'Objective' algorithm for maximum frequency estimation in Doppler spectral analysers

Automatic Max-Likelihood Envelope Detection Algorithm for Quantitative High-Frame-Rate Ultrasound for Neonatal Brain Monitoring

OBJECTIVE

Post-operative brain injury in neonates may result from disturbed cerebral perfusion, but accurate peri-operative monitoring is lacking. High-frame-rate (HFR) cerebral ultrasound could visualize and quantify flow in all detectable vessels using spectral Doppler; however, automated quantification in small vessels is challenging because of low signal amplitude. We have developed an automatic envelope detection algorithm for HFR pulsed wave spectral Doppler signals, enabling neonatal brain quantitative parameter maps during and after surgery.

METHODS

HFR ultrasound data from high-risk neonatal surgeries were recorded with a custom HFR mode (frame rate = 1000 Hz) on a Zonare ZS3 system. A pulsed wave Doppler spectrogram was calculated for each pixel containing blood flow in the image, and spectral peak velocity was tracked using a max-likelihood estimation algorithm of signal and noise regions in the spectrogram, where the most likely cross-over point marks the blood flow velocity. The resulting peak systolic velocity (PSV), end-diastolic velocity (EDV) and resistivity index (RI) were compared with other detection schemes, manual tracking and RIs from regular pulsed wave Doppler measurements in 10 neonates.

RESULTS

Envelope detection was successful in both high- and low-quality arterial and venous flow spectrograms. Our technique had the lowest root mean square error for EDV, PSV and RI (0.46 cm/s, 0.53 cm/s and 0.15, respectively) when compared with manual tracking. There was good agreement between the clinical pulsed wave Doppler RI and HFR measurement with a mean difference of 0.07.

CONCLUSION

The max-likelihood algorithm is a promising approach to accurate, automated cerebral blood flow monitoring with HFR imaging in neonates.

Stable Automatic Envelope Estimation for Noisy Doppler Ultrasound

Doppler ultrasound technology is widespread in clinical applications and is principally used for blood flow measurements in the heart, arteries, and veins. A commonly extracted parameter is the maximum velocity envelope. However, current methods of extracting it cannot produce stable envelopes in high noise conditions. This can limit clinical and research applications using the technology. In this article, a new method of automatic envelope estimation is presented. The method can handle challenging signals with high levels of noise and variable envelope shapes. Envelopes are extracted from a Doppler spectrogram image generated directly from the Doppler audio signal, making it less device-dependent than existing image-processing methods. The method's performance is assessed using simulated pulsatile flow, a flow phantom, and in vivo ascending aortic flow measurements and is compared with three state-of-the-art methods. The proposed method is the most accurate in noisy conditions, achieving, on average, for phantom data with signal-to-noise ratios (SNRs) below 10 dB, bias and standard deviation of 0.7% and 3.3% lower than the next-best performing method. In addition, a new method for beat segmentation is proposed. When combined, the two proposed methods exhibited the best performance using in vivo data, producing the least number of incorrectly segmented beats and 8.2% more correctly segmented beats than the next best performing method. The ability of the proposed methods to reliably extract timing indices for cardiac cycles across a range of signal quality is of particular significance for research and monitoring applications.

A Robust Automatic Ultrasound Spectral Envelope Estimation

Accurate estimation of ultrasound Doppler spectrogram envelope is essential for clinical pathological diagnosis of various cardiovascular diseases. However, due to intrinsic spectral broadening in the power spectrum and speckle noise existing in ultrasound images, it is difficult to obtain the accurate maximum velocity. Each of the standard existing methods has their own limitations and does not work well in complicated recordings. This paper proposes a robust automatic spectral envelope estimation method that is more accurate in phantom recordings and various in-vivo recordings than the currently used methods. Comparisons were performed on phantom recordings of the carotid artery with varying noise and additional in-vivo recordings. The accuracy of the proposed method was on average 8% greater than the existing methods. The experimental results demonstrate the wide applicability under different blood conditions and the robustness of the proposed algorithm.

Increased tissue oxygenation explains the attenuation of hyperemia upon repetitive pneumatic compression of the lower leg

The rapid hyperemia evoked by muscle compression is short lived and was recently shown to undergo a rapid decrease even in spite of continuing mechanical stimulation. The present study aims at investigating the mechanisms underlying this attenuation, which include local metabolic mechanisms, desensitization of mechanosensitive pathways, and reduced efficacy of the muscle pump. In 10 healthy subjects, short sequences of mechanical compressions ( n = 3–6; 150 mmHg) of the lower leg were delivered at different interstimulus intervals (ranging from 20 to 160 s) through a customized pneumatic device. Hemodynamic monitoring included near-infrared spectroscopy, detecting tissue oxygenation and blood volume in calf muscles, and simultaneous echo-Doppler measurement of arterial (superficial femoral artery) and venous (femoral vein) blood flow. The results indicate that 1) a long-lasting (>100 s) increase in local tissue oxygenation follows compression-induced hyperemia, 2) compression-induced hyperemia exhibits different patterns of attenuation depending on the interstimulus interval, 3) the amplitude of the hyperemia is not correlated with the amount of blood volume displaced by the compression, and 4) the extent of attenuation negatively correlates with tissue oxygenation ( r = −0,78, P < 0.05). Increased tissue oxygenation appears to be the key factor for the attenuation of hyperemia upon repetitive compressive stimulation. Tissue oxygenation monitoring is suggested as a useful integration in medical treatments aimed at improving local circulation by repetitive tissue compression.

NEW & NOTEWORTHY This study shows that 1) the hyperemia induced by muscle compression produces a long-lasting increase in tissue oxygenation, 2) the hyperemia produced by subsequent muscle compressions exhibits different patterns of attenuation at different interstimulus intervals, and 3) the extent of attenuation of the compression-induced hyperemia is proportional to the level of oxygenation achieved in the tissue. The results support the concept that tissue oxygenation is a key variable in blood flow regulation.

Adaptive Spectral Envelope Estimation for Doppler Ultrasound

Estimation of accurate maximum velocities and spectral envelope in ultrasound Doppler blood flow spectrograms are both essential for clinical diagnostic purposes. However, obtaining accurate maximum velocity is not straightforward due to intrinsic spectral broadening and variance in the power spectrum estimate. The method proposed in this paper for maximum velocity point detection has been developed by modifying an existing method-signal noise slope intersection, incorporating in it steps from an altered version of another method called geometric method. Adaptive noise estimation from the spectrogram ensures that a smooth spectral envelope is obtained postdetection of these maximum velocity points. The method has been tested on simulated Doppler signal with scatterers possessing a parabolic flow velocity profile constant in time, steady and pulsatile string phantom recordings, as well as in vivo recordings from uterine, umbilical, carotid, and subclavian arteries. The results from simulation experiments indicate a bias of less than 2.5% in maximum velocities when estimated for a range of peak velocities, Doppler angles, and SNR levels. Standard deviation in the envelope is low-less than 2% in the case of experiments done by varying the peak velocity and Doppler angle for steady phantom and simulated flow, and also less than 2% in the case of experiments done by varying SNR but keeping constant flow conditions for in vivo and simulated flow. Low variability in the envelope makes the prospect of using the envelope for automated blood flow measurements possible and is illustrated for the case of pulsatility index estimation in uterine and umbilical arteries.

Doppler indices in the umbilical arteries: influence of vessel curvature induced by bladder filling

Doppler indices are widely used to assess normal versus pathologic haemodynamics. In obstetrics, the assessment of abnormal values in some critical compartments, such as the umbilical arteries (UA), may be crucial in the clinical management of growth-restricted foetuses. It was recently proposed that the UA should be sampled in their perivesical portion (PVC), i.e., where they surround the foetal urinary bladder. However, measurements at this site could be biased by the degree of curvature of the vessel due to bladder filling. We investigated this possibility in vivo and in vitro, i.e., measurements on rubber tubes at different radii of curvature R(c). There was significant dependence of the Doppler indices A/B and PI on the vessel curvature and insonation angle; in fact, we recorded errors of about 25% when R(c) was 10 times larger than the radius of the vessel and about 100% when R(c) was five times larger than the radius of the vessel. Therefore, measurements of the UA at the PVC site should only be performed when the foetal bladder is empty.

Human factors as a source of error in peak Doppler velocity measurement

OBJECTIVE

The study was conducted to assess the error and variability that results from human factors in Doppler peak velocity measurement. The positioning of the Doppler sample volume in the vessel, adjustment of the Doppler gain and angle, and choice of waveform display size were investigated. We hypothesized that even experienced vascular technologists in a laboratory accredited by the Intersocietal Commission for Accreditation of Vascular Laboratories make significant errors and have significant variability in the subjective adjustments made during measurements.

METHODS

Problems of patient variability were avoided by having the four technologists measure peak velocities from an in vitro pulsatile flow model with unstenosed and 61% stenosed tubes. To evaluate inaccurate angle and sample volume positioning, a probe holder was used in some of the experiments to fix the Doppler angle at 60 degrees. The effect of Doppler gain was studied at three settings--low, ideal, and saturated gains--that were standardized from the ideal level chosen by consensus amongst the technologists. Two waveform display sizes were also investigated. Peak velocity measurement was assessed by comparison with true peak velocities. For each variable studied, average peak velocities were calculated from the 10 measurements made by each technologist and used to find the percent error from the true value, and the coefficient of variation was used to measure the variability.

RESULTS

Doppler angle, sample volume placement, and the Doppler gain were the most significant sources of error and variability. Inaccurate angle and placement increased the variability in measurements from 1% to 2% (range) to 4% to 6% for the straight tube and from 1% to 2% to 3% to 9% for the 61% stenosis. The peak velocity error was increased from 9% to 13% to 7% to 28% for the stenosis. Both measurement error and variability were strongly dependent on the Doppler gain level. At low gain, the error was approximately 10% less than the true value and at saturated gain, 20% greater. The display size only affected measurements from the stenosed tube, increasing the error from 9% to 13% to 15% to 24%.

CONCLUSIONS

Major factors affecting Doppler peak velocity measurement error and variability were identified. Inaccurate angle and sample volume placement increased the variability. The presence of a stenosis was found to increase the measurement errors. The error was found to depend on the Doppler gain setting, with greater variability at low and saturated gains and on the display size with a stenosis.

CLINICAL RELEVANCE

Doppler ultrasound peak velocity measurements are widely used for the diagnostic assessment of the severity of arterial stenoses. However, it is known that these measurements are often in error. We have identified subjective human factors introduced by the technologist and assessed their contribution to peak velocity measurement error and variability. It is to be hoped that by understanding this, improvements in the machine design and measurement methods can be made that will result in improved measurement accuracy and reproducibility.

Improved Maximum Frequency Estimation With Application to Instantaneous Mean Frequency Estimation of Surface Electromyography

The purpose of this study was to improve the maximum-frequency estimation. Three methods to estimate the maximum frequency of a bandlimited signal with additive white noise were compared. Two existing methods, the threshold-crossing method (TCM) and the hybrid method, were modified for time-frequency representations. A novel approach, the running-block threshold method (RBTM), was introduced. Based on calculation of detection probability (sensitivity) the RBTM improved the maximum-frequency estimate as compared with the TCM. The maximum-frequency estimation methods were also used to determine the integration interval for instantaneous mean-frequency (IMNF) estimation from synthesized surface electromyography containing white noise. Results showed that the IMNF estimate was improved by using any of the three methods and that the RBTM gave the best IMNF estimate.

Assessment of the effect of vessel curvature on Doppler measurements in steady flow

Blood vessel curvature is responsible for the appearance of nonaxial velocity components and for minor changes in the pattern of the axial flow. All the velocity components are expected to contribute to the Doppler signal produced by the ultrasound (US) backscattered by the insonated blood cells, the axial velocity, contributing to the actual volumetric blood flow, and the transverse velocity, causing the recirculating vortices. A detailed, separate analysis of the velocity components is, therefore, mandatory to quantify how vessel curvature can affect results and clinical diagnosis. Both experimental in vitro measures and numerical simulations were performed on a curved tube and the Doppler power spectra so obtained were compared. The satisfactorily agreement of the above spectra shows that the nonaxial velocity components are easily detectable with clinical equipment and that their amplitude, as expected, is not negligible and can bias Doppler measurements and resulting clinical diagnosis.

Estimation of the Doppler ultrasound maximal umbilical waveform envelope: I. Estimation method

We developed a parametric method of estimating the Doppler ultrasound (US) umbilical maximal flow waveform envelope that is robust to varying levels of signal-to-noise ratio (SNR). The method differs from previously proposed estimation algorithms in that it does not incorporate preliminary removal or reduction of noise; thus, avoiding potential resulting biases. Instead, we relied on a multiple time series interpretation that facilitates a regression approach. The maximal waveform shape was assumed to take the form of a periodic series of gamma functions with a hidden baseline that is typically not reached on the downward diastolic phase before the flow increases to the systolic peak. The waveform shape is fitted via optimisation of the cross correlation of the Doppler signal and a periodic reference function locating the cardiac cycles within the blood flow image. Starting values for the iterative optimisation process were obtained using nonstandard least squares regression. Assessments of the fit of the model to waveform data were carried out through visual inspection. In 7 of 327 images analysed (2.1%), there appeared to be some discrepancy between the waveform shape and the gamma waveform envelope, such as variations in systolic or diastolic flows. Modification of the estimation procedure to incorporate blood flow cycles of slightly different lengths and use of other functional forms may improve the fit for waveforms for which the gamma fit is poor. The method has been developed with special reference to umbilical blood flow images, but it can be used directly to model blood flow in other low-resistance vessels or adapted for other vessels with different shape characteristics.

An in vitro system for Doppler ultrasound flow studies in the stenosed carotid artery bifurcation

To investigate the correlation between disease severity and Doppler spectral measurements in the carotid artery bifurcation, a unique in vitro system has been developed that mimics the human vasculature with respect to both anatomy and flow perfusion. Agar-based carotid phantoms are perfused with a blood-mimicking fluid using a computer-controlled pump and realistic pulsatile flow waveform. A three-axis translational stage allows the lumen to be interrogated with a 0.6-microL Doppler sample volume at the desired spatial intervals using a semiautomated acquisition system, to collect 10 cardiac cycles of gated quadrature data at each site. Off-line analysis, including a 1024-point FFT, produces a 4-D (i.e., time-varying 3-D) Doppler velocity data set with 1.3-cm/s velocity resolution and 12-ms temporal resolution. Using this system, in vitro flow in bifurcations with both normal and stenosed lumen geometry (from 30% to 80% stenosis by NASCET criteria) can be studied, along with the effect of factors, such as stenosis geometry (concentric vs. eccentric) and flow rate, on the observed Doppler ultrasound (US) spectra and haemodynamic patterns.

Time-frequency parameters of the surface myoelectric signal for assessing muscle fatigue during cyclic dynamic contractions

The time-dependent shift in the spectral content of the surface myoelectric signal to lower frequencies has proven to be a useful tool for assessing localized muscle fatigue. Unfortunately, the technique has been restricted to constant-force, isometric contractions because of limitations in the processing methods used to obtain spectral estimates. A novel approach is proposed for calculating spectral parameters from the surface myoelectric signal during cyclic dynamic contractions. The procedure was developed using Cohen class time-frequency transforms to define the instantaneous median and mean frequency during cyclic dynamic contractions. Changes in muscle length, force, and electrode position contribute to the nonstationarity of the surface myoelectric signal. These factors, unrelated to localized fatigue, can be constrained and isolated for cyclic dynamic contractions, where they are assumed to be constant for identical phases of each cycle. Estimation errors for the instantaneous median and mean frequency are calculated from synthesized signals. It is shown that the instantaneous median frequency is affected by an error slightly lower than that related to the instantaneous mean frequency. In addition, we present a sample application to surface myoelectric signals recorded from the first dorsal interosseous muscle during repetitive abduction/adduction of the index finger against resistance. Results indicate that the variability of the instantaneous median frequency is related to the repeatability of the biomechanics of the exercise.

Quantitative Doppler measures in coiled vessels: investigation on excised umbilical veins

Quantitative assessment of umbilical venous blood velocity with Doppler ultrasound (US) must cope with the coiled structure of the vein inside the cord. Both an experimental and a theoretical approach showed remarkable variations in the insonation angle when the probe was moved along the vein, provided the inclination between the Doppler probe and the cord was kept constant. Inaccurate signal processing, stochastic variability and flow disturbances could, however, mask the influence of the geometry. The above hypotheses were assessed by investigating five cords in vitro a few hours after delivery from normal pregnancies at term. The Doppler signal was sampled at different sites along each cord and the mean Doppler shift estimated by FFT spectral analysis, both directly and through the noise rejection D'Alessio's algorithm, which proved effective in improving the Doppler shift estimate in condition of low signal-to-noise ratio (SNR).

Time-frequency methods applied to muscle fatigue assessment during dynamic contractions

This paper discusses the assessment of the electrical manifestations of muscle fatigue during dynamic contractions. In the past, the study of muscle fatigue was restricted to isometric constant force contractions because, in this contraction paradigm, the myoelectric signal may be considered as wide sense stationary over epochs lasting up to two or three seconds, and hence classic spectral estimation techniques may be applied. Recently, the availability of spectral estimation techniques specifically designed for nonstationary signal analysis made it possible to extend the employment of muscle fatigue assessment to cyclic dynamic contractions, thus increasing noticeably its possible clinical applications. After presenting the basics of time-frequency distributions, we introduce instantaneous spectral parameters well suited to tracking spectral changes due to muscle fatigue, discuss the issues of quasi-stationarity and quasi-cyclostationarity, and present different strategies of signal analysis to be utilized with cyclic dynamic contractions. We present preliminary results obtained by analyzing data collected from paraspinal muscles during repetitive lift movements, from the first dorsal interosseus during abduction-adduction movements of the index finger, and from knee flexors and extensors during isokinetic exercise. In conclusion, data herein reported demonstrate that the described techniques allow for evidencing the electrical manifestations of muscle fatigue in different paradigms of cyclic dynamic contractions. We believe that the extension of the objective assessment of the electrical manifestations of muscle fatigue from static to dynamic contractions may increase considerably the interest of researchers and clinicians and open new application fields, as ergonomics and sports medicine.

EMG assessment of back muscle function during cyclical lifting

A new approach to estimating the frequency compression of the surface EMG signal during cyclical dynamic exercise is described. The basic properties of the method are first developed using simulated EMG signals. Spectral compression is measured by defining the instantaneous median frequency from time-frequency representations of the signal derived from a transformation of the Cohen class. The technique is then used to process real EMG signals from paraspinal muscles during repetitive lifting. Our purpose was to use this new procedure to identify (a) whether changes in the instantaneous median frequency among concurrently active paraspinal muscles during repetitive trunk extension produces a 'fatigue pattern' that is indicative of normal functioning, and (b) whether this pattern is different when the subject produces a sustained isometric trunk extension. Four healthy subjects (26 +/- 4 years; 3 males, 1 female) were tested in both a Back Analysis System, for the production of a sustained static isometric contraction, and a LIDO-Lift Controller (Loredan), for repetitive lifting and lowering of a weighted box. EMG signals were recorded concurrently from six bilateral lumbar paraspinal regions during these tasks. The results demonstrate that static and dynamic tasks result in very different patterns of EMG spectral changes, suggestive of differences in load-sharing and underlying metabolic fatigue processes. Unlike the linear decrease in median frequency observed for static contractions, during dynamic contractions instantaneous median frequency behavior is non-linear and more complex. Examples are provided in which distinct periods of instantaneous median frequency decay are followed by periods of recovery during a single trial of repetitive lifting. It is hypothesized that this difference reflects a complex strategy of utilizing muscle load-sharing during strenuous dynamic exercise to provide periods of metabolic recovery that limit localized fatigue. New analysis procedures to characterize this complex behavior are needed to enhance the technique for assessment of impairment in patients with lower back pain.

Evaluation of cerebral arterial flow with transcranial Doppler ultrasound: theoretical development and phantom studies

Blood flow information available from transcranial Doppler ultrasound is usually derived from velocity alone because no knowledge of vessel caliber is available. In cases such as vasospasm, where vessel size changes, the inference of flow from velocity becomes questionable. A computational technique was used to calculate a flow index and 2 vessel area indices based on the first and zero moments of the Doppler power spectrum. These indices were tested in a steady and pulsatile flow phantom using 6 different diameter elastic tubes. Changes in the flow index showed good agreement with changes in timed volume flow for different flow rates. The vessel caliber indices correctly predicted changes in area when different diameter tubes were examined. These indices may prove useful in clinical settings where the constancy of flow or vessel diameter between studies are in question.

Evaluation of an automated real-time spectral analysis technique

An adaptive real-time Doppler peak-frequency tracing algorithm was evaluated in vitro and compared to manual peak-frequency traces. A computer-controlled pump was used to generate physiological flow waveforms in a vasculature-mimicking phantom. Spectral waveforms were obtained on an ATL HDI along with real-time estimates of diagnostic parameters, including maximum systolic, minimum diastolic, time-averaged peak frequencies and pulsatility and resistance indices. The effect of the signal-to-noise ratio on the measured parameters was investigated. The imprecision in the measured parameters was found to depend somewhat on the waveform shape; e.g., the imprecision in PI was 4.1% for a normal renal waveform and 8.5% for a waveform having reverse diastolic flow. The peak frequency envelopes of the same waveform data were traced manually by nine operators, and the resulting diagnostic parameters were compared to ones obtained from automated peak-frequency traces of the same waveform data. The agreement between parameters measured by the automated routine and those measured manually was found to depend somewhat on the waveform shape; e.g., the bias in the PI was 1.3% for a renal waveform lacking diastolic flow, and 12% for a waveform with reverse diastolic flow. The between-observer variations in the manual measurements ranged from 0.8% up to 9.4%. The overall variations associated with the automated traces were found to be smaller than or equal to those of the manual traces.

Estimation of shape characteristics of surface muscle signal spectra from time domain data

Myoelectric manifestations of muscle fatigue have been described by monitoring the first-order moment (mean frequency) of the power spectral density function during voluntary or electrically elicited sustained contractions. Higher order central moments provide additional information about the width, skewness, and kurtosis of the spectrum and its shape changes, thereby providing a description of slow nonstationarities more accurate than that allowed by the mean frequency alone. In 1986, B. Saltzberg introduced a method of representing the moments of the power spectral density function of band limited signals, without computing the Fourier transform, as weighted sums of samples of the autocorrelation function. If we allow for oversampling of the signal (and therefore of its autocorrelation function), more efficient weighted sums can be found which give Saltzberg's formula as a limiting case. The faster rate of decay of the weights implies a faster convergence of the estimates and the need to compute fewer samples of the autocorrelation function. The algorithm is particularly suitable for: 1) analysis of evoked potentials (M-waves), because it does not need zero padding to increase resolution and operates on any number of samples, and 2) on-line implementation by dedicated microprocessors performing simultaneous spectral moment analysis on a number of parallel channels.

Biophysical principles of vascular diagnosis

Visual inspection of the spectral composition of the Doppler signal as a function of time (sonogram) has been very helpful in detecting the presence of stenoses with substantial lumen narrowing causing abnormal flow patterns. Attempts to grade a stenosis based on the spectral width at peak systole were less successful because of the obscuring effects of the ultrasound beam width with respect to lumen diameter, dimensions of the sample volume, angle of observation, and spectral broadening due to vessel branching and bends. The introduction of color flow imaging has put emphasis on the width of the velocity distribution and the consistency of flow patterns within the region of interest. This technique requires a high resolution in space, velocity, and time necessitating the development of new velocity estimation algorithms. The observed flow patterns can be related to the echogenicity and local wall thickness of peripheral vessels. In addition, the displacement behavior of arterial walls over time provides information about the elasticity of the wall. Knowing the instantaneous velocity of arterial walls, it becomes possible to suppress selectively and adaptively the arterial wall contribution, allowing for the assessment of low blood flow velocities close to the wall and, hence, of wall shear rate. The latter development enables the study of the interaction of blood velocities and the metabolism and structure of the walls, providing possible clues for atherogenesis.

Comparison of the performance of three maximum Doppler frequency estimators coupled with different spectral estimation methods

The performance of three spectral techniques (FFT, AR Burg and ARMA) for maximum frequency estimation of the Doppler spectra is described. Different definitions of fmax were used: frequency at which spectral power decreases down to 0.1 of its maximum value, modified threshold crossing method (MTCM) and novel geometrical method. "Goodness" and efficiency of estimators were determined by calculating the bias and the standard deviation of the estimated maximum frequency of the simulated Doppler spectra with known statistics. The power of analysed signals was assumed to have the exponential distribution function. The SNR ratios were changed over the range from 0 to 20 dB. Different spectrum envelopes were generated. A Gaussian envelope approximated narrow band spectral processes (P. W. Doppler) and rectangular spectra were used to simulate a parabolic flow insonified with C. W. Doppler. The simulated signals were generated out of 3072-point records with sampling frequency of 20 kHz. The AR and ARMA models order selections were done independently according to Akaike Information Criterion (AIC) and Singular Value Decomposition (SVD). It was found that the ARMA model, computed according to SVD criterion, had the best overall performance and produced results with the smallest bias and standard deviation. In general AR(SVD) was better than AR(AIC). The geometrical method of fmax estimation was found to be more accurate than other tested methods, especially for narrow band signals.

Frequency response to retrospectively gated phase-contrast MR imaging: effect of interpolation

Retrospectively gated phase-contrast (PC) magnetic resonance velocity and volume flow measurements were evaluated in both in vitro and in vivo experiments. The accuracy of these measurements was found to be affected by the interpolation window width required in the reconstruction of retrospectively gated data. Interpolation modified the frequency content of the series of temporal measurements by decreasing the response at higher frequencies. With a series of sinusoidal flow waveforms, the frequency response of one specific implementation of retrospectively gated PC velocity measurements was experimentally determined. The experimental response agreed with the theoretical response predicted from an analysis of the interpolating function (2.2% root-mean-square difference). In vitro experiments with a simulated carotid flow waveform demonstrated errors in the systolic measurements that were a direct result of the modified frequency response. A volunteer study was also undertaken and confirmed the in vitro findings.

On-line estimation of myoelectric signal spectral parameters and nonstationarities detection

In this communication, we present a method for detecting nonstationarities of random time series with an approximately Gaussian distribution of amplitudes. This method is suitable for real time implementation. Here we report some results obtained by applying them to a time series of spectral parameters of surface myoelectric signals, collected during voluntary isometric contractions of human muscles. Moreover, we describe the computerized system that we used to implement our detector of nonstationarity. This system is based on the TMS 320C25 DSP chip and realizes on-line estimation and display of spectral parameters, as well as detection of their nonstationarities, featuring a sampling frequency up to 20 k samples/s. A friendly user interface, fully menu driven, allows the user to select different options during the system's operation by means of hot keys. The accuracy of the system was tested by comparing its estimates with those of an off-line system, previously characterized, which we took as a reference. The estimates of spectral parameters obtained by means of the two systems were always consistent. The on-line stationarity detector was able to recognize rates of variation of the spectral parameters as small as 1%/s during contractions lasting 10-15 s. This sensitivity makes it suitable for clinical application. The set of results herein presented has been selected to highlight the main characteristics of the system.

Real-time system for robust spectral parameter estimation in Doppler signal analysis

In assessing the level of stenosis in extracranial Doppler analysis, spectral analysis has until now been used qualitatively, for the most part. Owing to the many variables affecting the measurements (mainly noise level and instrument setting made subjectively by the operator), the reliability of the inferences on the degree of stenosis is not clearly definable. Under such conditions the need arises for algorithms and systems that can estimate spectral parameters with a higher degree of accuracy, to verify whether reliable inferences can indeed by made or if this technique is only a qualitative one. In the paper a real-time spectral analysis system is described. The system relies on a new spectral estimation algorithm which gives estimates with good robustness with respect to noise. Moreover, a clear measurement procedure which eliminates the many subjective factors affecting the estimates has also been proposed and used. The system has been evaluated with simulated signals and in clinical trials and has shown better performance than the commonly used commercial analysers.

Asymmetry of Doppler spectrum in stenosis differentiation

The asymmetry of the spectral distribution of ultrasonic Doppler flow velocity signals, assessed using the coefficient of skewness, is discussed as a criterion of stenosis differentiation. Its performance is compared with that of the index of turbulence intensity for both in vitro and in vivo flow Doppler signals, recorded distal to a stenosis. The power spectral distributions are computed using the direct Fourier transform and maximum likelihood method. The asymmetry of spectral distribution has proved to be a more efficient criterion than the turbulence intensity. The maximum likelihood method ensures better stenosis differentiation than the direct FFT method.