Direct Exponential Curve Resolution Algorithm Research Articles

Quadratic spacing of the effective gradient area for spatially encoded diffusion NMR

Diffusion NMR experiments rely on the measurement of signal attenuation as a function of the area of diffusion-encoding pulsed magnetic-field gradients. In conventional experiments, arbitrary series of gradient values can be used, and different gradient spacing strategies have different advantages. Ultrafast diffusion NMR relies on the spatial parallelisation of effective gradient area values to collect full 2D diffusion data sets in a single scan. Until recently, only linear spacing was available. We have shown that quadratic spacing can be achieved using a tailored frequency swept pulse. Here we describe the design of the pulse and validate it with numerical spin simulations, that make it possible to check the effect of the quadratic spacing pulse at different stages of the pulse sequence. We also show that quadratic spacing makes it possible to use a recently reported analysis method for diffusion NMR, the Matrix Pencil Method. We describe the results obtained with the MPM and those obtained with the direct exponential curve resolution algorithm (DECRA), which also requires quadratic gradient spacing. Overall, these developments open new opportunities for applications of spatially encoded diffusion experiments, such as ultrafast DOSY NMR and ultrafast Laplace NMR.

Comprehensive Structural Assessment of Linear Block Polymers by NMR and SEC

Block polymers are an important class of materials offering unique and useful properties different from random polymers. Because of their tailored structure, these materials present synthetic challenges. For this reason, it is necessary to provide a thorough structural analysis to drive the synthetic effort. We describe an analytical methodology that includes size exclusion chromatography (SEC), quantitative 13C NMR, and 1H pulsed gradient spin echo (PGSE) NMR coupled with direct exponential curve resolution algorithm (DECRA) data analysis. The combination of these complementary techniques provides a comprehensive assessment of the chemical structure of the final polymeric material, including the detection and quantification of homopolymer formation, compositional heterogeneity with molecular weight, and monomer sequencing. We present work on two different linear block polymers: poly(styrene-b-allyl methacrylate) and poly[styrene-b-(styrene-alt-maleic anhydride)].

Insight into human insulin aggregation revisited using NMR derived translational diffusion parameters.

The NMR derived translational diffusion coefficients were performed on unlabeled and uniformly labeled 13C,15N human insulin in water, both in neat, with zinc ions only, and in pharmaceutical formulation, containing only m-cresol as phenolic ligand, glycerol and zinc ions. The results show the dominant role of the pH parameter and the concentration on aggregation. The diffusion coefficient Dav was used for monitoring the overall average state of oligomeric ensemble in solution. The analysis of the experimental data of diffusion measurements, using the direct exponential curve resolution algorithm (DECRA) allows suggesting the two main components of the oligomeric ensemble. The 3D HSQC-iDOSY, (diffusion ordered HSQC) experiments performed on 13C, 15N-fully labeled insulin at the two pH values, 4 and 7.5, allow for the first time a more detailed experimental observation of individual components in the ensemble. The discussion involves earlier static and dynamic laser light scattering experiments and recent NMR derived translational diffusion results. The results bring new informations concerning the preparation of pharmaceutical formulation and in particular a role of Zn2+ ions. They also will enable better understanding and unifying the results of studies on insulin misfolding effects performed in solution by diverse physicochemical methods at different pH and concentration.

Dow successfully starts up a key facility for production of polyether polyols in Thailand

Methods have been developed and compared for the analysis of a glycerol-based polyether polyol using a low-field, medium-resolution NMR spectrometer, with an operating frequency of 29 MHz for 1H. Signal areas in the time and frequency domains were used to calculate the ethylene oxide (EO) content of individual samples. The time domain signals (free induction decay) were analysed using a new version of the direct exponential curve resolution algorithm (FID-DECRA). Direct analysis of the 1H NMR FT spectra gave percentage EO concentrations of reasonable accuracy (average percentage error of 1.3%) and precision (average RSD of 1.8%) when compared with results derived from high-field 13C NMR spectrometry. The direct FID-DECRA method showed a negative bias (−0.8±0.12% w/w) in the estimation of percentage EO concentration, but the precision (average RSD of 0.9%) was twice as good as that of direct spectral analysis. When the 13C NMR analysis was used as a reference method for univariate calibration of the 1H NMR procedures, the best accuracy (average percentage error of 0.5%) and precision (average RSD of 0.6%) were obtained using FID-DECRA, for EO concentrations in the range 14.8–15.5% w/w. An additional advantage of FID-DECRA is that the analytical procedure could be automated, which is particularly desirable for process analysis.

Acquisition strategy to obtain quantitative diffusion NMR data

Pulsed Gradient Spin Echo (PGSE) diffusion NMR experiments constitute a powerful tool for analyzing complex mixtures because they can in principle separate the NMR spectra of each mixture component. However, because these experiments intrinsically rely on spin echoes, they are traditionally regarded as non-quantitative, due to the signal attenuation caused by longitudinal (T1) and transverse (T2) nuclear magnetic relaxation during the rather long delays of the pulse sequence. Alternatively to the quantitative Direct Exponential Curve Resolution Algorithm (qDECRA) approach proposed by Antalek (J. Am. Chem. Soc. 128 (2006) 8402–8403), this work presents an acquisition strategy that renormalizes this relaxation attenuation using estimates of the T1 and T2 relaxation times for all the nuclei in the mixture, as obtained directly with the pulse sequence used to record the PGSE experiment. More specifically, it is shown that only three distinct PGSE experiments need to be recorded, each with a specific set of acquisition parameters. For small- and medium-sized molecules, only T1 is required for obtaining accurate quantification. For larger molecular weight species, which typically exhibit short T2 values, estimates of T2 must also be included but only a rough estimation is required. This appears fortunate because these data are especially hard to obtain with good accuracy when analyzing homonuclear scalar-coupled systems. Overall, the proposed methodology is shown to yield a quantification accuracy of ±5%, both in the absence and in the presence of spectral overlap, giving rise – at least, in our hands – to results that superseded those achieved by qDECRA, while requiring substantially less experimental time.

Quantitation of a polymorphic mixture of an active pharmaceutical ingredient with solid state 13C CPMAS NMR spectroscopy

Active pharmaceutical ingredients (API) often crystallise in several forms with significant differences in their physical properties. In pharmaceutical applications it is very important to be able to identify these polymorphs during drug manufacturing and storaging, also quantitative information about polymorphs is often required. Solid state 13C cross-polarisation (CP), magic angle spinning (MAS), nuclear magnetic resonance (NMR) spectroscopy was utilised in studying polymorphisity of an API with two polymorphic forms. Quantitative information was obtained from polymorphic mixtures, and a formulated product was also studied in order to determine the possibility of distinguishing between the two polymorphs in a low-dose formulation. Quantitative data was obtained using two methods: integration of signals from the dipolar dephased spectra, and a chemometric method known as Direct Exponential Curve Resolution Algorithm (DECRA). We concluded that the two polymorphs are easily identifiable based on their spectral differences. Quantitative results showed reasonable accuracy, and while identification of the polymorph present in formulation was not possible, traces of the API are detectable in as low dosage as 0.7% by weight using solid state NMR methods.

DoubleSlicing: A non-iterative single profile multi-exponential curve resolution procedure : Application to time-domain NMR transverse relaxation data

A new non-iterative curve resolution technique for resolving single decay profiles is proposed. The new technique, called DoubleSlicing, is based on the Decra (Direct Exponential Curve Resolution Algorithm) principle. While the original Decra was designed to resolve several decay curves simultaneously and thus fitting common pure exponentials, DoubleSlicing can resolve single decay profiles by a simple double data transformation followed by an analytical and unique three-way decomposition. The new approach is successfully demonstrated on experimental NMR CPMG relaxation data, measured on combinations of unmixed paramagnetic CuSO 4 solutions. Decay signals of the water component were acquired following an innovative experimental design that ensured no interaction between the components present in each sample under observation. DoubleSlicing proved to be accurate in estimating relaxation times differing in one order of magnitude (range: 19.6–159.4 ms). Its performance was comparable to discrete exponential fitting with the advantage of being much faster – in terms of computation time, DoubleSlicing outperformed exponential fitting by a factor of four.

Using PGSE NMR for chemical mixture analysis: Quantitative aspects

AbstractPulsed gradient spin echo NMR coupled with a data processing approach such as direct exponential curve resolution algorithm may be used to resolve individual components in a mixture. Differences in the diffusivities of the components lead to differences in their signal decay behavior in the experiment and allow for pure component spectra to be resolved. Because the experiment is echo‐based, differences in the relaxation behavior of the nuclei within the various components lead to nonquantitative spectra. As a consequence it is rarely used to directly determine the levels of the components quantitatively. This article explores the effects of signal loss in the PGSE NMR experiment because of relaxation and describes an extrapolation method to ultimately obtain quantitative pure component spectra from mixtures. Examples of surface‐modified nanoparticles are presented. © 2007 Wiley Periodicals, Inc.Concepts Magn Reson Part A 30A: 219–235, 2007.

Improved DECRA processing of DOSY data: correcting for non‐uniform field gradients

Mixture analysis using PFG-NMR (DOSY) data is, for many chemists, a valuable and increasingly popular technique where the NMR signals of different species are separated according to their diffusion coefficients. Where NMR signals overlap, however, it is often difficult to extract the spectra of pure components from experimental data. In such situations, it can often be helpful to use multivariate methods, which exploit all the available signal covariance, to resolve the spectra of the components of a mixture. The best-established and by some way the quickest such method, DECRA (Direct Exponential Curve Resolution Algorithm), unfortunately requires that data conform to a pure exponential decay as a function of gradient strength squared, while experimental data typically deviate significantly from this. If this deviation is known, the performance of DECRA can be greatly improved for components with similar diffusion coefficients by adjusting the choice of gradient strengths used.

Approaching the direct exponential curve resolution algorithm from a maximum likelihood perspective

The implementation of maximum likelihood parallel factor analysis (MLPARAFAC) in conjunction with the direct exponential curve resolution algorithm (DECRA) is described. DECRA takes advantage of the intrinsic exponential structure of some bilinear data sets to produce trilinear data by a simple shifting scheme, but this manipulation generates an error structure that is not optimally handled by traditional three-way chemometrics methods such as TLD and PARAFAC. In this work, the effects of these violations are studied using simulated and experimental data used in conjunction with the well-established TLD and PARAFAC. The results obtained by both methods are compared with the results obtained by MLPARAFAC, which is a method designed to optimally accomodate a variety of measurement error structures. The impact on the estimates of different parameters linked to the data sets and the DECRA method is investigated using simulated data. The results indicate that PARAFAC produces estimates of much poorer quality than TLD and MLPARAFAC. Also, it was found that the quality TLD estimates was comparable or only marginally poorer than the MLPARAFAC estimates. A number of commonly used algorithms were also compared to MLPARAFAC using two sets of published experimental data from kinetic studies. The MLPARAFAC estimates of rate constants were more precise than the other methods examined.

Effect of non‐exponential and multi‐exponential decay behavior on the performance of the direct exponential curve resolution algorithm (DECRA) in NMR investigations

AbstractThe effect of non‐exponential and multi‐exponential decay or relaxation behavior on the performance of the direct exponential curve resolution algorithm (DECRA) is investigated through a series of numerical simulations. Three different combinations of decay or relaxation behavior were investigated through DECRA analysis of simulated pulse gradient spin echo (PGSE) NMR diffusion spectra that contained the combination of two individual components. The diffusion decay behavior of one component was described by a single‐exponential decay, while the second component was described by either (1) a multi‐exponential decay, (2) a decay behavior described by the empirical Kohlrausch–Williams–Watts (KWW) relation or (3) a multi‐exponential decay behavior correlated with variations in the NMR spectral line shape. The magnitudes and types of errors produced during the DECRA analysis of spectral data with deviations from a pure single‐exponential decay behavior are presented. It is demonstrated that the deviation from single‐exponential decay impacts the resulting calculated line shapes, the calculated relative concentrations and the quantitative estimation of the decay or relaxation time constants of both components present in the NMR spectra. Copyright © 2004 John Wiley & Sons, Ltd.

Assessment of techniques for DOSY NMR data processing

Diffusion-ordered spectroscopy (DOSY) NMR is based on a pulse-field gradient spin-echo NMR experiment, in which components experience diffusion. Consequently, the signal of each component decays with different diffusion rates as the gradient strength increases, constructing a bilinear NMR data set of a mixture. By calculating the diffusion coefficient for each component, it is possible to obtain a two-dimensional NMR spectrum: one dimension is for the conventional chemical shift and the other for the diffusion coefficient. The most interesting point is that this two-dimensional NMR allows non-invasive “chromatography” to obtain the pure spectrum for each component, providing a possible alternative for LC-NMR that is more expensive and time-consuming. Potential applications of DOSY NMR include identification of the components and impurities in complex mixtures, such as body fluids, or reaction mixtures, and technical or commercial products, e.g. comprising polymers or surfactants. Data processing is the most important step to interpret DOSY NMR. Single channel methods and multivariate methods have been proposed for the data processing but all of them have difficulties when applied to real-world cases. The big challenge appears when dealing with more complex samples, e.g. components with small differences in diffusion coefficients, or severely overlapping in the chemical shift dimension. Two single channel methods, including SPLMOD and continuous diffusion coefficient (CONTIN), and two multivariate methods, called direct exponential curve resolution algorithm (DECRA) and multivariate curve resolution (MCR), are critically evaluated by simulated and real DOSY data sets. The assessments in this paper indicate the possible improvement of the DOSY data processing by applying iterative principal component analysis (IPCA) followed by MCR-alternating least square (MCR-ALS).

The use of PGSE NMR and DECRA for determining polymer composition

AbstractPulsed gradient spin‐echo (PGSE) NMR, when coupled with the appropriate data processing algorithm, is a useful method for mixture analysis. Direct exponential curve resolution algorithm (DECRA) is demonstrated as a method that may be used to obtain polymer composition information as a function of molecular weight for a poly(urea‐urethane). DECRA resolves both self‐diffusion coefficients and corresponding spectral components from a single experiment without the need for physical separation. Molecular weight estimates from the NMR data are compared with that determined by size‐exclusion chromatography (SEC). DECRA‐resolved spectral components are directly compared with NMR spectra of SEC fractions. Subtle compositional changes among three different polymer solutions are clearly detected by the NMR analysis. Copyright © 2002 John Wiley & Sons, Ltd.

Determination of the ethylene oxide content of polyether polyols by low-field 1H nuclear magnetic resonance spectrometry

Abstract Methods have been developed and compared for the analysis of a glycerol-based polyether polyol using a low-field, medium-resolution NMR spectrometer, with an operating frequency of 29 MHz for 1 H . Signal areas in the time and frequency domains were used to calculate the ethylene oxide (EO) content of individual samples. The time domain signals (free induction decay) were analysed using a new version of the direct exponential curve resolution algorithm (FID-DECRA). Direct analysis of the 1 H NMR FT spectra gave percentage EO concentrations of reasonable accuracy (average percentage error of 1.3%) and precision (average RSD of 1.8%) when compared with results derived from high-field 13 C NMR spectrometry. The direct FID-DECRA method showed a negative bias (−0.8±0.12% w/w) in the estimation of percentage EO concentration, but the precision (average RSD of 0.9%) was twice as good as that of direct spectral analysis. When the 13 C NMR analysis was used as a reference method for univariate calibration of the 1 H NMR procedures, the best accuracy (average percentage error of 0.5%) and precision (average RSD of 0.6%) were obtained using FID-DECRA, for EO concentrations in the range 14.8–15.5% w/w. An additional advantage of FID-DECRA is that the analytical procedure could be automated, which is particularly desirable for process analysis.

Towards Rapid and Unique Curve Resolution of Low-Field NMR Relaxation Data: Trilinear SLICING versus Two-Dimensional Curve Fitting

In this work an alternative method, named SLICING, for two-dimensional and noniterative T 2 decomposition of low-field pulsed NMR data (LF-NMR) is proposed and examined. The method is based on the Direct Exponential Curve Resolution Algorithm (DECRA) proposed by W. Windig and A. Antalek (1997, Chemom. Intell. Lab. Syst. 37, 241–254) and takes advantage of the fact that exponential decay functions, when translated in time, retain their characteristic relaxation times while only their relative amounts or concentrations change. By such simple translations (slicing) it is possible to create a new “pseudo” direction in the relaxation data and thus facilitate application of trilinear (multiway) data-analytical methods. For the application on LF-NMR relaxation data, the method has two basic requirements in practice: (1) two or more samples must be analyzed simultaneously and (2) all samples must contain the same qualities (i.e., identical sets of distinct T 2 values). In return, if these requirements are fulfilled, the SLICING (trilinear decomposition) method provides very fast and unique curve-resolution of multiexponential LF-NMR relaxation curves and, as a spin-off, calibrations to reference data referring to individual proton components require only scaling of the resulting unique concentrations. In this work the performance of the SLICING method (including multiple slicing schemes) is compared to a traditional two-dimensional curve fitting algorithm named MATRIXFIT through application to simulated data in a large-scale exhaustive experimental design and the results validated by application to two small real data sets. Finally a new algorithm, Principal Phase Correction (PPC) based on principal component analysis, is proposed for phase rotation of CPMG quadrature data, an important prerequisite to optimal SLICING analysis.

Quantitative analysis of low-field NMR signals in the time domain.

Two novel methods are described for direct quantitative analysis of NMR free induction decay (FID) signals. The methods use adaptations of the generalized rank annihilation method (GRAM) and the direct exponential curve resolution algorithm (DECRA). With FID-GRAM, the Hankel matrix of the sample signal is compared with that of a reference mixture to obtain quantitative data about the components. With FID-DECRA, a single-sample FID matrix is split into two matrices, allowing quantitative recovery of decay constants and the individual signals in the FID. Inaccurate results were obtained with FID-GRAM when there were differences between the frequency or transverse relaxation time of signals for the reference and test samples. This problem does not arise with FID-DECRA, because comparison with a reference signal is unnecessary. Application of FID-DECRA to 19F NMR data, which contained overlapping signals from three components, gave concentrations comparable to those derived from partial least squares (PLS) analysis of the Fourier transformed spectra. However, the main advantage of FID-DECRA was that accurate (<5% error) and precise (2.3% RSD) results were obtained using only one calibration sample, whereas with PLS, a training set of 10 standard mixtures was used to give comparable accuracy and precision.

Applications of the direct exponential curve resolution algorithm (DECRA) to solid state nuclear magnetic resonance and mid-infrared spectra

Applications of the direct exponential curve resolution algorithm (DECRA) to solid state nuclear magnetic resonance and mid-infrared spectra

Applications of the direct exponential curve resolution algorithm (DECRA) to solid state nuclear magnetic resonance and mid-infrared spectra

DECRA (direct exponential curve resolution algorithm) is a fast multivariate method used to resolve spectral data with concentration profiles that are linear combinations of exponential functions. DECRA has been previously applied to a wide variety of spectroscopies. Results are presented in this paper for two new application areas: solid state nuclear magnetic resonance spectra of polymorphic crystal mixtures and mid-infrared spectroscopy of chemical reactions. Furthermore, the paper will show the effect of the way the data set is split, which is a part of the algorithm, on the results. Copyright © 2000 John Wiley & Sons, Ltd.

Elucidation of Polymorph Mixtures Using Solid-State 13C CP/MAS NMR Spectroscopy and Direct Exponential Curve Resolution Algorithm

Polymorphic behavior has a broad impact on chemical technology influencing the solid-state properties of many materials from pigments to pharmaceuticals. The simultaneous presence of two or more polymorphs may introduce ambiguities in the characterization of materials using spectroscopy, diffraction, or scattering techniques. In this paper we present a solid-state 13C NMR method, together with the recently published direct exponential curve resolution algorithm, allows the elucidation of component spectra from the total spectrum of a mixture of polymorphs, previously characterized by X-ray diffraction.

Applications and new developments of the direct exponential curve resolution algorithm (DECRA). Examples of spectra and magnetic resonance images

Recently, a new multivariate analysis tool was developed to resolve mixture data sets, where the contributions (‘concentrations’) have an exponential profile. The new approach is called DECRA (direct exponential curve resolution algorithm). DECRA is based on the generalized rank annihilation method (GRAM). Examples will be given of resolving nuclear magnetic resonance spectra resulting from a diffusion experiment, spectra in the ultraviolet/visible region of a reaction and magnetic resonance images of the human brain. Copyright © 1999 John Wiley & Sons, Ltd.