Model transition

Zhao and Rezkallah (1993), Rezkallah (1996), and more recently Lowe and Rezkallah (1999) developed two-phase flow transition models for micro-gravity channel flows based on liquid and gas Weber numbers. Zhao and Rezkallah (1993) suggested Wees 1 as the upper boundary for the surface tension-dominated zone, and Wees 20 as the lower boundary for the inertia-dominated zone. 

This is, beyond all doubt, the most important process and the only one which has been already tackled with theoretically. Nevertheless, the prediction given by the classical overbarrier transition model is not correct for this collision [9] and the modified multichaimel Landau-Zener model developed by Boudjema et al. [34] caimot explain the experimental results for collision velocities higher than 0.2 a.u.. With regard to the collision energy range, we have thus performed a semi-classical [35] collisional treatment... 

The cumulative curve obtained from the transit time distribution in Figure 9 was fitted by Eq. (48) to determine the number of compartments. An additional compartment was added until the reduction in residual (error) sum of squares (SSE) with an additional compartment becomes small. An F test was not used, because the compartmental model with a fixed number of compartments contains no parameters. SSE then became the only criterion to select the best compartmental model. The number of compartments generating the smallest SSE was seven. The seven-compartment model was thereafter referred to as the compartmental transit model. 

The seven-compartment transit model may be physiologically sound. We may visualize that the first half of the first compartment represents the duodenum the second half of the first compartment, along with the second and third compartments, the jejunum and the rest of the compartments the ileum. The corresponding transit times in the duodenum, jejunum, and ileum are 14, 71, and 114 min, respectively. Considering the volumes and flow rates in these three segments [71,72], such an assignment seems reasonable. 

The compartmental absorption and transit model was developed based on the transit model. The assumptions for the CAT model include the following. 

Figure 10 The fraction of dose absorbed as a function of the effective human permeability. (---) Compartmental absorption and transit model (Eqs. (59) or (60)) (—) single-...

L. X. Yu, G. L. Amidon. A compart-mental absorption and transit model for estimating oral drug absorption. Int.J. Pharm. 1999, 386, 119-125. 

A special case in dissolution-limited bioavailability occurs when the assumption of sink condition in vivo fails that is, the drug concentration in the intestine is dose to the saturation solubility. Class IV compounds, according to BCS, are most prone to this situation due to the combination of low solubility and low permeability, although the same could also happen for class II compounds, depending primarily on the ratio between dose and solubility. Non-sink conditions in vivo lead to less than proportional increases of bioavailability for increased doses. This is illustrated in Fig. 21.8, where the fraction of drug absorbed has been simulated by use of an compartmental absorption and intestinal transit model [35] for different doses and for different permeabilities of a low-solubility, aprotic compound. 

In the phase transition model (4) long wavelength modes are coupled to short wavelengths modes by nonlinear couplings (21). It is not known whether this model can be solved exactly except for numerical methods. 

The activities of the indole carbazimidamide derivatives 5 at the 5-HT4 receptor were measured in vitro using the field-stimulated LMMP-GPI preparation (Table 1) followed by in vivo investigations applying the gastric emptying and intestinal transit models in the guinea-pig and rat. 

The STM (Simplified Transition Model) estimates investment to bring hydrogen FCV costs to competitive levels, investment costs for building H2 infrastructure, GHG-emission reductions and oil savings over time. 

Transition modelling estimating the investments required to bring hydrogen and fuel-cell vehicles to cost competitiveness... 

To study this buy-down process for hydrogen and fuel-cell vehicles, the Simplified Transition Model (STM) was used to aggregate costs over the entire fleet, based on the fuel-cell vehicle and hydrogen infrastructure costs previously described ... 

The transition-state model for these cyclizations (Scheme 34) differs fundamentally from the well-established Beckwith-Houk transition model for radical cyclizations [130,146-148]. Thus, while both models invoke chairlike transition states, without excluding the possibility of twist boatlike systems in some instances, the Beckwith-Houk model involves full conformational... 

Refinement and expansion of these steady-state mass balance approaches has led to the development of dynamic models which allow for estimation of the fraction absorbed as a function of time and can therefore be used to predict the rate of dmg absorption [37], These compartmental absorption and transit models (CAT) models have subsequently been used to predict pharmacokinetic profiles of drugs on the basis of in vitro dissolution and permeability characteristics and drug transit times in the intestine [38],... 

Yu LX and Amidon GL (1999) A Compartmental Absorption and Transit Model for Estimating Oral Drug Absorption. Int J Pharm 186 pp 119-125. 

Keywords Absorption In silico Mixing tank Maximum absorbable dose Mass balance approach Compartmental absorption Transit models... 

The basis for all CAT models is the fundamental understanding of the transit flow of drugs in the gastrointestinal tract. Yu et al. [61] compiled published human intestinal transit flow data from more than 400 subjects, and their work showed the human mean small intestinal transit time to be 199 min. and that seven compartments were optimal in describing the small intestinal transit process using a compartmental approach. In a later work, Yu et al. [58] showed that between 1 and 14 compartments were needed to optimally describe the individual small intestine transit times in six subjects but in agreement with the earlier study, the mean number of compartments was found to be seven. This compartmental transit model was further developed into a compartmental absorption and transit (CAT) model ([60], [63]). The assumptions made for this CAT model was that no absorption occurs in the stomach or in the colon and that dissolution is instantaneous. Yu et al. [59] extended the CAT model... 

Phase transition models, oscillatory reactions, 39 92-97 Phenanthrene... 

In the context of the Monod-Wyman-Changeux concerted-transition model for allosteric effects, one usually considers the effects of specific site occupancy on the behavior of other binding sites. Thus, a more correct... 

Note that negative cooperativity cannot occur in the Monod-Wyman-Changeux allosteric transition model, because the dissociation constant is equivalent for all sites. Thus, positive cooperativity can only result in this binding mechanism as a consequence of the recruitment of binding sites from the T-state in an all-or-none transition to the R-state. Any occurrence of negative cooperativity can be regarded as prima facie evidence... 

Furthermore, the Pefr data can be integrated with solubility/dissolution data to predict the oral absorption from the solid dosage form (see Chapter 10). Gastrointestinal transit absorption model (GITA) [12, 13], advanced compartmental absorption and transit model (ACAT, GastroPlus), advanced drug absorption and metabolism model (ADAM, SimCYP) and so on have been reported as useful integration models (see Chapter 10). 

Another important advance adding to the value of PBPK modeling in the pharmaceutical industry are physiological, mechanistic models developed to describe oral absorption in humans and preclinical species. Oral absorption is a complex process determined by the interplay of physiological and biochemical processes, physicochemical properties of the compound and formulation factors. Physiologically based models to predict oral absorption in animals and humans have recently been reviewed [18, 19] and several models are now commercially available. The commercial models have not been published in detail because of proprietary reasons but in essence they are transit models segmenting the gastrointestinal tract... 

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