Realistic Head Model Research Articles

MR electrical properties mapping using vision transformers and canny edge detectors.

We developed a 3D vision transformer-based neural network to reconstruct electrical properties (EP) from magnetic resonance measurements. Our network uses the magnitude of the transmit magnetic field of a birdcage coil, the associated transceive phase, and a Canny edge mask that identifies the object boundaries as inputs to compute the EP maps. We trained our network on a dataset of 10 000 synthetic tissue-mimicking phantoms and fine-tuned it on a dataset of 11 000 realistic head models. We assessed performance in-distribution simulated data and out-of-distribution head models, with and without synthetic lesions. We further evaluated our network in experiments for an inhomogeneous phantom and a volunteer. The conductivity and permittivity maps had an average peak normalized absolute error (PNAE) of 1.3% and 1.7% for the synthetic phantoms, respectively. For the realistic heads, the average PNAE for the conductivity and permittivity was 1.8% and 2.7%, respectively. The location of synthetic lesions was accurately identified, with reconstructed conductivity and permittivity values within 15% and 25% of the ground-truth, respectively. The conductivity and permittivity for the phantom experiment yielded 2.7% and 2.1% average PNAEs with respect to probe-measured values, respectively. The in vivo EP reconstruction truthfully preserved the subject's anatomy with average values over the entire head similar to the expected literature values. We introduced a new learning-based approach for reconstructing EP from MR measurements obtained with a birdcage coil, marking an important step towards the development of clinically-usable in vivo EP reconstruction protocols.

Semi-analytic three-shell forward calculation for magnetoencephalography

In previous studies, the magnetic lead field theorem in the quasi-static approximation was derived and used for the development of a method for the forward problem of MEG. It was applied and tested on a single-shell model of the human head and the question whether one shell is adequate enough for the calculation of the magnetic field is the main reason for this study. This forward method is based on the fundamental concept that one can calculate the lead field for MEG by decomposing it into two parts: the lead field of an arbitrary volume conductor that is already known and the gradient of basis functions that have to be harmonic, here derived from spherical harmonics. The problem then is reduced to evaluating the coefficients found in the basis functions. In this research we aim to improve the accuracy of the forward model, hence improving the localization accuracy in inverse methods by introducing a more detailed realistic head model. We here generalize the algorithm developed for a single-shell volume conductor to a three-shell volume conductor representing the brain, the skull and the skin with homogenous and isotropic conductivities in realistic ratios. The expansion to three shells could be tested as the three-shell algorithm is approaching the single-shell with high accuracy in special cases where three-shell solutions can also be calculated using a single-shell solution, especially for higher levels of expansion. The deviation in the calculation of the lead field is also evaluated when using three shells with realistic conductivities. The magnetic field turned out to differ to an important measurable extend in particular for deeper sources, making the three-shell algorithm substantially more accurate for these dipole locations.

Microwave Technique for Linear Skull Fracture Detection-Simulation and Experimental Study Using Realistic Human Head Models.

Microwave (MW) sensing is regarded as a promising technique for various medical monitoring and diagnostic applications due to its numerous advantages and the potential to be developed into a portable device for use outside hospital settings. The detection of skull fractures and the monitoring of their healing process would greatly benefit from a rapidly and frequently usable application that can be employed outside the hospital. This paper presents a simulation- and experiment-based study on skull fracture detection with the MW technique using realistic models for the first time. It also presents assessments on the most promising frequency ranges for skull fracture detection within the Industrial, Scientific and Medical (ISM) and ultrawideband (UWB) ranges. Evaluations are carried out with electromagnetic simulations using different head tissue layer models corresponding to different locations in the human head, as well as an anatomically realistic human head simulation model. The measurements are conducted with a real human skull combined with tissue phantoms developed in our laboratory. The comprehensive evaluations show that fractures cause clear differences in antenna and channel parameters (S11 and S21). The difference in S11 is 0.1-20 dB and in S21 is 0.1-30 dB, depending on the fracture width and location. Skull fractures with a less than 1 mm width can be detected with microwaves at different fracture locations. The detectability is frequency dependent. Power flow representations illustrate how fractures impact on the signal propagation at different frequencies. MW-based detection of skull fractures provides the possibility to (1) detect fractures using a safe and low-cost portable device, (2) monitor the healing-process of fractures, and (3) bring essential information for emerging portable MW-based diagnostic applications that can detect, e.g., strokes.

Improved Dipole Source Localization from Simultaneous MEG-EEG Data by Combining a Global Optimization Algorithm with a Local Parameter Search: A Brain Phantom Study.

Dipole localization, a fundamental challenge in electromagnetic source imaging, inherently constitutes an optimization problem aimed at solving the inverse problem of electric current source estimation within the human brain. The accuracy of dipole localization algorithms is contingent upon the complexity of the forward model, often referred to as the head model, and the signal-to-noise ratio (SNR) of measurements. In scenarios characterized by low SNR, often corresponding to deep-seated sources, existing optimization techniques struggle to converge to global minima, thereby leading to the localization of dipoles at erroneous positions, far from their true locations. This study presents a novel hybrid algorithm that combines simulated annealing with the traditional quasi-Newton optimization method, tailored to address the inherent limitations of dipole localization under low-SNR conditions. Using a realistic head model for both electroencephalography (EEG) and magnetoencephalography (MEG), it is demonstrated that this novel hybrid algorithm enables significant improvements of up to 45% in dipole localization accuracy compared to the often-used dipole scanning and gradient descent techniques. Localization improvements are not only found for single dipoles but also in two-dipole-source scenarios, where sources are proximal to each other. The novel methodology presented in this work could be useful in various applications of clinical neuroimaging, particularly in cases where recordings are noisy or sources are located deep within the brain.

Subject-specific atlas for automatic brain tissue segmentation of neonatal magnetic resonance images

Developing advanced systems for 3D brain tissue segmentation from neonatal magnetic resonance (MR) images is vital for newborn structural analysis. However, automatic segmentation of neonatal brain tissues is challenging due to smaller head size and inverted T1/T2 tissue contrast compared to adults. In this work, a subject-specific atlas based technique is presented for segmentation of gray matter (GM), white matter (WM), and cerebrospinal fluid (CSF) from neonatal MR images. It involves atlas selection, subject-specific atlas creation using random forest (RF) classifier, and brain tissue segmentation using the expectation maximization-Markov random field (EM-MRF) method. To increase the segmentation accuracy, different tissue intensity- and gradient-based features were used. Evaluation on 40 neonatal MR images (gestational age of 37–44 weeks) demonstrated an overall accuracy of 94.3% and an average Dice similarity coefficient (DSC) of 0.945 (GM), 0.947 (WM), and 0.912 (CSF). Compared to multi-atlas segmentation methods like SEGMA and EM-MRF with multiple atlases, our method improved accuracy by up to 4%, particularly in complex tissue regions. Our proposed method allows accurate brain tissue segmentation, a crucial step in brain magnetic resonance imaging (MRI) applications including brain surface reconstruction and realistic head model creation in neonates.

Flexible-Center Hat Complete Electrode Model for EEG Forward Problem.

This study aims to develop a more realistic electrode model by incorporating the non-uniform distribution of electrode contact conductance (ECC) and the shunting effects, to accurately solve EEG forward problem (FP). Firstly, a hat function is introduced to construct a more realistic hat-shaped distribution (HD) for ECC. Secondly, this hat function is modified by applying two parameters - offset ratio and offset direction - to account for the variability in ECC's center and to develop the flexible-center HD (FCHD). Finally, by integrating this FCHD into the complete electrode model (CEM) with the shunting effects, a novel flexible-center hat complete electrode model (FCH-CEM) is proposed and used to solve FP. Simulation experiments using a realistic head model demonstrate the necessity of FCH-CEM and its potential to improve the accuracy of the FP solution compared to current models, i.e., the point electrode model (PEM) and CEM. And compared to PEM, it has better performance under coarse mesh conditions (2 mm). Further experiments indicate the significance of considering shunting effects, as ignoring them results in larger errors than coarse mesh when the average contact conductance is large (101S/m2). The proposed FCH-CEM has better accuracy and performance than PEM and complements CEM in finer meshes, making it necessary for coarse meshes. This study proposes a novel model that enhances electrode modeling and FP accuracy, and provides new ideas and methods for future research.

Comparative analysis of non-invasive and invasive alternating electric fields therapy for malignant gliomas: a simulation study

Alternating electric fields (AEFs) at intermediate frequencies (100–300 kHz) and low intensities (1–3 V/cm) have shown promise as an effective approach for inhibiting cancer cell proliferation. However, a noticeable research gap exists in comparing the biophysical properties of invasive and non-invasive AEFs methods, and AEFs delivery strategies require further improvement. In this study, we constructed a realistic head model to simulate the effects of non-invasive and invasive AEFs on malignant gliomas. Additionally, a novel method was proposed involving the placement of a return electrode under the scalp. We simulated the electric field and temperature distributions in the brain tissue for each method. Our results underscore the advantages of invasive AEFs, showcasing their superior tumor-targeting abilities and reduced energy requirements. The analysis of brain tissue temperature changes reveals that non-invasive AEFs primarily generate heat at the scalp level, whereas invasive methods localize heat production within the tumor itself, thereby preserving surrounding healthy brain tissue. Our proposed invasive AEFs method also shows potential for selective electric field intervention. In conclusion, invasive AEFs demonstrate potential for precise and effective tumor treatment. Its enhanced targeting capabilities and limited impact on healthy tissue make it a promising avenue for further research in the realm of cancer treatment.

Impact of Titanium Skull Plate on Transcranial Magnetic Stimulation: Analysis of Induced Electric Fields

Background: Implanted titanium skull plates (TSPs) in cranioplasty are used to replace or reconstruct areas of the skull that have been damaged or removed due to trauma, surgery, or other medical conditions. However, the presence of a TSP in the head may influence the distribution of the electric field induced during transcranial magnetic stimulation (TMS) procedures. The purpose of this study was to determine how the presence of TSP would interfere with TMS-induced cortical electric fields. Methods: The TMS with a figure-of-eight coil was applied to a realistic head model with TSPs. The distribution of the induced electric field in head tissues was calculated by employing the impedance method, and the results were compared with that of a normal head without TSP. Results: Simulation results show that the distribution of the induced electric field has changed greatly for the head model with TSP. The maximum value of the induced electric field in head tissues was present under one of the circular coil wings rather than in the tissues beneath the junction of the two wings of the Fo8 coil. Conclusions: The induced electric field in deep brain regions was increased for the head model with TSP, which could potentially lead to deep brain stimulation. Since the presence of metallic TSP can greatly influence the distribution of the induced electric field in TMS applications, it is important to adjust the treatment scheme when considering TMS for individuals with cranial titanium plates.

A hybrid boundary element-finite element approach for solving the EEG forward problem in brain modeling.

This article introduces a hybrid BE-FE method for solving the EEG forward problem, leveraging the strengths of both the Boundary Element Method (BEM) and Finite Element Method (FEM). FEM accurately models complex and anisotropic tissue properties for realistic head geometries, while BEM excels in handling isotropic tissue regions and dipolar sources efficiently. The proposed hybrid method divides regions into homogeneous boundary element (BE) regions that include sources and heterogeneous anisotropic finite element (FE) regions. So, BEM models the brain, including dipole sources, and FEM models other head layers. Validation includes inhomogeneous isotropic/anisotropic three- and four-layer spherical head models, and a four-layer MRI-based realistic head model. Results for six dipole eccentricities and two orientations are computed using BEM, FEM, and hybrid BE-FE method. Statistical analysis, comparing error criteria of RDM and MAG, reveals notable improvements using the hybrid FE-BE method. In the spherical head model, the hybrid BE-FE method compared with FEM demonstrates enhancements of at least 1.05 and 38.31% in RDM and MAG criteria, respectively. Notably, in the anisotropic four-layer head model, improvements reach a maximum of 88.3% for RDM and 93.27% for MAG over FEM. Moreover, in the anisotropic four-layer realistic head model, the proposed hybrid method exhibits 55.4% improvement in RDM and 89.3% improvement in MAG compared to FEM. These findings underscore the proposed method is a promising approach for solving the realistic EEG forward problems, advancing neuroimaging techniques and enhancing understanding of brain function.

Insights from a model based study on optimizing non invasive brain electrical stimulation for Parkinson’s disease

Parkinson’s Disease (PD) is a disorder in the central nervous system which includes symptoms such as tremor, rigidity, and Bradykinesia. Deep brain stimulation (DBS) is the most effective method to treat PD motor symptoms especially when the patient is not responsive to other treatments. However, its invasiveness and high risk, involving electrode implantation in the Basal Ganglia (BG), prompt recent research to emphasize non-invasive Transcranial Electrical Stimulation (TES). TES proves to be effective in treating some PD symptoms with inherent safety and no associated risks. This study explores the potential of using TES, to modify the firing pattern of cells in BG that are responsible for motor symptoms in PD. The research employs a mathematical model of the BG to examine the impact of applying TES to the brain. This is conducted using a realistic head model incorporating the Finite Element Method (FEM). According to our findings, the firing pattern associated with Parkinson’s disease shifted towards a healthier firing pattern through the use of tACS. Employing an adaptive algorithm that continually monitored the behavior of BG cells (specifically, Globus Pallidus Pars externa (GPe)), we determined the optimal electrode number and placement to concentrate the current within the intended region. This resulted in a peak induced electric field of 1.9 v/m at the BG area. Our mathematical modeling together with precise finite element simulation of the brain and BG suggests that proposed method effectively mitigates Parkinsonian behavior in the BG cells. Furthermore, this approach ensures an improvement in the condition while adhering to all safety constraints associated with the current injection into the brain.

Shielded Cone Coil Array for Non-Invasive Deep Brain Magnetic Stimulation.

Non-invasive deep brain stimulation using transcranial magnetic stimulation is a promising technique for treating several neurological disorders, such as Alzheimer's and Parkinson's diseases. However, the currently used coils do not demonstrate the required stimulation performance in deep regions of the brain, such as the hippocampus, due to the rapid decay of the field inside the head. This study proposes an array that uses the cone coil method for deep stimulation. This study investigates the impact of magnetic core and shielding on field strength, focality, decay rate, and safety. The coil's size and shape effects on the electric field distribution in deep brain areas are also examined. The finite element method is used to calculate the induced electric field in a realistic human head model. The simulation results indicate that the magnetic core and shielding increase the electric field intensity and enhance focality but do not improve the field decay rate. However, the decay rate can be reduced by increasing the coil size at the expense of focality. By adopting an optimum cone structure, the proposed five-coil array reduces the electric field attenuation rate to reach the stimulation threshold in deep regions while keeping all other regions within safety limits. In vitro and in vivo experimental results using a head phantom and a dead pig's head validate the simulated results and confirm that the proposed design is a reliable and efficient candidate for non-invasive deep brain magnetic stimulation.

Magnetic Resonance Electrical Properties Tomography Based on Modified Physics-Informed Neural Network and Multiconstraints.

This paper presents a novel method based on leveraging physics-informed neural networks for magnetic resonance electrical property tomography (MREPT). MREPT is a noninvasive technique that can retrieve the spatial distribution of electrical properties (EPs) of scanned tissues from measured transmit radiofrequency (RF) in magnetic resonance imaging (MRI) systems. The reconstruction of EP values in MREPT is achieved by solving a partial differential equation derived from Maxwell's equations that lacks a direct solution. Most conventional MREPT methods suffer from artifacts caused by the invalidation of the assumption applied for simplification of the problem and numerical errors caused by numerical differentiation. Existing deep learning-based (DL-based) MREPT methods comprise data-driven methods that need to collect massive datasets for training or model-driven methods that are only validated in trivial cases. Hence we proposed a model-driven method that learns mapping from a measured RF, its spatial gradient and Laplacian to EPs using fully connected networks (FCNNs). The spatial gradient of EP can be computed through the automatic differentiation of FCNNs and the chain rule. FCNNs are optimized using the residual of the central physical equation of convection-reaction MREPT as the loss function (L). To alleviate the ill condition of the problem, we added multiconstraints, including the similarity constraint between permittivity and conductivity and the ℓ1 norm of spatial gradients of permittivity and conductivity, to the L. We demonstrate the proposed method with a three-dimensional realistic head model, a digital phantom simulation, and a practical phantom experiment at a 9.4T animal MRI system.

Modeling of blood flow in cerebral arterial circulation and its dynamic impact on electrical conductivity in a realistic multi-compartment head model

Background and ObjectiveThis study aims to assess the dynamic impact of non-Newtonian cerebral arterial circulation on electrical conductivity within a realistic multi-compartment head model. Evaluating this research question is crucial and challenging due to its relevance to electrophysiological modalities like transcranial electrical stimulation (tES), electro-/magnetoencephalography (EEG/MEG), and electrical impedance tomography (EIT). In these modalities, accurate forward modeling depends on the electrical conductivity, which is affected by complex tortuous vessel networks, limited data acquisition in Magnetic Resonance Imaging (MRI), and non-linear blood flow phenomena, including shear rate and viscosity in non-Newtonian fluid. MethodsTo obtain an approximation for the blood concentration, we first use Navier–Stokes equations (NSEs) to solve for the pressure and velocity of the blood in the major vessels. Then Fick's law is used to solve for the blood concentration in the tissues. Finally, Archie's law is used to estimate the electrical conductivity distribution based on the blood concentration. ResultsThe results, obtained with an open 7 Tesla MRI dataset, suggest that a dynamic model of cerebral blood flow (CBF) for both arterial and microcirculation can be established; we find blood pressure and electrical conductivity distributions given a numerically simulated pulse sequence and approximate the blood concentration and electrical conductivity inside the brain based on those. ConclusionsOur model provides an approximation of the dynamical blood flow and the corresponding electrical conductivity distribution in the different parts of the brain. The advantage of our approach is that it is applicable with limited a priori information about the blood flow and with an arbitrary head model distinguishing the arteries.

Electrophysiological brain imaging based on simulation-driven deep learning in the context of epilepsy

Identifying the location, the spatial extent and the electrical activity of distributed brain sources in the context of epilepsy through ElectroEncephaloGraphy (EEG) recordings is a challenging task because of the highly ill-posed nature of the underlying Electrophysiological Source Imaging (ESI) problem. To guarantee a unique solution, most existing ESI methods pay more attention to solve this inverse problem by imposing physiological constraints. This paper proposes an efficient ESI approach based on simulation-driven deep learning. Epileptic High-resolution 256-channels scalp EEG (Hr-EEG) signals are simulated in a realistic manner to train the proposed patient-specific model. More particularly, a computational neural mass model developed in our team is used to generate the temporal dynamics of the activity of each dipole while the forward problem is solved using a patient-specific three-shell realistic head model and the boundary element method. A Temporal Convolutional Network (TCN) is considered in the proposed model to capture local spatial patterns. To enable the model to observe the EEG signals from different scale levels, the multi-scale strategy is leveraged to capture the overall features and fine-grain features by adjusting the convolutional kernel size. Then, the Long Short-Term Memory (LSTM) is used to extract temporal dependencies among the computed spatial features. The performance of the proposed method is evaluated through three different scenarios of realistic synthetic interictal Hr-EEG data as well as on real interictal Hr-EEG data acquired in three patients with drug-resistant partial epilepsy, during their presurgical evaluation. A performance comparison study is also conducted with two other deep learning-based methods and four classical ESI techniques. The proposed model achieved a Dipole Localization Error (DLE) of 1.39 and Normalized Hamming Distance (NHD) of 0.28 in the case of one patch with SNR of 10 dB. In the case of two uncorrelated patches with an SNR of 10 dB, obtained DLE and NHD were respectively 1.50 and 0.28. Even in the more challenging scenario of two correlated patches with an SNR of 10 dB, the proposed approach still achieved a DLE of 3.74 and an NHD of 0.43. The results obtained on simulated data demonstrate that the proposed method outperforms the existing methods for different signal-to-noise and source configurations. The good behavior of the proposed method is also confirmed on real interictal EEG data. The robustness with respect to noise makes it a promising and alternative tool to localize epileptic brain areas and to reconstruct their electrical activities from EEG signals.

Applied machine learning for stroke differentiation by electrical impedance tomography with realistic numerical models

Electrical impedance tomography (EIT) may have potential to overcome existing limitations in stroke differentiation, enabling low-cost, rapid, and mobile data collection. Combining bioimpedance measurement technologies such as EIT with machine learning classifiers to support decision-making can avoid commonly faced reconstruction challenges due to the nonlinear and ill-posed nature of EIT imaging. Therefore, in this work, we advance this field through a study integrating realistic head models with clinically relevant test scenarios, and a robust architecture consisting of nested cross-validation and principal component analysis. Specifically, realistic head models are designed which incorporate the highly conductive layers of cerebrospinal fluid in the subarachnoid space and ventricles. In total, 135 unique models are created to represent a large patient population, with normal, haemorrhagic, and ischemic brains. Simulated EIT voltage data generated from these models are used to assess the classification performance of support vector machines. Parameters explored include driving frequency, signal-to-noise ratio, kernel function, and composition of binary classes. Classifier accuracy at 60 dB signal-to-noise ratio, reported as mean and standard deviation, are (79.92% ± 10.82%) for lesion differentiation, (74.78% ± 3.79%) for lesion detection, (77.49% ± 15.90%) for bleed detection, and (60.31% ± 3.98%) for ischemia detection (after ruling out bleed). The results for each method were obtained with statistics from 3 independent runs with 17,280 observations, polynomial kernel functions, and feature reduction of 76% by PCA (from 208 to 50 features). While results of this study show promise for stroke differentiation using EIT data, our findings indicate that the achievable accuracy is highly dependent on the classification scenario and application-specific classifiers may be necessary to achieve acceptable accuracy.

Directional sensitivity of cortical neurons towards TMS-induced electric fields

Abstract We derived computationally efficient average response models of different types of cortical neurons, which are subject to external electric fields from Transcranial Magnetic Stimulation. We used 24 reconstructions of pyramidal cells (PC) from layer 2/3, 245 small, nested, and large basket cells from layer 4, and 30 PC from layer 5 with different morphologies for deriving average models. With these models, it is possible to efficiently estimate the stimulation thresholds depending on the underlying electric field distribution in the brain, without having to implement and compute complex neuron compartment models. The stimulation thresholds were determined by exposing the neurons to TMS-induced electric fields with different angles, intensities, pulse waveforms, and field decays along the somato-dendritic axis. The derived average response models were verified by reference simulations using a high-resolution realistic head model containing several million neurons. The relative errors of the estimated thresholds between the average model and the reference model ranged between -3% and 3.7% in 98% of the cases, while the computation time was only a fraction of a second compared to several weeks. Finally, we compared the model behavior to TMS experiments and observed high correspondence to the orientation sensitivity of motor evoked potentials. The derived models were compared to the classical cortical column cosine model and to simplified ball-and-stick neurons. It was shown that both models oversimplify the complex interplay between the electric field and the neurons and do not adequately represent the directional sensitivity of the different cell types. The derived models are simple to apply and only require the TMS-induced electric field in the brain as input variable. The models and code are available to the general public in open-source repositories for integration into TMS studies to estimate the expected stimulation thresholds for an improved dosing and treatment planning in the future.

A hybrid 2D-FDTD/3D-MoM method used for the analysis of MRI RF coils

The design of radiofrequency (RF) coils is crucial for ultra-high field (UHF) magnetic resonance imaging (MRI) systems. To analyze RF coils, various numerical methods, such as finite-difference time-domain (FDTD) and method of moments (MoM), are usually adopted. In this paper, we present a novel hybrid approach that combines a two-dimensional (2D) FDTD with a three-dimensional (3D) MoM to analyze MRI RF problems. In our algorithm, the MoM is utilized for calculating the coil current, and FDTD is assigned for solving the electromagnetic (EM) fields in the imaging region. The hybrid method achieves superior efficiency and acceptable accuracy than using either method individually. To validate the hybrid method, we analyze an ellipse coil loaded with a uniform phantom and a realistic human head model, with the objective of tailoring the magnetic field intensity by adding a multilayer dielectric pad (DP). The results show an improvement in the magnetic field after optimizing the DP configuration. These simulation studies indicate the potential of the new numerical method for the design and analysis of RF systems for ultra-high field applications.

Low-cost, smartphone-based instant three-dimensional registration system for infant functional near-infrared spectroscopy applications.

To effectively apply functional near-infrared spectroscopy (fNIRS)/diffuse optical tomography (DOT) devices, a three-dimensional (3D) model of the position of each optode on a subject's scalp and the positions of that subject's cranial landmarks are critical. Obtaining this information accurately in infants, who rarely stop moving, is an ongoing challenge. We propose a smartphone-based registration system that can potentially achieve a full-head 3D scan of a 6-month-old infant instantly. The proposed system is remotely controlled by a custom-designed Bluetooth controller. The scanned images can either be manually or automatically aligned to generate a 3D head surface model. A full-head 3D scan of a 6-month-old infant can be achieved within 2s via this system. In testing on a realistic but static infant head model, the average Euclidean error of optode position using this device was 1.8mm. This low-cost 3D registration system therefore has the potential to permit accurate and near-instant fNIRS/DOT spatial registration.

Optimized high-definition tDCS in patients with skull defects and skull plates.

Transcranial direct current stimulation (tDCS) has been shown to benefit patients with brain lesions or traumatic brain injury (TBI). These patients usually have skull defects with different sizes and electrical conductivities. There is very little data in the literature that show how to optimally stimulate these patients with the presence of skull defects. Here we leveraged high-resolution (1 mm) realistic head models to explore the best montages targeting right beneath the skull defects with different sizes and conductivities. Specifically, open-source software ROAST was used to solve for the lead field on the publicly available MIDA model. Four different skull defects/plates were modeled with the center above the right primary motor cortex: a larger defect (10 cm diameter) modeled as either titanium or acrylic plate, and a smaller defect (2.5 cm diameter) modeled as either acute state filled with cerebrospinal fluid (CSF) or chronic state with scar tissue. Optimized stimulation with maximal intensity was run using ROAST targeting the right primary motor cortex. We show that optimized high-definition montages can achieve an average of 0.3 V/m higher stimulation intensities at the target compared to un-optimized montages (M1-SO or 4×1). Large skull defects with titanium or acrylic plates significantly reduce the stimulation intensity by about 80%, while small defects with acute (CSF) or chronic (scar) tissues significantly increase the stimulation intensity by about 200%. Furthermore, one can use M1-SO to achieve almost the same stimulation strength as the optimized montage if the skull has a large defect with titanium plate, and there is no significant difference in stimulation intensity between 4×1 montage and the optimized montage for small skull defects with scar tissue. Based on this work, future modeling studies leveraging individual anatomy of skull defects may help guide tDCS practice on patients with skull defects and skull plates.

Pressure–Poisson equation in numerical simulation of cerebral arterial circulation and its effect on the electrical conductivity of the brain

Background and ObjectiveThis study considers dynamic modeling of the cerebral arterial circulation and reconstructing an atlas for the electrical conductivity of the brain. Electrical conductivity is a governing parameter in several electrophysiological modalities applied in neuroscience, such as electroencephalography (EEG), transcranial electrical stimulation (tES), and electrical impedance tomography (EIT). While high-resolution 7-Tesla (T) Magnetic Resonance Imaging (MRI) data allow for reconstructing the cerebral arteries with a cross-sectional diameter larger than the voxel size, electrical conductivity cannot be directly inferred from MRI data. Brain models of electrophysiology typically associate each brain tissue compartment with a constant electrical conductivity, omitting any dynamic effects of cerebral blood circulation. Incorporating those effects poses the challenge of solving a system of incompressible Navier–Stokes equations (NSEs) in a realistic multi-compartment head model. However, using a simplified circulation model is well-motivated since, on the one hand, the complete system does not always have a numerically stable solution and, on the other hand, the full set of arteries cannot be perfectly reconstructed from the MRI data, meaning that any solution will be approximative. MethodsWe postulate that circulation in the distinguishable arteries can be estimated via the pressure–Poisson equation (PPE), which is coupled with Fick's law of diffusion for microcirculation. To establish a fluid exchange model between arteries and microarteries, a boundary condition derived from the Hagen–Poisseuille model is applied. The relationship between the estimated volumetric blood concentration and the electrical conductivity of the brain tissue is approximated through Archie's law for fluid flow in porous media. ResultsThrough the formulation of the PPE and a set of boundary conditions (BCs) based on the Hagen–Poisseuille model, we obtained an equivalent formulation of the incompressible Stokes equation (SE). Thus, allowing effective blood pressure estimation in cerebral arteries segmented from open 7T MRI data. ConclusionsAs a result of this research, we developed and built a useful modeling framework that accounts for the effects of dynamic blood flow on a novel MRI-based electrical conductivity atlas. The electrical conductivity perturbation obtained in numerical experiments has an appropriate overall match with previous studies on this subject. Further research to validate these results will be necessary.