Visualizing hidden components of envelopes non-parametrically in magnetic resonance spectroscopy: Phosphocholine, a breast cancer biomarker

Visualizing hidden components of envelopes non-parametrically in magnetic resonance spectroscopy:... A key advantage of rational polynomials as a quotient of two polynomials is their automatically built-in polar representation. Rational polynomials are thus the most suitable for describing functions with peaks, such as those in magnetic resonance spectra (MRS). The Padé approximant is the most important of these rational polynomials because of its uniqueness for the power series expansion of the given function. Non-parametric analysis through the fast Padé transform (FPT) is a convenient initial step for processing MRS time signals, since it can be carried out once the expansion coefficients of the polynomials are generated from the time signal, without polynomial rooting. We applied the FPT to synthesized MRS time signals similar to those encoded in vitro from breast cancer. Padé-based non-parametric envelopes generated with and without spectra partitioning are studied. Comparisons of these total shape spectra with the related Padé component spectra were made. Phosphocholine (PC) and phosphoethanolamine (PE), separated by a mere 0.001 parts per million of chemical shift, were resolved in the non-parametric partitioned envelopes. However, in the non-parametric FPT without partitioning, a single composite smooth Lorentzian peak (PC $$+$$ + PE) was generated in envelopes, with no indication whatsoever that two resonances were present. Subsequent parametric analysis (quantification) by the FPT confirmed that PC completely underlies the much more abundant PE. This problem, chosen to illustrate the usefulness in the non-parametric partitioned envelopes, has clinical implications. Namely, PC is a cancer biomarker which thus far was not identified with in vivo MRS using envelopes from the conventional Fourier-based (single-polynomial) processing. Journal of Mathematical Chemistry Springer Journals

Visualizing hidden components of envelopes non-parametrically in magnetic resonance spectroscopy: Phosphocholine, a breast cancer biomarker

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Springer International Publishing
Copyright © 2017 by The Author(s)
Chemistry; Physical Chemistry; Theoretical and Computational Chemistry; Math. Applications in Chemistry
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