Models, tissue partition coefficients

In a first stage, distribution was predicted with tissue composition-based equations and the estimated tissue partition coefficients were combined with clearance estimated by direct scaling of hepatocyte intrinsic clearance in a PBPK model as described earlier. 

Once the structure of the PBPK model is formulated, the next step is specifying the model parameters. These can be classified into a chemical-independent set of parameters (such as physiological characteristics, tissue volumes, and blood flow rates) and a chemical-specific set (such as blood/tissue partition coefficients, and metabolic biotransformation parameters). Values for the chemical-independent parameters are usually obtained from the scientific literature and databases of physiological parameters. Specification of chemical-specific parameter values is generally more challenging. Values for one or more chemical-specific parameters may also be available in the literature and databases of biochemical and metabolic data. Values for parameters that are not expected to have substantial interspecies differences (e.g., tissue/blood partition coefficients) can be imputed based on parameter values in animals. Parameter values can also be estimated by conducting in vitro experiments with human tissue. Partitioning of a chemical between tissues can be obtained by vial equilibration or equilibrium dialysis studies, and metabolic parameters can be estimated from in vitro metabolic systems such as microsomal and isolated hepatocyte syterns. Parameters not available from the aforementioned sources can be estimated directly from in vivo data, as discussed in Section 43.4.5. 

Dixon et al. (2001) described a preliminary PB-PK model to predict JP-8 concentrations in Air Force fuel-cell maintenance workers. The model used data from PB-PK models of naphthalene inhalation in mice and rats and nonane inhalation in rats. In addition to inhalation, a pathway of dermal exposure and a skin compartment were included. For highly exposed people, the PB-PK model was generally in agreement with exhaled-air naphthalene concentrations however, predictions for the low-exposure scenarios were grossly underestimated, especially in female workers, by a factor of 10. The model did not predict blood and urinary concentrations. The major limitation of the Dixon et al. (2001) study was the lack of appropriate human data (e.g., metabolic measures, blood and tissue partition coefficients, and diffusion rates). The Dixon et al. (2001) model predicted a rapid decline in naphthalene concentrations in all compartments after exposure except liver, fat, and brain. The model predicted accumulation in liver, brain, and fat tissues for a 7-day period that included 4-hr exposures on 5 days. Competition for enzyme does not occur only from interactions of different inhaled compounds. Interactions can also occur between inhaled compounds and metabolites formed in the body that require similar enzymes for biotransformation. Detailed kinetic studies with both benzene and -hexane show inhibition of later metabolic steps, phenol to hydroquinone or methyl -butyl ketone to 2,5-hexane dione, by high concentrations of inhaled benzene or hexane, respectively (Medinsky et al. 1989 Andersen and Clewell 1984). 

There are two types of parameters that can be employed to represent the extent of distribution in PK models. The first is a tissue partition coefficient Kj), and the second is a volume of distribution (F). The definition of each of these parameters is provided in the following sections. 

Membrane transport, as modeled by partition coefficient data, and tissue uptake do not appear to be limiting factors in the sequence of event(s) responsible for antitumor activity. Antitumor activity does not parallel the order of compound retention but does approximately parallel trends in toxicity (LD] g 30 data). The number of Pt atoms bound/DNA base nucleotide (Rb values) appears to parallel the antitumor activity of ois vs. trane. 

The generic structures, technical names, physical and chemical properties, and tissue partition coefficients of the 15 pyrethroids and their metabolites are provided in Tables D1-D15 of Appendix D. Physical property values for modeling were obtained using a 2D model, ACD 12 (Advanced Chemistry Development, Inc., Toronto, Canada). A QSAR 3D model (i.e., QikProp 3.0 (Schrodinger, LL)), used in the development of (fraction unbound to plasma protein), indicated that the differences in physical binding properties between isomers were small. Differences, however, exist in chemical properties as noted in metabolism studies reviewed in Sect. 5. Biotransformation and elimination paths for the pyrethroids that are presented in Tables E1-E15 of Appendix E incorporate preliminary metabolic rate data for PBPK/PD model development. 

Physiologically Based Phamiacokinetic (PBPK) Model—Comprised of a series of compartments representing organs or tissue groups with realistic weights and blood flows. These models require a variety of physiological information tissue volumes, blood flow rates to tissues, cardiac output, alveolar ventilation rates and, possibly membrane permeabilities. The models also utilize biochemical information such as air/blood partition coefficients, and metabolic parameters. PBPK models are also called biologically based tissue dosimetry models. 

Olive oil was the original model lipid for partition studies, and was used by Overton in his pioneering research [518,524], It fell out of favor since the 1960s, over concerns about standardizing olive oil from different sources. At that time, octanol replaced olive oil as the standard for partition coefficient measurements. However, from time to time, literature articles on the use of olive oil appear. For example, Poulin et al. [264] were able to demonstrate that partition coefficients based on olive oil-water better predict the in vivo adipose-tissue distribution of drugs, compared to those from octanol-water. The correlation between in vivo log Kp (adipose tissue-plasma) and log (olive oil-water) was 0.98 (r2), compared to 0.11 (r2) in the case of octanol. Adipose tissue is white fat, composed mostly of triglycerides. The improved predictive performance of olive oil may be due to its triglyceride content. 

Estimation methods for tissue-to-blood partition coefficients (i.e., Rt) have been the most prolific, no doubt due to the need for this parameter in most organ models. Both in vitro and in vivo parameter estimation techniques are available. 

JH Lin, Y Sugiyama, S Awazu, M Hanano. In vitro and in vivo evaluation of the tissue-to-blood partition coefficients for physiological pharmacokinetic models. J Pharmacokin Biopharm 10 637-647, 1982. 

HSG Chen, JF Gross. Estimation of tissue-to-plasma partition coefficients used in physiological pharmacokinetic models. J Pharmacokin Biopharm 7 117-125, 1979. 

Only a subset of the parameter values in the O Flaherfy model require inputs from the user to simulate blood and tissue lead concentrations. Lead-related parameters for which values can be entered into the model include fractional absorption from the gastrointestinal tract partition coefficients for lead in nonbone tissues and in the surface region of bone maximum capacity and half-saturation concentration for capacity-limited binding in the erythrocyte elimination clearance fractional clearance of lead from plasma into forming bone and the restricted permeability coefficients for lead diffusion within bone, from plasma into bone, and from bone into plasma (O Flaherty 1991a). 

Another method of predicting human pharmacokinetics is physiologically based pharmacokinetics (PB-PK). The normal pharmacokinetic approach is to try to fit the plasma concentration-time curve to a mathematical function with one, two or three compartments, which are really mathematical constructs necessary for curve fitting, and do not necessarily have any physiological correlates. In PB-PK, the model consists of a series of compartments that are taken to actually represent different tissues [75-77] (Fig. 6.3). In order to build the model it is necessary to know the size and perfusion rate of each tissue, the partition coefficient of the compound between each tissue and blood, and the rate of clearance of the compound in each tissue. Although different sources of errors in the models have been... 

There is no experimental evidence available to assess whether the toxicokinetics of -hexane differ between children and adults. Experiments in the rat model comparing kinetic parameters in weanling and mature animals after exposure to -hexane would be useful. These experiments should be designed to determine the concentration-time dependence (area under the curve) for blood levels of the neurotoxic /7-hcxane metabolite 2,5-hexanedione. w-Hcxanc and its metabolites cross the placenta in the rat (Bus et al. 1979) however, no preferential distribution to the fetus was observed. -Hexane has been detected, but not quantified, in human breast milk (Pellizzari et al. 1982), and a milk/blood partition coefficient of 2.10 has been determined experimentally in humans (Fisher et al. 1997). However, no pharmacokinetic experiments are available to confirm that -hexane or its metabolites are actually transferred to breast milk. Based on studies in humans, it appears unlikely that significant amounts of -hexane would be stored in human tissues at likely levels of exposure, so it is unlikely that maternal stores would be released upon pregnancy or lactation. A PBPK model is available for the transfer of M-hcxanc from milk to a nursing infant (Fisher et al. 1997) the model predicted that -hcxane intake by a nursing infant whose mother was exposed to 50 ppm at work would be well below the EPA advisory level for a 10-kg infant. However, this model cannot be validated without data on -hexane content in milk under known exposure conditions. 

Results in Table 31.3 indicate that the combination of TS and TC descriptors resulted in a highly predictive RR model = 0.895) the addition of three-dimensional and QC indices to the set of independent variables did not result in significant improvement in model quality. It may be noted that we have observed such results for various other physicochemical and biological properties including mutagenicity [25,54], boiling point [55], blood air partition coefficient [37], tissue air partition coefficient [46], etc. [24,30,45,56]. Only in limited cases, e.g., halocarbon toxicity [12], the addition of QC indices after TS and TC parameters resulted in significant improvement in QSAR model quality. 

Blood-tissue uptake rates (l< ) can often be approximated from data at early (t < 10 minutes) time points in IV studies, provided the blood has been washed from the organ (e.g., liver) or the contribution from blood to the tissue residue is subtracted (fat). High accuracy is not usually required since these parameters can be optimized to fit the data when they are used in more complex models. Tissue-blood recycling rates (A y) and residence times can be computed from partition coefficients if estimates of uptake rates are available. 

Extrapolation between species should ideally take into account metabolic routes, i.e., the absence or presence of metabolites, as well as the relative rate of formation of the individual metabolites. In PBPK models (Section 4.3.6), both aspects (nonlinearity, formation of active metabolites) are incorporated. This modeling technique uses compartments that correspond to actual tissues or tissue groups of the body. Size, blood flow, air flow, etc. are taken into account, in addition to specific compound-related parameters such as partition coefficients and metabolic rate data. Based on such studies, target-organ concentrations of active metabolites can be predicted in experimental animals and humans, thus providing the best possible basis for extrapolation (Feron et al. 1990). 

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