The T1 head template model used in Statistical Parametric Mapping Version 2000 (SPM2), was segmented into five layers (scalp, skull, CSF, grey and white matter) and implemented in 2 mm voxels. We designed a resistor mesh model (RMM), based on the finite volume method (FVM) to simulate the electrical properties of this head model along the three axes for each voxel. Then, we introduced four dipoles of high eccentricity (about 0.8) in this RMM, separately and simultaneously, to compute the potentials for two sets of conductivities. We used the direct cortical imaging technique (CIT) to recover the simulated dipoles, using 60 or 107 electrodes and with or without addition of Gaussian white noise (GWN). The use of realistic conductivities gave better CIT results than standard conductivities, lowering the blurring effect on scalp potentials and displaying more accurate position areas when CIT was applied to single dipoles. Simultaneous dipoles were less accurately localized, but good qualitative and stable quantitative results were obtained up to 5% noise level for 107 electrodes and up to 10% noise level for 60 electrodes, showing that a compromise must be found to optimize both the number of electrodes and the noise level. With the RMM defined in 2 mm voxels, the standard 128-electrode cap and 5% noise appears to be the upper limit providing reliable source positions when direct CIT is used. The admittance matrix defining the RMM is easy to modify so as to adapt to different conductivities. The next step will be the adaptation of individual real head T2 images to the RMM template and the introduction of anisotropy using diffusion imaging (DI).

A resistor mesh model (RMM) has been implemented to describe the electrical properties of the head and the configuration of the intracerebral current sources by simulation of forward and inverse problems in electroencephalogram/event related potential (EEG/ERP) studies. For this study, the RMM representing the three basic tissues of the human head (brain, skull and scalp) was superimposed on a spherical volume mimicking the head volume: it included 43 102 resistances and 14 123 nodes. The validation was performed with reference to the analytical model by consideration of a set of four dipoles close to the cortex. Using the RMM and the chosen dipoles, four distinct families of interpolation technique (nearest neighbour, polynomial, splines and lead fields) were tested and compared so that the scalp potentials could be recovered from the electrode potentials. The 3D spline interpolation and the inverse forward technique (IFT) gave the best results. The IFT is very easy to use when the lead-field matrix between scalp electrodes and cortex nodes has been calculated. By simple application of the Moore-Penrose pseudo inverse matrix to the electrode cap potentials, a set of current sources on the cortex is obtained. Then, the forward problem using these cortex sources renders all the scalp potentials.

A resistor mesh model (RMM) has been validated with reference to the analytical model by consideration of a set of four dipoles close to the cortex. The application of the RMM to scalp potential interpolation was detailed in Part 1. Using the RMM and the same four dipoles, the different methods of cortical mapping were compared and have shown the potentiality of this RMM for obtaining current and potential cortical distributions. The lead-field matrices are well-adapted tools, but the use of a square matrix of high dimension does not permit the inverse solution to be improved in the presence of noise, as a regularisation technique is necessary with noisy data. With the RMM, the transfer matrix and the cortical imaging technique proved to be easy to implement. Further development of the RMM will include application to more realistic head models with more accurate conductivities.

Bone thickness, anisotropy, and inhomogeneity have been reported to induce important variations in electroencephalogram (EEG) scalp potentials. To study this effect, we used an original three‐dimensional (3‐D) resistor mesh model described in spherical coordinates, consisting of 67,464 elements and 22,105 nodes arranged in 36 different concentric layers. After validation of the model by comparison with the analytic solution, potential variations induced by geometric and electrical skull modifications were investigated at the surface in the dipole plane and along the dipole axis, for several eccentricities and bone thicknesses. The resistor mesh permits one to obtain various configurations, as local modifications are introduced very easily. This has allowed several head models to be designed to study the effects of skull properties (thickness, anisotropy, and heterogeneity) on scalp surface potentials. Results show a decrease of potentials in bone, depending on bone thickness, and a very small decrease through the scalp layer. Nevertheless, similar scalp potentials can be obtained using either a thick scalp layer and a thin skull layer, and vice versa. It is thus important to take into account skull and scalp thicknesses, because the drop of potential in bone depends on both. The use of three different layers for skull instead of one leads to small differences in potential values and patterns. In contrast, the introduction of a hole in the skull highly increases the maximum potential value (by a factor of 11.5 in our case), because of the absence of potential drop in the corresponding volume. The inverse solution without any a priori knowledge indicates that the model with the hole gives the largest errors in both position and dipolar moment. Our results indicate that the resistor mesh model can be used as a robust and user‐friendly simulation tool in EEG or event‐related potentials. It makes it possible to build up real head models directly from anatomic magnetic resonance imaging without tessellation, and is able to take into account head heterogeneities very simply by changing volume elements conductivity. Hum. Brain Mapping 21:84–95, 2004. © 2003 Wiley‐Liss, Inc.

In electroencephalography (EEG) and event related potentials (ERP), localizing the electrical sources at the origin of scalp potentials (inverse problem) imposes, in a first step, the computation of scalp potential distribution from the simulation of sources (forward problem). This article proposes an alternative method for mimicing both the electrical and geometrical properties of the head, including brain, skull, and scalp tissue with resistors. Two resistor mesh models have been designed to reproduce the three-sphere reference model (analytical model). The first one (spherical resistor mesh) closely mimics the geometrical and electrical properties of the analytical model. The second one (cubic resistor mesh) is designed to conveniently handle anatomical data from magnetic resonance imaging. Both models have been validated, in reference to the analytical solution calculated on the three-sphere model, by computing the magnification factor and the relative difference measure. Results suggest that the mesh models can be used as robust and user-friendly simulation or exploration tools in EEG/ERP. (C) 2003 American Institute of Physics.

A spherical head model based on a resistor mesh is presented. Each resistor corresponds to the conducting electrical properties of a tissue volume. A current dipole is simulated by an electrical current source connected between two nodes in this mesh. The direct problem is solved and the accuracy of this model is evaluated in comparison with the analytical solution. The results show that the resistor mesh provides correct potential and scalp current density values. The model structure makes it easy to introduce conductivity heterogeneities such as stroke and skull anisotropy. First trials of an inverse method are also presented.

Several models of the human head have been published to study the activity of neural sources. The most widely used represents brain, skull and scalp tissues by three concentric spheres. For this model, an analytical solution of the direct problem, consisting in calculating potential mapping due to a dipole current source in the brain, exists. For a decade, models with numerical solutions have been developed, taking in account real geometry and conductivity of the head. We propose a new modelling approach based on a resistor mesh, each resistor representing a volume element of given geometry and conductivity. This paper presents the validation of this mesh model, which has been carried out in reference to the analytical solution, giving good results. The ability of the model to provide potentials everywhere in the mesh let us study the skull anisotropy smearing effect and also the effect of a conductivity heterogeneity. The corresponding modifications of spatial potential distribution are presented.

We present an analysis of spline interpolation technique used both for potential (V) and scalp current density (SCD) interpolation in event related potential (ERP) mapping. For a single current dipole with high eccentricity (0.8), and not pointing at any electrode, we compare the simulated signal to the interpolated one. The number of electrodes to use and the effect of noise level on the quality of the interpolation are discussed. We conclude that spherical spline interpolation technique is optimized with a 120 electrode head cap.

In this biomedical study we have tested a non invasive bioimpedance spectroscopy system for the detection of breast cancer. Three groups of women presenting tumors to T2, T1 and T0 tumor size have been screened. The experimental setup and conditions are described. The results and the limits of the experimental setup are analyzed. Possible improvements are discussed.

Ex vivo bioimpedance data measured on normal and cancerous female breast tissues are reported. They clearly show that the electrical properties of normal tissues, surrounding tissues, and carcinoma are different. These differences lie in the conductivity, in the characteristic frequency (frequency of the maximum of the imaginary part of the bioimpedance), and also in the shape of the Bode plots. Modeling using an R-S-Z(cpe) model is reported as mil as indexes extracted from the real and imaginary parts of the bioimpedance. Even if a classification of the different types of tissues remains a difficult task and leads to much less precise diagnosis than microscopic examination, the electrical behavior of mammary tissue could be used to develop a noninvasive technique for early breast cancer detection.

A method is proposed by which bioelectric impedance spectrometry is combined with bioelectric impedance imaging to provide noninvasive characterization of tissue. Multifrequency measurements are performed on a numerical phantom (a mesh of 208 square pixels, each side of the square being replaced by a RSC circuit to simulate tissue impedance). An impedance perturbation (characterized by a change in the characteristic frequency) placed on the circuit can be reconstructed thanks to a direct sensitivity matrix (DSM) determined by simulation and specially built for the numerical phantom. The reconstructed information in the pixel of the characteristic frequency and image of perturbations is shown

A phantom was designed for studying in vitro acquisition procedures and reconstruction algorithms for multifrequency electrical impedance tomography (EIT). The phantom mimics a circular region discretized in 208 square pixels whose sides are composed of Cole models. A modular design, based on plug-in boards, provides facilities for modifying the electrical parameters of any pixel. This phantom is used especially for studying tissue characterization by imaging the characteristic frequency

A multifrequency (1 kHz - 1 MHz) serial electrical impedance tomography (EIT) system has been developed. It is based on 16 active electrodes and can be extended up to 32. Each active electrode can be programmed for current driving and for measuring either the injected current or the voltage difference between adjacent electrodes, and includes calibration facilities. Real and imaginary parts of the impedance are obtained by applying a parametric identification method (extended Prony), but other techniques are easily adaptable. Image reconstruction is carried out using the Sheffield filtered back-projection algorithm. Characteristic frequency images are under development and should be of great interest to distinguish between normal and tumorous tissues.

Three parametric modelling approaches based on the Cole-Cole model are introduced. Comparison between modelling only the real part and modelling both the real and imaginary parts is carried out by simulations, in which random and systematic noise are considered, respectively. The results of modelling the in vitro data collected from sheep are given to reach the conclusions.

In several areas of clinical medicine, electrical impedance tomography could offer significant advantages over existing methods. These advantages have been supported by preliminary studies or by validation studies, which are described. The suggested applications are reviewed in this section. They mainly concern developments in impedance variations on brain, lung (neonatal, edema, emphysema), and heart; changes in blood volume, gastrointestinal system (gastric emptying, gastroesophageal reflux, pharyngeal transit time); pelvis (pelvis congestion); and thermal mapping in hyperthermia and breast (tissue characterization). The conductivity information at one frequency in a pixel is insufficient to take into account the very complex physiological mechanisms that underlie the observed impedance changes. To gain a better understanding of these mechanisms, research is currently being carried out on imaging of the imaginary part, parametric imaging, spectroscopic imaging, and 3D imaging, which are developed at the end of this section.

After a brief historical overview, the concept of electrical impedance is introduced as a principle of transduction calling attention to the possible mechanisms by which a physiological event may change impedance, i.e., by geometric, resistivity, and/or permittivity changes. Thereafter, since impedance measurements usually require the injection of current, its biological effects are discussed in order to establish the safety criteria. Finally, the elements found in an impedancimetric circuit and their respective nature are presented and described. The particular behavior of the biological impedance and the electrode/electrolyte interface appear immediately as strikingly important. The section ends with a bird's-eye view of the basic circuitry to measure impedance. Each subsection is closed by partial conclusions to underline the relevant concepts.