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<p>Based on the Hodgkin–Huxley (HH) model, this study introduces a memristor and incorporates magnetic flux as an additional variable, effectively equating the memristor channel current with electromagnetic induction current, thereby accounting for the time-varying magnetic fields generated by transmembrane ion movements during action potentials. Using the modified model, we simulated the burst firing of spreading depression (SD) and revealed its multi-timescale dynamical characteristics—observed in migraine and related neurological disorders—through fast–slow variable dissection. Furthermore, the regulatory effects of three types of external magnetic fields (static, single, and dual alternating) on SD were investigated. Results show that static magnetic fields of specific intensities can suppress SD discharges; bifurcation analysis indicates that increasing magnetic field strength narrows the range of ion concentration states available for SD initiation. A single alternating magnetic field requires both sufficient amplitude and high frequency to inhibit SD. Dual alternating magnetic fields exhibit a clear amplitude–frequency trade-off: higher amplitudes enable suppression at lower common frequencies or across broader frequency combinations, lower amplitudes require higher common frequencies. These findings reveal potential mechanisms for intervening in SD activity via external magnetic fields and offer novel theoretical insights for treating neurological disorders such as migraine. The flexibility in parameter selection further suggests that practical applications can be optimized by choosing amplitude–frequency pairs tailored to specific operational requirements.</p>

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Regulation of spreading depression by external magnetic fields through an improved Hodgkin–Huxley model with electromagnetic induction

  • 期刊论文

  • 发表日期：

    2026年6月19日

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  • Yingxin Wang,
  • Denggui Fan,
  • Feng Zhai,
  • Qingyun Wang

摘要

Based on the Hodgkin–Huxley (HH) model, this study introduces a memristor and incorporates magnetic flux as an additional variable, effectively equating the memristor channel current with electromagnetic induction current, thereby accounting for the time-varying magnetic fields generated by transmembrane ion movements during action potentials. Using the modified model, we simulated the burst firing of spreading depression (SD) and revealed its multi-timescale dynamical characteristics—observed in migraine and related neurological disorders—through fast–slow variable dissection. Furthermore, the regulatory effects of three types of external magnetic fields (static, single, and dual alternating) on SD were investigated. Results show that static magnetic fields of specific intensities can suppress SD discharges; bifurcation analysis indicates that increasing magnetic field strength narrows the range of ion concentration states available for SD initiation. A single alternating magnetic field requires both sufficient amplitude and high frequency to inhibit SD. Dual alternating magnetic fields exhibit a clear amplitude–frequency trade-off: higher amplitudes enable suppression at lower common frequencies or across broader frequency combinations, lower amplitudes require higher common frequencies. These findings reveal potential mechanisms for intervening in SD activity via external magnetic fields and offer novel theoretical insights for treating neurological disorders such as migraine. The flexibility in parameter selection further suggests that practical applications can be optimized by choosing amplitude–frequency pairs tailored to specific operational requirements.