Accurate quantification of in vivo³¹P NMR signals using the variable projection method and prior knowledge

Abstract

Free induction decay signals are analyzed by fitting a model function directly in the time domain. No starting values are needed for linear model parameters, and omission of corrupted data points poses no problems. A significant gain of accuracy is achieved by imposing prior knowledge about the model parameters.

Cramér–Rao bounds: an evaluation tool for quantitation

“…Methods based on non-linear least-squares fitting such as VARPRO [27][28][29] or AMARES 30 and some recent SVDbased methods allow one to include prior knowledge of the poles, 31,32 the frequencies 33 and the phases. 34 We note that prior knowledge is not always trustworthy in in vivo studies, e.g.…”

31P-magnetic resonance spectroscopy and 2H-magnetic resonance imaging studies of a panel of early-generation transplanted murine tumour models

“…Spectral analysis was performed by the VARPRO time-domain non-linear least squares method, yielding the following peak parameters: areas, frequencies, linewidths and phases (van der Veen et al, 1988;van den Boogaart et al, 1995). For each VARPRO analysis the first four data points were excluded from the fit to eliminate the influence of fast-decaying signals from immobilized phosphates that cause a baseline hump in the spectra.…”

The effects of age on kinetics of oxygen uptake and phosphocreatine in humans during exercise

“…A nominal 46 deg pulse was used with a repetition time of 1000 ms. Time-averaged FIDs were left shifted three points, to remove broad components from the spectra, and a 5 Hz exponential filter applied. Peak areas and positions were calculated from the 1024 points in the FID using an iterative, non-linear least-squares routine based on the VARPRO algorithm (Van Der Veen, DeBeer, Luyten & Van Ormondt, 1988), which fit Lorentzian line shapes to each peak. No correction for partial saturation was made since this was a serial study determining the kinetic time constants from relative changes in PCr and Pi and absolute quantities were not necessary.…”