Urea kinetic modeling

Gotch F. Urea kinetics modelling to guide hemodialysis therapy in adults. In Nissenson AR, Fine RN, eds. Dialysis therapy. Philadelphia Hanley and Belfus, 2002 117-21. 

The URR is an easy calculation and thus is frequently used to measure the delivered dialysis dose. However, the URR does not account for the contribution of convective removal of urea. The Kt/V is the dialyzer clearance of urea K) in L/h multiplied by the duration of dialysis (/) in hours, divided by the urea distribution volume of the patient (V) in liters. Kt/Vi a unitless parameter that quantitates the fraction of the patient s total body water that is cleared of urea during a dialysis session. Urea kinetic modeling, using special computer software, is the optimal means to determine the Kt/V. Kt/V can also be calculated by using the following equation. ... 

Daugirdas IT, Van Stone JC. Physiologic principles and urea kinetic modeling. In Daugirdas JT, Blake PG, Ing TS, eds. Handbook of Dialysis. Philadelphia, Lippincott Williams Wilkins, 2001 15 5. 

Dumler F, Schmidt R, Cruz C. Abbreviated method for urea kinetic modeling in continuous ambulatory peritoneal dialysis patients. Perit Dial Int 1993 13(Suppl 2) S50-S52. 

Formal urea kinetic modeling (UKM), which involves iterative solution of the differential equations, can be used to calculate an equilibrated Kt/V, which takes into account postdialysis solute rebound as urea moves from into the blood compartment from other spaces. Equilibrated Kt/Vs are typically about 0.2 units smaller than single pool Kt/Vs calculated from the same BUN results. 

Gotch FA, Lipps BJ, Keen ML, Panlilio F. 1996. Computerized urea kinetic modeling to prescribe and monitor delivered Kt/V (pKt/V, dKt/V) in peritoneal dialysis. Adv Petit Dial 12 43-45. 

A quantitative kinetic model of the polymerization of a-pyrrolidine and cyclo(ethyl urea) showed,43 that two effects occur the existence of two stages in the initiation reaction and the absence of an induction period and self-acceleration in a-pyrrolidine polymerization. It was also apparent that to construct a satisfactory kinetic model of polymerization, it was necessary to introduce a proton exchange reaction and to take into consideration the ratio of direct and reverse reactions. As a result of these complications, a complete mathematical model appears to be rather difficult and the final relationships can be obtained only by computer methods. Therefore, in contrast to the kinetic equations for polymerization of e-caprolactam and o-dodecalactam discussed above, an expression... 

The copper zeolites store large amounts of ammonia. This is an important feature of these catalysts, since ammonia stored at the surface at medium temperatures can be used at low temperatures, where it is not possible to dose urea due to by-product formation. It is, therefore, crucial to describe ammonia storage and desorption in a kinetic model accurately to be able to predict transient variations. 

This chapter is a review of the state of the art in kinetic modeling of ammonia/urea SCR over copper containing zeolites. Both fundamental detailed kinetic models as well as more globalized models are discussed. Several submodels are studied for the SCR system (i) ammonia adsorption and desorption, (ii) NO2 adsorption and desorption, (iii) water adsorption and desorption, (iv) ammonia oxidation, (v) NO oxidation, (vi) standard SCR, (vii) rapid SCR, (viii) slow NO2 SCR, (ix) N2O formation, and (x) urea decomposition and hydrolysis to produce ammonia. As can be seen from this large number of steps, this is a complex system. 

Different SCR reaction occurs depending on the NO2 to NOx ratio, where standard SCR occurs with NO only, rapid SCR with equimolar amount of NO and NO2, and slow NO2 SCR with NO2 only. In several global kinetic models, these three reactions are added. In more detailed models, more surface species are considered, for example, nitrites, nitrates, HNO3, oxygen, and hydroxyls. N2O is an unwanted by-product during the SCR process over copper zeolites that are increasing with the NO2 content. The mechanism for the N2O production is suggested to be from decomposition of ammonium nitrate. In addition, there are models available that incorporate the urea decomposition and hydrolysis, in addition to the SCR reactions. 

Another way to validate computed values is to consider the pH dependence of the apparent inhibition constant According to the kinetic model presented earlier, the variation of the apparent inhibition constant with pH is determined by the pK s of the free enzyme and of the enzyme-inhibitor complex. Substitution of the computed values into Eq. [66] indicates that the apparent inhibition constant should decrease significantly, at least by an order of magnitude, when the pH is changed from 5.5 to 7.0. However, measurements made with a cyclic urea inhibitor analog indicated no change in the value of the apparent inhibition constant in this pH range. 

Alkaline co-condensation to yield commercial resins and the products of reaction obtained thereof [93,94] as well as the kinetics of the co-condensation of mono methylol phenols and urea [104,105] have also been reported [17]. Model reactions in order to prove an urea-phenol-formaldehyde co-condensation (reaction of urea with methylolphenols) are described by Tomita and Hse [98,102, 106] and by Pizzi et al. [93,104] (Fig. 1). 

Direct experimental evidence for the existence of an ordered conformation of sugar nucleotides in solutions has been reported by Hirano,344 who observed characteristic optical-rotatory changes for a series of these compounds upon transition from water to concentrated urea solutions. The structural requirements for such an ordered conformation are still not clear. However, data at this point, based on indirect kinetic evidence from hydrogenation and hydroxylamin-olysis reactions (see Section IV, p. 360), seem to accord with the hypothetical model just described. Further studies on the conformations of sugar nucleotides in solution are highly desirable. 

They focus on the ID simulation of an urea SCR system. The system includes a model for N02 production on a DOC, a model for urea injection, urea decomposition and hydrolysis catalyst, a model for a vanadium-type SCR catalyst and a model for NH3 decomposition on a clean-up catalyst. The catalyst models consist of a ID monolith model with global kinetic reactions on the washcoat surface, kinetic parameters have been taken from literature or adjusted to experimental data from literature. The complete model was implemented in AVL BOOST (2006). AVL BOOST is an engine cycle and gas exchange simulation software tool, which allows for the building of a model of the entire engine. 

On the basis of kinetic studies on model compounds, it has been suggested that urea is O-coordinated to the nickel(II), which functions as a Lewis acid in the activation of urea towards... 

From a study of the enzyme kinetics with a range of substrates and inhibitors, and the chemistry of related metal-ion complexes, Dixon et al. [39] proposed a model of the environment of the active site and reaction cycle. Although differing in details from the structure as now determined, this mechanism provided a basis for understanding the functions of the two metal ions. One nickel ion (Ni-1) binds the urea, and the other nickel ion (Ni-2) binds a hydroxide ion that makes a nucleophilic attack on the urea, leading to the formation of a tetrahedral intermediate. 

Tillotson et al. (1980) Nitrification and urea hydrolysis by first-order kinetics NH3 volatilization by first-order kinetics from (NH4)2C03 formed from urea hydrolysis NH sorption by linear partition model NH and NOy plant uptake involving diffusion to roots. 

Biophysical studies of the urease metal centre in the presence and absence of inhibitors, in conjunction with kinetic data provide the model of the bi-Ni site shown in 1. Certain inhibitors are thought to bridge the two nickel atoms consistent with a bridged transition state during urea hydrolysis. The ligands for nickel are believed not to contain sulphur, however, an essential cysteine is proximal to the active site. Comparisons of diethylpyrocarbonate reactivity for apo- and halo-enzyme are consistent with His as a ligand to nickel (Lee et al., 1990). 

An alternative scenario was put forward based on the crystal structures of urease inhibited by either phosphate, diamidophosphate, or borate (4,5, 28). It gets some support from the kinetic findings for fluoride inhibition of urease (29), as well as from recent model calculations (30, 31). Boric acid, known to be a competitive inhibitor of urease, can be considered a good substrate analogue, since it is isoelectronic with urea and has the same shape and dimension. Bacillus pasteurii could be crystallized in the presence of boric acid. The structure reveals that a molecule of B(OH)3 is symmetrically spanning the nickel ions, replacing Wj, W2,... 

Both complexes 75 and 76 promote the hydrolysis of urea in a two-step process with the same initial rates (118). Heating of 75 or 76 in acetonitrile solution produced ammonia with kinetic first-order dependence on complex concentration and an observed rate constant of (7.7 0.5) x 10 " h to yield a cyanate complex as the reaction product. It remains unclear, however, which binding mode of urea (terminal or bridging as found in 76) facilitates the ehmination reaction. Ammonia elimination from the O bound terminal substrate appears to be in accordance with quantum chemical studies on that model system (34). Although no crystals could be obtained for the cyanate-containing reaction product, an analogous complex (77) with virtually identical Vas(OCN) (as = asymmetric) vibration (at 2164cm )... 

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