{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,20]],"date-time":"2026-08-20T11:27:29Z","timestamp":1787225249012,"version":"build-2736575974"},"reference-count":26,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"5","funder":[{"name":"ANID Millennium Science Initiative Program","award":["NCN19-161"],"award-info":[{"award-number":["NCN19-161"]}]},{"name":"FONDECYT Postdoctorado","award":["3240512"],"award-info":[{"award-number":["3240512"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Appl. Math."],"published-print":{"date-parts":[[2024,10,31]]},"abstract":"<jats:p>Abstract.<\/jats:p>\n                  <jats:p>This paper studies the phenomenon of conduction block in model neurons using high-frequency biphasic stimulation (HFBS). The focus is investigating the triggering of undesired onset action potentials when the HFBS is turned on. The approach analyzes the transient behavior of an averaged system corresponding to the FitzHugh\u2013Nagumo neuron model using Lyapunov and quasi-static methods. The first result provides a more comprehensive understanding of the onset activation through a mathematical proof of how to avoid it using a ramp in the amplitude of the oscillatory source. The second result tests the response of the blocked system to a piecewise linear stimulus, providing a quantitative description of how the HFBS strength translates into conduction block robustness. The results of this work can provide insights for the design of electrical neurostimulation therapies.<\/jats:p>","DOI":"10.1137\/24m1645632","type":"journal-article","created":{"date-parts":[[2024,9,16]],"date-time":"2024-09-16T04:01:09Z","timestamp":1726459269000},"page":"1910-1936","source":"Crossref","is-referenced-by-count":2,"title":["The Impact of High-Frequency-Based Stability on the Onset of Action Potentials in Neuron Models"],"prefix":"10.1137","volume":"84","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9974-324X","authenticated-orcid":true,"given":"Eduardo","family":"Cerpa","sequence":"first","affiliation":[{"name":"Instituto de Ingenier\u00eda Matem\u00e1tica y Computacional, Facultad de Matem\u00e1ticas, Pontificia Universidad Cat\u00f3lica de Chile, Avda.\u00a0Vicu\u00f1a Mackenna 4860, Santiago, Chile."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0005-5929-1425","authenticated-orcid":true,"given":"Nathaly","family":"Corrales","sequence":"additional","affiliation":[{"name":"Departamento de Matem\u00e1ticas, Universidad T\u00e9cnica Federico Santa Mar\u00eda, Avda. Vicu\u00f1a Mackenna 3939, Santiago, Chile."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2161-0356","authenticated-orcid":true,"given":"Mat\u00edas","family":"Courdurier","sequence":"additional","affiliation":[{"name":"Departamento de Matem\u00e1tica, Facultad de Matem\u00e1ticas, Pontificia Universidad Cat\u00f3lica de Chile, Avda. Vicu\u00f1a Mackenna 4860, Santiago, Chile."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4170-9281","authenticated-orcid":true,"given":"Leonel E.","family":"Medina","sequence":"additional","affiliation":[{"name":"Departamento de Ingenier\u00eda Inform\u00e1tica, Universidad de Santiago de Chile, Avda. V\u00edctor Jara 3659, Santiago, Chile."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1769-0055","authenticated-orcid":true,"given":"Esteban","family":"Paduro","sequence":"additional","affiliation":[{"name":"Corresponding author.\u00a0Instituto de Ingenier\u00eda Matem\u00e1tica y Computacional, Facultad de Matem\u00e1ticas, Pontificia Universidad Cat\u00f3lica de Chile, Avda.\u00a0Vicu\u00f1a Mackenna 4860, Santiago, Chile."}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2024,9,16]]},"reference":[{"key":"ref1","doi-asserted-by":"publisher","DOI":"10.1007\/s11517-010-0679-x"},{"key":"ref2","doi-asserted-by":"publisher","DOI":"10.1088\/1741-2560\/8\/6\/065007"},{"key":"ref3","doi-asserted-by":"publisher","DOI":"10.1088\/1741-2560\/5\/3\/001"},{"key":"ref4","doi-asserted-by":"publisher","DOI":"10.1109\/TNSRE.2004.834205"},{"key":"ref5","doi-asserted-by":"publisher","DOI":"10.1007\/s10827-006-0015-5"},{"key":"ref6","unstructured":"E. Cerpa, M. Courdurier, E. Hern\u00e1ndez, L. E. Medina, and E. Paduro, Approximation and Stability Results for the Parabolic FitzHugh-Nagumo System with Combined Rapidly Oscillating Sources, preprint, https:\/\/arxiv.org\/abs\/2305.00123, 2023."},{"key":"ref7","doi-asserted-by":"publisher","DOI":"10.1007\/s00285-022-01839-8"},{"key":"ref8","doi-asserted-by":"publisher","DOI":"10.1016\/j.pbiomolbio.2015.12.008"},{"key":"ref9","doi-asserted-by":"publisher","DOI":"10.1137\/S036301290342471X"},{"key":"ref10","doi-asserted-by":"publisher","DOI":"10.1016\/S0006-3495(61)86902-6"},{"key":"ref11","doi-asserted-by":"publisher","DOI":"10.1088\/1741-2560\/7\/6\/066003"},{"key":"ref12","volume-title":"Nonlinear Systems","author":"Khalil H. K.","year":"2002","edition":"3"},{"key":"ref13","doi-asserted-by":"publisher","DOI":"10.1007\/BF02344716"},{"key":"ref14","doi-asserted-by":"publisher","DOI":"10.1111\/ner.12100"},{"key":"ref15","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127404009685"},{"key":"ref16","doi-asserted-by":"publisher","DOI":"10.1088\/1741-2560\/4\/4\/005"},{"key":"ref17","doi-asserted-by":"publisher","DOI":"10.1016\/j.brs.2021.03.008"},{"key":"ref18","doi-asserted-by":"publisher","DOI":"10.1007\/s11071-011-0197-x"},{"key":"ref19","doi-asserted-by":"publisher","DOI":"10.1016\/0001-8708(78)90075-0"},{"key":"ref20","doi-asserted-by":"publisher","DOI":"10.1109\/TBME.2005.847561"},{"key":"ref21","doi-asserted-by":"publisher","DOI":"10.1038\/195712b0"},{"key":"ref22","doi-asserted-by":"crossref","unstructured":"T. L. Vrabec, N. Bhadra, J. S. Wainright, N. Bhadra, and K. L. Kilgore, A novel waveform for No-Onset nerve block combining direct current and kilohertz frequency alternating current, in 2013 6th International IEEE\/EMBS Conference on Neural Engineering (NER), 2013, pp. 283\u2013286, https:\/\/doi.org\/10.1109\/NER.2013.6695927.","DOI":"10.1109\/NER.2013.6695927"},{"key":"ref23","doi-asserted-by":"publisher","DOI":"10.1186\/s12984-019-0554-4"},{"key":"ref24","doi-asserted-by":"publisher","DOI":"10.1371\/journal.pone.0081402"},{"key":"ref25","doi-asserted-by":"publisher","DOI":"10.1371\/journal.pcbi.1007766"},{"key":"ref26","doi-asserted-by":"publisher","DOI":"10.1007\/s10827-021-00806-4"}],"container-title":["SIAM Journal on Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/24M1645632","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,20]],"date-time":"2026-08-20T11:01:07Z","timestamp":1787223667000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/24M1645632"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,9,16]]},"references-count":26,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2024,10,31]]}},"alternative-id":["10.1137\/24M1645632"],"URL":"https:\/\/doi.org\/10.1137\/24m1645632","relation":{},"ISSN":["0036-1399","1095-712X"],"issn-type":[{"value":"0036-1399","type":"print"},{"value":"1095-712X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,9,16]]}}}