A principled approach to conductivity uncertainty analysis in electric field calculations

Guilherme B. Saturnino, Axel Thielscher, Kristoffer Hougaard Madsen, Thomas R. Knösche, Konstantin Weise*

*Corresponding author for this work

Research output: Contribution to journalJournal articleResearchpeer-review

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Abstract

Uncertainty surrounding ohmic tissue conductivity impedes accurate calculation of the electric fields generated by non-invasive brain stimulation. We present an efficient and generic technique for uncertainty and sensitivity analyses, which quantifies the reliability of field estimates and identifies the most influential parameters. For this purpose, we employ a non-intrusive generalized polynomial chaos expansion to compactly approximate the multidimensional dependency of the field on the conductivities. We demonstrate that the proposed pipeline yields detailed insight into the uncertainty of field estimates for transcranial magnetic stimulation (TMS) and transcranial direct current stimulation (tDCS), identifies the most relevant tissue conductivities, and highlights characteristic differences between stimulation methods. Specifically, we test the influence of conductivity variations on (i) the magnitude of the electric field generated at each gray matter location, (ii) its normal component relative to the cortical sheet, (iii) its overall magnitude (indexed by the 98th percentile), and (iv) its overall spatial distribution. We show that TMS fields are generally less affected by conductivity variations than tDCS fields. For both TMS and tDCS, conductivity uncertainty causes much higher uncertainty in the magnitude as compared to the direction and overall spatial distribution of the electric field. Whereas the TMS fields were predominantly influenced by gray and white matter conductivity, the tDCS fields were additionally dependent on skull and scalp conductivities. Comprehensive uncertainty analyses of complex systems achieved by the proposed technique are not possible with classical methods, such as Monte Carlo sampling, without extreme computational effort. In addition, our method has the advantages of directly yielding interpretable and intuitive output metrics and of being easily adaptable to new problems.
Original languageEnglish
JournalNeuroImage
Volume188
Pages (from-to)821-834
Number of pages14
ISSN1053-8119
DOIs
Publication statusPublished - 2019

Keywords

  • Non-invasive brain stimulation
  • Numerical methods
  • Sensitivity analysis
  • Transcranial direct current stimulation
  • Transcranial magnetic stimulation
  • Uncertainty analysis

Cite this

Saturnino, Guilherme B. ; Thielscher, Axel ; Madsen, Kristoffer Hougaard ; Knösche, Thomas R. ; Weise, Konstantin. / A principled approach to conductivity uncertainty analysis in electric field calculations. In: NeuroImage. 2019 ; Vol. 188. pp. 821-834.
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abstract = "Uncertainty surrounding ohmic tissue conductivity impedes accurate calculation of the electric fields generated by non-invasive brain stimulation. We present an efficient and generic technique for uncertainty and sensitivity analyses, which quantifies the reliability of field estimates and identifies the most influential parameters. For this purpose, we employ a non-intrusive generalized polynomial chaos expansion to compactly approximate the multidimensional dependency of the field on the conductivities. We demonstrate that the proposed pipeline yields detailed insight into the uncertainty of field estimates for transcranial magnetic stimulation (TMS) and transcranial direct current stimulation (tDCS), identifies the most relevant tissue conductivities, and highlights characteristic differences between stimulation methods. Specifically, we test the influence of conductivity variations on (i) the magnitude of the electric field generated at each gray matter location, (ii) its normal component relative to the cortical sheet, (iii) its overall magnitude (indexed by the 98th percentile), and (iv) its overall spatial distribution. We show that TMS fields are generally less affected by conductivity variations than tDCS fields. For both TMS and tDCS, conductivity uncertainty causes much higher uncertainty in the magnitude as compared to the direction and overall spatial distribution of the electric field. Whereas the TMS fields were predominantly influenced by gray and white matter conductivity, the tDCS fields were additionally dependent on skull and scalp conductivities. Comprehensive uncertainty analyses of complex systems achieved by the proposed technique are not possible with classical methods, such as Monte Carlo sampling, without extreme computational effort. In addition, our method has the advantages of directly yielding interpretable and intuitive output metrics and of being easily adaptable to new problems.",
keywords = "Non-invasive brain stimulation, Numerical methods, Sensitivity analysis, Transcranial direct current stimulation, Transcranial magnetic stimulation, Uncertainty analysis",
author = "Saturnino, {Guilherme B.} and Axel Thielscher and Madsen, {Kristoffer Hougaard} and Kn{\"o}sche, {Thomas R.} and Konstantin Weise",
year = "2019",
doi = "10.1016/j.neuroimage.2018.12.053",
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A principled approach to conductivity uncertainty analysis in electric field calculations. / Saturnino, Guilherme B.; Thielscher, Axel; Madsen, Kristoffer Hougaard; Knösche, Thomas R.; Weise, Konstantin.

In: NeuroImage, Vol. 188, 2019, p. 821-834.

Research output: Contribution to journalJournal articleResearchpeer-review

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T1 - A principled approach to conductivity uncertainty analysis in electric field calculations

AU - Saturnino, Guilherme B.

AU - Thielscher, Axel

AU - Madsen, Kristoffer Hougaard

AU - Knösche, Thomas R.

AU - Weise, Konstantin

PY - 2019

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N2 - Uncertainty surrounding ohmic tissue conductivity impedes accurate calculation of the electric fields generated by non-invasive brain stimulation. We present an efficient and generic technique for uncertainty and sensitivity analyses, which quantifies the reliability of field estimates and identifies the most influential parameters. For this purpose, we employ a non-intrusive generalized polynomial chaos expansion to compactly approximate the multidimensional dependency of the field on the conductivities. We demonstrate that the proposed pipeline yields detailed insight into the uncertainty of field estimates for transcranial magnetic stimulation (TMS) and transcranial direct current stimulation (tDCS), identifies the most relevant tissue conductivities, and highlights characteristic differences between stimulation methods. Specifically, we test the influence of conductivity variations on (i) the magnitude of the electric field generated at each gray matter location, (ii) its normal component relative to the cortical sheet, (iii) its overall magnitude (indexed by the 98th percentile), and (iv) its overall spatial distribution. We show that TMS fields are generally less affected by conductivity variations than tDCS fields. For both TMS and tDCS, conductivity uncertainty causes much higher uncertainty in the magnitude as compared to the direction and overall spatial distribution of the electric field. Whereas the TMS fields were predominantly influenced by gray and white matter conductivity, the tDCS fields were additionally dependent on skull and scalp conductivities. Comprehensive uncertainty analyses of complex systems achieved by the proposed technique are not possible with classical methods, such as Monte Carlo sampling, without extreme computational effort. In addition, our method has the advantages of directly yielding interpretable and intuitive output metrics and of being easily adaptable to new problems.

AB - Uncertainty surrounding ohmic tissue conductivity impedes accurate calculation of the electric fields generated by non-invasive brain stimulation. We present an efficient and generic technique for uncertainty and sensitivity analyses, which quantifies the reliability of field estimates and identifies the most influential parameters. For this purpose, we employ a non-intrusive generalized polynomial chaos expansion to compactly approximate the multidimensional dependency of the field on the conductivities. We demonstrate that the proposed pipeline yields detailed insight into the uncertainty of field estimates for transcranial magnetic stimulation (TMS) and transcranial direct current stimulation (tDCS), identifies the most relevant tissue conductivities, and highlights characteristic differences between stimulation methods. Specifically, we test the influence of conductivity variations on (i) the magnitude of the electric field generated at each gray matter location, (ii) its normal component relative to the cortical sheet, (iii) its overall magnitude (indexed by the 98th percentile), and (iv) its overall spatial distribution. We show that TMS fields are generally less affected by conductivity variations than tDCS fields. For both TMS and tDCS, conductivity uncertainty causes much higher uncertainty in the magnitude as compared to the direction and overall spatial distribution of the electric field. Whereas the TMS fields were predominantly influenced by gray and white matter conductivity, the tDCS fields were additionally dependent on skull and scalp conductivities. Comprehensive uncertainty analyses of complex systems achieved by the proposed technique are not possible with classical methods, such as Monte Carlo sampling, without extreme computational effort. In addition, our method has the advantages of directly yielding interpretable and intuitive output metrics and of being easily adaptable to new problems.

KW - Non-invasive brain stimulation

KW - Numerical methods

KW - Sensitivity analysis

KW - Transcranial direct current stimulation

KW - Transcranial magnetic stimulation

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JO - NeuroImage

JF - NeuroImage

SN - 1053-8119

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