The Use of Biokinetics and In Vitro Methods in Toxicological Risk Evaluation

The Report and Recommendations of ECVAM Workshop 15^1,2

Reprinted with minor amendments from ATLA 24, 473-497

Bas J. Blaauboer³, Martin K. Bayliss⁴, José V. Castell⁵, Chris T.A. Evelo⁶, John M. Frazier⁷, Kees Groen⁸, Michael Gülden⁹, André Guillouzo¹⁰, Arendina M. Hissink¹¹, J. Brian Houston¹², Gunnar Johanson¹³, Joost de Jongh³, Gregory L. Kedderis¹⁴, Christoph A. Reinhardt¹⁵, Johannes J.M. van de Sandt¹¹, and Giovanna Semino¹⁶
³RITOX, Utrecht University, 3508 TD Utrecht, The Netherlands; ⁴Glaxo Wellcome, Department of Bioanalysis and Drug Metabolism, Park Road, Ware, Herts SG12 0DP, UK; ⁵Unidad de Hepatologia Experimental, Hospital Universitario La Fe, Avda de Campanar 21, 46009 Valencia, Spain; ⁶Department of Pharmacology, Section of Toxicology, University of Limburg, 6200 MD Maastricht, The Netherlands; ⁷US Air Force, Armstrong Laboratory, Wright Patterson Air Force Base, OH 45433-7400, USA; ⁸Department of Clinical Pharmacokinetics, Janssen Research Foundation, Turnhoutseweg 30, 2340 Beerse, Belguim; ⁹Cell Toxicology Section, Institute of Toxicology, University of Kiel, Weimarer Strasse 8, 24106 Kiel, Germany; ¹⁰INSERM U49, Unité de Recherches Hépatologiques, Hôpital de Pontchaillou, 35033 Rennes Cedex, France; ¹¹TNO Nutrition and Food Research Institute, Toxicology Division, 3700 AJ Zeist, The Netherlands; ¹²Department of Pharmacy, The University of Manchester, Oxford Road, Manchester M13 9PL, UK; ¹³Department of Toxicology, National Institute for Working Life, 171 84 Solna, Sweden; ¹⁴Chemical Industry Institute of Toxicology, Research Triangle Park, NC 27709, USA; ¹⁵Swiss Alternatives to Animal Testing (SAAT), P.O. Box 14, 8614 Bertschikon-Zurich, Switzerland; ¹⁶Laboratory of Toxicology, Institute of Pharmacological Sciences, Via Balzaretti 9, 20133 Milan, Italy.

¹ECVAM - The European Centre for the Validation of Alternative Methods. ²This document represents the agreed report of the participants as individual scientists.

Address for correspondence: Dr B.J. Blaauboer, RITOX, Utrecht University, P.O. Box 80.176, 3508 TD Utrecht, The Netherlands.

Address for reprints: ECVAM, TP 580, JRC Environment Institute, 21020 Ispra (VA), Italy

Preface

This is the report of the fifteenth of a series of workshops organised by the European Centre for the Validation of Alternative Methods (ECVAM). ECVAM's main goal, as defined in 1993 by its Scientific Advisory Committee, is to promote the scientific and regulatory acceptance of alternative methods which are of importance to the biosciences and which reduce, refine or replace the use of animals. One of the first priorities set by ECVAM was the implementation of procedures which would enable it to become well-informed about the state-of-the-art of non-animal test development and validation, and the potential for the possible incorporation of alternative tests into regulatory procedures. It was decided that this would be best achieved by the organisation of ECVAM workshops on specific topics, at which small groups of invited experts would review the current status of various types of in vitro tests and their potential uses, and make recommendations about the best ways forward (1).

The workshop on The Use of Biokinetics and In Vitro Methods in Toxicological Risk Evaluation was held in Utrecht, The Netherlands, on 21-23 March 1995, under the chairmanship of Bas Blaauboer (Research Institute of Toxicology, Utrecht, The Netherlands). The participants comprised scientists involved in the use of biokinetic models in academia, research institutes, and industry. The objective of the workshop was to evaluate the present status of our knowledge about the use of biokinetic models in toxicological risk evaluation, with particular emphasis on the use of in vitro and other non-animal data for developing biokinetic models. The role of biokinetic models with regard to integrating in vitro toxicity data into risk assessment procedures was also discussed. The conclusions and recommendations of the workshop participants concerning the use of biokinetics and in vitro methods in toxicological risk evaluation are outlined in this report.

Introduction

The toxicity of chemical substances can be described by two main sets of characteristics. One set comprises the parameters which describe the time course of the concentration of the compound in parts of the organism. These parameters relate to the kinetics ("biokinetics") of a substance. Ideally, biokinetic parameters provide an estimate of the concentration of a compound at the site of toxic action. The other set of features determining the toxicity of a compound describe the mode of toxic action and the resulting effects on the physiological processes in an organism. This is generally referred to as the "toxicodynamics" of the chemical.

The biokinetic behaviour of a substance in an organism can be described by a number of processes, including intake, uptake (absorption), bioavailability, distribution in the organism, biotransformation, and excretion. All of these processes depend upon the physicochemical properties of the compound as well as on characteristics of the organism. For example, the absorption of a compound from the gastrointestinal lumen, as well as via the lung epithelium and the skin, involves its passage through biomembranes; uptake into target tissues or cells also involves membrane passage. This process is highly dependent on the lipophilicity of a compound; lipophilic compounds generally pass more easily through membranes than hydrophilic compounds. Biological membranes also contain structures which either, passively or actively, act as carriers for certain compounds. In this way hydrophilic compounds are taken up into cells. Since the biokinetics of a compound depend upon a number of parameters that are, at least in part, characteristics of the intact organism, a complete description of the biokinetic behaviour of a substance by employing only non-animal test systems will be difficult, since the complexity of the intact organism must be taken into account.

Detailed knowledge of the mechanism of action of a compound is often necessary for a proper understanding of its toxicity. In vitro models can offer a more scientific approach to understanding mechanisms of toxicity, rather than merely describing toxic events as they are observed in laboratory animals or in humans. The ability to use human-derived in vitro models is of particular importance, since the extrapolation of animal data to humans is sometimes problematic due to the qualitative and quantitative interspecies differences in the metabolism and toxicity of a compound (2).

However, the lack of consideration of in vivo biokinetics when estimating the toxicity of a compound from in vitro cytotoxicity experiments can lead to misinterpretations. For example if, in vivo, the compound never actually reaches the type of cells which are used in vitro because of rapid metabolism in other tissues, the cytotoxicity of the compound for this cell type is irrelevant for its toxicity in vivo. Even if the toxicity for the target cells is properly determined in vitro, overestimation of the toxicity of the compound in vivo can occur if only a small proportion of a dose which is expected to be toxic is absorbed and/or distributed to the target cells. Alternatively, the toxicity of a compound can be underestimated if it is concentrated in certain organs, tissues or cells. Another reason for misinterpreting in vitro cytotoxicity results can be due to the loss of compound from the in vitro system by evaporation or via its binding to glass or plastic.

These factors emphasise the need to integrate data on the mechanisms of action of compounds with data on their biokinetic behaviour when conducting studies on their biological effects (3). It is obvious that much information can be derived from in vitro experiments, provided that the results are interpreted in the context of the in vivo situation. For example, knowledge of physicochemical data, such as volatility, solubility, and reactivity, cannot only be used for estimating exposure to a chemical, but can also be incorporated into predictions of the biokinetic behaviour. Properties such as lipophilicity, molecular size, ionisation, and binding to proteins are of importance for estimating the reactivity of a compound and its ability to cross biomembranes. Passive uptake from the milieu exterieur, and the distribution, accumulation, and excretion of a compound will, for the most part, be governed by these properties. These characteristics can all be determined in non-animal systems.

To characterise the specific cellular biokinetic behaviour of a compound, its uptake and subcellular distribution can be measured in relevant cell types. The choice of cells and culture systems to be used in such studies should be based on knowledge of possible uptake mechanisms (for example, carrier-mediated uptake or passive diffusion), and of the physiological roles of the cells, tissues and organs in vivo.

The compilation of data derived from a battery of different in vitro tests and other non-animal experiments can provide a basis for predicting the in vivo biokinetic behaviour, as well as the biological activity, of a compound (5). Computer models describing in vivo biokinetics, and possibly also the dynamics of a compound in vivo, can be very powerful tools in this respect. Such physiologically-based biokinetic (PB-BK) models are now beginning to have an impact in pharmacology and toxicology (6). PB-BK models have a number of applications. For example, biokinetic data derived from an experiment with a limited number of animals can provide the basis for establishing a PB-BK model which, in turn, can be used to design better and more focused experiments, which use fewer animals than would normally be employed. This approach can also help to predict the possible accumulation of a compound in certain organs, which may subsequently be the target for its toxic action.

More importantly in the context of this report is the notion that, to interpret in vitro toxicity data correctly, the data have to be understood in the context of the intact organism. In the following sections, an overview of the present opportunities for, and limitations of, the use of biokinetic modelling with respect to the integration of in vitro and other non-animal data in risk evaluations is given. The principles of PB-BK modelling are described, and reference is made in particular to: a) the determination of blood-tissue partition coefficients (PCs); b) special barriers for uptake in the organism and in individual tissues; and c) elimination processes.

Principles Of Biokinetic Modelling

Knowledge of the biokinetic behaviour of potentially noxious chemicals is essential for scientifically accurate assessments of human health risks resulting from chemical exposure. Understanding the absorption, distribution, metabolism, and excretion of toxic chemicals is necessary to predict the target organ concentrations of the chemical or its active metabolite(s). Putting this dynamic information into a mathematical framework, or model, allows the prediction of target organ concentrations of chemicals following exposure. Two types of compartmental biokinetic models are currently used to describe biological systems: a) data-based compartmental models; and b) physiologically-based compartmental models.

Data-based compartmental models are widely used for the analysis of clinical pharmacokinetic data to determine drug bioavailability, volume of distribution, and clearance. In data-based compartmental modelling, kinetic data is collected, a compartmental kinetic model is selected, and the model is fitted to the experimental data. Generally, a two-compartment model is fitted to the kinetic data. This simple model has a central compartment, assumed to be in equilibrium with the blood or plasma, which "communicates" with a deep compartment at empirical first-order rates. The kinetic model, however, does not necessarily reflect physiological or anatomical reality. The empirical rate constants in the model are complex conglomerates of the rates of actual physiological and biochemical processes involved in drug disposition. The values of the rate constants will be different when the kinetic model is fitted to data sets that are obtained under different experimental conditions. Thus, the data-based compartmental approach cannot be used effectively to extrapolate between different routes of compound administration or between species. The lack of predictive power of the data-based compartmental approach limits its value for human health risk assessment purposes, where data from animals given high oral doses of a substance are frequently used to try to estimate the human health risk from intermittent, low dose, inhalation exposures.

A second approach which has greater predictive power is physiologically-based compartmental kinetic modelling. In this approach, a physiologically realistic kinetic model is defined, which includes both physiological parameters (such as organ volumes, blood flows, and ventilation rates) and chemical-specific parameters (such as tissue solubility and biotransformation rates). These data can be obtained from the literature or by undertaking appropriate experiments. It is important to recognise that many physiological parameters (for example, regional blood flow) can vary during physical activity. The physiologically-based model can be used to predict the kinetic behaviour of the substance under study. Model output is compared with independently obtained experimental data. When the model output does not resemble the salient features of the experimental data, the model is refined with better descriptions of physiological reality or by including more appropriate estimates of the parameters. An important feature of the physiological approach is that it provides a dynamic means of hypothesis testing. Various levels of mechanistic detail can be included in the model, depending upon the experimental question being asked. Sensitivity analysis of the effect of changes in the values of the model parameters upon the output of the model can be used to identify critical model parameters. This can help in deciding how much uncertainty in the estimate of a model parameter is acceptable. The purpose of the physiologically-based model is to describe the behaviour of the chemical in the animal system, with the goal of having one set of parameters which will describe chemical behaviour. This approach allows extrapolation between different dosing routes and species, making it well suited for use in human health risk assessment.

The structure of a representative PB-BK model for volatile chemicals is shown in Figure 1. The compartments correspond to discrete organs or groups of organs. The volumes of the organ compartments (V_i) and blood flows to the compartments (Q_i) are based on physiological data. The tissue solubility of the chemical is accounted for by tissue-blood PCs (PC_i). The PC can be defined as the distribution ratio of a chemical between two dissimilar media. Tissue PCs can be measured in tissue homogenates in vitro, or can be estimated from steady-state tissue levels in vivo for compounds which are not rapidly metabolised. In the model structure shown in Figure 1, the lung is considered to be a compartment where gas exchange takes place. The model can be expanded to include other routes of exposure, such as oral, intravenous (iv), or intraperitoneal (ip). Chemical biotransformation is usually assumed to take place in the liver, but other metabolising compartments (such as lung or kidney) can be incorporated if necessary. Metabolism by cytochromes P450 and many other enzymes follows Michaelis-Menten saturation kinetics (equation 1):

v=	Vmax[S]
	Km + [S]

(Equation 1)

In this equation, v is the initial rate of the reaction, Vmax is defined as the maximal rate of the enzyme-catalysed reaction at infinite substrate concentration, Km is the substrate concentration which gives a rate which is half that of Vmax, and [S] is the substrate concentration. It is important to note that Km is not simply a binding constant, but is a complex kinetic constant that includes binding terms. Another important parameter is the Vmax/Km ratio, or the intrinsic clearance (C_int), which is the initial rate of the reaction at low substrate concentration. This term often has great relevance in vivo under low level exposure conditions which lead to low tissue concentrations of a chemical.

Figure 1: A Representative PBBK Model for a volatile chemical

alv = alveolar; art = arterial (blood); C = concentration; f = fat; inh = inhaled; L = liver; PC = partition coefficient; Q_alv = alveolar ventilation rate; Q = blood flow; r = rapidly perfused tissues; s = slowly perfused tissues; mixven = venous (blood)

The model is described on page 476.

Gas exchange in the lung is the major uptake route for volatile chemicals, and is often an important excretion pathway as well. It is assumed that there is a material balance between the chemical entering the lung and the chemical leaving the lung, and that an equilibrium is reached between the chemical in the blood and the chemical in the air. These assumptions are described by the following equations:

Q_alvC_inh + Q_cC_mixven = Q_alvC_exh + Q_cC_art

(Equation 2)

PC_bl,air = C_exh/C_art

(Equation 3)

where Q_alv is the alveolar ventilation rate, C_inh is the chemical concentration in inspired air, Q_tot is the total blood flow to the lung, C_v is the chemical concentration in blood entering the lung (which is considered to be venous, since it is mixed venous blood returning to the lung from various other organs), C_exh is the chemical concentration in exhaled air, C_art is the chemical concentration in arterial blood leaving the lung, and PC_bl,air is the blood-air PC.

Passive distribution of the chemical into a non-metabolising tissue can be described by:

dA_i	= V_i x	dC_i	= Q_i(C_art - C_mixven-i)
dt		dt

(Equation 4)

where A_i is the amount of chemical in tissue i, V_i is the volume of tissue i, C_i is the concentration of the chemical in tissue i, Q_i is the blood flow to tissue i, and C_vi is the chemical concentration in the venous blood leaving tissue i. Equation 3 complies with the material balance assumption, in that the change in the amount of chemical in tissue i equals the difference between the amount of the chemical entering the tissue with arterial blood and that leaving the tissue in venous blood. The equilibrium between the concentraton of the chemical in the tissue and that in the blood is described by:

c_mixven-i = C_i/PC_i

(Equation 5)

where P_Ci is the tissue-blood PC.

For a metabolising organ such as the liver, equation 4 is modified to include a term which accounts for the decrease in the chemical concentration due to its metabolism (dA_met/dt):

dA_L	= Q_L (C_art - C_mixven-l) -	dA_met
dt	= Q_L (C_art - C_mixven-l) -	dt

(Equation 6)

dA_met	=	(Vmax x C_mixven-L)	+ (Cl_f x C_mixven-L)
dt		(Km + C_mixven-L)

(Equation 7)

where the subscript L denotes liver. Equation 7 describes metabolism by a saturable Michaelis-Menten process and by a first-order pathway with the clearance term C_Lf. Many glutathione conjugation reactions follow pseudo first-order kinetics in vivo. Parameters describing more complex metabolic schemes or kinetic mechanisms can be incorporated into equation 7.

Thus, PB-BK models can be used to predict the target tissue concentrations of a chemical or its metabolite(s) following exposure. These data can then be correlated with target organ effects, to determine the most appropriate description of an internal dose. In some cases this may be the parent compound or metabolite concentration in the target tissue. However, in cases where a very reactive metabolite is formed, the rate of metabolite formation or the integrated metabolite concentration over time may be the most appropriate dosimeter. It has been clearly shown with many chemicals that the applied dose or exposure concentration (that is, mg/kg or ppm.h) is not the appropriate dosimeter for interspecies comparisons. This is because of interspecies differences in metabolic rates and pathways, and due to differences in alveolar ventilation rates and blood flows.

The simple PB-BK model shown in Figure 1 can be expanded to include salient features of the biological mechanisms involved in chemically-induced toxicity. This enhances the predictive powers of PB-BK models. Biotransformation parameters for use in establishing PB-BK models can be determined from in vitro kinetic studies. Nevertheless, this approach is not appropriate for chemicals which undergo significant extrahepatic metabolism. However, for most chemicals the liver is the major or sole organ involved in metabolism. The use of biokinetic models developed with parameters taken mainly from existing physiological and chemical databases, and/or obtained from in vitro biotransformation studies, will clearly reduce laboratory animal use and may be the only way to obtain kinetic data on the disposition of suspected human carcinogens in the target species (that is, in humans).

Body Distribution, Partition Coefficients, and the Use of Physicochemical Parameters.

In PB-BK modelling, the distribution of a compound between the various tissues of an organism is characterised by a series of tissue-blood PCs. In classical (that is, compartmental-based) kinetic modelling, the distribution of a compound is usually described by its volume of distribution (Vd). This can be considered as a measure for the "overall" partitioning of a compound between the blood and all of the tissues.

Partition coefficients have been determined in in vivo studies, in which a compound is delivered by constant infusion directly into the bloodstream of the animal. At steady-state, the tissue-blood PC for a non-eliminating organ is calculated by dividing the tissue concentration of the compound by its blood concentration. However, alternative methods have been developed, which use in vitro test systems. The tissue-air PCs of volatile compounds can be measured in vitro by incubating the compound with a homogenate of the appropriate tissue. The equilibrium distribution of the compound is then measured, for example by gas-chromatographic analysis of the air present in the headspace of the vial containing the homogenate/buffer mixture, either in the absence or presence of the tissue homogenate (7-9). Tissue-blood PCs can be calculated by dividing the tissue-air PCs by the respective blood-air PCs. Tissue-blood PCs of non-volatile compounds can be determined in vitro by using a number of methods which are based on incubating the compound with a buffered tissue homogenate (10, 11).

For compounds which do not bind to specific tissue components, the tissue-air and tissue-blood PCs represent the thermodynamic partitioning of a compound between the water and lipid fractions of the tissue (12, 13). In the case of protein binding, ionic and hydrogen binding may also be involved. Protein binding in blood affects the free plasma concentration of a compound, and may thus influence the concentration which is available for extravascular distribution and metabolism.

In the case of thermodynamic partitioning of a compound, physicochemical properties may be used to correlate the partitioning of compounds in non-biological systems with that in biological systems. Such correlations may also enable the estimation of PCs for chemically-related compounds. For a limited number of compounds, octanol-water PCs (K_ow) and oil-air PCs have been used as physicochemical descriptors (13-15). The K_ow can also be calculated by the fragment addition method (16, 17). A more detailed analysis of the data which are already available on PCs seems desirable. The development of quantitative structure-activity relationships (QSARs), which are already widely used in the fields of aquatic toxicology and environmental chemistry, could contribute to a reduction in the use of laboratory animals for distribution studies.

Special Barriers

Biokinetic models incorporate PCs for the compound between the blood and the tissues. Under flow-limited conditions, the distribution of a chemical is governed by these PCs and by the physiological characteristics of the organism. In the case where the transport of a compound from the blood to the tissue is limited by diffusion across the tissue boundaries, the specific characteristics of the different barriers existing between the milieu exterieur and the milieu interieur must be taken into account.

Uptake from the Gastrointestinal Tract

The gastrointestinal tract is an important route by which chemicals are digested and absorbed. Absorption of substances can take place along the entire tract, either by diffusion or by specialised transport processes. Nutrients pass from the gut lumen across the brush border cell membrane after binding to a specific transport protein, or through the intercellular tight junctions, thereby crossing the barrier between the external milieu and the organism. For absorption, a chemical has to diffuse across a series of separate barriers; these include, from the mucosal side, the mucus gel layer, the intestinal epithelial cells, the lamina propria, and the capillary endothelia. Of these, the single layer of epithelial cells appears to be the most significant barrier to the absorption of chemicals (18).

Alteration of gastrointestinal motility can also affect the absorption of xenobiotics. The entry of nutrients into the duodenum after a normal meal causes a radical change in motility patterns, with an irregular gut activity which is designed to speed up absorption (19). The precise pattern of mixing activity is influenced by the nature of the nutrient, with glucose producing the least activity while fat induces the most contractions, all of which are non-propulsive (20).

The absorption of a chemical from the gastrointestinal tract can also depend upon its physicochemical properties, such as lipid solubility and dissolution rate. While it is often stated in general terms that an increase in lipid solubility will increase the absorption of chemicals, an extremely lipid-soluble chemical will not dissolve in the gastrointestinal fluids and, therefore, its absorption will be low (21).

The amount of a chemical which enters the general systemic circulation following oral administration, that is the "bioavailability" of the chemical, depends upon a number of factors. Firstly, it depends upon the amount absorbed into the gastrointestinal cells. Subsequently, before it enters the general systemic circulation, the chemical can be biotransformed by the gastrointestinal cells, extracted by the liver and excreted into the bile, metabolised by the liver, or metabolised by the lung. The oral bioavailability of a compound is an important factor. In vitro determination of bioavailability involves the quantification of the time courses of the plasma concentrations of a compound administered by gavage and by iv injection; the areas-under-the-curve (AUC) determined for the two routes of administration are then compared. This procedure requires a large amount of test material and several animals, and it is time-consuming. Moreover, in vitro it is difficult to study certain specific factors which determine transmucosal transport.

Biokinetic Modelling

Several PB-BK models have been developed for studying the oral uptake of volatile compounds dissolved in drinking water. In these models, the gastrointestinal absorption is typically described as a first-order transfer from one compartment directly into the liver, since portal flow goes to the liver before it is recirculated in the systemic circulation (22, 23). This approach appears to be adequate for pure compounds and when aqueous vehicles are used, but when the compound is solubilised in oils, the model fails to provide an accurate description of the kinetics. Rat blood concentration profiles of lipophilic compounds administered by gavage in oil-based vehicles present several peaks, suggesting a delayed, pulsatile absorption. To describe the observed delay in absorption, a more complex description of the gastrointestinal tract can be included in the PB-BK model. The gastrointestinal tract can be split into two or more compartments; chemical absorption is assumed to occur from each compartment directly into the liver, following a first-order rate transfer. Transfer from one subcompartment to another has been simulated to occur with a first order rate process (24) or after a certain time interval (25). The latter approach combines a data-compartmental description of the gastrointestinal tract with a PB-PK model, and enables a good description of experimental blood and exhaled breath concentration time-course data in rats for several dosing conditions. A more physiologically-based approach to describe the different regions of the gastrointestinal tract in the rat has also been developed (26).

In general, there is a lack of knowledge about the membrane transport of almost all xenobiotics. Thus, it is often assumed in PB-BK modelling that the membrane resistances are not rate-controlling, and that the dominant variable is the amount of the compound which is distributed to the tissue in the blood. In some cases, as with the PB-BK model for methotrexate (27), the fact that the delivery of the compound from the gastrointestinal tract is membrane transport-limited, rather than blood flow-limited, is taken into account. The passage down the gut lumen is modelled by four compartments, and the absorption equation contains both saturable and non-saturable terms.

A more detailed description of the gastrointestinal tract incorporates the enterohepatic cycle from liver to the small intestine; this is required for those compounds which are rapidly excreted in the bile, and thus pass into the small intestine to be either reabsorbed or excreted in the faeces. The term representing the biliary secretion is added to the liver mass balance equation (27, 28).

Many factors must be considered when describing a complex process such as oral absorption. The vehicle and chemical characteristics, gut motility and gastric emptying, and the nutritional status of the experimental animals (fed or fasted) may considerably affect the rate of absorption of a compound. All of these parameters dictate the choice of model with regard to a simple or a more detailed description of the gastrointestinal tract. However, the use of complex models requires knowledge of rate constant values which describe the rate of transfer into and out of the various compartments. Most of these rate constants are not only unknown, but are extremely difficult to obtain.

In vitro cultures of gastric and intestinal mucosal cells may represent a useful model for characterising certain specific properties of chemicals, such as their permeabilities and transport. Since oral bioavailability is mainly controlled by the absorption of a compound through the intestinal epithelium, several in vitro models, using monolayers of intestinal epithelial cells, have been developed for studying the transport of chemicals across the intestinal epithelium and their metabolism. Many studies have demonstrated that systems based on human colon adenocarcinoma cells lines, such as Caco-2 and HT-29 (29-31), may be suitable models for studying the passive absorption of xenobiotics across the intestinal epithelium. A good correlation has been obtained between the absorption of compounds following oral administration in humans and their permeability coefficients as obtained with the Caco-2 model (32). Therefore, in vitro models may enable the absorption rate in vivo to be predicted. In vitro models can contribute to an understanding of the mechanism of absorption at the cellular level, whereas PB-BK models enable quantification of the absorption and distribution of compounds in the whole organism. The determination of permeability coefficients in in vitro epithelial cell systems, and their subsequent incorporaton into PB-BK models, could contribute to a more reliable simulation of the oral uptake of chemicals.

Uptake in the Lung

Inert Volatiles

In PB-BK models for inert volatiles, lung uptake (and excretion) is commonly described by combining lung tissue with alveolar air in a single, well-stirred compartment. In this "inert tube" or "alveolar uptake" model, the respiratory airways are assumed to act as inert tubes which merely conduct the substance to the alveolar region where the actual exchange between ambient air and body takes place. The alveolar uptake model has been shown to accurately predict the inhalation kinetics of a variety of inert volatile substances (33, 34).

The assumption underlying the use of a single, well-stirred compartment model is that both exhaled air and blood leaving the lung compartment are in equilibrium with the compartment itself, and that (at steady-state) the inflow rate, via inhalation and the entering blood, equals the outflow rate, via exhalation and the leaving blood. The net uptake rate may be calculated as:

v =	Q_alv x Q_c	x (PC_bl,air x [C_inh - C_mixven])
	Q_alv + (PC_bl,air x Q_c)

(Equation 8)

From this equation, it follows that the uptake rate is determined by five factors, namely: a) the concentration in ambient air (C_inh); b) the blood-air PC (PC_bl,air); c) the alveolar ventilation (Q_alv); d) the cardiac output (Q_tot); and e) the concentration in blood entering the lungs (C_mixven).

The uptake rate can be calculated once the five determinants are known. Values for alveolar ventilation and cardiac output are available in the literature, while blood-air PCs and metabolic rates can be determined in vitro, as discussed previously. Although metabolic rate can be measured in vitro, further modelling is required to calculate C_mixven from metabolic data. Furthermore, at non-steady-state conditions, such as at the beginning of an exposure, distribution around the body will affect the concentration of the chemical in the mixed venous blood returning to the lungs, thereby influencing the uptake rate. To predict lung uptake more exactly, a PB-BK model is, therefore, required.

Some cases are of special interest. Early during an exposure (or if metabolism is very high) the concentration of the chemical in returning blood (C_mixven) is very low. In addition, for substances with very high blood solubility (that is, high PC_bl,air values), Q_alv is negligible compared to PC_bl,air x Q_tot in the denominator of equation 8, which reduces to the product Q_alv x C_air. In other words, the uptake rate becomes limited by alveolar ventilation. For volatiles with very low blood solubility, equation 8 reduces to Q_tot x C_air x PC_bl,air; that is, the uptake rate is limited by cardiac output and blood solubility. During constant exposure, the concentration in mixed venous blood will rise, thereby decreasing the net uptake rate. Extensive redistribution in the body, biotransformation, and non-alveolar pathways of excretion tend to reduce the concentration of the chemical in mixed venous blood, thereby causing an increase in the uptake rate.

Obviously, any factors which change the numerical values of these five determinants will also affect the net uptake rate. For example, physical activity increases alveolar ventilation and cardiac output. For many volatiles this results in a marked increase in net uptake rate. In contrast, exposure to a metabolic inhibitor may decrease metabolism, and thus cause a reduced net uptake.

Reactive Volatiles

Experimental data suggest that the lung uptake of polar volatiles is not adequately described by the alveolar uptake model (35, 36). Water-soluble volatiles tend to absorb into the aqueous lining of the nose and respiratory act during inhalation "wash in", and then evaporate during exhalation ("wash out"). Several attempts have been made to model these wash in/wash out phenomena (35, 37). Wash in/wash out tends to decrease the amount of compound reaching the alveoli, and thus decreases the net uptake rate. On the other hand, absorption in the respiratory epithelium increases the likelihood of pre-alveolar uptake. The upper limit of the overall uptake rate is, of course, determined by pulmonary ventilation (38).

Since most of the volatiles which enter the respiratory tree will have contact with the walls of the airways, the possibilities of pre-alveolar or presystemic biotransformation and of irreversible binding must be considered (39). It is well known that nasal epithelium contains a variety of enzymes capable of xenobiotic transformation, such as carboxylesterases (40). Furthermore, Clara cells, which are located in the bronchial epithelium, are rich in cytochrome P450-mediated activities. The human nose has a relatively small internal surface area and humans tend to breath via the nose as well as the mouth. In contrast, rodents are characterised by a large internal nose surface area and nose-only breathing. This probably makes nasal uptake, metabolism, and wash in/wash out phenomena quantitatively much more important in rodents than in humans (41). However, pre-alveolar metabolism may also be important in humans, especially for reactive or easily transformed substances, such as formaldehyde and carboxyl esters. It has been suggested that the alveolar uptake model systematically overestimates lung uptake in rodents, possibly due to nasal wash in/wash out (42).

Particles

The factors determining the uptake rate of particle-associated substances are very different from those for volatiles. Particles are deposited by diffusion, impaction, and sedimentation, and the relative importance of these processes is determined by particle size, air velocity, and the anatomy of the nose and the respiratory tract (43, 44). The uptake rate of solutes associated with particles depends upon: a) the rate and site of their deposition; b) their redistribution and removal by mucociliary clearance; c) their dissolution from particles; and d) their diffusion in the mucus and the epithelium (45). Diffusion in the mucus and epithelium is thought to be the rate-limiting factor for large lipophilic molecules, such as polycyclic aromatic hydrocarbons (PAHs; 46), thereby creating sharp concentration gradients and high local concentrations. In such cases, the possibility of local, presystemic binding, biotransformation and other effects must be taken into account. For example, after inhalation exposure to particles containing PAHs, these molecules leave the particles relatively rapidly, and thus the site of exposure corresponds to the site of deposition. In contrast, in high dose instillation experiments in animals, the particles tend to aggregate and form deposits of crystalline PAHs. In this case, dissolution is slow relative to particle redistribution, and the site of PAH exposure corresponds to the site of particle retention rather than to the site of deposition (46).

Uptake via the Skin

The major functions of the skin include the prevention of water-loss and protection of the body against the external environment. To accomplish these functions, the skin is more than a passive protective shield. Several layers can be distinguished, of which the epidermis is the most external. The dermis forms the underlying connective tissue. The major cell type in the epidermis is the keratinocyte; more than 90% of all cells in this skin layer are keratinocytes. They undergo large morphological and biochemical changes while moving from the stratum basal to the stratum corneum. During this differentiation process, protein synthesis is directed toward the formation of structural proteins (cytokeratins and precursors of cornified envelopes) and, ultimately, lytic enzymes are released and the cellular metabolic activity is terminated. The terminally differentiated keratinocytes (corneocytes) then form the stratum corneum, in which the protein networks are orderly embedded in a matrix of lipids.

Percutaneous Absorption

The skin is not an absolute barrier, and percutaneous absorption is an important route of exposure for chemicals in the work-place and for therapeutic agents (47). Therefore, a lot of effort has been directed toward elucidating the mechanisms governing uptake via the skin. Several types of experiments have demonstrated that the stratum corneum is the rate-limiting barrier to the percutaneous absorption of topically applied substances. For example, removal of the stratum corneum by tape stripping results in a dramatic increase in permeability. There are several putative pathways of penetration across the stratum corneum (47); the transappendageal path, that is, absorption via hair follicles and sweat gland ducts, does not appear to make a significant contribution under steady-state conditions, but may play a role in the initial phase of percutaneous penetration. The intercellular route (absorption via the continuous intercellular lipids) seems to be the major pathway, rather than the paracellular route (absorption via both intercellular lipids and the protein networks of the corneocytes). The considerable length of this route, together with its unique lipid composition of predominantly ceramide, cholesterol and fatty acids, may explain the low permeability of the stratum corneum (47).

A recent model proposed to explain the barrier function of the skin is the domain mosaic model (48). In this model, lipids of the stratum corneum are segregated into crystalline/gel domains bordered by "grain borders", where lipids are in the fluid crystalline state. The latter domains permit the uptake of water (which is necessary for the proper functioning of the stratum corneum), and the percutaneous absorption of compounds.

Various biological and physicochemical factors can affect the uptake of substances via the skin. The lipid composition varies between anatomical sites and can result in differences in permeability. Furthermore, skin condition and age, blood circulation in the dermis, hydration, temperature, drug-binding, and cutaneous biotransformation can affect percutaneous absorption (47). Another important factor is the vehicle in which the chemical is dissolved, which may enhance percutaneous absorption.

In Vitro Models of Percutaneous Absorption

The percutaneous absorption of topically applied chemicals has been studied extensively in vitro (47). Frequently used models are diffusion cell chambers (49) and skin organ cultures (50). In these models, full thickness skin from experimental animals or human is kept in contact with a receptor fluid in which the absorbed portion of the topically applied substance is collected. This method provides a practical screening technique for establishing permeability rates. An additional advantage of these in vitro methods is that cutaneous metabolism can be studied selectively, without the interference of systemic metabolism. For this purpose, the receptor fluid can be analysed for the presence of metabolites of the parent compound. To incorporate biotransformation in in vitro absorption studies, care must be taken to keep the skin viable (47). A limitation of the above methods is the lack of microcirculation. To circumvent this disadvantage, percutaneous absorption can be studied in models in which the skin tissue is perfused (51).

Kinetic Modelling of Percutaneous Absorption

Transport across the skin can be largely explained by passive diffusion, which can, at steady-state, be described by:

J = k_p x (delta)C

(Equation 9)

in which J is the flux (moles/cm²/sec), k_p is the permeability coefficient (cm/sec), and (delta)C is the gradient across the membrane (moles/cm³). In modelling percutaneous absorption, the skin is often represented by two discrete compartments: the stratum corneum and the underlying viable tissue. Although the stratum corneum is relatively thin (10µm), the ability of a chemical to penetrate the skin depends crucially on the uptake in this epidermal layer. Within a certain range, the higher the lipophilicity the greater the penetration through the stratum corneum. A measure of the lipophilicity is the K_ow, but for volatile compounds the skin/air PC seems to be more appropriate (52). Many water-soluble compounds are absorbed to a larger extent than would be expected solely on the basis of their lipophilicities. This behaviour has been attributed to an "aqueous pore" mechanism, but the anomalously high k_p values of polar permeants can also be explained by their small molecular volumes. In addition, the melting point appears to be an important parameter for the prediction of skin permeability (53).

After passing through the stratum corneum, the absorbed chemical reaches the viable tissue (the epidermis and a part of the dermis) before being taken up by the microcirculation. Here, significant biotransformation may take place. Highly lipophilic compounds may be metabolised to more water-soluble products, which are then more easily transferred than the parent compound into the aqueous skin layers (50, 54). Blood flow is generally considered to be sufficiently fast to maintain the concentration of the compound at the base of the viable tissue effectively at zero. However, the blood flow through the skin is not only determined by the rate of flow but also by recruitment of new capillary beds. This results in an increase in the volume of tissue perfused, and may well have pharmacokinetic implications (55). Absorbed chemicals may not always reach the microcirculation. In addition to evaporation and the effects of washing the skin, the outward movement of keratinocytes followed by desquamation can be incorporated into PB-BK models as a route of elimination (56).

The Blood-Brain Barrier

The adult blood-brain barrier (BBB) in all warm-blooded vertebrates is characterised by both restrictive and permissive transport features which are established in vivo during late embryonic development. In vitro studies have recently become attractive due to the commercial availability of membrane inserts which permit easy access to both sides of the cell layer (57, 58). The maintenance and induction of the barrier functions, such as high electrical resistance, tight junction formation, and the appearance of marker antigens (for example, ZO-1 for tight junctions; y-glutamyl transpeptidase, P-glycoprotein), are dependent on the tightness of the endothelial sheet, local cellular contacts (co-culture with astrocytes, the glioma cell line, C6, or the neuroblastoma cell line, N2a), as well as on the presence of serum factors (59).

The uptake of compounds into the brain requires their passage through the tight endothelium of brain capillaries. The nature of this tight endothelium prohibits passive diffusion of non-lipophilic compounds; such chemicals can only reach the brain if active uptake mechanisms exist. For more lipophilic chemicals, passage from the blood into the brain is dependent on their physicochemical properties, among which their lipophilicity, extent of ionisation, and molecular size are the most important (60).

Apart from the use of these physicochemical parameters to estimate the passage of compounds through the BBB, a number of in vitro methods have been developed for studying this passage. These methods include the monolayer culture of endothelial cells derived from bovine brain capillaries; electrical resistance and the passage of chemicals through the monolayer can be measured in these cultures (59, 61, 62). A critical step in obtaining a functional in vitro system is the elimination of contaminating pericytes and the maintenance of specific functions of brain endothelial cells (for example, functional tight junctions and P-glycoprotein expression). The most promising model appears to be based on the co-culture of bovine brain endothelial cells with newborn rat hepatocytes (62, 63). In such systems, a selective permeability for lipophilic compounds has been observed, and a good correlation has been demonstrated with in vivo brain extraction levels. Other groups are working on immortalised endothelial cells but, at present, no cell line has been established which forms tight junctions.

An interesting alternative to using brain endothelial cell lines is the use of other in vitro systems which form tight junctions, for example, the kidney-derived Madin-Darby canine kidney (MDCK) cell line (64). However, these in vitro models need further characterisation before they can be used for biokinetic modelling purposes.

Elimination Processes

In PB-BK modelling, attention has also to be given to the processes by which compounds can be eliminated from the organism. The most important routes are exhalation (for volatile compounds), and excretion via the kidneys or via the bile (in the faeces). For non-volatile lipophilic compounds, excretion of the parent compound is usually limited, and biotransformation is needed in order to yield metabolites which are more hydrophilic.

Hepatic Metabolism

In constructing a PB-BK model, the role of the liver poses a particular problem, since this organ is not only a site for the distribution of the xenobiotic but invariably the major site of its metabolism, via interactions with a variety of enzyme systems. The combination of distribution and metabolism within the liver, which results in complex concentration gradients, together with the heterogenous nature of the liver itself, must be considered when defining the model. Despite these complexities, there has been recent notable success in relating the rate of in vitro metabolism to corresponding events in vivo.

The intrinsic clearance of many compounds can be determined from biokinetic parameters obtained from laboratory animals and man. The total plasma clearance is normally derived from the concentration-time profile following iv administration of a known dose. The plasma or total clearance is the sum of the individual routes of clearance, that is, of both renal and hepatic clearance. Hepatic clearance is a composite of biliary and metabolic clearances. Renal clearance is normally determined from the amount of unchanged drug excreted via the kidneys in a defined period, divided by the area under the plasma concentration-time curve for the same period. Biliary clearance can be determined in animal species in a similar manner to renal clearance. The hepatic (metabolic) clearance (Cl_H) is, therefore, the total plasma clearance minus the renal and biliary clearances.

These biokinetic parameters, along with values for liver blood flow and for the fraction of compound not bound to plasma proteins, are used with a liver model equation to calculate the intrinsic clearance. If the "well stirred" liver model is used (65), then intrinsic clearance (Cl_int) is calculated from the following:

Cl_int =	Cl_L
	F_u x (1 - Cl_L/Q_L)

Equation 10)

the fraction of drug unbound in the blood. The fraction of unbound drug can be determined by using standard protein binding techniques. The values for liver blood flow can be determined from the relationship outlined by Boxenbaum (66).

In vivo metabolic clearance can be predicted from in vitro kinetic data. Easily measurable parameters, such as Vmax and Km, can be scaled from the in vitro situation to provide whole body disposition kinetics. The basis of this procedure is that Cl_int is a pure measure of enzyme activity towards a drug in vivo, which is not influenced by other physiological determinants of clearance, such as hepatic blood flow or binding to blood components. For in vitro systems, the linear solution of the Michaelis-Menten equation (at substrate concentrations very much lower than the Km) provides a biochemical definition of Cl_int, namely the ratio Vmax/Km.

The in vivo metabolic clearance of a xenobiotic can be predicted from in vitro kinetic data by the use of a four stage strategy (67). Vmax and Km values can readily be determined by using either hepatic microsomes or freshly isolated hepatocytes. In addition, freshly isolated hepatocytes may be used to generate time profiles for the disappearance of the compound from the incubation medium, thereby providing an in vitro value for Cl_int. The second stage involves the use of scaling factors for microsomal protein recovery, hepatocellularity, and organ weight. The third stage of the strategy necessitates the use of a liver model (for example, the venous equilibration model) to express the kinetic data in terms of the circulating concentration of the chemical (blood or plasma) rather than the concentration at the enzyme site(s). This is necessary because physiological determinants of hepatic clearance (blood flow, blood binding, and tissue distribution of the compound) other than intrinsic clearance are often important in governing the extraction of the compound by the liver. The final stage in predicting in vivo kinetic behaviour from in vitro data involves consideration of other hepatic elimination routes, such as other metabolic pathways and the biliary excretion of a non-metabolised compound. In the majority of cases, clearance terms are additive and hence overall clearance may be readily described by terms which define parallel routes for the hepatic elimination of the compound.

There are crucial points which need to be considered before this strategy can be recommended for routine use: a) the validation of scaling gactors; b) the selection of liver models; and c) the predictivity of the approach.

Validation of Scaling Factors

Hepatic microsomal protein yield and hepatocellularity have been evaluated with respect to their suitability as scaling factors for microsomal and hepatocyte incubation systems with 25 compounds, all of which are metabolised by rat cytochromes P450 (67). For a 250 g rat with a liver weighing 11 g, a microsomal scaling factor of 500 mg (based on a recovery of 45 mg microsomal protein per g liver) and a hepatocyte scaling factor of 1.5 x 10⁹ cells (based on 1.35 x 10⁸ hepatocytes per g liver) can be employed. Both in vitro systems can be used to satisfactorily predict whether the extraction ratios of the compounds can be classified as low (<0.3) or high (>0.7). With the hepatocyte systems there is a particularly strong linear relationship between in vivo Cl_int and hepatocyte Cl_int over a range of three orders of magnitude; this has been demonstrated with data obtained from different laboratories, which is extremely encouraging for the use of such an approach for making quantitative predictions.

Selection of the Appropriate Liver Model

For xenobiotics with a high clearance, there is a large concentration difference across the liver. Therefore, to relate the rate of delivery (which is controlled by blood flow and binding) to the rate of metabolism, the selection of an appropriate liver model is important. The venous equilibration (well-stirred liver) model describes the liver in an identical fashion to other tissues in the PB-BK modelling approach. Uptake is perfusion-controlled rather than diffusion-controlled, and is restricted to compound which is not bound to protein. The distribution of the xenobiotic within the tissue is assumed to be homogenous and occurs instantaneously, generating a liver concentration which is equal to the venous concentration. In another model, the parallel tube model, the concentration of the xenobiotic declines exponentially along each of the identical, unconnected, parallel tubes (sinusoids). Other, more elaborate, models (for example, the axial dispersion model; 65) are stochastic in nature, and are more realistic in accounting for heterogeneity within the liver, albeit at the expense of greater mathematical complexity. Using the database of 25 compounds referred to previously, it was not possible to demonstrate whether one liver model was better than the others in predicting in vivo Cl_int from in vitro data. Thus, the simplest model, the venous equilibration model, would appear to be adequate for this type of analysis.

Predictive Value

If arbitrary limits are set for the precision of predictions of Cl_int from in vitro data of 2-fold (that is, between an underestimate of 50% and an overestimate of 100%) and 3-fold (an underestimation of 30% to an overestimation of 200%), the superiority of the hepatocyte system over the microsomal system is clearly demonstrated. With the database of 25 compounds referred to earlier (67), 69% and 94% of the data for hepatocytes are within the 2-fold and 3-fold limits, respectively. For microsomes, the corresponding values are 42% and 53%, respectively. In all cases, the microsomal data which are outside of the limits have Cl_int values greater than 10 ml/min per rat (that is, these are high clearance cases). It is, therefore, important to recognise the potential problem of accurately predicting high clearance values from microsomal data; hepatocyte data are preferable. Nevertheless, the nature of the relationship between hepatic clearance and Cl_int is such that a greater level of imprecision in the latter parameter can be accommodated as its magnitude increases. In many circumstances, it is the hepatic clearance per se which is the ultimate parameter of interest for PB-BK models. In contrast, in the low clearance situation, either in vitro system may be used with confidence to obtain Cl_int values and hence hepatic clearance values.

Use of Other In Vitro Metabolism Systems

Recent work has demonstrated that kinetic studies can be carried out in precision-cut liver slices with minor modifications to the typical in vitro approaches employed with microsomes and isolated hepatocytes, and thus the scaling of slice clearance values to the in vivo situation is feasible (68). Although data are limited, they clearly show that particular drugs can be classified into either high or low clearance compounds, and that the resolution is comparable to that obtained by using other in vitro methods. Also, studies undertaken with six drugs have demonstrated the same rank order of hepatic clearance in liver slices as that found in vivo, although in absolute terms the clearances of these drugs (which are all extensively metabolised by cytochrome P450) are underestimated by between 3- and 10-fold. It seems likely that simple linear scaling factors may not be adequate for undertaking in vivo predictions from data obtained with liver slices.

To date, no corresponding investigations have been conducted using hepatocyte monolayer cultures.

Current Position

On the basis of work undertaken with rat cytochrome P450 drug substrates, the simple degenerative models (Michaelis-Menten enzyme model; venous equilibration liver model and linear scaling factors) would appear to work satisfactorily for extrapolating data obtained with hepatic microsomes and hepatocyte suspensions to the in vivo situation. The more widespread applicability of these approaches to non-cytochrome P450 enzyme systems, and to predicting biokinetic parameters for humans, with their confounding inter-individual variabilities, needs to be assessed.

Renal Clearance

In spite of the fact that the kidney is a major organ of elimination for water soluble chemicals, many PB-BK models described in the literature do not explicitly include this organ. In these cases, urinary elimination is usually treated as a linear process, with the eliminated chemical being derived from the central (plasma) compartment. Even when the kidney is explicitly included in the model, specific elimination processes are not described, and often a linear process is assumed to describe the rate of elimination. To adequately model the filtration, secretion and reabsorption of chemicals in the kidney requires a more complex PB-BK model than is usually employed.

There are several important kinetic processes that occur in the kidney which influence the rate of elimination of chemicals in the urine. The first process is glomerular filtration, during which unbound, low molecular weight (<65,000), water-soluble chemicals are filtered into the renal tubular lumen with varying degrees of efficiency. Chemicals in this category pass through the tubular system, traversing various segments of the kidney in plug flow fashion. Each segment of the renal tubules has its own collection of enzymes and transport functions which influence the concentration and nature of the chemical in the luminal space. In some cases, the chemical can be specifically reabsorbed from the tubule lumen and concentrated in the tubular epithelial cells. Only about 25% of the plasma entering the kidney is filtered at the glomerulus; the remainder passes into the renal vasculature.

In the capillaries perfusing the basolateral surface of the renal tubular epithelia, some chemicals (in particular organic acids and bases) can be actively transported into tubular cells and ultimately secreted into the tubular lumen, thus increasing elimination above and beyond that predicted on the basis of glomerular filtration. Taking these processes into consideration, a PB-BK model for the kidney should include glomerular filtration, tubular reabsorption and tubular secretion. An even more accurate model describing renal function should take into account the counter-current flow behaviour in the kidney tubules, where reabsorption of water in the distal tubules concentrates chemical solutes, thus enhancing the reabsorption of chemicals which can easily diffuse across cellular membranes.

Another issue of importance with respect to the kidney is the relationship between chemical kinetics and dynamic responses, in particular cell-specific metabolism of xenobiotics and renal toxicity. The renal medulla is particularly susceptible to the effects of chemicals which undergo redox cycling, whereas the tubular epithelia are susceptible to glutathione conjugates, since these can be metabolised by β-lyase to reactive intermediates. Cell-specific activation of xenobiotics is an important consideration when modelling local sites of toxicity. In addition, modelling the relationship between renal tubular cytotoxicity and urinary and plasma markers of renal dysfunction will prove useful in the development of new risk assessment procedures for renal toxicants.

Validation of Kinetic Models

The application of in vitro models for risk evaluation is likely to be different for pharmaceuticals and environmental contaminants. However, a prerequisite for the systematic evaluation of any in vitro model is to possess in vivo data for both animal species and humans, in order to determine whether there is a correlation. These data allow the retrospective validation of the in vitro model, enabling its predictive capability to be determined. However, the limited availability of in vivo data for both animal species and humans makes the retrospective validation of biokinetic models difficult.

When considering biokinetic parameters, the published data reveal very few in vivo/in vitro correlations in animal species, and even fewer in humans. Advances in in vitro methodology have provided an opportunity to generate data which enable the prediction of in vivo kinetics. For example, several groups have used in vitro liver systems to determine intrinsic clearance by using the ratio of the Michaelis-Menten parameters Km and Vmax (67, 69). Unfortunately, these biokinetic parameters are rarely published for compounds which have been studied in laboratory animals or in humans, thus making the determination of intrinsic clearances from in vivo data difficult. To systematically evaluate and validate the in vitro model, it is necessary to have these in vivo data for a number of structurally diverse compounds.

In vitro biotransformation data are available for many compounds; these have been obtained predominantly with rat tissues. More recently, data have become available for human systems, which could be used to generate in vitro intrinsic clearance values. The publication of biokinetic data on the behaviour of novel chemical entities (pharmaceuticals) in animals is limited, but they are often available for humans. Thus, there are many gaps in our present knowledge. The only systematic in vitro/in vivo comparison, for a limited number of compounds, has been undertaken in the rat (67). The model employed appears promising, and needs to be validated further.

Most of the PB-BK models which have been published deal with the kinetics of pollutants following inhalation (23, 70-72). For many of these chemicals, some in vivo data are available for validating the model; these data have often been generated by the same group which developed the model. Complete data sets (different dose levels, different routes of exposure, different species, etc.) are rarely available for these environmental contaminants.

In general, the modelling of the kinetic behaviour of compounds after oral exposure is even more complicated than that following inhalation. An important part of the kinetic modelling of oral exposures is related to the biopharmaceutics of the matrix in which a compound is administered (73). This means that the biopharmaceutics should be incorporated in a (separate) module of the PB-BK model.

Two fundamental issues in biomathematical modelling were identified which need to be explored: a) model complexity; and b) parameter estimation. The more complex a model, the more difficult it becomes to validate its structure and parameters. From a practical point of view, the level of complexity of a model should be determined by the relevant phenomena which have to be described. Nevertheless, the appropriate level of complexity is not always known, and mathematical models evolve with time, as new knowledge and new experimental data become available. One approach to mathematical modelling is to initially "over model" (that is, to create a model of greater complexity than is ultimately required). This is useful for two reasons. Firstly, if a model is created with greater complexity than needed for a particular situation, turning on or off certain processes enables a quantitative evaluation of the impact of these processes on the behaviour of the model. If only the "simple" model is evaluated, the impact of processes which have been neglected (that is, those which were assumed not to be important) will never be known. Secondly, it is easy to "turn off" a process (usually by setting a scaling parameter to zero). However, if you start from a simplified model and then decide that a more complex process is needed, it usually involves significant reprogramming.

The second issue is, given the model complexity, how to uniquely define the large number of model parameters, particularly when there are numerous interactions between parameters. Firstly, it is important to note that as long as there are experimental errors in the measurement of the stated variables (plasma concentrations, tissue concentrations, etc.), even if all of the necessary measurements are taken from a single animal (to eliminate inter-individual variability), there will never be a unique set of model parameters. In all cases, a range of combinations of model parameters will give equally likely fits to the data. Thus, there is a need to define the acceptable range of parameter values for a particular modelling situation. Secondly, the amount of data available for validating the model influences the degree of credibility attributed to a model. Often there is a large amount of data available in the literature concerning the concentrations of chemicals in various tissues, the urinary and faecal excretion of the chemical, etc. These data may include various dose levels, and may be available for different tissues and exposure times, all of which contribute to the fitting of different model parameters. Unfortunately, data sets are not usually available which contain all of the essential variables over an adequate range of times and doses to uniquely define all of the model parameters. Nethertheless, this does not mean that the literature data are not useful. Model validation involves both qualitative and quantitative aspects. The large literature database can be effectively used to validate the model in qualitative terms. Such efforts will not precisely define all of the model parameters for a particular species, strain, sex or age (weight) group, but will allow the validity of the basic model structure to be confirmed; in addition, relatively broad limits on model parameters can be assigned. These limits act as a starting point for more careful evaluation of the model parameters in those cases where more complete measurements of the variables can be obtained. Sensitivity analysis becomes an important tool in the process of model re-evaluation, and can be used to direct future research efforts based upon knowledge of the dependency of model predictions on specific parameters (5).

Model parameters can be estimated by various techniques including, but not limited to, curve fitting, so that the model adequately predicts experimental results (tissue concentrations of the test chemical with time and at different doses, urinary excretion rates of the parent chemical and metabolites, etc). In PB-BK modelling, the parameters can be divided into two major classes: a) chemical- independent parameters (for example, tissue weights, water contents of tissues, lipid contents of tissues, blood flows to tissues, albumin concentrations in plasma, and rates of normal cell turnover); and b) chemical-dependent parameters.

The first set of parameters are fixed by the species, strain, sex, weight, nutritional status, disease status, etc. of the animal to be modelled. Mean values for these parameters, as well as intra-individual and inter-individual variability, must be known accurately from independent studies. Currently, the lack of this type of data is a significant problem for PB-BK modellers, and this must be addressed. Under no circumstances should chemical-independent parameters be adjusted by curve fitting exercises. Chemical-dependent parameters must be determined from experimental studies, conducted either in vivo or in vitro. As a last resort, chemical-dependent parameters can be estimated by fitting model simulations to in vivo kinetic data.

With respect to confirming that the model and its associated parameters are correct, the best that can be said is that the predictions of the model are consistent with the experimental database available. This is one definition of a "validated" model. The data which the model adequately simulates define the domain of validation of the model. Given new data, such as concentrations in different tissues, or data for different doses or routes of dosing, the model may or may not provide an accurate prediction. If a model is well designed and is consistent with the physiological and biochemical processes which are known to control the kinetics of the compound, then the model should accurately predict the behaviour of the compound in the new situation. This means that the domain of validity of the model is, in effect, greater than the domain of validation. The domain of validity of a model is related to the complexity of the model. In general, simple models will have a smaller domain of validity than more complex models, and thus the use of simple models is more restricted. A major objective of the modelling process is to maximise the domain of validity, and this is best achieved by retaining the maximum possible degree of model complexity.

The construction of a PB-PK model requires that certain assumptions are made about a number of physiological parameters. If modellers are not familiar with the details of physiological processes, they run the risk of including processes in their models which are not relevant or realistic. Expert opinion on the assumptions underlying the models should be, and in some cases already is, part of the validation of the model. Such an approach is not only required when defining the need to incorporate different organs in PB-BK models, but also when incorporating detailed information on enzyme kinetics. There should be a sound scientific rationale for the inclusion of data on enzyme inhibition, induction, and saturation.

In vitro kinetic models should be validated against independent sets of in vivo data (that is, those which have not been used during the development or initial evaluation of the model), obtained at several dose levels. The data obtained for non-linear dose ranges will indicate the strengths and weaknesses of the model. Furthermore, data sets should be available for different species and different routes of administration, to provide a basis for using the model to extrapolate between effects observed in particular species at certain chemical concentrations.

In conclusion, for the systemic evaluation and validation of PB-BK models there are not always sufficient data available, with perhaps the exception of data on the uptake and distribution of volatile compounds of low reactivities, such as organic solvents. Comprehensive validation of many PB-BK models, including undertaking in vitro/in vivo comparisons, remains to be carried out.

Applicability

Determination of In Vivo Toxic Potencies from In Vitro Toxicity Test Data

In order to use in vitro toxicity data for in vivo toxic potency assessments, effective concentrations determined in vitro have to be related to equivalent body doses. Provided that the target organs are known and that the in vitro effective concentrations can be transformed into equivalent target organ doses, PB-BK modelling would be the most suitable method for this extrapolation.

Recently, another, comparatively simple, approach for undertaking quantitative in vitro/in vivo extrapolations has been developed (74). In a first attempt, only the equilibrium distribution of xenobiotics governed by their lipophilicities and the relative volumes of the lipid and water spaces were taken into account. The relationships between the volumes of both compartments of distribution are tremendously different in cell culture systems compared with the in vivo situation in mammalian species. Two basic assumptions characterise this extrapolation method. At first, ignoring any other pharmacokinetic factors, and also plasma and tissue protein binding, both the in vitro and the in vivo system (model body) were considered to be simple two-compartment systems, with the total dose of a given substance being equally distributed between the water and the lipid compartments according to the K_ow. Secondly, it was assumed that a model body dose is equivalent to an in vitro effective nominal concentration (for example, the EC50), in which case it results in the same concentration in the water compartment of the model body and in the in vitro system. According to both assumptions, EC50 values can be related to equivalent model body doses (ED50 values) by the following equation:

ED50 = EC50	(K_ow x V_L,b + V_W,b)
	(K_ow x V_L,t + V_W,t)

(Equation 11)

The relative volumes of the lipid and water compartments of the model body (V_L,b and V_W,b, respectively) were assumed to be 0.1 and 0.6 litres/kg, respectively. The volumes of the corresponding compartments in vitro (V_L,t and V_W,t) were estimated to be 0.0003 and 1.0 litres/litre, respectively (74). With this parameter setting, the scaling factor for transforming EC50 values into ED50 values may vary between 0.6 and 333 (litres/kg), depending upon the K_ow of the compound.

This extrapolation model has been applied to EC50 values obtained for the effects of the first 30 MEIC (Multicenter Evaluation of In Vitro Cytotoxicity) reference chemicals (75) in primary cultures of spontaneously contracting rat skeletal muscle cells. The conversion of EC50 values into ED50 values altered the relative potencies, and considerably increased the agreement between the potencies at which the spontaneous contractions of the muscle cells in vitro were abolished and the acute toxic potencies of the compounds in vivo, as characterised by LD50 values (74). After further elaboration of the approach, by incorporating other relevant parameters which control distribution (for example, protein concentration and protein binding), this extrapolation method is considered to be suitable for evaluating the relevance of different endpoints for acute toxic potency assessments (76), and for inclusion in an in vitro testing strategy for classifying chemicals according to their acute toxic effects (77).

Links between Kinetic and Dynamic Modelling

The ability to predict toxicity in the context of undertaking quantitative risk assessments is dependent on the development of specific experimental/theoretical algorithms which describe dose/time-response relationships for toxicological responses in vivo. A predictive paradigm to attain this goal involves combining systemic kinetics, cellular toxicity and systemic dynamics for determining quantitative in vivo dose-response relationships (Figure 2). PB-BK modelling can be used to relate the external exposure scenario to some measure of the active dose of the chemical at the cellular target. Physiologically-based biodynamic (PB-BD) modelling can be used to describe the dose- and time-dependence of a cellular response to the delivered/active dose. Systemic PB-BD models can be developed to describe the relationship between cellular events and systemic responses observed clinically. The combination of these three components will allow for a quantitative evaluation of the dose-time-response relationship.

Figure 2: Components of a Predictive Paradigm for Dose-Response Relationships

The paradigm consists of three components: a) a systemic PBBK model to describe the relationship between exposure [E(t)] and the active dose of the chemical at the molecular target [A(t)]; b) a cellular PBBD model to describe the relationship between A(t) and the time-course of the cellular response [Cr(t)]; and c) a systemic PBBD model to describe the relationship between Cr(t) and the time-course of the observable systemic response [SR(t)]. The reverse arro loops indicate that responses occurring in the dynamic phase of the process can feed back and affect ongoing kinetic and dynamic processes. Lacking a mechanistic mathematical model for the cellular response, the possibility of using in vitro models to empirically describe this component of the paradigm should be explored.

The line separating kinetics from dynamics is difficult to draw. There is a tendency to think in terms of the kinetics phase ending with a description of the concentration of the active form of the toxicant at the molecular target, and the dynamics phase starting as a result of some subsequent alteration of the molecular target. However, this line of demarcation becomes fuzzy when we consider that there are feedback loops between cellular and systemic dynamic responses and kinetics.

The central focus of the predictive paradigm is the link between systemic kinetics and systemic dynamics (that is, the cellular dynamic response). To address this focal issue, a two-pronged approach is required involving theoretical tools (mathematical models of cellular dynamic processes) and empirical approaches (in vitro toxicity model systems). In the short-term, in vitro toxicity test systems incorporating differentiated cells and mechanistically defined endpoint measurements can provide a critical empirical link between systemic kinetic models and systemic dynamic models. In the long-term, it will prove necessary to establish new modelling techniques to describe cellular dynamic responses, otherwise it will not be possible to incorporate mechanistic knowledge into quantitative risk assessment processes. Without quantitative modelling tools, mechanistic information will only be useful in a qualitative sense.

The modelling of cellular dynamic processes is conceptually different to kinetic modelling, and involves the description of information processing. Modelling efforts must take into consideration processes such as signal transduction, amplification, feedback, feed-forward, etc. One area of dynamic modelling of interest is the regulation of the concentration of cellular constituents which are essential to the maintenance of normal cellular functions. Examples of these constituents include: a) calcium, which is an important regulator of cellular functions; b) ATP, which is the major energy source in the cell; c) hydrogen ions (pH), which regulate cellular functions; d) sodium and potasssium, which are important in maintaining transmembrane electrical potentials; and e) glutathione, which is important for the detoxification of certain compounds. As attempts are made to model the mechanisms of action of toxic chemicals, it will be necessary to develop quantitative models of these and other cellular constituents and incorporate them into the dynamic descriptions of toxicity.

A second area of interest to dynamic modellers is the regulation of gene expression. The induction of specific cellular proteins, in response to perturbations of the homeostatic regulation of the cellular environment following exposure to xenobiotics, is a well-defined effect. In some cases, the protein which is induced affects the kinetics of the inducing agent in a feedback mode. In other cases, the induced proteins may have a direct effect on the toxicological process. The induction of cellular stress proteins seems to be a protective mechanism in response to cellular damage. Changes in patterns of gene expression, and the resultant altered response of cells to growth stimuli over time, influence cell kinetics and the control of cellular proliferation. In all of these situations, the induced protein(s) will affect the dose-response relationship at low doses, thereby having an impact on the ability to predict the toxicological outcomes of chronic exposures to chemicals. Developing the capability to model these processes will improve our ability to reliably predict the impact of these dynamic responses on dose-response relationships.

Indirect molecular mechanisms of toxicity must also be taken into consideration. Some chemicals do not directly cause the observed toxicity at the cellular level. For example, the possible genotoxic effects of peroxisome proliferators are probably a consequence of free radical generation resulting from the alterations in intracellular functions caused by these chemicals (that is, the chemicals themselves are not directly genotoxic). The ability to model the indirect generation of free radicals will significantly improve the risk assessment process for an important sub-class of epigenetic carcinogens.

As indicated in Figure 2, there are feedback loops between the various components of the predictive paradigm. Cellular dynamic responses can influence systemic kinetics, and systemic dynamic responses can influence both systemic kinetics and cellular dynamics. Due to the lack of mechanistic mathematical models for cellular responses, the possibility of using in vitro models to empirically describe this component of the paradigm should be explored.

One important characteristic of biological systems is their ability, overtime, to modulate functions in response to adverse stimuli. There are numerous examples of biological systems adapting to chronic exposures to toxic chemicals. A classical example is the induction of the various cytochrome P450 isozymes in response to exposure to certain xenobiotics. The increased levels of these enzymes significantly alters the metabolic rates for many chemicals, thus influencing the kinetics of not only the inducing chemical itself, but also of other chemicals. Another example is the induction of metallothionein by various heavy metals. This protein binds the inducing metal and significantly alters the observed kinetics of the effector metal. Research in this area should be undertaken to: a) develop methods to predict the adaptive effects of chemicals which ultimately affect kinetic processes; and b) develop combined PB-BK/PB-BD models to quantitatively describe enzyme induction and its effects on systemic kinetics.

A related issue is our ability to describe the effects of overt toxicity on the kinetics of chemicals. Alterations in blood flow, enzymatic function, and physiological processes concomitant with pathological conditions can significantly influence the biokinetics of a chemical. The ability to incorporate these changes into kinetic models will greatly improve our ability to predict chronic effects.

The problem of modelling dynamic responses at both the cellular and systemic levels is more intractable than kinetic modelling at the present time. The major limitation to progress in dynamic modelling is the lack of knowledge concerning the sequence of events in vivo leading from cellular exposure to alterations in cellular functions and ultimately to overt systemic pathologies. As a consequence, it is difficult to define suitable in vitro endpoints which are appropriate markers for the pathogenic process at higher levels of biological organisation. Although this is a new field of investigation, some approaches to this problem have been attempted. Reitz et al (78) introduced cell killing into a PB-BD model for chloroform, to describe hepatic necrosis. The approach assumed a normal distribution of the sensitivities of hepatocytes to chloroform and adjusted the distribution parameters to fit with the observed hepatic necrosis data. Beck et al (79) reported a slightly different approach, but still relied on using the cell death relationship to describe the observed toxicity in vivo. The possibility of incorporating experimentally derived in vitro toxicity data into PB-BD models for predicting in vivo toxicity should be explored.

Future Perspectives

The ultimate question with new technologies is always whether and, if so, how they may be applied in practice. For PB-BK models, their application in risk assessment is the main objective. PB-BK modelling follows exposure modelling and precedes dynamic modelling. Therefore, PB-BK modelling will undoubtedly play a key role in both hazard prediction and risk assessment for pharmaceuticals and environmental contaminants. The essential difference between these is that, for drugs, the accepted risk is based on a health benefit/risk ratio, with an acceptable ratio depending on the type of disease for which the drug is prescribed, whereas for other chemicals there should be minimal, if any, risk of adverse effects. The uncertainty of setting safe exposure limits for chemicals based upon animal data in combination with either "quantitative risk extrapolation" for carcinogenic chemicals, or the "safety factor" approach for non-carcinogens, could be reduced by the application of PB-BK models.

For the risk evaluation of drugs, much more information is required and is available on their biokinetics, since patients are exposed to these compounds at levels that should result in biological effects. At present, the role of PB-BK models in drug discovery and development relates to their use for optimising drug design at early stages of discovery, and for optimising the clinical stages of drug development during the preclinical phase. In this respect, they can expedite the drug development process and reduce the number of animals which need to be used. Nevertheless, in the near future, the total replacement of animal studies during the drug discovery and preclinical phases of drug development is not feasible.

The incorporation of PB-BK and PB-BD modelling into risk assessment procedures opens up the possibility of making much better use of in vitro-derived toxicological data. The possibilities for developing biokinetic models based solely on in vitro-derived parameters should be further explored, as has been proposed in the ERGATT/CFN Integrated Toxicity Testing Scheme (ECITTS) programme (3, 4). Parts of this scheme are now being investigated. The vast amount of data which can be derived from detailed mechanistic studies conducted in in vitro systems can be much better employed for toxicological risk evaluations if biokinetic factors are also incorporated. When such data can be combined with predictions of the toxic potentials of compounds, making use of information about the physicochemical properties of these compounds and data on QSARs (5), an important step toward toxicological risk evaluations which are less dependent on animal experimentation will have been made.

Conclusions and Recommendations

Recent developments in modelling the biokinetic behaviour of compounds were discussed extensively during the workshop, including the difficulties encountered and the limitations of the approaches. It is hoped that the conclusions and recommendations outlined below will be of help in guiding future work in this field.

It is recommended that predictive PB-BK models be used instead of classical (descriptive) models. This will increase the possibilities for integrating in vitro data into models which can be used for hazard prediction and risk evaluation purposes.
There is no such thing as an "ideal biokinetic model". The model to be used should be adapted to the experimental needs on a case-by-case basis, and is dependent on the class of chemical to be studied.
A paradigm for biokinetic modelling (for laboratory animals and humans) should be established, which documents the physiological parameters required and which illustrates what is needed experimentally.
A database on biokinetic experiments should be established, to aid the development, evaluation, and validation of PB-BK models.
In order to construct a biokinetic model, it is necessary to have ready access to the data required (for example, partition coefficients; blood, plasma, and tissue levels of the compound). These data are not normally given in the published literature. Researchers should be encouraged to make them available.
Further research should be carried out on the physicochemical parameters which determine those partition coefficients of importance in biokinetic modelling.
Further research is needed on the biochemical and physiological characteristics of special barriers (gastrointestinal tract, lung, skin, and BBB). The penetration rates of chemicals across special barriers should be incorporated into biokinetic models.
Whereas in vitro data are available for particular biotransformation systems (especially cytochrome P450) in the rat, there are limited analogous data available for humans. More emphasis should be given to undertaking species comparisons, in order to be able to develop biokinetic models for predicting effects in humans. Nevertheless, it is recognised that human tissues are only available to a limited extent. The potential of using cell lines which heterologously express human enzymes, and the establishment of human microsome banks, should be evaluated. For drugs, in particular, reliable human in vivo data are available from clinical trials.
Biotransformation data on non-cytochrome P450 reactions in vitro are needed, and the scaling of such data should be addressed. Further research should be undertaken into the value of kinetic data on chemical biotransformation derived from in vitro systems which are already in widespread use for toxicity studies, for example, those obtained with monolayer cultures of primary hepatocytes.
The development of models for predicting the organ(s) in which compounds or their metabolites will accumulate should be encouraged. This could be helpful with respect to improving the design of in vitro and in vivo experiments.
To enable a meaningful incorporation of in vitro data on the kinetics (and toxicodynamics) of compounds into appropriate biokinetic models, a better understanding of the time course of exposure, and of processes such as adaptation and induction, is needed. The in vitro system should provide a reliable prediction of the relevant in vivo situation.
Biokinetic models should be expanded to describe the toxicodynamics of a compound. PB-BD models are now being developed, and it is recommended that a workshop on the use of these models should be held at some stage in the future.
The validation of biokinetic models should be undertaken with an independent set of data.
There is a need for a central evaluation of the usefulness of the different software systems which are being used in biokinetic modelling experiments, especially with respect to the comparability of the data generated.
Sensitivity analyses should be employed to identify potential sources of errors in the construction of biokinetic models. The objectives, methods used, and results of these analyses should be published.

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The Use of Biokinetics and In Vitro Methods in Toxicological Risk Evaluation

The Report and Recommendations of ECVAM Workshop 151,2

The Report and Recommendations of ECVAM Workshop 15^1,2