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PubMed1997

Quasi-steadiness approximation for the two-compartment solute kinetic model.

We analytically solved the equation of the variable volume, two-compartment solute kinetic model (TCSKM). From the solution, we constructed an expression of weekly concentration profiles developing in the patient's body by routine hemodialyses. Obtained formulas can be used to calculate Kt/V, solute reduction index (SRI), the solute generation rate (G) per unit distribution volume (V), and a mass transfer coefficient (MTC) between the two compartments. To estimate these parameters, the formulas only need three-point data during a dialysis, that is, pre-, one-hour, and post-dialysis solute concentrations instead of four that would otherwise be needed. A 48 hour data point is not required. The weekly concentration profiles can be easily calculated by the formulas. As examples of clinical applications, we calculated Kt/V, G/V, and SRI of urea, Cr, and uric acid using plasma data of 121 hemodialyzed patients. Then the results were compared with the single-compartment solute kinetic model (SCSKM). The obtained mean MTC/V values, that is, 1.08 (1/hr) for urea, 0.53 (1/hr) for Cr, and 1.11 (1/hr) for uric acid, were consistent with the previous works. SCSKM overestimated the mean G/V by 7.1%, 15.9%, and 10.0%, and the mean SRI by 6.7%, 18.6%, and 10.0%, for urea, Cr, and uric acid, respectively. The solute distribution volume ratio of TCSKM to SCSKM, (V)TCSKM/(V)SCSKM, depended on the value of MTC/V and the hemodialysis duration. Using pedometers, we measured the total number of steps the patients took during a week. We found that the total number of steps in a week was significantly correlated with the Cr generation rate (r = 0.285, P < 0.03), but that it was not significantly correlated with the other generation rates (r = 0.204, P > 0.09 for urea, and r = 0.209, P > 0.08 for uric acid). These data suggest that the Cr generation rate is related to the patient's physical activity. We conclude that the formulas can estimate an adequate dialysis prescription for the hemodialyzed patient.

Humans↗
PubMed2002

Development of a kinetic model for the NOx reduction process by potassium-containing coal pellets.

A four step kinetic model was developed to describe the NOx reduction process by potassium containing coal-pellets. The relevance and significance of the different steps considered in the model as well as the considerations assumed to introduce the equations associated to this model were properly discussed. The simulation both of the NOx reduction and carbon conversion evolution shows good agreement with the experimental data obtained throughout lifetime tests at 350 degrees C for samples with different potassium contents. The set of parameters predicted by the kinetic model have physical significance and are helpful in explaining the different behavior exhibited by the samples. Some of these parameters can be correlated with different features of the samples. The potassium loading influences mainly on the kinetic rate constant governing the NOx chemisorption step, thus explaining the increase in selectivity with the catalyst content exhibited by this type of samples.

Adsorption↗
PubMed2006

Contact time optimization of two-stage batch adsorber design using second-order kinetic model for the adsorption of phosphate onto alunite.

The adsorption of phosphate onto alunite in a batch adsorber has been studied. Four kinetic models including pseudo first- and second-order equation, intraparticle diffusion equation and the Elovich equation were selected to follow the adsorption process. Kinetic parameters, rate constants, equilibrium adsorption capacities and related correlation coefficients, for each kinetic model were calculated and discussed. It was shown that the adsorption of phosphate onto alunite could be described by the pseudo second-order equation. Adsorption of phosphate onto alunite followed the Langmuir isotherm. A model has been used for the design of a two-stage batch adsorber based on pseudo second-order adsorption kinetics. The model has been optimized with respect to operating time in order to minimize total operating time to achieve a specified amount of phosphate removal using a fixed mass of adsorbent. The results of two-stage batch adsorber design studies showed that the required times for specified amounts of phosphate removal significantly decreased. It is particularly suitable for low-cost adsorbents/adsorption systems when minimising operating time is a major operational and design criterion, such as, for highly congested industrial sites in which significant volume of effluent need to be treated in the minimum amount of time.

Adsorption↗
PubMed2005

Comparison of kinetic models to describe high pressure and gamma irradiation used to inactivate Vibrio vulnificus and Vibrio parahaemolyticus prepared in buffer solution and in whole oysters.

Comparisons of different models in inactivation kinetics were conducted on data obtained from high-pressure and gamma-irradiation processing. Vibrio vulnificus (MO-624) and Vibrio parahaemolyticus (O3:K6 TX-2103) suspended in phosphate-buffered saline (pH 7.4, 10(7) CFU/ml) were exposed to pressures from 207 to 379 MPa for 1 to 20 min. Inoculated whole oysters (106 CFU/g) were exposed to pressure from 276 to 379 MPa for 1 to 15 min. Pure cultures and inoculated oysters (10(6) CFU/g) also were irradiated (gamma irradiation) at doses of less than 3 kGy. Four mathematical models, the Bigelow model, Arrhenius equation, Fermi equation, and Weibull frequency distributions, were applied to microbial survival data, and performances of the different kinetic models were compared. Weibull frequency distributions can predict the high-pressure inactivation of Vibrio spp. with more accuracy in both pure cultures and inoculated oyster samples. The Fermi model provided a better description of gamma-irradiation inactivation kinetics compared with the traditional Bigelow model.

Animals↗
PubMed2002

Kinetic modeling of reactions in heated monosaccharide-casein systems.

In the present study, a kinetic model of the Maillard reaction occurring in heated monosaccharide-casein systems was proposed. Its parameters, the reaction rate constants, were estimated via multiresponse modeling. The determinant criterion was used as the statistical fit criterion instead of the familiar least squares to avoid statistical problems. The kinetic model was extensively tested by varying the reaction conditions. Different sugars (glucose, fructose, galactose, and tagatose) were studied regarding their effect on the reaction kinetics. This study has shown the power of multiresponse modeling for the unraveling of complicated reaction routes as occur in the Maillard reaction. The iterative process of proposing a model, confronting it with experiments, and criticizing the model was passed through four times to arrive at a model that was largely consistent with all results obtained. A striking difference was found between aldose and ketose sugars as suggested by the modeling results: not the ketoses themselves but only their reaction products were found to be reactive in the Maillard reaction.

Caseins↗
PubMed2002

Noncollisional kinetic model for non-neutral plasmas in a Penning trap: general properties and stationary solutions.

This work deals with a noncollisional kinetic model for non-neutral plasmas in a Penning trap. Using the spatial coordinates r, theta, z and the axial velocity v(z) as phase-space variables, a kinetic model is developed starting from the kinetic equation for the distribution function f(r,theta,z,v(z),t). In order to reduce the complexity of the model, the kinetic equations are integrated along the axial direction by assuming an ergodic distribution in the phase space (z,v(z)) for particles of the same axial energy epsilon and the same planar position. In this way, a kinetic equation for the z-integrated electron distribution F(r,theta,epsilon,t) is obtained taking into account implicitly the three-dimensionality of the problem. The general properties of the model are discussed, in particular the conservation laws. The model is also related to the fluid model that was introduced by Finn et al. [Phys. Plasmas 6, 3744 (1999); Phys. Rev. Lett. 84, 2401 (2000)] and developed by Coppa et al. [Phys. Plasmas 8, 1133 (2001)]. Finally, numerical investigations are presented regarding the stationary solutions of the model.

Journal Article↗
PubMed2002

Java Web Simulation (JWS); a web based database of kinetic models.

Software to make a database of kinetic models accessible via the internet has been developed and a core database has been set up at http://jjj.biochem.sun.ac.za/. This repository of models, available to everyone with internet access, opens a whole new way in which we can make our models public. Via the database, a user can change enzyme parameters and run time simulations or steady state analyses. The interface is user friendly and no additional software is necessary. The database currently contains 10 models, but since the generation of the program code to include new models has largely been automated the addition of new models is straightforward and people are invited to submit their models to be included in the database.

Computer Simulation↗
PubMed2006

Kinetic modeling of 2,4-dichlorophenoxyacetic acid (2,4-D) degradation in soil slurry by anodic fenton treatment.

Anodic Fenton treatment (AFT) has been shown to be a promising technology in pesticide wastewater treatment. However, no research has been conducted on the AFT application to contaminated soils. In this study, the 2,4-D degradation kinetics of AFT in a silt loam soil slurry were investigated for the first time, and the effects of various experimental conditions including initial 2,4-D concentration, Fenton reagent delivery rate, amount of humic acid (HA) addition, and pH were examined. The 2,4-D degradation in soil slurry by AFT was found to follow a two-stage kinetic model. During the early stage of AFT (the first 4-5 min), the 2,4-D concentration profile followed a pseudo-first-order kinetic model. In the later stage (typically after 5 or 6 min), the AFT kinetic model provided a better fit. This result is most likely due to the existence of (*)OH scavengers and 2,4-D sorption on soil. The Fe(2+) delivery rate was shown to be a more significant factor in degradation rate than the H(2)O(2) delivery rate when the Fe(2+)/H(2)O(2) ratios were in the range of 1:2 to 1:10. The presence of HA in soil lowered the AFT rate, most probably due to the competition with 2,4-D for consumption of (*)OH and increased sorption of 2,4-D on soil. The optimal pH for 2,4-D degradation in soil slurry by AFT was observed to be in the range of pH 2-3.

2,4-Dichlorophenoxyacetic Acid↗
PubMed1999

Kinetic modeling of the thermal aggregation of patatin.

A kinetic model of the thermal aggregation of patatin is presented based on chromatographic analysis of the proportions of nonaggregated and aggregated patatin. It was observed that the decrease of the amount of nonaggregated patatin proceeded initially quickly and was followed by slower aggregation at longer incubation times. It was shown that this behavior was not due to heterogeneity of the starting material. It was noted that overestimation of the amount of native molecules after a heat treatment, caused by refolding of the unfolded protein during the cooling step prior to the analysis, was significant and could not be neglected. Hence, corrections based on information on the structural properties of patatin were applied. Taking this into account, a model was proposed consisting of a first-order formation of reactive particles, followed by a second-order aggregation reaction. This model described the thermal aggregation of patatin rather accurately and was confirmed by experiments at various protein concentrations.

Carboxylic Ester Hydrolases↗
PubMed2002

Kinetic model for surface reconstruction.

A microscopic kinetic model for the alpha <==> beta [e.g., hex <==> 1x1 for Pt(100) and 1x2 <==> 1x1 for Pt(110)] surface reconstruction is investigated by means of the mean field approximation and Monte Carlo simulations. It considers homogeneous phase nucleation that induces small surface phase defects. These defects can grow or decline via phase border propagation in dependence on the chemical coverage by an adsorbate A (CO). An asymmetry in the adsorbate surface diffusion from one surface phase to the other gives rise to two critical coverages that determine the intervals of stability of the homogeneous alpha phase, the dynamically stable heterogeneous state, and the homogeneous beta phase. Both surfaces show a very similar qualitative behavior regarding the phase transitions that are of second order in both cases. As a result the experimentally observed nonlinear island growth rate and the critical coverages can be explained at a quantitative level.

Journal Article↗
PubMed1995

Kinetic modelling of in vitro lipid peroxidation experiments--'low level' validation of a model of in vivo lipid peroxidation.

Kinetic modelling overcomes some of the drawbacks of purely intuitive thinking in integrating information accumulated on chemical reactions involved in oxidative stress. However, it is important to assess if current knowledge about the reactions that mediate lipid peroxidation already allows satisfactory modelling of this process in near-to-physiological conditions. In this paper, a set of increasingly complex in vitro experiments on antioxidants (alpha-tocopherol and ascorbate) and lipid peroxidation in heterogeneous systems is simulated. Quantitative to semiquantitative agreement is found between experimental and simulation results. In addition, this theoretical analysis provided useful insights, suggested new hypotheses and experiments and pointed out relevant aspects needing further research. The results encourage and serve as partial validation for the formulation of relatively detailed mathematical models of in vivo lipid peroxidation. Some important aspects of the formulation and analysis of such models are discussed.

Antioxidants↗
PubMed2002

A kinetic model for surfactant inhibition of pentachlorophenol biodegradation.

A kinetic model is used to describe the effect of the nonionic surfactant Tergitol NP-10 (TNP10) on pentachlorophenol (PCP) biodegradation by Sphingomonas chlorophenolica sp. strain RA2. Different initial biomass to initial substrate ratios ranging from 13 to 418 were tested with 23 TNP10 concentrations ranging from 0 to 1500 mg/L. Tests were also conducted at 10 degrees C and 20 degrees C. No PCP biodegradation inhibition was observed at concentrations below the critical micelle concentration (CMC) of 50 mg/L. TNP10 concentrations above 100 to 200 mg/L were increasingly inhibitory to PCP biodegradation rates. This inhibition was best described by the Monod kinetic equation wherein the effect of TNP10 inhibition is reflected in the half-saturation constant (Ks). The value of the Ks increased from between 1.5 and 13.5 mg/L with no surfactant present to 44 to 131 mg/L at 1000 mg/L TNP10. Using a standard competitive inhibition approach, the inhibition constant for TNP10 was approximately 100 mg/L at both 10 degrees C and 20 degrees C.

Biodegradation, Environmental↗
PubMed2006

Solid-state kinetic models: basics and mathematical fundamentals.

Many solid-state kinetic models have been developed in the past century. Some models were based on mechanistic grounds while others lacked theoretical justification and some were theoretically incorrect. Models currently used in solid-state kinetic studies are classified according to their mechanistic basis as nucleation, geometrical contraction, diffusion, and reaction order. This work summarizes commonly employed models and presents their mathematical development.

Chemistry, Physical↗
PubMed2005

Kinetic models as a route to control acrylamide formation in food.

A kinetic model for the formation of acrylamide in potato, rye and wheat products has been derived, and kinetic parameters calculated for potato by multi-response modeling of reducing sugar (glucose and fructose), amino acid, asparagine and acrylamide concentrations with time. The kinetic mechanism shares, with Maillard browning, a rate limiting (probably dicarbonylic) intermediate, and includes reaction steps of this intermediate which are competitive with respect to acrylamide formation. A pathway representing physical and/or chemical losses of acrylamide accounts for the measured reduction of acrylamide yield at long reaction times. A mechanistic hypothesis regarding the competing reactions of Strecker aldehyde formation and tautomerization followed by beta-elimination to give acrylamide, features in the kinetic model and can be used to determine the factors which steer the reaction towards acrylamide. A predictive application of this model is for 'what-if' experiments to explore the conditions which lead to reduced acrylamide yields.

Acrylamide↗
PubMed2006

Duration of extracorporeal therapy in acute maple syrup urine disease: a kinetic model.

Maple syrup urine disease (MSUD, MIM 248600) can be complicated by metabolic crises necessitating extracorporeal removal therapy (ECRT). Since leucine levels are usually not immediately available during therapy, an accurate kinetic model of leucine plasma levels during removal would be useful to establish the duration of ECRT. Such a kinetic model is available for neonates undergoing continuous ECRT (CECRT) with a leucine clearance>or=35 ml min-1 1.73 m-2. The current study tests the validity of this model in older children. Plasma leucine levels were obtained from eleven ECRT sessions [seven CECRT and four intermittent hemodialysis (HDi) sessions] in seven children aged 1-14 years. No hemodynamic instability or neurological complications were observed during treatment. HDi provided a higher leucine clearance and required shorter sessions than CECRT (5.4+/-0.6 vs. 17.1+/-6.0 h). All patients regained precrisis neurological status except for one patient who had severe neurological damage (severe cerebral edema) at the time of dialysis and subsequently died despite efficient leucine removal. A leucine clearance>or=50 ml min-1 1.73 m-2 is required to obtain a kinetic model similar to that reported in neonates, both with CECRT and HDi. This model should be helpful in predicting the duration of therapy needed to attain desired leucine levels.

Acute Disease↗
PubMed2005

Kinetic modeling of ion conduction in KcsA potassium channel.

KcsA constitutes a potassium channel of known structure that shows both high conduction rates and selectivity among monovalent cations. A kinetic model for ion conduction through this channel that assumes rapid ion transport within the filter has recently been presented by Nelson. In a recent, brief communication, we used the model to provide preliminary explanations to the experimental current-voltage J-V and conductance-concentration g-S curves obtained for a series of monovalent ions (K(+),Tl(+), and Rb(+)). We did not assume rapid ion transport in the calculations, since ion transport within the selectivity filter could be rate limiting for ions other than native K(+). This previous work is now significantly extended to the following experimental problems. First, the outward rectification of the J-V curves in K(+) symmetrical solutions is analyzed using a generalized kinetic model. Second, the J-V and g-S curves for NH(4) (+) are obtained and compared with those of other ions (the NH(4) (+) J-V curve is qualitatively different from those of Rb(+) and Tl(+)). Third, the effects of Na(+) block on K(+) and Rb(+) currents through single KcsA channels are studied and the different blocking behavior is related to the values of the translocation rate constants characteristic of ion transport within the filter. Finally, the significantly decreased K(+) conductance caused by mutation of the wild-type channel is also explained in terms of this rate constant. In order to keep the number of model parameters to a minimum, we do not allow the electrical distance (an empirical parameter of kinetic models that controls the exponential voltage dependence of the dissociation rate) to vary with the ionic species. Without introducing the relatively high number of adjustable parameters of more comprehensive site-based models, we show that ion association to the filter is rate controlling at low concentrations, but ion dissociation from the filter and ion transport within the filter could limit conduction at high concentration. Although some experimental data from other authors were included to allow qualitative comparison with model calculations, the absolute values of the effective rate constants obtained are only tentative. However, the relative changes in these constants needed to explain qualitatively the experiments should be of significance.

Journal Article↗
PubMed2001

Study of inactivation of Lactobacillus plantarum in orange-carrot juice by means of pulsed electric fields: comparison of inactivation kinetics models.

The inactivation kinetics of Lactobacillus plantarum was studied in orange-carrot juice using high intensity pulsed electric fields. The results indicated that under the treatment conditions applied, 28.6, 32.0, and 35.8 kV/cm and treatment times ranging from 10.2 to 46.3 micros, the inactivation of L. plantarum obtained was up to 2.5 decimal reductions. Experimental and literature data were fitted to Bigelow, Hülsheger et al. and Peleg models and to Weibull frequency distribution function. Weibull was the one that best interpreted the data with accuracy factor values closer to 1.

Beverages↗
PubMed2005

Kinetic model of laccase-catalyzed oxidation of aqueous phenol.

Laccase from Trametes versicolor (EC 1.10.3.2) catalyzes the oxidation of aqueous phenol by oxygen and has demonstrated good potential for applications in various industrial and environmental processes. A kinetic model of this system has been developed to facilitate a better understanding of the mechanisms and rate-limiting steps of enzyme-catalyzed transformation and to eventually assist in the choice and design of suitable reactor systems. A kinetic model was derived based on the differential and mass balance equations that describe the interactions of various forms of the enzyme with the aromatic substrate and oxygen. This model also incorporated an expression accounting for enzyme inactivation over time due to the reaction environment. The model was validated by comparing model predictions with experimental observations of phenol transformation and oxygen consumption over time at a variety of enzyme concentrations. Excellent agreement was found between experimental data and predictions of the kinetic model. Sensitivity analyses demonstrated that the reaction between oxidized-laccase and phenol was the rate-limiting step.

Basidiomycota↗