Accurate Estimation Of Kinetic Parameters Research Articles

Optimization-derived blood input function using a kernel method and its evaluation with total-body PET for brain parametric imaging

Dynamic PET allows quantification of physiological parameters through tracer kinetic modeling. For dynamic imaging of brain or head and neck cancer on conventional PET scanners with a short axial field of view, the image-derived input function (ID-IF) from intracranial blood vessels such as the carotid artery (CA) suffers from severe partial volume effects. Alternatively, optimization-derived input function (OD-IF) by the simultaneous estimation (SIME) method does not rely on an ID-IF but derives the input function directly from the data. However, the optimization problem is often highly ill-posed. We proposed a new method that combines the ideas of OD-IF and ID-IF together through a kernel framework. While evaluation of such a method is challenging in human subjects, we used the uEXPLORER total-body PET system that covers major blood pools to provide a reference for validation. MethodsThe conventional SIME approach estimates an input function using a joint estimation together with kinetic parameters by fitting time activity curves from multiple regions of interests (ROIs). The input function is commonly parameterized with a highly nonlinear model which is difficult to estimate. The proposed kernel SIME method exploits the CA ID-IF as a priori information via a kernel representation to stabilize the SIME approach. The unknown parameters are linear and thus easier to estimate. The proposed method was evaluated using 18F-fluorodeoxyglucose studies with both computer simulations and 20 human-subject scans acquired on the uEXPLORER scanner. The effect of the number of ROIs on kernel SIME was also explored. ResultsThe estimated OD-IF by kernel SIME showed a good match with the reference input function and provided more accurate estimation of kinetic parameters for both simulation and human-subject data. The kernel SIME led to the highest correlation coefficient (R = 0.97) and the lowest mean absolute error (MAE = 10.5 %) compared to using the CA ID-IF (R = 0.86, MAE = 108.2 %) and conventional SIME (R = 0.57, MAE = 78.7 %) in the human-subject evaluation. Adding more ROIs improved the overall performance of the kernel SIME method. ConclusionThe proposed kernel SIME method shows promise to provide an accurate estimation of the blood input function and kinetic parameters for brain PET parametric imaging.

Explicit Solutions for Real-time Reversible Inhibition Kinetics using Lambert W Function: Towards Progress Curve Analysis

Accurate estimation of kinetic parameters is challenging due to the dynamics and mathematical nature of the chemical systems. This paper presents simple, yet efficient closed-form solutions for the enzymatic conversion of the substrate to the product in real-time derived using the Lambert W function. The real values of the Lambert W function were calculated from the Lambert package as implemented in MATLAB. The expressions exhibit remarkable robustness in estimating the parameters for randomized data at 1% to 4% variation in noise levels. Furthermore, unlike the initial rates method, the expressions estimate chemical kinetic parameters utilizing a full range of experimental data, thus minimizing the risk of missing information that would be detected at an extended time-span. Thus, the implementation of closed-form solutions presented in this paper for the estimation of kinetic parameters eliminates common pitfalls imposed by the initial rates and double reciprocal methods.
 Keywords: Enzyme, Lambert W function, Reversible inhibition, Closed-form solutions

Plasma radio-metabolite analysis of PET tracers for dynamic PET imaging: TLC and autoradiography

BackgroundIn molecular imaging with dynamic PET, the binding and dissociation of a targeted tracer is characterized by kinetics modeling which requires the arterial concentration of the tracer to be measured accurately. Once in the body the radiolabeled parent tracer may be subjected to hydrolysis, demethylation/dealkylation and other biochemical processes, resulting in the production and accumulation of different metabolites in blood which can be labeled with the same PET radionuclide as the parent. Since these radio-metabolites cannot be distinguished by PET scanning from the parent tracer, their contribution to the arterial concentration curve has to be removed for the accurate estimation of kinetic parameters from kinetic analysis of dynamic PET. High-performance liquid chromatography has been used to separate and measure radio-metabolites in blood plasma; however, the method is labor intensive and remains a challenge to implement for each individual patient. The purpose of this study is to develop an alternate technique based on thin layer chromatography (TLC) and a sensitive commercial autoradiography system (Beaver, Ai4R, Nantes, France) to measure radio-metabolites in blood plasma of two targeted tracers—[18F]FAZA and [18F]FEPPA, for imaging hypoxia and inflammation, respectively.ResultsRadioactivity as low as 17 Bq in 2 µL of pig’s plasma can be detected on the TLC plate using autoradiography. Peaks corresponding to the parent tracer and radio-metabolites could be distinguished in the line profile through each sample (n = 8) in the autoradiographic image. Significant intersubject and intra-subject variability in radio-metabolites production could be observed with both tracers. For [18F]FEPPA, 50% of plasma activity was from radio-metabolites as early as 5-min post injection, while for [18F]FAZA, significant metabolites did not appear until 50-min post. Simulation study investigating the effect of radio-metabolite in the estimation of kinetic parameters indicated that 32–400% parameter error can result without radio-metabolites correction.ConclusionTLC coupled with autoradiography is a good alternative to high-performance liquid chromatography for radio-metabolite correction. The advantages of requiring only small blood samples (~ 100 μL) and of analyzing multiple samples simultaneously, make the method suitable for individual dynamic PET studies.

Evaluation of droplet-based microfluidic platforms as a convenient tool for lipases and esterases assays

The accurate estimation of kinetic parameters is of fundamental importance for biochemical studies for research and industry. In this paper, we demonstrate the application of a modular microfluidic system for execution of enzyme assays that allow determining the kinetic parameters of the enzymatic reactions such as Vmax – the maximum rate of reaction and KM – the Michaelis constant. For experiments, the fluorogenic carbonate as a probe for a rapid determination of the kinetic parameters of hydrolases, such as lipases and esterases, was used. The microfluidic system together with the method described yields the kinetic constants calculated from the concentration of enzymatic product changes via a Michaelis–Menten model using the Lambert function W(x). This modular microfluidic system was validated on three selected enzymes (hydrolases).

Definitive screening designs for multistep kinetic models in flow

A definitive screening design (DSD) combined with reaction profiling was conducted using a flow reactor, in a short time frame, for the accurate estimation of kinetic parameters.

Denoising of dynamic PET images using a multi-scale transform and non-local means filter

Abstract The quantification of positron emission tomography (PET) images requires a time activity curve (TAC) to provide an accurate estimation of kinetic parameters. However, the low signals to noise ratio (SNR), the important level of noise, and the low spatial resolution of PET image make the extraction of the TAC a challenging task. In this study, we present a new method based on multi-scale and non-local means method (MNLM) to reduce noise in dynamic PET sequences of small animal heart. MNLM filter takes into account the temporal correlation between images in the dynamic measurement and benefits from the complementary properties of both the Shearlet transform and the wavelet transform to provide best reduction. The method was tested on dynamic digital mouse phantom and a preclinical rat study (n = 6). Based on a comparative study with three major algorithms reviewed on the state of the art, the data analysis proved the significance of the MNLM filter. In simulated data, the major finding of the study showed that at the highest noise level (7.68%), the model gave the best result (Chi-square = 4.06). Furthermore, it presented a notable gain in terms of PSNR and SSIM plot. In real data, the MNLM showed a better result in the computation of the contrast metric with a value of 27.04 ∓ 12.1 and the highest SNR with a value of 74.38 ∓ 9.2. This approach proved a better potential and could be considered as a valuable candidate to reduce noise in clinical system.

IPMP Global Fit – A one-step direct data analysis tool for predictive microbiology

The objective of this work is to develop and validate a unified optimization algorithm for performing one-step global regression analysis of isothermal growth and survival curves for determination of kinetic parameters in predictive microbiology. The algorithm is incorporated with user-friendly graphical interfaces (GUIs) to develop a data analysis tool, the USDA IPMP-Global Fit. The GUIs are designed to guide the users to easily navigate through the data analysis process and properly select the initial parameters for different combinations of mathematical models. The software is developed for one-step kinetic analysis to directly construct tertiary models by minimizing the global error between the experimental observations and mathematical models.The current version of the software is specifically designed for constructing tertiary models with time and temperature as the independent model parameters in the package. The software is tested with a total of 9 different combinations of primary and secondary models for growth and survival of various microorganisms. The results of data analysis show that this software provides accurate estimates of kinetic parameters. In addition, it can be used to improve the experimental design and data collection for more accurate estimation of kinetic parameters. IPMP-Global Fit can be used in combination with the regular USDA-IPMP for solving the inverse problems and developing tertiary models in predictive microbiology.

Rapid multistep kinetic model generation from transient flow data.

Today, the generation of kinetic models is still seen as a resource intensive and specialised activity. We report an efficient method of generating reaction profiles from transient flows using a state-of-the-art continuous-flow platform. Experimental data for multistep aromatic nucleophilic substitution reactions are collected from an automated linear gradient flow ramp with online HPLC at the reactor outlet. Using this approach, we generated 16 profiles, at 3 different inlet concentrations and 4 temperatures, in less than 3 hours run time. The kinetic parameters, 4 rate constants and 4 activation energies were fitted with less than 4% uncertainty. We derived an expression for the error in the observed rate constants due to dispersion and showed that such error is 5% or lower. The large range of operational conditions prevented the need to isolate individual reaction steps. Our approach enables early identification of the sensitivity of product quality to parameter changes and early use of unit operation models to identify optimal process-equipment combinations in silico, greatly reducing scale up risks.

Pulsed Micro-reactor: An alternative to estimating kinetic parameters of non-catalytic gas–solid reactions

A Pulsed Micro-reactor (PMR) technique is demonstrated as a simple and viable alternative to generate kinetic data for non-catalytic gas–solid reactions. An experimental test rig was designed and fabricated for this purpose. Oxidation of Cu using air and reduction of CuO using methane, encountered in a novel form of combustion known as Unmixed Combustion (UMC), were chosen as representative reactions in this study. Plug flow conditions in the reactor, essential for accurate estimation of kinetic parameters, was confirmed using a Residence Time Distribution (RTD) approach. A simple generic methodology, based on a uniform reaction model is presented which allowed for easy interpretation of data from this reactor system. While the methodology has been validated for both reactions which were prima facie found to be surface reaction controlled, it can easily be extended to pore diffusion limited reactions. The estimated values of reaction orders and activation energies for both reactions and the pre-exponential factor for oxidation were found to be in excellent agreement with those obtained using Thermo Gravimetric Analysis (TGA). A lower value of pre-exponential factor for reduction however was obtained in the present investigation. While the PMR, can provide an initial insight into the reaction mechanism, it can also be used to obtain reaction engineering data related to process development.

T1in high-grade glioma and the influence of different measurement strategies on parameter estimations in DCE-MRI

To investigate the evolution of T1 in tumor and the necessity of baseline T1 (T1 (0)) mapping for the accurate estimation of kinetic parameters during standard therapy using dynamic contrast enhanced (DCE) MRI in patients with high-grade glioma (HGG). Longitudinal DCE-MRI was performed in 23 patients (196 scans) with confirmed HGG. Kinetic parameters were derived from the extended Tofts model and analyzed both using fixed and pixel-wise T1 (0) values estimated from a Look-Locker sequence. Median tumor T1 value from all scans was used for fixed T1 (0) analysis. Dependence of accurate T1 (0) mapping for the estimation of the kinetic parameters was further investigated through computer simulations and histogram analysis. T1 in tumor increased significantly during and after treatment (P < 0.001). There was a linear correlation between the error in 1/T1 (0) and the resulting error in estimated parameters in both simulations and clinical data (r(2) >0.98 for all parameters). A strong correlation between the estimated longitudinal change in all kinetic parameters obtained using pixel-wise and fixed T1 (0) was observed (r(2) > 0.84 for all parameters). Histogram analysis revealed a linear change (r(2) > 0.62) in K(trans) normalized histogram peak height ratio as function of percentage deviation from the nominal T1 (0) value. No effect of T1 (0) histogram distribution on K(trans) was observed (P = 0.52). Temporal changes in the median kinetic parameters in tumor were equally well described using pixel-wise and fixed T1 (0) despite an increase in T1 (0) over time, suggesting that T1 mapping is not generally required in DCE-MRI based monitoring of glioma patients.

A Review on Gas‐Liquid Reactions in Light Oil Sweetening: Kinetics and Reactor Design Aspects

AbstractThiols in liquefied petroleum gas are undesirable due to their foul odor and corrosive nature. The process of removing these thiols is termed as sweetening. Metal phthalocyanines are reported to be the most effective sweetening catalyst. However, the solubility of metal phthalocyanine is low in aqueous medium. Thus, in an effort to further improve upon the existing catalysts, a novel cobalt phthalocyanine sulfonamide catalyst was developed. Laboratory and commercial evaluation of this catalyst showed enhanced activity as compared to a commercial catalyst with comparable stability. With proven higher activity, comparable stability, design of grass root oxidizer using this catalyst is the next step. Design of oxidizers for an extractive sweetening process based on this catalyst in grass root refineries requires a rigorous kinetic model. The paper reviews the literature on sweetening kinetics and focuses on the concepts of design of laboratory reactors for reaction kinetics studies for such gas‐liquid reactions. Laboratory reactor systems can be useful for accurate estimation of kinetic parameters which can then be used to design industrial reactors and predict their performance.

Validity of the Michaelis–Menten equation – steady‐state or reactant stationary assumption: that is the question

The Michaelis-Menten equation is generally used to estimate the kinetic parameters, V and K(M), when the steady-state assumption is valid. Following a brief overview of the derivation of the Michaelis-Menten equation for the single-enzyme, single-substrate reaction, a critical review of the criteria for validity of the steady-state assumption is presented. The application of the steady-state assumption makes the implicit assumption that there is an initial transient during which the substrate concentration remains approximately constant, equal to the initial substrate concentration, while the enzyme-substrate complex concentration builds up. This implicit assumption is known as the reactant stationary assumption. This review presents evidence showing that the reactant stationary assumption is distinct from and independent of the steady-state assumption. Contrary to the widely believed notion that the Michaelis-Menten equation can always be applied under the steady-state assumption, the reactant stationary assumption is truly the necessary condition for validity of the Michaelis-Menten equation to estimate kinetic parameters. Therefore, the application of the Michaelis-Menten equation only leads to accurate estimation of kinetic parameters when it is used under experimental conditions meeting the reactant stationary assumption. The criterion for validity of the reactant stationary assumption does not require the restrictive condition of choosing a substrate concentration that is much higher than the enzyme concentration in initial rate experiments.

Split dynamic MRI: Single bolus high spatial–temporal resolution and multi contrast evaluation of breast lesions

To test the feasibility of a novel "split dynamic" method in which high temporal and high spatial resolution dynamic MR images are acquired during a single bolus injection. High temporal resolution images were acquired using a three-dimensional (3D) dual-echo EPI sequence. The high spatial resolution images were acquired using a 3D T1 -weighted turbo field echo sequence. Simulations were performed to test the split dynamic method in terms of accuracy relative to a continuous acquisition and for temporal sampling requirements for accurate estimation of kinetic parameters. The method was tested in four patients where pharmacokinetic parameters were extracted from the high temporal resolution data. The split dynamic method enabled quantitative evaluation of both T1- and T2*-weighted characteristics. Simulations showed that splitting the dynamic acquisition does not significantly influence the reliability of parameter estimations. Simulation showed a required temporal resolution of 13, 16, and 8 s for accurate estimates of Ktrans, ve, and vp, respectively, and an optimal sampling interval between 2 and 6 s for peak R2*. The split dynamic sequence enabled detailed assessment of dynamic T1- and T2*-weighted contrast kinetics without compromising guidelines concerning spatial resolution.

Kinetic parameter estimation and simulation of trickle-bed reactor for hydrodesulfurization of crude oil

Hydrodesulfurization (HDS) of crude oil has not been reported widely in the literature and it is one of the most challenging tasks in the petroleum refining industry. In order to obtain useful models for HDS process that can be confidently applied to reactor design, operation and control, the accurate estimation of kinetic parameters of the relevant reaction scheme are required. In this work, an optimization technique is used in order to obtain the best values of kinetic parameters in trickle-bed reactor (TBR) process used for hydrodesulfurization (HDS) of crude oil based on pilot plant experiment. The optimization technique is based on minimization of the sum of the square errors (SSE) between the experimental and predicted concentrations of sulfur compound in the products using two approaches (linear (LN) and non-linear (NLN) regressions). A set of experiments were carried out in a continuous flow isothermal trickle-bed reactor using crude oil as a feedstock and the commercial cobalt–molybdenum on alumina (Co–Mo/γ-Al 2O 3) as a catalyst. The reactor temperature was varied from 335 to 400 °C, the hydrogen pressure from 4 to 10 MPa and the liquid hourly space velocity (LHSV) from 0.5 to 1.5 h −1, keeping constant hydrogen to oil ratio (H 2/oil) at 250 L/L. A steady-state heterogeneous model is developed based on two-film theory, which includes mass transfer phenomena in addition to many correlations for estimating physiochemical properties of the compounds. The hydrodesulfurization reaction is described by Langmuir–Hinshelwood kinetics. gPROMS software is employed for modelling, parameter estimation and simulation of hydrodesulfurization of crude oil in this work. The model simulations results were found to agree well with the experiments carried out in a wide range of the studied operating conditions. Following the parameter estimation, the model is used to predict the concentration profiles of hydrogen, hydrogen sulfide and sulfur along the catalyst bed length in gas, liquid and solid phase, which provides further insight of the process.

Biodegradation kinetics of benzene, methyl tert‐butyl ether, and toluene as a substrate under various substrate concentrations

AbstractOwing to the complexity of conventional methods and shortcomings in determining kinetic parameters, a convenient approach using the nonlinear regression analysis of Monod or Haldane type nonlinear equations is presented. This method has been proven to provide accurate estimates of kinetic parameters. The major work in this study consisted of the testing of aromatic compound‐degrading cultures in batch experiments for the biodegradation of benzene, methyl tert‐butyl ether (MTBE), and toluene. Additionally, batch growth data of three pure cultures (i.e., Pseudomonas aeruginosa YAMT421, Ralstonia sp. YABE411 and Pseudomonas sp. YATO411) isolated from an industrial petrochemical wastewater treatment plant under aerobic conditions were assessed with the nonlinear regression technique and with a trial‐and‐error procedure to determine the kinetic parameters. The growth rates of MTBE‐, benzene‐, and toluene‐degrading cultures on MTBE, benzene, and toluene were significant. Monod's model was a good fit for MTBE, benzene and toluene at low substrate concentrations. In contrast, Haldane's equation fitted well in substrate inhibition concentration. Monod and Haldane's expressions were found to describe the results of these experiments well, with fitting values higher than 98%. The kinetic parameters, including a maximum specific growth rate (µm), a half‐saturation constant (Ks), and an inhibition constant (Ki), were given. Copyright © 2007 Society of Chemical Industry

Integrating In Vitro Kinetic Data from Compounds Exhibiting Induction, Reversible Inhibition and Mechanism-Based Inactivation: In Vitro Study Design

Drug:drug interactions continue to be an obstacle for the pharmaceutical industry in the development of potential drug candidates. Considering the number of compounds that have been withdrawn from the market due to drug:drug interactions (e.g. cisapride, terfenadine and mibefradil), more pressure is placed on the pharmaceutical industry to investigate potential interactions prior to regulatory submission. In particular, induction and inhibition of drug metabolizing enzymes can profoundly alter the pharmacological and toxicological effects observed during monotherapy. However, due to differences in the expression and regulation of both metabolic enzymes and nuclear receptors responsible for induction, in vivo studies with pre-clinical species are not predictive of the human clinical situation. Although in vitro kinetic data also have limitations when extrapolating in vivo, in vitro testing has become more commonplace due to reduced cost and higher throughput. However, in the in vitro setting, complex enzyme kinetics can alter the estimation of kinetic parameters. Time-dependent or non-Michaelis-Menten kinetics can alter parameter estimates if experimental conditions are not optimal, and can therefore confound clinical predictions. Furthermore, mechanism-based inactivation (MBI) will reduce the active enzyme pool, both in vitro and in vivo, and thus complicate any parameter estimates. To further complicate matters, some compounds (e.g., ritonavir) inhibit, induce, as well as cause mechanism-based enzyme inactivation. For compounds such as ritonavir, the accurate estimation of kinetic parameters requires optimal experimental design at a minimum. This review will highlight the challenges in estimating enzyme kinetic parameters when both inhibition and induction are present, and will offer experimental viewpoints for the optimization of the experimental conditions.

Estimation of Kinetic Parameters for Nonisothermal Food Processes

ABSTRACT This work deals with the hypothesis that kinetic parameters for nonisothermal processes can be reliably obtained using a 1‐step method. Parameters were estimated for 3 typical processes: (1) no residence time distribution (RTD), (2) first‐order reaction with RTD, and (3) nth‐order reaction with RTD. When nonisothermal processes were approximated isothermally, k and δE were underestimated 80% to 3 orders of magnitude, and 30% to 1 order of magnitude, respectively. Reaction order was overestimated by up to 0.81. Therefore, accounting for thermal history and RTD is critical to obtain accurate estimates of kinetic parameters. The 1‐step method was also used to solve for equivalent isothermal temperatures and times for an arbitrary nonisothermal process.

Kinetic analysis for multiple substrate interaction at the active site of cytochrome P450

Cytochrome P450 enzymes (CYPs) are a superfamily of enzymes that play a prominent role in the metabolism of a vast array of drugs and xenobiotics. Cytochrome P450 isoforms possess an identical prosthetic group but different apoprotein structures that are responsible for the broad and overlapping substrate specificities. When two molecules coexist within the active site, some interactions may occur because of steric, electronic, and/or allosteric effects, leading to an alteration of kinetic properties from that of singly bound complexes. Therefore, appropriate kinetic models for unusual kinetics need to be developed according to the observed changes in apparent kinetic constants, to adequately fit experimental data and yield accurate estimates of kinetic parameters. Multiple binding site-mediated kinetics, involving CYP3A4, include mainly sigmoidicity or substrate activation partial inhibition, substrate inhibition, activation, and differential kinetics. In addition to CYP3A4, CYP2C9 and CYP1A2 contain two binding domains at the active site and to exhibit unusual kinetics.

Ontogeny of Na +/ D-glucose cotransport in guinea-pig jejunal vesicles: only one system is involved at both 20°C and 35°C

The kinetic parameters of Na +/ D-glucose cotransport were examined in fetal, newborn and adult guinea-pig jejunal brush-border membrane vesicles using a displacement curve and non-linear regression procedure. Our data indicated the presence of a single system with a K m of 0.34 ± 0.04 mM at both 20°C and 35°C. V max was increased by about 4-fold when the kinetic experiments were performed at 35°C. Since our results were not in agreement with the findings of Brot-Laroche et al. (J. Biol. Chem. (1986) 261, 6168–6176) which indicated the existence of a distinct D-glucose transport system in the adult guinea-pig jejunum at 35°C, we verified the influence of their experimental conditions on initial rate uptake measurements. In the presence of D-sorbitol instead of D-mannitol in the transport media, 70% inhibition of D-glucose uptake was observed, an effect which was attributable to contamination of sorbitol preparations by D-glucose. After removal of glucose contamination D-sorbitol did not significantly reduce the initial rate of D-glucose transport. These results led us to conclude the existence of a single D-glucose transport system in the guinea-pig small intestine and to stress the choice of experimental conditions as being crucial for an accurate estimation of kinetic parameters.