In vivomagnetic resonance spectroscopy by the fast Padé transform

Clinical value of N-acetyl mucinous compounds and lipid peaks in differentiating benign and malignant ovarian mucinous tumors by MR spectroscopy

PURPOSE

To retrospectively evaluate the clinical significance of the peaks of N-acetyl mucinous compounds (NAMC) at 2 ppm and lipid at 1.3 ppm in in-vivo proton magnetic resonance (MR) spectroscopy for distinguishing benign and malignant mucinous tumors in patients with ovarian masses.

METHODS

MR spectroscopy was performed in patients with pathologically diagnosed mucinous ovarian tumors at 3 T MRI system. The peaks of NAMC, lipid, and total choline compounds (tCho) were classified into three classes in comparison with the noise level by visual estimation. The NAMC concentration was quantified relative to unsuppressed water by using LCModel analysis.

RESULTS

A total of 27 ovarian mucinous tumors in 27 patients were included in this study. The NAMC peak was observed in all 27 mucinous tumors, and the lipid peak was observed in 14 of 27 tumors: 1 of 9 benign tumors (11%), and 13 of 18 malignant tumors (11 borderline malignancies and 7 carcinomas) (72%). The presence of the lipid peak for the diagnosis of malignant mucinous tumor showed generally better diagnostic ability than MR imaging, with a sensitivity of 72%, specificity of 89%, accuracy of 78%, PPV of 93%, and NPV of 62%. The concentration of the NAMC in malignant mucinous tumors tended to be higher than that in benign mucinous tumors, but there was no statistically significant difference.

CONCLUSIONS

The bimodal peaks of NAMC and lipid are suggestive of malignant mucinous tumors, and the presence of the lipid peak may be useful in distinguishing benign from malignant ovarian mucinous tumors.

Random Perturbations of Matrix Polynomials

A sum of a large-dimensional random matrix polynomial and a fixed low-rank matrix polynomial is considered. The main assumption is that the resolvent of the random polynomial converges to some deterministic limit. A formula for the limit of the resolvent of the sum is derived, and the eigenvalues are localised. Four instances are considered: a low-rank matrix perturbed by the Wigner matrix, a product HX of a fixed diagonal matrix H and the Wigner matrix X and two special matrix polynomials of higher degree. The results are illustrated with various examples and numerical simulations.

Fast Padé Transform Accelerated CSI for Hyperpolarized MRS

The fast Padé transform (FPT) is a method of spectral analysis that can be used to reconstruct nuclear magnetic resonance spectra from truncated free induction decay signals with superior robustness and spectral resolution compared with conventional Fourier analysis. The aim of this study is to show the utility of FPT in reducing of the scan time required for hyperpolarized ¹³C chemical shift imaging (CSI) without sacrificing the ability to resolve a full spectrum. Simulations, phantom, and in vivo hyperpolarized [1-¹³C] pyruvate CSI data were processed with FPT and compared with conventional analysis methods. FPT shows improved stability and spectral resolution on truncated data compared with the fast Fourier transform and shows results that are comparable to those of the model-based fitting methods, enabling a reduction in the needed acquisition time in ¹³C CSI experiments. Using FPT can reduce the readout length in the spectral dimension by 2-6 times in ¹³C CSI compared with conventional Fourier analysis without sacrificing the spectral resolution. This increased speed is crucial for ¹³C CSI because T1 relaxation considerably limits the available scan time. In addition, FPT can also yield direct quantification of metabolite concentration without the additional peak analysis required in conventional Fourier analysis.

Rapid multi-echo measurement of brain metabolite T₂ values at 7 T using a single-shot spectroscopic Carr-Purcell-Meiboom-Gill sequence and prior information

We present a method for the robust and accurate estimation of brain metabolite transverse relaxation times (T2 ) from multiple spin-echo data acquired with a single-shot Carr-Purcell-Meiboom-Gill (CPMG) spectroscopic sequence. Each acquired echo consists of a small number of complex time-domain data points. The amplitudes of the spectral components in each echo are calculated by solving a set of linear equations in which previously estimated frequencies and linewidths serve as prior information. These priors are obtained from a short MRS experiment in which a large number of time-domain data points are acquired, and are subsequently estimated using linear prediction with singular value decomposition (LPSVD) processing. We show that this process can be used to accurately and rapidly measure the T2 values for the main singlet resonances in single-volume MRS measurements in the brain. The proposed method can be generalized to any set of MRS experiments comprising repeated measurements of amplitude changes, e.g. as a function of an experimental parameter, such as TE, inversion time or diffusion weighting.

Exponential convergence rate (the spectral convergence) of the fast Padé transform for exact quantification in magnetic resonance spectroscopy

This study deals with the most challenging numerical aspect for solving the quantification problem in magnetic resonance spectroscopy (MRS). The primary goal is to investigate whether it could be feasible to carry out a rigorous computation within finite arithmetics to reconstruct exactly all the machine accurate input spectral parameters of every resonance from a synthesized noiseless time signal. We also consider simulated time signals embedded in random Gaussian distributed noise of the level comparable to the weakest resonances in the corresponding spectrum. The present choice for this high-resolution task in MRS is the fast Padé transform (FPT). All the sought spectral parameters (complex frequencies and amplitudes) can unequivocally be reconstructed from a given input time signal by using the FPT. Moreover, the present computations demonstrate that the FPT can achieve the spectral convergence, which represents the exponential convergence rate as a function of the signal length for a fixed bandwidth. Such an extraordinary feature equips the FPT with the exemplary high-resolution capabilities that are, in fact, theoretically unlimited. This is illustrated in the present study by the exact reconstruction (within machine accuracy) of all the spectral parameters from an input time signal comprised of 25 harmonics, i.e. complex damped exponentials, including those for tightly overlapped and nearly degenerate resonances whose chemical shifts differ by an exceedingly small fraction of only 10(-11) ppm. Moreover, without exhausting even a quarter of the full signal length, the FPT is shown to retrieve exactly all the input spectral parameters defined with 12 digits of accuracy. Specifically, we demonstrate that when the FPT is close to the convergence region, an unprecedented phase transition occurs, since literally a few additional signal points are sufficient to reach the full 12 digit accuracy with the exponentially fast rate of convergence. This is the critical proof-of-principle for the high-resolution power of the FPT for machine accurate input data. Furthermore, it is proven that the FPT is also a highly reliable method for quantifying noise-corrupted time signals reminiscent of those encoded via MRS in clinical neuro-diagnostics.

Exact quantification of time signals in Padé-based magnetic resonance spectroscopy

This study reports on the fast Padé transform (FPT) for parametric signal processing of realistically synthesized free induction decay curves whose main spectral features are similar to those encoded clinically from a healthy human brain by means of magnetic resonance spectroscopy (MRS). Here, for the purpose of diagnostics, it is of paramount importance to be able to perform accurate and robust quantification of the investigated time signals. This amounts to solving the challenging harmonic inversion problem as a spectral decomposition of the given time signal by means of reconstruction of the unknown total number of resonances, their complex frequencies and amplitudes yielding the peak positions, widths, heights and phases. On theoretical grounds, the FPT solves exactly this mathematically ill-conditioned inverse problem for any noiseless synthesized time signal comprised of an arbitrarily large (finite or infinite) number of damped complex exponentials with stationary and non-stationary polynomial-type amplitudes leading to Lorentzian (non-degenerate) and non-Lorentzian (degenerate) spectra. Convergent validation for this fact is given via the proof-of-principle which is thoroughly demonstrated by the exact numerical solution of a typical quantification problem from MRS. The presently designed study is a paradigm shift for signal processing in MRS with particular relevance to clinical oncology, due to the unprecedented capability of the fast Padé transform to unequivocally resolve and quantify isolated, tightly overlapped and nearly coincident resonances.