Recent Mechanistic Models

Therefore, it is advisable to fit (4.11) directly to experimental data using nonlinear regression. Conclusions concerning the release mechanisms can be based on the estimates for A and the regression line statistics [69]. 

Although the emphasis of this section will be on the most recent mechanistic approaches, the work of Fu et al. [70] published in 1976 should be mentioned since it deals with the fundamental release problem of a drug homogeneously distributed in a cylinder. In reality, Fu et al. [70] solved Fick s second law equation assuming constant cylindrical geometry and no interaction between drug molecules. These characteristics imply a constant diffusion coefficient in all three dimensions throughout the release process. Their basic result in the form of an analytical solution is 

Gao et al. [71, 72] developed a mathematical model to describe the effect of formulation composition on the drug release rate for hydroxypropyl methylcellulose-based tablets. An effective drug diffusion coefficient T , was found to control the rate of release as derived from a steady-state approximation of Fick s law in one dimension  

Although the empirical and semiempirical models described above provide ad- 

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The potential importance of homogeneous catalytic reactions in synthesis gas transformations (i.e., hydrogenation of carbon monoxide) has been widely recognized in recent years. In the first place, such systems could provide structural and mechanistic models for the currently more important, but more difficult to study, heterogeneous catalysts. Secondly, product selectivity is generally more readily achievable with homogeneous catalysts, and this would be an obviously desirable feature in an efficient process converting synthesis gas to useful chemicals and fuels. 

The mechanism of iridium-catalyzed hydrogenation remains unclear. Although several experimental [31, 53, 54] and computational [53, 55, 56] studies have been reported recently, further investigations will be necessary to establish a coherent mechanistic model. Until now, most studies have dealt with simple test substrates hence, it will be important to explore more complex and also industrially important substrates, in order to determine the full scope and limitations of iridium catalysis. 

In addition to the approaches covered in a recent review [20], the first comprehensive model covering receptor dimerization and internalization has been recently described [21], In this work, the authors use direct time-dependent measurement of the phosphorylation of the four ErbB receptor species, as well as protein quantitation to develop a comprehensive mechanistic model of receptor dimerization and internalization. Once this comprehensive, quantitative framework was developed, the authors were able to show that receptor dephosphorylation, a key step in the downregulation of ErbB-driven signaling, was restricted to intracellular compartments. 

It is important to establish the origin and magnitude of the acidity (and hence, the charge) of mineral surfaces, because the reactivity of the surface is directly related to its acidity. Several microscopic-mechanistic models have been proposed to describe the acidity of hydroxyl groups on oxide surfaces most describe the surface in terms of amphoteric weak acid groups (14-17), but recently a monoprotic weak acid model for the surface was proposed (U3). The models differ primarily in their description of the EDL and the assumptions used to describe interfacial structure. "Intrinsic" acidity constants that are derived from these models can have substantially different values because of the different assumptions employed in each model for the structure of the EDL (5). Westall (Chapter 4) reviews several different amphoteric models which describe the acidity of oxide surfaces and compares the applicability of these models with the monoprotic weak acid model. The assumptions employed by each of the models to estimate values of thermodynamic constants are critically examined. 

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... 

The mechanisms involved appear to be rather complex and several mechanistic models have been described (for a recent review see Jekel, 1998). Results from the references therein as well as from additional pilot and full-scale applications indicate that an optimal ozone dosage exists, typically in the lower range of 0.5-2 mg L l or, related to the DOC, 0.1-1 mg mg-1. The optimal point must be determined by tests in the combined treatment. 

Branching mechanisms involve both consecutive and parallel electron transfers. The most important application of the RRDE in this context has been to the electrochemical reduction of oxygen [175], on which a large amount of research has been done. Different mechanistic models give rise to different expressions linking the rate constants, which can be compared with experimental data as in previous sections, the most important is the variation of (iD / h ) with rotation speed. A summary of different models has recently appeared [176] the conclusion of which is that, at platinum, the model of Damjanovic et al. [177] is correct diagnostic criteria to test the model have been developed. 

The second example is for the precipitation of calcium carbonate from Ca(HC03)2 solutions. The mechanistic model was derived by Plummer et al. [40] from a kinetic study of the dissolution of Iceland spar crystals. The approach has more recently been extended to the interpretation of crystal growth [41]. The model is based upon the reaction between a partially dehydrated [Ca-HC03]+ complex or ion-pair and possible anionic reaction... 

Recently a comparative study of the asymmetric Diels-Alder reactions of both (5)-benzyl 2-p-tolylsulfinylacrylate (167) and (S)-benzyl methyl 2-p-tolylsulfinyl maleate (168) was carried out.104 Consequently, improved mechanistic models were developed in order to explain the behavior of such sulfinyl maleate and acrylate dienophiles in asymmetric Diels-Alder reactions.104 It was postulated that conformational equilibrium around the C-S bond must be completely shifted toward the rotamer with the sulfinyl oxygen in an s-cis arrangement (the most stable from an electrostatic point of view), making favored approach of the diene from the less hindered upper face supporting the lone electron pair (Fig. 7). The chelation of the sulfinyl and carbonyl oxygens with metals shifts the conformational equilibria... 

Recently, Wajant and Pfitzenmaier [155] have presented a different mechanistic model for cyanohydrin fisson catalysed by Manihot esculenta oxynitrilase. In this approach the cyanohydrin is orientated in the active site of the enzyme by hydrogen bonding. 

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