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MP-PCA denoising of kinetic ¹³C-MR spectra of human liver: performance analysis for synthetic and in vivo data

Simone Poli^1,2, Jessie Mosso^3,4, David Herzig⁵, Lia Bally⁵, and Roland Kreis^1,2
¹Magnetic Resonance Methodology, Institute of Diagnostic and Interventional Neuroradiology, University of Bern, Bern, Switzerland, Bern, Switzerland, ²Translational Imaging Center, Sitem-insel, Bern, Switzerland, Bern, Switzerland, ³CIBM Center for Biomedical Imaging, Switzerland, Lausanne, Switzerland, ⁴Animal Imaging and Technology, EPFL, Lausanne, Switzerland, Lausanne, Switzerland, ⁵Insel Hospital, University Hospital Bern, Department of Diabetes, Endocrinology, Nutritional Medicine and Metabolism UDEM, Bern, Switzerland, Bern, Switzerland

Synopsis

Keywords: Data Processing, Sparse & Low-Rank Models, liver, 13C-MRS, denoising, MP-PCA, 7T, human, metabolism

Motivation: Need to improve determination of kinetics for low-concentration metabolites using X-nuclear MRS.

Goal(s): Investigate potential benefits of denoising by Marchenko-Pastur Principal Component Analysis (MP-PCA) for extracting natural-abundance glycogen kinetics from ¹³C-MRS data.

Approach: MP-PCA applied on synthetic and human in-vivo hepatic ¹³C-MRS time-course datasets.

Results: MP-PCA substantially improves apparent SNR and reduces mean linear regression residuals, without introducing bias in slope estimates. MP-PCA is shown to be valuable for the determination of unknown physiologic time-courses of low-concentrated glycogen signals; here, specifically enabling use of lower D-glucose loads in combined deuterium metabolic imaging and ¹³C-MRS evaluations of hepatic glucose metabolism.

Impact: Our findings on MP-PCA's efficacy in enhancing the determination of glycogen kinetics by ¹³C-MRS broaden the understanding of denoising techniques in MR spectroscopy and ultimately impact researchers and clinicians who develop, assess, or apply MR techniques suffering from low SNR.

Introduction

¹³C-MRS is a well-established method for quantification of natural abundance glycogen concentrations in skeletal muscle and liver. The measurement of the variation in glycogen content and its determinants is of major interest in health^1,2 and disease^3–5. Monitoring of glucose (Glc) and glycogen levels after oral administration of D-Glc allows to dynamically assess hepatic Glc metabolism using interleaved deuterium metabolic imaging and ¹³C-MRS^6,7. ¹³C-MRS is strongly limited by SNR and observation of physiologic changes of glycogen content is challenging, especially for modest Glc loads.
Marchenko-Pastur Principal Component Analysis (MP-PCA)⁸ is a data-driven denoising technique that benefits from an objective rank selection. MP-PCA leverages the multidimensional structure of MRS data to separate redundant and correlated contributions across spectra from Gaussian noise. It has been applied to various MR settings^9–13, all characterized by high redundancy and constant noise. Though both requirements are met for series of ¹³C-MR spectra, a thorough investigation is required of whether relevant signal information might be discarded with the noise-attributed principal components (PCs) or spurious features introduced. Our aim is to assess the potential benefit of MP-PCA denoising for extraction of glycogen kinetics from ¹³C-MRS time series.

Methods

MR setting: 7T system (Terra, Siemens) with triple-tuned surface coil (Rapid Biomedical).
In-vivo data: acquisition with a ¹³C pulse-and-acquire sequence (adiabatic excitation, TR 600ms, 256 acquisitions, NOE but no decoupling ¹H-irradiation, acquisition time 2:34min) to capture 26 time-points until 150 minutes after D-Glc administration. Data processing and fitting with jMRUI¹⁴ and Fitaid¹⁵. In a IRB-approved study, ten healthy subjects received oral Glc loads of 60g (~0.75g/kg), and three subjects ingested lower amounts of 20g (0.25 g/kg) or 10g (0.15 g/kg).
Synthetic data: glycogen signal fitted and removed from a set of 26 in-vivo ¹³C-MR spectra. A scaled glycogen signal (obtained from the averaged fitted glycogen) was then reintroduced into the kinetic dataset to create a well-defined artificial linear glycogen increase or decrease (±0.5%,±1.0%,±2.5%,±5.0%,±10%,±25% of the original averaged glycogen signal) with spectra equally-spaced over time.
MP-PCA: for each dataset, complex-valued FIDs were Fourier-transformed and structured into a matrix. The first dimension of the matrix corresponds to the concatenation of the temporal course of real and imaginary spectral points and the second dimension is the spectral ppm-scale; resulting in a 52x1200 matrix, which was centered column-wise before MP-PCA. Statistical analysis included linear timecourse regression and t-tests between original and denoised data.

Results and Discussion

Fig-1 shows sample spectra. Averaged apparent glycogen SNR in frequency domain is 7.0±0.4 for original and 11.1±1.0 for denoised spectra. The doublet can be well fitted using prior knowledge of a doublet with predefined splitting, each line consisting of two Lorentzian components (60 and 150Hz width).
MP-PCA found 7 PCs for the synthetic datasets, 10±4 for the in-vivo spectra with 60g-intake, and 6±4 for the low-dose cases.
Fig-2 displays sample outcomes for synthetic data. Denoised datasets exhibit reduced variance with respect to the corresponding linear regression lines, while reproducing the imposed increases/decreases. Boxplots of residuals demonstrate the denoising efficiency. Table-1 summarizes statistical findings for synthetic data. Linear regression slopes are found to be significantly different from 0 for smaller imposed changes with denoising than without (significance for effects above 10% without denoising, but already >+2.5% and <-5% with denoising). The regression residuals decrease consistently with denoising. Paired t-tests reject the introduction of significant bias.
Fig-3 and Table-2 report in-vivo results. As above, regression residuals are reduced after denoising. Reduction of data variance is proven independently of the linear-regression analysis (which may be questioned since the time course is probably nonlinear in-vivo) by the consistent reduction of variance between glycogen levels from adjacent time points, where no physiological change is expected (repeat spectra within 5min). In most datasets, significance for linear change remains the same with and without denoising. Where significance is lost with denoising (especially so for low-dose cases), it can be concluded that it is likely an artifactual finding for the original data. Conversely, when regression becomes significant after denoising, it suggests the presence of a previously undetectable slope (as for synthetic data).

Conclusions

MP-PCA appears to be a valid instrument for improving evaluation statistics for the detection of temporal changes in hepatic glycogen content.
In particular, denoising may serve as a secondary validation to confirm the presence or absence of a linear increase of glycogen content in noisy in vivo ¹³C MRS time series, allowing the use of lower Glc loads in studies focusing on postprandial Glc metabolism.
The use of MP-PCA must be validated on simulated datasets for each use case.

Acknowledgements

This project is supported by the Swiss National Science Foundation (PCEGP3_186978) and Diabetes Center Bern and by the European Union's Horizon 2020 research and innovation program under the Marie Sklodowska-Curie grant agreement No 813120 (INSPiRE-MED).

References

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[6] Poli S, Emara AF, Ballabani E, et al. Interleaved 1H-MRI, 2H-MRSI and 13C-MRS for time-resolved in vivo elucidation of glucose metabolism in human liver at 7 T. In Proceedings of ISMRM 2022, #628.
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Figures

Fig.1. Single time-point spectra for a) original in vivo ¹³C-MRS data and b) after MP-PCA denoising. The ¹³C-spectra show mostly lipid resonances between 0 and 190 ppm with the resonances of current interest, the glycogen doublet at 100.5 ppm highlighted in the zoomed inset.

Fig. 2. Evaluation results for synthetic kinetic ¹³C-MRS data series before and after MP-PCA denoising for original (0%) and ±25% (in a)) as well as ±10% (in b)) glycogen signal change. Fitted linear kinetic time evolution is shown as dashed lines (essentially overlapping for with and without denoising). c), d): Boxplots of the linear regression residuals for each case before and after denoising.

Fig. 3. Time course results for in-vivo ¹³C-MRS data series before (left) and after (right) MP-PCA denoising, for a), b) 60g D-Glc intake and c), d) reduced D-Glc intake. Linear regression curves for the whole cohorts are shown with dashed lines. For each case, boxplots of the cohort regression residuals are shown. Data scaled to the average values found for the 4 spectra recorded before Glc load, plotted as time 0.

Table 1. Statistical analysis of original and denoised synthetic datasets. “Orig.”and “DN” denote original and denoised datasets, respectively. a) Linear regression results for individual series (correlation coefficient, regression slope, significance of slope, overall change from baseline, mean residuals). b) Correlation analysis between original and denoised data (correlation coefficient, regression slope and its significance, paired t-test p-value). Significance is only expected and found where overall temporal change dominates the noise.

Table 2. Statistical analysis of original and denoised in-vivo datasets. Subjects are labeled S1 through S10 for 60g D-Glc intake. Low1 to Low3 denote subjects with reduced D-Glc intake. a) Linear regression results for individual series (correlation coefficient, regression slope, significance of slope, overall change from baseline, mean residuals, and mean coefficient of variance from adjacent time points). b) Correlation analysis between original and denoised data. Significance is only expected where overall temporal change dominates the noise.

Proc. Intl. Soc. Mag. Reson. Med. 32 (2024)

2995

DOI: https://doi.org/10.58530/2024/2995