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The fast Padé transform for noisy magnetic resonance spectroscopic data from the prostate: potential contribution to individualized prostate cancer care

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Abstract

Magnetic resonance spectroscopy (MRS) and spectroscopic imaging (MRSI) can enhance prostate cancer diagnostics, but have limitations that are largely due to reliance upon conventional Fourier-based signal processing. MRS of the prostate is exceedingly difficult, due to high spectral density with numerous multiplet resonances. We apply advanced signal processing methods through the fast Padé transform (FPT) to time signals generated according to in vitro MRS data as encoded from normal glandular and stromal prostate as well as from prostate cancer. Random Gauss-distributed zero mean noise is added to the noise-free time signal. The high resolution capabilities are demonstrated: at short partial signal lengths \((N_{\mathrm{P}})\), converged total and component spectra from the prostate are generated by the FPT. In comparison, Fourier-based processing provides only rough, uninformative total shape spectra. Detailed analysis reveals the powerful, complementary features of the two variants \(\hbox {FPT}^{(\pm )}\) of the FPT in separating the copious spurious content from genuine resonances. At short \(N_{\mathrm{P}}\), the FPT resolved all the physical resonances, including multiplets and closely overlapping peaks of different metabolites, exactly reconstructing all the input spectral parameters, from which the metabolite concentrations were precisely computed. Systematic study of noise-corrupted time signals in the controlled setting is a critical step in benchmarking the FPT for clinical applications. We discuss how these results could increase the diagnostic accuracy of MRS and MRSI of the prostate, and how this could contribute to a more individualized care of patients with prostate cancer.

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Notes

  1. Since the partial signal length \(N_{\mathrm{P}} = 650\) is not of the form \(2^{{m}}\) (m is a positive integer), the discrete Fourier transform, DFT, is used.

  2. The expounded spectral analysis is concerned primarily with time signals from MRS. However, the developed theory via the \(\hbox {FPT}^{(\pm )}\) also holds true for MRSI. The technical difference between MRS and MRSI is in that the former and the latter are for single- and multi-voxel encoding, respectively, from the scanned tissue. Clinically, MRSI is necessary whenever there is a need for volume coverage of the imaged tissue. This occurs if there is a suspicion that a single voxel examined by MRS might be insufficiently representative of the actual status of the examined tissue.

Abbreviations

1D:

One dimensional

2D:

Two dimensional

ADC:

Apparent diffusion coefficient

au:

Arbitrary units

BPH:

Benign prostatic hypertrophy

Cho:

Choline

Cit:

Citrate

Cr:

Creatine

DCE:

Dynamic contrast-enhanced

DFT:

Discrete Fourier transform

DWI:

Diffusion weighted imaging

FFT:

Fast Fourier transform

FID:

Free induction decay

FPT:

Fast Padé transform

GPC:

Glycerophosphocholine

HRMAS:

High resolution magic angle spinning

m-Ins:

Myoinositol

MR:

Magnetic resonance

MRI:

Magnetic resonance imaging

MRS:

Magnetic resonance spectroscopy

MRSI:

Magnetic resonance spectroscopic imaging

NMR:

Nuclear magnetic resonance

PA:

Polyamine

PC:

Phosphocholine

PCM:

Personalized cancer medicine

ppm:

Parts per millions

PSA:

Prostate specific antigen

RF:

Radiofrequency

rms:

Root-mean-square

RT:

Radiation therapy

SNR:

Signal-to-noise ratio

SNS:

Signal-noise separation

Tau:

Taurine

TOCSY:

Total correlation spectroscopy

TRUS:

Trans-urethral ultrasound

TSP:

(3-(Trimethylsilyl-) 3,3,2,2-tetradeutero-propionic acid

ww:

Wet weight

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Acknowledgments

This work was supported by King Gustaf the 5th Jubilee Fund, Cancerfonden, the Karolinska Institute Research Fund and FoUU through Stockholm County Council to which the authors are grateful.

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  1. Department of Oncology-Pathology, Karolinska Institute, Building P-9, 2nd Floor, P.O. Box 260, 17176, Stockholm, Sweden

    Dževad Belkić & Karen Belkić

  2. School of Community and Global Health, Claremont Graduate University, Claremont, CA, USA

    Karen Belkić

  3. Institute for Prevention Research, Keck School of Medicine, University of Southern California, Alhambra, CA, USA

    Karen Belkić

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  1. Dževad Belkić
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Correspondence to Dževad Belkić.

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Belkić, D., Belkić, K. The fast Padé transform for noisy magnetic resonance spectroscopic data from the prostate: potential contribution to individualized prostate cancer care. J Math Chem 54, 707–764 (2016). https://doi.org/10.1007/s10910-015-0586-3

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