Automated Data Processing Workflows for Non‐Expert Users of NMR Facilities

ABSTRACT

The cost and complexity of modern NMR spectrometers have led to the establishment of centralized, ultrahigh‐field facilities with multiple instruments that benefit from shared infrastructure and expertise. Many users have no NMR background, as they come from diverse scientific fields. This requires either heavy involvement of NMR experts in the data treatment or that data processing workflows are made user‐friendly, robust, and amenable to automation. This paper discusses how at the Danish Center for Ultrahigh Field NMR Spectroscopy at Aarhus University we develop automated—or guided—data processing workflows to serve the broad community of users of the Center. By providing consistency checks in the algorithms and reporting intermediate results, our data analysis tools raise flags if they are—or are likely—failing. We illustrate this approach with two examples: an automated quantitative lipidomics workflow and a semi‐automated multi‐exponential relaxation analysis in food matrices. The lipidomics workflow uses ¹H–³¹P TOCSY spectra, database matching, and quantitative ³¹P measurements, while color‐coded reliability labels highlight potential pitfalls. The multi‐exponential relaxation analysis automatically determines an appropriate value for the regularization parameter via the L‐curve. Both examples show how guided automation reduces expert supervision and accelerates data processing. We plan to further refine these automated workflows, share our software openly, and explore additional application areas to foster a semi‐automated NMR facility.

Modern NMR spectrometers are typically organized in centralized, ultrahigh‐field facilities with multiple instruments that benefit from shared infrastructure and expertise. The acquisition of NMR experiments goes hand in hand with the analysis of the resulting data. Here, we address the need for user‐friendly and robust methods for data analysis that can be used by non‐expert users.

1. Introduction

NMR provides a wealth of information about the structure and dynamics of various chemical systems. NMR methods including data acquisition, −processing, and ‐analysis are now well established in many applications—such as in organic synthesis [1], metabolomics [2], quality control in the food industry [3], and pharmaceutical development [4]. NMR methods also continue to expand into new areas like advanced materials research and in vivo studies. The NMR community develops new methods and refines existing ones to tackle increasingly complex systems. Advanced data analysis is an inherent, central effort in the development of such methods.

Advanced data analysis methods in NMR should ideally be fully automated—or at least guided by user input—for several reasons. First, modern NMR spectrometers offer unprecedented sensitivity, resolution, and throughput, creating datasets at a rate that calls for automated or semi‐automated pipelines to keep pace [5, 6]. Second, with high levels of education and specialization, NMR staff should allocate their time to the development of new methods and analysis of critical samples while leaving tasks that could be automated to computers and robots [6]. Finally, the global investment in NMR by academia, industry, and consortia has led to a large number of toolboxes, scripts, and automation frameworks which could be linked to streamline workflows [7, 8, 9].

The maturity of the development of specific applications often decides the level of automation. In cases where new methods or new types of samples are involved, it would typically be appropriate to aim for semi‐automatic or guided, algorithms, whereas more well‐tested methods would be more suited for full automation. In the prior case, the analysis could be supported by reports providing transparent intermediate results or metrics of reliability [10]. Meanwhile, feedback from experienced users is invaluable for refining and validating these semi‐automated processes, ensuring they remain robust and adaptable to real‐world variations in samples or acquisition conditions [11]. Once methods become established and validated, fully automated implementations can be introduced, enabling routine analyses to run at high throughput with minimal supervision. A similar approach also holds for the automation of data acquisition methods and parameters, where established pulse sequences and parameter sets are applied to specific classes of samples—such as proteins, oils, and organic chemicals. Often, uniform acquisition parameters are selected for each class of sample with broad applicability to most samples within a group. Such a unified approach in automation of acquisition and processing could permit fully automated analysis.

It is of great importance for NMR centers around the world to expand the use of NMR into other application areas, and at the Danish Center for Ultrahigh‐Field NMR Spectroscopy, we have targeted materials science [12], sustainability [13], food science [14], and biology [15]. Needless to say, scientists of these fields usually do not have the expertise to use a variety of software programs commonly available to NMR scientists [7]. By developing easily accessible automated and semi‐automated analyses tools, we have enabled the analysis of large NMR datasets where individual analysis cannot be supervised by an expert NMR researcher. By providing consistency checks in the algorithms and reporting intermediate results, our data analysis tools raise flags if they are—or are likely—failing [11]. These early‐warning features are especially crucial during method development, where [1] automatic methods occasionally fail, [2] inspecting intermediate results can lead to new discoveries, or [3] when it is not realistic to develop a completely fail‐safe method from the beginning, and with the ease of use as a key concern [16, 17, 18].

The automated and semi‐automated processing and analysis paradigms are now implemented in new software that we are developing for our users. In this paper, we illustrate the impact of such an approach with two examples. The first is an automated quantitative lipidomics workflow using ¹H‐³¹P NMR spectroscopy, where the software can evaluate the precision of its own quantifications and communicates them via a simple visual report. This algorithm has already been published [18], and hence here only presented as a short review. The second example demonstrates semi‐automated multi‐exponential relaxation analysis in food matrices for providing information about the structure and dynamics of water and fat in food ingredients and products. Both methods have been tested and validated by non‐expert users each with tens of samples. The first example is based on Python and MATLAB codes. For the second example, the relaxation method is already implemented in the freely available software package EasyNMR. Through these examples we wish to highlight the practical benefits and broader applicability of guided automation in modern NMR applications.

2. Results and Discussion

2.1. Automatic Identification and Quantification of Phospholipids in Complex Mixtures

Lipidomics is a discipline that identifies and quantifies lipids in various complex mixtures through analytical chemistry tools [19], particularly mass spectrometry [20, 21] and NMR [22]. On the one hand, NMR lipidomic studies are challenged by highly complex mixtures and thereby complex NMR spectra—and hence the need for reliable assignment of spectra. On the other hand, NMR offers one‐ and multi‐dimensional spectra with ¹H, ¹³C, ³¹P [22] that can separate signals to reduce the complexity, thereby potentially allowing the identification of many lipid species at the same time. We proposed an automated pipeline to remove the bottleneck of manual peak assignment and quantification in the study of phospholipid mixtures by a combination of 2D ¹H‐³¹P heteronuclear correlation spectra and quantitative 1D ³¹P spectra. Such a data analysis requires substantial manpower and NMR expertise if done manually. In contrast, if done automatically, it enables the application of NMR‐based lipidomics by non‐NMR experts using automated setups—similar to the automated analysis of olive oil [23, 24, 25], honey [26], wine [27, 28], and juice [29] developed in food science.

The ³¹P chemical shift offers good separation of peaks for different phospholipid head groups [24], as the ³¹P chemical shift is highly sensitive to the chemical surroundings of the phosphorous atom, as shown in Figure 1. However, this sensitivity may also introduce unpredictable changes in the chemical shift upon small variations in the chemical composition. Examples of such unstable behavior could be seen in figure 2 and supplementary material of [18]. We found that 2D ¹H‐³¹P heteronuclear TOCSY experiments were very useful as the ¹H dimension is more stable and contains characteristic fingerprints of the individual lipids and thereby may be used to identify phospholipid types. The TOCSY experiment is not quantitative, so additional 1D ³¹P NMR experiments were needed to quantify the lipids. Our method has four steps in its pipeline:

1. Acquiring a 2D ¹H‐³¹P TOCSY [30] spectrum for the identification of phospholipids,

2. Automatic phospholipid identification using database matching of TOCSY spectra,

3. Acquiring a quantitative 1D ³¹P measurement for phospholipid concentration measurement, and

4. Confidence labeling (green/yellow/orange/red) for each phospholipid species.

FIGURE 1.

Overview of our ¹H‐³¹P NMR‐based lipidomics approach for phospholipid identification and quantification. This approach has four steps. (a) Measurement and analysis of ¹H‐³¹P heteronuclear TOCSY experiment with color‐coded labelling of different lipids in a complex mixture (Steps 1 and 2). (b) Quantitative ³¹P NMR spectrum of the same mixture indicating peak deconvolutions (Steps 3 and 4). The color coding in (b) indicates if the algorithm is successful (green, yellow) or experiences problems (orange, red). Abbreviated names are listed in Materials and Methods. Adapted with permission from [18]. Copyright 2016 American Chemical Society.

The proposed algorithm for automatic identification (Step 2) first analyses the ¹H traces of the ¹H‐³¹P TOCSY experiment and compares the peak patterns (positions and intensities) with a database of known lipids and their ¹H chemical shifts and typical intensities following the TOCSY transfer. We established this database using model compounds for which the lipid type was known [18]. Traces of the TOCSY spectrum are given a score for each of the lipids in the database according to agreement in terms of the number of observed peaks, peak positions, and peak intensities. If the score is beyond a certain threshold, the trace is positively identified as a specific type of lipid. In the example in Figure 1a, the different lipids are identified and assigned as highlighted by the colored strips. This corresponds to Steps 1 and 2 of the pipeline.

Steps 3 and 4 in the pipeline quantify lipids from quantitative 1D ³¹P NMR spectra—where overlap between peaks is minimal, and each phospholipid is represented as a single peak. ³¹P chemical shifts known from the 2D spectrum of the second step identify the corresponding peaks in the 1D ³¹P spectrum. For each ³¹P peak position, the method attempts the determination of the peak area using either peak deconvolution or numerical integration. Depending on the algorithm and success, a label for the reliability of the peak integration is given. Green indicates highly reliable results and means that there is a good match with a generalized Lorentzian peak shape and there is baseline on each side of the peak [4]. Yellow indicates an acceptable result and means that the peak is close to another peak and there is not baseline on both sides of the peak, but deconvolution and integration both lead to approximately the same results. Orange indicates a peak with a low signal‐to‐noise ratio (SNR) meaning that the peak should be manually inspected. Red indicates a missed result or failure of the automatic method, for example, due to strongly overlapping peaks, impurities, or other unknown signals. Figure 1b shows this labeling for 11 peaks with correct labelling (green and yellow) and eight peaks with red label that need manual inspection. In seven of the eight cases, this is due to low SNR and these are thus not a failure of the method itself. In the remaining failure case, the peak at 2.67 ppm has a significant overlap with another peak implying that the algorithm fails to quantify the lipid automatically.

To exemplify the use of our method, Figure 2 shows the time series‐analysis of enzymatic hydrolysis of soy lecithin. The algorithm identified 11 different lipids and was able to trace out the concentrations throughout the time series [18] as indicated in Figure 2b. Similar trends were observed in other studies of enzymatic hydrolysis products of lecithin [31, 32].

FIGURE 2.

Application of the automatic phospholipid quantification to a time‐series measurement of enzymatic digestion of soy lecithin. (a) Shows the quantity of different phospholipids in a spider‐web plot and (b) shows the quantitative ³¹P spectra at different times. Adapted with permission from [18]. Copyright 2016 American Chemical Society.

Autonomous algorithms are key to high‐throughput analyses by reducing human intervention and removing the requirement for labor‐intense manual NMR‐expert work. This opens the door for broader usage of the methods by non‐experts. However, there are many pitfalls in automatic data analyses, where data with different signal‐to‐noise ratios, potential impurities, and often unknown signals may create unpredictable results. It is therefore crucial that challenges in the automatic algorithm are identified and communicated to the user, as it greatly improves the quality of the data to associate them with a reliability score.

2.2. Automatic Inverse Laplace‐Transformation of Relaxation Data

NMR relaxation parameters can characterize the environments and dynamics of functional groups and molecules. In heterogeneous materials, time‐domain relaxation decay or recovery is usually analyzed by multi‐exponential methods that compute a relaxation time distribution [33]. The position, width, and intensity of peaks in the T ₁ and T ₂ relaxation time distributions inform of physicochemical properties of materials under investigation. These distributions are commonly used for quality control and process monitoring in energy, food, and chemical industries using data from low‐field permanent magnet NMR instruments. The inversion of noisy time‐domain data to relaxation time distributions is usually performed by regularization methods where a regularization parameter is employed to balance the residual norm (how well the model agrees with data) against the solution norm (how large the size of distribution is) [34]. A correct choice of the regularization parameter is crucial to the correct determination of the relaxation time distribution [34].

There are many other examples besides relaxation where such types of regularization methods are used—for example, in determining the structure of glass by magic angle spinning [35] and solid‐state NMR determination of the secondary structure of spider silk [36]. Failure to choose correct input parameters for regularization results in the failure of the method, but a correct choice requires significant expertise and appropriate data acquisition that pushes the routine and push‐button application of the method beyond the reach of non‐experts [37, 38, 39]. In our work, we decided to make the choice of regularization parameter automatic, or at least guided.

Here we focus on the Tikhonov regularization, where the relaxation time distribution $\mathbf{x}$ is found as the solution to the optimization problem

$$\underset{x_i\ge 0}{\min }\left\{{‖\mathbf{Ax}\mathbf{-}\mathbf{b}‖}_2^2+{\lambda }^2{‖\mathbf{x}‖}_2^2\right\}.$$ (1)

Here, ${‖\mathbf{Ax}\mathbf{-}\mathbf{b}‖}_2^2$ is the residual norm, ${‖\mathbf{x}‖}_2^2$ is the solution norm, and $\lambda$ is the regularization parameter. The forward mapping matrix $\mathbf{A}$ computes a model of the time‐domain data $\mathbf{Ax}$ for a given time and relaxation time constant vector, and $\mathbf{b}$ is the experimental data. Interested readers can refer to [33] for more information about the structure of $\mathbf{A}$. It should be noted that minimizing the solution norm is closely related to when entropy is maximized in the well‐known Maximum Entropy reconstructions [40].

Since $\lambda$ balances the contribution of the residual norm and solution norm to the objective function, it is important to understand how this parameter changes the optimization. If $\lambda$ is optimal, the fitting will provide the best possible match between experiment and model where the solution and residual norms are balanced. Too large values of $\lambda$ lead to smooth results where critical details are lost in the attempt to keep the solution norm as low as possible, whereas too small values of $\lambda$ result in sharp solutions where data in the time domain are overfit [34] implying that the solution norm increases. In a plot of the solution norm vs. residual norm this behavior will result in a curve that has the shape of an L, and for illustration, Figure 3 shows the effect of such sub‐optimal and optimal $\lambda$. The L‐curve is shown in Figure 3a, where low values of $\lambda$ (high solution norm, low residual norm) appear in the left side of the plot as an almost vertically rising line, whereas large values of $\lambda$ provide (low solution norm, high residual norm) that form the bottom part of the curve. The optimum value for $\lambda$ will be at the corner of the curve, where a good match between the model and the experiment is achieved (low residual norm), but the solution norm is as low as possible (avoid overfitting). The resulting inversions for different values of $\lambda$ are also shown in Figure 3. A very small $\lambda$ produces discrete peaks that do not appropriately represent the distribution of peaks in the relaxation time distribution (Figure 3b), the optimum value of $\lambda$ reproduces the true relaxation distribution (Figure 3c), and a too large $\lambda$ produces overly smooth T ₂ distributions (Figure 3d). From this example it is evident that the L‐curve provides a systematic way to choose the regularization parameter [41].

FIGURE 3.

The regularization parameter $\lambda$ determines the smoothness of relaxation time distribution and (a) the L‐curve guides the selection of $\lambda$. (b) Overly small $\lambda$ values produce discrete peaks; (c) correct, optimal $\lambda$ produces optimal smoothing that represent the true relaxation time distribution; and (d) large $\lambda$ produces overly smooth T ₂ distributions. The positions of ${\lambda }_{\text{discrete}}=1.83\times {10}^{-4}$, ${\lambda }_{\text{optimal}}=0.0234$, and ${\lambda }_{\text{smooth}}=2.98$ are shown on the L‐curve in (a).

We usually solve Equation (1) using non‐negative least squares (NNLS) solutions [42] with $\mathbf{x}$ vectors with a few hundreds to a few thousands of elements [33]. Such NNLS calculations are slow, particularly for large values of the regularization parameter and hampers obtaining an L‐curve within a reasonable computation time. By replacing a NNLS solution with a singular‐value‐decomposition (SVD) solution [34], we speed up the process of producing the L‐curve by several orders of magnitude. The two algorithms do not provide exactly the same result, but we learned that for the purpose of estimating the L‐curve, SVD solutions provide sufficiently good estimates.

Our workflow for determining an appropriate $\lambda$‐value has five steps of

1. Computing the estimate of the L‐curve using SVD solutions,

2. Locating the corner of the L‐curve,

3. Adjusting the regularization parameter,

4. Validating the regularization parameter using NNLS, and

5. Generating the final relaxation time distribution using the correct regularization parameter.

Figure 4 visualizes this workflow for a Carr‐Purcell‐Meiboom‐Gill (CPMG) dataset that determines the T ₂ relaxation time distribution for water in cream cheese. A report similar to that of Figure 4 is generated for each sample analyzed and could be consulted if automatic processing of data fails (see Supporting Information for further information). Properties of the sample and parameters of the method are discussed in the Materials and Methods section. Our software generates an automatic report that helps the user determine whether the automatic method was successful and produced expected results. Most importantly, the report shows the L‐curve (Figure 4a), as well as the slope (Figure 4c) and curvature (Figure 4d) of the L‐curve as a function of $\lambda$.

FIGURE 4.

Plots resulting from the automatic algorithm used determine the regularization parameter $\lambda$ for the inverse Laplace‐transformation. These figures will not need be inspected or interpreted by the regular user, unless the method fails to produce correct results. The data is for ¹H NMR relaxation of water in cream cheese. (a) Singular‐value‐decomposition‐calculated L‐curve (blue) and non‐negative‐least‐squares curve (orange). The latter curve is shown as individual points in (d) with the optimum choice highlighted in green. (c) L‐curve slope (in degrees from the plot in (a)) and (d) curvature. Candidate peaks are highlighted as gray or magenta circles, and the optimum choice of $\lambda$ as a green circle. The same color coding is used in all plots.

In the L‐curve (Figure 4a), the blue line represents the SVD‐accelerated solutions for 1024 values in a wide range of $\lambda$ from ${10}^{-6}$ to ${10}^3$, computed using the Python function scipy.sparse.linalg.svds [43]. This wide range ensures covering relevant regularization parameters for all possible experiments and datasets. Such a computation would take hours if it would be undertaken by the NNLS method using the Python function scipy.optimize.nnls [43]. Figure 4a represents Step 1 of the workflow.

Although the corner of the L‐curve in Figure 4a is clearly visible (marked by a red circle), we need to use a mathematical procedure for determining the $\lambda$ corresponding to this point. This corresponds to Step 2 of the workflow. The corner of the L‐curve is well‐known to have the largest curvature [44, 45]. However, in practical cases even larger curvatures are sometimes appearing for even lower values of $\lambda$ in the nearly vertical part of the L curve. Hence, we use two criteria to identify the corner: (i) there should be a local maximum of the curvature and (ii) the tangent of the L curve should have a slope of around −45° in the L‐curve plot (Figure 4a). We use two plots to guide the determination of $\lambda$ corresponding to the corner of the L‐curve: the slope of the L‐curve (derivative of the normalized solution norm vs. the normalized residual norm, plotted against $\lambda$, Figure 4b) and also the curvature of the L‐curve (second derivative of the normalized solution norm vs. the normalized residual norm, Figure 4c). We normalized the logarithms of the residual and solution norms to the [0 1] range before calculating the slope and curvature to make the method more stable for different datasets.

The graph of the curvature of L‐curve may display several extrema. We used a standard peak‐picking algorithm (scipy.signal.find_peaks in Python [43]) to determine these extrema. These points are highlighted on the curvature and slope plots by gray and magenta circles (see Figure 4c). We find that a stable means of determining the corner of the L‐curve is to search from the highest values of $\lambda$ and choose the point where the slope goes smaller than −45° and find the peak closest to this. For example, the chosen peak (magenta circle in Figure 4c) is also highlighted by a magenta circle in Figure 4a,d, which indeed corresponds to the corner of the L‐curve as shown in Figure 4a. This concludes Step 2 of the workflow.

In Step 3 of the workflow, $\lambda$ corresponding to the corner of the L‐curve is adjusted to obtain the best value for $\lambda$. In our laboratory, we generally seek a slightly lower values of $\lambda$—i.e. moving north‐west on the L‐curve—for solutions with more well‐resolved peaks, and lower residual norm—at the expense of slightly larger solution norm. For obtaining consistent and stable results, our algorithm determines the width (half width at half height, HWHH) of the selected curvature peak and selects a $\lambda$ that is smaller by the HWHH value. This position is labeled “best $\lambda$” and highlighted by a green circle in Figure 4. In the present example, this value was $\lambda =0.0021$. The above correction is most relevant when the corner of the L curve is relatively smooth like for the example shown in Figure 4a, and in agreement with what we often see for NMR relaxation data. However, we note that based on the final L curve in Figure 4b, users can make their own choice of $\lambda$.

Since the SVD and NNLS solutions are not identical, in the fourth step, the algorithm computes NNLS solutions in a smaller range of $\lambda$ in the vicinity of “best $\lambda$” to produce a small section of the true L‐curve. NNLS computations in this region are usually much faster than for larger values of $\lambda$. Figure 4b shows such a true L‐curve with the position of “best $\lambda$” labeled. Clearly, the algorithm's “best $\lambda$” is a good choice, as the corresponding point lies slightly north‐west of the L‐curve corner (corresponding to a tangent with slope −1). Therefore, by quickly inspecting the automated report of Figure 4, one can decide whether the algorithm was successful.

In the final step of the method, step 5, the time‐domain data and the relaxation time distribution are computed using the determined best $\lambda$. Figure 5a shows the experimental data with overlain fit. The corresponding T ₂ distribution is shown in Figure 5b. The algorithm identified one major component (T ₂ = 193 ms, 93.0% of the total intensity) and three minor components (T ₂ = 32, 73, and 623 ms with intensities of 2.2%, 1.3%, and 3.5%, respectively). The interpretation of these T ₂ components is beyond the scope of this work, as it would require additional information and complementary measurements to gain knowledge about the sample to make an assignment of the peaks to different components of the sample. However, the relaxation time distributions can be used to determine the composition or physical properties of materials such as food [46], rocks [47], and biological materials [48]. We are addressing the assignment of peaks in the relaxation time distributions in a future work. The supporting information shows an additional example where we apply the inversion method to a previously published ¹⁵N relaxation data of ¹⁵N‐labelled polycrystalline L‐histidine hydrochloride monohydrate [49].

FIGURE 5.

The time‐domain data (a) and T ₂ relaxation time distribution (b) for water (4.0 to 5.5 ppm region in the ¹H NMR spectrum) in cream cheese. The distribution is obtained using the best value for $\lambda \left(=0.0013\right)$ obtained using our automatic algorithm.

3. Conclusions

The ambition to broaden the application of NMR spectroscopy into other research fields requires the development of stable NMR methods and data analysis. In this study, we have given two examples of autonomous or semi‐automated NMR procedures: application of state‐of‐the‐art NMR methods to identify and quantify lipids and automatic analysis of multi‐exponential NMR relaxation. In both cases, the stability and necessary steps towards autonomous data analysis were highlighted and discussed.

4. Materials and Methods

4.1. Lipids

NMR experiments on phospholipids were performed by Balsgart et al. [18] and are reported here without further experimentation. Abbreviated names of phospholipids are listed in Table 1. NMR spectra were acquired with a 14.1 T magnet corresponding to 600 MHz and 243 MHz for ¹H and ³¹P, respectively.

TABLE 1.

—List of phospholipids referred to in this work.

Common name	Abbreviation
Phosphatidylcholine	PC
Lysophosphatidyl‐choline	LPC
Glycerophosphoryl‐choline	GPPC
Phosphatidylinositol	PI
Phosphatidylethanolamine	PE
Lysophosphatidylethanolamine	LLPE
Glycerophosphorylethanolamine	GPE
Phosphatidic acid	PA
Lysophosphatidic acid	LPA
Glycerophosphorylcholine acid	GPA
N‐acyl lysophosphatidylethanolamine	NAL
N‐acyl phosphatidylethanolamine	NAP
Triisobutylphosphate	TIBP

4.2. Cream Cheese

The organic Naturel BUKO cream cheese from Arla Foods amba (Viby, Denmark) had a composition of 25% fat (16% saturated), 2.8% carbohydrates, 4.5% protein, and 0.50% salt. The cream cheese sample (0.54 g) was carefully loaded into a 5‐mm NMR tube, using a 3‐mm tube attached to a syringe, without the introduction of air bubbles. The sample was left in the magnet for 30 min before the measurement to equilibrate the temperature. The CPMG experiment was undertaken with a built‐in Carr‐Purcell‐Meiboom‐Gill (CPMG) T ₂ measurement pulse sequence on a 43 MHz Magritek NMR spectrometer (Magritek GmbH, Aachen, Germany) at a temperature of 26.5°C with recycle delay of 7 s, 90° pulse length of 12.1 μs, acquisition time of 1.6 s, and 4 number of scans. Echo signals from 64 linearly distributed delay times from approximately 47 ms to 3 s were measured with an echo time of 500 μs.

Peer Review

The peer review history for this article is available at https://www.webofscience.com/api/gateway/wos/peer‐review/10.1002/mrc.5540.

Supporting information

Figure S1. ¹H CPMG experiment of cream cheese recorded at 43 MHz on a Magritek spectrometer. The spectrum displays two main peaks at 1.3 (fat) and 4.8 ppm (water). The integral region (4.0 to 5.5 ppm) used for the relaxation analysis is highlighted by a light blue box. The first trace is shown above the 2D spectrum.

Figure S2. Workflow for analyzing the 2D ¹H CPMG data of cream cheese. The experimental data is represented by the object entitled “9. 1H_CPMG”. This is transferred to the object “2. Process” which takes care of phasing the spectrum. From there the dataset follows three paths. First, the 2D data is plotted using the object “1. Plot”, which provides the output shown in Figure S1. Second, the dataset is passed through an object (“3. Trace”) that takes out the first horizontal trace and plots it in “4. Plot”. This corresponds to the 1D plot in Figure S1. Last, the data is sent to “5. Trace” which calculates the vertical integral in the 1H shift range 4.0–5.5 ppm and sends it to the relaxation module “8. Relaxation”. The relaxation module generates two outputs named “res” and “fit”. “res” shows the resulting T2 distribution (Figure 5b of the main text) and “fit” shows the match between experiment and model (Figure 5a).

Figure S3. Result of the automatic algorithm for determining the optimum value for 34𝜆. The panels are essentially identical to those shown in Figures 4 and 5 of the main text.

Figure S4. Graphs used to provide an overview of the automatic analysis leading to the determination of the optimum value for 34𝜆𝜆. The panels are essentially identical to those shown in Figure 4 of the main text.

Figure S5. ¹⁵N T1 relaxation data for uniformly ¹⁵N labeled L‐histidine hydrochloride monohydrate recorded at 22.3 T (950 MHz ¹H Larmor frequency) with a MAS rate of 12,413 Hz representing the T₁ decay resulting from ¹H‐¹⁵N CP followed by a longitudinal relaxation period. The data has previously been published [4]. The integral region from 175.5 to 177.0 ppm indicated by a blue box corresponding to the N^ε signal was used for the relaxation analysis.

Figure S6. Result of the relaxation analysis of ¹⁵N T₁ for N^ε in uniformly ¹⁵N labeled L‐histidine hydrochloride monohydrate at 22.3 T using a MAS rate of 12,413 Hz. The algorithm identifies two relaxation components in agreement with the expected [4] cross relaxation between N^ε and N^A. The algorithm found an optimum regularization parameter of 34𝜆𝜆𝜆 = 0.047.

Figure S7. Analysis of the L curve of the relaxation analysis of ¹⁵N T₁ for N^ε in uniformly ¹⁵N labeled L‐histidine hydrochloride monohydrate at 22.3 T using a MAS rate of 12,413 Hz.

Afrough A., Pérez‐Mendigorri M., and Vosegaard T., “Automated Data Processing Workflows for Non‐Expert Users of NMR Facilities,” Magnetic Resonance in Chemistry 63, no. 8 (2025): 604–612, 10.1002/mrc.5540.

Data Availability Statement

Details about the inversion algorithm and data handling are available in the Supporting Information. Experimental datasets and EasyNMR workflows are available through Zenodo at https://doi.org/10.5281/zenodo.15163468.