Journal of Mathematical Chemistry

, Volume 40, Issue 1, pp 85–103

Mathematical Optimization of in vivo NMR Chemistry Through the Fast Padé Transform: Potential Relevance for Early Breast Cancer Detection by Magnetic Resonance Spectroscopy

Article

DOI: 10.1007/s10910-006-9123-8

Cite this article as:
Belkić, D. & Belkić, K. J Math Chem (2006) 40: 85. doi:10.1007/s10910-006-9123-8

Mathematical advances in signal processing through the fast Padé transform (FPT) can greatly improve the information extracted via in vivo nuclear magnetic resonance (NMR) chemistry. The FPT is a frequency-dependent, non-linear rational polynomial approximation of the exact Maclaurin series, which dramatically improves resolution and signal-to-noise ratio in a stable manner with robust error analysis and provides precise numerical data for all the peak parameters (position, height, width and phase) for every true resonance including those that are weak and/or overlapping. The concentrations of many of the chemical constituents of tissues can thereby be accurately determined. These advantages of the FPT are particularly germane for in vivo NMR detection and quantification of a number of molecular markers of breast cancer, such as phosphocholine, as well as lactate, which cannot be assessed using standard Fourier data analytical techniques applied to in vivo NMR in the clinical setting.

Keywords

fast Padé transformNMR chemistryearly cancer diagnosticsbreast cancer

Abbreviations

CDP

cytosine diphosphate

CHESS

CHEmical Shift Selective

CI

confidence interval

FFT

fast Fourier transform

FPT

fast Padé transform

GPC

glycerophosphocholine

PA

Padé approximant

PC

phosphocholine

MR

magnetic resonance

MRI

magnetic resonance imaging

MRS

magnetic resonance spectroscopy

MRSI

magnetic resonance spectroscopic imaging

NMR

nuclear magnetic resonance

SD

standard deviation

SNR

signal to noise ratio

TE

echo time

Copyright information

© Springer Science+Business Media, Inc. 2006

Authors and Affiliations

  1. 1.Department of Oncology and PathologyKarolinska InstituteStockholmSweden
  2. 2.Institute for Prevention ResearchThe University of Southern California School of MedicineLos AngelesUSA