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<front>
<journal-meta>
<journal-id journal-id-type="publisher-id">Front. Neurosci.</journal-id>
<journal-title-group>
<journal-title>Frontiers in Neuroscience</journal-title>
<abbrev-journal-title abbrev-type="pubmed">Front. Neurosci.</abbrev-journal-title>
</journal-title-group>
<issn pub-type="epub">1662-453X</issn>
<publisher>
<publisher-name>Frontiers Media S.A.</publisher-name>
</publisher>
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<article-meta>
<article-id pub-id-type="doi">10.3389/fnins.2026.1778894</article-id>
<article-version article-version-type="Version of Record" vocab="NISO-RP-8-2008"/>
<article-categories>
<subj-group subj-group-type="heading">
<subject>Review</subject>
</subj-group>
</article-categories>
<title-group>
<article-title>Nonlinear dynamics and multiscale mechanisms of deep brain stimulation</article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname>Yuan</surname>
<given-names>Yue</given-names>
</name>
<xref ref-type="aff" rid="aff1"><sup>1</sup></xref>
<xref ref-type="aff" rid="aff2"><sup>2</sup></xref>
<uri xlink:href="https://loop.frontiersin.org/people/967224"/>
<role vocab="credit" vocab-identifier="https://credit.niso.org/" vocab-term="Writing &#x2013; original draft" vocab-term-identifier="https://credit.niso.org/contributor-roles/writing-original-draft/">Writing &#x2013; original draft</role>
</contrib>
<contrib contrib-type="author">
<name>
<surname>Yan</surname>
<given-names>Hao</given-names>
</name>
<xref ref-type="aff" rid="aff3"><sup>3</sup></xref>
<uri xlink:href="https://loop.frontiersin.org/people/3369083"/>
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</contrib>
<contrib contrib-type="author">
<name>
<surname>Zhang</surname>
<given-names>Kun</given-names>
</name>
<xref ref-type="aff" rid="aff3"><sup>3</sup></xref>
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</contrib>
<contrib contrib-type="author" corresp="yes">
<name>
<surname>Guo</surname>
<given-names>Zheshan</given-names>
</name>
<xref ref-type="aff" rid="aff3"><sup>3</sup></xref>
<xref ref-type="aff" rid="aff4"><sup>4</sup></xref>
<xref ref-type="corresp" rid="c001"><sup>&#x002A;</sup></xref>
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</contrib>
<contrib contrib-type="author" corresp="yes">
<name>
<surname>Wang</surname>
<given-names>Zhaoxiang</given-names>
</name>
<xref ref-type="aff" rid="aff1"><sup>1</sup></xref>
<xref ref-type="aff" rid="aff2"><sup>2</sup></xref>
<xref ref-type="corresp" rid="c001"><sup>&#x002A;</sup></xref>
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<aff id="aff1"><label>1</label><institution>Key Lab of Biomedical Engineering for Ministry of Education, College of Biomedical Engineering and Instrument Science, Zhejiang University</institution>, <city>Hangzhou</city>, <state>Zhejiang</state>, <country country="cn">China</country></aff>
<aff id="aff2"><label>2</label><institution>ZhejiangLab, Research Center for Life Sciences Computing</institution>, <city>Hangzhou</city>, <state>Zhejiang</state>, <country country="cn">China</country></aff>
<aff id="aff3"><label>3</label><institution>State Key Laboratory of Digital Medical Engineering, Key Laboratory of Biomedical Engineering of Hainan Province, School of Biomedical Engineering, Hainan University</institution>, <city>Sanya</city>, <country country="cn">China</country></aff>
<aff id="aff4"><label>4</label><institution>Sanya Research Institute of Hainan University</institution>, <city>Sanya</city>, <state>Hainan</state>, <country country="cn">China</country></aff>
<author-notes>
<corresp id="c001"><label>&#x002A;</label>Correspondence: Zheshan Guo, <email xlink:href="mailto:guozheshan@hainanu.edu.cn">guozheshan@hainanu.edu.cn</email>; Zhaoxiang Wang, <email xlink:href="mailto:wangzhaoxiang@zju.edu.cn">wangzhaoxiang@zju.edu.cn</email></corresp>
</author-notes>
<pub-date publication-format="electronic" date-type="pub" iso-8601-date="2026-02-06">
<day>06</day>
<month>02</month>
<year>2026</year>
</pub-date>
<pub-date publication-format="electronic" date-type="collection">
<year>2026</year>
</pub-date>
<volume>20</volume>
<elocation-id>1778894</elocation-id>
<history>
<date date-type="received">
<day>31</day>
<month>12</month>
<year>2025</year>
</date>
<date date-type="rev-recd">
<day>23</day>
<month>01</month>
<year>2026</year>
</date>
<date date-type="accepted">
<day>26</day>
<month>01</month>
<year>2026</year>
</date>
</history>
<permissions>
<copyright-statement>Copyright &#x00A9; 2026 Yuan, Yan, Zhang, Guo and Wang.</copyright-statement>
<copyright-year>2026</copyright-year>
<copyright-holder>Yuan, Yan, Zhang, Guo and Wang</copyright-holder>
<license>
<ali:license_ref start_date="2026-02-06">https://creativecommons.org/licenses/by/4.0/</ali:license_ref>
<license-p>This is an open-access article distributed under the terms of the <ext-link ext-link-type="uri" xlink:href="https://creativecommons.org/licenses/by/4.0/">Creative Commons Attribution License (CC BY)</ext-link>. The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.</license-p>
</license>
</permissions>
<abstract>
<p>Deep brain stimulation (DBS) is an established treatment for movement disorders and an expanding therapy for several neuropsychiatric conditions, yet its mechanisms of action remain incompletely understood. Early interpretations largely relied on linear and focal models, framing DBS as local excitation, inhibition, or a reversible lesion. Accumulating evidence, however, indicates that DBS reorganizes neural activity across multiple spatial and temporal scales, engaging distributed circuits and network-level dynamics. Here, we synthesize experimental, computational, and clinical findings supporting a nonlinear dynamical perspective on DBS. Within this framework, pathological brain states, such as excessive &#x03B2; synchrony in Parkinson&#x2019;s disease or hypersynchronous epileptic activity, can be conceptualized as maladaptive network regimes. DBS perturbs these regimes in a state-dependent manner, disrupting pathological synchrony, modulating intrinsic oscillations, inducing threshold-like state transitions, and, in some contexts, altering temporal complexity. This perspective helps explain why DBS effects depend on ongoing brain state and why modest changes in stimulation timing or pattern can produce disproportionate clinical effects. Rather than prescribing specific technologies, nonlinear dynamics provides an integrative framework for interpreting diverse DBS phenomena and for understanding the principles underlying adaptive, temporally patterned, and individualized neuromodulation strategies. Together, these insights position DBS as a state-dependent, network-level intervention operating within a nonlinear brain, complementing classical mechanisms and offering a unified lens through which to interpret its diverse therapeutic effects.</p>
</abstract>
<kwd-group>
<kwd>deep brain stimulation</kwd>
<kwd>network neuromodulation</kwd>
<kwd>neural synchrony</kwd>
<kwd>nonlinear dynamics</kwd>
<kwd>state-space dynamics</kwd>
</kwd-group>
<funding-group>
<funding-statement>The author(s) declared that financial support was received for this work and/or its publication. The research was supported by the National Natural Science Foundation of China (No. 52307259; No. 82560272), the Innovational Fund for Scientific and Technological Personnel of Hainan Province (No. KJRC 2023L01), the Project of Sanya Yazhou Bay Science and Technology City (No. SKJC-JYRC-2025-23).</funding-statement>
</funding-group>
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<table-count count="2"/>
<equation-count count="0"/>
<ref-count count="131"/>
<page-count count="9"/>
<word-count count="9221"/>
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<custom-meta-group>
<custom-meta>
<meta-name>section-at-acceptance</meta-name>
<meta-value>Neural Technology</meta-value>
</custom-meta>
</custom-meta-group>
</article-meta>
</front>
<body>
<sec sec-type="intro" id="sec1">
<label>1</label>
<title>Introduction</title>
<p>Deep brain stimulation (DBS) has emerged as a major therapeutic advance for neurological and psychiatric disorders characterized by dysfunctional neural circuits (<xref ref-type="bibr" rid="ref102">Sandoval-Pistorius et al., 2023</xref>). Since its clinical adoption in the 1990s, DBS has been applied to modulate distributed brain circuits underlying motor, cognitive, and affective functions, most prominently in Parkinson&#x2019;s disease, essential tremor, and dystonia, with expanding applications in epilepsy and selected psychiatric conditions (<xref ref-type="bibr" rid="ref76">Lozano et al., 2019</xref>; <xref ref-type="bibr" rid="ref125">Yu et al., 2019</xref>; <xref ref-type="bibr" rid="ref70">Li and Cook, 2018</xref>; <xref ref-type="bibr" rid="ref129">Zhang et al., 2024</xref>; <xref ref-type="bibr" rid="ref62">Krauss et al., 2021</xref>). Unlike ablative procedures, DBS provides adjustable and reversible neuromodulation through chronically implanted electrodes, enabling therapeutic intervention of pathological network activity (<xref ref-type="bibr" rid="ref76">Lozano et al., 2019</xref>; <xref ref-type="bibr" rid="ref62">Krauss et al., 2021</xref>). Although empirically optimized stimulation parameters, typically high-frequency stimulation (HFS), can produce robust and durable clinical benefits, the mechanisms through which DBS restores circuit function remain only partially understood (<xref ref-type="bibr" rid="ref102">Sandoval-Pistorius et al., 2023</xref>; <xref ref-type="bibr" rid="ref105">Shea et al., 2025</xref>).</p>
<p>Historically, DBS was interpreted within local and largely linear control models (<xref ref-type="bibr" rid="ref110">Vitek, 2002</xref>; <xref ref-type="bibr" rid="ref46">Herrington et al., 2016</xref>; <xref ref-type="bibr" rid="ref89">Miocinovic et al., 2013</xref>). In the basal ganglia &#x201C;rate model,&#x201D; Parkinsonian symptoms were attributed to excessive activity within specific nuclei (e.g., subthalamic nucleus, STN), and HFS was therefore viewed as a reversible lesion that suppressed pathological activity via depolarization block or recruitment of local inhibitory afferents (<xref ref-type="bibr" rid="ref89">Miocinovic et al., 2013</xref>; <xref ref-type="bibr" rid="ref20">Chiken and Nambu, 2016</xref>; <xref ref-type="bibr" rid="ref2">Albin et al., 1995</xref>; <xref ref-type="bibr" rid="ref34">Filali et al., 2004</xref>). However, experimental and clinical studies demonstrated that such focal mechanisms cannot fully explain DBS effects (<xref ref-type="bibr" rid="ref37">Florence et al., 2016</xref>). Stimulation can alter firing patterns in downstream neurons, evoke antidromic activity in cortical pathways, and reshape oscillatory synchronization across distributed networks (<xref ref-type="bibr" rid="ref45">Hashimoto et al., 2003</xref>; <xref ref-type="bibr" rid="ref65">Leblois et al., 2010</xref>; <xref ref-type="bibr" rid="ref53">Jakobs et al., 2019</xref>). Moreover, clinical improvement correlates more closely with modulation of pathological &#x03B2; synchrony than with simple rate suppression, motivating a shift from purely local explanations toward circuit-level models of DBS action (<xref ref-type="bibr" rid="ref12">Bronte-Stewart et al., 2009</xref>; <xref ref-type="bibr" rid="ref80">Mathiopoulou et al., 2024</xref>). Notably, this conceptual shift has paralleled advances in DBS technology, as recent sensing-enabled and adaptive systems introduce explicit state dependence and temporal structure that challenge purely static, linear interpretations (<xref ref-type="table" rid="tab1">Table 1</xref>).</p>
<table-wrap position="float" id="tab1">
<label>Table 1</label>
<caption>
<p>Timeline of technological development in DBS.</p>
</caption>
<table frame="hsides" rules="groups">
<thead>
<tr>
<th align="left" valign="top">Year/period</th>
<th align="left" valign="top">Milestone</th>
<th align="left" valign="top">Conceptual significance</th>
</tr>
</thead>
<tbody>
<tr>
<td align="left" valign="top">1947&#x2013;1970s</td>
<td align="left" valign="top">Foundations of stereotactic neurosurgery and chronic stimulation</td>
<td align="left" valign="top">Enabled precise targeting and long-term neuromodulation, establishing DBS as a controllable intervention</td>
</tr>
<tr>
<td align="left" valign="top">1987</td>
<td align="left" valign="top">HFS for tremor</td>
<td align="left" valign="top">Introduced HFS as a reversible alternative to lesions, shaping early linear and rate-based interpretations</td>
</tr>
<tr>
<td align="left" valign="top">1990s</td>
<td align="left" valign="top">STN and GPi identified as DBS targets in PD</td>
<td align="left" valign="top">Anchored DBS within basal ganglia circuit models and rate-based pathophysiology</td>
</tr>
<tr>
<td align="left" valign="top">1997&#x2013;2002</td>
<td align="left" valign="top">FDA approval for tremor and Parkinson&#x2019;s disease</td>
<td align="left" valign="top">Thalamic stimulation for essential tremor and Parkinsonian tremor (1997)<break/>STN/GPi stimulation for advanced PD symptoms (2002)</td>
</tr>
<tr>
<td align="left" valign="top">2013</td>
<td align="left" valign="top">Responsive/closed-loop stimulation</td>
<td align="left" valign="top">Introduced state dependence and feedback, challenging purely linear descriptions</td>
</tr>
<tr>
<td align="left" valign="top">2015</td>
<td align="left" valign="top">Directional leads</td>
<td align="left" valign="top">Enabled spatial selectivity, highlighting network-level rather than focal effects</td>
</tr>
<tr>
<td align="left" valign="top">2020&#x2013;2024</td>
<td align="left" valign="top">Sensing-enabled and adaptive DBS systems</td>
<td align="left" valign="top">Facilitated real-time monitoring and adaptive control, motivating dynamical and nonlinear frameworks</td>
</tr>
</tbody>
</table>
</table-wrap>
<p>Together, these findings establish DBS as a fundamentally circuit-level intervention, setting the stage for viewing stimulation not only as a modulator of firing patterns, but as a perturbation applied to an evolving network state (<xref ref-type="bibr" rid="ref92">Neumann et al., 2023</xref>; <xref ref-type="bibr" rid="ref78">Ma and Tang, 2017</xref>). HFS imposes a temporally structured drive that interacts with ongoing network dynamics, regularizing disordered firing and altering excitatory&#x2013;inhibitory balance (<xref ref-type="bibr" rid="ref34">Filali et al., 2004</xref>; <xref ref-type="bibr" rid="ref59">Johnson et al., 2020</xref>; <xref ref-type="bibr" rid="ref98">Reese et al., 2011</xref>; <xref ref-type="bibr" rid="ref124">Yu et al., 2018</xref>). At the population level, DBS suppresses excessive rhythmic synchronization, particularly &#x03B2; activity in Parkinson&#x2019;s disease, while promoting more flexible network states (<xref ref-type="bibr" rid="ref124">Yu et al., 2018</xref>; <xref ref-type="bibr" rid="ref119">Wilson and Moehlis, 2015</xref>; <xref ref-type="bibr" rid="ref100">Rubin and Terman, 2004</xref>). These effects propagate across hierarchically organized neural circuits through both orthodromic and antidromic pathways (<xref ref-type="bibr" rid="ref92">Neumann et al., 2023</xref>). Thus, therapeutic benefit likely reflects coordinated changes across spatial and temporal scales that reshape information flow within pathological networks, rather than a single dominant mechanism.</p>
</sec>
<sec id="sec2">
<label>2</label>
<title>Classical mechanisms of deep brain stimulation</title>
<sec id="sec3">
<label>2.1</label>
<title>Local suppression and excitation&#x2013;inhibition models</title>
<p>Early mechanistic accounts of DBS emphasized focal excitation or inhibition within the stimulated nucleus (<xref ref-type="bibr" rid="ref110">Vitek, 2002</xref>). In the classical basal ganglia rate model, these hypotheses proposed that therapeutic benefit reflected functional inactivation of an overactive structure (<xref ref-type="bibr" rid="ref34">Filali et al., 2004</xref>; <xref ref-type="bibr" rid="ref29">Dostrovsky et al., 2000</xref>). In Parkinson&#x2019;s disease, hyperactivity of STN was thought to increase inhibitory output from the globus pallidus internus (GPi), thereby suppressing thalamocortical drive. HFS of the STN or GPi was therefore viewed as a reversible lesion, silencing local neurons through depolarization block or synaptic failure (<xref ref-type="bibr" rid="ref20">Chiken and Nambu, 2016</xref>; <xref ref-type="bibr" rid="ref34">Filali et al., 2004</xref>; <xref ref-type="bibr" rid="ref104">Schor et al., 2022</xref>). This interpretation was supported by pharmacological inactivation studies and by observations that subsets of neurons near the electrode reduce their firing during stimulation (<xref ref-type="bibr" rid="ref34">Filali et al., 2004</xref>; <xref ref-type="bibr" rid="ref37">Florence et al., 2016</xref>; <xref ref-type="bibr" rid="ref29">Dostrovsky et al., 2000</xref>; <xref ref-type="bibr" rid="ref69">Levy et al., 2001</xref>).</p>
<p>However, purely local inhibition cannot account for several key observations. Effective STN stimulation can increase GPi firing, contrary to predictions of simple STN suppression (<xref ref-type="bibr" rid="ref98">Reese et al., 2011</xref>; <xref ref-type="bibr" rid="ref56">Jiruska et al., 2010</xref>). DBS can also simultaneously silence somatic activity while activating afferent and efferent axons (<xref ref-type="bibr" rid="ref56">Jiruska et al., 2010</xref>; <xref ref-type="bibr" rid="ref26">Deniau et al., 2010</xref>; <xref ref-type="bibr" rid="ref54">Jantz and Watanabe, 2013</xref>), indicating that stimulation reorganizes rather than eliminates neural activity. These findings revealed that lesion-like mechanisms capture only a subset of DBS effects and motivated broader circuit-level interpretations (<xref ref-type="bibr" rid="ref26">Deniau et al., 2010</xref>).</p>
</sec>
<sec id="sec4">
<label>2.2</label>
<title>Output regularization and disruption of pathological transmission</title>
<p>To resolve these inconsistencies, attention shifted from local suppression to models emphasizing disruption of pathological signaling (<xref ref-type="bibr" rid="ref20">Chiken and Nambu, 2016</xref>; <xref ref-type="bibr" rid="ref40">Grill et al., 2004</xref>). The informational lesion hypothesis proposed that DBS overrides abnormal activity patterns rather than simply reducing firing (<xref ref-type="bibr" rid="ref104">Schor et al., 2022</xref>; <xref ref-type="bibr" rid="ref86">Meissner et al., 2005</xref>). In this framework, HFS regularizes axonal output: while somatic firing near the electrode may decrease, stimulated axons are driven to fire in a highly regular, time-locked pattern (<xref ref-type="bibr" rid="ref98">Reese et al., 2011</xref>; <xref ref-type="bibr" rid="ref1">Agnesi et al., 2015</xref>). This imposed pattern masks endogenous pathological signals and prevents their propagation through the network (<xref ref-type="bibr" rid="ref20">Chiken and Nambu, 2016</xref>; <xref ref-type="bibr" rid="ref98">Reese et al., 2011</xref>; <xref ref-type="bibr" rid="ref112">Wang et al., 2018</xref>; <xref ref-type="bibr" rid="ref33">Feng et al., 2017</xref>; <xref ref-type="bibr" rid="ref19">Chiken and Nambu, 2014</xref>).</p>
<p>Consistent with this view, clinical improvement correlates weakly with changes in mean fire rate but more strongly with disruption of abnormal temporal structure, particularly pathological oscillations (<xref ref-type="bibr" rid="ref20">Chiken and Nambu, 2016</xref>; <xref ref-type="bibr" rid="ref19">Chiken and Nambu, 2014</xref>). By imposing a regular high-frequency drive, often described as &#x201C;jamming,&#x201D; DBS functionally decouples the target nucleus from the broader circuit, creating an informational lesion even when neurons remain active (<xref ref-type="bibr" rid="ref37">Florence et al., 2016</xref>; <xref ref-type="bibr" rid="ref45">Hashimoto et al., 2003</xref>; <xref ref-type="bibr" rid="ref65">Leblois et al., 2010</xref>; <xref ref-type="bibr" rid="ref86">Meissner et al., 2005</xref>). This emphasis on temporal structure marked a conceptual advance beyond purely excitatory&#x2013;inhibitory accounts.</p>
</sec>
<sec id="sec5">
<label>2.3</label>
<title>Network propagation and antidromic recruitment</title>
<p>If DBS regularizes axonal output, its effects are expected to propagate beyond the stimulation site. Indeed, DBS produces network-wide consequences through both orthodromic and antidromic activation of axonal pathways (<xref ref-type="bibr" rid="ref79">Malekmohammadi et al., 2018</xref>; <xref ref-type="bibr" rid="ref81">McConnell et al., 2012</xref>; <xref ref-type="bibr" rid="ref60">Kang and Lowery, 2014</xref>). STN stimulation influences downstream basal ganglia structures while simultaneously driving antidromic activity in upstream cortical projections (<xref ref-type="bibr" rid="ref59">Johnson et al., 2020</xref>; <xref ref-type="bibr" rid="ref71">Li et al., 2012</xref>). Short-latency cortical responses observed in animal and human studies provide direct evidence for rapid recruitment of cortico-subthalamic projections (<xref ref-type="bibr" rid="ref59">Johnson et al., 2020</xref>; <xref ref-type="bibr" rid="ref71">Li et al., 2012</xref>; <xref ref-type="bibr" rid="ref88">Miocinovic et al., 2018</xref>).</p>
<p>In addition, DBS can also recruit axonal collaterals, producing divergent effects across multiple downstream targets (<xref ref-type="bibr" rid="ref43">Hammond et al., 2008</xref>; <xref ref-type="bibr" rid="ref3">Anderson et al., 2018</xref>). For example, STN stimulation modulates pallidal output while simultaneously engaging brainstem and cortical modulatory systems, leading to widespread transmitter release and circuit reconfiguration (<xref ref-type="bibr" rid="ref3">Anderson et al., 2018</xref>; <xref ref-type="bibr" rid="ref5">Bar-Gad et al., 2004</xref>). These findings establish DBS as a network-level intervention whose effects depend on the embedding circuitry, rather than a purely focal manipulation of a single nucleus (<xref ref-type="bibr" rid="ref106">Sobesky et al., 2022</xref>; <xref ref-type="bibr" rid="ref83">McIntyre and Hahn, 2010</xref>).</p>
</sec>
<sec id="sec6">
<label>2.4</label>
<title>Limitations of classical linear models</title>
<p>Together, classical models identify several experimentally supported mechanisms: local inhibitory effects, axonal activation and output regularization, disruption of pathological transmission, and distributed network engagement (summarized in <xref ref-type="table" rid="tab2">Table 2</xref>) (<xref ref-type="bibr" rid="ref34">Filali et al., 2004</xref>; <xref ref-type="bibr" rid="ref98">Reese et al., 2011</xref>; <xref ref-type="bibr" rid="ref29">Dostrovsky et al., 2000</xref>; <xref ref-type="bibr" rid="ref19">Chiken and Nambu, 2014</xref>; <xref ref-type="bibr" rid="ref79">Malekmohammadi et al., 2018</xref>; <xref ref-type="bibr" rid="ref81">McConnell et al., 2012</xref>; <xref ref-type="bibr" rid="ref28">Dorval et al., 2010</xref>; <xref ref-type="bibr" rid="ref99">Rosenbaum et al., 2014</xref>; <xref ref-type="bibr" rid="ref66">Lee et al., 2011</xref>). Each of these mechanisms is experimentally supported and likely contributes under specific conditions. However, DBS effects vary substantially across disorders, brain states, and stimulation parameters, and cannot be fully explained by any single mechanism in isolation. Instead, therapeutic outcomes appear to depend on how these mechanisms interact and are expressed within the broader network (<xref ref-type="bibr" rid="ref82">McIntyre and Anderson, 2016</xref>; <xref ref-type="bibr" rid="ref120">Wu et al., 2021</xref>; <xref ref-type="bibr" rid="ref38">Gittis and Sillitoe, 2024</xref>).</p>
<table-wrap position="float" id="tab2">
<label>Table 2</label>
<caption>
<p>Proposed deep brain stimulation mechanisms.</p>
</caption>
<table frame="hsides" rules="groups">
<thead>
<tr>
<th align="left" valign="top">Descriptive level</th>
<th align="left" valign="top">Core interpretation</th>
<th align="left" valign="top">Representative evidence</th>
</tr>
</thead>
<tbody>
<tr>
<td align="left" valign="top">Local neuronal effects</td>
<td align="left" valign="top">HFS suppresses or alters activity near the electrode, mimicking a reversible lesion</td>
<td align="left" valign="top">Reduced firing in subsets of neurons; symptom relief after focal inactivation</td>
</tr>
<tr>
<td align="left" valign="top">Axonal output shaping</td>
<td align="left" valign="top">DBS regularizes axonal output despite variable somatic firing</td>
<td align="left" valign="top">Stimulus-locked axonal firing; weak correlation between mean firing rate and clinical benefits</td>
</tr>
<tr>
<td align="left" valign="top">Network propagation</td>
<td align="left" valign="top">DBS-evoked effects propagate through connected circuits via orthodromic and antidromic pathways</td>
<td align="left" valign="top">Cortical responses to STN-DBS; modulation of distributed basal ganglia&#x2013;cortical networks</td>
</tr>
<tr>
<td align="left" valign="top">Dynamical state modulation</td>
<td align="left" valign="top">DBS perturbs global network dynamics in a state-dependent manner</td>
<td align="left" valign="top">Changes in synchrony, oscillatory structure, and variability across brain states</td>
</tr>
</tbody>
</table>
</table-wrap>
<p>From this perspective, the limitations of classical accounts arise not from the absence of relevant mechanisms, but from the difficulty of describing how their interactions evolve across different system states (<xref ref-type="bibr" rid="ref76">Lozano et al., 2019</xref>; <xref ref-type="bibr" rid="ref83">McIntyre and Hahn, 2010</xref>; <xref ref-type="bibr" rid="ref91">Neumann et al., 2023</xref>). Classical models primarily characterize local or circuit-level processes, yet offer limited insight into why DBS efficacy often exhibits strong state dependence, threshold-like transitions, and sensitivity to stimulation history (<xref ref-type="bibr" rid="ref120">Wu et al., 2021</xref>; <xref ref-type="bibr" rid="ref91">Neumann et al., 2023</xref>; <xref ref-type="bibr" rid="ref30">Dovzhenok et al., 2012</xref>; <xref ref-type="bibr" rid="ref130">Zheng et al., 2020</xref>). Importantly, these mechanisms are therefore not rendered obsolete by higher-level dynamical descriptions; rather, they constitute the substrates through which stimulation acts, while a nonlinear dynamical perspective captures how their combined effects are integrated across time and network state (<xref ref-type="bibr" rid="ref76">Lozano et al., 2019</xref>; <xref ref-type="bibr" rid="ref119">Wilson and Moehlis, 2015</xref>; <xref ref-type="bibr" rid="ref83">McIntyre and Hahn, 2010</xref>; <xref ref-type="bibr" rid="ref38">Gittis and Sillitoe, 2024</xref>; <xref ref-type="bibr" rid="ref91">Neumann et al., 2023</xref>). This view motivates treating DBS as a perturbation applied to a complex dynamical system, capable of reshaping pathological brain states toward more adaptive regimes.</p>
</sec>
</sec>
<sec id="sec7">
<label>3</label>
<title>Nonlinear mechanisms of neuromodulation: synchrony, rhythms, and complex dynamics</title>
<p>Whereas classical models emphasize local effects on individual neurons or nuclei, a nonlinear-dynamics perspective considers how DBS alters the global state of distributed networks (<xref ref-type="bibr" rid="ref83">McIntyre and Hahn, 2010</xref>; <xref ref-type="bibr" rid="ref9">Breakspear, 2017</xref>). HFS often evokes system-level responses that cannot be reduced to a linear sum of single-cell effects. Instead, DBS disrupts pathological synchrony, reorganizes intrinsic oscillations, and reshapes coordinated activity across spatial and temporal scales (<xref ref-type="bibr" rid="ref20">Chiken and Nambu, 2016</xref>; <xref ref-type="bibr" rid="ref104">Schor et al., 2022</xref>; <xref ref-type="bibr" rid="ref22">De Hemptinne et al., 2015</xref>; <xref ref-type="bibr" rid="ref118">Wilson et al., 2011</xref>). In this framework, DBS acts in a state-dependent manner, with outcomes shaped by ongoing network activity and stimulation timing (<xref ref-type="bibr" rid="ref16">Cagnan et al., 2017</xref>; <xref ref-type="bibr" rid="ref75">Little et al., 2013</xref>).</p>
<p>In the following sections, we outline four interrelated nonlinear processes through which these effects can be described: (i) disruption of pathological synchrony (<xref ref-type="bibr" rid="ref81">McConnell et al., 2012</xref>; <xref ref-type="bibr" rid="ref13">Brown, 2007</xref>); (ii) modulation of intrinsic oscillations (<xref ref-type="bibr" rid="ref100">Rubin and Terman, 2004</xref>; <xref ref-type="bibr" rid="ref22">De Hemptinne et al., 2015</xref>; <xref ref-type="bibr" rid="ref77">Ma et al., 2019</xref>); (iii) induction of network state transitions via bifurcation-like mechanisms (<xref ref-type="bibr" rid="ref9">Breakspear, 2017</xref>; <xref ref-type="bibr" rid="ref114">Wang et al., 2022</xref>; <xref ref-type="bibr" rid="ref42">Gu et al., 2015</xref>); and (iv) restoration of long-range temporal correlations (LRTC) and dynamical complexity (<xref ref-type="bibr" rid="ref50">Hohlefeld et al., 2012</xref>; <xref ref-type="bibr" rid="ref113">Wang et al., 2024</xref>). These descriptions are not competing mechanisms but complementary analytical perspectives operating at different levels, from population synchrony and rhythmic structure to state-space organization and multiscale temporal integration. Overlaps between them therefore reflect differences in descriptive level rather than distinct causal explanations.</p>
<p>Although many illustrative examples are drawn from Parkinson&#x2019;s disease, the nonlinear principles discussed here are not disease-specific. Instead, disease specificity arises from differences in pathological network organization, stimulation targets, and paradigms (<xref ref-type="bibr" rid="ref53">Jakobs et al., 2019</xref>; <xref ref-type="bibr" rid="ref61">Koeglsperger et al., 2019</xref>). While distinct conditions may benefit from alternative stimulation strategies, such as irregular or stochastic inputs, the present review focuses on principles associated with HFS, the most widely applied clinical paradigm (<xref ref-type="bibr" rid="ref76">Lozano et al., 2019</xref>; <xref ref-type="bibr" rid="ref111">Wagle Shukla et al., 2017</xref>).</p>
<sec id="sec8">
<label>3.1</label>
<title>Disrupting pathological synchrony</title>
<p>At the level of population coherence, excessive neuronal synchrony is a core pathophysiological feature of several brain disorders, including Parkinson&#x2019;s disease and epilepsy (<xref ref-type="bibr" rid="ref109">Uhlhaas and Singer, 2006</xref>). In Parkinson&#x2019;s disease, bradykinesia and rigidity are closely linked to exaggerated &#x03B2;-band synchrony within basal ganglia&#x2013;cortical circuits (<xref ref-type="bibr" rid="ref13">Brown, 2007</xref>; <xref ref-type="bibr" rid="ref44">Hammond et al., 2007</xref>), whereas epileptic seizures arise from abrupt, hypersynchronous discharges across large neuronal populations (<xref ref-type="bibr" rid="ref57">Jiruska et al., 2013</xref>). From a nonlinear-dynamics perspective, these excessively coherent patterns can be viewed as pathological attractors: self-stabilizing network states that are resistant to perturbation (<xref ref-type="bibr" rid="ref9">Breakspear, 2017</xref>; <xref ref-type="bibr" rid="ref25">Deco and Jirsa, 2012</xref>). A principal goal of DBS is therefore to destabilize these synchronous attractors and promote more flexible, desynchronized network dynamics (<xref ref-type="bibr" rid="ref83">McIntyre and Hahn, 2010</xref>; <xref ref-type="bibr" rid="ref22">De Hemptinne et al., 2015</xref>; <xref ref-type="bibr" rid="ref118">Wilson et al., 2011</xref>).</p>
<p>Converging evidence indicates that DBS achieves therapeutic benefit primarily by disrupting pathological synchrony rather than simply suppressing neural activity (<xref ref-type="bibr" rid="ref63">Kromer and Tass, 2020</xref>; <xref ref-type="bibr" rid="ref97">Qasim et al., 2016</xref>; <xref ref-type="bibr" rid="ref85">Medeiros and Moraes, 2014</xref>; <xref ref-type="bibr" rid="ref64">Kuhn et al., 2004</xref>). In Parkinson&#x2019;s disease, effective STN stimulation acutely reduces &#x03B2;-band power within the STN and connected cortical regions, and the magnitude of &#x03B2; suppression closely parallels clinical improvement (<xref ref-type="bibr" rid="ref63">Kromer and Tass, 2020</xref>; <xref ref-type="bibr" rid="ref97">Qasim et al., 2016</xref>; <xref ref-type="bibr" rid="ref85">Medeiros and Moraes, 2014</xref>; <xref ref-type="bibr" rid="ref64">Kuhn et al., 2004</xref>). Similar reductions following dopamine-replacement therapy reinforce the view that excessive &#x03B2; synchrony reflects a core network abnormality (<xref ref-type="bibr" rid="ref80">Mathiopoulou et al., 2024</xref>). Previous studies further suggest that HFS shifts STN activity from rhythmic synchrony to irregular, asynchronous firing, largely through asynchronous GABAergic input from the external globus pallidus (<xref ref-type="bibr" rid="ref119">Wilson and Moehlis, 2015</xref>; <xref ref-type="bibr" rid="ref61">Koeglsperger et al., 2019</xref>; <xref ref-type="bibr" rid="ref122">Xu et al., 2025</xref>). Thus, symptom relief appears to arise from normalization of aberrant &#x03B2; synchrony, rather than compensation for dopamine loss alone (<xref ref-type="bibr" rid="ref80">Mathiopoulou et al., 2024</xref>; <xref ref-type="bibr" rid="ref119">Wilson and Moehlis, 2015</xref>; <xref ref-type="bibr" rid="ref122">Xu et al., 2025</xref>; <xref ref-type="bibr" rid="ref31">Eusebio et al., 2011</xref>; <xref ref-type="bibr" rid="ref90">Moran et al., 2012</xref>; <xref ref-type="bibr" rid="ref108">Tass and Hauptmann, 2007</xref>).</p>
<p>Comparable desynchronizing effects are observed in epilepsy. In hippocampal models, typically studied in anesthetized rats, HFS suppresses hypersynchronous epileptiform discharges even when overall activity levels remain similar: neurons continue to fire, but in a disorganized, non-bursting manner that lacks seizure-like coherence (<xref ref-type="bibr" rid="ref115">Wang et al., 2021</xref>). Although hippocampal circuitry differs from basal ganglia networks, these findings illustrate a general stimulation principle whereby axonal activation disrupts pathological signal propagation and decouples downstream neuronal populations. Consistent with this view, clinical recordings show that anterior thalamic DBS produces frequency-dependent desynchronization, with stimulation &#x003E;45&#x202F;Hz reducing hippocampal and cortical synchrony and suppressing epileptiform events (<xref ref-type="bibr" rid="ref124">Yu et al., 2018</xref>). Moreover, spatially distributed or temporally irregular stimulation can enhance seizure suppression, consistent with a synchrony-disruption mechanism (<xref ref-type="bibr" rid="ref24">de Oliveira et al., 2018</xref>; <xref ref-type="bibr" rid="ref4">Arcot Desai et al., 2014</xref>).</p>
<p>Together, these findings support a unifying framework in which DBS acts by destabilizing maladaptive synchronous states, such as &#x03B2; oscillations in Parkinson&#x2019;s disease or hypersynchronous discharges in epilepsy, and shifting networks toward more irregular yet functionally stable regimes (<xref ref-type="bibr" rid="ref119">Wilson and Moehlis, 2015</xref>; <xref ref-type="bibr" rid="ref118">Wilson et al., 2011</xref>). Importantly, DBS does not simply silence neural activity; rather, it selectively disrupts pathological coherence while preserving healthier asynchronous dynamics, distinguishing it from classical inhibitory models.</p>
</sec>
<sec id="sec9">
<label>3.2</label>
<title>Oscillatory modulation and rhythmic network intervention</title>
<p>At the level of rhythmic organization, brain function is fundamentally organized by oscillations across multiple frequency bands, and many neurological disorders are marked by abnormalities in these rhythms (<xref ref-type="bibr" rid="ref80">Mathiopoulou et al., 2024</xref>; <xref ref-type="bibr" rid="ref14">Buzs&#x00E1;ki, 2006</xref>). In Parkinson&#x2019;s disease, for example, &#x03B2;-band activity becomes excessively prominent within motor circuits and is widely regarded as a network signature of bradykinesia and rigidity (<xref ref-type="bibr" rid="ref79">Malekmohammadi et al., 2018</xref>; <xref ref-type="bibr" rid="ref13">Brown, 2007</xref>). DBS directly perturbs these rhythms and oscillatory dynamics. Clinical recordings show that STN-DBS rapidly suppresses &#x03B2; power in both the STN and motor cortex, with the degree of suppression closely paralleling clinical improvement (<xref ref-type="bibr" rid="ref12">Bronte-Stewart et al., 2009</xref>; <xref ref-type="bibr" rid="ref80">Mathiopoulou et al., 2024</xref>). Importantly, the oscillatory effects of DBS differ partly from those of dopaminergic therapy: while levodopa preferentially reduces low-&#x03B2; synchrony, DBS tends to suppress &#x03B2; activity more broadly and can, in some patients, induce stimulation-locked high-frequency oscillations consistent with circuit entrainment (<xref ref-type="bibr" rid="ref45">Hashimoto et al., 2003</xref>; <xref ref-type="bibr" rid="ref80">Mathiopoulou et al., 2024</xref>; <xref ref-type="bibr" rid="ref81">McConnell et al., 2012</xref>; <xref ref-type="bibr" rid="ref17">Cheyne, 2013</xref>; <xref ref-type="bibr" rid="ref95">Priori et al., 2004</xref>; <xref ref-type="bibr" rid="ref58">Johnson et al., 2008</xref>).</p>
<p>DBS also modulates rhythms beyond the &#x03B2; range. In essential tremor, thalamic stimulation suppresses tremor-related oscillations at ~4&#x2013;6&#x202F;Hz (<xref ref-type="bibr" rid="ref7">Benabid et al., 1991</xref>; <xref ref-type="bibr" rid="ref87">Milosevic et al., 2018</xref>). In epilepsy, DBS can disrupt hypersynchronous epileptiform activity and promote faster, lower-amplitude rhythms associated with more stable network states (<xref ref-type="bibr" rid="ref36">Fisher et al., 2010</xref>; <xref ref-type="bibr" rid="ref35">Fisher, 2023</xref>). Experimental studies further demonstrate that HFS can markedly suppress low-frequency oscillations, including hippocampal theta activity (4&#x2013;8&#x202F;Hz) during CA1 stimulation and ~9-Hz rhythms in the globus pallidus externus (GPe) and substantia nigra pars reticulata (SNr) during STN stimulation, with corresponding reductions in theta-locked spiking and local-field-potential power (<xref ref-type="bibr" rid="ref1">Agnesi et al., 2015</xref>; <xref ref-type="bibr" rid="ref81">McConnell et al., 2012</xref>; <xref ref-type="bibr" rid="ref77">Ma et al., 2019</xref>). These effects reflect restructuring of temporal organization, not merely rate changes: spike timing becomes decoupled from dominant rhythms, indicating coordinated modulation across cellular and population levels. Consistent with this view, coordinated-reset stimulation deliberately applies spatiotemporally patterned inputs to disrupt pathological synchrony and produce longer-lasting desynchronization (<xref ref-type="bibr" rid="ref94">Popovych and Tass, 2012</xref>; <xref ref-type="bibr" rid="ref32">Fan and Wang, 2015</xref>).</p>
<p>Taken together, these findings support a frequency-domain account of DBS: stimulation acts as a network-level intervention on oscillatory dynamics, suppressing pathological synchrony, restoring physiological rhythmic organization, and recalibrating cross-frequency interactions (<xref ref-type="bibr" rid="ref81">McConnell et al., 2012</xref>; <xref ref-type="bibr" rid="ref83">McIntyre and Hahn, 2010</xref>; <xref ref-type="bibr" rid="ref103">Scherer et al., 2020</xref>; <xref ref-type="bibr" rid="ref121">Xiao et al., 2018</xref>). Crucially, therapeutic benefit depends not only on stimulation intensity but on how stimulation interacts with ongoing intrinsic rhythms&#x2014;a hallmark of nonlinear dynamical control.</p>
</sec>
<sec id="sec10">
<label>3.3</label>
<title>Bifurcation-like state transitions and critical dynamics</title>
<p>At the level of state-space dynamics, DBS can be viewed as a driver of transitions between distinct network states (<xref ref-type="bibr" rid="ref9">Breakspear, 2017</xref>). When neural circuits operate near critical points, small perturbations can precipitate abrupt and distinct changes in network dynamics, analogous to mathematical bifurcations (<xref ref-type="bibr" rid="ref23">De Maesschalck and Wechselberger, 2015</xref>). Many pathological brain states can therefore be conceptualized as attractors in network state space, such as the stable &#x03B2;-oscillatory regime in Parkinson&#x2019;s disease or recurrent epileptiform discharges in epilepsy (<xref ref-type="bibr" rid="ref44">Hammond et al., 2007</xref>; <xref ref-type="bibr" rid="ref101">Saggio et al., 2020</xref>; <xref ref-type="bibr" rid="ref55">Jirsa et al., 2014</xref>; <xref ref-type="bibr" rid="ref10">Brittain and Brown, 2014</xref>). HFS can be regarded as an external forcing input that displaces the system from these attractors and, under suitable conditions, carries it across a critical threshold into a more physiological regime (<xref ref-type="bibr" rid="ref100">Rubin and Terman, 2004</xref>; <xref ref-type="bibr" rid="ref83">McIntyre and Hahn, 2010</xref>).</p>
<p>Computational work strongly supports this interpretation. The chaotic desynchronization hypothesis proposes that appropriately patterned HFS destabilizes a pathologically synchronized population, pushing it into a high-dimensional, irregular regime that abolishes the coherent rhythm sustaining symptoms (<xref ref-type="bibr" rid="ref119">Wilson and Moehlis, 2015</xref>; <xref ref-type="bibr" rid="ref100">Rubin and Terman, 2004</xref>; <xref ref-type="bibr" rid="ref118">Wilson et al., 2011</xref>). Related principles underlie coordinated-reset stimulation, in which pulses delivered at distinct phases fragment a synchronized population into weakly coupled clusters, inducing longer-lasting desynchronization via plasticity-dependent reorganization (<xref ref-type="bibr" rid="ref32">Fan and Wang, 2015</xref>; <xref ref-type="bibr" rid="ref117">Wang and Wang, 2017</xref>; <xref ref-type="bibr" rid="ref116">Wang et al., 2016</xref>; <xref ref-type="bibr" rid="ref107">Tass, 2003</xref>). Experimental evidence further reveals threshold-like transitions and abrupt changes in firing patterns under sustained HFS, consistent with bifurcation-like dynamics observed <italic>in vivo</italic> and attributable to nonlinear axonal and network mechanisms (<xref ref-type="bibr" rid="ref114">Wang et al., 2022</xref>; <xref ref-type="bibr" rid="ref126">Yuan et al., 2025</xref>). In hippocampal epilepsy models, brief HFS can precipitate after-discharges, whereas longer trains delivered at the same intensity suppress seizures entirely, indicating a nonlinear dependence on stimulation duration, whereby prolonged stimulation carries the system beyond the seizure bifurcation into a more stable, non-seizing state (<xref ref-type="bibr" rid="ref115">Wang et al., 2021</xref>; <xref ref-type="bibr" rid="ref101">Saggio et al., 2020</xref>; <xref ref-type="bibr" rid="ref68">Lesser et al., 1999</xref>).</p>
<p>More recent electrophysiological studies indicate that DBS interacts with intrinsic nonlinearities rather than acting as a purely linear drive (<xref ref-type="bibr" rid="ref83">McIntyre and Hahn, 2010</xref>; <xref ref-type="bibr" rid="ref84">McIntyre et al., 2004</xref>). Within clinically relevant frequency ranges, subtle changes in inter-pulse interval (IPI) or amplitude can push the system across critical thresholds, producing abrupt transitions between qualitatively distinct activity patterns, including alternating regimes of sustained firing and quiescence (<xref ref-type="bibr" rid="ref114">Wang et al., 2022</xref>; <xref ref-type="bibr" rid="ref126">Yuan et al., 2025</xref>; <xref ref-type="bibr" rid="ref128">Zhang et al., 2020</xref>; <xref ref-type="bibr" rid="ref52">Hu et al., 2023</xref>; <xref ref-type="bibr" rid="ref131">Zheng et al., 2021</xref>). Strikingly, even when mean frequency and pulse count are held constant, re-ordering the intervals can markedly alter responses, indicating proximity to bifurcation points where fine temporal structure determines the emergent state (<xref ref-type="bibr" rid="ref130">Zheng et al., 2020</xref>; <xref ref-type="bibr" rid="ref39">Grill, 2018</xref>; <xref ref-type="bibr" rid="ref47">Hess et al., 2013</xref>). Modeling studies attribute this sensitivity to nonlinear recovery of voltage-gated sodium channels and activity-dependent potassium accumulation, giving rise to intermittent conduction failure and bistability (<xref ref-type="bibr" rid="ref130">Zheng et al., 2020</xref>; <xref ref-type="bibr" rid="ref126">Yuan et al., 2025</xref>; <xref ref-type="bibr" rid="ref123">Yang et al., 2006</xref>; <xref ref-type="bibr" rid="ref41">Gu and Chen, 2014</xref>). Thus, neural responses to DBS depend not simply on mean frequency but on the precise temporal pattern of stimulation, reflecting history-dependent integration in a system poised near bifurcation (<xref ref-type="bibr" rid="ref47">Hess et al., 2013</xref>; <xref ref-type="bibr" rid="ref11">Brocker et al., 2017</xref>).</p>
<p>Together, these observations suggest that DBS influences neural circuits not merely by altering mean firing rates, but by reorganizing patterns of activity across populations, leading to changes in synchrony, variability, and state stability (<xref ref-type="bibr" rid="ref62">Krauss et al., 2021</xref>; <xref ref-type="bibr" rid="ref112">Wang et al., 2018</xref>; <xref ref-type="bibr" rid="ref33">Feng et al., 2017</xref>). Such effects are consistent with a reshaping of the underlying dynamical landscape of neural circuits. By pushing networks across critical thresholds and out of pathological attractor states, DBS can trigger abrupt, nonlinear state transitions that destabilize maladaptive synchrony and reset brain dynamics toward more physiological regimes.</p>
</sec>
<sec id="sec11">
<label>3.4</label>
<title>Restoring complex dynamics and multiscale integration</title>
<p>At the level of multiscale temporal organization, healthy brain activity is scale-free and fractal, reflected in LRTC across multiple time scales (<xref ref-type="bibr" rid="ref73">Linkenkaer-Hansen et al., 2001</xref>; <xref ref-type="bibr" rid="ref15">Buzs&#x00E1;ki and Mizuseki, 2014</xref>). Such correlations are often interpreted as signatures of near-critical dynamics, a regime associated with flexible information processing and multiscale coordination (<xref ref-type="bibr" rid="ref18">Chialvo, 2010</xref>; <xref ref-type="bibr" rid="ref6">Beggs and Timme, 2012</xref>). In EEG and MEG recordings, robust LRTC are observed in healthy individuals, whereas several neurological disorders, including Parkinson&#x2019;s disease, epilepsy and disorders of consciousness, show attenuated temporal correlations, suggesting a shift toward less adaptive dynamical regimes (<xref ref-type="bibr" rid="ref50">Hohlefeld et al., 2012</xref>; <xref ref-type="bibr" rid="ref73">Linkenkaer-Hansen et al., 2001</xref>; <xref ref-type="bibr" rid="ref74">Linkenkaer-Hansen et al., 2004</xref>; <xref ref-type="bibr" rid="ref8">Bhattacharya et al., 2005</xref>; <xref ref-type="bibr" rid="ref49">Hohlefeld et al., 2013</xref>; <xref ref-type="bibr" rid="ref72">Liang et al., 2018</xref>).</p>
<p>From a nonlinear-dynamics perspective, DBS may influence these properties indirectly by disrupting excessive synchrony and preventing network activity from collapsing into low-dimensional attractors (<xref ref-type="bibr" rid="ref46">Herrington et al., 2016</xref>; <xref ref-type="bibr" rid="ref83">McIntyre and Hahn, 2010</xref>). Experimental studies in hippocampal and cortical preparations demonstrate that periodic or patterned stimulation can enhance downstream temporal complexity and increase the Hurst exponent, even when the stimulus itself lacks scale-free structure (<xref ref-type="bibr" rid="ref113">Wang et al., 2024</xref>; <xref ref-type="bibr" rid="ref49">Hohlefeld et al., 2013</xref>; <xref ref-type="bibr" rid="ref127">Yuan et al., 2024</xref>). Clinically, changes in spectral scaling and LRTC have been reported in cortical and subcortical recordings during DBS in some patient cohorts, consistent with partial restoration of multiscale temporal organization (<xref ref-type="bibr" rid="ref50">Hohlefeld et al., 2012</xref>; <xref ref-type="bibr" rid="ref49">Hohlefeld et al., 2013</xref>; <xref ref-type="bibr" rid="ref67">Lee et al., 2025</xref>).</p>
<p>Nevertheless, evidence for LRTC modulation remains heterogeneous and context dependent. While robust effects have been observed in cortical recordings, their stability within basal ganglia nuclei, particularly under chronic stimulation, remains less well established, and LRTC measures are sensitive to recording duration, noise, and behavioral state (<xref ref-type="bibr" rid="ref50">Hohlefeld et al., 2012</xref>; <xref ref-type="bibr" rid="ref73">Linkenkaer-Hansen et al., 2001</xref>; <xref ref-type="bibr" rid="ref21">Darbin et al., 2006</xref>). Moreover, although metrics such as the Hurst exponent provide valuable insight into statistical structure and dynamical regime, they are not currently practical as real-time control variables in clinical DBS, where simpler biomarkers such as &#x03B2;-band power or burst dynamics are more readily measurable (<xref ref-type="bibr" rid="ref50">Hohlefeld et al., 2012</xref>; <xref ref-type="bibr" rid="ref27">Dimitriadis and Linden, 2016</xref>; <xref ref-type="bibr" rid="ref93">Nikulin et al., 2012</xref>).</p>
<p>Accordingly, restoration of temporal complexity should be viewed not as a primary mechanism of DBS, but as a higher-level descriptor of how network dynamics reorganize following stimulation. Within this framework, LRTC and related measures offer a complementary lens for understanding how DBS reshapes information processing across time scales, rather than a replacement for established rate- or oscillation-based accounts (<xref ref-type="bibr" rid="ref50">Hohlefeld et al., 2012</xref>; <xref ref-type="bibr" rid="ref113">Wang et al., 2024</xref>; <xref ref-type="bibr" rid="ref49">Hohlefeld et al., 2013</xref>). This perspective highlights both the promise and the current limitations of applying nonlinear dynamical metrics to clinical neuromodulation. Accordingly, changes in temporal complexity and LRTC should be interpreted as descriptive markers of network reorganization rather than as disease-specific or target-specific mechanisms of DBS.</p>
</sec>
</sec>
<sec id="sec12">
<label>4</label>
<title>Clinical implications and technological outlook</title>
<p>Viewing DBS through a nonlinear dynamics lens emphasizes its state-dependent interaction with ongoing network activity rather than portraying stimulation as a uniform high-frequency pacemaker (<xref ref-type="bibr" rid="ref83">McIntyre and Hahn, 2010</xref>; <xref ref-type="bibr" rid="ref9">Breakspear, 2017</xref>). The therapeutic goal becomes stabilizing networks within a regime that preserves flexibility while preventing pathological synchrony. Importantly, this perspective does not replace established rate- or oscillation-based accounts but provides a complementary framework for understanding why identical stimulation parameters can yield different outcomes across brain states.</p>
<p>From this viewpoint, closed-loop or adaptive DBS can be interpreted as a practical implementation of state-dependent intervention. In current clinical systems, adaptive stimulation is typically triggered by readily measurable biomarkers such as &#x03B2;-band power or &#x03B2;-burst dynamics (<xref ref-type="bibr" rid="ref75">Little et al., 2013</xref>; <xref ref-type="bibr" rid="ref96">Priori et al., 2013</xref>), without requiring explicitly nonlinear metrics. Nonlinear theory does not mandate such approaches, but helps explain why timing stimulation to emerging pathological states can be more effective than continuous delivery, by selectively perturbing networks when they approach maladaptive regimes.</p>
<p>A second implication concerns temporal patterning. Experimental and modeling studies demonstrate that neural circuits integrate inputs nonlinearly, such that stimulation timing and pattern can critically shape network responses even when mean frequency is held constant (<xref ref-type="bibr" rid="ref39">Grill, 2018</xref>; <xref ref-type="bibr" rid="ref47">Hess et al., 2013</xref>). Strategies such as stochastic IPI, phase-specific stimulation, multi-frequency inputs or coordinated-reset protocols may selectively disrupt pathological rhythms while limiting entrainment (<xref ref-type="bibr" rid="ref94">Popovych and Tass, 2012</xref>; <xref ref-type="bibr" rid="ref107">Tass, 2003</xref>; <xref ref-type="bibr" rid="ref39">Grill, 2018</xref>; <xref ref-type="bibr" rid="ref48">Hoang et al., 2017</xref>). DBS is therefore better viewed as precision temporal modulation, not a fixed paradigm (<xref ref-type="bibr" rid="ref62">Krauss et al., 2021</xref>).</p>
<p>Finally, personalization of neuromodulation reflects inter-individual differences in anatomy, connectivity, and baseline dynamics, motivating patient-specific targeting and parameter selection (<xref ref-type="bibr" rid="ref92">Neumann et al., 2023</xref>; <xref ref-type="bibr" rid="ref51">Horn et al., 2020</xref>). Such personalization can be achieved within linear or biophysical frameworks, including digital twin models. Nonlinear perspectives contribute by offering additional insight into differences in network stability, sensitivity to perturbation, or proximity to critical transitions, and are therefore best viewed as complementary tools for interpretation and offline optimization rather than mandatory control principles.</p>
<p>Together, these considerations position nonlinear dynamics as an interpretive framework that enriches, rather than dictates, technological development. In practice, robust biomarkers such as &#x03B2;-band activity remain central to clinical implementation, while dynamical metrics may assist in mechanistic understanding and parameter optimization.</p>
</sec>
<sec sec-type="conclusions" id="sec13">
<label>5</label>
<title>Conclusion</title>
<p>DBS has evolved from being viewed primarily as a balance between excitation and inhibition to a network-level intervention acting within a complex, nonlinear brain. A nonlinear-dynamical perspective complements classical mechanisms by framing DBS as a state-dependent perturbation that disrupts maladaptive synchrony, reshapes network dynamics, and preserves functional flexibility. This framework helps explain why modest changes in stimulation timing or pattern can yield disproportionate effects and why clinical outcomes depend on the state of the brain.</p>
<p>Rather than implying a shift in therapeutic goals or technologies, this perspective provides an integrative lens for understanding how diverse DBS effects emerge across scales. In this view, DBS is best understood not as a means of simple rate suppression, but as an intervention that stabilizes pathological networks while maintaining adaptive variability, supporting restoration of healthy network function rather than enforcing rigid control.</p>
</sec>
</body>
<back>
<sec sec-type="author-contributions" id="sec14">
<title>Author contributions</title>
<p>YY: Writing &#x2013; original draft. HY: Writing &#x2013; review &#x0026; editing. KZ: Writing &#x2013; review &#x0026; editing. ZG: Writing &#x2013; original draft. ZW: Funding acquisition, Writing &#x2013; review &#x0026; editing, Writing &#x2013; original draft.</p>
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<fn-group>
<fn fn-type="custom" custom-type="edited-by" id="fn0001">
<p>Edited by: <ext-link ext-link-type="uri" xlink:href="https://loop.frontiersin.org/people/3226617/overview">Alessio Franci</ext-link>, University of Liege, Belgium</p>
</fn>
<fn fn-type="custom" custom-type="reviewed-by" id="fn0002">
<p>Reviewed by: <ext-link ext-link-type="uri" xlink:href="https://loop.frontiersin.org/people/1799752/overview">Mariia Popova</ext-link>, University Medical Center Hamburg-Eppendorf, Germany</p>
<p><ext-link ext-link-type="uri" xlink:href="https://loop.frontiersin.org/people/3138844/overview">Thomas Stojsavljevic Jr.</ext-link>, Beloit College, United States</p>
</fn>
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