f Brain evoked potential topographic mapping based on the diffuse approximation D. Bouattoura 1"2 P. Gaillard 2 P. Villon 3 F. Langevin 4 1Heudiasyc UMR CNRS 6599, Universite de Technologie de Compiegne, BP 20529, F-60205 Compiegne cedex, France 2Laboratoire de Mod61isation et S0rete des Systemes, Universit~ de Technologie de Troyes, Troyes, France 3Departement G6nie des Systemes Mdcaniques, Universit~ de Technologie de Compi~gne, Compi~gne, France 4D~par~ement Genie Biomedical, Universite de Technologie de Compi~gne, Compiegne, France Abstract m Evoked potential mapping is a convenient technique to describe brain electrical activity using pictorial representation. A new interpolation method based on the diffuse approximation is applied to represent evoked potential distribution over the skull. The method retains most of the attractive features of the finite-element method but does not require explicit elements. In the simulation examples, the human head is assumed to be a single-layer sphere with homogeneous conductivity, and Ary eccentricity transformation is considered to approximate the more realistic three-shell model. The patterns shown in the computed maps suggest the ability of the proposed method to extract coherent information from the data from different electrodes. In the application protocol, visual evoked potentials are used to test the method with a realistic head shape. Keywords--Evoked potentials, Topographic mapping, Diffuse approximation Med. Biol. Eng. Comput., 1998, 36, 415-421 1 Introduction TOPOGRAPHICMAPPING is a tool widely used in neural elec- trophysiology to obtain a general representation of the mea- sured electrical activity on the surface of the skull (DUFFY et al., 1979; CUFFIN and COHEN, 1979). In evoked potential mapping, the distribution of the field can be displayed as maps using isopotential lines (contours) or patches for sequential time instants within the stimulation cycle. This implies, necessarily, that the analysis of one stimulation cycle involves many maps. To perform the brain mapping reconstruction correctly, it is important to take into consideration two crucial points: 9 the discrete spatial sampling involved by the number and location of electrodes, as much as possible uniformly spaced over the cortical region of interest or the whole head; this condition is due to the electromagnetic proper- ties of the biological media from cortex to skull (NUNEZ, 1981); different electrode configurations, usually based on 16, 32, 64 or even 124 leads, are used (GEVrNS, 1984) 9 the geometrical description of the head, usually modelled as a sphere (BARTH et aL, 1986), and the interpolation procedure. Nevertheless, such a lack of local precision in the computed map does not affect the ability of the representation to give an approximate pictorial description of the focusing of brain Correspondence should be addressed to Dr. Bouattoura; email: dj.bouattoura@utc.fr First received 8 March 1996 and in final form 4 February 1998 9 IFMBE: 1998 Medical & Biological Engineering & Computing July 1998 activities. The need for' better precision arises when the aim is to have an anatomical correlation of the possible sources of the detected potential, which is not the focus of this paper. To obtain an image of overall activity, it is necessary to interpolate values at new points between those recorded at electrode sites. Indeed, map quality depends closely on the spatial sampling and the interpolation method. Several approaches have been proposed to interpolate brain activity with a spherical model of the head, such as linear weighting interpolation in electro-encephalogram mapping (WALTER et al., 1984) and evoked potential mapping (DESMEDT et al., 1987), polynomial interpolation (ASHIDA et aL, 1984) and spline interpolation (PERRIN et al., 1989). Even though these approaches have quite different theoretical bases, they produce very similar interpolated maps and have a unique, major advantage: they are easy to implement. For more realistic models of the head, numerical methods are necessary to obtain a correct representation of the potential distribution. YAN et al. (1991) analysed the human head using the finite-element method, by investigating the effects of the eye orbit structure. ABBOUD et al. (1994) proposed a method based on finite-volume discretisation for calculating the poten- tial distribution in a four-layer spherical volume conductor due to a dipole current source. The reasons for the success of the finite-element method are well known: the local character of the approximations, the ability to deal with complex geometrical domains and the existence of a large set of approximation schemes adapted to various problems but embedded in a unified formulation. However, this method presents two main drawbacks. First, the approximation solutions provided by this approach present limited regularity. Generally, the solution itself is continuous, 415