Electric lead field for a piecewise homogeneous volume conductor model of the head

A new method is presented for computing the electric lead field of a realistic head shape model which has piecewise homogenous conductivity. The basic formulae are derived using the well-known reciprocity theorem. Previously described methods are also based upon this theorem, but these first calculate the electric potential inside the head by a scalar boundary element method (BEM), and then approximate the ohmic current density by some sort of gradient. In contrast, this paper proposes the direct evaluation of the ohmic current density by discretizing the vector Green's second identity which leads to a rector version of BEM. This approach also allows the derivation of the same equations for the three concentric spheres model as obtained by Rush and Driscoll (1969). The results of simulations on a spherical head model indicate that the use of a vector BEM leads to an improvement of accuracy in the computation of the ohmic current density with respect to those reported previously, in term of different measures of error.

[1]  A. van Oosterom,et al.  The potential distribution generated by surface electrodes in inhomogeneous volume conductors of arbitrary shape , 1991, IEEE Transactions on Biomedical Engineering.

[2]  K. Foster,et al.  Dielectric properties of tissues and biological materials: a critical review. , 1989, Critical reviews in biomedical engineering.

[3]  R PLONSEY,et al.  RECIPROCITY APPLIED TO VOLUME CONDUCTORS AND THE ECG. , 1963, IEEE transactions on bio-medical engineering.

[4]  M. Lynn,et al.  The Use of Multiple Deflations in the Numerical Solution of Singular Systems of Equations, with Applications to Potential Theory , 1968 .

[5]  D. A. Driscoll,et al.  Current Distribution in the Brain From Surface Electrodes , 1968, Anesthesia and analgesia.

[6]  Kazutomo Yunokuchi,et al.  Tests of EEG localization accuracy using implanted sources in the human brain , 1991, Annals of neurology.

[7]  G. Fein,et al.  Improved method for computation of potentials in a realistic head shape model , 1995, IEEE Transactions on Biomedical Engineering.

[8]  S. Sato,et al.  How well does a three-sphere model predict positions of dipoles in a realistically shaped head? , 1993, Electroencephalography and clinical neurophysiology.

[9]  R. McFee,et al.  Electrocardiographic Leads: I. Introduction , 1953, Circulation.

[10]  F. J. Claydon,et al.  A volume conductor model of the thorax for the study of defibrillation fields , 1988, IEEE Transactions on Biomedical Engineering.

[11]  Onno W. Weier,et al.  On the numerical accuracy of the boundary element method (EEG application) , 1989, IEEE Transactions on Biomedical Engineering.

[12]  D. Lehmann,et al.  Low resolution electromagnetic tomography: a new method for localizing electrical activity in the brain. , 1994, International journal of psychophysiology : official journal of the International Organization of Psychophysiology.

[13]  P. Morse,et al.  Methods of theoretical physics , 1955 .

[14]  R E Ideker,et al.  Eccentric dipole in a spherical medium: generalized expression for surface potentials. , 1973, IEEE transactions on bio-medical engineering.

[15]  J. D. Munck.  A linear discretization of the volume conductor boundary integral equation using analytically integrated elements (electrophysiology application) , 1992 .

[16]  P. Nunez,et al.  Electric fields of the brain , 1981 .

[17]  D. A. Driscoll,et al.  EEG electrode sensitivity--an application of reciprocity. , 1969, IEEE transactions on bio-medical engineering.

[18]  Jorge J. Riera,et al.  Discrete Spline Electric-Magnetic Tomography (DSPECT) Based on Realistic Neuroanatomy , 2000 .

[19]  Grace Wahba,et al.  8. Fredholm Integral Equations of the First Kind , 1990 .

[20]  G. Wahba.  Spline models for observational data , 1990 .

[21]  H. Schwan,et al.  THE CONDUCTIVITY OF LIVING TISSUES , 1957, Annals of the New York Academy of Sciences.

[22]  D. B. Heppner,et al.  Considerations of quasi-stationarity in electrophysiological systems. , 1967, The Bulletin of mathematical biophysics.

[23]  Robert W. Dykes,et al.  Conductivity in the somatosensory cortex of the cat — evidence for cortical anisotropy , 1979, Brain Research.

[24]  D. Brody,et al.  A model which demonstrates the quantitative relationship between the electromotive forces of the heart and the extremity leads. , 1953, American heart journal.

[25]  John W. Evans,et al.  A Theoretical Basis for Determining Heart-Lead Relationships of the Equivalent Cardiac Multipole , 1961 .