Using reciprocity for relating the simulation of transcranial current stimulation to the EEG forward problem

To explore the relationship between transcranial current stimulation (tCS) and the electroencephalography (EEG) forward problem, we investigate and compare accuracy and efficiency of a reciprocal and a direct EEG forward approach for dipolar primary current sources both based on the finite element method (FEM), namely the adjoint approach (AA) and the partial integration approach in conjunction with a transfer matrix concept (PI). By analyzing numerical results, comparing to analytically derived EEG forward potentials and estimating computational complexity in spherical shell models, AA turns out to be essentially identical to PI. It is then proven that AA and PI are also algebraically identical even for general head models. This relation offers a direct link between the EEG forward problem and tCS. We then demonstrate how the quasi-analytical EEG forward solutions in sphere models can be used to validate the numerical accuracies of FEM-based tCS simulation approaches. These approaches differ with respect to the ease with which they can be employed for realistic head modeling based on MRI-derived segmentations. We show that while the accuracy of the most easy to realize approach based on regular hexahedral elements is already quite high, it can be significantly improved if a geometry-adaptation of the elements is employed in conjunction with an isoparametric FEM approach. While the latter approach does not involve any additional difficulties for the user, it reaches the high accuracies of surface-segmentation based tetrahedral FEM, which is considerably more difficult to implement and topologically less flexible in practice. Finally, in a highly realistic head volume conductor model and when compared to the regular alternative, the geometry-adapted hexahedral FEM is shown to result in significant changes in tCS current flow orientation and magnitude up to 45° and a factor of 1.66, respectively

Unification of optimal targeting methods in transcranial electrical stimulation

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.Fil: Fernandez Corazza, Mariano. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Investigaciones en Electrónica, Control y Procesamiento de Señales. Universidad Nacional de La Plata. Instituto de Investigaciones en Electrónica, Control y Procesamiento de Señales; ArgentinaFil: Turovets, Sergei. University of Oregon; Estados UnidosFil: Muravchik, Carlos Horacio. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Investigaciones en Electrónica, Control y Procesamiento de Señales. Universidad Nacional de La Plata. Instituto de Investigaciones en Electrónica, Control y Procesamiento de Señales; Argentina. Provincia de Buenos Aires. Gobernación. Comisión de Investigaciones Científicas; Argentin

Optimal use of EEG recordings to target active brain areas with transcranial electrical stimulation

To demonstrate causal relationships between brain and behavior, investigators would like to guide brain stimulationusing measurements of neural activity. Particularly promising in this context are electroencephalography (EEG) and transcranial electrical stimulation (TES), as they are linked by a reciprocity principle which, despite being known for decades, has not led to a formalism for relating EEG recordings to optimal stimulation parameters. Here we derive a closed-form expression for the TES configuration that optimally stimulates (i.e., targets) the sources of recorded EEG, without making assumptions about source location or distribution. We also derive a duality between TES targeting and EEG source localization, and demonstrate that in cases where source localization fails, so does the proposed targeting. Numerical simulations with multiple head models confirm these theoretical predictions and quantify the achieved stimulation in terms of focality and intensity. We show that constraining the stimulation currents automatically selects optimal montages that involve only a few (4−7) electrodes, with only incremental loss in performance when targeting focal activations. The proposed technique allows brain scientists and clinicians to rationally target the sources of observed EEG and thus overcomes a major obstacle to the realization of individualized or closed-loop brain stimulation

Transcranial direct current stimulation and sports performance

The application of transcranial direct current stimulation (tDCS) hasmoved fromthe laboratory to the wider community. This form of non-invasive brain stimulation has been shown in a number of controlled animal and human experiments, over nearly five decades, to modulate brain physiology, cognitive functions, and behavior. While its effects are variable across and within individuals, it is not unreasonable to state that tDCS harbors the potential to enhance executive and physical human performance. In a society increasingly driven to succeed with less effort, performance enhancement with an intervention that has an excellent safety record, is well tolerated, relatively inexpensive and readily available, is particularly appealing. Here, we offer a perspective on tDCS for the enhancement of physical performance in sport

Variability of head tissues’ conductivities and their impact in electrical brain activity research

The presented thesis endeavoured to establish the impact that the variability in electrical conductivity of human head tissues has on electrical brain imaging research, particularly transcranial direct current stimulation (tDCS) and electroencephalography (EEG). A systematic meta-analysis was firstly conducted to determine the consistency of reported measurements, revealing significant deviations in electrical conductivity measurements predominantly for the scalp, skull, GM, and WM. Found to be of particular importance was the variability of skull conductivity, which consists of multiple layers and bone compositions, each with differing conductivity. Moreover, the conductivity of the skull was suggested to decline with participant age and hypothesised to correspondingly impact tDCS induced fields. As expected, the propositioned decline in the equivalent (homogeneous) skull conductivity as a function of age resulted in reduced tDCS fields. A further EEG analysis also revealed, neglecting the presence of adult sutures and deviation in proportion of spongiform and compact bone distribution throughout the skull, ensued significant errors in EEG forward and inverse solutions. Thus, incorporating geometrically accurate and precise volume conductors of the skull was considered as essential for EEG forward analysis and source localisation and tDCS application. This was an overarching conclusion of the presented thesis. Individualised head models, particularly of the skull, accounting for participant age, the presence of sutures and deviation in bone composition distribution are imperative for electrical brain imaging. Additionally, it was shown that in vivo, individualised measurements of skull conductivity are further required to fully understand the relationship between conductivity and participant demographics, suture closure, bone compositions, skull thickness and additional factors

Variation in Reported Human Head Tissue Electrical Conductivity Values

Electromagnetic source characterisation requires accurate volume conductor models representing head geometry and the electrical conductivity field. Head tissue conductivity is often assumed from previous literature, however, despite extensive research, measurements are inconsistent. A meta-analysis of reported human head electrical conductivity values was therefore conducted to determine significant variation and subsequent influential factors. Of 3121 identified publications spanning three databases, 56 papers were included in data extraction. Conductivity values were categorised according to tissue type, and recorded alongside methodology, measurement condition, current frequency, tissue temperature, participant pathology and age. We found variation in electrical conductivity of the whole-skull, the spongiform layer of the skull, isotropic, perpendicularly- and parallelly-oriented white matter (WM) and the brain-to-skull-conductivity ratio (BSCR) could be significantly attributed to a combination of differences in methodology and demographics. This large variation should be acknowledged, and care should be taken when creating volume conductor models, ideally constructing them on an individual basis, rather than assuming them from the literature. When personalised models are unavailable, it is suggested weighted average means from the current meta-analysis are used. Assigning conductivity as: 0.41 S/m for the scalp, 0.02 S/m for the whole skull, or when better modelled as a three-layer skull 0.048 S/m for the spongiform layer, 0.007 S/m for the inner compact and 0.005 S/m for the outer compact, as well as 1.71 S/m for the CSF, 0.47 S/m for the grey matter, 0.22 S/m for WM and 50.4 for the BSCR