Uncertainty Analysis in Transcranial Magnetic Stimulation Using Nonintrusive Polynomial Chaos Expansion
We propose a framework of nonintrusive polynomial chaos methods for transcranial magnetic stimulation (TMS) to investigate the influence of the uncertainty in the electrical conductivity of biological tissues on the induced electric field. The conductivities of three different tissues, namely, cereb...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Weise, Konstantin [verfasserIn] |
|---|
| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2015 |
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| Übergeordnetes Werk: |
Enthalten in: IEEE transactions on magnetics - New York, NY : IEEE, 1965, 51(2015), 7, Seite 1-8 |
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| Übergeordnetes Werk: |
volume:51 ; year:2015 ; number:7 ; pages:1-8 |
| Links: |
|---|
| DOI / URN: |
10.1109/TMAG.2015.2390593 |
|---|
| Katalog-ID: |
OLC1966664672 |
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| 520 | |a We propose a framework of nonintrusive polynomial chaos methods for transcranial magnetic stimulation (TMS) to investigate the influence of the uncertainty in the electrical conductivity of biological tissues on the induced electric field. The conductivities of three different tissues, namely, cerebrospinal fluid, gray matter (GM), and white matter, are modeled as uniformly distributed random variables. The investigations are performed on a simplified model of a cortical gyrus/sulcus structure. The statistical moments are calculated by means of a generalized polynomial chaos expansion using a regression and cubature approach. Furthermore, the results are compared with the solutions obtained by stochastic collocation. The accuracy of the methods to predict random field distributions was compared by applying different grids and orders of expansion. An investigation on the convergence of the expansion showed that in the present framework, an order 4 expansion is sufficient to determine results with an error of <;1%. The results indicate a major influence of the uncertainty in electrical conductivity on the induced electric field. The standard deviation exceeds values of 20%-40% of the mean induced electric field in the GM. A sensitivity analysis revealed that the uncertainty in electrical conductivity of the GM affects the solution the most. This paper outlines the importance of exact knowledge of the electrical conductivities in TMS in order to provide reliable numerical predictions of the induced electric field. Furthermore, it outlines the performance and the applicability of spectral methods in the framework of TMS for future studies. | ||
| 650 | 4 | |a electrical conductivity | |
| 650 | 4 | |a order 4 expansion | |
| 650 | 4 | |a cerebrospinal fluid conductivity modeling | |
| 650 | 4 | |a uncertain systems | |
| 650 | 4 | |a induced electric field prediction | |
| 650 | 4 | |a generalized polynomial chaos expansion | |
| 650 | 4 | |a gray matter conductivity modeling | |
| 650 | 4 | |a sensitivity analysis | |
| 650 | 4 | |a Coils | |
| 650 | 4 | |a Sensitivity | |
| 650 | 4 | |a nonintrusive polynomial chaos expansion | |
| 650 | 4 | |a chaos | |
| 650 | 4 | |a numerical analysis | |
| 650 | 4 | |a Conductivity | |
| 650 | 4 | |a TMS | |
| 650 | 4 | |a simplified cortical gyrus-sulcus structure model | |
| 650 | 4 | |a Interpolation | |
| 650 | 4 | |a Uncertainty | |
| 650 | 4 | |a random processes | |
| 650 | 4 | |a electric fields | |
| 650 | 4 | |a expansion order | |
| 650 | 4 | |a uniformly distributed random variable modeling | |
| 650 | 4 | |a regression analysis | |
| 650 | 4 | |a regression approach | |
| 650 | 4 | |a numerical prediction | |
| 650 | 4 | |a uncertainty analysis | |
| 650 | 4 | |a finite element method | |
| 650 | 4 | |a mean induced electric field | |
| 650 | 4 | |a brain models | |
| 650 | 4 | |a standard deviation | |
| 650 | 4 | |a GM conductivity modeling | |
| 650 | 4 | |a random field distribution prediction | |
| 650 | 4 | |a spectral method applicability | |
| 650 | 4 | |a bioelectric phenomena | |
| 650 | 4 | |a monte carlo method | |
| 650 | 4 | |a stochastic processes | |
| 650 | 4 | |a biological tissue electrical conductivity | |
| 650 | 4 | |a statistical moment calculation | |
| 650 | 4 | |a statistical analysis | |
| 650 | 4 | |a transcranial magnetic stimulation | |
| 650 | 4 | |a Eddy current | |
| 650 | 4 | |a stochastic collocation | |
| 650 | 4 | |a expansion convergence | |
| 650 | 4 | |a cubature approach | |
| 650 | 4 | |a electrical conductivity uncertainty effect | |
| 650 | 4 | |a white matter conductivity modeling | |
| 650 | 4 | |a biological tissues | |
| 650 | 4 | |a neurophysiology | |
| 650 | 4 | |a polynomials | |
| 650 | 4 | |a Electric fields | |
| 650 | 4 | |a Magnetic fields | |
| 650 | 4 | |a Mathematical models | |
| 650 | 4 | |a Health aspects | |
| 650 | 4 | |a Polynomials | |
| 650 | 4 | |a Electric stimulation | |
| 650 | 4 | |a Usage | |
| 650 | 4 | |a Models | |
| 700 | 1 | |a Di Rienzo, Luca |4 oth | |
| 700 | 1 | |a Brauer, Hartmut |4 oth | |
| 700 | 1 | |a Haueisen, Jens |4 oth | |
| 700 | 1 | |a Toepfer, Hannes |4 oth | |
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10.1109/TMAG.2015.2390593 doi PQ20160617 (DE-627)OLC1966664672 (DE-599)GBVOLC1966664672 (PRQ)c2633-ad15ef901945f51ef58d697b1944251ae7e2eedad3ef8f38934503067fa1cba40 (KEY)0061452120150000051000700001uncertaintyanalysisintranscranialmagneticstimulati DE-627 ger DE-627 rakwb eng 620 DNB 33.75 bkl 33.16 bkl Weise, Konstantin verfasserin aut Uncertainty Analysis in Transcranial Magnetic Stimulation Using Nonintrusive Polynomial Chaos Expansion 2015 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier We propose a framework of nonintrusive polynomial chaos methods for transcranial magnetic stimulation (TMS) to investigate the influence of the uncertainty in the electrical conductivity of biological tissues on the induced electric field. The conductivities of three different tissues, namely, cerebrospinal fluid, gray matter (GM), and white matter, are modeled as uniformly distributed random variables. The investigations are performed on a simplified model of a cortical gyrus/sulcus structure. The statistical moments are calculated by means of a generalized polynomial chaos expansion using a regression and cubature approach. Furthermore, the results are compared with the solutions obtained by stochastic collocation. The accuracy of the methods to predict random field distributions was compared by applying different grids and orders of expansion. An investigation on the convergence of the expansion showed that in the present framework, an order 4 expansion is sufficient to determine results with an error of <;1%. The results indicate a major influence of the uncertainty in electrical conductivity on the induced electric field. The standard deviation exceeds values of 20%-40% of the mean induced electric field in the GM. A sensitivity analysis revealed that the uncertainty in electrical conductivity of the GM affects the solution the most. This paper outlines the importance of exact knowledge of the electrical conductivities in TMS in order to provide reliable numerical predictions of the induced electric field. Furthermore, it outlines the performance and the applicability of spectral methods in the framework of TMS for future studies. electrical conductivity order 4 expansion cerebrospinal fluid conductivity modeling uncertain systems induced electric field prediction generalized polynomial chaos expansion gray matter conductivity modeling sensitivity analysis Coils Sensitivity nonintrusive polynomial chaos expansion chaos numerical analysis Conductivity TMS simplified cortical gyrus-sulcus structure model Interpolation Uncertainty random processes electric fields expansion order uniformly distributed random variable modeling regression analysis regression approach numerical prediction uncertainty analysis finite element method mean induced electric field brain models standard deviation GM conductivity modeling random field distribution prediction spectral method applicability bioelectric phenomena monte carlo method stochastic processes biological tissue electrical conductivity statistical moment calculation statistical analysis transcranial magnetic stimulation Eddy current stochastic collocation expansion convergence cubature approach electrical conductivity uncertainty effect white matter conductivity modeling biological tissues neurophysiology polynomials Electric fields Magnetic fields Mathematical models Health aspects Polynomials Electric stimulation Usage Models Di Rienzo, Luca oth Brauer, Hartmut oth Haueisen, Jens oth Toepfer, Hannes oth Enthalten in IEEE transactions on magnetics New York, NY : IEEE, 1965 51(2015), 7, Seite 1-8 (DE-627)129602078 (DE-600)241508-2 (DE-576)015095789 0018-9464 nnns volume:51 year:2015 number:7 pages:1-8 http://dx.doi.org/10.1109/TMAG.2015.2390593 Volltext http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=7006714 http://search.proquest.com/docview/1694450388 GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-PHY GBV_ILN_70 GBV_ILN_170 33.75 AVZ 33.16 AVZ AR 51 2015 7 1-8 |
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10.1109/TMAG.2015.2390593 doi PQ20160617 (DE-627)OLC1966664672 (DE-599)GBVOLC1966664672 (PRQ)c2633-ad15ef901945f51ef58d697b1944251ae7e2eedad3ef8f38934503067fa1cba40 (KEY)0061452120150000051000700001uncertaintyanalysisintranscranialmagneticstimulati DE-627 ger DE-627 rakwb eng 620 DNB 33.75 bkl 33.16 bkl Weise, Konstantin verfasserin aut Uncertainty Analysis in Transcranial Magnetic Stimulation Using Nonintrusive Polynomial Chaos Expansion 2015 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier We propose a framework of nonintrusive polynomial chaos methods for transcranial magnetic stimulation (TMS) to investigate the influence of the uncertainty in the electrical conductivity of biological tissues on the induced electric field. The conductivities of three different tissues, namely, cerebrospinal fluid, gray matter (GM), and white matter, are modeled as uniformly distributed random variables. The investigations are performed on a simplified model of a cortical gyrus/sulcus structure. The statistical moments are calculated by means of a generalized polynomial chaos expansion using a regression and cubature approach. Furthermore, the results are compared with the solutions obtained by stochastic collocation. The accuracy of the methods to predict random field distributions was compared by applying different grids and orders of expansion. An investigation on the convergence of the expansion showed that in the present framework, an order 4 expansion is sufficient to determine results with an error of <;1%. The results indicate a major influence of the uncertainty in electrical conductivity on the induced electric field. The standard deviation exceeds values of 20%-40% of the mean induced electric field in the GM. A sensitivity analysis revealed that the uncertainty in electrical conductivity of the GM affects the solution the most. This paper outlines the importance of exact knowledge of the electrical conductivities in TMS in order to provide reliable numerical predictions of the induced electric field. Furthermore, it outlines the performance and the applicability of spectral methods in the framework of TMS for future studies. electrical conductivity order 4 expansion cerebrospinal fluid conductivity modeling uncertain systems induced electric field prediction generalized polynomial chaos expansion gray matter conductivity modeling sensitivity analysis Coils Sensitivity nonintrusive polynomial chaos expansion chaos numerical analysis Conductivity TMS simplified cortical gyrus-sulcus structure model Interpolation Uncertainty random processes electric fields expansion order uniformly distributed random variable modeling regression analysis regression approach numerical prediction uncertainty analysis finite element method mean induced electric field brain models standard deviation GM conductivity modeling random field distribution prediction spectral method applicability bioelectric phenomena monte carlo method stochastic processes biological tissue electrical conductivity statistical moment calculation statistical analysis transcranial magnetic stimulation Eddy current stochastic collocation expansion convergence cubature approach electrical conductivity uncertainty effect white matter conductivity modeling biological tissues neurophysiology polynomials Electric fields Magnetic fields Mathematical models Health aspects Polynomials Electric stimulation Usage Models Di Rienzo, Luca oth Brauer, Hartmut oth Haueisen, Jens oth Toepfer, Hannes oth Enthalten in IEEE transactions on magnetics New York, NY : IEEE, 1965 51(2015), 7, Seite 1-8 (DE-627)129602078 (DE-600)241508-2 (DE-576)015095789 0018-9464 nnns volume:51 year:2015 number:7 pages:1-8 http://dx.doi.org/10.1109/TMAG.2015.2390593 Volltext http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=7006714 http://search.proquest.com/docview/1694450388 GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-PHY GBV_ILN_70 GBV_ILN_170 33.75 AVZ 33.16 AVZ AR 51 2015 7 1-8 |
| allfields_unstemmed |
10.1109/TMAG.2015.2390593 doi PQ20160617 (DE-627)OLC1966664672 (DE-599)GBVOLC1966664672 (PRQ)c2633-ad15ef901945f51ef58d697b1944251ae7e2eedad3ef8f38934503067fa1cba40 (KEY)0061452120150000051000700001uncertaintyanalysisintranscranialmagneticstimulati DE-627 ger DE-627 rakwb eng 620 DNB 33.75 bkl 33.16 bkl Weise, Konstantin verfasserin aut Uncertainty Analysis in Transcranial Magnetic Stimulation Using Nonintrusive Polynomial Chaos Expansion 2015 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier We propose a framework of nonintrusive polynomial chaos methods for transcranial magnetic stimulation (TMS) to investigate the influence of the uncertainty in the electrical conductivity of biological tissues on the induced electric field. The conductivities of three different tissues, namely, cerebrospinal fluid, gray matter (GM), and white matter, are modeled as uniformly distributed random variables. The investigations are performed on a simplified model of a cortical gyrus/sulcus structure. The statistical moments are calculated by means of a generalized polynomial chaos expansion using a regression and cubature approach. Furthermore, the results are compared with the solutions obtained by stochastic collocation. The accuracy of the methods to predict random field distributions was compared by applying different grids and orders of expansion. An investigation on the convergence of the expansion showed that in the present framework, an order 4 expansion is sufficient to determine results with an error of <;1%. The results indicate a major influence of the uncertainty in electrical conductivity on the induced electric field. The standard deviation exceeds values of 20%-40% of the mean induced electric field in the GM. A sensitivity analysis revealed that the uncertainty in electrical conductivity of the GM affects the solution the most. This paper outlines the importance of exact knowledge of the electrical conductivities in TMS in order to provide reliable numerical predictions of the induced electric field. Furthermore, it outlines the performance and the applicability of spectral methods in the framework of TMS for future studies. electrical conductivity order 4 expansion cerebrospinal fluid conductivity modeling uncertain systems induced electric field prediction generalized polynomial chaos expansion gray matter conductivity modeling sensitivity analysis Coils Sensitivity nonintrusive polynomial chaos expansion chaos numerical analysis Conductivity TMS simplified cortical gyrus-sulcus structure model Interpolation Uncertainty random processes electric fields expansion order uniformly distributed random variable modeling regression analysis regression approach numerical prediction uncertainty analysis finite element method mean induced electric field brain models standard deviation GM conductivity modeling random field distribution prediction spectral method applicability bioelectric phenomena monte carlo method stochastic processes biological tissue electrical conductivity statistical moment calculation statistical analysis transcranial magnetic stimulation Eddy current stochastic collocation expansion convergence cubature approach electrical conductivity uncertainty effect white matter conductivity modeling biological tissues neurophysiology polynomials Electric fields Magnetic fields Mathematical models Health aspects Polynomials Electric stimulation Usage Models Di Rienzo, Luca oth Brauer, Hartmut oth Haueisen, Jens oth Toepfer, Hannes oth Enthalten in IEEE transactions on magnetics New York, NY : IEEE, 1965 51(2015), 7, Seite 1-8 (DE-627)129602078 (DE-600)241508-2 (DE-576)015095789 0018-9464 nnns volume:51 year:2015 number:7 pages:1-8 http://dx.doi.org/10.1109/TMAG.2015.2390593 Volltext http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=7006714 http://search.proquest.com/docview/1694450388 GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-PHY GBV_ILN_70 GBV_ILN_170 33.75 AVZ 33.16 AVZ AR 51 2015 7 1-8 |
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10.1109/TMAG.2015.2390593 doi PQ20160617 (DE-627)OLC1966664672 (DE-599)GBVOLC1966664672 (PRQ)c2633-ad15ef901945f51ef58d697b1944251ae7e2eedad3ef8f38934503067fa1cba40 (KEY)0061452120150000051000700001uncertaintyanalysisintranscranialmagneticstimulati DE-627 ger DE-627 rakwb eng 620 DNB 33.75 bkl 33.16 bkl Weise, Konstantin verfasserin aut Uncertainty Analysis in Transcranial Magnetic Stimulation Using Nonintrusive Polynomial Chaos Expansion 2015 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier We propose a framework of nonintrusive polynomial chaos methods for transcranial magnetic stimulation (TMS) to investigate the influence of the uncertainty in the electrical conductivity of biological tissues on the induced electric field. The conductivities of three different tissues, namely, cerebrospinal fluid, gray matter (GM), and white matter, are modeled as uniformly distributed random variables. The investigations are performed on a simplified model of a cortical gyrus/sulcus structure. The statistical moments are calculated by means of a generalized polynomial chaos expansion using a regression and cubature approach. Furthermore, the results are compared with the solutions obtained by stochastic collocation. The accuracy of the methods to predict random field distributions was compared by applying different grids and orders of expansion. An investigation on the convergence of the expansion showed that in the present framework, an order 4 expansion is sufficient to determine results with an error of <;1%. The results indicate a major influence of the uncertainty in electrical conductivity on the induced electric field. The standard deviation exceeds values of 20%-40% of the mean induced electric field in the GM. A sensitivity analysis revealed that the uncertainty in electrical conductivity of the GM affects the solution the most. This paper outlines the importance of exact knowledge of the electrical conductivities in TMS in order to provide reliable numerical predictions of the induced electric field. Furthermore, it outlines the performance and the applicability of spectral methods in the framework of TMS for future studies. electrical conductivity order 4 expansion cerebrospinal fluid conductivity modeling uncertain systems induced electric field prediction generalized polynomial chaos expansion gray matter conductivity modeling sensitivity analysis Coils Sensitivity nonintrusive polynomial chaos expansion chaos numerical analysis Conductivity TMS simplified cortical gyrus-sulcus structure model Interpolation Uncertainty random processes electric fields expansion order uniformly distributed random variable modeling regression analysis regression approach numerical prediction uncertainty analysis finite element method mean induced electric field brain models standard deviation GM conductivity modeling random field distribution prediction spectral method applicability bioelectric phenomena monte carlo method stochastic processes biological tissue electrical conductivity statistical moment calculation statistical analysis transcranial magnetic stimulation Eddy current stochastic collocation expansion convergence cubature approach electrical conductivity uncertainty effect white matter conductivity modeling biological tissues neurophysiology polynomials Electric fields Magnetic fields Mathematical models Health aspects Polynomials Electric stimulation Usage Models Di Rienzo, Luca oth Brauer, Hartmut oth Haueisen, Jens oth Toepfer, Hannes oth Enthalten in IEEE transactions on magnetics New York, NY : IEEE, 1965 51(2015), 7, Seite 1-8 (DE-627)129602078 (DE-600)241508-2 (DE-576)015095789 0018-9464 nnns volume:51 year:2015 number:7 pages:1-8 http://dx.doi.org/10.1109/TMAG.2015.2390593 Volltext http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=7006714 http://search.proquest.com/docview/1694450388 GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-PHY GBV_ILN_70 GBV_ILN_170 33.75 AVZ 33.16 AVZ AR 51 2015 7 1-8 |
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10.1109/TMAG.2015.2390593 doi PQ20160617 (DE-627)OLC1966664672 (DE-599)GBVOLC1966664672 (PRQ)c2633-ad15ef901945f51ef58d697b1944251ae7e2eedad3ef8f38934503067fa1cba40 (KEY)0061452120150000051000700001uncertaintyanalysisintranscranialmagneticstimulati DE-627 ger DE-627 rakwb eng 620 DNB 33.75 bkl 33.16 bkl Weise, Konstantin verfasserin aut Uncertainty Analysis in Transcranial Magnetic Stimulation Using Nonintrusive Polynomial Chaos Expansion 2015 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier We propose a framework of nonintrusive polynomial chaos methods for transcranial magnetic stimulation (TMS) to investigate the influence of the uncertainty in the electrical conductivity of biological tissues on the induced electric field. The conductivities of three different tissues, namely, cerebrospinal fluid, gray matter (GM), and white matter, are modeled as uniformly distributed random variables. The investigations are performed on a simplified model of a cortical gyrus/sulcus structure. The statistical moments are calculated by means of a generalized polynomial chaos expansion using a regression and cubature approach. Furthermore, the results are compared with the solutions obtained by stochastic collocation. The accuracy of the methods to predict random field distributions was compared by applying different grids and orders of expansion. An investigation on the convergence of the expansion showed that in the present framework, an order 4 expansion is sufficient to determine results with an error of <;1%. The results indicate a major influence of the uncertainty in electrical conductivity on the induced electric field. The standard deviation exceeds values of 20%-40% of the mean induced electric field in the GM. A sensitivity analysis revealed that the uncertainty in electrical conductivity of the GM affects the solution the most. This paper outlines the importance of exact knowledge of the electrical conductivities in TMS in order to provide reliable numerical predictions of the induced electric field. Furthermore, it outlines the performance and the applicability of spectral methods in the framework of TMS for future studies. electrical conductivity order 4 expansion cerebrospinal fluid conductivity modeling uncertain systems induced electric field prediction generalized polynomial chaos expansion gray matter conductivity modeling sensitivity analysis Coils Sensitivity nonintrusive polynomial chaos expansion chaos numerical analysis Conductivity TMS simplified cortical gyrus-sulcus structure model Interpolation Uncertainty random processes electric fields expansion order uniformly distributed random variable modeling regression analysis regression approach numerical prediction uncertainty analysis finite element method mean induced electric field brain models standard deviation GM conductivity modeling random field distribution prediction spectral method applicability bioelectric phenomena monte carlo method stochastic processes biological tissue electrical conductivity statistical moment calculation statistical analysis transcranial magnetic stimulation Eddy current stochastic collocation expansion convergence cubature approach electrical conductivity uncertainty effect white matter conductivity modeling biological tissues neurophysiology polynomials Electric fields Magnetic fields Mathematical models Health aspects Polynomials Electric stimulation Usage Models Di Rienzo, Luca oth Brauer, Hartmut oth Haueisen, Jens oth Toepfer, Hannes oth Enthalten in IEEE transactions on magnetics New York, NY : IEEE, 1965 51(2015), 7, Seite 1-8 (DE-627)129602078 (DE-600)241508-2 (DE-576)015095789 0018-9464 nnns volume:51 year:2015 number:7 pages:1-8 http://dx.doi.org/10.1109/TMAG.2015.2390593 Volltext http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=7006714 http://search.proquest.com/docview/1694450388 GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-PHY GBV_ILN_70 GBV_ILN_170 33.75 AVZ 33.16 AVZ AR 51 2015 7 1-8 |
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The conductivities of three different tissues, namely, cerebrospinal fluid, gray matter (GM), and white matter, are modeled as uniformly distributed random variables. The investigations are performed on a simplified model of a cortical gyrus/sulcus structure. The statistical moments are calculated by means of a generalized polynomial chaos expansion using a regression and cubature approach. Furthermore, the results are compared with the solutions obtained by stochastic collocation. The accuracy of the methods to predict random field distributions was compared by applying different grids and orders of expansion. An investigation on the convergence of the expansion showed that in the present framework, an order 4 expansion is sufficient to determine results with an error of <;1%. The results indicate a major influence of the uncertainty in electrical conductivity on the induced electric field. The standard deviation exceeds values of 20%-40% of the mean induced electric field in the GM. 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Weise, Konstantin ddc 620 bkl 33.75 bkl 33.16 misc electrical conductivity misc order 4 expansion misc cerebrospinal fluid conductivity modeling misc uncertain systems misc induced electric field prediction misc generalized polynomial chaos expansion misc gray matter conductivity modeling misc sensitivity analysis misc Coils misc Sensitivity misc nonintrusive polynomial chaos expansion misc chaos misc numerical analysis misc Conductivity misc TMS misc simplified cortical gyrus-sulcus structure model misc Interpolation misc Uncertainty misc random processes misc electric fields misc expansion order misc uniformly distributed random variable modeling misc regression analysis misc regression approach misc numerical prediction misc uncertainty analysis misc finite element method misc mean induced electric field misc brain models misc standard deviation misc GM conductivity modeling misc random field distribution prediction misc spectral method applicability misc bioelectric phenomena misc monte carlo method misc stochastic processes misc biological tissue electrical conductivity misc statistical moment calculation misc statistical analysis misc transcranial magnetic stimulation misc Eddy current misc stochastic collocation misc expansion convergence misc cubature approach misc electrical conductivity uncertainty effect misc white matter conductivity modeling misc biological tissues misc neurophysiology misc polynomials misc Electric fields misc Magnetic fields misc Mathematical models misc Health aspects misc Polynomials misc Electric stimulation misc Usage misc Models Uncertainty Analysis in Transcranial Magnetic Stimulation Using Nonintrusive Polynomial Chaos Expansion |
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620 DNB 33.75 bkl 33.16 bkl Uncertainty Analysis in Transcranial Magnetic Stimulation Using Nonintrusive Polynomial Chaos Expansion electrical conductivity order 4 expansion cerebrospinal fluid conductivity modeling uncertain systems induced electric field prediction generalized polynomial chaos expansion gray matter conductivity modeling sensitivity analysis Coils Sensitivity nonintrusive polynomial chaos expansion chaos numerical analysis Conductivity TMS simplified cortical gyrus-sulcus structure model Interpolation Uncertainty random processes electric fields expansion order uniformly distributed random variable modeling regression analysis regression approach numerical prediction uncertainty analysis finite element method mean induced electric field brain models standard deviation GM conductivity modeling random field distribution prediction spectral method applicability bioelectric phenomena monte carlo method stochastic processes biological tissue electrical conductivity statistical moment calculation statistical analysis transcranial magnetic stimulation Eddy current stochastic collocation expansion convergence cubature approach electrical conductivity uncertainty effect white matter conductivity modeling biological tissues neurophysiology polynomials Electric fields Magnetic fields Mathematical models Health aspects Polynomials Electric stimulation Usage Models |
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ddc 620 bkl 33.75 bkl 33.16 misc electrical conductivity misc order 4 expansion misc cerebrospinal fluid conductivity modeling misc uncertain systems misc induced electric field prediction misc generalized polynomial chaos expansion misc gray matter conductivity modeling misc sensitivity analysis misc Coils misc Sensitivity misc nonintrusive polynomial chaos expansion misc chaos misc numerical analysis misc Conductivity misc TMS misc simplified cortical gyrus-sulcus structure model misc Interpolation misc Uncertainty misc random processes misc electric fields misc expansion order misc uniformly distributed random variable modeling misc regression analysis misc regression approach misc numerical prediction misc uncertainty analysis misc finite element method misc mean induced electric field misc brain models misc standard deviation misc GM conductivity modeling misc random field distribution prediction misc spectral method applicability misc bioelectric phenomena misc monte carlo method misc stochastic processes misc biological tissue electrical conductivity misc statistical moment calculation misc statistical analysis misc transcranial magnetic stimulation misc Eddy current misc stochastic collocation misc expansion convergence misc cubature approach misc electrical conductivity uncertainty effect misc white matter conductivity modeling misc biological tissues misc neurophysiology misc polynomials misc Electric fields misc Magnetic fields misc Mathematical models misc Health aspects misc Polynomials misc Electric stimulation misc Usage misc Models |
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Uncertainty Analysis in Transcranial Magnetic Stimulation Using Nonintrusive Polynomial Chaos Expansion |
| abstract |
We propose a framework of nonintrusive polynomial chaos methods for transcranial magnetic stimulation (TMS) to investigate the influence of the uncertainty in the electrical conductivity of biological tissues on the induced electric field. The conductivities of three different tissues, namely, cerebrospinal fluid, gray matter (GM), and white matter, are modeled as uniformly distributed random variables. The investigations are performed on a simplified model of a cortical gyrus/sulcus structure. The statistical moments are calculated by means of a generalized polynomial chaos expansion using a regression and cubature approach. Furthermore, the results are compared with the solutions obtained by stochastic collocation. The accuracy of the methods to predict random field distributions was compared by applying different grids and orders of expansion. An investigation on the convergence of the expansion showed that in the present framework, an order 4 expansion is sufficient to determine results with an error of <;1%. The results indicate a major influence of the uncertainty in electrical conductivity on the induced electric field. The standard deviation exceeds values of 20%-40% of the mean induced electric field in the GM. A sensitivity analysis revealed that the uncertainty in electrical conductivity of the GM affects the solution the most. This paper outlines the importance of exact knowledge of the electrical conductivities in TMS in order to provide reliable numerical predictions of the induced electric field. Furthermore, it outlines the performance and the applicability of spectral methods in the framework of TMS for future studies. |
| abstractGer |
We propose a framework of nonintrusive polynomial chaos methods for transcranial magnetic stimulation (TMS) to investigate the influence of the uncertainty in the electrical conductivity of biological tissues on the induced electric field. The conductivities of three different tissues, namely, cerebrospinal fluid, gray matter (GM), and white matter, are modeled as uniformly distributed random variables. The investigations are performed on a simplified model of a cortical gyrus/sulcus structure. The statistical moments are calculated by means of a generalized polynomial chaos expansion using a regression and cubature approach. Furthermore, the results are compared with the solutions obtained by stochastic collocation. The accuracy of the methods to predict random field distributions was compared by applying different grids and orders of expansion. An investigation on the convergence of the expansion showed that in the present framework, an order 4 expansion is sufficient to determine results with an error of <;1%. The results indicate a major influence of the uncertainty in electrical conductivity on the induced electric field. The standard deviation exceeds values of 20%-40% of the mean induced electric field in the GM. A sensitivity analysis revealed that the uncertainty in electrical conductivity of the GM affects the solution the most. This paper outlines the importance of exact knowledge of the electrical conductivities in TMS in order to provide reliable numerical predictions of the induced electric field. Furthermore, it outlines the performance and the applicability of spectral methods in the framework of TMS for future studies. |
| abstract_unstemmed |
We propose a framework of nonintrusive polynomial chaos methods for transcranial magnetic stimulation (TMS) to investigate the influence of the uncertainty in the electrical conductivity of biological tissues on the induced electric field. The conductivities of three different tissues, namely, cerebrospinal fluid, gray matter (GM), and white matter, are modeled as uniformly distributed random variables. The investigations are performed on a simplified model of a cortical gyrus/sulcus structure. The statistical moments are calculated by means of a generalized polynomial chaos expansion using a regression and cubature approach. Furthermore, the results are compared with the solutions obtained by stochastic collocation. The accuracy of the methods to predict random field distributions was compared by applying different grids and orders of expansion. An investigation on the convergence of the expansion showed that in the present framework, an order 4 expansion is sufficient to determine results with an error of <;1%. The results indicate a major influence of the uncertainty in electrical conductivity on the induced electric field. The standard deviation exceeds values of 20%-40% of the mean induced electric field in the GM. A sensitivity analysis revealed that the uncertainty in electrical conductivity of the GM affects the solution the most. This paper outlines the importance of exact knowledge of the electrical conductivities in TMS in order to provide reliable numerical predictions of the induced electric field. Furthermore, it outlines the performance and the applicability of spectral methods in the framework of TMS for future studies. |
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<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000caa a2200265 4500</leader><controlfield tag="001">OLC1966664672</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20220223135052.0</controlfield><controlfield tag="007">tu</controlfield><controlfield tag="008">160206s2015 xx ||||| 00| ||eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1109/TMAG.2015.2390593</subfield><subfield code="2">doi</subfield></datafield><datafield tag="028" ind1="5" ind2="2"><subfield code="a">PQ20160617</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)OLC1966664672</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)GBVOLC1966664672</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(PRQ)c2633-ad15ef901945f51ef58d697b1944251ae7e2eedad3ef8f38934503067fa1cba40</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(KEY)0061452120150000051000700001uncertaintyanalysisintranscranialmagneticstimulati</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-627</subfield><subfield code="b">ger</subfield><subfield code="c">DE-627</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1=" " ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="082" ind1="0" ind2="4"><subfield code="a">620</subfield><subfield code="q">DNB</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">33.75</subfield><subfield code="2">bkl</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">33.16</subfield><subfield code="2">bkl</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Weise, Konstantin</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Uncertainty Analysis in Transcranial Magnetic Stimulation Using Nonintrusive Polynomial Chaos Expansion</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2015</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">Text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">ohne Hilfsmittel zu benutzen</subfield><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Band</subfield><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">We propose a framework of nonintrusive polynomial chaos methods for transcranial magnetic stimulation (TMS) to investigate the influence of the uncertainty in the electrical conductivity of biological tissues on the induced electric field. The conductivities of three different tissues, namely, cerebrospinal fluid, gray matter (GM), and white matter, are modeled as uniformly distributed random variables. The investigations are performed on a simplified model of a cortical gyrus/sulcus structure. The statistical moments are calculated by means of a generalized polynomial chaos expansion using a regression and cubature approach. Furthermore, the results are compared with the solutions obtained by stochastic collocation. The accuracy of the methods to predict random field distributions was compared by applying different grids and orders of expansion. An investigation on the convergence of the expansion showed that in the present framework, an order 4 expansion is sufficient to determine results with an error of <;1%. The results indicate a major influence of the uncertainty in electrical conductivity on the induced electric field. The standard deviation exceeds values of 20%-40% of the mean induced electric field in the GM. A sensitivity analysis revealed that the uncertainty in electrical conductivity of the GM affects the solution the most. This paper outlines the importance of exact knowledge of the electrical conductivities in TMS in order to provide reliable numerical predictions of the induced electric field. 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