IEEE BIBE th IEEE International Conference on BioInformatics and BioEngineering, November 10-13, Chania, Greece Towards an Overall 3-D Vector Field Reconstruction via Discretization and a Linear Equations System CBP: Cognitive Brain Signal Processing Lab Chrysa Papadaniil, Student Member Leontios Hadjileontiadis, Senior Member Aristotle University of Thessaloniki

CBP: Cognitive Brain Signal Processing Lab IEEE BIBE th IEEE International Conference on BioInformatics and BioEngineering, November 10-13, Chania, Greece ? Forward Problem ? ? Inverse Problem Ill posed ?

CBP: Cognitive Brain Signal Processing Lab IEEE BIBE th IEEE International Conference on BioInformatics and BioEngineering, November 10-13, Chania, Greece Representation of the active brain areas using a number of dipoles Different methodologies: A priori postulation of the dipoles, solution of the forward problem, parameters change until the solution agrees with the scalp measurements Bayesian estimation Beamforming

CBP: Cognitive Brain Signal Processing Lab IEEE BIBE th IEEE International Conference on BioInformatics and BioEngineering, November 10-13, Chania, Greece Given the measured scalp potentials, what is the electrostatic field inside the head? Mapping of the brain to a set of active effective states Mapping of the brain to a set of active effective states No a priori assumptions No a priori assumptions Reduced complexity (we ignore the electromagnetic properties of different tissues) Reduced complexity (we ignore the electromagnetic properties of different tissues)

CBP: Cognitive Brain Signal Processing Lab IEEE BIBE th IEEE International Conference on BioInformatics and BioEngineering, November 10-13, Chania, Greece VFT formula for line integrals

CBP: Cognitive Brain Signal Processing Lab IEEE BIBE th IEEE International Conference on BioInformatics and BioEngineering, November 10-13, Chania, Greece Recovering a 2D field from integral data is by definition underdetermined – only one component could be determined (irrotational or solenoidal) Possible solution: Both transversal and longitudinal measurements (Braun and Hauck) Drawback: Very few applications allow for both kinds measurements Suggested approach: Instead of working in the continuous domain, we reconstruct the field in specific sampling points arranged in a grid, where there is data redundancy we may use many line orientations passing through every point and then view their recordings as weighted sums of the local vector fields Cartesian components

CBP: Cognitive Brain Signal Processing Lab IEEE BIBE th IEEE International Conference on BioInformatics and BioEngineering, November 10-13, Chania, Greece P Recovery of the field in the centers of the tiles Ideal point sensors regularly placed at the domain s border Tracing line connecting two boundary sensors A B Starting from the foot of perpendicular, we discretize the line with a step of Δs Q ΔsΔs

CBP: Cognitive Brain Signal Processing Lab IEEE BIBE th IEEE International Conference on BioInformatics and BioEngineering, November 10-13, Chania, Greece

CBP: Cognitive Brain Signal Processing Lab IEEE BIBE th IEEE International Conference on BioInformatics and BioEngineering, November 10-13, Chania, Greece Improved 2D-VFT reconstruction using probabilistic weights to account for the non uniform placement of the sensors (Radon requirement for medical accuracy image reconstruction) Sampling bounds for the Radon parameters Robust formulation Existence of upper bound to the solution error Discretization serves as regularization for the ill-posed problem

CBP: Cognitive Brain Signal Processing Lab IEEE BIBE th IEEE International Conference on BioInformatics and BioEngineering, November 10-13, Chania, Greece Improved 2D-VFT reconstruction using probabilistic weights to account for the non uniform placement of the sensors (Radon requirement for medical accuracy image reconstruction) Sampling bounds for the Radon parameters Robust formulation Existence of upper bound to the solution error Discretization serves as regularization for the ill-posed problem Our first goal: The extension of the methodology to 3 dimensions

CBP: Cognitive Brain Signal Processing Lab IEEE BIBE th IEEE International Conference on BioInformatics and BioEngineering, November 10-13, Chania, Greece

CBP: Cognitive Brain Signal Processing Lab IEEE BIBE th IEEE International Conference on BioInformatics and BioEngineering, November 10-13, Chania, Greece

CBP: Cognitive Brain Signal Processing Lab IEEE BIBE th IEEE International Conference on BioInformatics and BioEngineering, November 10-13, Chania, Greece We considered fields produced by electric monopoles (irrotational) Estimation of the right part of the integrals by the voltage difference between two sensors points Simulation of the field inside the head The theoretical field and the voltage values in the sensors locations were calculated using Coulombs law b was determined from all the sensors combinations differences and A using the methodology presented Relative and angular errors estimated for comparison

IEEE BIBE th IEEE International Conference on BioInformatics and BioEngineering, November 10-13, Chania, Greece

IEEE BIBE th IEEE International Conference on BioInformatics and BioEngineering, November 10-13, Chania, Greece 4 point sources at (10, 10, 10), (-10, 10, -10), (10, 10, 0), (-10, -10, 0)

CBP: Cognitive Brain Signal Processing Lab IEEE BIBE th IEEE International Conference on BioInformatics and BioEngineering, November 10-13, Chania, Greece The discretization of both the field domain and the scanning lines creates data redundancy, allowing for the recovery of all the components of the unknown 3D field only from boundary data. Next Steps Sampling bounds study for the 3D space Advanced techniques of discretizing the 3D field domain (FEM) More realistic head models

IEEE BIBE th IEEE International Conference on BioInformatics and BioEngineering, November 10-13, Chania, Greece Goals Advancing the state of the art in vector field tomography Brain cognitive processes research ++pic from cbp.iti

IEEE BIBE th IEEE International Conference on BioInformatics and BioEngineering, November 10-13, Chania, Greece EGI 300 geodesic system High resolution data acquisition (dEEG) High resolution data acquisition (dEEG) 256 channels 256 channels Full head coverage Full head coverage Patient friendly Patient friendly CBP: Cognitive Brain Signal Processing Lab *Pictures from

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