L1-norm vs. L2-norm fitting in optimizing focal multi-channel tES stimulation: linear and semidefinite programming vs. weighted least squares

•Comparative results using L1-norm regularized L1-norm fitting (L1L1) against L1-norm regularized L2-norm fitting (L1L2) and Tikhonov’s regularized least-squares (TLS) methods for the calculations.•Examination of state-of-the-art 8 and 20 active electrode channel montage for Multi-Channel Transcrani...

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Veröffentlicht in:Computer methods and programs in biomedicine Jg. 226; S. 107084
Hauptverfasser: Galaz Prieto, Fernando, Rezaei, Atena, Samavaki, Maryam, Pursiainen, Sampsa
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Elsevier B.V 01.11.2022
Schlagworte:
Least squares
Linear programming
Metaheuristics
Non-Invasive brain stimulation
Semidefinite programming
Transcranial electrical stimulation (tES)
Linear programming
Semidefinite programming
Transcranial electrical stimulation (tES)
Metaheuristics
Non-Invasive brain stimulation
Least squares
ISSN:0169-2607, 1872-7565, 1872-7565
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Zusammenfassung:•Comparative results using L1-norm regularized L1-norm fitting (L1L1) against L1-norm regularized L2-norm fitting (L1L2) and Tikhonov’s regularized least-squares (TLS) methods for the calculations.•Examination of state-of-the-art 8 and 20 active electrode channel montage for Multi-Channel Transcranial Electrical Stimulation (MC-TES) exercise, i.e., applying more than two electrodes during brain stimulation session.•Analysis of reconstructions, electric fields, current distribution and montage using different number of active electrodes available and applied through a two-stage metaheuristic-based constraints on different regions of the brain. Background and Objective: This study focuses on Multi-Channel Transcranial Electrical Stimulation, a non-invasive brain method for stimulating neuronal activity under the influence of low-intensity currents. We introduce a mathematical formulation for finding a current pattern that optimizes an L1-norm fit between a given focal target distribution and volumetric current density inside the brain. L1-norm is well-known to favor well-localized or sparse distributions compared to L2-norm (least-squares) fitted estimates. Methods: We present a linear programming approach that performs L1-norm fitting and penalization of the current pattern (L1L1) to control the number of non-zero currents. The optimizer filters a large set of candidate solutions using a two-stage metaheuristic search from a pre-filtered set of candidates. Results: The numerical simulation results obtained with both 8- and 20-channel electrode montages suggest that our hypothesis on the benefits of L1-norm data fitting is valid. Compared to an L1-norm regularized L2-norm fitting (L1L2) via semidefinite programming and weighted Tikhonov least-squares method (TLS), the L1L1 results were overall preferable for maximizing the focused current density at the target position, and the ratio between focused and nuisance current magnitudes. Conclusions: We propose the metaheuristic L1L1 optimization approach as a potential technique to obtain a well-localized stimulus with a controllable magnitude at a given target position. L1L1 finds a current pattern with a steep contrast between the anodal and cathodal electrodes while suppressing the nuisance currents in the brain, hence, providing a potential alternative to modulate the effects of the stimulation, e.g., the sensation experienced by the subject.
Bibliographie:ObjectType-Article-1
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ISSN:0169-2607
1872-7565
1872-7565
DOI:10.1016/j.cmpb.2022.107084