A key issue in understanding how the brain functions is the ability to correlate functional information with anatomical localisation. Functional information can be provided by a variety of techniques like positron emission tomography (PET), functional MRI (fMRI), electroencephalography (EEG), magnetoencephalography (MEG) or transcranial magnetic stimulation (TMS). All these methods provide different, but complementary, information about the functional areas of the brain. PET and fMRI provide spatially accurate picture of brain regions involved in a given task. TMS permits to infer the contribution of the stimulated brain area to the task under investigation. EEG and MEG, which reflects brain activity directly, have temporal accuracy of the order of a millisecond. TMS, EEG and MEG are offset by their low spatial resolution. In this thesis, we propose two methods to improve the spatial accuracy of method based on TMS and EEG. The first part of this thesis presents an automatic method to improve the localisation of TMS points. The method enables real-time visualisation and registration of TMS evoked responses and MRI. A MF digitiser is used to sample approximately 200 points on the subject's head following a specific digitisation pattern. Registration is obtained by minimising the RMS point to surface distance, computed efficiently using the Euclidean distance transform. Functional maps are created from TMS evoked responses projected onto the brain surface previously segmented from MRI. The second part presents the possibilities to set up a brain-computer interface (BCI) based on reconstructed sources of EEG activity and the parameters to adjust. Reconstructed sources could improve the EEG spatial accuracy as well as add biophysical information on the origin of the signal. Both informations could improve the BCI classification step. Eight BCIs are built to enable comparison between electrode-based and reconstructed source-based BCIs. Tests on detection of laterality of upcoming hand movement demonstrate the interest of reconstructed sources.

No description available.

High-quality factor oscillators are often used in measurements of verysmall force since they exhibit an enhanced sensitivity in the narrow frequencyband around resonance. Forces containing frequencies outside this frequencyband are often not detectable and the total force acting on the oscillatorremains unknown. In this thesis we present methods to eciently use theavailable bandwidth around resonance to reconstruct the force from partialspectral information.We apply the methods to dynamic atomic force microscopy (AFM) wherea tip at the end of a small micro-cantilever oscillates close to a sample surface.By reconstructing the force between the tip and the surface we can deducedierent properties of the surface. In contrast, in conventional AFM only oneof the many frequency components of the time-dependent tip-surface forceallowing for only qualitative conclusions about the tip-surface force.To increase the number of measurable frequency components we developed Intermodulation AFM (ImAFM). ImAFM utilizes frequency mixing ofa multifrequency drive scheme which generates many frequencies in the response to the nonlinear character of the tip-surface interaction. ImAFM,amplitude-modulated AFM and frequency-modulated AFM can be considered as special cases of narrow-band AFM, where the tip motion can bedescribed by a rapidly oscillating part and a slowly-varying envelope function. Using the concept of force quadratures, each rapid oscillation cycle canbe analyzed individually and ImAFM measurements can be interpreted as arapid measurement of the dependence of the force quadratures on the oscillation amplitude or frequency. To explore the limits of the force quadraturesdescription we introduce the force disk which is a complete description of thetip-surface force in narrow-band AFM at xed static probe height.We present a polynomial force reconstruction method for multifrequencyAFM data. The polynomial force reconstruction is a linear approximativeforce reconstruction method which is based on nding the parameters of amodel force which best approximates the tip-surface force. Another classof reconstruction methods are integral techniques which aim to invert theintegral relation between the tip-surface force and the measured spectraldata. We present an integral method, amplitude-dependence force spectroscopy (ADFS), which reconstructs the conservative tip-surface force fromthe amplitude-dependence of the force quadratures. Together with ImAFMwe use ADFS to combine high-resolution AFM imaging at high speeds withhighly accurate force measurements in each point of an image. For the measurement of dissipative forces we discuss how methods from tomography canbe used to reconstruct forces that are a function of both tip position andvelocity.The methods developed in this thesis are not limited to dynamic AFM andwe describe them in the general context of a harmonic oscillator subject to anexternal force. We hope that theses methods contribute to the transformationof AFM from a qualitative imaging modality into quantitative microscopy andwe hope that they nd application in other measurements which exploit theenhanced sensitivity of a high-quality factor oscillator. / <p>QC 20130527</p>

Photodynamic therapy (PDT) derives its tumour selectivity from preferential photosensitizer accumulation and short light penetration in tissue. However, additional strategies are needed to improve the therapeutic index of PDT in oncological applications where light is delivered interstitially to large volumes (e.g. prostate), or when adjacent normal tissue is extremely sensitive (e.g. brain). Much research to improve PDT's selectivity is directed towards developing targeted photosensitizers. Here, I present two alternative strategies to improve PDT's selectivity, without compromising its efficacy. For interstitial delivery, I investigated whether customizable cylindrical diffusers can be used to deliver light doses that conform better to target geometries, specifically the prostate. Additionally, I examined whether the neuroprotectant erythropoietin, used as an adjuvant to PDT for brain tumours, can reduce the sensitivity of normal tissue, thereby improving treatment selectivity. To determine if tailored diffusers constitute an improvement over conventional ones, I introduce a novel optimization algorithm for treatment planning. I also analyze the sensitivity of the resulting plans to changes in the optical properties and diffuser placement. These results are contextualized by a mathematical formalism to characterize the light dose distributions arising from tailored diffusers. In parallel, I investigate the neuroprotective effects of erythropoietin in PDT of primary cortical neurons in culture and normal rat brain in vivo. I show that the most important parameter determining prostate coverage is the number of diffusers employed. Moreover, while tailored diffusers do offer an improvement over conventional ones, the improvement is likely masked by perturbations introduced by the uncertainties of light delivery. Although these results largely discard the use of tailored diffusers in prostate PDT, significant insight has been gained into PDT treatment planning, and tailored diffusers may still be advantageous in more complicated geometries. Additionally, I show that erythropoietin does not improve survival of PDT-treated neurons PDT, nor reduces the volume of necrosis in vivo, for the ranges of conditions and doses studied. To our knowledge, this is the first time this strategy has been tested in brain PDT and deserves to be investigated further, by using later time-points, functional outcomes, and other neuroprotectants.

Photodynamic therapy (PDT) derives its tumour selectivity from preferential photosensitizer accumulation and short light penetration in tissue. However, additional strategies are needed to improve the therapeutic index of PDT in oncological applications where light is delivered interstitially to large volumes (e.g. prostate), or when adjacent normal tissue is extremely sensitive (e.g. brain). Much research to improve PDT's selectivity is directed towards developing targeted photosensitizers. Here, I present two alternative strategies to improve PDT's selectivity, without compromising its efficacy. For interstitial delivery, I investigated whether customizable cylindrical diffusers can be used to deliver light doses that conform better to target geometries, specifically the prostate. Additionally, I examined whether the neuroprotectant erythropoietin, used as an adjuvant to PDT for brain tumours, can reduce the sensitivity of normal tissue, thereby improving treatment selectivity. To determine if tailored diffusers constitute an improvement over conventional ones, I introduce a novel optimization algorithm for treatment planning. I also analyze the sensitivity of the resulting plans to changes in the optical properties and diffuser placement. These results are contextualized by a mathematical formalism to characterize the light dose distributions arising from tailored diffusers. In parallel, I investigate the neuroprotective effects of erythropoietin in PDT of primary cortical neurons in culture and normal rat brain in vivo. I show that the most important parameter determining prostate coverage is the number of diffusers employed. Moreover, while tailored diffusers do offer an improvement over conventional ones, the improvement is likely masked by perturbations introduced by the uncertainties of light delivery. Although these results largely discard the use of tailored diffusers in prostate PDT, significant insight has been gained into PDT treatment planning, and tailored diffusers may still be advantageous in more complicated geometries. Additionally, I show that erythropoietin does not improve survival of PDT-treated neurons PDT, nor reduces the volume of necrosis in vivo, for the ranges of conditions and doses studied. To our knowledge, this is the first time this strategy has been tested in brain PDT and deserves to be investigated further, by using later time-points, functional outcomes, and other neuroprotectants.

No description available.

It has long been known that any activity that results in changes in subsurface pressure, such as hydrocarbon production or waste or water reinjection, also causes underground deformations and movement, which can be described in terms of volumetric changes. Such deformations induce surface movement, which has a significant environmental impact. Induced surface deformations are measurable as vertical displacements; horizontal displacements; and tilts, which are the gradient of the surface deformation. The initial component of this study is a numerical model developed in C++ to predict and calculate surface deformations based on assumed subsurface volumetric changes occurring in a reservoir. The model is based on the unidirectional expansion technique using equations from Okada’s theory of dislocations (Okada, 1985). A second numerical model calculates subsurface volumetric changes based on surface deformation measurements, commonly referred to as solving for the inverse case. The inverse case is an ill-posed problem because the input is comprised of measured values that contain error. A regularization technique was therefore developed to help solve the ill-posed problem. A variety of surface deformation data sets were analyzed in order to determine the surface deformation input data that would produce the best solution and the optimum reconstruction of the initial subsurface volumetric changes. Tilt measurements, although very small, were found to be much better input than vertical displacement data for finding the inverse solution. Even in an ideal case with 0 % error, tilts result in a smaller RMSE (about 12 % smaller in the case studied) and thus a better resolution. In realistic cases with error, adding only 0.55 % of the maximum random error in the surface displacement data affects the back-calculated results to a significant extent: the RMSE increased by more than 13 times in the case studied. However, in an identical case using tilt measurements as input, adding 20 % of the maximum surface tilt value as random error increased the RMSE by 7 times, and remodelling the initial distribution of the volumetric changes in the subsurface was still possible. The required area of observation can also be reduced if tilt measurements are used. The optimal input includes tilt measurements in both directions: dz/dx and dz/dy. iv With respect to the number of observation points chosen, when tilts are used with an error of 0 %, very good resolution is obtainable using only 0.4 % of the unknowns as the number of benchmarks. For example, using only 10 observation points for a reservoir with 2500 elements, or unknowns resulted in an acceptable reconstruction. With respect to the sensitivity of the inverse solution to the depth of the reservoir and to the geometry of the observation grid, the deeper the reservoir, the more ill-posed the problem. The geometry of the benchmarks also has a significant effect on the solution of the inverse problem.

It has long been known that any activity that results in changes in subsurface pressure, such as hydrocarbon production or waste or water reinjection, also causes underground deformations and movement, which can be described in terms of volumetric changes. Such deformations induce surface movement, which has a significant environmental impact. Induced surface deformations are measurable as vertical displacements; horizontal displacements; and tilts, which are the gradient of the surface deformation. The initial component of this study is a numerical model developed in C++ to predict and calculate surface deformations based on assumed subsurface volumetric changes occurring in a reservoir. The model is based on the unidirectional expansion technique using equations from Okada’s theory of dislocations (Okada, 1985). A second numerical model calculates subsurface volumetric changes based on surface deformation measurements, commonly referred to as solving for the inverse case. The inverse case is an ill-posed problem because the input is comprised of measured values that contain error. A regularization technique was therefore developed to help solve the ill-posed problem. A variety of surface deformation data sets were analyzed in order to determine the surface deformation input data that would produce the best solution and the optimum reconstruction of the initial subsurface volumetric changes. Tilt measurements, although very small, were found to be much better input than vertical displacement data for finding the inverse solution. Even in an ideal case with 0 % error, tilts result in a smaller RMSE (about 12 % smaller in the case studied) and thus a better resolution. In realistic cases with error, adding only 0.55 % of the maximum random error in the surface displacement data affects the back-calculated results to a significant extent: the RMSE increased by more than 13 times in the case studied. However, in an identical case using tilt measurements as input, adding 20 % of the maximum surface tilt value as random error increased the RMSE by 7 times, and remodelling the initial distribution of the volumetric changes in the subsurface was still possible. The required area of observation can also be reduced if tilt measurements are used. The optimal input includes tilt measurements in both directions: dz/dx and dz/dy. iv With respect to the number of observation points chosen, when tilts are used with an error of 0 %, very good resolution is obtainable using only 0.4 % of the unknowns as the number of benchmarks. For example, using only 10 observation points for a reservoir with 2500 elements, or unknowns resulted in an acceptable reconstruction. With respect to the sensitivity of the inverse solution to the depth of the reservoir and to the geometry of the observation grid, the deeper the reservoir, the more ill-posed the problem. The geometry of the benchmarks also has a significant effect on the solution of the inverse problem.

Reconstruction of continuous signals from a number of their discrete samples is central to digital signal processing. Digital devices can only process discrete data and thus processing the continuous signals requires discretization. After discretization, possibility of unique reconstruction of the source signals from their samples is crucial. The classical sampling theory provides bounds on the sampling rate for unique source reconstruction, known as the Nyquist sampling rate. Recently a new sampling scheme, Compressive Sensing (CS), has been formulated for sparse signals. CS is an active area of research in signal processing. It has revolutionized the classical sampling theorems and has provided a new scheme to sample and reconstruct sparse signals uniquely, below Nyquist sampling rates. A signal is called (approximately) sparse when a relatively large number of its elements are (approximately) equal to zero. For the class of sparse signals, sparsity can be viewed as prior information about the source signal. CS has found numerous applications and has improved some image acquisition devices. Interesting instances of CS can happen, when apart from sparsity, side information is available about the source signals. The side information can be about the source structure, distribution, etc. Such cases can be viewed as extensions of the classical CS. In such cases we are interested in incorporating the side information to either improve the quality of the source reconstruction or decrease the number of the required samples for accurate reconstruction. A general CS problem can be transformed to an equivalent optimization problem. In this thesis, a special case of CS with side information about the feasible region of the equivalent optimization problem is studied. It is shown that in such cases uniqueness and stability of the equivalent optimization problem still holds. Then, an efficient reconstruction method is proposed. To demonstrate the practical value of the proposed scheme, the algorithm is applied on two real world applications: image deblurring in optical imaging and surface reconstruction in the gradient field. Experimental results are provided to further investigate and confirm the effectiveness and usefulness of the proposed scheme.

<p>The computational success of density functional theory relies on the construction of suitable approximations to the exchange-correlation energy functional. Use of functional approximations depending explicitly upon the density alone appear unable to address all aspects of many-body interactions, such as the fundamental constraint that the ground state energy is a piecewise linear function of the total number of electrons, and the ability to model nonlocal effects. Functionals depending explicitly upon occupied and unoccupied Kohn–Sham orbitals are considered necessary to address these and other issues. This dissertation considers certain issues relevant to the successful implementation of explicitly orbital-dependent functionals through the optimized effective potential (OEP) approach, as well as extending the potential functional formalism that provides the formal basis for the OEP approach to systems in the presence of noncollinear magnetic fields.</p><p>The self-consistent implementation of orbital-dependent energy functionals is correctly done through the optimized effective potential approach—minimization of the ground state energy with respect to the Kohn–Sham potential that generates the set of orbitals employed in the energy evaluation. The focus on the potential can be problematic in finite basis set approaches as determining the exchange-correlation potential in this manner is an inverse problem which, depending upon the combination of orbital and potential basis sets employed, is often ill-posed. The ill-posed nature manifests itself as nonphysical exchange-correlation potentials and total energies. We address the problem of determining meaningful exchange-correlation potentials for arbitrary combinations of orbital and potential basis sets through an L-curve regularization approach based on biasing towards smooth potentials in the energy minimization. This approach generates physically reasonable potentials for any combination of basis sets as shown by comparisons with grid-based OEP calculations on atoms, and through direct comparison with DFT calculations employing functionals not depending on orbitals for which OEP can also be performed. This work ensures that the OEP methodology can be considered a viable many-body computational methodology.</p><p>A separate issue of our OEP implementation is that it can suffer from a lack of size-extensivity—the total energy of a system of infinitely separated monomers may not scale linearly with the total number of monomers depending upon how we construct the Kohn–Sham potential. Typically, a fixed reference potential is employed to aid in the convergence of a finite basis set expansion of the Kohn–Sham potential. This reference potential can be utilized to ensure other desirable properties of the resulting potential. In particular, it can enforce the correct asymptotic behavior. The Fermi–Amaldi potential is often used for this purpose but suffers from size-nonextensivity owing to the explicit dependence of the potential on the total number of electrons. This error is examined and shown to be rather small and rapidly approaches a limiting linear behavior. A size-extensive reference potential with the correct asymptotic behavior is suggested and examined.</p><p>We also consider a formal aspect of the potential-based approach that provides the underlying justification of the OEP methodology. The potential functional formalism of Yang, Ayers, and Wu is extended to include systems in the presence of noncollinear magnetic fields. In doing so, a solution to the nonuniqueness issue associated with mapping between potentials and wave functions in such systems is provided, and a computational implementation of the OEP in noncollinear systems is suggested.</p><p>Finally, as an example of an issue for which orbital-dependent functionals seem necessary to obtain a correct description, we consider the ground state structures of C_{4<italic>N</italic> + 2} rings which are believed to exhibit a geometric transition from angle-alternation (<italic>N</italic> ≤ 2) to bond-alternation (<italic>N</italic> > 2). So far, no published DFT approach has been able to reproduce this behavior owing to the tendency of common density functional approximations to bias towards delocalized electron densities. Calculations are presented with the rCAM-B3LYP exchange-correlation functional that correctly predict the structural evolution of this system. This is rationalized in terms of the recently proposed delocalization error for which rCAM-B3LYP explicitly attempts to address.</p> / Dissertation