In silico modeling and simulation of organ‐on‐a‐chip systems to support data analysis and a priori experimental design

Abstract

Organ‐on‐a‐chip (OoC) systems are a promising new class of in vitro devices that can combine various tissues, cultured in different compartments, linked by media flow. The properties of these novel in vitro systems linked to increased physiological relevance of culture conditions may lead to more in vivo‐relevant cell phenotypes, enabling better in vitro pharmacology and toxicology assessment. Improved cell activities combined with longer lasting cultures offer opportunities to improve the characterization of absorption, distribution, metabolism, and excretion (ADME) processes, potentially leading to more accurate prediction of human pharmacokinetics (PKs). The inclusion of barrier tissue elements and metabolically competent tissue types results in complex concentration‐time profiles (in vitro PK) for test drugs and their metabolites that require appropriate mathematical modeling of in vitro data for parameter estimation. In particular, modeling is critical to estimate in vitro ADME parameters when multiple different tissues are combined in a single device. Therefore, sophisticated in silico data analysis and a priori experimental design are highly recommended for OoC experiments in a manner not needed with standard ADME screening. The design of the experiment should be optimized based on an investigation of the structural characteristics of the in vitro system, the ADME features of the test compound and any available knowledge of cell phenotypes. This tutorial aims to provide such a modeling framework to inform experimental design and refine parameter estimation in a Gut‐Liver OoC (the most studied multi‐organ systems to predict the oral drug PKs) to improve translatability of data generated in such complex cellular systems.

INTRODUCTION

Prediction of pharmacokinetic (PK), pharmacodynamic (PD), and safety profiles of drug candidates in human remains a significant challenge during early drug development. Prospective prediction of clinical PK/PD behavior often relies on in vitro data. Particularly in the field of drug metabolism and PKs (DMPKs), in vitro‐in vivo extrapolation (IVIVE) has become the standard prediction method, superseding allometric scaling methods which do not take into account many of the differences between species. Many independent in vitro assays have been established to measure various absorption, distribution, metabolism, and excretion (ADME) properties which allow IVIVE using relevant physiologically‐based scaling factors. ¹ Data from these assays are then included in physiologically‐based pharmacokinetic (PBPK) models to simulate the in vivo PK profile of a drug in plasma and organs of interest. ² , ³ , ⁴ , ⁵ , ⁶

Many in vitro systems do not fully recapitulate the in vivo features of a given tissue and therefore the extrapolation may not accurately predict the in vivo outcome. ⁷ , ⁸ , ⁹ , ¹⁰ In addition, current in vitro systems have the drawback of a limited longevity of cell phenotype which constrains their application for certain scenarios, such as low clearance drugs. An emerging alternative to the standard cellular systems are microfluidic organ‐on‐a‐chip (OoC) systems, which can include multiple cell types and allow study of multiple ADME properties in a single experiment. Other approaches include co‐cultures, ¹¹ 3D primary human hepatocyte spheroids, ¹² multi‐well spheroids, ¹³ and chimeric mice with humanized livers. ¹⁴ An OoC is a 3D microfluidic cell culture that is able to simulate mechanical and physiological responses of an organ system. ¹⁵ , ¹⁶ Tissue types that may be cultured include brain, lungs, gut, heart, kidneys, liver, prostate, skin, and bones. ¹⁶ , ¹⁷ , ¹⁸ , ¹⁹ , ²⁰ , ²¹ The basic characteristic of OoC devices is the presence of a microflow system that extends cell viability and retention of drug‐metabolizing enzyme activity. ²² It was demonstrated that the addition of microflow improved cell longevity and preserved initial levels of drug‐metabolizing enzyme activities for at least 4 days. ¹² , ¹³ , ¹⁴ , ²³ The microflow also allows connection of different compartments containing different cell types (representing individual tissues) to generate experimental systems with complex tissue‐drug interactions and, consequently, complex drug concentration‐time profiles.

The estimation of a single ADME parameter from established in vitro systems generally does not require advanced mathematical modeling because a single ADME process dominates the measured changes in drug concentration and the drug concentrations are homogeneous within the sampled parts of the system. In contrast, OoC systems often have separate compartments with different drug concentrations. The drug concentration in a compartment changes with time due to more than one process acting simultaneously (e.g. medium flow in and out of the compartment, drug movement into and out of cells, drug metabolism, and evaporation from the medium). In addition, removal of samples for drug concentration measurement depletes drug and medium (but not cells), changing the system make‐up. The multiple parameter estimation needed for multi‐OoC systems requires the application of advanced mathematical modeling. ²⁴ , ²⁵ , ²⁶ Compartmental models are generally applied to multi‐OoCs because they are able to consider the compound concentrations in each of the physical OoC compartments simultaneously. A model for a multi‐OoC is analogous to a PBPK model of the human body in that the output is dependent upon system‐related properties (e.g., volume of a compartment and medium flow rate) and compound‐related features that need to be combined together to simulate the experimental outcome.

Currently, one of the most important OoC system for ADME characterization is the Gut‐Liver OoC, which encapsulates the most relevant features for the prediction of bioavailability (F) and hepatic clearance in vivo. The F can be represented as the product of the fraction absorbed, the fraction escaping intestinal first‐pass metabolism, and the fraction escaping hepatic first‐pass metabolism/excretion. ²⁷ The Gut‐Liver OoC system contains the minimal components required for estimation of each of these processes. It is made up of three physical compartments: gut apical and basolateral sides that are separated by a confluent layer of intestinal cells and a hepatic compartment containing liver cells (Figure 1a). A constant microflow links the medium in the hepatic compartment to the basolateral side and vice versa.

FIGURE 1.

(a) Illustration of a Gut‐Liver OoC system from CN Bio Ltd as reported by Milani et al. ²⁴ The exact system design will differ for other providers. (b) Steps for the in silico prediction of human in vivo PK and a proposed approach for the design of OoC experiments based on system optimization, cell donor selection and optimization of sampling times. (c) Graphical representation of the compartmental model applied for study of MDZ. A detailed graphic representation of the MDZ model is reported in the Figure S7. ADME, absorption, distribution, metabolism, and excretion; MDZ, midazolam; OoC, organ‐on‐a‐chip; P _app, apparent permeability; CL_int, in vitro intrinsic clearance; PBPK, physiologically‐based pharmacokinetic; PK, pharmacokinetic.

This tutorial describes the utility of a design of experiment (DOE) process for a commercial Gut‐Liver OoC (Figure 1a). It is based on our recent experience with the prodrug mycophenolate mofetil and its metabolites. ²⁴ The article is comprised of three main sections: (1) OoC system selection and the design of the experiment considering the physical aspects of the system, such as compartment volumes, medium flow rates, and medium evaporation, (2) selection of the most appropriate cell donor based on the phenotype required for the preclinical investigation, and (3) use of the information from these two sections to establish the most informative samples to be collected (with regard to sampling site and timing; Figure 2a).

FIGURE 2.

(a) Representation of the approach reported in this tutorial. After investigation of the influence of the system parameters on the in vitro DMPK results, the selection of the proper cell donors for the test compound and the Gut‐Liver OoC proceeds. The addition of the in vitro DMPK parameters from the standard in vitro systems allows to optimize the sampling points. Simulations and the GDSA allow to optimize the sampling times in order to get the more informative points for the fitting and reduce the risk of being below the limit of quantification. All of these in silico analyses are done to improve the accuracy of the in vitro DMPK estimation with a direct impact on the IVIVE. More detailed information with a report of the system parameters is in Table S1. (b) Proposed experimental workflow using the Gut‐Liver OoC from the first experiment using the suggested in silico modeling approach. In blue are reported the steps from the proposed method to optimize the fitrst experiment with a Gut‐Liver OoC. ADME, absorption, distribution, metabolism, and excretion; DMPK, drug metabolism and pharmacokinetics; GDSA, global dynamic sensitivity analysis; IVIVE, in vitro‐in vivo extrapolation; OoC, organ‐on‐a‐chip; PK, pharmacokinetic.

OoC experiments currently have high cost and low throughput and are therefore most likely to be applied to answer high value questions for a small number of drug molecules per year. In the ADME area, this is likely to involve the more accurate measurement of metabolism, bio‐distribution, and drug‐drug interaction DDI properties to enhance human PK and DDI predictions for a small number of promising molecules that have already been quite well profiled using high throughput ADME screening assays. Time invested in experimental design is therefore warranted because of the complexity of the Gut‐Liver OoC system, the low throughput and the high cost. Such proactive work to improve the accuracy of predicted ADME parameters is analogous to the methods established to enhance clinical trial design ²⁸ , ²⁹ although such methods are rarely applied for in vitro studies. ²⁴ , ³⁰ The determined ADME parameters can be taken forward for human PK prediction, as illustrated in Figure 1b. More in detail, the aim of first performing a simulation and planning the OoC experiment based upon that simulation was to reduce the need for a pilot experiment followed by a more refined definitive experiment. The input data for the simulation can be obtained from the high throughput ADME screening assays. In the instance that the OoC experiment provides data substantially different to expectations and ADME parameters cannot be calculated with sufficient confidence, then a new experiment can be planned based upon the OoC data collected in an iterative manner (Figure 2b). If the parameters obtained from the Gut‐Liver OoC differ from those predicted by standard in vitro systems, it indicates that the Gut‐Liver OoC was able to capture some DMPK processes that were not present in the standard in vitro systems. To illustrate this, a case example is shown for the well‐characterized drug midazolam (MDZ; Figure 1c). The proposed approach applied for the Gut‐Liver OoC can be re‐adapted for any multi‐OoC applied in an ADME setting (Figure 2b).

RESULTS AND DISCUSSION

System parameter optimization

In the following sections, the impact of some key system parameters on the experimental design are demonstrated. Figure 2a provides an overview and more detailed information is available in Table S1.

Surface area and apical side volume of the Transwell

The surface area and apical side volume are investigated as they have a significant impact on the intestinal permeability assessment.

The surface area of the transwell determines the number of intestinal cells present in the system and hence their total metabolic capability. In combination with the drug permeability, the rate of drug molecule influx into the OoC system is also determined by the transwell area. The apical side volume is usually defined by the transwell area multiplied by the height of medium above the gut cells. A larger apical volume can enable more sampling from this compartment, potentially allowing larger total quantities of drug to be applied to the system but also result in a longer time for drug absorption and system equilibration.

The first set of simulations aimed to assess the impact of transwell surface area and apical compartment volume on the experiment (Figure 3a). The typical volumes of the apical compartment, as recommended by the manufacturer were considered for different devices with transwell surface areas corresponding to the different formats commonly used (from 6‐ to 96‐well plates). The reported commercial transwells of 0.33 and 1.12 cm² were also directly applied in two Gut‐Liver OoC studies. ²⁴ , ²⁶ Figure 3a illustrates the impact of the surface area on the in vitro PK profiles of a metabolically stable compound with low permeability (e.g., etoposide, P _app of 0.4 nm/s, ³¹ additional information is available in the Supplementary Information). A larger surface area produces a faster increase of the drug concentration in the basolateral compartment with detectable compound (limit of quantification [LOQ] of 0.001 μM) after 1 h of incubation for the 4.67 cm² transwell (Figure 3a). Conversely, detection of the compound in the basolateral side requires an incubation duration of at least 24 h when the surface area of the transwell is relatively small (e.g., 0.143 cm² 96‐well inserts). Therefore, compounds with low permeability should ideally be tested in a system with a larger surface area and limited apical side volume in order to improve the accuracy of the P _app determination by inclusion of meaningful apical compartment drug depletion data. Because the transwell surface area is proportional to the total number of enterocytes, the choice of transwell dimensions also impacts drug depletion and metabolite formation rates (e.g., 0.1 cm² is estimated to contain ~57,000 enterocytes considering a diameter of 14.9 μm/cell reported by Ho et al. ³² ). Although there are advantages of using a large surface area for moderate and low permeable compounds, highly permeable compounds may be rapidly depleted from the apical side with potential measurability issues. A large surface area with a limited volume of drug in medium added to the apical compartment may also result in inaccuracy of the actual apical volume estimation due to a significant retained medium volume next to the cells.

FIGURE 3.

Simulations for a compound with very low intestinal permeability (P _app = 0.4 nm/s) and for a Gut‐Liver OoC with: (a) four different commercial transwells with surface area of 0.143, 0.33, 1.12, and 4.67 cm² and corresponding volumes of the apical side of 75, 100, 500 and 1500 μL, respectively. (b) The same compound was investigated for a fixed surface area (1.12 cm²) and with varying volumes of the apical compartment. The typical volume of 500 μL was varied by the factors 0.33, 0.5, one, two, and three‐fold. The limit of quantification for the compound in the basolateral and liver compartments was considered to be 0.001 μM and is reported with the dotted line in black. The sampling times were 0, 0.5, 1, 2, 4, 8, 24, and 48 h for all three experiments with the different transwells. Additional information about input parameters is provided in the Supplementary Information (Table S1). The profiles in the basolateral side from the different SA of the transwell area are overlapped. The liver compartment was omitted for clarity. The dots represent the sampling points in all plots. OoC, organ‐on‐a‐chip; P _app, apparent permeability.

Because the dimensions of the transwell are plate‐dependent, a potential method to modulate the apical concentration‐time profile could be achieved by varying the volume of the apical side while maintaining the same surface area, whereas still ensuring cells are adequately covered with medium (Figure 3b). In the simulation, the surface area was maintained at 1.12 cm² whereas the volume of the apical compartment (typical 500 μL) was varied by 0.33, 0.5, one, two, and three‐fold. A decrease in apical volume of threefold resulted in apical side depletion of around ~5% after 96 h of incubation, whereas an increase of threefold the depletion was only 0.5%. In contrast, the volume variation did not significantly affect the concentration‐time profiles in the basolateral and liver compartments, and the compound was detectable (concentration higher than the LOQ of 0.001 μM) after 4 h of incubation. The minimal difference observed in this example among the different profiles in the basolateral compartments is generalizable only when the concentration in the apical side is much higher than that in the basolateral side. In a scenario with a drug with higher permeability, a significant difference in the concentration‐time profiles was seen also in the basolateral side (Figure S1). Therefore, the surface area and the volume have a significant effect on the profiles in both the apical and basolateral compartments. With a priori information on the permeability of the drug, the most suitable combination of surface area and volume can be selected (within the constraints of the selected OoC system) to ensure meaningful and detectable changes in the concentration‐time profiles in the apical and basolateral compartment.

Sampling and medium volume evaporation

The concentration‐time profile is affected differently by the sampling volume and the medium evaporation, leading to a biased prediction of the DMPK parameters.

Most ADME screening assays do not need to consider the effect of medium evaporation or media volume reductions for a number of reasons: (1) experiments are often performed over a short period of time, minimizing evaporation effects; (2) experiments are performed as “end point” determinations with medium/cell sampling only occurring once and no need to consider any perturbation of the remaining system by sampling; (3) experiments are often homogeneous (e.g., microsomal suspensions) so drug, medium, and enzyme concentration ratios remain unchanged by sampling. OoC systems are different; because they run for a considerable period of time, sampling from them removes drug and medium but not cells, and multiple samples need to be collected from a single “well.” The effect of sampling volumes and medium evaporation therefore needs to be considered, especially for high metabolic stability drugs where concentration‐time profiles may be affected by these processes. The required sampling volume is also highly dependent on the sample preparation requirements and the sensitivity of the analytical method. Removal of multiple samples from each compartment of the Gut‐Liver OoC, can significantly change the experimental conditions. In addition, evaporation from the medium over time needs to be taken into account. ²⁴ Although the medium evaporation and the sampling volume affect the disappearance and the appearance of the substrates and the metabolites in the medium, their influence of the experimental outcome are different and are discussed in detail in this section. Two sets of simulations are reported here in order to demonstrate the impact of medium evaporation and removal by sampling from the apical compartment. The input data for mycophenolic acid and its metabolite mycophenolic acid β‐D‐glucuronide were used. ²⁴ A detailed description can be found in the Supplementary Information (Tables S3 and S4). The first set of simulations shows the effect of sampling from the apical side using sampling volumes of 5, 15, 30, and 45 μL while assuming no medium evaporation (Figure 4a). In the case of cells immobilized on a scaffold (as in this OoC), the removal of volume at each sampling time does not affect the number of cells. However, it results in an increase of the cell to medium volume ratio. This effect is more pronounced with higher sampling volumes and longer incubation times (Figure S2), especially when the initial volume of the apical compartment is relatively low. In the example presented here, an increase in apparent cell density (cell to medium volume ratio) of 15% was already observed after the second sampling time of 2 h when the sampling volume was greater than or equal to 30 μL and the initial volume of the apical side was 325 μL. The reduction of the volume due to sampling can be introduced in the fitting model to reproduce the experimental condition. In addition, the sampling volume may significantly increase the cell to medium ratio, leading to an increase in the elimination rate constant which could result in an overestimation of the apparent clearance if this is not accounted for.

FIGURE 4.

Simulation data using input parameters of Mycophenolic acid from a Gut‐Liver OoC. ²⁴ The term “Conc. Sub.” and “Amount. Sub.” refer to the concentration and amount of Mycophenolic acid, respectively. (a) Effect of the sampling (25 μL) from the apical side on the volume, cell density, substrate concentration and amount. The dotted lines represent a variation of 15% of the initial volume and cell density. Only sampling with 5 μL permits to reduce the volume and increase the cell density within 15% of the initial value. (b) Effect of sampling (15 μL) and medium evaporation with four different k _ev on the volume, cell density, substrate concentration and amount. Because the mole of compound in the sample aliquot is removed from the medium at each sampling time the concentration is not affected by the sampling in contrast to the amount which is subjected to a sudden depletion. Concentration reported in log scale for both (a) and (b) panels. Additional figures reporting the basolateral and liver compartments are reported in the Supplementary Information (Figures S2 and S3). OoC, organ‐on‐a‐chip.

Another relevant phenomenon, leading to volume reduction over the incubation time (V(t)), is medium evaporation. Although both sampling and evaporation contribute to reduction in medium volume over time, their effects on the experimental outcome are different. This is demonstrated in the second set of simulations which investigates medium evaporation from the apical and liver compartments for a range of evaporation constants (k _ev; Figure 4b). The volume of the basolateral side was considered to be constant due to medium recirculation. ²⁴ Whereas sampling results in a sudden loss of the medium, evaporation causes a continuous reduction of the medium (Figure 4b). In addition, whereas sampling affects the medium volume but not the drug concentration, medium evaporation leads to a minor increase in drug concentration. As for the medium volume sampling, the evaporation also affected the cell to medium ratio (Figure 4b). Medium evaporation depends on several factors which may not be under the control of the experimenter: surface area of the well, the humidity of the plate/incubator, air flow around the device, and the incubation temperature. ²³ Medium evaporation can be quantified from the residual volume in the compartment. ²³ , ²⁴ In the simulations reported in Figure 4b, the evaporation and the samplings of 15 μL from the apical side showed a low impact on the concentration of the substrate. However, higher impact was observed in the basolateral side for MPA and its metabolite as reported in the additional plots reporting the concentration versus time profile in all compartments for the substrate and the metabolite (Figure S3). The current analysis clearly demonstrates that the reduction of the medium volume by sampling and/or evaporation should be experimentally measured and accounted for via mathematical modeling. However, it is not possible to generalize the bias of the sampling and the evaporation medium effect due to the dependency on the DMPK properties of the test compound.

Selection of the cell donors

Until pooled donor or other cell products representing population average drug metabolism/transport characteristics become available for OoC, the selection of cells derived from individual donors is crucial as it affects the concentration‐time profile of the drug, which has a direct impact on the human PK predictions.

There is a large interindividual variability in the activities drug metabolizing enzymes due to the influences of age, sex, enzyme induction by drugs and foodstuffs, and genetic polymorphisms. Some individuals may completely lack expression of functional CYP2D6, ³³ UGT2B10, ³⁴ or FMO ³⁵ due to genetic polymorphism. Expression levels of CYPs and UGTs have been seen to vary at least 10‐fold and frequently more than 100‐fold between different individuals. ³⁵ Individual donor variability was recently explored in commercially available batches of human hepatocytes by Horiuchi et al. ³⁶

The problem of donor variability has been addressed in other ADME assays by pooling of donors to generate a “population average” preparation of cells or subcellular fractions. This has the benefit of enabling better comparison of results among experimental systems, facilitating extrapolation of the data, avoiding undue influence of genetic polymorphisms/other individual donor characteristics, and improving experiment to experiment reproducibility. Mixed gender pools of human liver microsomes are routinely prepared with 150 or 200 donors and pooled hepatocytes for suspension cultures routinely include 10 or 20 donors. Donor pooling becomes more challenging for new experimental systems where the of different cells has not yet been established. Despite steady improvement in induced pluripotent stem cell and organoid‐derived cells, the requirement for in vivo relevant drug metabolism activities still results currently in the use of primary donor cells (as discussed here), and in particular the available donor‐derived hepatocytes that have the capability to be cultured within the OoC system. As with clinical data, many factors can affect hepatocyte drug metabolizing enzyme phenotype: donor genetic background, gender, age, prior use of drugs, diet, smoking or alcohol, underlying liver disease, and in addition also the preparation and storage of the cells. ³⁷ Selection of the donor may also be limited to lots of cells that can attach to a given OoC scaffold.

To enable extrapolation of the OoC results and modeling of drug metabolism to the wider population, the selected hepatocytes need to either (1) represent the population average across a wide range of drug metabolizing enzymes, (2) possess a specific phenotype that is well‐understood and relevant to the drug being studied, and (3) allow the calculation of the extrapolation factor (EF).

The activity distributions of 12 metabolic enzymes from 128 donors collated from the BioIVT database were investigated (Figure 5). Knowledge of the enzymes responsible for metabolism of the test drug (fraction metabolized) will ideally be available prior to the Gut‐Liver OoC experiment and will guide the selection of the most representative donors to get a “population average” value from the experiment. Indeed, the most representative donors for a certain fraction metabolized are within the 95% or even better the 67% interval of confidence (Figure 5). The normality of the distribution, mean, and standard deviation are reported in Table S5. For many enzymes, a clear deviation from normal distribution was noted (Shapiro's test coefficient <0.05), whereas the activity showed unimodal distribution (expect for CYP2C19) and consequently data were transformed using Box‐Cox transformations (Table S5).

FIGURE 5.

The distribution of the metabolic activities expressed as activity in pmol/min/Mio cells (available in the catalogue of BioIVT for the hepatocyte donors). The blue and red shaded lines represent the 95% and 67% of confidence interval. AO, ST, CYP, and UGT refer to aldehyde oxidase, sulfotransferase, cytochromes P450, and uridine 5′‐diphospho‐glucuronosyltransferase, respectively. Number of donors per isoform separated by gender is available in Table S5. Midazolam (MDZ) and testosterone (testos.) were used as probe substrates of CYP3A4.

Additional information, including the lambda distribution with confidence level of 95%, is shown in Figure S5. Further details on the metabolic activity correlation among enzymes, the investigation of the sex effect on the metabolic activity, and the outliers for the respective enzyme activity distribution are reported in the Supplementary Information in the paragraph “Analysis of the enterocyte and hepatocyte activities.” The gut cell metabolic activity evaluation is reported in the Supplementary Information “Gut metabolic activity,” Table S7 and Figure S6.

Optimization of the sampling points – MDZ case example

Optimizing the sampling times for the first experiment can reduce the number of experiments and improve the prediction of the DMPK parameters.

When performing an OoC experiment there are usually practical limits to the number of samples that can be taken as well as the times when personnel are available to collect the samples. One approach to experiment optimization is to perform a preliminary experiment using a standard protocol and on the basis of such results design the final experiment. Where the OoC system is well understood and there is prior (even if not completely accurate) information about the drug, a modeling approach can be used to better plan the OoC experiment often eliminating the need for a two‐step experimental process. This can be especially helpful when there may be a delay of many days between when a preliminary and follow‐up experiment might be performed (e.g., due to ordering of new chips or the time required to culture new cells).

The previous two sections reported the optimization of the OoC system setup and selection of the best cell donor. Final aspect to consider is the optimization of the sampling times (Figure 1b) and this approach is based on prior information to increase confidence in parameter value determination and to enable successful IVIVE. Because multi‐OoCs are generally used for drug candidates already selected based on available ADME data from standard in vitro systems, these existing data can be used to optimize the first OoC experiment. The optimization of the first experiment with the Gut‐Liver OoC is discussed here. Two factors are of particular importance, selection of the right timepoints to maximize the information obtained from the experiment and ensuring that the volume available for sampling does not interfere with function of the micro‐pump system or available nutrients for the cells. The number of samples are limited and they need to be carefully timed in order to obtain accurate and precise parameter estimates. Prerequisites include: (i) knowledge of all the system‐related parameters including the analytical sensitivity with the respective LOQ; (ii) the structure of the compartmental model; and (iii) existing data from standard in vitro systems, for example, P _app, from Caco2 cells, intestinal and hepatic clearance from primary cells, or HLM/HIM for a Gut‐Liver OoC experiment.

The proposed method can be divided into four main steps which starts with the acquisition of the in vitro input DMPK parameters from standard in vitro systems and ends with the verification of the selected sampling times (Figure 2). To illustrate these steps, MDZ has been selected as a case example making use of both literature and internal Roche data (Table S6). Midazolam 1'‐hydroxy Midazolam (1'‐OH‐MDZ) parameters that were estimated from the Gut‐Liver OoC are: P _app (MDZ), P _app (1′‐OH‐MDZ), CL_int,gut (MDZ), CL_int,hep (MDZ), and CL_int,hep (1′‐OH‐MDZ; Figure 1c). In this example, the sampled compartments are: the apical compartment, the basolateral compartment, and the liver compartment and samples are limited to three from each compartment. Concentration determinations of both MDZ and 1′‐OH‐MDZ were made from the same sampled volume of 50 μL for the basolateral and liver compartments and 20 μL for the apical compartment. Using the selected set of sampling times, the volume of the basolateral and liver compartments remained above the minimum volume recommended by the manufacturer of 2250 μL.

Step 1: Compound input parameter acquisition

Preliminary data might be used to build a preliminary compartmental model and input parameters to predict the most likely experimental outcomes of the first experiment (Figure 2, detailed system parameters are available in the Table S1). In the context of the optimization of the experiment, the uncertainty or the lack of knowledge is based on the expected heterogeneity between the input parameters used in the simulated experiments and the output from the actual experiment. The experimental uncertainty is comprised of (a) donor‐related biological variability of drug‐metabolizing enzyme activities, (b) analytical uncertainty, and (c) system‐parameter uncertainty (Figure 2; e.g., the gut‐liver flow rate and the number of viable cells). For a Gut‐Liver OoC system, four different scenarios with different uncertainty and mathematical application have been evaluated, as summarized in Table S8.

Midazolam case study. The in vitro Gut‐Liver OoC system applied for this example has the same characteristics as reported by Milani et al. ²⁴ Data for MDZ and 1′‐OH‐MDZ were collected from different sources and the same cells donor characteristics were applied as in the Gut‐Liver OoC study (data, source, and the respective uncertainty are reported in Table S6).

Step 2: Model identifiability and simulation of the most likely experimental outcome

After confirming the identifiability of the proposed mathematical model for in vitro DMPK parameters estimation was identifiable, two of the four previously described scenarios were analyzed as examples of different data sources. In the first example (scenario 2 in the “Methods”), OoC hepatocytes and gut cells were assumed to come from a different donor to those used in the prior in vitro parameter determination and the activity EF was used to simulate the most likely experimental outcome. In addition to the uncertainty from the scaling, parameter uncertainty was also included in the simulations. In the second example (scenario 4 in the “Methods”), it was assumed that the in vitro DMPK parameters from the hepatocyte and enterocyte CYP3A4 activities corresponded to the typical distribution of the activities from the BioIVT database and Ho et al. ³² (additional information in the Table S9).

The simulations correctly captured the distributions of the input parameters combined with the other uncertainties in a Gut‐Liver OoC device. It was evident that the fourth scenario resulted in larger variability within the 5th and the 95th percentiles (Figure 6b) compared to the first one (Figure 6a), which can be attributed to the large variability of CYP3A4 reported in both enterocytes and hepatocytes. In combination with the sensitivity analysis reported below, this simulation is also useful to avoid selection of sampling times potentially below the LOQ. The LOQ is a parameter that should be available before experimental work starts with the Gut‐Liver OoC because it depends on the medium composition and the analytical method used to quantify the compounds.

FIGURE 6.

Simulations from the midazolam case study with the 50th, 5th, and 95th percentile reported using either (a) the same cell donors or (b) scaling using the distribution of CYP3A4 reported in the enterocytes and hepatocytes from Ho et al. ³² and BIOIVT, respectively. Parameter distribution for the profiles reported in panel B are available in Figure S8.

Step 3: Global dynamic sensitivity analysis

An efficient and useful experimental design should consider a range of the most likely experimental outcomes based on the expected uncertainty of each predicted parameter. Concentration data in each compartment (e.g., concentration of the substrate in the apical side) provide information for the estimation of a certain parameter (e.g., P _app). However, this information is not the same in all compartments for every parameter. In addition, the utility of the information is also highly affected by the time at which sample is collected because it depends on the compound concentration and rate of change of concentration. For this reason, a global dynamic sensitivity analysis (GDSA) is more informative because it explores the variation of the prediction sensitivity over time. The method reported by Morris ³⁸ was used in the case study with MDZ. Because this is a variance‐based method, the parameters are provided with the respective associated uncertainty. In addition to the GDSA, the sampling time determination needs to take into account the concentration versus time profiles from the simulation (Figure 6a) to detect if at a given sampling time the drug and/or the metabolites are below the LOQ.

Midazolam case study. The parameter distribution in the GDSA considered in the MDZ case assumed that parameters were within two standard deviations in the log‐normal distribution (around 95% of the values) from scenario 1 (Figure 7a). From the scaling of scenario 1, the parameter distribution was a log‐normal distribution due to the exponential error used to introduce parameter uncertainty. The higher the value of sensitivity analysis (μ*), the greater the information of the parameter (P _app [MDZ], P _app [1′‐OH‐MDZ], CL_int,ent [MDZ], CL_int,ent [MDZ], and CL_int,hep [1′‐OH‐MDZ]) at that specific sampling time. The sensitivity signal (μ*) of P _app (MDZ) increased relatively quickly, in the apical side (highest value around 15 h) and even more in the basolateral side (highest value around ~5 h; Figure 7b), emphasizing the importance of sampling times at the beginning of the incubation in both compartments in order to have a high confidence in correct parameter estimation. Similarly, CL_int,ent (MDZ) and CL_int,hep (MDZ) had a rapid increase of μ* in the basolateral and liver compartments. Because a rapid equilibrium is established between the basolateral compartment and the liver compartment (Figure 6a), the GDSA showed a very high similarity in shape of concentration profile for both compartments and for every parameter (Figure 7b). Although the GDSA estimate suggested confidence in correct parameter estimation for three MDZ parameters within an incubation time of maximum 24 h, definition of the parameters for the metabolite 1′‐OH‐MDZ required an incubation of at least 48 h. Indeed, μ* for CL_int,hep (1′‐OH‐MDZ) was the highest after 48 h (Figure 7b). In addition, μ* for the P _app (1′‐OH‐MDZ) in the apical compartment reached its highest value around 24 h, but with a fast increase compared to CL_int,hep (1′‐OH‐MDZ). It is clear that the combination of the sampling times to use for the first experiment with MDZ in order to predict P _app (MDZ), CL_int,ent (MDZ), CL_int,hep (MDZ), P _app (1′‐OH‐MDZ), and CL_int,hep (1′‐OH‐MDZ) had to take into account the diversity of information generated for the five parameters over time. The decision to perform the experiment for a short incubation time and concentrate the sampling points at the beginning of the incubation might improve the prediction of the MDZ parameters, but at the same time it would reduce the accuracy of the metabolite parameters. In addition to the GDSA, a careful evaluation of the best sampling times needs to be performed in conjunction with LOQ values for all species and the medium of sampling. Assuming an LOQ of 0.001 μM for all species and in all compartments from Figure 6a, the LOQ was exceeded only at the end of the simulated incubation (>48 h) for MDZ in the basolateral compartment and liver compartment.

FIGURE 7.

(a) Distribution of parameters related to the uncertainty used in the concentration versus time profiles simulation for midazolam metabolism. The dotted and dashed lines represent the range of two standard deviations above and below the mean in the log distribution after the back‐transformation in the linear domain (the range that would be expected to include about 95% of the parameters in the distribution) and the median of the distribution, respectively. (b) The u* (intensity of the signal) for all estimated parameters over time. The respective sigma value from the Morris’ screening are provided in the Supplementary Information (Figure S9).

Step 4: Verification

The set of sampling times defined by GDSA (Table S10) were verified by the simulation‐estimation method. The simulated concentration‐time profiles of 100 experiments based on the parameter distribution information were fitted. The verification and comparison of estimated parameters was performed for both sets of sampling times (with and without GDSA refinement) using three replicate analyses.

Midazolam case study. The verification of the sampling times after the GDSA (Table 1) showed an improved predictability of the parameters, with rmse% less than or equal to 32% and aafe values close to 1 (Table S10). Evaluation of an experimental set up where last sample time in the liver compartment was set as 8 h instead of 24 h (all other sampling times were identical as above), had a significant impact on the accuracy of the estimate of CL_int,hep (1′‐OH‐MDZ). This finding is in agreement with GDSA which identified necessity for more extended sampling for this particular parameter (Table 1). The rmse% and the aafe were 2.3 and 2.7‐fold higher than in the experiment with the optimized sampling times. However, it is important to highlight that the outcome and the information generated from this analysis with MDZ is specific for this drug and in this specific design of the Gut‐Liver OoC. Therefore, a generalization cannot be made from this analysis for other drug molecules or other OoC systems and an ad hoc evaluation needs to be performed for each drug/cells/GLoC system combination.

TABLE 1.

Table reporting the verification of the sampling times from an optimized experiment and a suboptimized experiment (Table S10).

Parameter	Typical value	Median est.	rmse	rmse%	aafe
P app (gut) MDZ	324	323 (318)	19 (25)	6.6 (7.6)	1.0 (1.0)
P app (gut) 1′‐OH‐MDZ	324	316 (338)	96 (104)	29 (32)	1.0 (1.1)
CLint,gut MDZ	17	17 (17)	3.4 (3.3)	20 (20)	1.0 (1.0)
CLint,hep MDZ	105	106 (102)	20 (24)	19 (22)	1.0 (1.0)
CLint,hep 1′‐OH‐MDZ	7.0	7.2 (7.4)	2.2 (5.2)	32 (75)	1.2 (3.2)

Note: Outside and inside of the brackets are reported the statistic parameters for the optimized and sub‐optimized sampling times, respectively. The estimates were generated from sampling of 100 most likely experiments in replicate of three as reported in the “Methods” section.

Abbreviations: MDZ, midazolam; P _app, apparent permeability; CLint, in vitro intrinsic clearance.

After the first experiment with optimized sampling, the model used for the DOE can be applied for the parameter prediction. Selection of the best model is based on the Bayesian information criterion to avoid any model misspecification. If the model used for DOE is not the best after fitting, the user should repeat the experiment adapting the design and making use of the ADME parameters predicted from the first experiment (Figure 2b). In addition, the parameter uncertainty evaluation needs to be performed with the log‐likelihood method ²⁴ and therefore verified to ensure that the uncertainty is normal distributed around the predicted value. In case the uncertainty of any parameter does not meet the required variability for appropriate IVIVE, an additional experiment is required with the DOE method updated with the predicted parameters.

METHODS

System parameter optimization

This section reports the methodology used to generate the simulation reported in this tutorial using the in the Gut‐Liver chip (Figure 1a). A set of simulations was run to highlight the impact of the surface area/volume ratio of the gastrointestinal compartment, sampling volume, and medium evaporation on the experimental outcome. The specific information and input parameters used for the simulations are reported in Tables S2–S4. The codes in R are available in the Git‐Hub repository.

Gut compartment: Surface area and apical side volume of the transwell

Two different simulations have been performed to examine the input of these system features. Firstly, the typical commercial Transwell surface area and volumes, specified by the manufacturer, were investigated. The explored surface areas were: 0.143, 0.33, 1.12, and 4.67 cm² with corresponding apical volumes of 75, 100, 500, and 1500 μL, respectively. To highlight the effect of intestinal permeability, a low P _app value of the test compound (0.4 nm/s) and no metabolism in the gut and liver were assumed. Additional input parameters are reported in Table S1. Second, the impact of changing the surface area to apical volume ratio was explored by assuming transwells with 1/3, 1/2, one, two, and three‐fold of 1.12 cm² all with a constant apical volume of 500 μL. The other input parameters are reported in Table S2.

Sampling volume and medium volume evaporation

The sampling volume and medium evaporation are particularly important for OoC systems as These systems use low volumes and perform long‐term studies (increased loss of medium due to evaporation). Both of these factors affect the ratio between cells and the medium volume over time and may therefore lead to apparent nonlinearity in PKs in vitro.

Simulations to investigate sampling and evaporation were performed using input data and compound parameters for mycophenolic acid, as reported previously. ²⁴ The first set of simulations investigated the effect of sampling volume on (i) the volume of the apical side, (ii) the intestinal cell density in the apical side, (iii) the concentration of the test compound, and (iv) the amount of compound in the apical side. The most relevant information concerning the medium depletion are reported below, and further details are reported in Table S3. The sampling times considered in the simulations were 0.5, 1, 2, 8 h in the apical side with a variable sampling volume of 5, 15, 30, and 45 μL. The change in the medium volume due to sampling was explicitly included in the model. ²³ , ²⁴ In the second set of simulations, reduction in the medium volume due to sampling was set as 15 μL and evaporation was also considered. Evaporation in the apical and liver compartment was considered to follow a zero‐order process with a rate constant of 0 (no evaporation), 0.01, 0.03, and 0.05 μL/min based upon a value determined previously. ²⁴ The medium evaporation constant (k _ev) is evaluated with Equation 1:

$$k_{\mathrm{ev}}=\frac{V_{\mathrm{i}}-V_{\mathrm{f}}}{\text{incubation time}}$$ (1)

where V _i and V _f, represent the initial and the final medium volume, respectively. Although, both sampling and evaporation reduce the medium volume over time, the first process does not affect drug concentrations whereas the second does.

Selection of the cell donors

As with the selection of subjects for a clinical study, the selection of the cell cultures/cell donors is a highly influential experimental factor, as donors differ greatly in drug metabolizing enzyme and transporter activity. Intestinal and hepatic cell donors should be selected for the experiment based on the metabolic activity of the enzymes involved. Therefore, a statistical exploration of the activity distribution (pmol/min/Mio cells) was performed for potential sources of human hepatocytes. To this end, activity data were taken from the commercial BioIVT database (https://bioivt.com) for 128 different donors (database used in the analysis was downloaded in March 2020 and most recent version available at this link). The activity was reported based on specific probes for cytochrome P450s (CYPs) CYP2A6, CYP2B6, CYP2C8, CYP2C9, CYP2C19, CYP2D6, CYP2E1, and CYP3A4 (using both probe MDZ and testosterone as probe substrates), aldehyde oxidase (AO), UDP‐glucuronosyltransferase (UGT) UGT1A1, and sulfotransferase (ST). It should be noted that the activities of a given enzyme were not reported for all donors. Data from donors with unquantifiable activities were removed from the dataset and the statistical analysis. A similar approach was also considered for enterocytes, but the number of individuals with enzyme activity data was only 24 donors and was limited to UGT (7‐hydroxycoumarin as probe substrate), CYP2C8, CYP2C9, CYP2C19, CYP2E1, CYP3A4, CYP2J2, CES2, and ST enzymes. ³² As a first step, the distribution of activity data was evaluated. The investigation was performed with Hartigans's test for unimodality ³⁹ at a significance level (p) of less than 0.05. Test for normality of each enzymatic activity distribution was performed using the actual and normal distribution density (Q–Q plots) and Shapiro's test. A one‐way analysis of variance (ANOVA) test was performed to detect any significant difference in the enzymatic activity distribution between male and female hepatocyte donors (additional information about the applied method is available in the Supplementary Information). The script to run the statistical analysis is available in the github repository.

How can we account for variability in enzyme activity?

Accounting for the inter‐donor variability in the OoC simulations reflects the most likely distribution observed in the activity distribution for a certain enzyme in order to better reflect the clinical outcome. Because the activity distribution from the enzyme activity was generally demonstrated to be non‐normal, a simple use of the mean and the standard deviation to inform the model was not appropriate. The Box‐Cox power transformation is a common method to transform a non‐normal distribution into a normal distribution. ⁴⁰ Log and/ or Box‐Cox transformations were performed using the lambda values estimated using the maximum likelihood method. Every element in the distribution assumes a new value after the Box‐Cox transformation in accordance with the scheme below which is possible to use with positive values (Equation 2):

$$y\left(\lambda \right)=\left\{\begin{array}{cc}\frac{y^{\lambda }-1}{\lambda },& \text{if}\lambda \ne 0\\ \ln \left(y\right),& \text{if}\lambda =0\end{array}\right.$$ (2)

When lambda assumes a value of zero, the Box‐Cox transformation produces a log distribution of the original data. The lambda distribution based on the log‐likelihood profile was performed in order to find the lambda value of the distribution within the 95% confidence level.

Optimization of the sampling points

In this section, we reported the method to optimize the sampling times of the first experiment with a Gut‐Liver OoC (Figure 1a) using MDZ data from standard in vitro systems.

Model generation and identifiability assessment

To avoid overparameterization when setting up the OoC model structure, it is essential to test for structural identifiability prior to performing any experimental design or data analysis. Based on the OoC features (e.g., compartmental volume) and the expectation for the compound of interest, an a priori identifiability assessment can be performed without any experimental data. ⁴¹ , ⁴² To perform the identifiability assessment the only information necessary is the model structure, the compartments which can be dosed and the compartments from which samples can be taken. A structurally identifiable model does not automatically mean that all parameters are ultimately deterministically identifiable or can be estimated with high precision (see GDSA and optimal design part). However, if the model is not structurally identifiable, then parameter estimation should not be performed. Instead, alternatives should be considered, such as inclusion of sampling from additional compartments, additional conditions to the experiments (e.g., arm with an inhibitor of one of the PK processes described by the model), or decrease in the number of parameters estimated. ²⁴ A free software DAISY is applied for structural identifiability evaluation. ⁴²

Prior information to inform experimental design in organ‐on‐a‐chip

To simulate and potentially optimize an experimental design for more successful in vivo translatability, prior information is needed. This information can originate from experimental data of other established in vitro systems or from pilot OoC studies. For the Gut‐Liver OoC, the minimal information required includes intestinal and hepatic intrinsic clearance and intestinal permeability. The level of confidence required in a parameter estimate (e.g., the standard error) is also relevant because it influences the most likely experimental scenario with direct consequences for the DOE. In the context of the optimization of the experiment, the uncertainty is based on the expected heterogeneity between the input parameters and the output from the actual experiment. Higher confidence in the experimental design will be achieved if the prior information comes from experiments using the same hepatocyte and enterocyte donors as used in the Gut‐Liver OoC. As preliminary data for the DOE, the intestinal and hepatic clearances from high‐throughput screening assays run using suspended enterocytes and suspended hepatocytes can be extremely informative for the DOE. In addition, the intestinal permeability might be evaluated in Caco2 cells which are the standard cells for P _app investigation. The different scenarios and their respective scaling methods are reported in full below and are summarized in Table S8. The expected clearance from the Gut‐Liver OoC (CL_OoC) is extrapolated (Equation 3) based on the EF which changes for each of the scenarios described below and the clearance of the test compound in the reference in vitro model mediated by enzyme x (CL_ref). All the parameters extrapolated using the methods described above need to include their own uncertainty from the experiment with a standard system; this is implemented by inclusion of a random effect.

$${\mathrm{CL}}_{\mathrm{OoC}}=\mathrm{EF}·{\mathrm{CL}}_{\mathrm{ref}}·e^{\mathit{\eta i}}$$ (3)

The parameters η_i were normal distributed with mean 0 and standard deviation determined by the uncertainty of the CL_ref.

Different scenarios of prior information

Scenario 1: Preliminary data originate from the same cell donor. This information will significantly improve the translation from available experimental data to the OoC, as in this case the expected experimental uncertainty is determined only by the parameter uncertainty and not by additional inter‐donor variability because EF₁ = 1.

Scenario 2: Preliminary data originate from a different cell donor but enzyme activities of both donors are known. Data originating from different cell donors than those used in the Gut‐Liver OoC can also be applied if the activity of the major enzyme isoforms has been measured. In this case, CL_OoC from different donors can be extrapolated using the EF (EF₂, Equation 44). Scaling should be performed based on the major metabolizing enzyme.

$${\mathrm{EF}}_2=\frac{{\text{Activity}}_x\mathrm{OoC}}{{\text{Activity}}_x\mathrm{ref}}$$ (4a)

where Activity _x OoC and Activity _x ref, represent the typical activity of the donor used in the OoC model and the reference in vitro model. A limitation of this method is the general lack of knowledge of the major metabolic enzymes during the initial stages of drug development. Alternatively, a representative pool of human suspended hepatocytes can also be used and the median of the pool metabolic activity of a certain enzyme isoform (Activity pool _x ref) can be used to obtain EF₂:

$${\mathrm{EF}}_2=\frac{{\text{Activity}}_x\mathrm{OoC}}{{\text{Activity pool}}_x\mathrm{ref}}$$ (4b)

Scenario 3: If prior experiments were performed with pooled HLM, an extrapolation to clearance per million cells is required in order to use this information in the OoC system. Due to differences in enzymes and cofactors present, this approach is limited to those metabolic enzymes which are present and active in both microsomes and hepatocytes. However, in the absence of any other data, the EF (EF₃) can be used, as shown in Equation 5.

$${\mathrm{EF}}_3=\text{tvMPPGL}{e}^{\mathit{\eta i}}\frac{1}{\mathrm{HC}}$$ (5)

where tvMPPGL the milligram of protein per gram of organ of the cells donors (usually considered as 40 mg protein per g of liver), η is the individual random effect ($i$) of MPPGL, $i$ is a sample of individual $i$ which originates from a normal distribution with zero‐mean and variance ω and HC is the hepatocellularity which is generally considered 120 × 10⁶ cells per gram of liver. ⁴³ , ⁴⁴ , ⁴⁵ , ⁴⁶ Contrary to the previous EF₁ and EF₂ values, which were dimensionless, EF₃ has units of mg of protein/number of cells ensuring appropriate unit conversion. Although, not commonly available, the MPPGL of the hepatocyte donor can be applied as reported in Equation S1 when known. However, the proposed scaling has a certain limitation due to the difficulty to link the protein concentration with the actual metabolic activity of a given donor.

Scenario 4: Preliminary data originate from a different cell donor and enzyme activity is unknown. This scenario carries the largest uncertainty and relies on the characterization of the enzyme distributions presented above. This method is very useful when input CL_OoC comes from a source which does not report the lot number or when the user wants to investigate a larger range of variability in the DOE.

First, the clearance is extrapolation based on the activity of the predominant enzyme Activity_xOoC using the typical lambda of the power‐transformation of the activity distribution, as reported in Equation 2. The random effect due to the standard deviation in the Box‐Cox domain is also reported (${\eta }_i\mathrm{BC}$) as additional error (Equation 6a). Afterward, the obtained Activity_xOoC_BC in the Box‐Cox domain is back‐transformed to the linear domain as Activity_xOoC with Equation 6b. The Activity_xOoC is divided by the median of the activity distribution for the probe substrate for the x enzyme to get the EF (EF₄; Equation 6c) which is used for the scaling of clearance.

$$\text{Activityx}{\mathrm{OoC}}_{\mathrm{BC}}=\frac{\text{Activity}{\mathrm{OoC}}^{{\mathrm{\lambda }}_x}-1}{\lambda }+{\eta }_i\mathrm{BC}$$ (6a)

$$\begin{array}{c}\text{Activityx}\mathrm{OoC}=e^{\frac{\ln \left(\text{Activityx}{\mathrm{OoC}}_{\mathrm{BC}}·{\mathrm{\lambda }}_x+1\right)}{{\mathrm{\lambda }}_x}}\hfill \end{array}$$ (6b)

$${\mathrm{EF}}_4=\frac{\text{Activity}{\mathrm{OoC}}_x}{\text{Median}\left(\text{Activity}{\mathrm{OoC}}_x\right)}$$ (6c)

The scaling of the intestinal permeability data is performed using the surface area of the transwell used (Equation 7):

$${\mathrm{CL}}_{\text{perm}}\mathrm{OoC}=P_{\mathrm{app},\mathrm{ref}}\mathit{SA}$$ (7)

where ${\mathrm{CL}}_{\text{perm}}\mathrm{OoC}$ is the intestinal permeability predicted in the Gut‐Liver OoC, $P_{\mathrm{app},\mathrm{ref}}$, and SA are the in vitro intestinal permeability from the standard in vitro experiment and the surface area of the transwell in the Gut‐Liver OoC experiment, respectively.

In addition to the drug‐related parameters, the user is free to investigate and introduce any additional uncertainty based on the experimental system and condition for a given parameter (P). Indeed, uncertainties in the intercompartment medium flow rate (Q) unbound fraction, or medium evaporation might also be introduced (Equation 8).

$$P_i=P{e}^{\mathit{\eta i}}$$ (8)

Simulation of experimental outcomes

In order to demonstrate the practical use of the proposed in silico workflow, an experiment was simulated using data for MDZ and its metabolite 1′‐OH‐MDZ (Figure 1c and more details are available in Figure S7). Midazolam was administered in the apical compartment and passively absorbed across the intestinal cells to reach the basolateral compartment. In the enterocytes, MDZ is metabolized by CYP3A4 to form 1′‐OH‐MDZ which is able to exit the cells on both apical and basolateral sides. In addition, MDZ is metabolized in the hepatocytes to form the same metabolite, which diffuses out from the hepatocytes into the hepatocyte medium compartment, which equilibrates with the basolateral compartment via medium flow. 1′‐OH‐MDZ from the basolateral side may permeate into the apical compartment. The 1′‐OH‐MDZ is also further metabolized by glucuronidation in the hepatocytes. The estimated parameters are: P _app (MDZ), P _app (1′‐OH‐MDZ), CL_int,gut (MDZ), CL_int,hep (MDZ), and CL_int,hep (1′‐OH‐MDZ). The input data were reported as the typical value with associated uncertainty and are given in Table S9. In addition, the system‐parameters, such as the interconnection gut‐liver medium flow rate (Q), the number of enterocytes, and hepatocytes were included. The uncertainty was based on the data reported by Milani et al. ²⁴ where an uncertainty in Q of 20% was defined by the system provider (CN Bio Ltd.), whereas the uncertainty in the number of cells was 15% based on the measured inter‐well variability. ²⁴ Additional parameters were the unbound fraction of the drug and the metabolite in the apical and basolateral medium used in the experiment, which were predicted from the fraction unbound in plasma, assuming the same affinity to human albumin and body surface area ²³ (Equation S2 reported in the Supplementary Information). The experimental observations were the concentration of MDZ and 1′‐OH‐MDZ in the apical, basolateral, and liver compartments. The 2500 experiments were simulated in order to have a large number of possible scenarios. The compartmental model was generated with five ordinary differential equations (ODEs) for the substrate and five additional ODEs for the metabolite (Figure S7). In addition, the metabolic clearance was assumed not to be limited by cell permeability. All parameters with their respective uncertainty and the model structure are reported in the Supplementary Information (Table S9). The 2500 profiles were summarized and reported as the 50th, 5^th, and 95th percentiles.

Global dynamic sensitivity analysis

A critical first step for the design of an experiment involves a GDSA. ²⁴ There are different methods available to perform a sensitivity analysis with the two most common being the variance‐based method. ³⁸ , ⁴⁷ Performance of a sensitivity analysis requires selection of input parameters. The range of the five estimated in vitro DMPK parameters for performing the GDSA was chosen based on simulation results, specifically selecting the values that fell within the 95% confidence interval. Whereas the other parameters were fixed at their typical value. The GDSA was performed with Morris's variance‐based method, ³⁸ as this has been used previously for the Gut‐Liver OoC. ²⁴ The GDSA provides two major outputs: μ _i * and σ _i . The μ _i * is a measure for the overall influence of input x _i (e.g., clearance) on the output (i.e., concentration‐time profiles), the higher the value, the stronger the impact. The σ _i reflects the linearity of the influence, a parameter with σ _i close to 0 suggests linear behavior, whereas a large value of σ _i suggests a nonlinearity or interaction among the parameters. A visual inspection of how μ _i * changes over time can identify influential sampling times for a given parameter i and compartment.

Verification of the proposed sampling points

In order to assess the validity of the selected sampling times from the GDSA, a simulation‐estimation approach was applied. ²³ From the 2500 simulated experiments, 100 were sampled having all five in vitro DMPK parameter values in the confidence interval used in the GDSA. The 100 simulated experiments were fitted in order to back estimate the five DMPK parameters. The experiments were sequentially used as input files in Phoenix 64 (8.3.5.340) using the library RsNLME available in R. The number of replicates (n) was generated by copying n times the selected experiment and by adding a residual unexplained variability (RUV) of 15%. The addition of the RUV permitted generation of experiment replicates with the same parameters but having different observed concentrations based on the analytical uncertainty, cell manipulation, or any experimental variability due to manual procedures. The model structure applied in Phoenix 64 had the same characteristic of that applied to generate the simulated experiment. In addition, with the purpose to verify the model with actual experimental conditions, the parameters affected by uncertainty were considered as fixed in Phoenix and corresponding to their typical values (e.g., number of cells). The verification of the sampling times from the GDSA was evaluated using the median, the root mean square error (rmse), the rmse%, and the absolute average fold error (aafe; Equation 9) from the DMPK parameters obtained by the 100 simulated experiments. The aafe was generated with the Equation 9:

$$\text{aafe}={10}^{\frac{1}{n}{\sum }_i\left|\mathit{log}\frac{x_i}{\widehat{x_i}}\right|}$$ (9)

where n is the number of observations, and x _i and x̂ _i are the predicted and observed parameters, respectively.

Software tools

All the in silico evaluations were performed in R (4.1.2) and more specifically diptest (0.76–0) was applied for the Hartigans's test for unimodality; stats (4.1.2) was applied for the evaluation of the normality of the enzymatic activity distribution; corrplot (0.92) was applied for the graphical visualization of the correlation matrix between different enzyme activities; forecast (8.16) and AID (2.7) was applied for the Box‐Cox transformation and normality and homogeneity (Barlett's method) investigations; MASS (7.3–54) was applied in order to find the lambda value of the Box‐Cox transformation of the distribution within the 95% confidence level, and onewaytests (2.6) for the ANOVA test. The ODE solver applied to generate the simulations was RxODE (1.1.4). The sensitivity analysis was performed with ODEsensitivity (1.1.2), and the fitting of the simulated data with the commercial R package Certara.RsNLME (1.1.0; Certara). The graphic representation was performed in ggplot2 (3.3.5).

CONCLUSIONS

The OoC systems offer the promise of more in vivo‐like tissue phenotypes and long‐term experimental performance, thus potentially providing systems better suited for IVIVE and human PK predictions via PBPK modeling. The complexity of these multi/tissue, multicompartment systems require appropriate modeling approaches for data analysis and simultaneous to derive multiple DMPK parameters. In addition, mechanistic modeling can be used to plan meaningful experiments and derive unbiased and accurate ADME parameters from such in vitro experiments for subsequent PBPK modeling to predict PK and DDI. This tutorial proposes a general in silico workflow to improve the preclinical decision when complex OoC devices, such as the Gut‐Liver OoC, are applied in DMPK. It clearly illustrates the necessity for optimized experimental conditions to obtain accurate DMPK parameters to be used for IVIVE. In addition, the approach illustrates the informative use of prior experimental data from standard in vitro systems, together with modeling, to predict the best sampling condition and support experimental design in complex OoC systems.

FUNDING INFORMATION

This study was funded by F. Hoffmann‐La Roche Research Postdoctoral Fellowship programme (N.M.).

CONFLICT OF INTEREST STATEMENT

The authors declared no competing interests for this work.

Supporting information

Data S1

Milani N, Parrott N, Galetin A, Fowler S, Gertz M. In silico modeling and simulation of organ‐on‐a‐chip systems to support data analysis and a priori experimental design. CPT Pharmacometrics Syst Pharmacol. 2024;13:524‐543. doi: 10.1002/psp4.13110

DATA AVAILABILITY STATEMENT

Data made publicly available by BioIVT. Data accessed March 2020.