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PubMed2005

Adaptive local refinement of the electron density, one-particle density matrices, and electron orbitals by hierarchical wavelet decomposition.

The common experience that the distribution and interaction of electrons widely vary by scanning over various parts of a molecule is incorporated in the atomic-orbital expansion of wave functions. The application of Gaussian-type atomic orbitals suffers from the poor representation of nuclear cusps, as well as asymptotic regions, whereas Slater-type orbitals lead to unmanageable computational difficulties. In this contribution we show that using the toolkit of wavelet analysis it is possible to find an expansion of the electron density and density operators which is sufficiently precise, but at the same time avoids unnecessary complications at smooth and slightly detailed parts of the system. The basic idea of wavelet analysis is a coarse description of the system on a rough grid and a consecutive application of refinement steps by introducing new basis functions on a finer grid. This step could highly increase the number of required basis functions, however, in this work we apply an adaptive refinement only in those regions of the molecule, where the details of the electron structure require it. A molecule is split into three regions with different detail characteristics. The neighborhood of a nuclear cusp is extremely well represented by a moderately fine wavelet expansion; the domains of the chemical bonds are reproduced at an even coarser resolution level, whereas the asymptotic tails of the electron structure are surprisingly precise already at a grid distance of 0.5 a.u. The strict localization property of wavelet functions leads to an especially simple calculation of the electron integrals.

Journal Article↗
PubMed1999

Detection of abnormal high-frequency components in the QRS complex by the wavelet transform in patients with idiopathic dilated cardiomyopathy.

In order to investigate whether increased fine, fractionated signals within the QRS complex can detect arrhythmogenic substrates and how these fine signals link with ventricular mechanical dysfunction, wavelet analysis was performed on averaged QRS complexes obtained from the left precordial lead in 26 patients with idiopatic dilated cardiomyopathy (IDCM) and in 12 normal subjects. The number of local maxima and the duration of the wavelet transform were significantly greater in patients with IDCM than in normal subjects; the number at 100 Hz was 8.8+/-3.1 vs 6.0+/-1.1 (p<0.01), and the duration at 100Hz was 93+/-15 vs 75+/-7ms (p<0.01). Both of these indices were greater in the patients with than in those without late potentials, repetitive ventricular premature beats or cardiac death. In addition, significant inverse curvilinear relationships were observed between the left ventricular ejection fraction and both the number of local maxima and the duration of the wavelet transform. In conclusion, fine fragmented signals in the QRS complex detected by wavelet analysis would be an important marker for potentially arrhythmogenic substrates and seemed to progress in parallel with left ventricular mechanical dysfunction in IDCM.

Adolescent↗
PubMedDate not supplied

[Self-similarity in variability of human heart variability at various stages of ontogenesis].

We consider the potential of applying wavelet analysis to fluctuations found in physiological systems. We focus on cardiac interbeat interval time series (RR-intervals) from a group of young adults and children and fetus heart beat rate time series (antepartum cardiotocography), because the wavelet analysis of these heart rate dynamics may provide important practical diagnostic and prognostic information not obtainable with current approaches. We show that all the signals analyzed are self-similar and propose a method for estimating this scaling feature.

Adolescent↗
PubMed2002

Wavelet entropy analysis of event-related potentials indicates modality-independent theta dominance.

Sensory/cognitive stimulation elicits multiple electroencephalogram (EEG)-oscillations that may be partly or fully overlapping over the time axis. To evaluate co-existent multi-frequency oscillations, EEG responses to unimodal (auditory or visual) and bimodal (combined auditory and visual) stimuli were analyzed by applying a new method called wavelet entropy (WE). The method is based on the wavelet transform (WT) and quantifies entropy of short segments of the event-related brain potentials (ERPs). For each modality, a significant transient decrease of WE emerged in the post-stimulus EEG epoch indicating a highly-ordered state in the ERP. WE minimum was always determined by a prominent dominance of theta (4-8 Hz) ERP components over other frequency bands. Event-related 'transition to order' was most pronounced and stable at anterior electrodes, and after bimodal stimulation. Being consistently observed across different modalities, a transient theta-dominated state may reflect a processing stage that is obligatory for stimulus evaluation, during which interfering activations from other frequency networks are minimized.

Acoustic Stimulation↗
PubMed2005

Functional magnetic resonance imaging activation detection: fuzzy cluster analysis in wavelet and multiwavelet domains.

PURPOSE: To present novel feature spaces, based on multiscale decompositions obtained by scalar wavelet and multiwavelet transforms, to remedy problems associated with high dimension of functional magnetic resonance imaging (fMRI) time series (when they are used directly in clustering algorithms) and their poor signal-to-noise ratio (SNR) that limits accurate classification of fMRI time series according to their activation contents. MATERIALS AND METHODS: Using randomization, the proposed method finds wavelet/multiwavelet coefficients that represent the activation content of fMRI time series and combines them to define new feature spaces. Using simulated and experimental fMRI data sets, the proposed feature spaces are compared to the cross-correlation (CC) feature space and their performances are evaluated. In these studies, the false positive detection rate is controlled using randomization. To compare different methods, several points of the receiver operating characteristics (ROC) curves, using simulated data, are estimated and compared. RESULTS: The proposed features suppress the effects of confounding signals and improve activation detection sensitivity. Experimental results show improved sensitivity and robustness of the proposed method compared to the conventional CC analysis. CONCLUSION: More accurate and sensitive activation detection can be achieved using the proposed feature spaces compared to CC feature space. Multiwavelet features show superior detection sensitivity compared to the scalar wavelet features.

Algorithms↗
PubMed2001

Topological distribution of oddball 'P300' responses.

This report describes the frequency response of the oddball paradigm upon auditory stimuli. Other reports related to wavelet analysis of the same ERPs (Demiralp et al., 1999) and the application of visual signals (Schürmann et al., this volume) indicate that the P300 response has a dominant delta response oscillation, independent of the modality of the stimulation. Moreover, the adaptive digital filtering and the wavelet analysis lead to very similar results, confirming that delta responses are real brain responses as already mentioned, by Başar et al. (this volume). The theta response has a second late response window in comparison to auditory evoked potentials. Moreover, the functional significance of the selectively distributed theta and delta systems of the brain will be clearly demonstrated. Signal detection, short-term memory, and decision-making processes are discussed.

Animals↗
PubMed1994

Wavelet-type analysis of transient-evoked otoacoustic emissions.

A transient-evoked otoacoustic emission (TEOAE) is a sound originating in the cochlea in response to a brief acoustic stimulus, such as a click. The response is typically a weak (25 dB SPL maximum) signal that lasts 20-40 ms. Analysis of TEOAEs is promising as a noninvasive technique for understanding cochlear function and as a diagnostic tool in identifying hearing loss. A TEOAE database was collected on many subjects, some of which were administered quinine to study the effect of the drug on TEOAE. Historically, FFT techniques have not worked well on TEOAE data because of the nonstationary nature of the signals. We have used a wavelet-like approach in analyzing the data by employing a set of equal-bandwidth filters, which have revealed the emission energy to be concentrated in the 800-2000 Hz range. This type of analysis is shown to be useful in examining the time progression of different frequency bands of the click-evoked emissions in subjects who took quinine.

Acoustic Stimulation↗
PubMed1997

Analysis of the equine jumping technique by accelerometry.

The purpose of this study was to demonstrate the relationships between jumping technique and dorsoventral acceleration measured at the sternum. Eight saddle horses of various jumping abilities competed on a selective experimental show jumping course including 14 obstacles. An accelerometric belt fastened onto the thorax continuously measured the dorsoventral acceleration during the course. At each jump, 11 locomotor parameters (acceleration peaks, durations and stride frequency) were obtained from the dorsoventral acceleration-time curves. The type of obstacle significantly influenced the hindlimb acceleration peak at take-off and the landing acceleration peak (P<0.01). The poor jumpers exhibited a higher mean forelimb acceleration peak at take-off, a higher forelimb/hindlimb ratio between peaks of acceleration (F/H), and a lower approach stride frequency than good jumpers. Knocking over an obstacle was significantly associated with a low hindlimb acceleration peak at take-off and a high F/H ratio (P<0.01). In order to observe the continuous changes in the frequency domain of the dorsoventral acceleration during the approach and take-off phase, a Morlet's wavelet analysis was computed for each horse jumping over a series of 3 vertical obstacles. Different patterns of time-frequency images obtained by wavelet analysis were found when the horse either knocked over a vertical obstacle or cleared it. In the latter case, the image pattern showed an instantaneous increase in stride frequency at the end of the approach phase, and a marked energy content in the middle frequency range at take-off.

Acceleration↗
PubMed2000

Spike sorting based on discrete wavelet transform coefficients.

Using the novel mathematical technique known as wavelet analysis, a new method (WSC) is presented to sort spikes according to a decomposition of neural signals in the time-frequency space. The WSC method is implemented by a pyramidal algorithm that acts upon neural signals as a bank of quadrature mirror filters. This algorithm is clearly explained and an overview of the mathematical background of wavelet analysis is given. An artificial spike train, especially designed to test the specificity and sensibility of sorting procedures, was used to assess the performance of the WSC method as well as of methods based on principal component analysis (PCA) and reduced feature set (RFS). The WSC method outperformed the other two methods. Its superior performance was largely due to the fact that spike profiles that could not be separated by previous methods (because of the similarity of their temporal profile and the masking action of noise) were separable by the WSC method. The WSC method is particularly noise resistant, as it implicitly eliminates the irrelevant information contained in the noise frequency range. But the main advantage of the WSC method is its use of parameters that describe the joint time-frequency localization of spike features to build a fast and unspecialized pattern recognition procedure.

Action Potentials↗
PubMed2004

Attenuated respiratory modulation of chemoreflex-mediated sympathoexcitation in patients with chronic heart failure.

BACKGROUND: Enhanced hypercapnic chemoreflex in chronic heart failure could modulate sympathetic nerve activity in a different manner depending on the severity of heart failure. This study was designed to evaluate the dynamic aspects of sympathoexcitation caused by central hypercapnic chemoreflex in patients with chronic heart failure. METHODS AND RESULTS: In 21 patients with chronic heart failure, wavelet analysis was applied to elucidate the spectral components of muscle sympathetic nerve activity (MSNA) and instantaneous ventilation during hypercapnic chemoreceptor stimulation. Hypercapnia increased MSNA (83+/-8 versus 29+/-9 %, P<.01) and ventilation (209+/-27 versus 190+/-21%, P<.05) more in 12 symptomatic patients than in 9 asymptomatic patients. This hypercapnic chemoreflex exerted a greater influence on the sympathetic limb than on the ventilatory limb in the symptomatic patients. The wavelet analysis revealed that the within-breath sympathoinhibition in the symptomatic patients was attenuated as compared with that in the asymptomatic patients (0.33+/-0.03 vs. 0.44+/-0.04, P<.05). CONCLUSIONS: The enhanced chemoreflex sympathetic drive and relative attenuation of ventilatory sympathoinhibition could contribute to exaggerated sympathoexcitation in patients with heart failure when they are exposed to carbon dioxide during exercise or sleep apnea.

Chemoreceptor Cells↗
PubMed2004

Wavelet-based analysis of transient electromagnetic wave propagation in photonic crystals.

Photonic crystals and optical bandgap structures, which facilitate high-precision control of electromagnetic-field propagation, are gaining ever-increasing attention in both scientific and commercial applications. One common photonic device is the distributed Bragg reflector (DBR), which exhibits high reflectivity at certain frequencies. Analysis of the transient interaction of an electromagnetic pulse with such a device can be formulated in terms of the time-domain volume integral equation and, in turn, solved numerically with the method of moments. Owing to the frequency-dependent reflectivity of such devices, the extent of field penetration into deep layers of the device will be different depending on the frequency content of the impinging pulse. We show how this phenomenon can be exploited to reduce the number of basis functions needed for the solution. To this end, we use spatiotemporal wavelet basis functions, which possess the multiresolution property in both spatial and temporal domains. To select the dominant functions in the solution, we use an iterative impedance matrix compression (IMC) procedure, which gradually constructs and solves a compressed version of the matrix equation until the desired degree of accuracy has been achieved. Results show that when the electromagnetic pulse is reflected, the transient IMC omits basis functions defined over the last layers of the DBR, as anticipated.

Journal Article↗
PubMed2006

Frequency modulation between low- and high-frequency components of the heart rate variability spectrum.

Interactions among physiological mechanisms are abundant in biomedical signals, and they may exist to maintain efficient homeostasis. For example, sympathetic and parasympathetic neural activities interact to either elevate or depress the heart rate to maintain homeostasis. There has been considerable effort devoted to developing algorithms that can detect interactions between various physiological mechanisms. However, methods used to detect the presence of interactions between the sympathetic and parasympathetic nervous systems, to take one example, have had limited success. This may be because interactions in physiological systems are non-linear and non-stationary. The goal of this work was to identify non-linear interactions between the sympathetic and parasympathetic nervous systems in the form of frequency and amplitude modulations in human heart-rate data (n=6). To this end, wavelet analysis was performed, followed by frequency analysis of the resultant wavelet decomposed signals in several frequency brackets we define as: very low frequency (f<0.04 Hz), low frequency (0.04-0.15 Hz) and high frequency (0.15-0.4 Hz). Our analysis suggests that the high-frequency bracket is modulated by the low-frequency bracket in the heart rate data obtained in both upright and sitting positions. However, there was no evidence of amplitude modulation among these frequencies.

Algorithms↗
PubMed2005

A comparison of changes in rhythms of sacral skin blood flow in response to heating and indentation.

OBJECTIVE: To differentiate blood flow control mechanisms associated with indentation from those associated with heating and to discern heat-induced and pressure-induced changes by comparing the effect of externally applied stress on skin blood flow (SBF) to the response to externally applied heat. DESIGN: Repeated-measures design. SETTING: A university research laboratory. PARTICIPANTS: Ten healthy, young adults (5 men, 5 women; mean age +/- standard deviation, 30.0+/-3.1y). Intervention Incremental heat (35 degrees -45 degrees C, 1 degrees step/min) and pressure (0-60 mmHg, 5 mmHg step/3 min) on the sacrum using a computer-controlled indenter. Sessions for heat and pressure protocols were separated by 7+/-2 days. MAIN OUTCOME MEASURES: We used a Laserflo Blood Perfusion Monitor 2 and Softip pencil probe to measure capillary blood perfusion and wavelet analysis to decompose the blood flow signal. The power spectrum was divided into 5 ranges corresponding to metabolic, neurogenic, myogenic, respiratory, and cardiac control mechanisms. The average relative (ie, normalized) power in each frequency range was computed to determine of the relative contribution of each control mechanism. RESULTS: Power in the myogenic frequency range was higher after incremental pressure and lower after incremental heating, whereas power in the metabolic frequency range was lower after incremental pressure and higher after incremental heating ( P <.01). Mean blood flow decreased as pressure increased from 0 to 15 mmHg; mean blood flow increased as pressure increased from 15 to 60 mmHg. CONCLUSIONS: SBF, as recorded by the laser Doppler, suggests that there may be a myogenic control mechanism mediating blood flow after incremental tissue loads and that a metabolic control mechanism may mediate blood flow after heat application to the tissue. The study of local blood flow control mechanisms and their response to pathomechanical perturbations may be possible using wavelet analysis of blood flow oscillations. More research is needed to establish the clinical utility of these findings in the development of support surfaces intended to reduce the risk of developing pressure ulcers.

Adult↗
PubMed2002

Diagnosis of breast tumors with sonographic texture analysis using wavelet transform and neural networks.

To increase the ability of ultrasonographic technology for the differential diagnosis of solid breast tumors, we describe a novel computer-aided diagnosis (CADx) system using neural networks for classification of breast tumors. Tumor regions and surrounding tissues are segmented from the physician-located region-of-interest (ROI) images by applying our proposed segmentation algorithm. Cooperating with the segmentation algorithm, three feasible features, including variance contrast, autocorrelation contrast and distribution distortion of wavelet coefficients, were extracted from the ROI images for further classification. A multilayered perceptron (MLP) neural network trained using error back-propagation algorithm with momentum was then used for the differential diagnosis of breast tumors on sonograms. In the experiment, 242 cases (including benign breast tumors from 161 patients and carcinomas from 82 patients) were sampled with k-fold cross-validation (k = 10) to evaluate the performance. The receiver operating characteristic (ROC) area index for the proposed CADx system is 0.9396 +/- 0.0183, the sensitivity is 98.77%, the specificity is 81.37%, the positive predictive value is 72.73% and the negative predictive value is 99.24%. Experimental results showed that our diagnosis model performed very well for breast tumor diagnosis.

Breast Diseases↗
PubMed2000

Optical near-field data analysis through time-frequency distributions: application to the characterization and separation of the image spectral content by reassignment.

The near-field optical images have been traditionally analyzed by Fourier analysis and, recently, by wavelet analysis. Those data are nonstationary, which means that their spectral content varies with time, owing to the scanning-probe recording process; therefore time-frequency representations are, potentially, powerful tools for local characteristics extraction or shape separation, since they distribute the energy of the analyzed signal over the time and frequency variables and faithfully depict the signal local behavior. In this study we show that Cohen's class time-frequency distributions and their modified version by the reassignment method are appropriate tools for the analysis of near-field optical data. We demonstrate this by using these tools first on simulated data and second on experimental near-field optical images. Within this context we observe that time-frequency analysis allows one to easily characterize local frequencies, which involves a possible separation of relevant optical signal from artifacts.

Journal Article↗
PubMed2005

An approach to verifying delayed menarche in Japanese female athletes. Analysis by wavelet interpolation method.

AIM: The theory of delayed menarche in female athletes, despite some evidence for such a delay, has not yet been verified. We examined a means to verify this hypothesis by comparing ages at menarche and at peak height velocity (PHV) derived from the wavelet interpolation method (WIM) for female athletes and non-athletes (control group). METHODS: We identified age at maximum peak velocity as the index of the physical maturation rate by WIM. We then conducted a study involving 144 female athletes in their 1st year at University in the Tokai area, all of whom had competed in a national high school sports competition (athlete group). Past school records of these subjects' heights from the 1st grade of elementary to the 3rd year of senior high school (1984-1995) were collected, and ages at menarche were ascertained from questionnaires. A control group of 78 non-athletes was similarly examined. RESULTS: This difference (interval) between age at menarche and age at PHV was 1.62 years (SD=1.25) in the athlete group and 1.08 years (SD=0.74) in the control group. The difference between the 2 groups was statistically significant (P<0.01). This finding provides evidence that menarche in female athletes is delayed in relation to physical maturation rate. CONCLUSIONS: This result alone cannot establish whether athletic training is the only cause of this delay; however, an approach to verifying the hypothesis of delayed menarche in female athletes has been established by this finding.

Adolescent↗