Patent Application: US-27670094-A

Abstract:
the spatial resolution of electroencephalograph medical images is improved using &# 34 ; deblurring &# 34 ; based on a digital computer based analysis using volumetric finite elements and a biophysical model of the passive electrical conductivity of a subject &# 39 ; s head .

Description:
the present invention is illustrated in fig1 . as shown therein , there are three main processes , represented in three vertical columns of subprocess boxes . the processes are : 1 ) computation of deblurring matrix ; 2 ) determination of scalp surface elements from eeg electrode coordinates ; and 3 ) computation of deblurred eeg data . the left column shows how the inverted finite element transformation matrix ( deblurring matrix ) is computed from data about head shape and size and tissue thicknesses . these data are obtained from mr images or from direct head measurements and anthropometric data and are used to automatically compute scalp , skull and outer brain surfaces . imaginary mathematical radial ray vectors are radially projected through the computed scalp , skull and outer brain surfaces and prism shaped finite elements are made from triangles on two adjacent surfaces whose edges are defined by connecting points of intersection ( mesh points ) of the ray vectors with the three surfaces . conductivity factors for scalp , skull , and diploe ( porous bone layer ) are obtained by estimation as described in u . s . patent application ser . no . 07 / 868 , 724 , now u . s . pat . no . 5 , 331 , 970 , or by reference to anthropometric data as described herein . these conductivity values are then used , in a software program run on a digital computer , to determine the actual conductivity of each finite element , and a transformation matrix relating the potential distribution at the brain ( cortical ) surface with the potential distribution at the scalp is computed using poisson &# 39 ; s equation . this transformation matrix is inverted , an operation made possible by the manner of constructing volumetric finite elements from mesh points defined by radial ray vectors . the middle column shows how the boundaries of the scalp surface elements are determined from the eeg electrode coordinates . first , eeg electrode coordinates are determined by direct measurement or estimation as described in u . s . pat . no . 5 , 119 , 816 . these coordinates are then aligned with the computed scalp surface using fiducial reference points and mathematical surface alignment algorithms as described in u . s . pats . no . 4 , 736 , 751 and 5 , 119 , 816 . the boundaries of the scalp surface elements are then determined by a common area of patches determined by the aligned scalp electrode coordinates and the scalp mesh points defined by the radial ray vectors . the fight column shows how the deblurred eeg data are computed from the eeg data measured at the scalp . first the scalp - recorded eeg is interpolated to make a potential distribution which can be associated with each of the scalp surface elements ( the finite element vertices at the scalp surface ) as determined from process 2 ). then the deblurred eeg data are computed by multiplying the interpolated eeg data by the inverted transformation matrix determined in process 1 ). 1 . more automated finite element modeling of scalp and skull layers with mris the air / scalp , scalp / skull , and skull / cortex tissue boundaries are found automatically using a software program for boundary surface detection , in a digital computer , by exploiting the facts that these surfaces are relatively large and are characterized by significant image contrast in tl - weighted mris . the mri image data is preferably entered into the digital computer memory using a tape drive or a black - white scanner . the first - order and second - order partial derivatives of the 3 - d image intensity function , e ( x , y , z ), are estimated at multiple spatial resolutions ( scales ), using 3 - d filter kernels derived from the uniform tricubic b - spline basis function . at each scale , candidate surfaces of interest are automatically constructed that pass through local extrema of the magnitude of the 3 - d image intensity gradient , |∇ e |. the candidate surfaces are sorted first by the number of points that they contain , then by the average image intensity gradient magnitude |∇ ve | across the surfaces , and last by the spatial extents of the boxes that bound the surfaces . typically this automatically identifies the three surfaces of interest , which delineate the scalp and skull layers . fig2 shows an example of this process . the accuracy of the automatic surface identification is checked by confirming that the skull / cortex surface is contained completely within the scalp / skull surface , which in turn is contained completely within the air / scalp surface . also , it is verified that the gradient vector ∇ e is directed generally inward ( toward the centroid of the surface ) across the air / scalp and skull / cortex surfaces , and directed generally outward ( away from the centroid of the surface ) across the scalp / skull surface . finite element mesh points are derived when a chosen set of regulating ray vectors is radially projected through the computed scalp , skull , and outer brain surfaces . the mesh points on the scalp , skull and outer brain surfaces are triangularized , and prism - shaped finite elements are formed from two triangles located on adjacent surfaces . fig3 illustrates this process . the accuracy of the deblurred data is affected by the spatial distance between finite element mesh points and the spatial relations among finite element vertices within each finite element . the choice of the regulating set of ray vectors used to construct the finite element model &# 34 ; regulates &# 34 ; these factors . the choice of number of ray vectors determines the spatial distance between mesh points , and choice of the configuration of these ray vectors determines the condition number of the forward solution matrix which , in turn , determines the stability of the explicitly - inverted finite element transformation matrix used in subsequent deblurring operations . we have found that a set of unit length vectors , which are the vertices of a group of triangles whose sides have nearly equal length , is an optimal solution . 2 . finite element modeling of scalp and skull layers without mris 2 . 1 constructing a subject - specific head model from tape measurements and a subject &# 39 ; s physical attributes information regarding an individual subject &# 39 ; s head shape and size , body weight , sex and age along with anthropometric statistics on scalp and skull thicknesses and conductivities are used to construct a subject - specific head model when mri data is not available . the subject &# 39 ; s actual head shape can be derived either from direct measurement with a three dimensional digitizer as described in u . s . pat . no . 5 , 119 , 816 , from automatic or manual measurement of several standard cross - directional lines and classification according to predetermined head shape classes as described in u . s . pat . no . 5 , 119 , 816 . these data are interpolated as needed and are used to construct a scalp surface model . in the simplest case , the nasion to inion distance , the distance between preauricular notches and the circumference of the head are measured with a tape measure , classified according to predetermined head shape class and a rough approximated scalp surface model is computed . the subject &# 39 ; s physical attributes such as height , weight , age , sex and race are then used to approximate the scalp and skull layer thicknesses at different spatial locations on the head using thickness formulae described in the literature ( pensler and mccarthy , 1985 ; adeloye et al , 1975 ). a non - linear parametric estimation technique is employed to improve the reported formulae using measured skull and scalp thicknesses from mris derived from a diverse group population of subjects . choosing a set of regulating ray vectors is the same as described in section 1 . 3 . finite element mesh points at the scalp are derived by radially projecting a chosen set of regulating ray vectors through the scalp surface model obtained from head measurements . then skull and outer brain mesh points are determined by moving the scalp mesh points radially inward along each ray vector by the appropriate local scalp and skull thickness derived from the tissue thickness formulae . the mesh points on the scalp , skull and outer brain surfaces are triangularized , and prism - shaped finite elements are formed from two triangles located on adjacent surfaces . the deblurring algorithm uses the finite element method ( fem ) to discretize poisson &# 39 ; s equation which is used to solve the bioelectric volume conduction problem . a fundamental formula is derived from the finite element method which yields the numerical forward solution of the potential distribution at the scalp by multiplying a fem - based transfomation matrix ( embodying a model of the conducting tissues ) by the conical ( outer brain ) potential distribution . since the conical potential distribution is unknown and since the controlling information is measured at the scalp , this formula has to be iterated using an optimization scheme until a suitable set of conical data is found whose forward solution best fits the measured scalp data as described in u . s . patent application ser . no . 07 / 868 , 724 , now u . s . pat . no . 5 , 331 , 970 . however , the volumetric finite elements ( three - dimensional volumes ) representing the conducting tissues can be generated in a manner such that the corresponding fem - based transformation matrix is invertible . therefore the desired cortical data can be derived by directly multiplying the inverted transformation matrix by the measured scalp data . the fem modeling strategies described in sections 1 and 2 were designed and developed to accommodate this direct approach to extract the desired cortical data . the improved deblurring procedure was developed based on the notion that the resulting deblurring region , ω , obtained with strategies outlined in sections 1 and 2 has a total of 3 * n fem mesh points where each tissue delineating surface has n fem mesh points . the boundary of the region ω is bordered by the scalp surface and the outer brain surface extending from the top of the head to a cut - off surface determined by the intersection points of the edge vectors of the chosen set of regulating ray vectors with the three tissue delineating surfaces . if the designated outer brain surface has rn fem edge points , the boundary surface of this deblurring region ω will have a total of 2 * n + m fem mesh points with n points on the scalp surface , n points on outer brain surface and m points on the edges of the scalp / skull border . with this fem montage , poisson &# 39 ; s equation is discretized and the fundamental numerical formula is established as follows : where u 1 represents the n potential values at the scalp surface , u 3 represents the n + m potential values at the outer brain and the cut - off surfaces . the resulting matrix a is the fem - based transformation matrix that has a dimension of n ×( n + m ). a detailed discussion on how to derive eq . ( 1 ) can be found in u . s . patent application 07 / 868 , 724 , now u . s . pat . no . 5 , 331 , 970 . to warrant a unique solution , the existing deblurring region ω is modified slightly when the physical locations of the fem outer brain edge points are clamped to the scalp / skull edge points such that the total number of fem points on the boundary surface of the modified deblurring region becomes 2 * n and the corresponding numerical formula becomes : with this direct matrix inversion approach , the computational performance of the deblurring method has been improved by a factor of about 10 , 000 . fig4 a and 4b show an example of application of the improved deblurring method . fig4 a shows scalp eeg data recorded during stimulation of a middle finger of the left hand . fig4 b shows the same data after application of the deblurring method . the above implementation uses a two layered finite element model which represents the scalp and skull as homogeneous tissues . though good results have been reported with this modeling strategy ( gevins et al . 1994 ), we have found that further improvement can be made by modeling the skull as a three - layered , sandwich - like structure consisting of two different tissue types : the inner and outer tables ( layers ) of resistive compact bone separated by a highly conductive porous bone layer called the diploe . a numerical simulation study ( which utilized finite element models that represented the skull as either a homogeneous or an inhomogeneous tissue ) has shown that improperly modeling the skull as a homogeneous tissue can overestimate the cortical potential magnitudes by 25 to 37 percent though the spatial pattern generally remains unchanged . although two more tissue delineating surfaces ( outer - table / diploe and dipole / inner - table ) can be introduced for the mri - based and mri - less fem modeling strategies , it has been reported by law ( 1993 ) that the outer table and inner table have a uniform thickness for most subjects . therefore intersection points of the chosen ray vector with the outer - table / diploe and diploe / inner - table surfaces are found by moving the scalp / skull and skull / outer brain intersection points by a fixed amount along the given ray vector . to warrant a unique solution , the physical locations of the fem outer brain edge points will still be clamped to the scalp / skull edge points such that the resulting matrix a is still square and invertible . adeloye , a ., kattan , k . r . and silverman , f . n . 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