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Bode Plots Construction01:24

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The Bode plot is an essential tool in control system analysis, mapping the frequency response of a system through a magnitude plot and a phase plot, both against a logarithmic frequency axis. To construct a Bode plot, consider the transfer function H(ω):
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Frequency-dependent and capacitive tissue electrical properties in spinal cord stimulation models.

Niranjan Khadka1, Boshuo Wang2, Marom Bikson1

  • 1Department of Biomedical Engineering, The City College of New York, CUNY, New York, NY.

Biorxiv : the Preprint Server for Biology
|December 9, 2024
PubMed
Summary

The quasi-static approximation (QSA) is valid for spinal cord stimulation (SCS) E-field and heating predictions across most spinal tissue dielectric spectrums. QSA remains reliable for voltage-controlled SCS and up to 10 kHz for current-controlled SCS.

Keywords:
Dielectric propertiesFrequency-dependent electrical propertiesQuasi-static approximationSpinal Cord StimulationTissue capacitance

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Area of Science:

  • Biomedical Engineering
  • Computational Neuroscience
  • Medical Physics

Background:

  • Spinal cord stimulation (SCS) models predict therapeutic outcomes by simulating electric fields (E-fields).
  • Current SCS models often use the quasi-static approximation (QSA), neglecting frequency-dependent tissue properties and wave propagation effects.
  • The accuracy of QSA for SCS, particularly at higher frequencies, requires detailed investigation.

Purpose of the Study:

  • To assess the impact of frequency-dependent conductivity and permittivity on E-fields during SCS.
  • To compare the accuracy of QSA with a frequency-dependent finite element method (FEM) model for SCS.
  • To evaluate the effects of tissue properties on spinal cord heating and E-field waveform distortion.

Main Methods:

  • Implemented a frequency-dependent FEM to model SCS across frequencies from 1 Hz to 10 MHz.
  • Simulated voltage-controlled (VC) and current-controlled (CC) SCS at epidural space, spinal cord, and root locations.
  • Compared FEM results with QSA predictions using varied tissue conductivity and assessed spinal cord heating and waveform distortion.

Main Results:

  • Tissue-specific electric properties and stimulation mode significantly impacted E-field magnitudes.
  • For VC-SCS, frequency-dependent properties yielded E-fields comparable to QSA with doubled epidural fat conductivity.
  • CC-SCS E-fields were minimally affected by frequency-dependent properties up to 10 kHz; spinal cord heating was unaffected by these properties in CC-SCS.

Conclusions:

  • QSA is a valid method for predicting SCS-induced E-fields and heating in spinal tissues across the alpha and beta dispersion regions for VC-SCS.
  • QSA remains reliable for CC-SCS up to 10 kHz, despite frequency-dependent tissue properties.
  • The study highlights the importance of considering tissue electrical properties and stimulation modes for accurate SCS modeling.