Leandro Beltrachini

Ultra‐low‐field (ULF) MRI is emerging as an alternative modality to high field (HF) MRI due to its lower cost, minimal siting requirements, portability and enhanced accessibility—factors that enable large‐scale deployment. Although ULF‐MRI exhibits a lower signal‐to‐noise ratio (SNR), advanced imaging and data‐driven denoising methods enabled by high‐performance computing have made contrasts like diffusion‐weighted imaging (DWI) feasible at ULF. This study investigates the potential and limitations of ULF tractography, using data acquired on a 0.064 T commercially available mobile point‐of‐care MRI scanner. The results demonstrate that most major white matter bundles can be successfully retrieved in healthy adult brains within clinically tolerable scan times. This study also examines the recovery of diffusion tensor imaging (DTI)‐derived scalar maps, including fractional anisotropy and mean diffusivity. Strong correspondence is observed between scalar maps obtained with ULF‐MRI and those acquired at high field strengths. Furthermore, fibre orientation distribution functions reconstructed from ULF data show good agreement with high‐field references, supporting the feasibility of using ULF‐MRI for reliable tractography. These findings open new opportunities to use ULF‐MRI in studies of brain health, development and disease progression—particularly in populations traditionally underserved due to geographic or economic constraints. The results show that robust assessments of white matter microstructure can be achieved with ULF‐MRI, effectively democratising microstructural MRI and extending advanced imaging capabilities to a broader range of research and clinical settings where resources are typically limited.

Objective. Inclusion of individualised electrical conductivities of head tissues is crucial for the accuracy of electrical source imaging techniques based on electro/magnetoencephalography and the efficacy of transcranial electrical stimulation. Parametric electrical impedance tomography (pEIT) is a method to cheaply and non-invasively estimate them using electrode arrays on the scalp to apply currents and measure the resulting potential distribution. Conductivities are then estimated by iteratively fitting a forward model to the measurements, incurring a prohibitive computational cost that is generally lowered at the expense of accuracy. Reducing the computational cost associated with the forward solutions would improve the accessibility of this method and unlock new capabilities. Approach. We introduce reduced order modelling (ROM) to massively speed up the calculations of these solutions for arbitrary conductivity values. Main results. We demonstrate this new ROM-pEIT framework using a realistic head model with six tissue compartments, with minimal errors in both the approximated numerical solutions and conductivity estimations. We show that the computational complexity required to reach a multi-parameter estimation with a negligible relative error is reduced by more than an order of magnitude when using this framework. Furthermore, we illustrate the benefits of this new framework in a number of practical cases, including its application to real pEIT data from three subjects. Significance. Results suggest that this framework can transform the use of pEIT for seeking personalised head conductivities, making it a valuable tool for researchers and clinicians.

Objective: Inclusion of individualised electrical conductivities of head tissues is crucial for the accuracy of electrical source imaging techniques based on electro/magnetoencephalography and the efficacy of transcranial electrical stimulation. Parametric electrical impedance tomography (pEIT) is a method to cheaply and non-invasively estimate them using electrode arrays on the scalp to apply currents and measure the resulting potential distribution. Conductivities are then estimated by iteratively fitting a forward model to the measurements, incurring a prohibitive computational cost that is generally lowered at the expense of accuracy. Reducing the computational cost associated with the forward solutions would improve the accessibility of this method and unlock new capabilities. Approach: We introduce reduced order modelling (ROM) to massively speed up the calculations of these solutions for arbitrary conductivity values. Main results: We demonstrate this new ROM-pEIT framework using a realistic head model with six tissue compartments, with minimal errors in both the approximated numerical solutions and conductivity estimations. We show that the computational complexity required to reach a multi-parameter estimation with a negligible relative error is reduced by more than an order of magnitude when using this framework. Furthermore, we illustrate the benefits of this new framework in a number of practical cases, including its application to real pEIT data from three subjects. Significance: Results suggest that this framework can transform the use of pEIT for seeking personalised head conductivities, making it a valuable tool for researchers and clinicians.

Objective. Source imaging is a principal objective for electroencephalography (EEG), the solutions of which require forward problem (FP) computations characterising the electric potential distribution on the scalp due to known sources. Additionally, the EEG-FP is dependent upon realistic, anatomically correct volume conductors and accurate tissue conductivities, where the skull is particularly important. Skull conductivity, however, deviates according to bone composition and the presence of adult sutures. The presented study therefore analyses the effect the presence of adult sutures and differing bone composition have on the EEG-FP and inverse problem (IP) solutions. Approach. Utilising a well-established head atlas, detailed head models were generated including compact and spongiform bone and adult sutures. The true skull conductivity was considered as inhomogeneous according to spongiform bone proportion and sutures. The EEG-FP and EEG-IP were solved and compared to results employing homogeneous skull models, with varying conductivities and omitting sutures, as well as using a hypothesised aging skull conductivity model. Main results. Significant localised FP errors, with relative error up to 85%, were revealed, particularly evident along suture lines and directly related to the proportion of spongiform bone. This remained evident at various ages. Similar EEG-IP inaccuracies were found, with the largest (maximum 4.14 cm) across suture lines. Significance. It is concluded that modelling the skull as an inhomogeneous layer that varies according to spongiform bone proportion and includes differing suture conductivity is imperative for accurate EEG-FP and source localisation calculations. Their omission can result in significant errors, relevant for EEG research and clinical diagnosis.

Optically pumped magnetometers (OPMs) are quickly widening the scopes of noninvasive neurophysiological imaging. The possibility of placing these magnetic field sensors on the scalp allows not only to acquire signals from people in movement, but also to reduce the distance between the sensors and the brain, with a consequent gain in the signal‐to‐noise ratio. These advantages make the technique particularly attractive to characterise sources of brain activity in demanding populations, such as children and patients with epilepsy. However, the technology is currently in an early stage, presenting new design challenges around the optimal sensor arrangement and their complementarity with other techniques as electroencephalography (EEG). In this article, we present an optimal array design strategy focussed on minimising the brain source localisation error. The methodology is based on the Cramér‐Rao bound, which provides lower error bounds on the estimation of source parameters regardless of the algorithm used. We utilise this framework to compare whole head OPM arrays with commercially available electro/magnetoencephalography (E/MEG) systems for localising brain signal generators. In addition, we study the complementarity between EEG and OPM‐based MEG, and design optimal whole head systems based on OPMs only and a combination of OPMs and EEG electrodes for characterising deep and superficial sources alike. Finally, we show the usefulness of the approach to find the nearly optimal sensor positions minimising the estimation error bound in a given cortical region when a limited number of OPMs are available. This is of special interest for maximising the performance of small scale systems to ad hoc neurophysiological experiments, a common situation arising in most OPM labs.

Objective: Understanding the induced current flow from transcranial direct current stimulation (tDCS) is essential for determining the optimal dose and treatment. Head tissue conductivities play a key role in the resulting electromagnetic fields. However, there exists a complicated relationship between skull conductivity and participant age, that remains unclear. We explored how variations in skull electrical conductivities, particularly as a suggested function of age, affected tDCS induced electric fields. Approach: Simulations were employed to compare tDCS outcomes for different intensities across head atlases of varying age. Three databases were chosen to demonstrate differing variability in skull conductivity with age and how this may affect induced fields. Differences in tDCS electric fields due to proposed age-dependent skull conductivity variation, as well as deviations in grey matter, white matter and scalp, were compared and the most influential tissues determined. Main results: tDCS induced peak electric fields significantly negatively correlated with age, exacerbated by employing proposed age-appropriate skull conductivity (according to all three datasets). Uncertainty in skull conductivity was the most sensitive to changes in peak fields with increasing age. These results were revealed to be directly due to changing skull conductivity, rather than head geometry alone. There was no correlation between tDCS focality and age. Significance: Accurate and individualised head anatomy and in vivo skull conductivity measurements are essential for modelling tDCS induced fields. In particular, age should be taken into account when considering stimulation dose to precisely predict outcomes.

The original publication of the article unfortunately contain mistakes. It has been corrected in this correction.

Objective . The subtraction approach is known for being a theoretically-rigorous and accurate technique for solving the forward problem in electroencephalography by means of the finite element method. One key aspect of this approach consists of computing integrals of singular kernels over the discretised domain, usually referred to as potential integrals. Several techniques have been proposed for dealing with such integrals, all of them approximating the results at the expense of reducing the accuracy of the solution. In this paper, we derive analytic formulas for the potential integrals, reducing approximation errors to a minimum. Approach . Based on volume coordinates and Gauss theorems, we obtained parametric expressions for all the element matrices needed in the formulation assuming first order basis functions defined on a tetrahedral mesh. This included solving potential integrals over triangles and tetrahedra, for which we found compact and efficient formulas. Main results . Comparison with numerical quadrature schemes allowed us to test the advantages of the methodology proposed, which were found of great relevance for highly-eccentric sources, as those found in the somatosensory and visual cortices. Moreover, the availability of compact formulas allowed for an efficient implementation of the technique, which resulted in similar computational cost than the simplest numerical scheme. Significance . The analytical subtraction approach is the optimal subtraction-based methodology with regard to accuracy. The computational cost is similar to that obtained with the lowest order numerical integration scheme, making it a competitive option in the field. The technique is highly relevant for improving electromagnetic source imaging results utilising individualised head models and anisotropic electric conductivity fields without imposing impractical mesh requirements.

Data sharing is a key factor for ensuring reproducibility and transparency of scientific experiments, and neuroimaging is no exception. The vast heterogeneity of data formats and imaging modalities utilised in the field makes it a very challenging problem. In this context, the Brain Imaging Data Structure (BIDS) appears as a solution for organising and describing neuroimaging datasets. Since its publication in 2015, BIDS has gained widespread attention in the field, as it provides a common way to arrange and share multimodal brain images. Although the evident benefits it presents, BIDS has not been widely adopted in the field of MRI yet and we believe that this is due to the lack of a go-to tool to create and managed BIDS datasets. Motivated by this, we present the BIDS Toolbox, a web service to manage brain imaging datasets in BIDS format. Different from other tools, the BIDS Toolbox allows the creation and modification of BIDS-compliant datasets based on MRI data. It provides both a web interface and REST endpoints for its use. In this paper we describe its design and early prototype, and provide a link to the public source code repository.

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.