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...

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Bibliographic Details
Published in:IEEE transactions on magnetics 2015-07, Vol.51 (7), p.1-8
Main Authors: Weise, Konstantin, Di Rienzo, Luca, Brauer, Hartmut, Haueisen, Jens, Toepfer, Hannes
Format: Article
Language:English
Subjects:
Chaos theory
Coils
Conductivity
Eddy current
Electric fields
Electrical conductivity
Electrical resistivity
finite element method
Interpolation
Magnetism
Mathematical models
monte carlo method
Polynomials
regression analysis
Resistivity
Sensitivity
sensitivity analysis
statistical analysis
stochastic processes
transcranial magnetic stimulation
uncertain systems
Uncertainty
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Summary: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
ISSN:0018-9464
1941-0069
DOI:10.1109/TMAG.2015.2390593