Efecto de la presión hiperbárica y diferentes presiones parciales de gases sobre la modulación vegetativa de la respuesta cardiaca : aplicación de métodos lineales y no lineales en el análisis de VFC

Programa de doctorado: Actividad Física, Salud y Rendimiento Deportivo

Meditación Zen y fenómenos de sincronización y resonancia en el sistema cardiorespiratorio. Análisis Wavelet

[ES] El interés científico en la meditación ha crecido significativamente en las últimas décadas. La meditación es, tal vez, la práctica más adecuada para investigar las propiedades intrínsecas del Sistema nervioso autónomo (SNA), dado que conlleva un estado de total inmovilidad física y de cierto aislamiento del exterior (interiorización). En meditación, ya que no hay movimiento físico, el patrón respiratorio es ajustado según el proceso mental. Así, la modulación que ejerce la respiración sobre la frecuencia cardiaca está relacionada a la cualidad y al enfoque de la atención en la práctica. De los resultados obtenidos en nuestra investigación, podemos concluir que hay patrones específicos de variabilidad de la frecuencia cardiaca (VFC) que parecen reflejar fases o etapas en la práctica. Así, sujetos con una experiencia en meditación similar tienden a mostrar patrones análogos de variabilidad cardiaca. A medida que se progresa en la práctica meditativa, los diferentes sistemas oscilantes tienden a interaccionar entre ellos, hasta culminar con la aparición de un efecto resonante que establece un ?nuevo orden? en el sistema. Este proceso parece reflejar cambios graduales en la actividad del SNA para alcanzar un "modo de funcionamiento de bajo coste", donde los diversos mecanismos oscilatorios que intervienen en el control de la circulación sanguínea operan a la misma frecuencia. El fenómeno de resonancia implica un ?modo de funcionamiento de bajo coste? que probablemente favorece la práctica de la meditación. Así, este estado de ?orden? (aunque no sin variabilidad) podría ser considerado un atractor, al cual el sistema tiende a evolucionar cuando se haya alcanzado un nivel avanzado de mindfulness. El concepto de atractor, procedente de las modernas teorías que tratan con la dinámica de sistemas complejos no-lineales, parece mostrarse útil para describir de manera heurística el comportamiento del sistema en estados meditativos profundos. Los resultados obtenidos en esta tesis apoyan y complementan otros trabajos anteriores, además se añade la idea de una adaptación fisiológica gradual a la práctica de la meditación mindfulness, caracterizada por cambios específicos en la regulación autonómica de la VFC en las diferentes etapas de la práctica. Para el análisis de las series fisiológicas, de carácter fuertemente no lineal, se han implementado técnicas basadas en el análisis Wavelet y Dinámica Simbólica.

Multiresolution spherical wavelet analysis in global seismic tomography

Every seismic event produces seismic waves which travel throughout the Earth. Seismology is the science of interpreting measurements to derive information about the structure of the Earth. Seismic tomography is the most powerful tool for determination of 3D structure of deep Earth's interiors. Tomographic models obtained at the global and regional scales are an underlying tool for determination of geodynamical state of the Earth, showing evident correlation with other geophysical and geological characteristics. The global tomographic images of the Earth can be written as a linear combinations of basis functions from a specifically chosen set, defining the model parameterization. A number of different parameterizations are commonly seen in literature: seismic velocities in the Earth have been expressed, for example, as combinations of spherical harmonics or by means of the simpler characteristic functions of discrete cells. With this work we are interested to focus our attention on this aspect, evaluating a new type of parameterization, performed by means of wavelet functions. It is known from the classical Fourier theory that a signal can be expressed as the sum of a, possibly infinite, series of sines and cosines. This sum is often referred as a Fourier expansion. The big disadvantage of a Fourier expansion is that it has only frequency resolution and no time resolution. The Wavelet Analysis (or Wavelet Transform) is probably the most recent solution to overcome the shortcomings of Fourier analysis. The fundamental idea behind this innovative analysis is to study signal according to scale. Wavelets, in fact, are mathematical functions that cut up data into different frequency components, and then study each component with resolution matched to its scale, so they are especially useful in the analysis of non stationary process that contains multi-scale features, discontinuities and sharp strike. Wavelets are essentially used in two ways when they are applied in geophysical process or signals studies: 1) as a basis for representation or characterization of process; 2) as an integration kernel for analysis to extract information about the process. These two types of applications of wavelets in geophysical field, are object of study of this work. At the beginning we use the wavelets as basis to represent and resolve the Tomographic Inverse Problem. After a briefly introduction to seismic tomography theory, we assess the power of wavelet analysis in the representation of two different type of synthetic models; then we apply it to real data, obtaining surface wave phase velocity maps and evaluating its abilities by means of comparison with an other type of parametrization (i.e., block parametrization). For the second type of wavelet application we analyze the ability of Continuous Wavelet Transform in the spectral analysis, starting again with some synthetic tests to evaluate its sensibility and capability and then apply the same analysis to real data to obtain Local Correlation Maps between different model at same depth or between different profiles of the same model.

Le funzioni wavelet nelle applicazioni scientifiche

Le wavelet sono una nuova famiglia di funzioni matematiche che permettono di decomporre una data funzione nelle sue diverse componenti in frequenza. Esse combinano le proprietà dell’ortogonalità, il supporto compatto, la localizzazione in tempo e frequenza e algoritmi veloci. Sono considerate, perciò, uno strumento versatile sia per il contenuto matematico, sia per le applicazioni. Nell’ultimo decennio si sono diffuse e imposte come uno degli strumenti migliori nell’analisi dei segnali, a fianco, o addirittura come sostitute, dei metodi di Fourier. Si parte dalla nascita di esse (1807) attribuita a J. Fourier, si considera la wavelet di A. Haar (1909) per poi incentrare l’attenzione sugli anni ’80, in cui J. Morlet e A. Grossmann definiscono compiutamente le wavelet nel campo della fisica quantistica. Altri matematici e scienziati, nel corso del Novecento, danno il loro contributo a questo tipo di funzioni matematiche. Tra tutti emerge il lavoro (1987) della matematica e fisica belga, I. Daubechies, che propone le wavelet a supporto compatto, considerate la pietra miliare delle applicazioni wavelet moderne. Dopo una trattazione matematica delle wavalet, dei relativi algoritmi e del confronto con il metodo di Fourier, si passano in rassegna le principali applicazioni di esse nei vari campi: compressione delle impronte digitali, compressione delle immagini, medicina, finanza, astonomia, ecc. . . . Si riserva maggiore attenzione ed approfondimento alle applicazioni delle wavelet in campo sonoro, relativamente alla compressione audio, alla rimozione del rumore e alle tecniche di rappresentazione del segnale. In conclusione si accenna ai possibili sviluppi e impieghi delle wavelet nel futuro.

Wavelet analysis of heart rate variability related to nocturnal frontal lobe epilepsy seizures

Introduction: Nocturnal frontal lobe epilepsy (NFLE) is a distinct syndrome of partial epilepsy whose clinical features comprise a spectrum of paroxysmal motor manifestations of variable duration and complexity, arising from sleep. Cardiovascular changes during NFLE seizures have previously been observed, however the extent of these modifications and their relationship with seizure onset has not been analyzed in detail. Objective: Aim of present study is to evaluate NFLE seizure related changes in heart rate (HR) and in sympathetic/parasympathetic balance through wavelet analysis of HR variability (HRV). Methods: We evaluated the whole night digitally recorded video-polysomnography (VPSG) of 9 patients diagnosed with NFLE with no history of cardiac disorders and normal cardiac examinations. Events with features of NFLE seizures were selected independently by three examiners and included in the study only if a consensus was reached. Heart rate was evaluated by measuring the interval between two consecutive R-waves of QRS complexes (RRi). RRi series were digitally calculated for a period of 20 minutes, including the seizures and resampled at 10 Hz using cubic spline interpolation. A multiresolution analysis was performed (Daubechies-16 form), and the squared level specific amplitude coefficients were summed across appropriate decomposition levels in order to compute total band powers in bands of interest (LF: 0.039062 - 0.156248, HF: 0.156248 - 0.624992). A general linear model was then applied to estimate changes in RRi, LF and HF powers during three different period (Basal) (30 sec, at least 30 sec before seizure onset, during which no movements occurred and autonomic conditions resulted stationary); pre-seizure period (preSP) (10 sec preceding seizure onset) and seizure period (SP) corresponding to the clinical manifestations. For one of the patients (patient 9) three seizures associated with ictal asystole were recorded, hence he was treated separately. Results: Group analysis performed on 8 patients (41 seizures) showed that RRi remained unchanged during the preSP, while a significant tachycardia was observed in the SP. A significant increase in the LF component was instead observed during both the preSP and the SP (p<0.001) while HF component decreased only in the SP (p<0.001). For patient 9 during the preSP and in the first part of SP a significant tachycardia was observed associated with an increased sympathetic activity (increased LF absolute values and LF%). In the second part of the SP a progressive decrease in HR that gradually exceeded basal values occurred before IA. Bradycardia was associated with an increase in parasympathetic activity (increased HF absolute values and HF%) contrasted by a further increase in LF until the occurrence of IA. Conclusions: These data suggest that changes in autonomic balance toward a sympathetic prevalence always preceded clinical seizure onset in NFLE, even when HR changes were not yet evident, confirming that wavelet analysis is a sensitive technique to detect sudden variations of autonomic balance occurring during transient phenomena. Finally we demonstrated that epileptic asystole is associated with a parasympathetic hypertonus counteracted by a marked sympathetic activation.

Wavelet estimation in diffusions with periodicity

Wir betrachten einen zeitlich inhomogenen Diffusionsprozess, der durch eine stochastische Differentialgleichung gegeben wird, deren Driftterm ein deterministisches T-periodisches Signal beinhaltet, dessen Periodizität bekannt ist. Dieses Signal sei in einem Besovraum enthalten. Wir schätzen es mit Hilfe eines nichtparametrischen Waveletschätzers. Unser Schätzer ist von einem Wavelet-Dichteschätzer mit Thresholding inspiriert, der 1996 in einem klassischen iid-Modell von Donoho, Johnstone, Kerkyacharian und Picard konstruiert wurde. Unter gewissen Ergodizitätsvoraussetzungen an den Prozess können wir nichtparametrische Konvergenzraten angegeben, die bis auf einen logarithmischen Term den Raten im klassischen iid-Fall entsprechen. Diese Raten werden mit Hilfe von Orakel-Ungleichungen gezeigt, die auf Ergebnissen über Markovketten in diskreter Zeit von Clémencon, 2001, beruhen. Außerdem betrachten wir einen technisch einfacheren Spezialfall und zeigen einige Computersimulationen dieses Schätzers.

Wavetrack, implementazione ottimizzata di un algoritmo di pitch tracking basato su wavelet

WaveTrack é un'implementazione ottimizzata di un algoritmo di pitch tracking basato su wavelet, nello specifico viene usata la trasformata Fast Lifting Wavelet Transform con la wavelet di Haar. La libreria è stata scritta nel linguaggio C e tra le sue peculiarità può vantare tempi di latenza molto bassi, un'ottima accuratezza e una buona flessibilità d'uso grazie ad alcuni parametri configurabili.

Trasformate wavelet

La presente tesi vuole dare una descrizione delle Trasformate Wavelet indirizzata alla codifica dell’immagine in formato JPEG2000. Dopo aver quindi descritto le prime fasi della codifica di un’immagine, procederemo allo studio dei difetti derivanti dall’analisi tramite la Trasformata Discreta del Coseno (utilizzata nel formato predecessore JPEG). Dopo aver quindi descritto l’analisi multirisoluzione e le caratteristiche che la differenziano da quest’ultima, analizzeremo la Trasformata Wavelet dandone solo pochi accenni teorici e cercando di dedurla, in una maniera più indirizzata all’applicazione. Concluderemo la tesi descrivendo la codifica dei coefficienti calcolati, e portando esempi delle innumerevoli applicazioni dell’analisi multirisoluzione nei diversi campi scientifici e di trasmissione dei segnali.

Analyse zur Auswirkung der irreversiblen Wavelet-Kompression (JPEG2000) auf CT-Bildverarbeitungs- und Darstellungsalgorithmen

Der technische Fortschritt konfrontiert die medizinische Bildgebung wie keine andere Sparte der Medizin mit einem rasanten Anstieg zu speichernder Daten. Anschaffung, Wartung und Ausbau der nötigen Infrastruktur entwickeln sich zunehmend zu einem ökonomischen Faktor. Ein Verfahren, welches diesem Trend etwas entgegensetzten könnte ist die irreversible Bilddatenkompression. Sie ist seit über 10 Jahren Gegenstand vieler Studien, deren Ergebnisse sich wiederum in Empfehlungen zum Einsatz irreversibler Kompression mehrerer nationaler und internationaler Organisation, wie CAR, DRG, RCR und ESR wiederspiegeln. Tenor dieser Empfehlungen ist, dass der Einsatz von moderater irreversibler Bilddatenkompression sicher und sinnvoll ist. Teil dieser Empfehlungen sind auch Angaben über das Maß an Kompression, ausgedrückt in Kompressionsraten, welche je nach Untersuchung und anatomischer Region als sicher anwendbar gelten und keinen diagnostisch relevanten Verlust der komprimierten Bilder erzeugen.rnVerschiedene Kompressionsalgorithmen wurden vorgeschlagen. Letztendlich haben sich vor allem die beiden weit verbreiteten Algorithmen JPEG und JPEG2000 bewährt. Letzterer erfährt in letzter Zeit zunehmen Anwendung, aufgrund seiner einfacheren Handhabung und seiner umfangreichen Zusatzfunktionen.rnAufgrund rechtlich-ethischer Bedenken hat die irreversible Kompression keine breite praktische Anwendung finden können. Dafür verantwortlich ist unter anderem auch die Unklarheit, wie sich irreversible Kompression auf Nach- und Weiterverarbeitung (sog. Postprocessing) medizinischer Bilder, wie Segmentierung, Volumetrie oder 3D-Darstellung, auswirkt. Bisherige Studien zu diesem Thema umfassen vier verschiedene Postprocessing-Algorithmen. Die untersuchten Algorithmen zeigten sich bei verlustbehafteter Kompression im Bereich der erwähnten, publizierten Kompressionsraten weitgehend unbeeinflusst. Lediglich die computergestützte Messung von Stenosegraden in der digitalen Koronarangiographie kollidiert mit den in Großbritannien geltenden Empfehlungen. Die Verwendung unterschiedlicher Kompressionsalgorithmen schränkt die allgemeinernAussagekraft dieser Studienergebnisse außerdem ein.rnZur Erweiterung der Studienlage wurden vier weitere Nach- und Weiterverarbeitungsalgorithmen auf ihre Kompressionstoleranz untersucht. Dabei wurden die Kompressionsraten von 8:1, 10:1 und 15:1 verwendet, welche um die empfohlenen Kompressionsraten von CAR, DRG, RCR und ESR liegen und so ein praxisnahes Setting bieten. Als Kompressionsalgorithmus wurde JPEG2000 verwendet, aufgrund seiner zunehmenden Nutzung in Studien sowie seiner bereits erwähnten Vorzüge in Sachen Handhabung und Zusatzfunktionen. Die vier Algorithmen umfassten das 3D-Volume rendering von CT-Angiographien der Becken-Bein-Gefäße, die Computer-assistierte Detektion von Lungenrundherden, die automatisierte Volumetrie von Leberrundherden und die funktionelle Bestimmung der Ejektionsfraktion in computertomographischen Aufnahmen des Herzens.rnAlle vier Algorithmen zeigten keinen Einfluss durch irreversibler Bilddatenkompression in denrngewählten Kompressionsraten (8:1, 10:1 und 15:1). Zusammen mit der bestehenden Literatur deuten die Ergebnisse an, dass moderate irreversible Kompression im Rahmen aktueller Empfehlungen keinen Einfluss auf Nach- und Weiterverarbeitung medizinischer Bilder hat. Eine explizitere Vorhersage zu einem bestimmten, noch nicht untersuchten Algorithmus ist jedoch aufgrund der unterschiedlichen Funktionsweisen und Programmierungen nicht sicher möglich.rnSofern ein Postprocessing Algorithmus auf komprimiertes Bildmaterial angewendet werden soll, muss dieser zunächst auf seine Kompressionstoleranz getestet werden. Dabei muss der Test eine rechtlich-ethische Grundlage für den Einsatz des Algorithmus bei komprimiertem Bildmaterial schaffen. Es sind vor allem zwei Optionen denkbar, die Testung institutsintern, eventuell unter Zuhilfenahme von vorgefertigten Bibliotheken, oder die Testung durch den Hersteller des Algorithmus.

Trasformata di Fourier e trasformata Wavelet

Questo elaborato si concentra sullo studio della trasformata di Fourier e della trasformata Wavelet. Nella prima parte della tesi si analizzano gli aspetti fondamentali della trasformata di Fourier. Si definisce poi la trasformata di Fourier su gruppi abeliani finiti, richiamando opportunamente la struttura di tali gruppi. Si mostra che calcolare la trasformata di Fourier nel quoziente richiede un minor numero di operazioni rispetto a calcolarla direttamente nel gruppo di partenza. L'ultima parte dell'elaborato si occupa dello studio delle Wavelet, dette ondine. Viene presentato quindi il sistema di Haar che permette di definire una funzione come serie di funzioni di Haar in alternativa alla serie di Fourier. Si propone poi un vero e proprio metodo per la costruzione delle ondine e si osserva che tale costruzione è strettamente legata all'analisi multirisoluzione. Un ruolo cruciale viene svolto dall'identità di scala, un'identità algebrica che permette di definire certi coefficienti che determinano completamente le ondine. Interviene poi la trasformata di Fourier che riduce la ricerca dei coefficienti sopra citati, alla ricerca di certe funzioni opportune che determinano esplicitamente le Wavelet. Non tutte le scelte di queste funzioni sono accettabili. Ci sono vari approcci, qui viene presentato l'approccio di Ingrid Daubechies. Le Wavelet costituiscono basi per lo spazio di funzioni a quadrato sommabile e sono particolarmente interessanti per la decomposizione dei segnali. Sono quindi in relazione con l'analisi armonica e sono adottate in un gran numero di applicazioni. Spesso sostituiscono la trasformata di Fourier convenzionale.

Wavelet-denoising of electroencephalogram and the absolute slope method: a new tool to improve electroencephalographic localization and lateralization

OBJECTIVE: In ictal scalp electroencephalogram (EEG) the presence of artefacts and the wide ranging patterns of discharges are hurdles to good diagnostic accuracy. Quantitative EEG aids the lateralization and/or localization process of epileptiform activity. METHODS: Twelve patients achieving Engel Class I/IIa outcome following temporal lobe surgery (1 year) were selected with approximately 1-3 ictal EEGs analyzed/patient. The EEG signals were denoised with discrete wavelet transform (DWT), followed by computing the normalized absolute slopes and spatial interpolation of scalp topography associated to detection of local maxima. For localization, the region with the highest normalized absolute slopes at the time when epileptiform activities were registered (>2.5 times standard deviation) was designated as the region of onset. For lateralization, the cerebral hemisphere registering the first appearance of normalized absolute slopes >2.5 times the standard deviation was designated as the side of onset. As comparison, all the EEG episodes were reviewed by two neurologists blinded to clinical information to determine the localization and lateralization of seizure onset by visual analysis. RESULTS: 16/25 seizures (64%) were correctly localized by the visual method and 21/25 seizures (84%) by the quantitative EEG method. 12/25 seizures (48%) were correctly lateralized by the visual method and 23/25 seizures (92%) by the quantitative EEG method. The McNemar test showed p=0.15 for localization and p=0.0026 for lateralization when comparing the two methods. CONCLUSIONS: The quantitative EEG method yielded significantly more seizure episodes that were correctly lateralized and there was a trend towards more correctly localized seizures. SIGNIFICANCE: Coupling DWT with the absolute slope method helps clinicians achieve a better EEG diagnostic accuracy.

A Wavelet Analysis of Pliopleistocene Climate Indicators: A New View of Periodicity Evolution

Wavelet analysis offers an alternative to Fourier based time-series analysis, and is particularly useful when the amplitudes and periods of dominant cycles are time dependent. We analyse climatic records derived from oxygen isotopic ratios of marine sediment cores with modified Morlet wavelets. We use a normalization of the Morlet wavelets which allows direct correspondence with Fourier analysis. This provides a direct view of the oscillations at various frequencies, and illustrates the nature of the time-dependence of the dominant cycles.

Quality assessment by region in spot images fused by means dual-tree complex wavelet transform

This work is motivated in providing and evaluating a fusion algorithm of remotely sensed images, i.e. the fusion of a high spatial resolution panchromatic image with a multi-spectral image (also known as pansharpening) using the dual-tree complex wavelet transform (DT-CWT), an effective approach for conducting an analytic and oversampled wavelet transform to reduce aliasing, and in turn reduce shift dependence of the wavelet transform. The proposed scheme includes the definition of a model to establish how information will be extracted from the PAN band and how that information will be injected into the MS bands with low spatial resolution. The approach was applied to Spot 5 images where there are bands falling outside PAN’s spectrum. We propose an optional step in the quality evaluation protocol, which is to study the quality of the merger by regions, where each region represents a specific feature of the image. The results show that DT-CWT based approach offers good spatial quality while retaining the spectral information of original images, case SPOT 5. The additional step facilitates the identification of the most affected regions by the fusion process.