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Exact quantification of time signals from magnetic resonance spectroscopy by the fast Padé transform with applications to breast cancer diagnostics

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Abstract

Mathematical modeling via the fast Padé transform (FPT) is applied according to experimental NMR data encoded from (a) normal, non-infiltrated breast tissue, (b) benign pathology (fibroadenoma) and (c) malignant breast tissue. At a partial signal length N P  = 1500, the FPT provided exact reconstruction of all the input spectral parameters for the time signals corresponding to the normal, benign as well as to the malignant lesions. The converged parametric results remained stable at longer signal lengths. The Padé absorption spectra yielded unequivocal resolution of all the extracted physical metabolites, even of those that were nearly completely overlapping (phosphocholine and phosphoethanolamine at 3.22 ppm). The capacity of the FPT to resolve and precisely quantify the physical resonances as encountered in normal versus benign versus malignant breast is demonstrated. In particular, the FPT unambiguously delineated and quantified diagnostically important metabolites such as lactate, as well as choline, phosphocholine and glycerophosphocholine that are very closely overlapping and may represent MR-retrievable molecular markers of breast cancer. This was achieved by the FPT without any fitting or numerical integration of peak areas. We conclude that these advantages of the FPT could be of definite benefit for breast cancer diagnostics via NMR and that this line of investigation should continue with encoded data from benign and malignant breast tissue, in vitro and in vivo. We anticipate that Padé-optimized MRS will reduce the false positive rates of MR-based modalities and further improve their sensitivity. Once this is achieved, and given that MR entails no ionizing radiation, new possibilities for screening/early detection open up, especially for risk groups, e.g. Padé-optimized MRS could be used with greater surveillance frequency among younger women with high breast cancer risk.

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Abbreviations

Ala:

Alanine

au:

Arbitrary units

β-Glc:

Beta-glucose

CDP:

Cytosine diphosphate

Cho:

Choline

FID:

Free induction decay

FFT:

Fast Fourier transform

FPT:

Fast Padé transform

FWHM:

Full width at half maximum

GPC:

Glycerophosphocholine

HLSVD:

Hankel–Lanczos singular value decomposition

Lac:

Lactate

m-Ino:

Myoinositol

MR:

Magnetic resonance

MRI:

Magnetic resonance imaging

MRS:

Magnetic resonance spectroscopy

MRSI:

Magnetic resonance spectroscopic imaging

NMR:

Nuclear magnetic resonance

PA:

Padé approximant

ppm:

Parts per million

PC:

Phosphocholine

PE:

Phosphoethanolamine

SNR:

Signal-to-noise ratio

SNS:

Signal–noise separation

Tau:

Taurine

TE:

Echo time

TSP:

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

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Authors and Affiliations

  1. Department of Oncology-Pathology, Karolinska Institute, P.O. Box 260, Stockholm, 17176, Sweden

    Dževad Belkić & Karen Belkić

  2. Institute for Prevention Research, University of Southern California Keck School of Medicine, Los Angeles, CA, 91803, USA

    Karen Belkić

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  1. Dževad Belkić
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  2. Karen Belkić
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Correspondence to Dževad Belkić.

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Belkić, D., Belkić, K. Exact quantification of time signals from magnetic resonance spectroscopy by the fast Padé transform with applications to breast cancer diagnostics. J Math Chem 45, 790–818 (2009). https://doi.org/10.1007/s10910-008-9462-8

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