Forward models using real intracerebral DBS measurements 

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The multi-modalities for epilepsy diagnosis

Epilepsy surgery can be highly effective in treating refractory epilepsy if performed on properly selected patients with well-delineated ictal foci. If the resection of volume containing the ictal foci remains tricky, the prior greatest challenge is accurate localization. In a first step, the localization of the region for the seizure onset depends on seizure semiology, scalp EEG and imagery modalities like MRI and PET. In some patients for the localization of the foci, it is necessary to obtain further information. The neurologist has then recourse to other, more invasive methods like SEEG and ECoG.

Non-invasive methods

The most frequent non-invasive method is EEG recordings, which can be used in correlation with anatomical imaging modalities such as MRI. The introduction of several non-invasive functional neuro-imaging methods, including single-photon emission computed tomography (SPECT), positron emission tomography (PET) and functional MRI, has modified the assessment of the pre-surgical epilepsy evaluation. The pre-surgical checkups can call upon various modalities in order to identify the epileptic zone (the foci), as well as the functional cerebral ranges which the surgical resection must absolutely spare.
• EEG (electrical potential of the scalp surface) is the first examination carried out, which can be supplemented by a video-EEG (simultaneous acquisitions of the video and EEG) in order to study the precise semiological characteristics of the seizures. The temporal resolution of EEG is in the temporal scales of the explored process. But EEG has disadvantages such as depen-dency on cortical surface effects like artefact and low spatial resolution (scalp surface). The cerebral electrical activity is modified by the protective elements of the brain: meninges with the cerebrospinal fluid (very conducting), the skull (very insulating material), and the scalp (good conductor). Their joint action decreases the amplitude of the waves (more selective frequencies from 15 to 30 Hz) and spreads the contours. Thus the EEG does not contains fast oscillations, whereas they are very abundant on the electrocorticogram (obtained when the electrodes are directly on the cortex).
• MRI (Magnetic Resonance Imaging), based on the absorption and emission of radio-frequency energy, is the second fundamental examination in the browsing of epileptic syndromes, mak-ing it possible to highlight most of the anatomical lesions like dysplasias. Focal cortical dys-plasia (FCD) is the most common malformation of cortical development in patients with med-ically intractable epilepsy and MRI plays an important role in the pre-surgical evaluation. However, the spatial resolution of FCD is difficult to define with MRI.
• PET (Positron Emission Tomography) with FDG (Fludeoxyglucose) is also another interesting method because it translates the cerebral metabolic activity, i.e. it is representative of the brain functioning whose ranges of dysfunction can thus be highlighted. Fixing of nuclear marker increases in the cerebral ranges whose activity is most intense (epileptic seizure for example) and decreases in the less functional areas.
• SPECT (Single-Photon Emission Computed Tomography) uses radioactivity in nuclear imagery, which is characterized by the detection of photons resulting directly or indirectly from the disintegration of a radionuclide. SPECT is a tomographic nuclear medical imaging method which makes it possible to carry out image reconstructions in three dimensions of organs and their metabolism, by means of a number of gamma cameras which turn around the patient. The principle of SPECT is close to that of PET. The main difference is that in PET, one detects a pair of photons, whereas in SPECT, one detects one photon. Therefore, the SPECT images are less spatially accurate but they do not require the tracer to emit positrons. SPECT can thus be used with tracers whose disintegration is slower and which can be transported and stored much more easily.
• Computed tomography (or CT-scan) measures the absorption of the X-rays by tissues and can be exploited in the case of immediate assumption of responsibility for a first epileptic seizure. However, the restored images suffer from a sensitivity shortage, in particular for small lesions.
• Functional magnetic resonance imaging (or fMRI, for functional MRI) is a representation of the blood-oxygen-level-dependent (BOLD) contrast. fMRI is an MRI procedure that measures the brain activity by detecting associated variations in the blood flow. Cerebral blood flow is the blood supply to the brain in a given time, it varies according to the consumed glucose in the different brain structures. fMRI enables scientists to study neuronal functioning with a temporal resolution of about one second. The spatial resolution of fMRI is about a few millimeters.
• Magnetoencephalography (MEG) is a relatively new non-invasive technology conceived to record the extremely weak magnetic field of the brain (85). The principle of MEG is based on the measurement of magnetic fields generated by the displacement of ions induced by the elec-trical activity of neurons, by means of sensors located in the neighborhoods of the head. The temporal resolution of MEG is excellent (around 1 ms), like for EEG/SEEG. From its physical principle, MEG measures mainly intracellular currents, whereas EEG collects rather extracel-lular and voluminal currents (71). As a result, it can locate sources more easily than the scalp EEG and, contrary to SEEG, it is non-invasive. Even if it brings important information on the localization and propagation of the seizures, MEG remains a complex and very costly technol-ogy. It has mostly been applied to studie the evoked potentials. Current MEG systems have between 50 and 200 sensors or SQUIDs (Superconducting QUantum Interference Devices).

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Empirical Mode Decomposition (EMD)

EMD is a data-based decomposition method that processes linear/non-linear, stationary/non-stationary signals (101). Nowadays, EMD is considered as a standard method for multiscale decomposition and time-frequency analysis of real-world signals (see (37, 128, 174, 228)). EMD is built on the assumption that a signal can be iteratively decomposed into a finite set of different oscillation modes called Intrinsic Mode Functions (IMFs). The IMFs (or modes) mus follow the two following conditions :
1. the number of extrema and the number of zero crossing do not differ by plus one.
2. the local mean, calculated with the lower and upper envelopes (respectively defined by the local
minima and local maxima of the signal) must be null at each point. That is to say that the envelopes
must be symmetric.
Until now, there is no analytical formulation of EMD algorithm, but rather EMD can be expressed in the series of procedures or steps Steps of EMD algorithm is summarized in table 2.1 Each ith SEEG signal is decomposed according to: xi(t) = XJ j=1 IMFi, j(t) (2.13).

Filtering-GEVD approach

Depending on the context, the source separation problem can be approached by a GEVD formulation, which spatially filters mixed sources using prior information. In (151), a unified solution summarizes the assumptions for successful estimation. A GEVD application to separate maternal ECG from foetal ECG has shown the possibility to rank the estimated sources in order of periodicity (177). Different types of artifacts have been removed from EEG recordings (4, 80). Finally, Tome (202) has presented a first GEVD computation with filtered signals using a Finite Impulse Response (FIR) filter when sources are separable in a spectral representation.
GEVD is a decomposition that requires two matrices. The first one corresponds to the correlation matrix RX built from SEEG channels X of dimension (M N): RX = 1 N XXT (2.30). The second one is a correlation matrix RY calculated likewise with a matrix Y defined by Y = H(X), where the operator H() represents a temporal filtering function applied to each row in X. The assumption is thus made that certain sources before the mixture have different spectral characteristics.
More precisely, this operator carries out a preprocessing for each SEEG channel with one of the filtering algorithms defined in section 2.2.1.

Table of contents :

1 Introduction 
1.1 The Brain .
1.2 Bioelectricity of the brain
1.2.1 Model of a Neuron
1.2.2 Main brain rhythms
1.2.3 Bioelectrical fields
1.3 Epilepsy .
1.3.1 Seizure of epilepsy
1.3.2 Epilepsy treatment
1.3.3 The temporal lobe epilepsy
1.4 The multi-modalities for epilepsy diagnosis
1.4.1 Non-invasive methods
1.4.2 Invasive methods
1.5 EEG and SEEG measurements
1.5.1 The electrical stimulation
1.5.1.1 Stimulation and networks mechanism in epilepsy
1.5.1.2 The amygdala-hippocampal stimulation
1.6 Objectives of the thesis
2 Multidimensional decomposition. Application to DBS separation in SEEG/EEG 
2.1 Introduction
2.2 Methods and Model
2.2.1 Filtering approaches
2.2.1.1 Savitzky-Golay Filter (SGF)
2.2.1.2 Singular Spectrum Analysis (SSA)
2.2.1.3 Empirical Mode Decomposition (EMD)
2.2.1.4 Fast Intrinsic Mode Decomposition (IMD)
2.2.2 Multidimensional analysis
2.2.2.1 Filtering-GEVD approach
2.2.2.2 Multi-channel SSA (MSSA)
2.2.2.3 Multivariate EMD (MEMD)
2.2.2.4 Blind Source Separation (BSS)
2.3 (S)EEG data analysis using presented methods: examples and discussion
2.3.1 Filtration and decomposition methods (mono-channel)
2.3.2 Multichannel separation methods
2.4 DBS source extraction from SEEG measurements
2.4.1 DBS-SEEG acquisition
2.4.2 Discussion of the DBS model
2.5 Simulations and real datasets
2.5.1 Synthetic datasets
2.5.2 Real datasets
2.6 Experiments and Results
2.6.1 Parameters selection
2.6.2 Estimation of performance
2.6.3 Simulated SEEG data
2.6.4 Real SEEG analysis
2.7 Conclusion
3 Localization of SEEG electrodes 
3.1 Introduction and motivation of study
3.2 Image Acquisition
3.3 Registration
3.3.1 Mutual information
3.3.2 Optimization
3.4 Matter segmentation
3.4.1 Head tissue (matter) segmentation using MRI
3.4.2 Non-brain tissue segmentation using CT
3.4.2.1 Detailed algorithm
3.4.3 Summary of segmentation process for 5 matters
3.5 Electrode localization
3.5.1 Skull Stripping
3.5.2 Correlation of the pattern
3.5.3 Identification of the Multicaptor
3.5.4 Optimization of 3D localization
3.5.5 Localization results and conclusion
4 Forward modeling in vivo using DBS source 
4.1 Physical and mathematical formulation of forward problem
4.1.1 Notations
4.1.2 Maxwell’s equations and quasi-static approximation
4.1.3 Primary and secondary currents
4.1.4 Final electric potential equation
4.2 Infinite homogeneous medium
4.3 Primary currents
4.4 Boundary conditions
4.5 Spherical models
4.5.1 Single sphere method
4.5.2 Multi-sphere method
4.6 Realistic head models
4.6.1 BEM .
4.6.2 FEM .
4.6.2.1 Linear shape functions
4.6.2.2 Solving Linear equation system
4.6.3 Meshing .
4.7 Summary and implementation of methods
4.8 Conclusion
5 Validation and results: Forward models using real intracerebral DBS measurements 
5.1 DBS source approximation models in FEM
5.1.1 Error criterion for forward models accuracy
5.1.2 Dipole and Source-Sink
5.2 Sensitivity analysis of (S)EEG froward models
5.2.1 Infinite Homogenous medium (IHM)
5.2.2 Spherical models
5.2.3 Realistic models
5.2.3.1 BEM .
5.2.3.2 FEM .
5.2.3.3 One compartment BEM/FEM
5.2.4 Performance and summary of applied methods
5.3 Validation of forward models in real deep brain stimulation (DBS) measurements
5.3.1 Propagation data extraction
5.3.2 Configuration of multi-electrode and stimulation dipole
5.3.3 Results and discussion
5.4 Influence of the CSF/Gray/White matter conductivity ratio in SEEG/EEG
5.4.1 Optimization of CSF/Gray/White conductivities
5.5 Conclusion
6 Conclusion and Perspectives 
6.1 Summary of the thesis
6.2 Discussion and Perspectives
6.3 Conclusion
Bibliography 

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