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Mathematical modeling of an NMR chemistry problem in ovarian cancer diagnostics

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Abstract

We use mathematical modeling via the fast Padé transform (FPT) with respect to a theoretically-designed problem based on time signals that are similar to NMR data as encoded from benign and malignant ovarian cyst fluid. The FPT reconstructed exactly all the input spectral parameters by using exceedingly small fractions of the full time signals both for those corresponding to the benign, as well as to the malignant case. The converged parametric results remained stable thereafter at longer signal lengths. The Padé absorption spectra yielded clear resolution of all the extracted physical metabolites. The capacity of the FPT to resolve and precisely quantify the physical resonances as encountered in benign versus malignant ovarian cystic fluid is demonstrated. The practical significance of such findings is enhanced by the avoidance of the time signals’ exponential tail which is embedded in the background, leading to problems in quantification. Without any fitting or numerical integration of peak areas, the FPT reliably yields the metabolite concentrations of major importance for distinguishing benign from malignant ovarian lesions. Thus, the FPT provides distinct advantages relative to the standard Fourier methodology, which is also stable, but has a number of drawbacks. These include limited resolution capacity, as well as non-parametric estimation, so that only a shape spectrum is generated and post-processing is necessary via, e.g., fitting or numerical integrations which are not unique. The FPT is also distinguished from other competitive parametric methods, which are generally unstable as a function of signal length N at a fixed bandwidth and, therefore, particularly unsuitable to clinical data. We conclude that these advantages of the FPT could be of definite benefit for ovarian cancer diagnostics via NMR and that this line of investigation should continue with encoded data from benign and malignant ovarian tissue, in vitro and in vivo. This avenue is of clinical urgency for early ovarian cancer detection, a goal which is still elusive and achievement of which would confer a major survival benefit.

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Abbreviations

Ala:

Alanine

au:

Arbitrary units

Cho:

Choline

COSY:

2 dimensional correlated spectroscopy

Cr:

Creatine

Crn:

Creatinine

C met :

Metabolite concentration

C ref :

Reference concentration

CT:

Computerized tomography

DFT:

Discrete Fourier transform

DLP:

Decimated linear predictor

DPA:

Decimated Padé approximant

DSD:

Decimated signal diagonalization

FFT:

Fast Fourier transform

FID:

Free induction decay

FPT:

Fast Padé transform

Glc:

Glucose

Gln:

Glutamine

Iso:

Isoleucine

HLSVD:

Hankel-Lanczos Singular Value Decomposition

Lac:

Lactate

Lys:

Lysine

Met:

Methionine

MR:

Magnetic resonance

MRI:

Magnetic resonance imaging

MRS:

Magnetic resonance spectroscopy

MRSI:

Magnetic resonance spectroscopic imaging

NMR:

Nuclear magnetic resonance

PA:

Padé approximant

PLCO Trial:

Prostate, Lung, Colorectal and Ovarian Trial

ppm:

Parts per million

SCS:

Statistical classification strategy

SNR:

Signal-to-noise ratio

ST:

Shanks transform

Thr:

Threonine

TVUS:

Transvaginal ultrasound

Val:

Valine

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Authors and Affiliations

  1. Department of Oncology-Pathology, Karolinska Institute, 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

Authors
  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. Mathematical modeling of an NMR chemistry problem in ovarian cancer diagnostics. J Math Chem 43, 395–425 (2008). https://doi.org/10.1007/s10910-007-9279-x

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  • DOI: https://doi.org/10.1007/s10910-007-9279-x

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