{"paper":{"title":"A Mathematical Characterization of Neural Activation Induced by Temporal Interference Stimulation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"Amplitudes and beat frequency together decide whether temporal interference stimulation leaves a neuron quiet, produces brief spikes, or drives continuous firing.","cross_cats":["q-bio.NC"],"primary_cat":"math.DS","authors_text":"Antoine Chaillet, Esteban Paduro, Mario Sigalotti","submitted_at":"2026-05-16T02:18:51Z","abstract_excerpt":"Temporal Interference Stimulation (TIS) is a non-invasive neuromodulation technique in which two high-frequency sinusoidal currents with slightly different frequencies generate a low-frequency envelope that can activate deep neural structures. This study investigates the conditions under which TIS elicits action potentials in a single neuron modeled by the FitzHugh-Nagumo system. This research integrates phase-plane analysis and geometric singular perturbation to develop a mathematical framework for analyzing TIS. By combining a mathematical analysis of differential equations with computer sim"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"The amplitudes and beat frequency jointly determine whether the neuron remains quiescent, exhibits only transient responses, or undergoes persistent (tonic) firing.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The FitzHugh-Nagumo equations, together with the geometric singular perturbation reduction, faithfully capture the activation thresholds of real neurons under the envelope produced by temporal interference stimulation (abstract, paragraph 3).","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Mathematical analysis of the FitzHugh-Nagumo model shows that TIS amplitudes and beat frequency jointly control whether a neuron remains quiescent, produces transient responses, or exhibits tonic firing.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Amplitudes and beat frequency together decide whether temporal interference stimulation leaves a neuron quiet, produces brief spikes, or drives continuous firing.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"ebce5e3d1baeaa229ca965c50a9f5010294a1c4dcd6bc9657b32ddc9401d2144"},"source":{"id":"2605.16761","kind":"arxiv","version":1},"verdict":{"id":"f0fe3c75-9969-40ac-aabd-49961d2cfe59","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-19T19:51:36.719247Z","strongest_claim":"The amplitudes and beat frequency jointly determine whether the neuron remains quiescent, exhibits only transient responses, or undergoes persistent (tonic) firing.","one_line_summary":"Mathematical analysis of the FitzHugh-Nagumo model shows that TIS amplitudes and beat frequency jointly control whether a neuron remains quiescent, produces transient responses, or exhibits tonic firing.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The FitzHugh-Nagumo equations, together with the geometric singular perturbation reduction, faithfully capture the activation thresholds of real neurons under the envelope produced by temporal interference stimulation (abstract, paragraph 3).","pith_extraction_headline":"Amplitudes and beat frequency together decide whether temporal interference stimulation leaves a neuron quiet, produces brief spikes, or drives continuous firing."},"integrity":{"clean":false,"summary":{"advisory":1,"critical":0,"by_detector":{"doi_compliance":{"total":1,"advisory":1,"critical":0,"informational":0}},"informational":0},"endpoint":"/pith/2605.16761/integrity.json","findings":[{"note":"DOI in the printed bibliography is fragmented by whitespace or line breaks. 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Cerpa, N. Corrales, M. Courdurier, L. E. Medina, and E. Paduro. The Impact of High-Frequency-Based Stability on the Onset of Action Potentials in Neuron Models.SIAM Journal on Applied Mathematics, ","work_id":"2bef9e63-e5ac-45ff-a059-e2075ac85811","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"10.1007/s00285-022-","year":2023,"title":"E. Cerpa, M. Courdurier, E. Hernández, L. E. Medina, and E. Paduro. A partially averaged system to model neuron responses to interferential current stimulation.J. Math. Biol., 86(1):8, 2023. doi:10.10","work_id":"8941e15c-da43-4495-9227-eadc46f2c657","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"10.3934/dcds.2026001","year":2025,"title":"E.Cerpa, M.Courdurier, E.Hernández, L.E.Medina, andE.Paduro. Approximationandstabilityresultsfor the parabolic FitzHugh-Nagumo system with combined rapidly oscillating sources.Discrete and Continuous ","work_id":"9d9365d2-4224-42b5-86dc-f560a0c13b3f","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"10.1016/j.cell.2017.05.024","year":2017,"title":"N. Grossman, D. Bono, N. Dedic, S. B. Kodandaramaiah, A. Rudenko, H.-J. Suk, A. M. Cassara, E. Neufeld, N. Kuster, L.-H. Tsai, A. Pascual-Leone, and E. S. Boyden. Noninvasive Deep Brain Stimulation vi","work_id":"fc00dcf9-dddc-4157-8237-70dcf8f29387","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":29,"snapshot_sha256":"b5add79e32ae51658d0fca6e7ee4b4f82cb32ce8bf75318a790458e405ca231d","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}