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1. Interpolated functional manifold for functional near-infrared spectroscopy analysis at group level

Author

Shender-María Ávila-Sansores, Gustavo Rodríguez-Gómez, Felipe Orihuela-Espina, Ilias Tachtsidis, and Consejo Nacional de Ciencia y Tecnología (CONACYT) de México

Subjects
Paper, Classical group, Surface (mathematics), topology, Jaccard index, Mean squared error, Neuroscience (miscellaneous), 01 natural sciences, law.invention, 010309 optics, 03 medical and health sciences, 0302 clinical medicine, 0903 Biomedical Engineering, law, 0103 physical sciences, functional near-infrared spectroscopy, Radiology, Nuclear Medicine and imaging, Radial basis function, Mathematics, manifold, Radiological and Ultrasound Technology, 1004 Medical Biotechnology, functional connectivity, Research Papers, Group analysis, connectivity analysis, 1109 Neurosciences, Manifold (fluid mechanics), Algorithm, 030217 neurology & neurosurgery, Interpolation
Abstract

Significance: Solutions for group-level analysis of connectivity from fNIRS observations exist, but groupwise explorative analysis with classical solutions is often cumbersome. Manifold-based solutions excel at data exploration, but there are infinite surfaces crossing the observations cloud of points. Aim: We aim to provide a systematic choice of surface for a manifold-based analysis of connectivity at group level with small surface interpolation error. Approach: This research introduces interpolated functional manifold (IFM). IFM builds a manifold from reconstructed changes in concentrations of oxygenated ΔcHbO2 and reduced ΔcHbR hemoglobin species by means of radial basis functions (RBF). We evaluate the root mean square error (RMSE) associated to four families of RBF. We validated our model against psychophysiological interactions (PPI) analysis using the Jaccard index (JI). We demonstrate the usability in an experimental dataset of surgical neuroergonomics. Results: Lowest interpolation RMSE was 1.26e − 4 ± 1.32e − 8 for ΔcHbO2 [A.U.] and 4.30e − 7 ± 2.50e − 13 [A.U.] for ΔcHbR. Agreement with classical group analysis was JI = 0.89 ± 0.01 for ΔcHbO2. Agreement with PPI analysis was JI = 0.83 ± 0.07 for ΔcHbO2 and JI = 0.77 ± 0.06 for ΔcHbR. IFM successfully decoded group differences [ANOVA: ΔcHbO2: F ( 2,117 ) = 3.07; p

Published
2020

2. A regularized least-squares radial point collocation method (RLS-RPCM) for adaptive analysis.

Author

Kee, Bernard B. T., Liu, G. R., and Lu, C.

Subjects
*PAPER, *COLLOCATION methods, *MATHEMATICAL analysis, *MESHFREE methods, *RADIAL basis functions, *STABILIZING agents
Abstract

This paper presents a stabilized meshfree method formulated based on the strong formulation and local approximation using radial basis functions (RBFs). The purpose of this paper is two folds. First, a regularization procedure is developed for stabilizing the solution of the radial point collocation method (RPCM). Second, an adaptive scheme using the stabilized RPCM and residual based error indicator is established. It has been shown in this paper that the features of the meshfree strong-form method can facilitated an easier implementation of adaptive analysis. A new error indicator based on the residual is devised and used in this work. As shown in the numerical examples, the new error indicator can reflect the quality of the local approximation and the global accuracy of the solution. A number of examples have been presented to demonstrate the effectiveness of the present method for adaptive analysis. [ABSTRACT FROM AUTHOR]

Published
2007
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