RESUMEN
One of the major questions in high-density transcranial electrical stimulation (TES) is: given a region of interest (ROI) and electric current limits for safety, how much current should be delivered by each electrode for optimal targeting of the ROI? Several solutions, apparently unrelated, have been independently proposed depending on how "optimality" is defined and on how this optimization problem is stated mathematically. The least squares (LS), weighted LS (WLS), or reciprocity-based approaches are the simplest ones and have closed-form solutions. An extended optimization problem can be stated as follows: maximize the directional intensity at the ROI, limit the electric fields at the non-ROI, and constrain total injected current and current per electrode for safety. This problem requires iterative convex or linear optimization solvers. We theoretically prove in this work that the LS, WLS and reciprocity-based closed-form solutions are specific solutions to the extended directional maximization optimization problem. Moreover, the LS/WLS and reciprocity-based solutions are the two extreme cases of the intensity-focality trade-off, emerging under variation of a unique parameter of the extended directional maximization problem, the imposed constraint to the electric fields at the non-ROI. We validate and illustrate these findings with simulations on an atlas head model. The unified approach we present here allows a better understanding of the nature of the TES optimization problem and helps in the development of advanced and more effective targeting strategies.
Asunto(s)
Corteza Cerebral/fisiología , Modelos Biológicos , Neuroimagen/normas , Estimulación Transcraneal de Corriente Directa/normas , Atlas como Asunto , Simulación por Computador , Humanos , Neuroimagen/métodos , Estimulación Transcraneal de Corriente Directa/métodosRESUMEN
OBJECTIVE: To estimate scalp, skull, compact bone, and marrow bone electrical conductivity values based on electrical impedance tomography (EIT) measurements, and to determine the influence of skull modeling details on the estimates. METHODS: We collected EIT data with 62 current injection pairs and built five 6-8 million finite element (FE) head models with different grades of skull simplifications for four subjects, including three whose head models serve as Atlases in the scientific literature and in commercial equipment (Colin27 and EGI's Geosource atlases). We estimated electrical conductivity of the scalp, skull, marrow bone, and compact bone tissues for each current injection pair, each model, and each subject. RESULTS: Closure of skull holes in FE models, use of simplified four-layer boundary element method-like models, and neglecting the CSF layer produce an overestimation of the skull conductivity of 10%, 10%-20%, and 20%-30%, respectively (accumulated overestimation of 50%-70%). The average extracted conductivities are 288 ± 53 (the scalp), 4.3 ± 0.08 (the compact bone), and 5.5 ± 1.25 (the whole skull) mS/m. The marrow bone estimates showed large dispersion. CONCLUSION: Present EIT estimates for the skull conductivity are lower than typical literature reference values, but previous in vivo EIT results are likely overestimated due to the use of simpler models. SIGNIFICANCE: Typical literature values of 7-10 mS/m for skull conductivity should be replaced by the present estimated values when using detailed skull head models. We also provide subject specific conductivity estimates for widely used Atlas head models.
Asunto(s)
Conductividad Eléctrica , Procesamiento de Imagen Asistido por Computador/métodos , Cráneo/diagnóstico por imagen , Tomografía/métodos , Adulto , Impedancia Eléctrica , Electroencefalografía , Análisis de Elementos Finitos , Cabeza/diagnóstico por imagen , Cabeza/fisiología , Humanos , Masculino , Persona de Mediana Edad , Modelos Biológicos , Cuero Cabelludo/diagnóstico por imagen , Cuero Cabelludo/fisiología , Cráneo/fisiologíaRESUMEN
We extend the diffusion tensor (DT) signal model for multiple-coil acquisition systems. Considering the sum-of-squares reconstruction method, we compute the Cramér-Rao bound (CRB) assuming the widely accepted noncentral chi distribution. Within this framework, we assess the effect of noise in DT estimation and other measures derived from it, as a function of the number of acquisition coils, as well as other system parameters. We show the applications of CRB in many actual problems related to DT estimation: we compare different gradient field setup schemes proposed in the literature and show how the CRB can be used to choose a convenient one; we show that for fiber-type anisotropy tensors the ellipsoidal area ratio (EAR) can be estimated with less error than other scalar factors such as the fractional anisotropy (FA) or the relative anisotropy (RA), and that for this type of anisotropy tensors, increasing the number of coils is equivalent to increasing the signal-to-noise ratio, i.e., the information of the different coils can be regarded as independent. Also, we present results showing the CRB of several parameters for actual DT-MRI data. We conclude that the CRB is a valuable tool to optimal experiment design in DT-related studies.