 In spite of these issues, the model can capture the mean values of [BS] as reported by Reppas et al 2015 (Fig.6B). It should be mentioned that the terminal ileum is a complicated region with distinctive motility with respect to the distal ileum, which regulates emptying into the colon. However, the model captures adequately the observed data with the mean simulated [BS] profile matching surprisingly closely the observed mean [BS] (Fig.6B), taking into account that the model was informed only with the meal time and the number of subjects.  (Fig.5B), could be applied to the model. Specifically, higher passive absorption can be applied alongside higher fraction of bile salt available for absorption. However, colonic absorption is more complicated, as metabolism of the conjugated bile salts takes place by the microbiota and absorption kinetics of the unconjugated BS will in general differ from the conjugated forms. The current model uses absorption kinetics of unconjugated BS based on the available data 24 but it does not account for luminal metabolism. Furthermore, the passive absorption coefficient is derived from a single bile acid, specifically chenodeoxycholate (CDCA). However, this parameter is expected to differ for each bile acid albeit such information is not available. Furthermore, the mean fluid volume in the colonic compartment was ~10 mL whereas Diakidou     , adding more complexity to accurate prediction of [BS] over time. However, it is essential to have deep knowledge of human physiology and the drawbacks/limitations of the methods used to obtain these data. It is the intention of this work to further contribute to the overall effort for more mechanistic PBPK models enabling improved predictivity of oral absorption.