Enhanced tES and tDCS computational models by meninges emulation

Objective. Understanding how current reaches the brain during transcranial electrical stimulation (tES) underpins efforts to rationalize outcomes and optimize interventions. To this end, computational models of current flow relate applied dose to brain electric field. Conventional tES modeling considers distinct tissues like scalp, skull, cerebrospinal fluid (CSF), gray matter and white matter. The properties of highly conductive CSF are especially important. However, modeling the space between skull and brain as entirely CSF is not an accurate representation of anatomy. The space conventionally modeled as CSF is approximately half meninges (dura, arachnoid, and pia) with lower conductivity. However, the resolution required to describe individual meningeal layers is computationally restrictive in an MRI-derived head model. Emulating the effect of meninges through CSF conductivity modification could improve accuracy with minimal cost. Approach. Models with meningeal layers were developed in a concentric sphere head model. Then, in a model with only CSF between skull and brain, CSF conductivity was optimized to emulate the effect of meningeal layers on cortical electric field for multiple electrode positions. This emulated conductivity was applied to MRI-derived models. Main results. Compared to a model with conventional CSF conductivity (1.65 S m−1), emulated CSF conductivity (0.85 S m−1) produced voltage fields better correlated with intracranial recordings from epilepsy patients. Significance. Conventional tES models have been validated using intracranial recording. Residual errors may nonetheless impact model utility. Because CSF is so conductive to current flow, misrepresentation of the skull-brain interface as entirely CSF is not realistic for tES modeling. Updating the conventional model with a CSF conductivity emulating the effect of the meninges enhances modeling accuracy without increasing model complexity. This allows existing modeling pipelines to be leveraged with a simple conductivity change. Using 0.85 S m−1 emulated CSF conductivity is recommended as the new standard in non-invasive brain stimulation modeling

Translational Modeling of Non-Invasive Electrical Stimulation

Seminal work in the early 2000’s demonstrated the effect of low amplitude non-invasive electrical stimulation in people using neurophysiological measures (motor evoked potentials, MEPs). Clinical applications of transcranial Direct Current Stimulation (tDCS) have since proliferated, though the mechanisms are not fully understood. Efforts to refine the technique to improve results are on-going as are mechanistic studies both in vivo and in vitro. Volume conduction models are being applied to these areas of research, especially in the design and analysis of clinical montages. However, additional research on the parameterization of models remains. In this dissertation, Finite Element Method (FEM) models of current flow were developed for clinical applications. The first image-derived models of obese subjects were developed to assess the relative impact of fat delineation from skin. Body mass index and more broadly inter-individual differences were considered. The effect of incorporating the meninges was predicted from CAD-based (Computer Aided Design) models before being translated into image-derived head models as an “emulated” CSF conductivity. These predictions were tested in a recently validated database of head models. Multi-scale models of transcutaneous vagus nerve stimulation (tVNS) were developed by coupling image-derived volume conduction models with physiological compartment modeling. The impact of local tissue inhomogeneities on fiber activation were considered

EEG OSCILLATORY ACTIVITIES FROM HUMAN MOTOR BRAIN

Motor skills are essential in people’s daily life in exploring and interacting with the ambient environment. Impairments to motor functions affect the acquisition of motor skills, which not only reduce the quality of life, but also impose heavy economic burdens to sufferers and their families. Oscillatory activities in electroencephalography (EEG), such as the mu rhythm, present functional correlation to motor functions, which provide accessible windows to understand underlying neural mechanism in healthy persons and perform diagnoses in patients with various motor impairments. It is thus of significant importance to further investigate classic and/or identify new motor-related EEG oscillatory activities. In this dissertation, EEG oscillations from both infants and adults are investigated to uncover motor-related neural information noninvasively from the human brain regarding their developmental changes and movement representations of body parts, respectively. In typical developing infants at 5-7 months of age, knowledge about mu rhythm development is expanded by capturing subtle developmental changes of its characteristics in a fine age resolution, through the development of new spatio-spectral analysis of EEG data recorded longitudinally on a weekly basis. In adults, motor tasks involving fine body parts are studied to investigate EEG resolutions in decoding movements/motor imageries of individual fingers, which have only been addressed in large body parts in literature. Discriminative information in EEG oscillations about motor tasks of fine body parts is revealed through the discovery of a novel type of spectral structures in EEG, which exhibits better sensitivity to movements of fine body parts than the classic mu rhythm. The findings in this dissertation broaden the scope of neural information in EEG oscillations in relation to motor functions, and contribute to the understanding about human motor functions at various life stages. These results and technologies are promising to be translated to patient studies in the future

Reduction of conductivity uncertainty propagations in the inverse problem of EEG source analysis

In computer simulations, the response of a system under study depends on the input parameters. Each of these parameters can be assigned a fixed value or a range of values within the input parameter space for system performance evaluations. Starting from values of the input parameters and a certain given model, the so-called forward problem can be solved that needs to approximate the output of the system. Starting from measurements related to the output of the system model it is possible to determine the state of the system by solving the so-called inverse problem. In the case of a non-linear inverse problem, non-linear minimization techniques need to be used where the forward model is iteratively evaluated for different input parameters. The accuracy of the solution in the inverse problem is however decreased due to the noise available in the measurements and due to uncertainties in the system model. Uncertainties are parameters for which their values are not exactly known and/or that can vary in time and/or depend on the environment. These uncertainties have, for given input parameter values, an influence on the forward problem solution. This forward uncertainty propagation leads then to errors in the inverse solutions because the forward model is iteratively evaluated for recovering the inverse solutions. Until now, it was assumed that the recovery errors could not be reduced. The only option was to either quantify the uncertain parameter values as accurate as possible or to reflect the uncertainty in the inverse solutions, i.e. determination of the region in parameter space wherein the inverse solution is likely to be situated. The overall aim of this thesis was to develop reduction techniques of inverse reconstruction errors so that the inverse problem is solved in a more robust and thus accurate way. Methodologies were specifically developed for electroencephalography (EEG) source analysis. EEG is a non-invasive technique that measures on the scalp of the head, the electric potentials induced by the neuronal activity. EEG has several applications in biomedical engineering and is an important diagnostic tool in clinical neurophysiology. In epilepsy, EEG is used to map brain areas and to receive source localization information that can be used prior to surgical operation. Starting from Maxwell’s equations in their quasi-static formulation and from a physical model of the head, the forward problem predicts the measurements that would be obtained for a given configuration of current sources. The used headmodels in this thesis are multi-layered spherical head models. The neural sources are parameterized by the location and orientation of electrical dipoles. In this thesis, a set of limited number of dipole sources is used as source model leading to a well posed inverse problem. The inverse problem starts from measured EEG data and recovers the locations and orientations of the electrical dipole sources. A loss in accuracy of the recovered neural sources occurs because of noise in the EEG measurements and uncertainties in the forward model. Especially the conductivity values of scalp, skull and brain are not well known since these values are difficult to measure. Moreover, these uncertainties can vary from person to person, in time, etc. In this thesis, novel numerical methods are developed so to provide new approaches in the improvement of spatial accuracy in EEG source analysis, taking into account model uncertainties. Nowadays, the localization of the electrical activity in the brain is still a current and challenging research topic due to the many difficulties arising e.g. in the process of modeling the head and dealing with the not well known conductivity values of its different tissues. Due to uncertainty in the conductivity value of the head tissues, high values of errors are introduced when solving the EEG inverse problem. In order to improve the accuracy of the solution of the inverse problem taking into account the uncertainty of the conductivity values, a new mathematical approach in the definition of the cost function is introduced and new techniques in the iterative scheme of the inverse reconstruction are proposed. The work in this thesis concerns three important phases. In a first stage, we developed a robust methodology for the reduction of errors when reconstructing a single electrical dipole in the case of a single uncertainty. This uncertainty concerns the skull to soft tissue conductivity ratio which is an important parameter in the forward model. This conductivity ratio is difficult to quantify and depends from person to person. The forward model that we employed is a three shell spherical head model where the forward potentials depend on the conductivity ratio. We reformulated the solution of the forward problem by using a Taylor expansion around an actual value of the conductivity ratio which led to a linear model of the solution for the simulated potentials. The introduction of this expanded forward model, led to a sensitivity analysis which provided relevant information for the reconstruction of the sources in EEG source analysis. In order to develop a technique for reducing the errors in inverse solutions, some challenging mathematical questions and computational problems needed to be tackled. We proposed in this thesis the Reduced Conductivity Dependence (RCD) method where we reformulate the traditional cost function and where we incorporated some changes with respect to the iterative scheme. More specifically, in each iteration we include an internal fitting procedure and we propose selection of sensors. The fitting procedure makes it possible to have an as accurate as possible forward model while the selection procedure eliminates the sensors which have the highest sensitivity to the uncertain skull to brain conductivity ratio. Using numerical experiments we showed that errors in reconstructed electrical dipoles are reduced using the RCD methodology in the case of no noise in measurements and in the case of noise in measurements. Moreover, the procedure for the selection of electrodes was thoroughly investigated as well as the influence of the use of different EEG caps (with different number of electrodes). When using traditional reconstruction methods, the number of electrodes has not a high influence on the spatial accuracy of the reconstructed single electrical dipole. However, we showed that when using the RCD methodology the spatial accuracy can be even more increased. This because of the selection procedure that is included within the RCD methodology. In a second stage, we proposed a RCD method that can be applied for the reconstruction of a limited number of dipoles in the case of a single uncertainty. The same ideas were applied onto the Recursively Applied and Projected Multiple Signal Classification (RAP-MUSIC) algorithm. The three shell spherical head model was employed with the skull to brain conductivity ratio as single uncertainty. We showed using numerical experiments that the spatial accuracy of each reconstructed dipole is increased, i.e. reduction of the conductivity dependence of the inverse solutions. Moreover, we illustrated that the use of the RCD-based subspace correlation cost function leads to a high efficiency even for high noise levels. Finally, in a third stage, we developed a RCD methodology for the reduction of errors in the case of multiple uncertainties. We used a five shell spherical head model where conductivity ratios with respect to skull, cerebrospinal fluid, and white matter were uncertain. The cost function as well as the fitting and selection procedure of the RCD method were extended. The numerical experiments showed reductions in the reconstructed electrical dipoles in comparison with the traditional methodology and also compared to the RCD methodology developed for dealing with a single uncertainty