Classification of auditory ERPs for ADHD detection in children

Attention deficit hyperactivity disorder (ADHD) is one of the children’s most common neurodevelopmental conditions. ADHD diagnosis is based on evaluating inattention, hyperactivity, and impulsivity symptoms that interfere with or reduce daily functioning. Although electroencephalography (EEG) tests...

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Autores:
Mercado Aguirre, Isabela
Contreras Ortiz, Sonia Helena
Gutiérrez Ruiz, Karol Patricia
Tipo de recurso:
Fecha de publicación:
2025
Institución:
Universidad Tecnológica de Bolívar
Repositorio:
Repositorio Institucional UTB
Idioma:
eng
OAI Identifier:
oai:repositorio.utb.edu.co:20.500.12585/13248
Acceso en línea:
https://hdl.handle.net/20.500.12585/13248
https://doi.org/10.1080/03091902.2025.2477506
Palabra clave:
ADHD
EEG
ERP
Machine learning
LEMB
Rights
embargoedAccess
License
Attribution-NonCommercial-NoDerivs 3.0 United States
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dc.title.none.fl_str_mv Classification of auditory ERPs for ADHD detection in children
title Classification of auditory ERPs for ADHD detection in children
spellingShingle Classification of auditory ERPs for ADHD detection in children
ADHD
EEG
ERP
Machine learning
LEMB
title_short Classification of auditory ERPs for ADHD detection in children
title_full Classification of auditory ERPs for ADHD detection in children
title_fullStr Classification of auditory ERPs for ADHD detection in children
title_full_unstemmed Classification of auditory ERPs for ADHD detection in children
title_sort Classification of auditory ERPs for ADHD detection in children
dc.creator.fl_str_mv Mercado Aguirre, Isabela
Contreras Ortiz, Sonia Helena
Gutiérrez Ruiz, Karol Patricia
dc.contributor.author.none.fl_str_mv Mercado Aguirre, Isabela
Contreras Ortiz, Sonia Helena
Gutiérrez Ruiz, Karol Patricia
dc.subject.keywords.none.fl_str_mv ADHD
EEG
ERP
Machine learning
topic ADHD
EEG
ERP
Machine learning
LEMB
dc.subject.armarc.none.fl_str_mv LEMB
description Attention deficit hyperactivity disorder (ADHD) is one of the children’s most common neurodevelopmental conditions. ADHD diagnosis is based on evaluating inattention, hyperactivity, and impulsivity symptoms that interfere with or reduce daily functioning. Although electroencephalography (EEG) tests are used for ADHD diagnosis, they are generally considered a complement to clinical evaluation. This paper proposes an approach to classify EEG records of children with ADHD and control cases. We identified and extracted relevant features from EEG signals of 47 children (22 diagnosed with ADHD and 25 controls) and evaluated machine learning techniques for classification. We used the 2-tone oddball paradigm to elicit the subjects’ auditory event-related potentials (ERP), and we recorded EEG signals with a portable headset for approximately five minutes. In the feature extraction stage, we included measures from cognitive evoked potentials, frequency bands power, chaos quantification, and bispectral analysis, in addition to the age of the children and the number of high-pitched tones the children counted during the test. The SVM and Trees algorithms obtained the best performance for 86.36% accuracy and 95.45% sensitivity. These findings demonstrate the potential of portable EEG-based systems to complement standard clinical assessments, offering an objective, time-efficient, and accessible approach to support early ADHD diagnosis. Achieving high accuracy and sensitivity in classification is critical to reducing the risk of misdiagnosis and ensuring timely intervention, ultimately improving patient outcomes.
publishDate 2025
dc.date.accessioned.none.fl_str_mv 2025-04-07T15:43:33Z
dc.date.available.none.fl_str_mv 2025-04-07T15:43:33Z
dc.date.issued.none.fl_str_mv 2025-03-21
dc.date.submitted.none.fl_str_mv 2025-04-04
dc.date.embargoEnd.none.fl_str_mv 2026/03/21
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dc.identifier.citation.none.fl_str_mv Mercado-Aguirre, I., Gutiérrez-Ruiz, K., & Contreras-Ortiz, S. H. (2025). Classification of auditory ERPs for ADHD detection in children. Journal of Medical Engineering & Technology, 1–10. https://doi.org/10.1080/03091902.2025.2477506
dc.identifier.uri.none.fl_str_mv https://hdl.handle.net/20.500.12585/13248
dc.identifier.doi.none.fl_str_mv https://doi.org/10.1080/03091902.2025.2477506
dc.identifier.instname.none.fl_str_mv Universidad Tecnológica de Bolívar
dc.identifier.reponame.none.fl_str_mv Repositorio Universidad Tecnológica de Bolívar
identifier_str_mv Mercado-Aguirre, I., Gutiérrez-Ruiz, K., & Contreras-Ortiz, S. H. (2025). Classification of auditory ERPs for ADHD detection in children. Journal of Medical Engineering & Technology, 1–10. https://doi.org/10.1080/03091902.2025.2477506
Universidad Tecnológica de Bolívar
Repositorio Universidad Tecnológica de Bolívar
url https://hdl.handle.net/20.500.12585/13248
https://doi.org/10.1080/03091902.2025.2477506
dc.language.iso.none.fl_str_mv eng
language eng
dc.relation.cites.none.fl_str_mv Mercado-Aguirre IM, Gutierrez-Ruiz KP, Contreras-Ortiz SH. 16th International Symposium on Medical Information Processing and Analysis. EEG feadhdture selection for ADHD detection in children. International Society for Optics and Photonics; 2020. Vol. 11583. p. 115830S.
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dc.format.extent.none.fl_str_mv 10 páginas
dc.format.mimetype.none.fl_str_mv application/pdf
dc.coverage.spatial.none.fl_str_mv Colombia, Cartagena (Bolívar)
dc.publisher.faculty.none.fl_str_mv Ingeniería
dc.publisher.sede.none.fl_str_mv Campus Tecnológico
dc.publisher.discipline.none.fl_str_mv Maestría en Ingeniería
dc.source.none.fl_str_mv Journal of Medical Engineering and Technology
institution Universidad Tecnológica de Bolívar
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spelling Mercado Aguirre, IsabelaContreras Ortiz, Sonia Helenavirtual::513-1Gutiérrez Ruiz, Karol Patriciavirtual::514-1Colombia, Cartagena (Bolívar)2025-04-07T15:43:33Z2025-04-07T15:43:33Z2025-03-212025-04-042026/03/21Mercado-Aguirre, I., Gutiérrez-Ruiz, K., & Contreras-Ortiz, S. H. (2025). Classification of auditory ERPs for ADHD detection in children. Journal of Medical Engineering & Technology, 1–10. https://doi.org/10.1080/03091902.2025.2477506https://hdl.handle.net/20.500.12585/13248https://doi.org/10.1080/03091902.2025.2477506Universidad Tecnológica de BolívarRepositorio Universidad Tecnológica de BolívarAttention deficit hyperactivity disorder (ADHD) is one of the children’s most common neurodevelopmental conditions. ADHD diagnosis is based on evaluating inattention, hyperactivity, and impulsivity symptoms that interfere with or reduce daily functioning. Although electroencephalography (EEG) tests are used for ADHD diagnosis, they are generally considered a complement to clinical evaluation. This paper proposes an approach to classify EEG records of children with ADHD and control cases. We identified and extracted relevant features from EEG signals of 47 children (22 diagnosed with ADHD and 25 controls) and evaluated machine learning techniques for classification. We used the 2-tone oddball paradigm to elicit the subjects’ auditory event-related potentials (ERP), and we recorded EEG signals with a portable headset for approximately five minutes. In the feature extraction stage, we included measures from cognitive evoked potentials, frequency bands power, chaos quantification, and bispectral analysis, in addition to the age of the children and the number of high-pitched tones the children counted during the test. The SVM and Trees algorithms obtained the best performance for 86.36% accuracy and 95.45% sensitivity. These findings demonstrate the potential of portable EEG-based systems to complement standard clinical assessments, offering an objective, time-efficient, and accessible approach to support early ADHD diagnosis. Achieving high accuracy and sensitivity in classification is critical to reducing the risk of misdiagnosis and ensuring timely intervention, ultimately improving patient outcomes.Universidad Tecnológica de Bolívar10 páginasapplication/pdfengAttribution-NonCommercial-NoDerivs 3.0 United Stateshttp://creativecommons.org/licenses/by-nc-nd/3.0/us/info:eu-repo/semantics/embargoedAccesshttp://purl.org/coar/access_right/c_f1cfJournal of Medical Engineering and TechnologyClassification of auditory ERPs for ADHD detection in childreninfo:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_2df8fbb1http://purl.org/coar/version/c_970fb48d4fbd8a85ADHDEEGERPMachine learningLEMBMercado-Aguirre IM, Gutierrez-Ruiz KP, Contreras-Ortiz SH. 16th International Symposium on Medical Information Processing and Analysis. EEG feadhdture selection for ADHD detection in children. International Society for Optics and Photonics; 2020. Vol. 11583. p. 115830S.IngenieríaCampus TecnológicoMaestría en IngenieríaInvestigadoresFabiano GA, Pelham WE, Majumdar A, et al. Elementary and middle school teacher perceptions of attention-deficit/hyperactivity disorder prevalence. In: Child and Youth Care Forum. New York: Springer; 2013. p. 87–99. Vol. 42.Slater J, Joober R, Koborsy BL, et al. Can electroencephalography (EEG) identify ADHD subtypes? a systematic review. Neurosci Biobeh Rev. 2022;139:104752.Lenartowicz A, Loo SK. Use of eeg to diagnose adhd. Curr Psychiatry Rep. 2014;16(11):498. doi: 10.1007/s11920-014-0498-0.Kaur S, Singh S, Arun P, et al. Event-related potential analysis of ADHD and control adults during a sustained attention task. Clin EEG Neurosci. 2019;50(6):389–403. doi: 10.1177/1550059419842707.Marquardt L, Eichele H, Lundervold AJ, et al. Event-related-potential (ERP) correlates of performance monitoring in adults with attention-deficit hyperactivity disorder (ADHD). Front Psychol. 2018;9:485. doi: 10.3389/fpsyg.2018.00485.Dallmer-Zerbe I, Popp F, Lam AP, et al. Transcranial alternating current stimulation (TACS) as a tool to modulate p300 amplitude in attention deficit hyperactivity disorder (ADHD): preliminary findings. Brain Topogr. 2020;33(2):191–207. doi: 10.1007/s10548-020-00752-x.Kaiser A, Aggensteiner PM, Baumeister S, et al. Earlier versus later cognitive event-related potentials (ERPS) in attention-deficit/hyperactivity disorder (ADHD): a meta-analysis. Neurosci Biobehav Rev. 2020;112:117–134. doi: 10.1016/j.neubiorev.2020.01.019.Moavero R, Marciano S, Pro S, et al. Event-related potentials in ADHD associated with tuberous sclerosis complex: a possible biomarker of symptoms severity? Front Neurol. 2020;11:546. doi: 10.3389/fneur.2020.00546.Ogrim G, Kropotov JD. Event related potentials (ERPS) and other EEG based methods for extracting biomarkers of brain dysfunction: examples from pediatric attention deficit/hyperactivity disorder (ADHD). JoVE. 2020;(157):e60710. doi: 10.3791/60710.Picken C, Clarke AR, Barry RJ, et al. The theta/beta ratio as an index of cognitive processing in adults with the combined type of attention deficit hyperactivity disorder. Clin EEG Neurosci. 2020;51(3):167–173. doi: 10.1177/1550059419895142.Arns M, Conners CK, Kraemer HC. A decade of EEG theta/beta ratio research in ADHD: a meta-analysis. J Atten Disord. 2013;17(5):374–383. doi: 10.1177/1087054712460087.Kaur S, Arun P, Singh S, et al. Eeg based decision support system to diagnose adults with ADHD; 2018 p. 87–91 Available from: https://ieeexplore.ieee.org/document/8748412/(open in a new window).Kaur S, Singh S, Arun P, et al. Phase space reconstruction of EEG signals for classification of ADHD and control adults. Clin EEG Neurosci. 2020;51(2):102–113. Sep;:doi: 10.1177/1550059419876525.Tenev A, Markovska-Simoska S, Kocarev L, et al. Machine learning approach for classification of ADHD adults. Int J Psychophysiol. 2014; Jul93(1):162–166. 5. doi: 10.1016/j.ijpsycho.2013.01.008.Mueller A, Candrian G, Grane VA, et al. Discriminating between ADHD adults and controls using independent ERP components and a support vector machine: a validation study. Nonlinear Biomed Phys. 2011; Dec5(1):5–2. doi: 10.1186/1753-4631-5-5.Kovatchev B, Cox D, Hill R, et al. A psychophysiological marker of attention deficit/hyperactivity disorder (ADHD)—defining the EEG consistency index. Appl Psychophysiol Biofeedback. 2001;26(2):127–140. doi: 10.1023/a:1011339206875.Moghaddari M, Lighvan MZ, Danishvar S. Diagnose ADHD disorder in children using convolutional neural network based on continuous mental task EEG. Comput Methods Programs Biomed. 2020; 97:105738. doi: 10.1016/j.cmpb.2020.105738.Chen H, Chen W, Song Y, et al. EEG characteristics of children with attention-deficit/hyperactivity disorder. Neuroscience. 2019;406:444–456. 1. doi: 10.1016/j.neuroscience.2019.03.048.Vahid A, Bluschke A, Roessner V, et al. Deep learning based on event-related EEG differentiates children with ADHD from healthy controls. J Clin Med. 2019;8(7):1055. doi: 10.3390/jcm8071055.Pereda E, García-Torres M, Melián-Batista B, et al. The blessing of dimensionality: feature selection outperforms functional connectivity-based feature transformation to classify ADHD subjects from EEG patterns of phase synchronisation. PLoS One. 2018; 13(8):e0201660. doi: 10.1371/journal.pone.0201660.Bashiri A, Shahmoradi L, Beigy H, et al. Quantitative EEG features selection in the classification of attention and response control in the children and adolescents with attention deficit hyperactivity disorder. Future Sci OA. 2018; 4(5):FSO292–1. doi: 10.4155/fsoa-2017-0138Mercado-Aguirre IM, Gutiérrez-Ruiz K, Contreras-Ortiz SH. 2019 XXII Symposium on Image, Signal Processing and Artificial Vision (STSIVA) Acquisition and analysis of cognitive evoked potentials using an emotiv headset for ADHD evaluation in children. In: IEEE; 2019. p. 1–5.Thuraisingham RA, Tran Y, Boord P, et al. Analysis of eyes open, eye closed EEG signals using second-order difference plot. Med Biol Eng Comput. 2007; 45(12):1243–1249. doi: 10.1007/s11517-007-0268-9.Katayama J, Polich J. P300 from one-, two-, and three-stimulus auditory paradigms. Int J Psychophysiol. 1996; 23(1-2):33–40. doi: 10.1016/0167-8760(96)00030-x.Goodin D, Desmedt J, Maurer K, et al. Ifcn recommended standards for long-latency auditory event-related potentials. report of an ifcn committee. Electroencephalogr Clin Neurophysiol. 1994;91(1):18–20. doi: 10.1016/0013-4694(94)90014-0.Bishop DV, Hardiman M, Uwer R, et al. Maturation of the long-latency auditory ERP: step function changes at start and end of adolescence. Dev Sci. 2007;10(5):565–575. doi: 10.1111/j.1467-7687.2007.00619.x.Gehricke JG, Kruggel F, Thampipop T, et al. The brain anatomy of attention-deficit/hyperactivity disorder in young adults–a magnetic resonance imaging study. PLoS One. 2017;12(4):e0175433. doi: 10.1371/journal.pone.0175433.Peisch V, Rutter T, Wilkinson CL, et al. Sensory processing and p300 event-related potential correlates of stimulant response in children with attention-deficit/hyperactivity disorder: a critical review. Clin Neurophysiol. 2021;132(4):953–966. doi: 10.1016/j.clinph.2021.01.015.Zhang Q, Luo C, Ngetich R, et al. Visual selective attention p300 source in frontal-parietal lobe: erp and fmri study. Brain Topogr. 2022;35(5-6):636–650. doi: 10.1007/s10548-022-00916-x.Mercado-Aguirre IM, Gutierrez-Ruiz KP, Contreras-Ortiz SH. 16th International Symposium on Medical Information Processing and Analysis. EEG feadhdture selection for ADHD detection in children. International Society for Optics and Photonics; 2020. Vol. 11583. p. 115830S.Adeli H, Zhou Z, Dadmehr N. Analysis of EEG records in an epileptic patient using wavelet transform. J Neurosci Methods. 2003; Feb123(1):69–87. 3. doi: 10.1016/s0165-0270(02)00340-0.Markazi SA, Qazi S, Stergioulas LS, et al. 2006 International Conference of the IEEE Engineering in Medicine and Biology Society; Wavelet filtering of the p300 component in event-related potentials. In: IEEE; 2006. p 1719–1722.Subasi A. EEG signal classification using wavelet feature extraction and a mixture of expert model. Expert Syst Appl. 2007; 32(4)(4):1084–1093. doi: 10.1016/j.eswa.2006.02.005.Comerchero MD, Polich J. P3a and p3b from typical auditory and visual stimuli. Clin Neurophysiol. 1999; Jan110(1):24–30. doi: 10.1016/s0168-5597(98)00033-1.Barry RJ, Clarke AR, Johnstone SJ, et al. Electroencephalogram theta/beta ratio and arousal in attention-deficit/hyperactivity disorder: evidence of independent processes. Biol Psychiatry. 2009; Aug66(4):398–401. doi: 10.1016/j.biopsych.2009.04.027.Inc TM. Root-mean-square value. Available from: https://www.mathworks.com/help/matlab/ref/rms.html;jsessionid=a59fa4351d9da1569878dde7f600(open in a new window).Ghassemi F, Hassan-Moradi M, Tehrani-Doost M, et al. Using non-linear features of EEG for ADHD/normal participants’ classification. Procedia - Social and Behavioral Sciences. 2012;32:148–152. 4. doi: 10.1016/j.sbspro.2012.01.024.Lai D, Chen G. Statistical analysis of lyapunov exponents from time series: a jacobian approach. Math Comput Modell. 1998; Apr27(7):1–9. doi: 10.1016/S0895-7177(98)00032-6.Rosenstein MT, Collins JJ, De Luca CJ. A practical method for calculating largest lyapunov exponents from small data sets. Physica D. 1993; May65(1-2):117–134. doi: 10.1016/0167-2789(93)90009-PBenSaïda A. 2018. Chaos test;. Available from: https://la.mathworks.com/matlabcentral/fileexchange/22667-chaos-test(open in a new window).Sigl JC, Chamoun NG. An introduction to bispectral analysis for the electroencephalogram. J Clin Monit. 1994;10(6):392–404. doi: 10.1007/BF01618421.Hagihira S, Takashina M, Mori T, et al. Practical issues in bispectral analysis of electroencephalographic signals. Anesth Analg. 2001;93(4):966–970, table of contents. doi: 10.1097/00000539-200110000-00032.Li D, Li X, Hagihira S, et al. Cross-frequency coupling during isoflurane anaesthesia as revealed by electroencephalographic harmonic wavelet bicoherence. Br J Anaesth. 2013; 110(3):409–419. doi: 10.1093/bja/aes397.Swami A. 2003. Hosa - higher order spectral analysis toolbox. Available from: https://la.mathworks.com/matlabcentral/fileexchange/3013-hosa-higher-order-spectral-analysis-toolbox(open in a new window).Tor HT, Ooi CP, Lim-Ashworth NS, et al. Automated detection of conduct disorder and attention deficit hyperactivity disorder using decomposition and nonlinear techniques with eeg signals. Comput Methods Programs Biomed. 2021;200:105941. doi: 10.1016/j.cmpb.2021.105941.Ruiz KG, Iriarte DCC, Mendoza AH. Funcionamiento ejecutivo y habilidades adaptativas en un niño de 11 años con diagnóstico de tea en comorbilidad con tda. Tesis Psicológica. 2020;15(1):74–89McAuley T, Chen S, Goos L, et al. Is the behavior rating inventory of executive function more strongly associated with measures of impairment or executive function? J Int Neuropsychol Soc. 2010;16(3):495–505. doi: 10.1017/S1355617710000093.Torske T, Naerland T, Bettella F, et al. Autism spectrum disorder polygenic scores are associated with every day executive function in children admitted for clinical assessment. 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