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Pileckyte I, Soto-Faraco S. Sensory stimulation enhances visual working memory capacity. COMMUNICATIONS PSYCHOLOGY 2024; 2:109. [PMID: 39558084 PMCID: PMC11574275 DOI: 10.1038/s44271-024-00158-6] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/30/2024] [Accepted: 11/06/2024] [Indexed: 11/20/2024]
Abstract
Visual working memory (vWM) plays a crucial role in visual information processing and higher cognitive functions; however, it has a very limited capacity. Recently, several studies have successfully modulated vWM capacity in humans using entrainment with transcranial alternate current stimulation (tACS) by targeting parietal theta in a frequency-specific manner. In the current study, we aim to expand upon these findings by utilizing sensory instead of electrical stimulation. Across six behavioral experiments (combined N = 209), we applied rhythmic visual and auditory sensory stimulation at 4 Hz and 7 Hz, aiming to modulate vWM capacity. Collectively, the results showed an overall robust improvement with sensory stimulation at either frequency, compared to baseline. However, contrary to our prediction, 7 Hz stimulation tended to slightly outperform 4 Hz stimulation. Importantly, the observed facilitatory effect was mainly driven by the low-capacity sub-group of participants. Follow-up experiments using the Attention Network Test (ANT) and pupillometry measures did not find evidence that this effect could be directly attributed to modulation of phasic or tonic arousal. We speculate that our results differed from those obtained with tACS due to targeting functionally different theta oscillations, or the modulation of participants' temporal expectations.
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Affiliation(s)
- Indre Pileckyte
- Departament d'Enginyeria, Center for Brain & Cognition, Universitat Pompeu Fabra, Barcelona, Spain.
| | - Salvador Soto-Faraco
- Departament d'Enginyeria, Center for Brain & Cognition, Universitat Pompeu Fabra, Barcelona, Spain
- Institució Catalana de Recerca i Estudis Avançats (ICREA), Barcelona, Spain
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Gulbinaite R, Nazari M, Rule ME, Bermudez-Contreras EJ, Cohen MX, Mohajerani MH, Heimel JA. Spatiotemporal resonance in mouse primary visual cortex. Curr Biol 2024; 34:4184-4196.e7. [PMID: 39255789 DOI: 10.1016/j.cub.2024.07.091] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/05/2023] [Revised: 07/08/2024] [Accepted: 07/29/2024] [Indexed: 09/12/2024]
Abstract
Human primary visual cortex (V1) responds more strongly, or resonates, when exposed to ∼10, ∼15-20, and ∼40-50 Hz rhythmic flickering light. Full-field flicker also evokes the perception of hallucinatory geometric patterns, which mathematical models explain as standing-wave formations emerging from periodic forcing at resonant frequencies of the simulated neural network. However, empirical evidence for such flicker-induced standing waves in the visual cortex was missing. We recorded cortical responses to flicker in awake mice using high-spatial-resolution widefield imaging in combination with high-temporal-resolution glutamate-sensing fluorescent reporter (iGluSnFR). The temporal frequency tuning curves in the mouse V1 were similar to those observed in humans, showing a banded structure with multiple resonance peaks (8, 15, and 33 Hz). Spatially, all flicker frequencies evoked responses in V1 corresponding to retinotopic stimulus location, but some evoked additional peaks. These flicker-induced cortical patterns displayed standing-wave characteristics and matched linear wave equation solutions in an area restricted to the visual cortex. Taken together, the interaction of periodic traveling waves with cortical area boundaries leads to spatiotemporal activity patterns that may affect perception.
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Affiliation(s)
- Rasa Gulbinaite
- Netherlands Institute for Neuroscience, Meibergdreef 47, 1105 BA Amsterdam, the Netherlands.
| | - Mojtaba Nazari
- Canadian Centre for Behavioral Neuroscience, University of Lethbridge Lethbridge, AB T1K 3M4, Canada
| | - Michael E Rule
- School of Engineering Mathematics and Technology, University of Bristol, Queen's Building, Bristol BS8 1TR, UK
| | | | - Michael X Cohen
- Radboud University Medical Center, Donders Institute for Brain, Cognition, and Behaviour, 6525 EN Nijmegen, the Netherlands
| | - Majid H Mohajerani
- Canadian Centre for Behavioral Neuroscience, University of Lethbridge Lethbridge, AB T1K 3M4, Canada; Department of Psychiatry, Douglas Hospital Research Centre, McGill University, 6875 Boulevard LaSalle, Montréal, QC H4H 1R3, Canada
| | - J Alexander Heimel
- Netherlands Institute for Neuroscience, Meibergdreef 47, 1105 BA Amsterdam, the Netherlands
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Oppermann H, Thelen A, Haueisen J. Single-trial EEG analysis reveals burst structure during photic driving. Clin Neurophysiol 2024; 159:66-74. [PMID: 38350295 DOI: 10.1016/j.clinph.2024.01.005] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/30/2023] [Revised: 12/06/2023] [Accepted: 01/20/2024] [Indexed: 02/15/2024]
Abstract
OBJECTIVE Photic driving in the human visual cortex evoked by intermittent photic stimulation is usually characterized in averaged data by an ongoing oscillation showing frequency entrainment and resonance phenomena during the course of stimulation. We challenge this view of an ongoing oscillation by analyzing unaveraged data. METHODS 64-channel EEGs were recorded during visual stimulation with light flashes at eight stimulation frequencies between 7.8 and 23 Hz for fourteen healthy volunteers. Time-frequency analyses were performed in averaged and unaveraged data. RESULTS While we find ongoing oscillations in the averaged data during intermittent photic stimulation, we find transient events (bursts) of activity in the unaveraged data. Both resonance and entrainment occur for the ongoing oscillations in the averaged data and the bursts in the unaveraged data. CONCLUSIONS We argue that the continuous oscillations in the averaged signal may be composed of brief, transient bursts in single trials. Our results can also explain previously observed amplitude fluctuations in averaged photic driving data. SIGNIFICANCE Single-trial analyses might consequently improve our understanding of resonance and entrainment phenomena in the brain.
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Affiliation(s)
- Hannes Oppermann
- Institute of Biomedical Engineering and Informatics, Technische Universität Ilmenau, Ilmenau, Germany.
| | - Antonia Thelen
- eemagine Medical Imaging Solutions GmbH, Berlin, Germany.
| | - Jens Haueisen
- Institute of Biomedical Engineering and Informatics, Technische Universität Ilmenau, Ilmenau, Germany; Department of Neurology, Biomagnetic Center, University Hospital Jena, Jena, Germany.
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Tsoneva T, Garcia-Molina G, Desain P. Electrophysiological model of human temporal contrast sensitivity based on SSVEP. Front Neurosci 2023; 17:1180829. [PMID: 37599998 PMCID: PMC10433170 DOI: 10.3389/fnins.2023.1180829] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/06/2023] [Accepted: 06/27/2023] [Indexed: 08/22/2023] Open
Abstract
The present study aims to connect the psychophysical research on the human visual perception of flicker with the neurophysiological research on steady-state visual evoked potentials (SSVEPs) in the context of their application needs and current technological developments. In four experiments, we investigated whether a temporal contrast sensitivity model could be established based on the electrophysiological responses to repetitive visual stimulation and, if so, how this model compares to the psychophysical models of flicker visibility. We used data from 62 observers viewing periodic flicker at a range of frequencies and modulation depths sampled around the perceptual visibility thresholds. The resulting temporal contrast sensitivity curve (TCSC) was similar in shape to its psychophysical counterpart, confirming that the human visual system is most sensitive to repetitive visual stimulation at frequencies between 10 and 20 Hz. The electrophysiological TCSC, however, was below the psychophysical TCSC measured in our experiments for lower frequencies (1-50 Hz), crossed it when the frequency was 50 Hz, and stayed above while decreasing at a slower rate for frequencies in the gamma range (40-60 Hz). This finding provides evidence that SSVEPs could be measured even without the conscious perception of flicker, particularly at frequencies above 50 Hz. The cortical and perceptual mechanisms that apply at higher temporal frequencies, however, do not seem to directly translate to lower frequencies. The presence of harmonics, which show better response for many frequencies, suggests non-linear processing in the visual system. These findings are important for the potential applications of SSVEPs in studying, assisting, or augmenting human cognitive and sensorimotor functions.
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Affiliation(s)
- Tsvetomira Tsoneva
- Department of Digital Engagement, Cognition and Behavior, Philips Research, Eindhoven, Netherlands
- Centre for Cognition, Donders Institute for Brain, Cognition and Behaviour, Radboud University, Nijmegen, Netherlands
| | - Gary Garcia-Molina
- Sleep Number Labs, San Jose, CA, United States
- Center for Sleep and Consciousness, University of Wisconsin, Madison, WI, United States
| | - Peter Desain
- Centre for Cognition, Donders Institute for Brain, Cognition and Behaviour, Radboud University, Nijmegen, Netherlands
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Springer SD, Erker TD, Schantell M, Johnson HJ, Willett MP, Okelberry HJ, Rempe MP, Wilson TW. Disturbances in primary visual processing as a function of healthy aging. Neuroimage 2023; 271:120020. [PMID: 36914104 PMCID: PMC10123380 DOI: 10.1016/j.neuroimage.2023.120020] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/29/2022] [Revised: 02/21/2023] [Accepted: 03/10/2023] [Indexed: 03/13/2023] Open
Abstract
For decades, visual entrainment paradigms have been widely used to investigate basic visual processing in healthy individuals and those with neurological disorders. While healthy aging is known to be associated with alterations in visual processing, whether this extends to visual entrainment responses and the precise cortical regions involved is not fully understood. Such knowledge is imperative given the recent surge in interest surrounding the use of flicker stimulation and entrainment in the context of identifying and treating Alzheimer's disease (AD). In the current study, we examined visual entrainment in eighty healthy aging adults using magnetoencephalography (MEG) and a 15 Hz entrainment paradigm, while controlling for age-related cortical thinning. MEG data were imaged using a time-frequency resolved beamformer and peak voxel time series were extracted to quantify the oscillatory dynamics underlying the processing of the visual flicker stimuli. We found that, as age increased, the mean amplitude of entrainment responses decreased and the latency of these responses increased. However, there was no effect of age on the trial-to-trial consistency in phase (i.e., inter-trial phase locking) nor amplitude (i.e., coefficient of variation) of these visual responses. Importantly, we discovered that the relationship between age and response amplitude was fully mediated by the latency of visual processing. These results indicate that aging is associated with robust changes in the latency and amplitude of visual entrainment responses within regions surrounding the calcarine fissure, which should be considered in studies examining neurological disorders such as AD and other conditions associated with increased age.
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Affiliation(s)
- Seth D Springer
- Institute for Human Neuroscience, Boys Town National Research Hospital, Boys Town, NE, USA; College of Medicine, University of Nebraska Medical Center, Omaha, NE, USA
| | - Tara D Erker
- Institute for Human Neuroscience, Boys Town National Research Hospital, Boys Town, NE, USA; College of Engineering, University of Nebraska - Lincoln, Lincoln, NE, USA
| | - Mikki Schantell
- Institute for Human Neuroscience, Boys Town National Research Hospital, Boys Town, NE, USA; College of Medicine, University of Nebraska Medical Center, Omaha, NE, USA
| | - Hallie J Johnson
- Institute for Human Neuroscience, Boys Town National Research Hospital, Boys Town, NE, USA
| | - Madelyn P Willett
- Institute for Human Neuroscience, Boys Town National Research Hospital, Boys Town, NE, USA
| | - Hannah J Okelberry
- Institute for Human Neuroscience, Boys Town National Research Hospital, Boys Town, NE, USA
| | - Maggie P Rempe
- Institute for Human Neuroscience, Boys Town National Research Hospital, Boys Town, NE, USA; College of Medicine, University of Nebraska Medical Center, Omaha, NE, USA
| | - Tony W Wilson
- Institute for Human Neuroscience, Boys Town National Research Hospital, Boys Town, NE, USA; College of Medicine, University of Nebraska Medical Center, Omaha, NE, USA; Department of Pharmacology & Neuroscience, Creighton University, Omaha, NE, USA.
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Sciortino P, Kayser C. Steady state visual evoked potentials reveal a signature of the pitch-size crossmodal association in visual cortex. Neuroimage 2023; 273:120093. [PMID: 37028733 DOI: 10.1016/j.neuroimage.2023.120093] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/02/2023] [Revised: 03/31/2023] [Accepted: 04/04/2023] [Indexed: 04/08/2023] Open
Abstract
Crossmodal correspondences describe our tendency to associate sensory features from different modalities with each other, such as the pitch of a sound with the size of a visual object. While such crossmodal correspondences (or associations) are described in many behavioural studies their neurophysiological correlates remain unclear. Under the current working model of multisensory perception both a low- and a high-level account seem plausible. That is, the neurophysiological processes shaping these associations could commence in low-level sensory regions, or may predominantly emerge in high-level association regions of semantic and object identification networks. We exploited steady-state visual evoked potentials (SSVEP) to directly probe this question, focusing on the associations between pitch and the visual features of size, hue or chromatic saturation. We found that SSVEPs over occipital regions are sensitive to the congruency between pitch and size, and a source analysis pointed to an origin around primary visual cortices. We speculate that this signature of the pitch-size association in low-level visual cortices reflects the successful pairing of congruent visual and acoustic object properties and may contribute to establishing causal relations between multisensory objects. Besides this, our study also provides a paradigm can be exploited to study other crossmodal associations involving visual stimuli in the future.
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Wan Z, Li M, Liu S, Huang J, Tan H, Duan W. EEGformer: A transformer-based brain activity classification method using EEG signal. Front Neurosci 2023; 17:1148855. [PMID: 37034169 PMCID: PMC10079879 DOI: 10.3389/fnins.2023.1148855] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/20/2023] [Accepted: 03/06/2023] [Indexed: 04/11/2023] Open
Abstract
Background The effective analysis methods for steady-state visual evoked potential (SSVEP) signals are critical in supporting an early diagnosis of glaucoma. Most efforts focused on adopting existing techniques to the SSVEPs-based brain-computer interface (BCI) task rather than proposing new ones specifically suited to the domain. Method Given that electroencephalogram (EEG) signals possess temporal, regional, and synchronous characteristics of brain activity, we proposed a transformer-based EEG analysis model known as EEGformer to capture the EEG characteristics in a unified manner. We adopted a one-dimensional convolution neural network (1DCNN) to automatically extract EEG-channel-wise features. The output was fed into the EEGformer, which is sequentially constructed using three components: regional, synchronous, and temporal transformers. In addition to using a large benchmark database (BETA) toward SSVEP-BCI application to validate model performance, we compared the EEGformer to current state-of-the-art deep learning models using two EEG datasets, which are obtained from our previous study: SJTU emotion EEG dataset (SEED) and a depressive EEG database (DepEEG). Results The experimental results show that the EEGformer achieves the best classification performance across the three EEG datasets, indicating that the rationality of our model architecture and learning EEG characteristics in a unified manner can improve model classification performance. Conclusion EEGformer generalizes well to different EEG datasets, demonstrating our approach can be potentially suitable for providing accurate brain activity classification and being used in different application scenarios, such as SSVEP-based early glaucoma diagnosis, emotion recognition and depression discrimination.
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Affiliation(s)
- Zhijiang Wan
- The First Affiliated Hospital of Nanchang University, Nanchang University, Nanchang, Jiangxi, China
- School of Information Engineering, Nanchang University, Nanchang, Jiangxi, China
- Industrial Institute of Artificial Intelligence, Nanchang University, Nanchang, Jiangxi, China
| | - Manyu Li
- School of Information Engineering, Nanchang University, Nanchang, Jiangxi, China
| | - Shichang Liu
- School of Computer Science, Shaanxi Normal University, Xi’an, Shaanxi, China
| | - Jiajin Huang
- Faculty of Information Technology, Beijing University of Technology, Beijing, China
| | - Hai Tan
- School of Computer Science, Nanjing Audit University, Nanjing, Jiangsu, China
| | - Wenfeng Duan
- The First Affiliated Hospital of Nanchang University, Nanchang University, Nanchang, Jiangxi, China
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Park Y, Lee K, Park J, Bae JB, Kim SS, Kim DW, Woo SJ, Yoo S, Kim KW. Optimal flickering light stimulation for entraining gamma rhythms in older adults. Sci Rep 2022; 12:15550. [PMID: 36114215 PMCID: PMC9481621 DOI: 10.1038/s41598-022-19464-2] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/24/2021] [Accepted: 08/30/2022] [Indexed: 11/09/2022] Open
Abstract
With aging, optimal parameters of flickering light stimulation (FLS) for gamma entrainment may change in the eyes and brain. We investigated the optimal FLS parameters for gamma entrainment in 35 cognitively normal old adults by comparing event-related synchronization (ERS) and spectral Granger causality (sGC) of entrained gamma rhythms between different luminance intensities, colors, and flickering frequencies of FLSs. ERS entrained by 700 cd/m2 FLS and 32 Hz or 34 Hz FLSs was stronger than that entrained by 400 cd/m2 at Pz (p < 0.01) and 38 Hz or 40 Hz FLSs, respectively, at both Pz (p < 0.05) and Fz (p < 0.01). Parieto-occipital-to-frontotemporal connectivities of gamma rhythm entrained by 700 cd/m2 FLS and 32 Hz or 34 Hz FLSs were also stronger than those entrained by 400 cd/m2 at Pz (p < 0.01) and 38 Hz or 40 Hz FLSs, respectively (p < 0.001). ERS and parieto-occipital-to-frontotemporal connectivities of entrained gamma rhythms did not show significant difference between white and red lights. Adverse effects were comparable between different parameters. In older adults, 700 cd/m2 FLS at 32 Hz or 34 Hz can entrain a strong gamma rhythm in the whole brain with tolerable adverse effects.
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Affiliation(s)
- Yeseung Park
- Department of Neuropsychiatry, Seoul National University Bundang Hospital, Seongnam, Republic of Korea.,Department of Brain and Cognitive Science, Seoul National University College of Natural Sciences, Seoul, Republic of Korea
| | - Kanghee Lee
- Department of Neuropsychiatry, Seoul National University Bundang Hospital, Seongnam, Republic of Korea
| | - Jaehyeok Park
- School of Electrical Engineering, Korea Advanced Institute of Science and Technology (KAIST), Daejeon, Republic of Korea
| | - Jong Bin Bae
- Department of Neuropsychiatry, Seoul National University Bundang Hospital, Seongnam, Republic of Korea.,Department of Psychiatry, Seoul National University College of Medicine, Seoul, Republic of Korea
| | - Sang-Su Kim
- Department of Biomedical Engineering, Chonnam National University, Yeosu, Republic of Korea
| | - Do-Won Kim
- Department of Biomedical Engineering, Chonnam National University, Yeosu, Republic of Korea
| | - Se Joon Woo
- Department of Ophthalmology, Seoul National University College of Medicine, Seoul, Republic of Korea.,Department of Ophthalmology, Seoul National University Bundang Hospital, Seongnam, Republic of Korea
| | - Seunghyup Yoo
- School of Electrical Engineering, Korea Advanced Institute of Science and Technology (KAIST), Daejeon, Republic of Korea
| | - Ki Woong Kim
- Department of Neuropsychiatry, Seoul National University Bundang Hospital, Seongnam, Republic of Korea. .,Department of Brain and Cognitive Science, Seoul National University College of Natural Sciences, Seoul, Republic of Korea. .,Department of Psychiatry, Seoul National University College of Medicine, Seoul, Republic of Korea.
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α Phase-Amplitude Tradeoffs Predict Visual Perception. eNeuro 2022; 9:ENEURO.0244-21.2022. [PMID: 35105658 PMCID: PMC8868024 DOI: 10.1523/eneuro.0244-21.2022] [Citation(s) in RCA: 15] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/25/2021] [Revised: 01/12/2022] [Accepted: 01/16/2022] [Indexed: 11/21/2022] Open
Abstract
Spontaneous α oscillations (∼10 Hz) have been associated with various cognitive functions, including perception. Their phase and amplitude independently predict cortical excitability and subsequent perceptual performance. However, the causal role of α phase-amplitude tradeoffs on visual perception remains ill-defined. We aimed to fill this gap and tested two clear predictions from the pulsed inhibition theory according to which α oscillations are associated with periodic functional inhibition. (1) High-α amplitude induces cortical inhibition at specific phases, associated with low perceptual performance, while at opposite phases, inhibition decreases (potentially increasing excitation) and perceptual performance increases. (2) Low-α amplitude is less susceptible to these phasic (periodic) pulses of inhibition, leading to overall higher perceptual performance. Here, cortical excitability was assessed in humans using phosphene (illusory) perception induced by single pulses of transcranial magnetic stimulation (TMS) applied over visual cortex at perceptual threshold, and its postpulse evoked activity recorded with simultaneous electroencephalography (EEG). We observed that prepulse α phase modulates the probability to perceive a phosphene, predominantly for high-α amplitude, with a nonoptimal phase for phosphene perception between -π/2 and -π/4. The prepulse nonoptimal phase further leads to an increase in postpulse-evoked activity [event-related potential (ERP)], in phosphene-perceived trials specifically. Together, these results show that α oscillations create periodic inhibitory moments when α amplitude is high, leading to periodic decrease of perceptual performance. This study provides strong causal evidence in favor of the pulsed inhibition theory.
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Solving the SSVEP Paradigm Using the Nonlinear Canonical Correlation Analysis Approach. SENSORS 2021; 21:s21165308. [PMID: 34450750 PMCID: PMC8439358 DOI: 10.3390/s21165308] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 06/07/2021] [Revised: 07/31/2021] [Accepted: 08/01/2021] [Indexed: 01/16/2023]
Abstract
This paper presents the implementation of nonlinear canonical correlation analysis (NLCCA) approach to detect steady-state visual evoked potentials (SSVEP) quickly. The need for the fast recognition of proper stimulus to help end an SSVEP task in a BCI system is justified due to the flickering external stimulus exposure that causes users to start to feel fatigued. Measuring the accuracy and exposure time can be carried out through the information transfer rate-ITR, which is defined as a relationship between the precision, the number of stimuli, and the required time to obtain a result. NLCCA performance was evaluated by comparing it with two other approaches-the well-known canonical correlation analysis (CCA) and the least absolute reduction and selection operator (LASSO), both commonly used to solve the SSVEP paradigm. First, the best average ITR value was found from a dataset comprising ten healthy users with an average age of 28, where an exposure time of one second was obtained. In addition, the time sliding window responses were observed immediately after and around 200 ms after the flickering exposure to obtain the phase effects through the coefficient of variation (CV), where NLCCA obtained the lowest value. Finally, in order to obtain statistical significance to demonstrate that all approaches differ, the accuracy and ITR from the time sliding window responses was compared using a statistical analysis of variance per approach to identify differences between them using Tukey's test.
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