Encoded in vivo time signals from the ovary in magnetic resonance spectroscopy: poles and zeros as the cornerstone for stability of response functions of systems to external perturbations

Abstract

In order to handle encoded data from magnetic resonance spectroscopy (MRS), advanced signal processing methods are vital. This is presently carried out using the fast Padé transform (FPT) applied to in vivo MRS time signals encoded from the ovary. We examine the essential features of the response function, namely the spectral poles and zeros, as the key to stability of the system to external excitations. Noise is separated from signal by reliance upon the multi-level signature of Froissart doublets. Our focus is upon eliminating the oversensitivity to alterations in model order K, through systematic examination of poles and zeros, as well as Padé-reconstructed total shape spectra, spectral parameters and component shape spectra. This comprehensive examination of convergence of all variables under study includes investigation of the combined role of spectra averaging and time signal extrapolation. Comparisons are made throughout between the results for six model orders (K = 575, 585,ldots , 625) with an increment of ten and eleven model orders (K = 575, 580,ldots , 625) with an increment of 5. It is demonstrated that for the reconstructed poles and zeros, as well as for magnitudes and phases, spectra averaging and Padé-based extrapolation of time signals are essential for the stability of the system and for the accurate retrieval of resonances. Full convergence is achieved when spectra averaging and extrapolation are applied together. Spectra averaging and extrapolation are also shown to be needed to obtain stabilized results to the level of stochasticity for the component spectra for the six and the eleven model orders. Without spectra averaging and extrapolation, there were noticeable variances for the six and the eleven model orders with regard to all the variables under study. The present analysis and results have important implications for expediting the robust quantification by the FPT. All the analysis herein was applied to in vivo MRS data encoded on a 3 T scanner from a borderline serous cystic ovarian tumor. This clinical problem has been chosen in light of the urgent need to develop effective methods for early detection of ovarian cancer. The overriding motivation is to improve survival for women afflicted with this malignancy. The reported results further hone the Padé-designed methodology for practical applications of in vivo MRS and, therefore, are anticipated to help in achieving the stated goal.