Two-dimensional linear-combination model fitting of magnetic resonance spectra to define the macromolecule baseline using FiTAID, a Fitting Tool for Arrays of Interrelated Datasets

To propose the determination of the macromolecular baseline (MMBL) in clinical 1H MR spectra based on T(1) and T(2) differentiation using 2D fitting in FiTAID, a general Fitting Tool for Arrays of Interrelated Datasets.

An integrative transcranial magnetic stimulation mapping technique using non-linear curve fitting

The aim of this study is to develop a new simple method for analyzing one-dimensional transcranial magnetic stimulation (TMS) mapping studies in humans. Motor evoked potentials (MEP) were recorded from the abductor pollicis brevis (APB) muscle during stimulation at nine different positions on the scalp along a line passing through the APB hot spot and the vertex. Non-linear curve fitting according to the Levenberg-Marquardt algorithm was performed on the averaged amplitude values obtained at all points to find the best-fitting symmetrical and asymmetrical peak functions. Several peak functions could be fitted to the experimental data. Across all subjects, a symmetric, bell-shaped curve, the complementary error function (erfc) gave the best results. This function is characterized by three parameters giving its amplitude, position, and width. None of the mathematical functions tested with less or more than three parameters fitted better. The amplitude and position parameters of the erfc were highly correlated with the amplitude at the hot spot and with the location of the center of gravity of the TMS curve. In conclusion, non-linear curve fitting is an accurate method for the mathematical characterization of one-dimensional TMS curves. This is the first method that provides information on amplitude, position and width simultaneously.

Quantitative 1H-magnetic resonance spectroscopy of human brain: Influence of composition and parameterization of the basis set in linear combination model-fitting

Localized short-echo-time (1)H-MR spectra of human brain contain contributions of many low-molecular-weight metabolites and baseline contributions of macromolecules. Two approaches to model such spectra are compared and the data acquisition sequence, optimized for reproducibility, is presented. Modeling relies on prior knowledge constraints and linear combination of metabolite spectra. Investigated was what can be gained by basis parameterization, i.e., description of basis spectra as sums of parametric lineshapes. Effects of basis composition and addition of experimentally measured macromolecular baselines were investigated also. Both fitting methods yielded quantitatively similar values, model deviations, error estimates, and reproducibility in the evaluation of 64 spectra of human gray and white matter from 40 subjects. Major advantages of parameterized basis functions are the possibilities to evaluate fitting parameters separately, to treat subgroup spectra as independent moieties, and to incorporate deviations from straightforward metabolite models. It was found that most of the 22 basis metabolites used may provide meaningful data when comparing patient cohorts. In individual spectra, sums of closely related metabolites are often more meaningful. Inclusion of a macromolecular basis component leads to relatively small, but significantly different tissue content for most metabolites. It provides a means to quantitate baseline contributions that may contain crucial clinical information.