Physiologically based pharmacokinetic (PBPK) modelling tools: how to fit with our needs?

ABSTRACT

In 2005, a survey compared a number of commercial PBPK software available at the time, mainly focusing on ‘ready to use’ modelling tools. Since then, these tools and software have been further developed and improved to allow modellers to perform WB-PBPK modelling including ADME processes at a high level of sophistication. This review presents a comparison of the features, values and limitations of both the ‘ready to use’ software and of the traditional user customizable software that are frequently used for the building and use of PBPK models, as well as the challenges associated with the various modelling approaches regarding their current and future use. PBPK models continue to be used more and more frequently during the drug development process since they represent a quantitative, physiologically realistic platform with which to simulate and predict the impact of various potential scenarios on the pharmacokinetics and pharmacodynamics of drugs. The ‘ready to use’ PBPK software has been a major factor in the increasing use of PBPK modelling in the pharmaceutical industry, opening up the PBPK approach to a broader range of users. The challenge is now to educate and to train scientists and modellers to ensure their appropriate understanding of the assumptions and the limitations linked both to the physiological framework of the ‘virtual body’ and to the scaling methodology from in vitro to in vivo (IVIVE). Copyright © 2012 John Wiley & Sons, Ltd.

Introduction

As the time and cost required in developing a new drug increase, the research and development (R & D) budgets and spending of the pharmaceutical industry have consequently increased vastly during the past decade. Between 2001 and 2010 the number of new drug approvals has remained more or less stable at around 23 per year [1]. This stability in the approval rate can be reasonably explained by the decrease in the number of applications filed by pharmaceutical companies over the past 15 years [1]. In the same period of time, the economic environment has constrained governments of developed countries to limit their spending in health care with, in particular, a strong control of the price policy for marketed drugs. These trends have led to mergers of several pharmaceutical companies and to reductions in R & D staff and budgets over the past few years [2]. Thus, the urgent challenge to the pharmaceutical industry is the improvement of R & D efficiency in the selection and development of only the molecules that are most likely to become new drugs. Modelling and simulation (M & S) plays an increasingly important role in this challenge, as it has already been essential in the aircraft industry; for example in the 1990s, the Boeing 777 was the first jetliner to be 100 percent digitally designed using three-dimensional computer graphics [3]. Indeed, the value of M & S and in particular pharmacokinetic/pharmacodynamic (PK/PD) modelling, and its use as early as possible in the drug development process is now well established [4, 5, 6, 7, 8].

Among the various modelling approaches currently employed in the field of pharmacokinetics, the physiologically based pharmacokinetic (PBPK) approach has been recognized to ‘have great potential to assist in the optimal design, selection and development of drugs’ as demonstrated in a workshop held in Washington, D.C in 2002. [9]. At the time, PBPK modelling was already commonly used and well accepted in the field of risk assessment [10], but its use was limited in pharmaceutical research and development for several reasons [11], such as the lack of appropriate training and education for modellers, the complexity of the models and the code required to write them.

Over the 10 past years, the number of articles involving PBPK modelling has largely increased, demonstrating the widespread use of this approach within the scientific community [12, 13, 14, 15, 16, 17, 18]. Moreover, pharmaceutical companies are now including this modelling approach in dossiers submitted to the regulatory agencies: between 2008 and 2010, the FDA reviewed seven investigational new drug (IND) and six new drug applications (NDA) containing PBPK modelling and simulations [19], many more than the number of submissions received previously.

Whole body physiologically based pharmacokinetic (WB-PBPK) models are pharmacokinetic models consisting of a physiologically realistic compartmental structure into which input parameters from different sources (e.g. in silico predictions, in vitro or in vivo experiments) can be combined to predict plasma and tissue concentration–time profiles. Consequently, one of the key reasons behind the development and the improvement of this modelling approach is the availability of sophisticated software tools allowing the integration of the physiological structure, biochemical mechanisms and drug-related properties.

In 2005, an interesting survey was published [20] comparing several commercial PBPK software packages available at that stage, mainly focusing on ‘ready to use’ PBPK tools. Since then, further development of these tools has increased their levels of sophistication, while also aiming to increase their accessibility to the wider scientific and pharmaceutical community through improvement of their graphical user interfaces and detailed training and technical support [21, 22, 23, 24]. This review briefly compares the features of two main types of software currently used for PBPK modelling, and summarizes their values and limitations. The first category, referred to as ‘open’ software in this review, denotes those software packages which are not specifically designed with PBPK modelling in mind and which require the user to write and code his own model equations and functions. The second category, referred to as ‘designed’ software, comprises the aforementioned ‘ready to use’ PBPK tools which have been developed expressly for PBPK modelling and as such have several additional functionalities and ‘user-friendliness’, geared to enable their widespread use for this purpose.

Materials and Methods

PBPK model structure and parameterization

PBPK models differ from classical PK models (e.g. one- or two-compartmental PK models) in that they traditionally employ what is commonly known as a ‘bottom-up’ approach, as opposed to the ‘top-down’ approach [21] of classical models. This implies that, rather than estimating model parameters based on in vivo data (usually in the form of plasma or blood concentration versus time profiles), parameters are determined a priori from in vitro experiments, in silico predictions, or in vivo data when required. However, it is also possible to use a mixture of ‘bottom-up’ and ‘top-down’ approaches while maintaining the physiological structure and parameterization of the PBPK model, and estimating certain parameters for which it is deemed necessary. The nature of the PBPK model structure – where compartments represent either individual organs or groups of physiologically similar organs – allows the majority of the model parameters to be thought of as physiologically meaningful since they represent real body systems such as tissue volumes and blood flows, and biochemical processes such as enzymatic drug metabolism and transporter-driven membrane transfer. It is helpful to consider a PBPK model as being composed of two main parts – an anatomical ‘backbone’ which contains species-specific physiological parameters which are not dependent on the drug and can therefore be applied to any compound, and then the drug-specific part which consists of the individual drug's ADME properties applied to the relevant processes within each tissue compartment.

An example of a relatively simple PBPK model is depicted in Figure 1. This shows the individual organs relevant to the various pharmacokinetic processes (e.g. liver, kidneys, intestine) and grouped tissues with physiologically and pharmacokinetically similar properties, which are all interconnected by the systemic circulation, which is often divided into arterial and venous blood flows. A series of mass-balance differential equations describe the rate of change of the amount of drug within each compartment, including the major process contributing to the fate of the drug in the system [11, 12]. These physical, biochemical and physiological processes play a role in the absorption, distribution and elimination of a drug, and therefore have to be precisely and accurately translated by mathematical equations on the basis of several assumptions. The accuracy of the prediction of these processes by the model depends both on the present knowledge of physiology, and on the biochemical mechanisms known to be important for the drug(s) studied [12]. For some tissues or processes, the choice of model structure or equations can be complicated by the existence of several different options reported in the literature. Some examples are briefly discussed below.

Figure 1. Structure of a whole-body PBPK model. Compartments represent organs or tissues, arrows represent blood flows

The well-stirred model is the most commonly employed way to model hepatic clearance, due to its widespread use and its mathematical simplicity [24]. However, for some extensively metabolized drugs, the liver clearance may be better predicted using more mechanistic models which either consider the liver as a series of parallel tubes in which the concentration of the drug decreases along the length of the tubes (the parallel tube model), or a single compartment assuming axial dispersion, resulting in an intermediate degree of mixing (the dispersion model) [25]. It may not be clear a priori which model will perform the best; often a modeller will have to test several or all of the options available before making a decision.

For highly permeable drugs, distribution into tissues can often be described simply by a flow-limited model, which assumes passive membrane diffusion and a homogeneous tissue concentration of the drug that is in instantaneous equilibrium with the blood concentration. However, for compounds that are substrates of active drug transporters (efflux, uptake or both), their tissue uptake may also be influenced by their membrane permeability and the capacity and affinity of one or more transporters [26]. In this case, the membrane rate-limited model may be more appropriate, as it divides the tissue into two (or more) compartments to separate the tissue from its vasculature, or the intracellular space from the extracellular fluid. Furthermore, the individual or combined effects of uptake or efflux transporters can be applied at the relevant membrane by including their terms in the mass transfer rate equations. Transporters have a significant impact on the liver distribution of a drug and consequently have an impact on the overall rate of hepatic metabolism. Several recent publications have highlighted the importance of active transporter-driven uptake on the hepatic disposition of certain types of drugs, such as statins, and some have proposed mechanistic models separating active uptake from intrinsic metabolism in hepatocyte incubations [27, 28]. Since the aim of such models is to extrapolate the experimentally determined uptake and clearance parameters to their in vivo equivalents, the next logical step is to incorporate them into a PBPK model, as has been done by Paine et al.[29], and others. This differs from the approach of Pang and Durk [30], since the latter PBPK model further incorporates transporter processes, which are estimated from fitting to in vivo concentration data. These two approaches highlight the increasing flexibility of PBPK models and their implementation; while fitting to in vivo data was previously thought to be a feature of classical models, it can be useful to fit certain PBPK model parameters for which in vitro data are lacking or IVIVE scaling factors are not well established.

The combined effects of several processes on a single tissue are particularly well illustrated when simulating oral absorption in the gastrointestinal (GI) tract with more complex tissue models such as the one shown in Figure 2. As a compound passes along the GI tract lumen and is exposed to the apical membrane of the enterocyte layer, it will cross this barrier at a rate that is influenced by physiological (size, surface area), physicochemical (pH, dissolution rate) and biochemical (metabolism enzymes, transporters) processes that vary along the length of the GI tract from the duodenum to the colon. Various GI tract models have been proposed, among the most sophisticated of these are Simcyp's advanced dissolution, absorption and metabolism (ADAM) model [31], and the intestinal models included in Gastroplus [32] and PKSim [33]. More in-depth comparisons of the various GI models are available in the literature [34].

Figure 2. Structure of the gut model [28]. Each section is composed of three ‘layers’: the lumen, the epithelium (including metabolism/elimination – M or E – and transporter efflux – P-gp – if needed) and the wall (intestinal mucosa). A compartment representing the portal vein collects blood flows coming from the six sections and goes directly to the liver

Once the physiological model structure has been chosen and translated using adequate mathematical equations, the choice of appropriate physiological input parameter values presents another challenge for the model developer or user. Among the most important physiological parameters to consider are body weight, tissue volumes, cardiac output, tissue blood flows, tissue composition, enzyme and transporter abundances, and membrane surface areas. Obviously, these parameter values vary from one species to another, but they also vary within a single species due to interindividual variability, or even within a single individual as a function of age, genetic polymorphisms and disease state. When the known variability of the physiological parameters is incorporated into the model, a realistic population composed of many subjects can be simulated, rather than a single average individual. Therefore the accuracy of PBPK model predictions is not solely dependent on obtaining accurate drug-specific parameters and their IVIVE scaling methods, but also on the choice of physiological parameter mean values and their variabilities. It is therefore important to maintain an up to date knowledge of the literature, in order to ensure the use of the latest published values and the impact of these parameters on predictions in published examples. Many modelling groups and PBPK software companies keep extensive databases to achieve this task – at Servier, for example, this physiological parameter database is directly linked to the PBPK modelling software to provide the model with physiological parameters as soon as they are updated. All relevant preclinical species (e.g. rat, dog, monkey, human) and human target populations (e.g. Caucasians, Japanese, healthy volunteers, hepatic insufficiency) must be included in the database. A large number of these parameters are available in literature [35, 36], although some of them are still missing, and still others show such a wide variability that the choice of the appropriate value is not straightforward.

The drug-specific elements of a PBPK model include the drug's membrane permeability, plasma and tissue protein binding, blood-to-plasma ratio, tissue-to-blood partition coefficients (K_p) and intrinsic clearances for both metabolic and transporter-driven processes. These properties define how the drug behaves in a physiological system. These model input parameters are derived either from in silico predictions based on the chemical structure (logP, pK_a, polar surface area), from in vitro experiments designed to mimic certain bodily environments, or from in vivo measurements. In 2007, Fagerholm evaluated the various methods available for the scaling of in vitro measurements for the prediction of hepatic metabolic clearance [37], renal clearance [38], intestinal metabolism [39] and absorption [40], and volume of distribution [41]. This in vitro-in vivo extrapolation (IVIVE) can be considered a part of the foundation of PBPK modelling.

Modelling tools/software

As mentioned, we have divided the software currently used for PBPK modelling into two categories – open and designed software. Some examples from both categories are listed in Table 1. Many of the examples given of open software were originally developed for the engineering and mathematical disciplines, while nowadays their applications have been expanded to include pharmacokinetic and PBPK modelling. This was a natural transition, since PBPK models belong to the same class of dynamic systems (linear or non linear) that are commonly applied in engineering. Before the advent of more specialized PBPK tools, users were limited to writing their own models from scratch using these software, requiring them to learn the specific coding language used in the software, as well as their expertise in the fields of physiology and pharmacokinetics. As such, a PBPK modeller was required to have a wide grasp of these inter-disciplinary and programming skills. More recently, some of these software have included specific PK and PBPK modules and equation libraries, combined with a visual graphical interface. These additions can allow the rapid generation of a standard PBPK model template, which already contains the standard code and equations. Some examples in this class are acslX, WinNonlin Phoenix, MATLAB-Simulink, SAAM, ADAPT, MCSIM, NONMEM and Berkeley-Madonna.

Table 1. Some of the commonly used software and tools currently used to perform PBPK modelling

Open software	acslX	http://www.acslx.com
	(Aegis Technologies)
	MATLAB-simulink	http://www.mathworks.com
	(The Mathworks Inc.)
	ADAPT 5	http://bmsr.usc.edu/
	(University of Southern California)
	Berkeley-Madonna	http://www.berkeleymadonna.com
	(University of California)
	MCSIM	http://www.gnu.org/software/mcsim/
	SAAM II	http://depts.washington.edu/saam2/
	(University of Washington)
Designed software	Cloe PK	http://www.cyprotex.com/cloepredict/
	(Cyprotex Ltd)
	GastroPlus	http://www.simulations-plus.com
	(Simulations Plus Inc.)
	MEDICI-PK	http://www.cit-wulkow.de/
	(Computing in Technology)
	PK-Sim	http://www.systems-biology.com
	(Bayer Technologies Services)
	Simcyp Simulator	http://www.simcyp.com
	(Simcyp Ltd)

The category referred to as designed software appeared around the beginning of the 21st century, and has since undergone vast development and improvement. Several members of this type of software were originally intended to model one specific area of the ADME process, such as absorption (Gastroplus) or metabolism (Simcyp), but have since evolved into sophisticated whole body PBPK modelling tools. Other examples of this type of software are provided in Table 1. Software of this type consists of a pre-coded PBPK framework, with the equations generally hidden ‘behind the scenes’, combined with all of the necessary physiological parameters which may or may not be available to be modified by the user, along with their variability and correlations where possible. These types of software aim to provide modellers with a user-friendly interface with which to enter drug-specific parameters, and to select certain model options in order to perform various tasks such as simulation, parameter estimation and sensitivity analysis. The model structure may be more or less flexible, depending on the particular software, and may allow the choice between flow-limited or permeability-limited tissues, modification of the study design, the target population, and so on.

Results

The open software originating from the engineering disciplines allow the building of any mathematical model on the basis of a specific coding language and, in some cases, with the support of a graphical user interface (GUI). This interface allows the graphically aided connection of predefined (equations already written) building blocks to obtain the complete structure of the intended model. Figure 3 gives an example of a WB-PBPK model written in acslX, with the GUI showing the model compartments and their connections with the systemic circulation, and the model code for one of the compartments (liver) which can be freely edited by the user.

Figure 3. PBPK model built from the graphical user interface (GUI) of the acslX software

This open source environment gives complete flexibility for users to define the model structure, to write or modify the equations, to specify their own parameter values, and to adapt all these to the needs, the knowledge and the specific questions arising at the time of model development. Since the modeller completely controls the model equations and the development process of the PBPK model he/she can adapt the system to include new parameters coming from the team performing the in vitro experiments or new IVIVE insights recently mentioned in literature. The testing exercises (‘what if’ questions) are in theory limited only by imagination, with a healthy dose of reality given the physiological boundaries or knowledge of the drug. Of course, with such power comes great responsibility, and a modeller who makes a change or addition to the standard PBPK model structure or its parameters must clearly state this change, along with the scientific reasons behind it, so that theoretically another modeller could understand and reconstruct the process if required.

Aside from WB-PBPK modelling, perhaps one of the greatest strengths of open software is the possibility to ‘scale down’ – to reconstruct mathematically a single organ or cellular system in order to align it with data obtained in its corresponding in vitro environment. This has seen increasingly widespread popularity among certain groups, notably that of Sugiyama, whose publications cite the use of SAAM for their reported PBPK models of hepatic uptake and biliary clearance of pravastatin [42], concentration-dependent intestinal permeability of P-gp substrates [43], and others. The group of Pang have also been instrumental in contributing new insights into physiological modelling of transporter-mediated processes and metabolite kinetic, again using open modelling software to write and solve their models of intestinal and zonal hepatic transport and metabolism, which when incorporated into WB-PBPK models are able to account for phenomena such as route-dependent metabolism which were not explainable when using simpler, more standard PBPK models [44]. Within the pharmaceutical industry, several publications by the R & D DMPK group of AstraZeneca have also reported the use of software such as WinNonlin and Berkley Madonna in the construction of their hepatocyte PBPK models [29, 45, 46].

In order to take advantage of all of the features of open software, modellers have to obtain sufficient expertise in the programming language and the modelling process itself. When writing somewhat complex models such as those cited above, it is difficult to ‘just muddle through’: an inexperienced user may spend a long time trying to debug the program, or may make incorrect assumptions or mathematical errors without being highlighted to this fact. These problems will obviously increase with the model's complexity. This additional complexity may arise from a greater number of model compartments, more mechanistic structure in certain influential compartments (e.g. the GI tract), and the modelling of multiple compounds simultaneously; such as metabolites, inhibitors and co-administered drugs. And it is not merely enough to know how to develop a model and run a simulation – useful outputs such as graphs, tables and reports must also be created and organized which may require further coding and knowledge of the specific software.

As mentioned previously, it is desirable to maintain an up to date database of physiological parameters from which to feed the PBPK model. Despite this, many of the recently published examples using PBPK modelling cite the ‘standard’ publications by Davies et al.[35] or Brown et al.[36], which date from 1993 and 1997, respectively. The probable reason for this is that they are fairly comprehensive, and in the case of Brown et al., specifically published with the intention of their use in PBPK models. The advantage of using these values is that they are ‘tried and tested’, therefore consistent with other groups who use the same parameters. An obvious disadvantage is that these publications are over 10 years old, and therefore more recently obtained values perhaps measured with more sophisticated experimental techniques could potentially be more accurate. However, the challenge of building and maintaining a comprehensive, up to date physiological database can be both resource-heavy and time consuming, particularly for small modelling teams in the highly charged environment of industrial drug development.

The designed software requires less mathematical and programming skills as they propose a ready to use interface (‘user-friendly’) to facilitate the selection of a model structure. A modeller does not need to learn the programming language required to code the PBPK model; the code is ‘hidden’ in the internal workings of the software. The five designed software mentioned in this review allow the building of a generic WB-PBPK model with the same objective: to provide blood and tissue concentration profiles after single or multiple administration of the drug(s) of interest. They also have their specificities depending on the skills of their development teams and their history. The main features of each software are summarized in Table 2.

Table 2. Summary of the features of selected designed software for PBPK modelling

	ChloePK	GastroPlus	Medici-PK	PK-Sim/MoBi	SimCyp
Species	Human, rat, mouse	Human, rat, dog, mouse, monkey and user defined	Species can be defined and configured arbitrarily, e.g. human, rat, mouse, dog, no fixed set	Human, rat, dog, mouse, monkey, minipig	Human, rat, dog, mouse
Routes of administration	i.v., p.o.	i.v., p.o., ocular, pulmonary, lingual, sublingual, buccal	i.v., p.o.	i.v., p.o. subcutaneous, dermal, user defined (e.g. pulmonary)	i.v., p.o., pulmonary, skin
Oral route features	Physiological compartmental absorption and transit, incorporating simulation of GI tract lumenal volume dynamics, dissolution and absorption	ACAT model including gastric retentive, dispersed, and integral tablet controlled release formulations, bile salts effects, intestinal metabolism and transporters	Special models can be added by user-defined (differential) equations, which in turn can be related to the basic model	Physiological GIT model including controlled release formulations, intestinal metabolism and transporters, enterohepatic recirculation	ADAM model including controlled release formulations, intestinal metabolism and transporters
Distribution	Perfusion-limited tissues. Fixed model structure	Automatic calculation of Kps. Perfusion-limited or permeability-limited tissues. User can add tissues and customize physiology including tissue parameters	Automatic calculation of Kps. Perfusion-limited or permeability-limited tissues. User can add tissues and customize physiology including tissue parameters	Automatic calculation of Kps. Perfusion-limited or permeability-limited tissues. User can add tissues and customize physiology including tissue parameters	Automatic calculation of Kps. Perfusion-limited tissues. User can customize physiology including tissue parameters
Metabolism	Based on intrinsic clearance	Database for CYP abundance and turnover in liver, intestine or user defined in any compartments/organs (add-on module) - mutiple metabolites - The PK of metabolites can be tracked	User defined in any compartments/organs	User defined in any compartments/organs, protein expression database for all organs - multiple metabolites - The PK of metabolites can be tracked	Extensive database for CYP and some UGTs abundance and turnover in liver, intestine and kidney - multiple metabolites - The PK of metabolites can be tracked
Input/output management	Web portal - Excel and pdf files for output	Input: Databases created on the fly. User defined models - Output: flexible output options for user customizable charts and tables of all compartment and tissue mass and concentrations as function of time	Input: user defined data/parameters (GUI), possible control by COM/OLE-interface - Output: standard output, user-defined output functions, Excel export	Input: database of user defined compounds/ DrugBank data; MoBi® models: SBML, SCAMP - Output: data: Excel, models: export to Matlab® and R	Input: databases of ready-to-use and user defined models - Output: predefined Excel files + database
Transporters	Not explicit; implicitly included in intestinal permeability by use of Caco-2 permeability as input to the model	Uptake and efflux - user defined in any compartments/organs. Apical and basolateral membranes for intestine, liver and kidney. Predefined in intestine. (add-on module)	Uptake and efflux - user defined in any compartments/organs, additional SBML models can be included	Uptake and efflux - user defined in any compartments/organs - protein expression database for all organs	Uptake and efflux - predefined in intestine, liver, brain and kidney
Sensitivity analysis/Parameters estimation	Interactive sensitivity analysis in excel format	User defined Parameter Sensitivity Analysis (PSA) and batch runs included - parameter optimization (add-on module).	Yes	Predefined sensitivity analysis - parameter identification routines integrated, user-defined via interface to Matlab® and R	Predefined sensitivity analysis and parameter optimisation (and batch processing)
Input/output management	Web portal - Excel and pdf files for output	Input: Databases created on the fly. User defined models - Output: flexible output options for user customizable charts and tables of all compartment and tissue mass and concentrations as function of time.	Input: user defined data/parameters (GUI), possible control by COM/OLE-interface - Output: standard output, user-defined output functions, Excel export	Input: database of user defined compounds/ DrugBank data; MoBi® models: SBML, SCAMP - Output: data: Excel, models: export to Matlab® and R	Input: databases of ready-to-use and user defined models - Output: predefined Excel files + database
DDI	No	Steady-state and full dynamic PBPK - Competitive and time-dependent inhibition - induction - compound and metabolites	Full PBPK - Competitive and time-dependent inhibition - compound and metabolites	Steady-state and full PBPK - Competitive and time-dependent inhibition - induction - compound and metabolites	Steady-state and full PBPK - Competitive and time-dependent inhibition - induction - compound and metabolites
IVIVC	No	Yes, classical calculations and mechanistic ACAT.	Not directly	Yes	Yes
PBPK/PD	No	Yes. PBPK tissue unbound concentrations (compound or metabolite). Automated model selection and optimization	Yes	Yes, user defined reaction networks/disease models can be integrated using MoBi®	Yes. Predefined models
Virtual trials	No	Yes (American and Asian population or user defined)	Yes (user defined population)	Yes (database within the software)	Yes (database containing different populations)
Paediatric module	No	Yes	No	Yes	Yes (add-on module)

Examples of the use of this type of software in the literature are numerous, and it is not within the scope of this paper to review them all. We can point to certain examples, such as that published by Hoffman-La Roche, in which Gastroplus was used as part of the preclinical formulation development strategy [47]. In this way, the time-consuming element of model building and development was avoided, the background science was already there, and the authors were able to concentrate on the practical and strategic aspects, rather than the model building itself. A recent publication cites the use of PK-Sim in the simulation of concentrations of the anticancer drug etoposide in children, based on the scale-down of the adult PBPK model [48]. Potentially complex dosing regimens for anticancer compounds, as well as various pharmacokinetic processes (saturable metabolism by CYP and UGT, biliary excretion, influx transport and renal tubular secretion) were able to be incorporated into the etoposide adult model, and when in vitro data were unavailable, certain parameters were estimated from fitting to the adult in vivo data. Where appropriate, these were then fixed for the paediatric simulations, and the physiological parameter values were modified to those in the paediatric population library. The simulated etoposide concentrations were reported to be in good agreement with observed data. This kind of simulation exercise can help to design pharmacokinetic studies in patient groups such as children, where there is little prior knowledge available, or where ethical issues are a concern. Software such as Simcyp have allowed the time-dependent simulation of clinical drug–drug interactions (DDI), which can show improvement in predictions compared with the static approach, not only because of the dynamic changes reflective of ‘real life’ pharmacokinetic processes on the substrate and inhibitor, but also because of the ability to select the physiologically relevant concentrations at the site of inhibition – intracellular, portal vein, gut lumen – rather than plasma concentrations. Additionally, the effects of population characteristics such as enzyme genotype (e.g. CYP2C19 [49]), and disease state (e.g. mild, moderate and severe liver cirrhosis [50]) have been simulated with success.

The examples given here are by no means an exhaustive list of the vast capabilities of this type of software, and many of the packages mentioned contain similar functionalities. The important point to note is that this category of software can be used by scientists who understand the concepts of PBPK modelling but who lack the computer programming expertise or the time to create their own models. And crucially, the inclusion of ready-to-use physiological databases, compound files and population libraries allows simulation in patients of a range of disease states, genetic make-up and demographics. The answer to a ‘what-if’ question can be easily obtained in just a few clicks of a mouse.

Significantly, users can readily take advantage of the dedicated and knowledgeable teams behind the development of this type of software in the scientific community through publications, forums, consortia and workshops dedicated to several applications. Two-way communication between users and the software developers is actively encouraged, both to aid the users with scientific or technical issues or the implementation of new features, and also to provide the developers with feedback and requirements for future directions. Consequently the knowledge and experience of the users, and the development of the software are both improved.

Obviously, as this category of software includes a ready-to-use interface combined with predefined options for the model building, the modellers are limited to the backbone model structure imposed by the software; in the past it was generally not possible to add or remove organs although some designed software have additional features leading to semi (Simcyp, Gastroplus) or complete (PK-Sim, Medici-PK) flexibility for modellers with expertise.

However, as the users do not require the discipline and knowledge to create the model they may not fully understand the limitations or dangers of certain assumptions. Consequently, simply by selecting certain options ‘blindly’ they could result in a PBPK model with poor or even no realistic meaning for the compound(s) of interest. Similarly, users with poor PBPK modelling experience can easily misinterpret results if they do not sufficiently understand where they come from, i.e. assumptions, parameter relationships. The combination of the multitude of options now available in this kind of software may lead to a model complexity that can leave the user unsure of which parameters or processes are responsible for a poor prediction versus the observed data.

Finally, the outputs illustrating the results of the simulations or parameter estimations are generally restricted to those imposed by the software. The customization of tables and graphics depends on the features or the data export tools included in the package, while the export of results to a database may require users to develop their own tools to achieve the transfer of relevant data in the correct format.

Discussion

A PBPK model is a mechanistic physiological framework combining the drug related information from various sources (e.g. in vitro, in vivo, in silico). It allows the testing of several assumptions that change all along the development process and the quantitative prediction of drug pharmacokinetics (and increasingly, pharmacodynamics) in theoretically any population or species for which physiological and demographical data exist.

Although PBPK modelling has been, and still is, widely used for the risk assessment of environmental chemicals, it is now increasingly used in the pharmaceutical field. Several reasons may explain this evolution in modelling strategy within the pharmaceutical industry. Since the first workshop dedicated to PBPK modelling in drug development in 2002 the practical application of PBPK modelling has been demonstrated for several purposes: drug screening [51], first-in-man predictions [23], drug–drug interactions [16, 52] and predictions in specific populations [14, 50, 53]. Many workshops, congresses and training courses worldwide include specific sessions devoted to PBPK. Overall, we have seen a vast improvement in communication between software developers and users of the PBPK modelling approach over the past decade. In parallel, in vitro and in silico tools have been further developed to aid even earlier drug selection in the industry, reducing both cost and time of development. The development of such tools has reinforced the need to determine appropriate scaling factors to extrapolate experimentally determined parameters to their equivalent in vivo systems (IVIVE) which has in turn driven the development and improvement of software with which to link all of the relevant parameters within the framework of a PBPK model.

Manufacturers of designed software take advantage of their specific focus on PBPK to build and develop specialized tools with this specific intention, aided and driven by their scientifically knowledgeable and often academically based research teams. While some elements of the model structure and parameters can be modified by the user, certain changes are not permitted for valid reasons (e.g. predefined allometric relationships), and for others only values within a certain range are allowed (e.g. physiological boundaries). This controlled flexibility avoids the model becoming too empirical or physiologically unrealistic. These software companies generally provide extensive scientific and technical support aiding the correct use of the tool and some, such as Simcyp, offer training courses and practical workshops combining the theoretical principles of IVIVE with the specific features of their packages. This goes some way to easing the fears sometimes associated with the use of designed software – that a ‘blind reliance’ on them, with no questioning of their assumptions, coding and equations, may lead to a loss of modelling expertise within the ADME/PK development teams, and that incorrect conclusions drawn from improper model use or poor experience puts the reputation of the entire approach at risk.

It could then be suggested that the prior selection or training of specific people with the appropriate combination of biochemical, physiological, mathematical and IT skills is no longer a requirement, as it seems to be ever more possible to ‘learn on the job’. Previously, PBPK modelling using open source software could only be achieved by a dedicated team of a few modellers who created, used and updated their own PBPK models. Consequently, within a company the PBPK modelling approach was reliant on these few specialized people, and, equally importantly, was dependent on good communication between them and the various teams involved in both preclinical and clinical development. The creation of such teams was often a daunting prospect, exacerbated by the potential loss of knowledge and expertise due to the departure of team members, conflicting views of modellers with various levels of experience within the team, or poor communication within the team, or between the team and other departments.

However, the above statements should be taken with caution. We do not suggest that modellers should no longer make the effort to arm themselves with a broad and fundamental knowledge of the various concepts mentioned in the previous paragraph. Rather that the attaining of these skills is no longer a bottleneck, but should be a continual education process.

The use of open software has several important advantages. Generally these software packages are cheaper than designed software, and can be used for multiple applications, e.g. classical PK and PK/PD modelling, population PK modelling, modelling of in vitro systems and individual tissues or cellular processes (‘open-loop’ modelling), WB-PBPK (‘closed-loop’ modelling), statistical data analysis and mining, and molecular modelling. As the model code may have to be user-written, these software necessitate the user's understanding of the scientific reasoning behind their equations, and therefore the knowledge and responsibility to decide how and whether certain model equations or parameters can be changed. Increasingly, members of the open software group are including PBPK ‘toolkits’ or add-ins, as well as webinars to explain and promote their use, so in fact the overlap between the two software classes is becoming more and more pronounced. It could be concluded therefore that the availability of designed software ‘promotes’ PBPK modelling and its accessibility within the pharmaceutical industry by simplifying the technical use of such models and extending their availability to non-modellers, while the open software allows more experienced modellers to go ‘one step further’ in terms of model complexity and flexibility. Rather than PBPK modellers requiring extensive knowledge in many scientific fields, i.e. molecular chemistry, ADME processes, physiology, pharmacogenetics, in vitro, they can begin modelling before obtaining expertise in all of these fields, provided that they maintain good and regular communication with those who possess this knowledge, and thus build up their own experience over time.

This paper has only briefly mentioned the ‘add-ons’ to the PBPK modelling approach – such as sensitivity analysis, parameter estimation, PK/PD, links to efficacy and disease models. The combination of these tools further shifts the boundaries between straight PBPK modelling, classical PK modelling via parameter estimation, and dose–exposure–response relationships. This tendency certainly allows users a more enriching/informative modelling experience but requires a large background too.

Of course, the choice of modelling software is not the only determinant on the success of the PBPK approach. Since one of the traditional foundations of PBPK modelling is the IVIVE of ADME processes, the selection of the extrapolation model by software developers or model-writers can have a huge impact on the success of predictions. A recently published initiative of the Pharmaceutical Research and Manufacturers of America (PhRMA) aimed to assess the performance of various ADME prediction methods and models in the prediction of human pharmacokinetics from preclinical and in vitro data [54, 55, 56, 57, 58]. This extensive evaluation concluded that, for the compound dataset studied, the PBPK approach generally poorly predicted the distribution, and the absorption, or intestinal and hepatic first-pass clearance. The authors noted that these poor predictions could be due to the fact that the currently used IVIVE scaling methodologies tested during the evaluation were originally developed on the basis of hydrophilic compounds in Class 1 of the Biopharmaceutical Classification System (BCS). Many of the compounds in the PhRMA dataset were Class 2 and 4 drugs (poorly permeable, lipophilic), and perhaps new or modified scaling approaches may need to be developed for these types of drugs. The importance, and increasing frequency of published models distinguishing transporter-mediated active uptake or efflux from intrinsic metabolic enzyme activity within the same in vitro or in vivo system illustrates this point. A PBPK modeller looking to incorporate transporter data into their model must have a good understanding of the various transporter-expressing in vitro models, including which specific transporters and enzymes are expressed, their relative or absolute abundances within the system, specificity of substrate or inhibitor probes, or other mechanisms involved. Even when the in vitro system is well understood, it is still often difficult to extrapolate this information when there is a lack of physiological knowledge in the in vivo system, e.g. the abundance of transporters in a certain organ or tissue is unknown, or when the in vitro transporter expression or activity differs from that of the in vivo system. However, despite certain current limitations in our knowledge of the extrapolation of transporter and certain enzyme activities, it is clear that PBPK models are still the best way to attempt to solve the complex interplays in certain organs and for certain complicated processes such as the first-pass effect observed after oral administration.

Conclusion

In the future, PBPK models will continue to be used more and more frequently [59] as they represent a quantitative, physiologically realistic platform with which to simulate preclinical and human pharmacokinetics using a wide variety of different information gathered during the drug development process. Moreover, a drug's pharmacodynamic properties can be linked directly to PBPK models, in order quantitatively to evaluate the dose–exposure–response relationship. The software designated as ‘designed software’ in this review have contributed to the earlier, and increasingly frequent use of PBPK modelling within the pharmaceutical industry. The challenge is now to educate and train scientists and modellers to ensure their good understanding of the assumptions and the limitations linked both to the physiological framework of the ‘virtual body’ and to the scaling methodology of drug-specific parameters from in vitro to in vivo (IVIVE). Clearly, the manufacturers and developers of designed software should, and generally do, play an important role in this challenge through the organization of dedicated workshops and training courses. Likewise, pharmaceutical companies, and in particular their management teams must realize the importance of continual training and experience to those who carry out the modelling, in order to keep up with developments in the field regarding the physiological and biochemical mechanisms vital to the model, and the in vitro methodologies employed in the laboratory in order to obtain the drug-specific parameters which can be used in the model. Open software will continue to provide the flexibility to analyse in-house results obtained from specific in vitro systems (e.g. Caco-2, hepatocytes) by the construction of mechanistic mathematical models representing the systems. This also has the benefit of providing the modeller with knowledge of the basic principles of mass balance, pharmacokinetic differential equations, clearance and volume concepts, and so on. This sort of modelling exercise on a small-scale system can aid modellers to extrapolate their understanding to larger whole organ or whole body systems, and to challenge or add to the existing models present in designed software. It is proposed therefore that both types of software (open and designed) ought to be employed by a successful modelling and simulation team, to take advantage of the rapid and user-friendly nature of the simulations performed using the designed software, as well as the knowledge and technical support of the development teams behind them, but also to allow greater flexibility in translating in-house results from specific in vitro systems using open software.

Acknowledgements

The authors would like to thank Michael Bolger (GastroPlus), Masoud Jamei (Simcyp), Simon Thomas (Cyprotex), Stephan Willmann (Bayer Technology Services) and Michael Wulkow (CiT GmbH) for helping them to summarize the features of the selected ‘designed’ software.