The project has resulted in several substantial advances at the theoretical, algorithmic, and hardware levels. New Electroencephalographic imaging strategies have been investigated and developed, linear-in-complexity solutions have been obtained, ad-hoc hardware architectures speeding up key operational elements have been achieved, and overall framework for real-time inversion and VR visualization has been engineered and developed. Among other results, this project has notably resulted in the first family of boundary element formulations of the EEG problem capable of accounting for anisotropies and inhomogeneities of the brain medium within an Integral Equation (IE) framework. Moreover, we have obtained the first application of spectral Calderon strategies to EEG and the consequent reduction to linear complexity of the associated solvers. Finally, SABRE delivered a benchmarking framework for source-based BCI which will serve communities well beyond those directly impacted by the objectives of this project. As expected the results of these scientific efforts are being released as open source tools for the benefit of the scientific community and of the citizenship at large.
Detailed Description of Project’s outcomes
WP1 New EEG Forward Formulations and Algorithmic Accelerations
Task 1.1 – Development of a new surface BEM formulation for the EEG problem
The task has been accomplished by obtaining (i) the introduction of a new way of discretizing the forward EEG problem. This technique was based on a new mixed discretization and resulted in a formulation of increased computational efficiency and precision with respect to all previously available schemes of the same nature. The details on this new technique have been reported in a full paper accepted for publication in one of the leading journals of the field. (ii) The introduction of a new fast matrix vector multiplication technique that performs the main EEG imaging task in linear complexity instead of a quadratic one. The dissemination of this contribution is in review and the preprint material is publicly available.
Task 1.2 – Development of a complete surfacic potential-to-volume current mapping via integration with Distributed Source Algorithms.
We have obtained the first Volume-element boundary integral formulation ever developed for solving the EEG forward problem. The general idea is that a volume boundary element method, differently from the surface boundary element methods currently used in literature, can handle inhomogeneities and anisotropies like the finite element techniques do. At the same time the new solver keeps the levels of accuracy and numerical stability ensured by the most advanced boundary element methods in literature, from which it borrows the virtuous strategies for ensuring high levels of precision. On top of that, the new formulation, when complemented with acceleration and regularization strategies developed in this project, also have the additional unequalled feature of allowing for a fast inverse in solution of the EEG forward problem with only a linear computational complexity (the standard complexity is cubic) which is a key enabling element obtained by SABRE.
Task 1.3 – Interface with WP2 (ad-hoc hardware acceleration) and WP3 (OpenViBE).
After detailed profiling analyses, the key computational bottleneck element within the inverse source chain has been identified. A new hardware implementation strategy of the inverse operation has been achieved and published. Moreover, with a synergic effort between IMT and INRIA teams, OpenViBE has been adapted and interfaced with the EEG equipment (both low and high resolution) and it is currently the main tool for extracting real time data from all the project devices and for injecting them in the inverse source machineries.
WP2 Ad-hoc Hardware Accelerations
Task 2.1 – Feasibility assessments and behavioral modeling
A detailed software benchmarking campaign has been run on all key computational elements of the BCI and inverse source brain chain. Three possible elements of computational delay have been identified and further analysis has selected one that has the highest impact. Both theoretical and numerical techniques have been adopted and the numerical integration for simplectic structures has been identified as the element to speed up on hardware.
Task 2.2 – Basic operators and system design.
After identifying the key bottleneck in the computational architecture, further profiling has identified key operations which have been completely reengineered. The focus was put on the inverse and inverse square root operators. The Newton-Raphson method has been chosen. It is an iterative algorithm, which allows to roughly double the number of bits of precision at each iteration, with an acceptable amount of resources. A new Newton-Raphson implementation, which does not require any memory block, has been proposed. This solution allows to reach the maximum available computing frequency on Xilinx FPGAs. Both proposed architectures are totally generic, and thus can be easily integrated in any hardware architecture. The viability of an ASIC implementation of these operators has been investigated. In 65nm CMOS, each operator reaches a computing performance of about 40 Gop/s/mm², which improves the literature results by a factor of 5.
Task 2.3 –ASIC implementation and test.
As foreseen by the project plan, this Task is still undergoing.
WP3 Software Integration and Exploitation of Algorithmic Accelerations
Task 3.1 – OpenViBE software integration and adaptation.
An intense and collaborative effort has been undertaken in order to adapt OpenViBE features to the specific setting required by this project. This has been successfully accomplished and now the OpenViBE framework is the main tool to extract real time data from the high-resolution EEG system which SABRE is leveraging on. Moreover, in order to increase the visibility and impact of our scientific effort, we decided that a data-analytical, controlled study of the involved methods was necessary. To this end, we extracted some key BCI techniques of the OpenVIBE real-time platform into a Matlab-based data-analysis framework, complemented them with state-of-the-art inverse BCI techniques, and added a possibility to generate diagnostic data from valid Computational Physics via SABRE forward models. This lead to the creation of a new open source environment, called simBCI, where comparisons between different BCI strategies can be done in a scientifically sound and reproducible way. The software will be made publicly available for the greater benefit of the scientific community and beyond.
Task 3.2 – Accelerated EEG-based brain visualization.
A proper VR framework has been developed in Unity 3D and tailored with the increasingly rich and featured solvers obtained in WP1. The environment allows for connection with fast solver engines and allows for real time interactions both with forward and with inverse solutions. Brain layers and volume data are already implemented, brain fibers inclusion is currently underway.
Task 3.3 – Accelerated BCI-based interaction
A large part of study using the simBCI framework has been identifying the advantages of the inverse source-based approach in different conditions. For example, we can consider BCI session and trial lengths, different assumptions about the generative processes, as well as robustness of the techniques towards localized or global artifacts that can confuse BCI techniques. We have also studied the inclusion of ad-hoc, physiologically inspired priors within the overall BCI framework. First prototypical inverse source-based schemes have been developed with a large number of possible inverse algorithms. The current work under this Task is focusing in wiring in the hardware accelerators for even increased complexity of the treated problems and on finalizing a pipeline directly applicable to experimental trials with subjects.