Prospective and retrospective motion correction in diffusion magnetic resonance imaging of the human brain.

Diffusion-weighting in magnetic resonance imaging (MRI) increases the sensitivity to molecular Brownian motion, providing insight in the micro-environment of the underlying tissue types and structures. At the same time, the diffusion weighting renders the scans sensitive to other motion, including bulk patient motion. Typically, several image volumes are needed to extract diffusion information, inducing also inter-volume motion susceptibility. Bulk motion is more likely during long acquisitions, as they appear in diffusion tensor, diffusion spectrum and q-ball imaging. Image registration methods are successfully used to correct for bulk motion in other MRI time series, but their performance in diffusion-weighted MRI is limited since diffusion weighting introduces strong signal and contrast changes between serial image volumes. In this work, we combine the capability of free induction decay (FID) navigators, providing information on object motion, with image registration methodology to prospectively--or optionally retrospectively--correct for motion in diffusion imaging of the human brain. Eight healthy subjects were instructed to perform small-scale voluntary head motion during clinical diffusion tensor imaging acquisitions. The implemented motion detection based on FID navigator signals is processed in real-time and provided an excellent detection performance of voluntary motion patterns even at a sub-millimetre scale (sensitivity≥92%, specificity>98%). Motion detection triggered an additional image volume acquisition with b=0 s/mm2 which was subsequently co-registered to a reference volume. In the prospective correction scenario, the calculated motion-parameters were applied to perform a real-time update of the gradient coordinate system to correct for the head movement. Quantitative analysis revealed that the motion correction implementation is capable to correct head motion in diffusion-weighted MRI to a level comparable to scans without voluntary head motion. The results indicate the potential of this method to improve image quality in diffusion-weighted MRI, a concept that can also be applied when highest diffusion weightings are performed.

Situating forensic traces in time

Situating events and traces in time is an essential problem in investigations. To date, among the typical ques- 21¦tions issued in forensic science, time has generally been unexplored. The reason for this can be traced to the 22¦complexity of the overall problem, addressed by several scientists in very limited projects usually stimulated 23¦by a specific case. Considering that such issues are recurrent and transcending the treatment of each trace 24¦separately, the formalisation of a framework to address dating issues in criminal investigation is undeniably 25¦needed. Through an iterative process consisting of extracting recurrent aspects discovered from the study of 26¦problems encountered by practitioners and reported in the literature, common mechanisms were extracted 27¦and provide understanding of underlying factors encountered in forensic practise. Three complementary ap- 28¦proaches are thus highlighted and described to formalise a preliminary framework that can be applied for the 29¦dating of traces, objects, persons and indirectly events.

Mynodbcsv: Lightweight Zero-Config Database Solution for Handling Very Large CSV Files.

Volumes of data used in science and industry are growing rapidly. When researchers face the challenge of analyzing them, their format is often the first obstacle. Lack of standardized ways of exploring different data layouts requires an effort each time to solve the problem from scratch. Possibility to access data in a rich, uniform manner, e.g. using Structured Query Language (SQL) would offer expressiveness and user-friendliness. Comma-separated values (CSV) are one of the most common data storage formats. Despite its simplicity, with growing file size handling it becomes non-trivial. Importing CSVs into existing databases is time-consuming and troublesome, or even impossible if its horizontal dimension reaches thousands of columns. Most databases are optimized for handling large number of rows rather than columns, therefore, performance for datasets with non-typical layouts is often unacceptable. Other challenges include schema creation, updates and repeated data imports. To address the above-mentioned problems, I present a system for accessing very large CSV-based datasets by means of SQL. It's characterized by: "no copy" approach - data stay mostly in the CSV files; "zero configuration" - no need to specify database schema; written in C++, with boost [1], SQLite [2] and Qt [3], doesn't require installation and has very small size; query rewriting, dynamic creation of indices for appropriate columns and static data retrieval directly from CSV files ensure efficient plan execution; effortless support for millions of columns; due to per-value typing, using mixed text/numbers data is easy; very simple network protocol provides efficient interface for MATLAB and reduces implementation time for other languages. The software is available as freeware along with educational videos on its website [4]. It doesn't need any prerequisites to run, as all of the libraries are included in the distribution package. I test it against existing database solutions using a battery of benchmarks and discuss the results.

Investigation of field and diffusion time dependence of the diffusion-weighted signal at ultrahigh magnetic fields.

Over the last decade, there has been a significant increase in the number of high-magnetic-field MRI magnets. However, the exact effect of a high magnetic field strength (B0 ) on diffusion-weighted MR signals is not yet fully understood. The goal of this study was to investigate the influence of different high magnetic field strengths (9.4 T and 14.1 T) and diffusion times (9, 11, 13, 15, 17 and 24 ms) on the diffusion-weighted signal in rat brain white matter. At a short diffusion time (9 ms), fractional anisotropy values were found to be lower at 14.1 T than at 9.4 T, but this difference disappeared at longer diffusion times. A simple two-pool model was used to explain these findings. The model describes the white matter as a first hindered compartment (often associated with the extra-axonal space), characterized by a faster orthogonal diffusion and a lower fractional anisotropy, and a second restricted compartment (often associated with the intra-axonal space), characterized by a slower orthogonal diffusion (i.e. orthogonal to the axon direction) and a higher fractional anisotropy. Apparent T2 relaxation time measurements of the hindered and restricted pools were performed. The shortening of the pseudo-T2 value from the restricted compartment with B0 is likely to be more pronounced than the apparent T2 changes in the hindered compartment. This study suggests that the observed differences in diffusion tensor imaging parameters between the two magnetic field strengths at short diffusion time may be related to differences in the apparent T2 values between the pools. Copyright © 2013 John Wiley & Sons, Ltd.

Parametric estimation of pulse arrival time: a robust approach to pulse wave velocity.

Pulse wave velocity (PWV) is a surrogate of arterial stiffness and represents a non-invasive marker of cardiovascular risk. The non-invasive measurement of PWV requires tracking the arrival time of pressure pulses recorded in vivo, commonly referred to as pulse arrival time (PAT). In the state of the art, PAT is estimated by identifying a characteristic point of the pressure pulse waveform. This paper demonstrates that for ambulatory scenarios, where signal-to-noise ratios are below 10 dB, the performance in terms of repeatability of PAT measurements through characteristic points identification degrades drastically. Hence, we introduce a novel family of PAT estimators based on the parametric modeling of the anacrotic phase of a pressure pulse. In particular, we propose a parametric PAT estimator (TANH) that depicts high correlation with the Complior(R) characteristic point D1 (CC = 0.99), increases noise robustness and reduces by a five-fold factor the number of heartbeats required to obtain reliable PAT measurements.

A pseudo-spectral method for the simulation of poro-elastic seismic wave propagation in 2D polar coordinates using domain decomposition

We present a novel numerical approach for the comprehensive, flexible, and accurate simulation of poro-elastic wave propagation in 2D polar coordinates. An important application of this method and its extensions will be the modeling of complex seismic wave phenomena in fluid-filled boreholes, which represents a major, and as of yet largely unresolved, computational problem in exploration geophysics. In view of this, we consider a numerical mesh, which can be arbitrarily heterogeneous, consisting of two or more concentric rings representing the fluid in the center and the surrounding porous medium. The spatial discretization is based on a Chebyshev expansion in the radial direction and a Fourier expansion in the azimuthal direction and a Runge-Kutta integration scheme for the time evolution. A domain decomposition method is used to match the fluid-solid boundary conditions based on the method of characteristics. This multi-domain approach allows for significant reductions of the number of grid points in the azimuthal direction for the inner grid domain and thus for corresponding increases of the time step and enhancements of computational efficiency. The viability and accuracy of the proposed method has been rigorously tested and verified through comparisons with analytical solutions as well as with the results obtained with a corresponding, previously published, and independently bench-marked solution for 2D Cartesian coordinates. Finally, the proposed numerical solution also satisfies the reciprocity theorem, which indicates that the inherent singularity associated with the origin of the polar coordinate system is adequately handled.

Taking "Galton's problem" Seriously : Towards a Theory of Policy Diffusion

This article builds on the recent policy diffusion literature and attempts to overcome one of its major problems, namely the lack of a coherent theoretical framework. The literature defines policy diffusion as a process where policy choices are interdependent, and identifies several diffusion mechanisms that specify the link between the policy choices of the various actors. As these mechanisms are grounded in different theories, theoretical accounts of diffusion currently have little internal coherence. In this article we put forward an expected-utility model of policy change that is able to subsume all the diffusion mechanisms. We argue that the expected utility of a policy depends on both its effectiveness and the payoffs it yields, and we show that the various diffusion mechanisms operate by altering these two parameters. Each mechanism affects one of the two parameters, and does so in distinct ways. To account for aggregate patterns of diffusion, we embed our model in a simple threshold model of diffusion. Given the high complexity of the process that results, strong analytical conclusions on aggregate patterns cannot be drawn without more extensive analysis which is beyond the scope of this article. However, preliminary considerations indicate that a wide range of diffusion processes may exist and that convergence is only one possible outcome.

Diffusion-weighted spectroscopy: a novel approach to determine macromolecule resonances in short-echo time 1H-MRS.

Quantification of short-echo time proton magnetic resonance spectroscopy results in >18 metabolite concentrations (neurochemical profile). Their quantification accuracy depends on the assessment of the contribution of macromolecule (MM) resonances, previously experimentally achieved by exploiting the several fold difference in T(1). To minimize effects of heterogeneities in metabolites T(1), the aim of the study was to assess MM signal contributions by combining inversion recovery (IR) and diffusion-weighted proton spectroscopy at high-magnetic field (14.1 T) and short echo time (= 8 msec) in the rat brain. IR combined with diffusion weighting experiments (with δ/Δ = 1.5/200 msec and b-value = 11.8 msec/μm(2)) showed that the metabolite nulled spectrum (inversion time = 740 msec) was affected by residuals attributed to creatine, inositol, taurine, choline, N-acetylaspartate as well as glutamine and glutamate. While the metabolite residuals were significantly attenuated by 50%, the MM signals were almost not affected (< 8%). The combination of metabolite-nulled IR spectra with diffusion weighting allows a specific characterization of MM resonances with minimal metabolite signal contributions and is expected to lead to a more precise quantification of the neurochemical profile.

A pseudo-spectral method for simulating of poro-elastic seismic wave propagation in complex borehole environments

We present a novel numerical approach for the comprehensive, flexible, and accurate simulation of poro-elastic wave propagation in cylindrical coordinates. An important application of this method is the modeling of complex seismic wave phenomena in fluid-filled boreholes, which represents a major, and as of yet largely unresolved, computational problem in exploration geophysics. In view of this, we consider a numerical mesh consisting of three concentric domains representing the borehole fluid in the center, the borehole casing and the surrounding porous formation. The spatial discretization is based on a Chebyshev expansion in the radial direction, Fourier expansions in the other directions, and a Runge-Kutta integration scheme for the time evolution. A domain decomposition method based on the method of characteristics is used to match the boundary conditions at the fluid/porous-solid and porous-solid/porous-solid interfaces. The viability and accuracy of the proposed method has been tested and verified in 2D polar coordinates through comparisons with analytical solutions as well as with the results obtained with a corresponding, previously published, and independently benchmarked solution for 2D Cartesian coordinates. The proposed numerical solution also satisfies the reciprocity theorem, which indicates that the inherent singularity associated with the origin of the polar coordinate system is handled adequately.

Time-lapse and probabilistic inversion strategies for plane-wave electromagnetic data.

L'utilisation efficace des systèmes géothermaux, la séquestration du CO2 pour limiter le changement climatique et la prévention de l'intrusion d'eau salée dans les aquifères costaux ne sont que quelques exemples qui démontrent notre besoin en technologies nouvelles pour suivre l'évolution des processus souterrains à partir de la surface. Un défi majeur est d'assurer la caractérisation et l'optimisation des performances de ces technologies à différentes échelles spatiales et temporelles. Les méthodes électromagnétiques (EM) d'ondes planes sont sensibles à la conductivité électrique du sous-sol et, par conséquent, à la conductivité électrique des fluides saturant la roche, à la présence de fractures connectées, à la température et aux matériaux géologiques. Ces méthodes sont régies par des équations valides sur de larges gammes de fréquences, permettant détudier de manières analogues des processus allant de quelques mètres sous la surface jusqu'à plusieurs kilomètres de profondeur. Néanmoins, ces méthodes sont soumises à une perte de résolution avec la profondeur à cause des propriétés diffusives du champ électromagnétique. Pour cette raison, l'estimation des modèles du sous-sol par ces méthodes doit prendre en compte des informations a priori afin de contraindre les modèles autant que possible et de permettre la quantification des incertitudes de ces modèles de façon appropriée. Dans la présente thèse, je développe des approches permettant la caractérisation statique et dynamique du sous-sol à l'aide d'ondes EM planes. Dans une première partie, je présente une approche déterministe permettant de réaliser des inversions répétées dans le temps (time-lapse) de données d'ondes EM planes en deux dimensions. Cette stratégie est basée sur l'incorporation dans l'algorithme d'informations a priori en fonction des changements du modèle de conductivité électrique attendus. Ceci est réalisé en intégrant une régularisation stochastique et des contraintes flexibles par rapport à la gamme des changements attendus en utilisant les multiplicateurs de Lagrange. J'utilise des normes différentes de la norme l2 pour contraindre la structure du modèle et obtenir des transitions abruptes entre les régions du model qui subissent des changements dans le temps et celles qui n'en subissent pas. Aussi, j'incorpore une stratégie afin d'éliminer les erreurs systématiques de données time-lapse. Ce travail a mis en évidence l'amélioration de la caractérisation des changements temporels par rapport aux approches classiques qui réalisent des inversions indépendantes à chaque pas de temps et comparent les modèles. Dans la seconde partie de cette thèse, j'adopte un formalisme bayésien et je teste la possibilité de quantifier les incertitudes sur les paramètres du modèle dans l'inversion d'ondes EM planes. Pour ce faire, je présente une stratégie d'inversion probabiliste basée sur des pixels à deux dimensions pour des inversions de données d'ondes EM planes et de tomographies de résistivité électrique (ERT) séparées et jointes. Je compare les incertitudes des paramètres du modèle en considérant différents types d'information a priori sur la structure du modèle et différentes fonctions de vraisemblance pour décrire les erreurs sur les données. Les résultats indiquent que la régularisation du modèle est nécessaire lorsqu'on a à faire à un large nombre de paramètres car cela permet d'accélérer la convergence des chaînes et d'obtenir des modèles plus réalistes. Cependent, ces contraintes mènent à des incertitudes d'estimations plus faibles, ce qui implique des distributions a posteriori qui ne contiennent pas le vrai modèledans les régions ou` la méthode présente une sensibilité limitée. Cette situation peut être améliorée en combinant des méthodes d'ondes EM planes avec d'autres méthodes complémentaires telles que l'ERT. De plus, je montre que le poids de régularisation des paramètres et l'écart-type des erreurs sur les données peuvent être retrouvés par une inversion probabiliste. Finalement, j'évalue la possibilité de caractériser une distribution tridimensionnelle d'un panache de traceur salin injecté dans le sous-sol en réalisant une inversion probabiliste time-lapse tridimensionnelle d'ondes EM planes. Etant donné que les inversions probabilistes sont très coûteuses en temps de calcul lorsque l'espace des paramètres présente une grande dimension, je propose une stratégie de réduction du modèle ou` les coefficients de décomposition des moments de Legendre du panache de traceur injecté ainsi que sa position sont estimés. Pour ce faire, un modèle de résistivité de base est nécessaire. Il peut être obtenu avant l'expérience time-lapse. Un test synthétique montre que la méthodologie marche bien quand le modèle de résistivité de base est caractérisé correctement. Cette méthodologie est aussi appliquée à un test de trac¸age par injection d'une solution saline et d'acides réalisé dans un système géothermal en Australie, puis comparée à une inversion time-lapse tridimensionnelle réalisée selon une approche déterministe. L'inversion probabiliste permet de mieux contraindre le panache du traceur salin gr^ace à la grande quantité d'informations a priori incluse dans l'algorithme. Néanmoins, les changements de conductivités nécessaires pour expliquer les changements observés dans les données sont plus grands que ce qu'expliquent notre connaissance actuelle des phénomenès physiques. Ce problème peut être lié à la qualité limitée du modèle de résistivité de base utilisé, indiquant ainsi que des efforts plus grands devront être fournis dans le futur pour obtenir des modèles de base de bonne qualité avant de réaliser des expériences dynamiques. Les études décrites dans cette thèse montrent que les méthodes d'ondes EM planes sont très utiles pour caractériser et suivre les variations temporelles du sous-sol sur de larges échelles. Les présentes approches améliorent l'évaluation des modèles obtenus, autant en termes d'incorporation d'informations a priori, qu'en termes de quantification d'incertitudes a posteriori. De plus, les stratégies développées peuvent être appliquées à d'autres méthodes géophysiques, et offrent une grande flexibilité pour l'incorporation d'informations additionnelles lorsqu'elles sont disponibles. -- The efficient use of geothermal systems, the sequestration of CO2 to mitigate climate change, and the prevention of seawater intrusion in coastal aquifers are only some examples that demonstrate the need for novel technologies to monitor subsurface processes from the surface. A main challenge is to assure optimal performance of such technologies at different temporal and spatial scales. Plane-wave electromagnetic (EM) methods are sensitive to subsurface electrical conductivity and consequently to fluid conductivity, fracture connectivity, temperature, and rock mineralogy. These methods have governing equations that are the same over a large range of frequencies, thus allowing to study in an analogous manner processes on scales ranging from few meters close to the surface down to several hundreds of kilometers depth. Unfortunately, they suffer from a significant resolution loss with depth due to the diffusive nature of the electromagnetic fields. Therefore, estimations of subsurface models that use these methods should incorporate a priori information to better constrain the models, and provide appropriate measures of model uncertainty. During my thesis, I have developed approaches to improve the static and dynamic characterization of the subsurface with plane-wave EM methods. In the first part of this thesis, I present a two-dimensional deterministic approach to perform time-lapse inversion of plane-wave EM data. The strategy is based on the incorporation of prior information into the inversion algorithm regarding the expected temporal changes in electrical conductivity. This is done by incorporating a flexible stochastic regularization and constraints regarding the expected ranges of the changes by using Lagrange multipliers. I use non-l2 norms to penalize the model update in order to obtain sharp transitions between regions that experience temporal changes and regions that do not. I also incorporate a time-lapse differencing strategy to remove systematic errors in the time-lapse inversion. This work presents improvements in the characterization of temporal changes with respect to the classical approach of performing separate inversions and computing differences between the models. In the second part of this thesis, I adopt a Bayesian framework and use Markov chain Monte Carlo (MCMC) simulations to quantify model parameter uncertainty in plane-wave EM inversion. For this purpose, I present a two-dimensional pixel-based probabilistic inversion strategy for separate and joint inversions of plane-wave EM and electrical resistivity tomography (ERT) data. I compare the uncertainties of the model parameters when considering different types of prior information on the model structure and different likelihood functions to describe the data errors. The results indicate that model regularization is necessary when dealing with a large number of model parameters because it helps to accelerate the convergence of the chains and leads to more realistic models. These constraints also lead to smaller uncertainty estimates, which imply posterior distributions that do not include the true underlying model in regions where the method has limited sensitivity. This situation can be improved by combining planewave EM methods with complimentary geophysical methods such as ERT. In addition, I show that an appropriate regularization weight and the standard deviation of the data errors can be retrieved by the MCMC inversion. Finally, I evaluate the possibility of characterizing the three-dimensional distribution of an injected water plume by performing three-dimensional time-lapse MCMC inversion of planewave EM data. Since MCMC inversion involves a significant computational burden in high parameter dimensions, I propose a model reduction strategy where the coefficients of a Legendre moment decomposition of the injected water plume and its location are estimated. For this purpose, a base resistivity model is needed which is obtained prior to the time-lapse experiment. A synthetic test shows that the methodology works well when the base resistivity model is correctly characterized. The methodology is also applied to an injection experiment performed in a geothermal system in Australia, and compared to a three-dimensional time-lapse inversion performed within a deterministic framework. The MCMC inversion better constrains the water plumes due to the larger amount of prior information that is included in the algorithm. The conductivity changes needed to explain the time-lapse data are much larger than what is physically possible based on present day understandings. This issue may be related to the base resistivity model used, therefore indicating that more efforts should be given to obtain high-quality base models prior to dynamic experiments. The studies described herein give clear evidence that plane-wave EM methods are useful to characterize and monitor the subsurface at a wide range of scales. The presented approaches contribute to an improved appraisal of the obtained models, both in terms of the incorporation of prior information in the algorithms and the posterior uncertainty quantification. In addition, the developed strategies can be applied to other geophysical methods, and offer great flexibility to incorporate additional information when available.

Thalamic connectivity in patients with essential tremor treated with MR imaging-guided focused ultrasound: in vivo fiber tracking by using diffusion-tensor MR imaging.

PURPOSE: To use diffusion-tensor (DT) magnetic resonance (MR) imaging in patients with essential tremor who were treated with transcranial MR imaging-guided focused ultrasound lesion inducement to identify the structural connectivity of the ventralis intermedius nucleus of the thalamus and determine how DT imaging changes correlated with tremor changes after lesion inducement. MATERIALS AND METHODS: With institutional review board approval, and with prospective informed consent, 15 patients with medication-refractory essential tremor were enrolled in a HIPAA-compliant pilot study and were treated with transcranial MR imaging-guided focused ultrasound surgery targeting the ventralis intermedius nucleus of the thalamus contralateral to their dominant hand. Fourteen patients were ultimately included. DT MR imaging studies at 3.0 T were performed preoperatively and 24 hours, 1 week, 1 month, and 3 months after the procedure. Fractional anisotropy (FA) maps were calculated from the DT imaging data sets for all time points in all patients. Voxels where FA consistently decreased over time were identified, and FA change in these voxels was correlated with clinical changes in tremor over the same period by using Pearson correlation. RESULTS: Ipsilateral brain structures that showed prespecified negative correlation values of FA over time of -0.5 or less included the pre- and postcentral subcortical white matter in the hand knob area; the region of the corticospinal tract in the centrum semiovale, in the posterior limb of the internal capsule, and in the cerebral peduncle; the thalamus; the region of the red nucleus; the location of the central tegmental tract; and the region of the inferior olive. The contralateral middle cerebellar peduncle and bilateral portions of the superior vermis also showed persistent decrease in FA over time. There was strong correlation between decrease in FA and clinical improvement in hand tremor 3 months after lesion inducement (P < .001). CONCLUSION: DT MR imaging after MR imaging-guided focused ultrasound thalamotomy depicts changes in specific brain structures. The magnitude of the DT imaging changes after thalamic lesion inducement correlates with the degree of clinical improvement in essential tremor.

Diffusion tensor imaging shows structural remodeling of stroke mirror region: results from a pilot study.

Background: The role of the non-injured hemisphere in stroke recovery is poorly understood. In this pilot study, we sought to explore the presence of structural changes detectable by diffusion tensor imaging (DTI) in the contralesional hemispheres of patients who recovered well from ischemic stroke. Methods: We analyzed serial DTI data from 16 stroke patients who had moderate initial neurological deficits (NIHSS scores 3-12) and good functional outcome at 3-6 months (NIHSS score 0 or modified Rankin Score ≤1). We segmented the brain tissue in gray and white matter (GM and WM) and measured the apparent diffusion coefficient (ADC) and fractional anisotropy in the infarct, in the contralesional infarct mirror region as well as in concentrically expanding regions around them. Results: We found that GM and WM ADC significantly increased in the infarct region (p < 0.01) from acute to chronic time points, whereas in the infarct mirror region, GM and WM ADC increased (p < 0.01) and WM fractional anisotropy decreased (p < 0.05). No significant changes were detected in other regions. Conclusion: DTI-based metrics are sensitive to regional structural changes in the contralesional hemisphere during stroke recovery. Prospective studies in larger cohorts with varying levels of recovery are needed to confirm our findings.

Estimation of jump-diffusion processes via empirical characteristic functions

Preface The starting point for this work and eventually the subject of the whole thesis was the question: how to estimate parameters of the affine stochastic volatility jump-diffusion models. These models are very important for contingent claim pricing. Their major advantage, availability T of analytical solutions for characteristic functions, made them the models of choice for many theoretical constructions and practical applications. At the same time, estimation of parameters of stochastic volatility jump-diffusion models is not a straightforward task. The problem is coming from the variance process, which is non-observable. There are several estimation methodologies that deal with estimation problems of latent variables. One appeared to be particularly interesting. It proposes the estimator that in contrast to the other methods requires neither discretization nor simulation of the process: the Continuous Empirical Characteristic function estimator (EGF) based on the unconditional characteristic function. However, the procedure was derived only for the stochastic volatility models without jumps. Thus, it has become the subject of my research. This thesis consists of three parts. Each one is written as independent and self contained article. At the same time, questions that are answered by the second and third parts of this Work arise naturally from the issues investigated and results obtained in the first one. The first chapter is the theoretical foundation of the thesis. It proposes an estimation procedure for the stochastic volatility models with jumps both in the asset price and variance processes. The estimation procedure is based on the joint unconditional characteristic function for the stochastic process. The major analytical result of this part as well as of the whole thesis is the closed form expression for the joint unconditional characteristic function for the stochastic volatility jump-diffusion models. The empirical part of the chapter suggests that besides a stochastic volatility, jumps both in the mean and the volatility equation are relevant for modelling returns of the S&P500 index, which has been chosen as a general representative of the stock asset class. Hence, the next question is: what jump process to use to model returns of the S&P500. The decision about the jump process in the framework of the affine jump- diffusion models boils down to defining the intensity of the compound Poisson process, a constant or some function of state variables, and to choosing the distribution of the jump size. While the jump in the variance process is usually assumed to be exponential, there are at least three distributions of the jump size which are currently used for the asset log-prices: normal, exponential and double exponential. The second part of this thesis shows that normal jumps in the asset log-returns should be used if we are to model S&P500 index by a stochastic volatility jump-diffusion model. This is a surprising result. Exponential distribution has fatter tails and for this reason either exponential or double exponential jump size was expected to provide the best it of the stochastic volatility jump-diffusion models to the data. The idea of testing the efficiency of the Continuous ECF estimator on the simulated data has already appeared when the first estimation results of the first chapter were obtained. In the absence of a benchmark or any ground for comparison it is unreasonable to be sure that our parameter estimates and the true parameters of the models coincide. The conclusion of the second chapter provides one more reason to do that kind of test. Thus, the third part of this thesis concentrates on the estimation of parameters of stochastic volatility jump- diffusion models on the basis of the asset price time-series simulated from various "true" parameter sets. The goal is to show that the Continuous ECF estimator based on the joint unconditional characteristic function is capable of finding the true parameters. And, the third chapter proves that our estimator indeed has the ability to do so. Once it is clear that the Continuous ECF estimator based on the unconditional characteristic function is working, the next question does not wait to appear. The question is whether the computation effort can be reduced without affecting the efficiency of the estimator, or whether the efficiency of the estimator can be improved without dramatically increasing the computational burden. The efficiency of the Continuous ECF estimator depends on the number of dimensions of the joint unconditional characteristic function which is used for its construction. Theoretically, the more dimensions there are, the more efficient is the estimation procedure. In practice, however, this relationship is not so straightforward due to the increasing computational difficulties. The second chapter, for example, in addition to the choice of the jump process, discusses the possibility of using the marginal, i.e. one-dimensional, unconditional characteristic function in the estimation instead of the joint, bi-dimensional, unconditional characteristic function. As result, the preference for one or the other depends on the model to be estimated. Thus, the computational effort can be reduced in some cases without affecting the efficiency of the estimator. The improvement of the estimator s efficiency by increasing its dimensionality faces more difficulties. The third chapter of this thesis, in addition to what was discussed above, compares the performance of the estimators with bi- and three-dimensional unconditional characteristic functions on the simulated data. It shows that the theoretical efficiency of the Continuous ECF estimator based on the three-dimensional unconditional characteristic function is not attainable in practice, at least for the moment, due to the limitations on the computer power and optimization toolboxes available to the general public. Thus, the Continuous ECF estimator based on the joint, bi-dimensional, unconditional characteristic function has all the reasons to exist and to be used for the estimation of parameters of the stochastic volatility jump-diffusion models.