- Email: [email protected]
Tridimensional animated brain mapping from conventional paper-ink EEG recordings
Computers in Biology and Medicine 34 (2004) 591 – 600 http://www.intl.elsevierhealth.com/journals/cobm
Tridimensional animated brain mapping from conventional paper-ink EEG recordings I. Gonz/aleza , A. Eblen-Zajjurb;∗ a
Dpto. de Matem atica, Faciultad de Ciencias y Tecnolog a, FACYT, Universidad de Carabobo, P.O. Box 3798, El trigal, Valencia, Venezuela b Dpto. de Ciencias Fisiol ogicas, Faciultad de Ciencias de la Salud, FCS Universidad de Carabobo, P.O. Box 3798, El trigal, Valencia, Venezuela
Abstract One of the most powerful functional evaluations of the electrical activity of the brain is the EEG imaging, but wide clinical use is limited by its costs. It is also of clinical, academic and scienti4c interest to obtain brain electrical maps from old paper/ink, patient recordings. The aim of the present study was the development of a computer system designed to obtain bidimensional and tridimensional maps, continuous movie map display and mosaic presentation from conventional paper/ink EEG recordings. The wave amplitude was manually measured with a translucent template from conventional 8- to 16-channel EEG paper recordings using 10 –20 monopolar montage for one or both hemispheres. The computer system allows the selection of the number and location of electrodes, input of amplitude values, and the map display mode. The electrical brain 4eld was generated from amplitude measurements by a spherical splines interpolation algorithm on a conventional PentiumJ -based computer. The interpolated surface was represented on a semi-sphere modeled skull. The EEG maps displayed with pseudo-color or gray scales can be rotated, zoomed in or zoomed out and/or printed for clinical reports. Movie animation or mosaic display of space-temporal EEG voltage changes were generated by processing sequential amplitude measurements. This system represents a cost-e8ective method for EEG mapping from conventional paper/Ink EEG equipments. ? 2003 Elsevier Ltd. All rights reserved. Keywords: EEG mapping; EEG imaging; Spherical spline; PC
1. Introduction EEG imaging is a modern and useful technique for functional evaluation of the brain’s electrical activity, but the cost of the equipment is a limitation for its wide clinical use [1–3]. At ∗
Corresponding author. Tel.: +58-241-8679-820; fax: +58-241-8225-290. E-mail addresses: [email protected] (I. Gonz/alez), [email protected] (A. Eblen-Zajjur).
0010-4825/$ - see front matter ? 2003 Elsevier Ltd. All rights reserved. doi:10.1016/j.compbiomed.2003.06.002
592
I. Gonz alez, A. Eblen-Zajjur / Computers in Biology and Medicine 34 (2004) 591 – 600
present, despite many disadvantages, the vast majority of clinical EEG systems, not only in the third world but also in developed countries, are conventional polygraphic paper recorders [4] that produce signals impossible to input directly into the computer. Digital imaging methods like EEG mapping or video mapping of the wave’s amplitude or frequency are good alternatives to improve the eEcacy of the brain electrical activity analysis [1,5–8] especially for epilepsy, cerebrovascular disease and dementia [9], but this method is only available in reference or specialized centers due to its high cost. On the other hand, this method has made it possible to analyze patient data of clinical, academic and/or scienti4c interest, but only where old paper/ink EEG recordings are available. Mathematical methods like modeling, interpolation, contour mapping, bi- or tridimensional representations and/or movie displays required to perform EEG imaging are easy to 4nd today in any mathematical and/or statistical software (MatlabJ , StatisticaJ , SPSSJ , SigmaPlotJ , MapleJ , SurferJ , etc.) even at a low cost. The two most used interpolation algorithms for EEG mapping are the nearest neighbor [5–8] and the spherical-spline [10–12]. Statistical evidence suggests that the optimal model for three-dimensional EEG mapping is a non-linear spline interpolation [11,13]. In the present study a technique based on the spherical splines interpolation algorithm [1,10,11] was implemented on a PentiumJ -based computer to obtain from conventional EEG paper/ink records and with a simple manual conversion process, EEG maps with di8erent display techniques such as contour, pseudo colored bi- or tridimensional brain activity maps and video sequences of EEG activity. This inexpensive approach has not been described in past similar works. 2. Methods 2.1. Data collection The source of data is any conventional paper/ink EEG record performed with electrodes located on the skull following the international 10/20 system which is based on the percentage from distances between skull anatomical landmarks [14]. For the present study, signals from up to 16 head electrodes were recorded against ground as a monopolar recording [7–11] on a conventional polygraphic paper/ink EEG equipment. At single or multiple speci4c time instants, selected by the physician, wave amplitudes were hand measured directly from paper records by means of a translucent calibrated template which can be easily designed and printed by the user on an ink-jet overhead 4lm (Fig. 1). Three long horizontal lines allow matching with the channel mid-trace. An orthogonal calibrated vertical scale with 20 mm (1 mm=div) was drawn over each horizontal line allowing precise amplitude measurements (Fig. 1). Using this calibrated template, measurement at a speci4c time instant, i.e., in an 8-channel EEG record, can be performed manually in about 120 s. Voltage values are entered through keyboard in the data input display of the program which allows selection of the electrode location and the brain hemisphere to be analyzed (Fig. 2). If more than one time instant is analyzed then a digital reconstruction of voltage sequences is performed for visual control of traces (Fig. 2, left panel). Once data input is 4nished, two display modes can be chosen: animation or mosaic (Fig. 2, middle of the right panel). A directory of saved images is available for speci4c and independent frame recalls (Fig. 2, bottom of the right panel).
I. Gonz alez, A. Eblen-Zajjur / Computers in Biology and Medicine 34 (2004) 591 – 600
593
Fig. 1. Conventional EEG paper record from an 8-lead monopolar, left montage. Wave amplitudes at a particular time instant of all channels were measured with the help of a calibrated template printed on an overhead 4lm. The measure scale is calibrated in V=div or mm/div.
Fig. 2. The data input of the system allows the selection of the hemisphere, display mode, and the input of wave amplitudes at speci4c electrode locations. If more than one time instant is entered then a reconstructed EEG record is displayed on the left panel. A directory of EEG data is presented on the right panel.
2.2. Computer processing The skull was idealized to a semi-sphere [13] with a radius equal to 1. Over the three-dimensional scalp surface obtained from this model, electrode location coordinates (x; y; z) were identi4ed. Central Cz, nasion and inion have coordinates (0; 0; 1), (1; 0; 0) and (−1; 0; 0), respectively. In this model all
594
I. Gonz alez, A. Eblen-Zajjur / Computers in Biology and Medicine 34 (2004) 591 – 600
(b)
(a)
Fig. 3. (a) The interpolated surface of electrical 4eld potential and the triangular grid surface of the semi-sphere idealized skull are presented; (b) the bilinearly interpolated color of the electrical brain 4eld was assigned to the corresponding path of the skull model.
electrode locations follow the 10 –20 international system. An interpolation algorithm was applied to estimate the scalp electrical 4eld potential from measured values of electrode sites. Locations in the skull model used for the interpolation process were obtained from the vertices of a triangular grid surface generated by the marching cubes method [15,16] over the semi-sphere (Fig. 3). The brain 4eld potential was generated from amplitude measurements by a spherical splines interpolation algorithm [10,11,17–19]; the obtained surface can be seen intuitively such as a thin elastic spherical shell that has been deformed by point forces [12,19]. Let p ˜ i ; i = 1; : : : ; N be the location vector of one of N measurement electrodes and let Vi = V (˜ pi ) be the potential at the point p ˜ i on the surface of the semi-sphere. The spherical spline assumes that the potential V (˜ p) at any point p ˜ on the surface of the semi-sphere, can be written as V (˜ p ) = c0 +
N
cj gm (cos(˜ p; p ˜ j ));
(1)
1 2n + 1 Pn (x) 4 n=1 (n(n + 1))m
(2)
j=1
where gm is given by ∞
gm (x) =
and where Pn is the nth degree Legendre polynomial, x = cos(˜ p; p ˜ j ) is the cosine of the angle between the vectors p ˜ and p ˜ j . Eq. (1) is simply the general expression for the electric potential over the semi-sphere surface [19]. In practice, the sum in gm (x) Eq. (2) must be truncated to some 4nite number of terms, depending upon the value of the parameter m. In the present study, the number of terms in Eq. (2) to perform the interpolation was 17 with m = 1. The coeEcients cj s and the scalar c0 are determinates to satisfy two conditions: 4rst, the interpolation function V (˜ p) must be equal to the measured values when it is evaluated for that
I. Gonz alez, A. Eblen-Zajjur / Computers in Biology and Medicine 34 (2004) 591 – 600
595
electrode value, i.e., Vi = c 0 +
N
cj gm (cos(˜ pi ; p ˜ j )):
j=1
The second condition establishes that N
cj = 0:
j=1
These two conditions are combined in a linear equation system where the cj s are a solution of Gm C + c0 1 = V; 1t C = 0; where C = [c1 ; c2 ; : : : ; cN ]t , 1 = [1; 1; : : : ; 1]t , V = [V1 ; V2 ; : : : ; VN ]t , the vector of the measured at the electrodes of measure and Gm is an N × N matrix of coeEcients (Gm )ij = gm (cos(˜ pi ; p ˜ j )). The superscript t denotes the transposed matrix. All voltages V (˜ p) over the grid points de4ne the assigned color to data that represents the electrical potential 4eld. The assigned color to every point p of the surface is proportional to the value V (˜ p). Bilinear interpolation of color values from each vertex determines the color of each path of the triangular surface. Then, the interpolated 4eld potential was mapped on the idealized skull as a pseudo color or gray level scale (Fig. 3). The pseudo color scale (Fig. 4) was designed on the basis of 16 levels ranging from high voltages assigned to the red color (or white in the gray scale), yellow and green color for intermediate values, to low voltages assigned to the blue color (or black in the gray scale). The use of a gray level scale reduces printing costs for routine clinical analysis without loss in diagnostic accuracy due to the fact that the system always performs the same 16-level voltage scale either in pseudo color or gray mode. Evaluation of the hemispheric EEG asymmetry is a common clinical practice to enhance diagnostic capability. This kind of evaluation can be performed by the generation of left and right hemisphere maps from voltages measured at the same time instant of the record, thus allowing identi4cation and localization of electrical asymmetries in all skull views. To allow adequate hemisphere map matching, the pseudo color scale must have the same voltage range for both maps. 3. Results Sequential measures on paper recordings were made to obtain maps and movie displays of the brain electrical activity. After data input, the image generation time was almost instantaneous or took a few seconds when several images were generated for the movie animation or mosaic display. 3.1. EEG image display options The resulting brain electrical activity maps can be displayed in three di8erent modes: single frame, movie or mosaic display. Single and movie display are presented in four orthogonal views: frontal, occipital, lateral and sagital. Movie animation of voltage changes over time is obtained by displaying
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Fig. 4. EEG map obtained from wave amplitude measurements at a speci4c time instant. Movie display of a sequential voltage changes at di8erent time instants is made possible by the movie control keys (bottom of the display). Four views (Frontal, Lateral, Occipital and Superior) of the skull are presented. A sixteen-level gray scale of voltages (V) is presented on the right. The map sequence velocity can be controlled by the corresponding slide control at the bottom of the screen.
a rapid sequence of time-speci4c still maps (Fig. 4), this mode increases the time resolution and shows the time course upon anatomical location in the analysis of a brain’s electrical activity. All single frames of the movie animation can be individually printed. In the mosaic display mode, 2–25 still EEG maps (selected by the user) are presented in sequence in a matrix format (Fig. 5). This mode allows 3D rotation, zoom and printout of any individual map mosaic. Input voltage values, but not images, are stored by the system as a numerical matrix from which EEG maps can be reconstructed at any time, thus saving disk space. The screen catcher menu option can be used to capture brain activity maps for backup and/or image post processing. 3.2. Clinical application An EEG map (Fig. 5) from a 55-year-old man with Alzheimer’s disease was obtained from a conventional 11 monopolar, left hemisphere, EEG paper record showing a left frontal high-voltage area. This area has a concentrical decay. Additional low-voltage areas are seen in mid-temporal and parieto-occipital areas which are better seen on the lateral view. The time evolutions of these areas are better evaluated with the movie display which is made from multiple EEG maps at times
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597
Fig. 5. Mosaic display of a sequential EEG map from 10 ms to 90 ms indicated at the right top of each image. Any of these images can be rotated and/or zoomed in or zoomed out.
ranging from 10 to 90 ms presented in Fig. 5, where a sequence of 9 EEG maps featuring the high-voltage frontal area previously described at the beginning of the record, and vanishing after 20 ms, simultaneously the two voltage areas at temporal and parieto-occipital loci are present from the beginning of the recording up to 40 ms, after which a new occipital high-voltage area appears from 30 ms up to 70 ms of the record. Images of brain activity at 80 and 90 ms are characterized by two temporal high-voltage areas. Fig. 6 presents the voltage maps from left and right brain hemispheres from a male 63-year-old patient with a right frontotemporal glioma and left hemiparesis. Conventional EEG record shows slow, high-voltage, irregular waves in the right frontal area spreading toward posterior areas. The electrical brain maps evidence a strong voltage asymmetry with the right hemisphere showing high-voltage activity predominantly at frontal areas in contrast to normal voltage values seen at the left hemisphere map. Di8erent skull views (superior, lateral, frontal and occipital) o8er information about anatomical extension of the electrical changes, thus allowing a precise comparison between both hemisphere asymmetric activities. 4. Discussion The present study describes a computational technique to obtain EEG maps from conventional 8- to 16-channel EEG paper/ink records. This technique is able to display contour and bi- or tridimensional
598
I. Gonz alez, A. Eblen-Zajjur / Computers in Biology and Medicine 34 (2004) 591 – 600 Left hemisphere
Lateral view
µV
Lateral view
14.07
Right hemisphere
13.3 12.53 11.76 10.99 9.44 8.68 7.91
Frontal view
Occipital view
7.14 6.37
Occipital view
Frontal view
Superior view
Superior view
10.22
5.6 4.93 4.06 3.29 2.52 1.75
Fig. 6. Voltage maps from left and right brain hemispheres from a male 63-year-old patient with a right frontotemporal glioma and left hemiparesis. Strong voltage asymmetry is seen with the right hemisphere high-voltage activity at frontal areas and normal voltage values in the left hemisphere.
brain activity maps as well as a series of time-speci4c still maps as a video. The development of EEG imaging software has been orientated to visualize 2D or 3D maps from patient data recorded by digital EEG [20]; this technically logical approach excludes from the brain mapping all conventional EEG paper recorded and stored data. This fact is true not only for the vast majority of EEG paper recorders still in use but also for a lot of old EEG paper records with high clinical, academic and scienti4c relevance which require a complementary analysis by the EEG mapping technique. The inexpensive approach described in the present study has not been described in past similar works and ful4lls this need. Advantages such as the use of widely available personal computer platform, no hardware installation requirements, intuitive and user-friendly operation enable the consideration of the system described here as an alternative for EEG paper record complementary analysis. It is important to point out that brain electrical activity mapping, despite its clear advantages, should be used only by highly clinical EEG skilled physicians and only together with traditional EEG trace interpretation [9,21]. 4.1. Software availability The complete source code of the program is available for non-commercial use at no cost from the authors via email and subscription to the user group. 5. Summary EEG mapping is a useful complementary technique in the analysis of brain electrical activity. Conventional paper/ink recordings are still widely used not only in the third world but also in developed countries. Conventional EEG paper records from clinical cases which have academic and scienti4c interest could be more useful if an EEG map analysis would be available. The system described in the present study uses voltage values measured directly from conventional 8 or more channels paper/ink recordings at precise time point or time intervals. On a pentium-based computer,
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the system implements a spherical spline interpolation generating 2D-countour maps, free-rotating 3D-maps, multiple views, continuous movie maps and mosaic presentations of the electrical brain activity on a semi-spherical idealized skull. Acknowledgements The authors wish to thank Dr. Virginia Vivas for critical reading of the manuscript and to the Referee for valuable comments. This study was supported by Consejo de Desarrollo Cient/L4co y Human/Lstico of Universidad de Carabobo, Venezuela, Grant CDCH-UC-2235. References [1] M.H. Giard, F. Peronet, J. Pernier, F. Mauguiere, O. Bertrand, Sequential colour mapping system of brain potentials, Comput. Method Prog. Biomed. 20 (1985) 9–16. [2] M.R. Nuwer, The development of EEG brain mapping, J. Clin. Neurophysiol. 7 (1990) 459–471. [3] I. Gonz/alez, A. Eblen-Zajjur, A computer system for 3D animated mapping of the brain electrical activity (EEG) by biharmonic splines interpolation, in: N. Troyani, M. Cerrolaza (Eds.), M/etodos num/ericos en ingenier/La y ciencias aplicadas, SVMNI, Caracas, 2000, pp. 9–15. [4] F. Lopes Da Silva, EEG analysis: theory and practice, in: E. Niedermeyer, F. Lopes Da Silva (Eds.), Electroencephalography, Urban & Schwarzenberg, Baltimore, 1987. [5] R. Coppola, M.S. Buschbaum, F. Rigal, Computer generation of surface distribution maps of measures of brain activity, Comput. Biol. Med. 12 (1982) 191–199. [6] M.S. Buschbaum, F. Rigal, R. Coppola, J. Cappelletti, C. King, J. Johnson, A new system for gray-level surface distribution maps of electrical activity, Electroencephalogr. Clin. Neurophysiol. 53 (1982) 237–242. [7] F.H. Du8y, The BEAM method for neurophysiological diagnosis, Ann. N.Y. Acad. Sci. 457 (1985) 19–34. [8] F.H. Du8y, Clinical value of topographic mapping and quanti4ed neurophysiology, Arch. Neurol. 46 (1989) 1133–1134. [9] M.R. Nuwer, Assessment of digital EEG, quantitative EEG, and EEG brain mapping: report of the American academy of neurology and the American clinical neurophysiology society, Neurology 49 (1997) 277–292. [10] F. Perrin, J. Pernier, O. Bertrand, J.F. Echallier, Spherical splines for scalp potential and current density mapping, Electroencephalogr. Clin. Neurophysiol. 72 (1989) 184–187. [11] L. SouSet, M. Toussaint, R. Luthringer, J. Gresser, R. Minot, J.P. Macher, A statistical evaluation of the main interpolation methods applied to 3-dimensional EEG mapping, Electroencephalogr. Clin. Neurophysiol. 79 (1991) 393–402. [12] A.C.K. Soong, J.C. Lind, G.R. Shaw, Z.J. Koles, Systematic comparisons of interpolation techniques in topographic brain mapping, Electroencephalogr. Clin. Neurophysiol. 87 (1993) 185–195. [13] B. Yvert, O. Bertrand, M. Thevenet, J.F. Echallier, J. Pernier, A systematic evaluation of the spherical model accuracy in EEG dipole localization, Electroencephalogr. Clin. Neurophysiol. 102 (1997) 452–459. [14] W. Cobb, Report of the committee on methods of clinical examination in electroencephalography, Electroencephalogr. Clin. Neurophysiol. 10 (1958) 370–375. [15] E.W. Lorensen, H.E. Cline, Marching cubes: a high resolution 3D surface construction algorithm, Comput. Graphics 21 (1987) 163–169. [16] B. Yvert, O. Bertrand, M.J.F. Echallier, J. Pernier, Improved forward EEG calculations using local mesh re4nement of realistic head geometries, Neurophysiology 95 (1995) 381–392. [17] G. Wahba, Spline interpolation and smoothing on the sphere, SIAM J. Sci. Stat. Comput. 2 (1981) 5–16. [18] T.C. Ferree, Spline Interpolation of the Scalp EEG, Electrical Geodesics, Inc. Technical Note, Portland, 2000, pp. 1–5.
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[19] E.M. Fletcher, C.L. Kussmaul, G.R. Mangun, Estimation of interpolation errors in scalp topographic mapping, Electroencephalogr. Clin. Neurophysiol. 98 (1996) 422–434. [20] T. Heinonen, A. Lahtinen, V. Hakkinen, Implementation of three-dimensional EEG brain mapping, Comput. Biomed. Res. 32 (1999) 123–131. [21] M.R. Nuwer, On the controversies about clinical use of EEG brain mapping, Brain Topogr. 3 (1990) 103–111. Ignacio Gonz#alez graduated in Mathematics from the Universidad Central de Venezuela, Caracas, and obtained an MSc degree in Mathematics from the same university. He is currently Assistant Professor of mathematics, Departamento de Matem/atica, Facultad de Ciencias y Tecnolog/La, Universidad de Carabobo. His research interests are mathematical analysis of biological signals and random processes. Antonio Eblen-Zajjur graduated in Medicine from the Universidad de Carabobo, Venezuela, and obtained a PhD degree magna cum laude from the Ruprecht-Karl UniversitTat Heidelberg, Germany, postdoctoral fellow at the Instituto Venezolano de Investigaciones Cient/L4cas, Venezuela. He is currently Associate Professor at the Departamento de Ciencias Fisiol/ogicas, Facultad de Ciencias de la Salud, Universidad de Carabobo. His research interests are neuronal networks, nociception, sensory code and analysis of biological signals.
Tridimensional animated brain mapping from conventional paper-ink EEG recordings I. Gonz/aleza , A. Eblen-Zajjurb;∗ a
Dpto. de Matem atica, Faciultad de Ciencias y Tecnolog a, FACYT, Universidad de Carabobo, P.O. Box 3798, El trigal, Valencia, Venezuela b Dpto. de Ciencias Fisiol ogicas, Faciultad de Ciencias de la Salud, FCS Universidad de Carabobo, P.O. Box 3798, El trigal, Valencia, Venezuela
Abstract One of the most powerful functional evaluations of the electrical activity of the brain is the EEG imaging, but wide clinical use is limited by its costs. It is also of clinical, academic and scienti4c interest to obtain brain electrical maps from old paper/ink, patient recordings. The aim of the present study was the development of a computer system designed to obtain bidimensional and tridimensional maps, continuous movie map display and mosaic presentation from conventional paper/ink EEG recordings. The wave amplitude was manually measured with a translucent template from conventional 8- to 16-channel EEG paper recordings using 10 –20 monopolar montage for one or both hemispheres. The computer system allows the selection of the number and location of electrodes, input of amplitude values, and the map display mode. The electrical brain 4eld was generated from amplitude measurements by a spherical splines interpolation algorithm on a conventional PentiumJ -based computer. The interpolated surface was represented on a semi-sphere modeled skull. The EEG maps displayed with pseudo-color or gray scales can be rotated, zoomed in or zoomed out and/or printed for clinical reports. Movie animation or mosaic display of space-temporal EEG voltage changes were generated by processing sequential amplitude measurements. This system represents a cost-e8ective method for EEG mapping from conventional paper/Ink EEG equipments. ? 2003 Elsevier Ltd. All rights reserved. Keywords: EEG mapping; EEG imaging; Spherical spline; PC
1. Introduction EEG imaging is a modern and useful technique for functional evaluation of the brain’s electrical activity, but the cost of the equipment is a limitation for its wide clinical use [1–3]. At ∗
Corresponding author. Tel.: +58-241-8679-820; fax: +58-241-8225-290. E-mail addresses: [email protected] (I. Gonz/alez), [email protected] (A. Eblen-Zajjur).
0010-4825/$ - see front matter ? 2003 Elsevier Ltd. All rights reserved. doi:10.1016/j.compbiomed.2003.06.002
592
I. Gonz alez, A. Eblen-Zajjur / Computers in Biology and Medicine 34 (2004) 591 – 600
present, despite many disadvantages, the vast majority of clinical EEG systems, not only in the third world but also in developed countries, are conventional polygraphic paper recorders [4] that produce signals impossible to input directly into the computer. Digital imaging methods like EEG mapping or video mapping of the wave’s amplitude or frequency are good alternatives to improve the eEcacy of the brain electrical activity analysis [1,5–8] especially for epilepsy, cerebrovascular disease and dementia [9], but this method is only available in reference or specialized centers due to its high cost. On the other hand, this method has made it possible to analyze patient data of clinical, academic and/or scienti4c interest, but only where old paper/ink EEG recordings are available. Mathematical methods like modeling, interpolation, contour mapping, bi- or tridimensional representations and/or movie displays required to perform EEG imaging are easy to 4nd today in any mathematical and/or statistical software (MatlabJ , StatisticaJ , SPSSJ , SigmaPlotJ , MapleJ , SurferJ , etc.) even at a low cost. The two most used interpolation algorithms for EEG mapping are the nearest neighbor [5–8] and the spherical-spline [10–12]. Statistical evidence suggests that the optimal model for three-dimensional EEG mapping is a non-linear spline interpolation [11,13]. In the present study a technique based on the spherical splines interpolation algorithm [1,10,11] was implemented on a PentiumJ -based computer to obtain from conventional EEG paper/ink records and with a simple manual conversion process, EEG maps with di8erent display techniques such as contour, pseudo colored bi- or tridimensional brain activity maps and video sequences of EEG activity. This inexpensive approach has not been described in past similar works. 2. Methods 2.1. Data collection The source of data is any conventional paper/ink EEG record performed with electrodes located on the skull following the international 10/20 system which is based on the percentage from distances between skull anatomical landmarks [14]. For the present study, signals from up to 16 head electrodes were recorded against ground as a monopolar recording [7–11] on a conventional polygraphic paper/ink EEG equipment. At single or multiple speci4c time instants, selected by the physician, wave amplitudes were hand measured directly from paper records by means of a translucent calibrated template which can be easily designed and printed by the user on an ink-jet overhead 4lm (Fig. 1). Three long horizontal lines allow matching with the channel mid-trace. An orthogonal calibrated vertical scale with 20 mm (1 mm=div) was drawn over each horizontal line allowing precise amplitude measurements (Fig. 1). Using this calibrated template, measurement at a speci4c time instant, i.e., in an 8-channel EEG record, can be performed manually in about 120 s. Voltage values are entered through keyboard in the data input display of the program which allows selection of the electrode location and the brain hemisphere to be analyzed (Fig. 2). If more than one time instant is analyzed then a digital reconstruction of voltage sequences is performed for visual control of traces (Fig. 2, left panel). Once data input is 4nished, two display modes can be chosen: animation or mosaic (Fig. 2, middle of the right panel). A directory of saved images is available for speci4c and independent frame recalls (Fig. 2, bottom of the right panel).
I. Gonz alez, A. Eblen-Zajjur / Computers in Biology and Medicine 34 (2004) 591 – 600
593
Fig. 1. Conventional EEG paper record from an 8-lead monopolar, left montage. Wave amplitudes at a particular time instant of all channels were measured with the help of a calibrated template printed on an overhead 4lm. The measure scale is calibrated in V=div or mm/div.
Fig. 2. The data input of the system allows the selection of the hemisphere, display mode, and the input of wave amplitudes at speci4c electrode locations. If more than one time instant is entered then a reconstructed EEG record is displayed on the left panel. A directory of EEG data is presented on the right panel.
2.2. Computer processing The skull was idealized to a semi-sphere [13] with a radius equal to 1. Over the three-dimensional scalp surface obtained from this model, electrode location coordinates (x; y; z) were identi4ed. Central Cz, nasion and inion have coordinates (0; 0; 1), (1; 0; 0) and (−1; 0; 0), respectively. In this model all
594
I. Gonz alez, A. Eblen-Zajjur / Computers in Biology and Medicine 34 (2004) 591 – 600
(b)
(a)
Fig. 3. (a) The interpolated surface of electrical 4eld potential and the triangular grid surface of the semi-sphere idealized skull are presented; (b) the bilinearly interpolated color of the electrical brain 4eld was assigned to the corresponding path of the skull model.
electrode locations follow the 10 –20 international system. An interpolation algorithm was applied to estimate the scalp electrical 4eld potential from measured values of electrode sites. Locations in the skull model used for the interpolation process were obtained from the vertices of a triangular grid surface generated by the marching cubes method [15,16] over the semi-sphere (Fig. 3). The brain 4eld potential was generated from amplitude measurements by a spherical splines interpolation algorithm [10,11,17–19]; the obtained surface can be seen intuitively such as a thin elastic spherical shell that has been deformed by point forces [12,19]. Let p ˜ i ; i = 1; : : : ; N be the location vector of one of N measurement electrodes and let Vi = V (˜ pi ) be the potential at the point p ˜ i on the surface of the semi-sphere. The spherical spline assumes that the potential V (˜ p) at any point p ˜ on the surface of the semi-sphere, can be written as V (˜ p ) = c0 +
N
cj gm (cos(˜ p; p ˜ j ));
(1)
1 2n + 1 Pn (x) 4 n=1 (n(n + 1))m
(2)
j=1
where gm is given by ∞
gm (x) =
and where Pn is the nth degree Legendre polynomial, x = cos(˜ p; p ˜ j ) is the cosine of the angle between the vectors p ˜ and p ˜ j . Eq. (1) is simply the general expression for the electric potential over the semi-sphere surface [19]. In practice, the sum in gm (x) Eq. (2) must be truncated to some 4nite number of terms, depending upon the value of the parameter m. In the present study, the number of terms in Eq. (2) to perform the interpolation was 17 with m = 1. The coeEcients cj s and the scalar c0 are determinates to satisfy two conditions: 4rst, the interpolation function V (˜ p) must be equal to the measured values when it is evaluated for that
I. Gonz alez, A. Eblen-Zajjur / Computers in Biology and Medicine 34 (2004) 591 – 600
595
electrode value, i.e., Vi = c 0 +
N
cj gm (cos(˜ pi ; p ˜ j )):
j=1
The second condition establishes that N
cj = 0:
j=1
These two conditions are combined in a linear equation system where the cj s are a solution of Gm C + c0 1 = V; 1t C = 0; where C = [c1 ; c2 ; : : : ; cN ]t , 1 = [1; 1; : : : ; 1]t , V = [V1 ; V2 ; : : : ; VN ]t , the vector of the measured at the electrodes of measure and Gm is an N × N matrix of coeEcients (Gm )ij = gm (cos(˜ pi ; p ˜ j )). The superscript t denotes the transposed matrix. All voltages V (˜ p) over the grid points de4ne the assigned color to data that represents the electrical potential 4eld. The assigned color to every point p of the surface is proportional to the value V (˜ p). Bilinear interpolation of color values from each vertex determines the color of each path of the triangular surface. Then, the interpolated 4eld potential was mapped on the idealized skull as a pseudo color or gray level scale (Fig. 3). The pseudo color scale (Fig. 4) was designed on the basis of 16 levels ranging from high voltages assigned to the red color (or white in the gray scale), yellow and green color for intermediate values, to low voltages assigned to the blue color (or black in the gray scale). The use of a gray level scale reduces printing costs for routine clinical analysis without loss in diagnostic accuracy due to the fact that the system always performs the same 16-level voltage scale either in pseudo color or gray mode. Evaluation of the hemispheric EEG asymmetry is a common clinical practice to enhance diagnostic capability. This kind of evaluation can be performed by the generation of left and right hemisphere maps from voltages measured at the same time instant of the record, thus allowing identi4cation and localization of electrical asymmetries in all skull views. To allow adequate hemisphere map matching, the pseudo color scale must have the same voltage range for both maps. 3. Results Sequential measures on paper recordings were made to obtain maps and movie displays of the brain electrical activity. After data input, the image generation time was almost instantaneous or took a few seconds when several images were generated for the movie animation or mosaic display. 3.1. EEG image display options The resulting brain electrical activity maps can be displayed in three di8erent modes: single frame, movie or mosaic display. Single and movie display are presented in four orthogonal views: frontal, occipital, lateral and sagital. Movie animation of voltage changes over time is obtained by displaying
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Fig. 4. EEG map obtained from wave amplitude measurements at a speci4c time instant. Movie display of a sequential voltage changes at di8erent time instants is made possible by the movie control keys (bottom of the display). Four views (Frontal, Lateral, Occipital and Superior) of the skull are presented. A sixteen-level gray scale of voltages (V) is presented on the right. The map sequence velocity can be controlled by the corresponding slide control at the bottom of the screen.
a rapid sequence of time-speci4c still maps (Fig. 4), this mode increases the time resolution and shows the time course upon anatomical location in the analysis of a brain’s electrical activity. All single frames of the movie animation can be individually printed. In the mosaic display mode, 2–25 still EEG maps (selected by the user) are presented in sequence in a matrix format (Fig. 5). This mode allows 3D rotation, zoom and printout of any individual map mosaic. Input voltage values, but not images, are stored by the system as a numerical matrix from which EEG maps can be reconstructed at any time, thus saving disk space. The screen catcher menu option can be used to capture brain activity maps for backup and/or image post processing. 3.2. Clinical application An EEG map (Fig. 5) from a 55-year-old man with Alzheimer’s disease was obtained from a conventional 11 monopolar, left hemisphere, EEG paper record showing a left frontal high-voltage area. This area has a concentrical decay. Additional low-voltage areas are seen in mid-temporal and parieto-occipital areas which are better seen on the lateral view. The time evolutions of these areas are better evaluated with the movie display which is made from multiple EEG maps at times
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Fig. 5. Mosaic display of a sequential EEG map from 10 ms to 90 ms indicated at the right top of each image. Any of these images can be rotated and/or zoomed in or zoomed out.
ranging from 10 to 90 ms presented in Fig. 5, where a sequence of 9 EEG maps featuring the high-voltage frontal area previously described at the beginning of the record, and vanishing after 20 ms, simultaneously the two voltage areas at temporal and parieto-occipital loci are present from the beginning of the recording up to 40 ms, after which a new occipital high-voltage area appears from 30 ms up to 70 ms of the record. Images of brain activity at 80 and 90 ms are characterized by two temporal high-voltage areas. Fig. 6 presents the voltage maps from left and right brain hemispheres from a male 63-year-old patient with a right frontotemporal glioma and left hemiparesis. Conventional EEG record shows slow, high-voltage, irregular waves in the right frontal area spreading toward posterior areas. The electrical brain maps evidence a strong voltage asymmetry with the right hemisphere showing high-voltage activity predominantly at frontal areas in contrast to normal voltage values seen at the left hemisphere map. Di8erent skull views (superior, lateral, frontal and occipital) o8er information about anatomical extension of the electrical changes, thus allowing a precise comparison between both hemisphere asymmetric activities. 4. Discussion The present study describes a computational technique to obtain EEG maps from conventional 8- to 16-channel EEG paper/ink records. This technique is able to display contour and bi- or tridimensional
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Lateral view
µV
Lateral view
14.07
Right hemisphere
13.3 12.53 11.76 10.99 9.44 8.68 7.91
Frontal view
Occipital view
7.14 6.37
Occipital view
Frontal view
Superior view
Superior view
10.22
5.6 4.93 4.06 3.29 2.52 1.75
Fig. 6. Voltage maps from left and right brain hemispheres from a male 63-year-old patient with a right frontotemporal glioma and left hemiparesis. Strong voltage asymmetry is seen with the right hemisphere high-voltage activity at frontal areas and normal voltage values in the left hemisphere.
brain activity maps as well as a series of time-speci4c still maps as a video. The development of EEG imaging software has been orientated to visualize 2D or 3D maps from patient data recorded by digital EEG [20]; this technically logical approach excludes from the brain mapping all conventional EEG paper recorded and stored data. This fact is true not only for the vast majority of EEG paper recorders still in use but also for a lot of old EEG paper records with high clinical, academic and scienti4c relevance which require a complementary analysis by the EEG mapping technique. The inexpensive approach described in the present study has not been described in past similar works and ful4lls this need. Advantages such as the use of widely available personal computer platform, no hardware installation requirements, intuitive and user-friendly operation enable the consideration of the system described here as an alternative for EEG paper record complementary analysis. It is important to point out that brain electrical activity mapping, despite its clear advantages, should be used only by highly clinical EEG skilled physicians and only together with traditional EEG trace interpretation [9,21]. 4.1. Software availability The complete source code of the program is available for non-commercial use at no cost from the authors via email and subscription to the user group. 5. Summary EEG mapping is a useful complementary technique in the analysis of brain electrical activity. Conventional paper/ink recordings are still widely used not only in the third world but also in developed countries. Conventional EEG paper records from clinical cases which have academic and scienti4c interest could be more useful if an EEG map analysis would be available. The system described in the present study uses voltage values measured directly from conventional 8 or more channels paper/ink recordings at precise time point or time intervals. On a pentium-based computer,
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the system implements a spherical spline interpolation generating 2D-countour maps, free-rotating 3D-maps, multiple views, continuous movie maps and mosaic presentations of the electrical brain activity on a semi-spherical idealized skull. Acknowledgements The authors wish to thank Dr. Virginia Vivas for critical reading of the manuscript and to the Referee for valuable comments. This study was supported by Consejo de Desarrollo Cient/L4co y Human/Lstico of Universidad de Carabobo, Venezuela, Grant CDCH-UC-2235. References [1] M.H. Giard, F. Peronet, J. Pernier, F. Mauguiere, O. Bertrand, Sequential colour mapping system of brain potentials, Comput. Method Prog. Biomed. 20 (1985) 9–16. [2] M.R. Nuwer, The development of EEG brain mapping, J. Clin. Neurophysiol. 7 (1990) 459–471. [3] I. Gonz/alez, A. Eblen-Zajjur, A computer system for 3D animated mapping of the brain electrical activity (EEG) by biharmonic splines interpolation, in: N. Troyani, M. Cerrolaza (Eds.), M/etodos num/ericos en ingenier/La y ciencias aplicadas, SVMNI, Caracas, 2000, pp. 9–15. [4] F. Lopes Da Silva, EEG analysis: theory and practice, in: E. Niedermeyer, F. Lopes Da Silva (Eds.), Electroencephalography, Urban & Schwarzenberg, Baltimore, 1987. [5] R. Coppola, M.S. Buschbaum, F. Rigal, Computer generation of surface distribution maps of measures of brain activity, Comput. Biol. Med. 12 (1982) 191–199. [6] M.S. Buschbaum, F. Rigal, R. Coppola, J. Cappelletti, C. King, J. Johnson, A new system for gray-level surface distribution maps of electrical activity, Electroencephalogr. Clin. Neurophysiol. 53 (1982) 237–242. [7] F.H. Du8y, The BEAM method for neurophysiological diagnosis, Ann. N.Y. Acad. Sci. 457 (1985) 19–34. [8] F.H. Du8y, Clinical value of topographic mapping and quanti4ed neurophysiology, Arch. Neurol. 46 (1989) 1133–1134. [9] M.R. Nuwer, Assessment of digital EEG, quantitative EEG, and EEG brain mapping: report of the American academy of neurology and the American clinical neurophysiology society, Neurology 49 (1997) 277–292. [10] F. Perrin, J. Pernier, O. Bertrand, J.F. Echallier, Spherical splines for scalp potential and current density mapping, Electroencephalogr. Clin. Neurophysiol. 72 (1989) 184–187. [11] L. SouSet, M. Toussaint, R. Luthringer, J. Gresser, R. Minot, J.P. Macher, A statistical evaluation of the main interpolation methods applied to 3-dimensional EEG mapping, Electroencephalogr. Clin. Neurophysiol. 79 (1991) 393–402. [12] A.C.K. Soong, J.C. Lind, G.R. Shaw, Z.J. Koles, Systematic comparisons of interpolation techniques in topographic brain mapping, Electroencephalogr. Clin. Neurophysiol. 87 (1993) 185–195. [13] B. Yvert, O. Bertrand, M. Thevenet, J.F. Echallier, J. Pernier, A systematic evaluation of the spherical model accuracy in EEG dipole localization, Electroencephalogr. Clin. Neurophysiol. 102 (1997) 452–459. [14] W. Cobb, Report of the committee on methods of clinical examination in electroencephalography, Electroencephalogr. Clin. Neurophysiol. 10 (1958) 370–375. [15] E.W. Lorensen, H.E. Cline, Marching cubes: a high resolution 3D surface construction algorithm, Comput. Graphics 21 (1987) 163–169. [16] B. Yvert, O. Bertrand, M.J.F. Echallier, J. Pernier, Improved forward EEG calculations using local mesh re4nement of realistic head geometries, Neurophysiology 95 (1995) 381–392. [17] G. Wahba, Spline interpolation and smoothing on the sphere, SIAM J. Sci. Stat. Comput. 2 (1981) 5–16. [18] T.C. Ferree, Spline Interpolation of the Scalp EEG, Electrical Geodesics, Inc. Technical Note, Portland, 2000, pp. 1–5.
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[19] E.M. Fletcher, C.L. Kussmaul, G.R. Mangun, Estimation of interpolation errors in scalp topographic mapping, Electroencephalogr. Clin. Neurophysiol. 98 (1996) 422–434. [20] T. Heinonen, A. Lahtinen, V. Hakkinen, Implementation of three-dimensional EEG brain mapping, Comput. Biomed. Res. 32 (1999) 123–131. [21] M.R. Nuwer, On the controversies about clinical use of EEG brain mapping, Brain Topogr. 3 (1990) 103–111. Ignacio Gonz#alez graduated in Mathematics from the Universidad Central de Venezuela, Caracas, and obtained an MSc degree in Mathematics from the same university. He is currently Assistant Professor of mathematics, Departamento de Matem/atica, Facultad de Ciencias y Tecnolog/La, Universidad de Carabobo. His research interests are mathematical analysis of biological signals and random processes. Antonio Eblen-Zajjur graduated in Medicine from the Universidad de Carabobo, Venezuela, and obtained a PhD degree magna cum laude from the Ruprecht-Karl UniversitTat Heidelberg, Germany, postdoctoral fellow at the Instituto Venezolano de Investigaciones Cient/L4cas, Venezuela. He is currently Associate Professor at the Departamento de Ciencias Fisiol/ogicas, Facultad de Ciencias de la Salud, Universidad de Carabobo. His research interests are neuronal networks, nociception, sensory code and analysis of biological signals.