The tool, described in the journal Magnetic Resonance by Tiago B. Moraes and colleagues at the Universidade de São Paulo and the Instituto Federal de Educação, Ciência e Tecnologia de São Paulo, automates the inverse Laplace transform, or ILT, a mathematical operation that converts raw relaxation signals into physically meaningful distributions of relaxation times. Unlike the famous Fourier transform, which turns oscillatory signals into frequency spectra, the ILT handles the monotonic, exponentially decaying signals produced by low-field relaxometry experiments. The result is a relaxogram: a curve whose peaks reveal the different populations of spins, and therefore of molecules and microscopic environments, hiding inside a sample. For foods, seeds, soils and other heterogeneous biological materials, those peaks can encode water content, oil mobility, pore structure and a host of quality parameters that matter to scientists and industry alike.

The mathematics behind the ILT is deceptively simple to state and notoriously difficult to execute. A measured relaxation signal is modeled as a weighted sum, or more precisely an integral, of exponential decays, each characterized by a relaxation time and an amplitude. Recovering the full continuous distribution of relaxation times from a finite, noisy set of data points is what mathematicians call an ill-posed inverse problem: tiny amounts of noise in the input can produce enormous, wildly oscillating artifacts in the output. This is why the ILT cannot be computed naively, and why the field has developed a family of specialized algorithms over the decades, including CONTIN, UpenWin, the Butler–Reeds–Dawson method, truncated singular value decomposition and non-negative least squares, each balancing stability, resolution and robustness in its own way.

The São Paulo team’s implementation rests on a well-established combination: non-negative least squares constrained optimization, Tikhonov regularization and singular value decomposition. Tikhonov regularization adds a smoothing penalty to the inversion, suppressing the spurious oscillations that noise would otherwise amplify, while the non-negativity constraint enforces the physical reality that amplitudes in a relaxation distribution cannot be negative. The regularization parameter, alpha, controls the trade-off between resolution and stability: larger values produce broader, smoother peaks that are less sensitive to noise, while smaller values sharpen features at the risk of amplifying artifacts. In the current version of the WebApp, the user selects alpha manually, guided by knowledge of the sample and the signal-to-noise ratio, with typical values ranging from 0.01 to 10. The authors note that automated selection strategies, such as the L-curve method, may be incorporated in future releases.

What sets the new platform apart is not the underlying mathematics, which the group had previously implemented as a local routine for OriginLab software, but its accessibility and generality. The WebApp is built in Python using the NumPy numerical library and Plotly visualization tools, deployed via Docker on secure servers at the University of São Paulo. It runs entirely platform-independently and accepts data from instruments of any manufacturer, a meaningful point in a market now served by companies including Bruker, Magritek, Oxford, Nanalysis, SpinLock, FIT and Niumag. Users upload a simple text file containing a time axis and one or more signal columns, choose the experiment type, set a handful of parameters and receive relaxation time distributions, fit curves, residuals and downloadable data within seconds or minutes.

The platform supports the three pulse sequences that dominate practical time-domain NMR: Carr–Purcell–Meiboom–Gill, or CPMG, which probes transverse relaxation, and inversion recovery and saturation recovery, which probe longitudinal relaxation. Each sequence corresponds to a different kernel function in the integral equation, describing how the exponential components grow or decay in the raw signal. The interface also offers practical pre-processing options that experienced practitioners know are essential: baseline correction to eliminate offsets that would otherwise generate artificial peaks, signal normalization, removal of corrupted initial points caused by spectrometer dead time, and flexible definition of the relaxation time window and its discretization. Multiple signals sharing a common time axis can be processed in a single batch, which is particularly convenient for monitoring dynamic processes such as drying, hydration or aging.

Validation was carried out with both simulated and real data, and the results are reassuring. Synthetic signals were generated from known log-Gaussian distributions of relaxation times, with Gaussian white noise added at levels of 1, 2 and 5 percent. Up to 2 percent noise, the recovered distributions accurately reproduced the true peak positions, widths and relative amplitudes, with deviations of peak centers remaining within a few percent, consistent with established ILT software. At 5 percent noise, the characteristic ill-posedness of the problem began to manifest as spurious peaks, a well-documented limitation of all ILT methods rather than a flaw specific to this implementation. The authors also provide practical guidance for users: acquire signals with a full decay and a stable baseline, watch the signal-to-noise ratio, choose the relaxation time window carefully, and keep processing parameters consistent when comparing multiple samples.

The experimental demonstration is a vivid illustration of what the technique can reveal. The team measured nine maize seeds on an 11.3 MHz benchtop spectrometer using a CPMG sequence, first when the seeds were dry with less than 10 percent moisture, then after 24 hours of water absorption, and finally after several days when germination had begun. In the dry seeds, the dominant relaxation peak sat at around 1 millisecond, with smaller features near 40 and 150 milliseconds. After a day of imbibition, the main peak had shifted to 3 milliseconds and broadened, while the minor peaks also moved and widened, reflecting water uptake and the growing heterogeneity of the seed’s internal structure. In germinated seeds, the peaks shifted and broadened further, tracking changes in molecular mobility and compartmentalization. These trends match previously published TD-NMR studies of maize seed vigor, confirming that the web tool reproduces established scientific findings.

The same core algorithm has already proven its worth across a striking range of applications by the research group and collaborators: food analysis, beef aging and color prediction, physiological disorders in poultry and mangoes, plant and seed science, enzymatic activity in cassava roots, and even the forensic detection of counterfeit spirits through analysis of bottle caps. By wrapping this validated machinery in a free, browser-based interface, the authors have effectively lowered the cost of entry to advanced relaxometry analysis to zero. For laboratories in developing regions, for small research groups without budgets for proprietary analysis software, and above all for students encountering NMR for the first time, the WebApp transforms a forbidding numerical procedure into a few clicks. The developers offer example data files on the home page and a video tutorial demonstrating the workflow, and uploaded data are processed temporarily and automatically discarded, never stored or logged. As compact NMR instruments continue to spread through agro-industry, food science and education, tools like this one may prove as important to the field’s growth as the magnets themselves, turning a specialized mathematical technique into a shared resource for anyone curious about what lies inside a seed, a fruit or a drop of oil.

Subject of Research: An open-access WebApp for inverse Laplace transform analysis of time-domain nuclear magnetic resonance signals

Article Title: An open-access WebApp for inverse Laplace transform analysis of time-domain nuclear magnetic resonance signals

Article References: Moraes, T. B., Von Atzingen, G. V., Mazzero, L. P., Mendes, W. S., Zacharias, M. B., & Cardinali, M. C. B. (2026). An open-access WebApp for inverse Laplace transform analysis of time-domain nuclear magnetic resonance signals. Magnetic Resonance, 7(1), 39-51. https://doi.org/10.5194/mr-7-39-2026

Image Credits: AI Generated

DOI: 10.5194/mr-7-39-2026

Keywords: nuclear magnetic resonance, inverse Laplace transform, TD-NMR, relaxometry, WebApp, open-access software, Tikhonov regularization, non-negative least squares, CPMG, low-field NMR, food science, seed analysis

The toolkit, called mSigSDK, was developed by Aaron Ge and colleagues at the National Cancer Institute’s Division of Cancer Epidemiology and Genetics, working with collaborators at the University of Maryland School of Medicine and Brazil’s National Laboratory of Scientific Computing. Rather than building yet another signature-fitting algorithm, the team took a different approach: mSigSDK is an orchestration layer, a JavaScript-based software development kit that loads into a tested desktop browser through a single dynamic import, with no installation whatsoever. Once loaded, it can run analyses entirely on the user’s own device, meaning that sensitive genomic data — the mutation spectra and mutation annotation format rows that describe a patient’s tumor — never have to leave the computer they sit on.

At the heart of the problem mSigSDK addresses is a quiet but consequential inconsistency in the field. Several mature packages for mutational signature analysis exist, most prominently written in R and Python, and each has its own conventions for input data, its own fitting algorithms, and its own quirks. The choice of fitting tool can meaningfully affect the results a researcher obtains, which makes triangulating across multiple tools highly desirable. Yet doing so has been operationally expensive: a scientist would need to install and maintain several environments, convert data between formats, and manually reconcile outputs. Worse, no standard machine-readable format existed to capture the parameters of an analysis, the evidence supporting a review, and the provenance of the results — the kind of documentation that makes a computational finding reproducible and trustworthy.

mSigSDK tackles this by wrapping four established analysis tools — SigProfilerAssignment, MuSiCal, deconstructSigs, and sigminer — behind a uniform adapter layer. Through that layer, the kit orchestrates the tools so they can be run side by side on the same data without the user touching their individual installation requirements or input formats. The SDK also adds its own browser-native non-negative least squares fitting, a standard mathematical approach for estimating how much each known reference signature contributed to a tumor’s observed mutation pattern, as well as non-negative matrix factorization-based exploratory extraction, which allows researchers to discover novel signatures rather than only testing against a fixed catalogue such as the COSMIC reference set.

The engineering achievement here is substantial. Running R and Python code inside a browser is possible thanks to technologies like WebR and Pyodide, which compile those language runtimes to WebAssembly, but mSigSDK goes further by making the whole experience seamless. A zero-install demonstration reached a fully rendered local report in roughly 1.82 seconds. The kit emits configurable, rule-based review evidence — essentially automated documentation of why an analysis reached its conclusions — and serializes portable, schema-validated reports with built-in visualization and export. That means an analysis performed on one machine can be packaged as a machine-readable file, checked against a formal schema, and shared or archived with its full provenance intact.

Privacy is a central design consideration. Because analysis runs locally, mutation spectra and mutation annotation format rows stay on the user’s device by default. The authors are transparent about one caveat: optional reference-context helpers may transmit genomic coordinates to public endpoints unless a strict-local mode is enabled. This kind of explicit, switchable data-flow control is increasingly important as genomics moves into clinical settings where patient data cannot simply be uploaded to a remote server. A browser-native tool that keeps raw data on-device while still offering state-of-the-art analysis could lower the barrier for hospitals and research groups working under strict data governance rules.

The validation work behind the paper is unusually thorough. The team tested each of the four adapters against the corresponding package running locally on 38 single-base substitution spectra from lung adenocarcinoma samples in the Pan-Cancer Analysis of Whole Genomes project. Three of the four adapters reproduced their package’s local execution exactly, and the fourth matched to floating-point precision. The kit’s data converter matched SigProfilerMatrixGenerator version 1.3.6 exactly for single-base substitution spectra in both 96-channel and 1,536-channel formats, for double-base substitution spectra in the 78-channel format, and for the 83-channel small insertion-deletion classification, provided that repeat and microhomology annotations derived from SigProfilerMatrixGenerator were supplied to mSigSDK. In other words, running these tools in the browser yields the same numbers as running them on a desktop installation.

But the benchmarks also revealed something the field should pay attention to. Across 2,700 synthetic spectra generated at three noise levels, the mean cosine similarity of estimated exposures exceeded 0.96 for all tools — meaning the overall mixture of signatures was recovered well. Yet the mean per-spectrum F1 score for identifying which signatures were genuinely active ranged from 0.532 to 0.924 at 10 percent noise, a striking spread. On real PCAWG data, all tools reconstructed the observed spectra well, with mean cosine similarities between 0.982 and 0.994, but they disagreed sharply on how many signatures were active per sample, calling anywhere from 4.13 to 17.39 active signatures. This confirms that the choice of fitting tool matters, and it makes the case for multi-tool triangulation all the more compelling.

Speed is another highlight. Warm-start refitting — re-estimating signature exposures when a small change is made to the input — took between 18.2 and 73.7 milliseconds on Windows and 22.2 to 44.6 milliseconds on macOS for 120 samples. For the heavier scenario of 300 samples against 40 reference signatures, refitting completed in 1.80 to 6.81 seconds on Windows and 2.12 to 5.89 seconds on macOS. Those are interactive timescales, fast enough for a researcher to adjust parameters and see updated results in real time, something that batch-oriented command-line workflows have never offered.

The broader significance of mSigSDK may lie less in any single benchmark than in what it signals about the future of scientific software. By combining multi-tool orchestration, exploratory signature extraction, rule-based review evidence, and schema-validated reporting in a zero-install browser environment, the kit lowers the cost of doing rigorous, reproducible, and privacy-preserving mutational signature analysis to nearly zero. Developed with support from the National Cancer Institute’s Intramural Research Program and released as open access, it invites a much wider community — from large consortia to individual labs in resource-limited settings — to interrogate the mutational histories written into cancer genomes. If the fingerprints in our DNA are a diary, mSigSDK hands more readers than ever the pen-light needed to read it.

Subject of Research: Browser-native computational analysis of cancer mutational signatures

Article Title: mSigSDK: browser-native computation of mutational signatures

Article References: Ge, A., Zhang, T., Martins, Y. C., Landi, M. T., Park, B., Chen, K., Balasubramanian, J., & Almeida, J. S. (2026). mSigSDK: browser-native computation of mutational signatures. BMC Bioinformatics. https://doi.org/10.1186/s12859-026-06681-z

Image Credits: AI Generated

DOI: 10.1186/s12859-026-06681-z

Keywords: mutational signatures, cancer genomics, JavaScript, browser-native computation, bioinformatics software, SigProfilerAssignment, MuSiCal, deconstructSigs, sigminer, non-negative least squares, PCAWG, reproducibility