Clearances model development

PBPK models have also been used to explain the rate of excretion of inhaled trichloroethylene and its major metabolites (Bogen 1988 Fisher et al. 1989, 1990, 1991 Ikeda et al. 1972 Ramsey and Anderson 1984 Sato et al. 1977). One model was based on the results of trichloroethylene inhalation studies using volunteers who inhaled 100 ppm trichloroethylene for 4 horns (Sato et al. 1977). The model used first-order kinetics to describe the major metabolic pathways for trichloroethylene in vessel-rich tissues (brain, liver, kidney), low perfused muscle tissue, and poorly perfused fat tissue and assumed that the compartments were at equilibrium. A value of 104 L/hour for whole-body metabolic clearance of trichloroethylene was predicted. Another PBPK model was developed to fit human metabolism data to urinary metabolites measured in chronically exposed workers (Bogen 1988). This model assumed that pulmonary uptake is continuous, so that the alveolar concentration is in equilibrium with that in the blood and all tissue compartments, and was an expansion of a model developed to predict the behavior of styrene (another volatile organic compound) in four tissue groups (Ramsey and Andersen 1984). 

Physicochemical parameters determine several characteristics of the compound, like binding, partition, permeability or excretion. When building a PBPK model the level of information available for a drug may vary depending on the status of the development and the experiments performed. For model development the unknown parameters might be assumed and refined when the experiment is performed or some of the parameters can be estimated by the model, for example the different clearance values describing renal, hepatic and other excretions. 

Covariate Model Development. Treatment (with and without ritonavir) would be included as a potential covariate on clearance. Influence of AAG on clearance and of weight on volume and clearance were also included as potential covariate relationships. Assay site was also included as a potential covariate for residual error. 

We present a pediatric population PK (PPK) model development example to illustrate the impact that the model development approach to scaling parameters by size can have on pediatric PPK analyses a typical pediatric study is included. It is intuitive that patient size will affect PK parameters such as clearance, apparent volume, and intercompartmental clearance and that the range of patient size in most pediatric PPK data sets is large. Thus, it is expected that in most pediatric PPK studies subject size will affect multiple PK parameters. However, because there are complex interactions between covariates and parameters in pediatric populations, there are also intrinsic pitfalls of stepwise forward covariate inclusion. Selection of significant covariates via backward elimination has appeal in nonlinear model building however, it requires knowledge of the relationship between the covariate and model parameters (linear vs. nonlinear impact) and can encounter numerical difficulties with complex models and limited volume of data often available from pediatric studies. Thus, there is a need for PK analysis of pediatric data to treat size as a special covariate. Specifically, it is important to incorporate it into the model, in a mechanistically appropriate manner, prior to evaluations of other covariates. 

A major objective of fundamental studies on hollow-fiber hemofliters is to correlate ultrafiltration rates and solute clearances with the operating variables of the hemofilter such as pressure, blood flow rate, and solute concentration in the blood. The mathematical model for the process should be kept relatively simple to facilitate day-to-day computations and allow conceptual insights. The model developed for Cuprophan hollow fibers in this study has two parts (1) intrinsic transport properties of the fibers and (2) a fluid dynamic and thermodynamic description of the test fluid (blood) within the fibers. 

Respiratory Tract Clearance. This portion of the model identifies the principal clearance pathways within the respiratory tract. The model was developed to predict the retention of various radioactive materials. Figure 3-7 presents the compartmental model and is linked to the deposition model (Figure 3-6) and to reference values presented in Table 3-9. Table 3-9 provides clearance rates and deposition fractions for each compartment for insoluble particles. The table provides rates of insoluble particle transport for each of the compartments, expressed as a fraction per day and also as half-time. ICRP (1994a) also developed modifying factors for some of the parameters, such as age, smoking, and disease status. Parameters of the clearance model are based on human evidence for the most part, although particle retention in airway walls is based on experimental data from animal experiments. 

Earlier in model development, a 3-compartment model was tested and its inclusion in the model was questionable. To see whether with the additional data a 3-compartment model should be used, the model estimates for the third compartment were set equal to 1/10 the intercompartmental clearance and peripheral volume values. Table 5.9 presents the model parameter estimates. The AIC of the Model 8 was 3.567, an improvement over Model 6. Visual examination of the goodness of fit plots, however, showed an improvement in fit with intravenous and inhalational administration, but now the intranasal route was not as well predicted (Fig. 5.11). That loss from the second dosing compartment occurred but not from the first dosing compartment, and it did not make much sense. Hence, first-order loss from Cl was added back into the model under two different conditions (Model 9 in Fig. 5.5). In the first condition, the rate of loss from Cl was treated as equal to the rate of loss from C2. With this model the AIC was 3.584, which was not an improvement over Model 8. Under the second condition, unique rate constants for each dosing compartment were examined. Like Model 5, the rate of loss from Cl kept hitting its lower bound of zero, indicating the kiossi should be removed from the model. Both these models were then discarded. 

One goal of population pharmacokinetic models is to relate subject-specific characteristics or covariates, e.g., age, weight, or race, to individual pharmacokinetic parameters, such as clearance. There are many different methods to determine whether such a relationship exists, some of which were discussed previously in the chapter, and they can be characterized as either manual or automated in nature. With manual methods, the user controls the model development process. In contrast, automated methods proceed based on an algorithm defined by the user a priori and a computer, not the user, controls the model development process. Consequently, the automated methods are generally considered somewhat less subjective than manual procedures. The advantage of the automated method is its supposed lack of bias and ability to rapidly test many different models. The advantage of the manual method is that the user... 

Base model development proceeded from a 1-compartment model (ADVAN1 TRANS2) estimated using first-order conditional estimation with interaction (FOCE-I) in NONMEM (Version 5.1 with all bug fixes as of April 2005). All pharmacokinetic parameters were treated as random effects and residual error was modeled using an additive and exponential (sometimes called an additive and proportional) error model. Initial values for the fixed effects were obtained from the literature (Xuan et al., 2000) systemic clearance (CL) of 4.53 L/h and volume of distribution (VI) of 27.3 L. Initial values for the variance components was set to 32% for all, except the additive term in the residual error which was set equal to 1 mg/L. The model successfully converged with an OFV of 20.141. The results are shown in Table 9.4. 

A recent study compared different mathematical models developed to correlate compound structures with hepatic clearance [56]. The models were all established using a representative dataset of 22 extensively metabolized compounds with their in vivo and in vitro physiological characteristics. The mathematical prediction models... 

Scale models are a real asset in the effective and efficient layout and sometimes process development of a plant. Although any reasonable scale can be used, the degree of detail varies considerably with the type of process, plant site, and overall size of the project. In some instances cardboard, wooden, or plastic blocks cut to a scale and placed on a cross-section scale board will serve the purpose. Other more elaborate units include realistic scale models of tlie individual items of equipment. These are an additional aid in visualizing clearances, orientation, etc. 

TFL is an important sub-discipline of nano tribology. TFL in an ultra-thin clearance exists extensively in micro/nano components, integrated circuit (IC), micro-electromechanical system (MEMS), computer hard disks, etc. The impressive developments of these techniques present a challenge to develop a theory of TFL with an ordered structure at nano scale. In TFL modeling, two factors to be addressed are the microstructure of the fluids and the surface effects due to the very small clearance between two solid walls in relative motion [40]. 

The ICRP (1994b, 1995) developed a Human Respiratory Tract Model for Radiological Protection, which contains respiratory tract deposition and clearance compartmental models for inhalation exposure that may be applied to particulate aerosols of americium compounds. The ICRP (1986, 1989) has a biokinetic model for human oral exposure that applies to americium. The National Council on Radiation Protection and Measurement (NCRP) has also developed a respiratory tract model for inhaled radionuclides (NCRP 1997). At this time, the NCRP recommends the use of the ICRP model for calculating exposures for radiation workers and the general public. Readers interested in this topic are referred to NCRP Report No. 125 Deposition, Retention and Dosimetry of Inhaled Radioactive Substances (NCRP 1997). In the appendix to the report, NCRP provides the animal testing clearance data and equations fitting the data that supported the development of the human mode for americium. 

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