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Sensitivity analysis for the EEG forward problem.

Troparevsky MI, Rubio D, Saintier N - Front Comput Neurosci (2010)

Bottom Line: Both functions were considered by some authors who compared their results for different dynamical systems (see Banks and Bihari, 2001; Kappel and Batzel, 2006; Banks et al., 2008).Afterward we compute the GSF for the same model.We perform some numerical experiments for both types of sensitivity functions and compare the results.

View Article: PubMed Central - PubMed

Affiliation: Departamento de Matemática, Facultad de Ingeniería, Universidad de Buenos Aires Buenos Aires, Argentina.

ABSTRACT
Sensitivity analysis can provide useful information when one is interested in identifying the parameter θ of a system since it measures the variations of the output u when θ changes. In the literature two different sensitivity functions are frequently used: the traditional sensitivity functions (TSF) and the generalized sensitivity functions (GSF). They can help to determine the time instants where the output of a dynamical system has more information about the value of its parameters in order to carry on an estimation process. Both functions were considered by some authors who compared their results for different dynamical systems (see Banks and Bihari, 2001; Kappel and Batzel, 2006; Banks et al., 2008). In this work we apply the TSF and the GSF to analyze the sensitivity of the 3D Poisson-type equation with interfaces of the forward problem of electroencephalography. In a simple model where we consider the head as a volume consisting of nested homogeneous sets, we establish the differential equations that correspond to TSF with respect to the value of the conductivity of the different tissues and deduce the corresponding integral equations. Afterward we compute the GSF for the same model. We perform some numerical experiments for both types of sensitivity functions and compare the results.

No MeSH data available.


Traditional sensitivity functions (in absolute value) for the dipole position rq = (0. 3, 0.4, 0) and different moments (DM) M, (A) DM M = (6, 8, 0) (radial) (B) DM M = (1, −1, 1) (C) DM M = (4, 3, −2) (D) DM M = (4, −3, 0) (tangential).
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Figure 2: Traditional sensitivity functions (in absolute value) for the dipole position rq = (0. 3, 0.4, 0) and different moments (DM) M, (A) DM M = (6, 8, 0) (radial) (B) DM M = (1, −1, 1) (C) DM M = (4, 3, −2) (D) DM M = (4, −3, 0) (tangential).

Mentions: In Figure 2, we show the absolute value of the TSF on the scalp for the same dipole location rq = (0.3, 0.4, 0) and different dipoles moments. The stars indicate the positions of the scalp electrodes. In order to compare both sensitivity functions we have put an M at the position of the electrode where the two highest values of GSFinc are achieved.


Sensitivity analysis for the EEG forward problem.

Troparevsky MI, Rubio D, Saintier N - Front Comput Neurosci (2010)

Traditional sensitivity functions (in absolute value) for the dipole position rq = (0. 3, 0.4, 0) and different moments (DM) M, (A) DM M = (6, 8, 0) (radial) (B) DM M = (1, −1, 1) (C) DM M = (4, 3, −2) (D) DM M = (4, −3, 0) (tangential).
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC2958054&req=5

Figure 2: Traditional sensitivity functions (in absolute value) for the dipole position rq = (0. 3, 0.4, 0) and different moments (DM) M, (A) DM M = (6, 8, 0) (radial) (B) DM M = (1, −1, 1) (C) DM M = (4, 3, −2) (D) DM M = (4, −3, 0) (tangential).
Mentions: In Figure 2, we show the absolute value of the TSF on the scalp for the same dipole location rq = (0.3, 0.4, 0) and different dipoles moments. The stars indicate the positions of the scalp electrodes. In order to compare both sensitivity functions we have put an M at the position of the electrode where the two highest values of GSFinc are achieved.

Bottom Line: Both functions were considered by some authors who compared their results for different dynamical systems (see Banks and Bihari, 2001; Kappel and Batzel, 2006; Banks et al., 2008).Afterward we compute the GSF for the same model.We perform some numerical experiments for both types of sensitivity functions and compare the results.

View Article: PubMed Central - PubMed

Affiliation: Departamento de Matemática, Facultad de Ingeniería, Universidad de Buenos Aires Buenos Aires, Argentina.

ABSTRACT
Sensitivity analysis can provide useful information when one is interested in identifying the parameter θ of a system since it measures the variations of the output u when θ changes. In the literature two different sensitivity functions are frequently used: the traditional sensitivity functions (TSF) and the generalized sensitivity functions (GSF). They can help to determine the time instants where the output of a dynamical system has more information about the value of its parameters in order to carry on an estimation process. Both functions were considered by some authors who compared their results for different dynamical systems (see Banks and Bihari, 2001; Kappel and Batzel, 2006; Banks et al., 2008). In this work we apply the TSF and the GSF to analyze the sensitivity of the 3D Poisson-type equation with interfaces of the forward problem of electroencephalography. In a simple model where we consider the head as a volume consisting of nested homogeneous sets, we establish the differential equations that correspond to TSF with respect to the value of the conductivity of the different tissues and deduce the corresponding integral equations. Afterward we compute the GSF for the same model. We perform some numerical experiments for both types of sensitivity functions and compare the results.

No MeSH data available.