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.

Parameter-free extraction of the functional network topology from intracranial EEG recordings: a time-resolved study of graph properties in focal onset seizures

Rationale: Focal onset epileptic seizures are due to abnormal interactions between distributed brain areas. By estimating the cross-correlation matrix of multi-site intra-cerebral EEG recordings (iEEG), one can quantify these interactions. To assess the topology of the underlying functional network, the binary connectivity matrix has to be derived from the cross-correlation matrix by use of a threshold. Classically, a unique threshold is used that constrains the topology [1]. Our method aims to set the threshold in a data-driven way by separating genuine from random cross-correlation. We compare our approach to the fixed threshold method and study the dynamics of the functional topology. Methods: We investigate the iEEG of patients suffering from focal onset seizures who underwent evaluation for the possibility of surgery. The equal-time cross-correlation matrices are evaluated using a sliding time window. We then compare 3 approaches assessing the corresponding binary networks. For each time window: * Our parameter-free method derives from the cross-correlation strength matrix (CCS)[2]. It aims at disentangling genuine from random correlations (due to finite length and varying frequency content of the signals). In practice, a threshold is evaluated for each pair of channels independently, in a data-driven way. * The fixed mean degree (FMD) uses a unique threshold on the whole connectivity matrix so as to ensure a user defined mean degree. * The varying mean degree (VMD) uses the mean degree of the CCS network to set a unique threshold for the entire connectivity matrix. * Finally, the connectivity (c), connectedness (given by k, the number of disconnected sub-networks), mean global and local efficiencies (Eg, El, resp.) are computed from FMD, CCS, VMD, and their corresponding random and lattice networks. Results: Compared to FMD and VMD, CCS networks present: *topologies that are different in terms of c, k, Eg and El. *from the pre-ictal to the ictal and then post-ictal period, topological features time courses that are more stable within a period, and more contrasted from one period to the next. For CCS, pre-ictal connectivity is low, increases to a high level during the seizure, then decreases at offset. k shows a ‘‘U-curve’’ underlining the synchronization of all electrodes during the seizure. Eg and El time courses fluctuate between the corresponding random and lattice networks values in a reproducible manner. Conclusions: The definition of a data-driven threshold provides new insights into the topology of the epileptic functional networks.

A Nonstationary Space-Time Gaussian Process Model for Partially Converged Simulations

In the context of expensive numerical experiments, a promising solution for alleviating the computational costs consists of using partially converged simulations instead of exact solutions. The gain in computational time is at the price of precision in the response. This work addresses the issue of fitting a Gaussian process model to partially converged simulation data for further use in prediction. The main challenge consists of the adequate approximation of the error due to partial convergence, which is correlated in both design variables and time directions. Here, we propose fitting a Gaussian process in the joint space of design parameters and computational time. The model is constructed by building a nonstationary covariance kernel that reflects accurately the actual structure of the error. Practical solutions are proposed for solving parameter estimation issues associated with the proposed model. The method is applied to a computational fluid dynamics test case and shows significant improvement in prediction compared to a classical kriging model.

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.