Selection of the order of autoregressive models for spectral analysis of Doppler ultrasound signals.

Autoregressive modelling includes a model identification procedure, that is, it is necessary to choose the order of the autoregressive (AR) process that best describes the given finite record (frame) of the signal. Four previously suggested procedures to choose the "best order" of AR processes have been tested: The "first zero crossing" of the autocorrelation function (FZC), the "final prediction error" (FPE), "Akaike's information criterion" (AIC), and the "criterion autoregressive transfer-function" (CAT). It was found that: (i) For more than 98% of the 1280 frames of Doppler signals analyzed the order selected by the various criteria was ten or less. (ii) For the same records of Doppler signals, FPE, AIC and CAT behave in a very similar manner, but the FZC criterion underestimates the order in relation to the others. (iii) For true AR processes, the order selected is frequently different from the true AR order when frames of 64 samples are used. When more samples are used FPE, AIC and CAT tend to select the correct order. (iv) The effect on the spectral estimate of using too high a model order is usually insignificant, while using too low an order can change the estimate more dramatically, that is, overestimating the model order is better than underestimating it.

A real-time autoregressive spectrum analyzer for Doppler ultrasound signals.

A system based on a digital signal processor and a microcomputer has been programmed to estimate the maximum entropy autoregressive (AR) power spectrum of ultrasonic Doppler shift signals and display the results in the form of a sonogram in real-time on a computer screen. The system, which is based on a TMS 320C25 digital signal processor chip, calculates spectra with 128 frequency components from 64 samples of the Doppler signal. The samples are collected at a programmable rate of up to 40.96 kHz, and the computation of each spectrum takes typically 3.2 ms. The feasibility of on-line AR spectral estimation makes this type of analysis an attractive alternative to the more conventional fast Fourier transform approach to the analysis of Doppler ultrasound signals.

A study of the spectral broadening of simulated Doppler signals using FFT and AR modelling.

Doppler ultrasound is used clinically to detect stenosis in the carotid artery. The presence of stenosis may be identified by disturbed flow patterns distal to the stenosis that cause spectral broadening in the spectrum of the Doppler signal around peak systole. This paper investigates the behaviour of the spectral broadening index (SBI) derived from wide-band spectra obtained using autoregressive modelling (AR), compared with the SBI based on the fast-Fourier transform (FFT) spectra. Simulated Doppler signals were created using white noise and shaped filters to analyse spectra typically found around the systolic peak and to assess the magnitude and variance of AR and FFT-SBI for a range of signal-to-noise ratios. The results of the analysis show a strong correlation between the indices calculated using the FFT and AR algorithms. Despite the qualitative improvement of the AR spectra over the FFT, the estimation of SBI for short data frames is not significantly improved using AR.

The relationship between time averaged intensity weighted mean velocity, and time averaged maximum velocity in neonatal cerebral arteries.

It is usual practice to calculate the mean velocity of blood flow in neonatal cerebral vessels from the intensity weighted mean (IWM) Doppler shift signal. Theoretically however the maximum frequency envelope could be used for similar purposes, and indeed may have certain advantages. The purpose of this study was to confirm the suitability of the maximum frequency method. Good quality Doppler recordings from the anterior cerebral and middle cerebral arteries of both term and very low birth weight babies were analyzed by both methods and compared. A small number of recordings were then deliberately degraded, either by the addition of noise or by the use of inappropriate filters, and reanalyzed. The results of these comparisons suggest that the maximum frequency follower should be the follower of choice for neonatal cerebral blood flow studies.

Detection of asphyxia using heart rate variability.

The long-term aims of this study are to find a parameter derived from the ECG that has a high sensitivity and specificity to asphyxia and, once we know or suspect that asphyxia occurred, to estimate how severe it was. We carried out a pilot study in which 24 adult Wistar rats were anaesthetised and subjected to controlled asphyxia for specified durations. We measured the pH, 'neurological score' and the ECG, extracting from this heart rate and heart rate variability (HRV). We have developed a technique capable of detecting asphyxia in less than 1 min, based on monitoring the ECG and estimating HRV by measuring the standard deviation of normal RR intervals (the RR interval is the time interval between two consecutive R-points of the QRS complex). In all cases the heart rate decreased and HRV increased, by an average of 46 +/- 33 ms in relation to the baseline, at the onset of asphyxia. The comparison of the base level of HRV after and before asphyxia shows promise for the estimation of the severity of the episode; however, the limitations of this study should be noted as they include the small size of the cohort and the methods of analysis.

Analysis of QRS-T subtraction in unipolar atrial fibrillation electrograms.

This paper presents a QRS-T subtraction approach for atrial fibrillation (AF) intracardiac atrial electrograms (AEG). It also presents a comparison between the proposed method and two alternative ventricular subtraction techniques: average beat subtraction (ABS) using a fixed length window and an approach based on flat interpolation for QRS cancellation. Areas of the atrium close to the mitral valve showed stronger ventricular influence on the AEGs when compared with the remaining atrial regions. Ventricular influence affects the spectral power distribution of the AEG and can also affect the estimation of the dominant frequency unless the whole ventricular activity influence (QRS-T) is removed. The average power after QRS-T subtraction is significantly reduced for frequencies above 10 Hz (mostly associated with QRS complexes), as well as for frequencies between 3 and 5.5 Hz, (mostly related to T waves). The results indicate that the proposed approach removes ventricular influence on the AF AEGs better than the QRS cancellation method. Spectral analysis showed that both the ABS and the proposed method do well and no method should be preferred to the other. In the time domain, the proposed approach is matched to the lengths and timings of onset and offset for individual QRS-T segments while the ABS approach uses an arbitrary length around the QRS for the pattern used for QRS-T removal.

QRS subtraction for atrial electrograms: flat, linear and spline interpolations.

The main objective of this article is to implement and compare QRS subtraction techniques for intra-cardiac atrial electrograms based on using the surface ECG as a reference. A band-pass filter between 8 and 20 Hz followed by rectification, and then a low-pass filter at 6 Hz are used for QRS detection. QRS subtraction was performed using three different approaches: flat, linear and spline interpolations. QRS subtraction affects the power of the signals but it normally does not affect the dominant frequency. The average power of the atrial electrograms after QRS subtraction is significantly reduced for frequencies above 10 Hz.

Spectral broadening of clinical Doppler signals using FFT and autoregressive modelling.

OBJECTIVE: This paper investigates the behaviour of the spectral broadening index (SBI) derived from spectra obtained using autoregressive (AR) modelling compared to that of SBI based on fast Fourier transform (FFT) analysis of clinical Doppler ultrasound scans. METHODS: Doppler signals from internal carotid arteries of patients with normal and diseased vessels with up to 80% stenosis were analysed. A threshold at -6 dB of the maximum magnitude component of each individual spectrum was implemented to reject low-level noise. The SBI was obtained using the maximum and the mean frequency envelopes extracted from the sonogram. RESULTS: A qualitative improvement in both the appearance of the AR sonograms and the shape of the individual AR spectra was noticeable. The AR approach consistently produced narrower spectra than the FFT and the shapes of the frequency envelopes derived from the AR sonogram and the FFT sonogram were also rather different. Despite these differences a strong correlation was observed between the value of the FFT-based SBI and the AR-based SBI. The mean value of the FFT-SBI is larger than that of the AR-SBI and the variance of the FFT-SBI is smaller than that of the AR-SBI based on a set of at least 20 sequentially recorded heartbeats. CONCLUSIONS: It was established that, for all cases where significant stenosis was present, a statistically significant value for SBI could be obtained using four or more heartbeats if five spectra around the peak systole were used to estimate the SBI of each individual heartbeat. No quantitative advantage in using the AR approach over the FFT for the determination of SBI was obtained due to the poorer variance of the AR-SBI and the additional computational complexity of the AR approach.

An automatic system for capturing and processing ultrasonic Doppler signals and blood pressure signals.

A totally automatic system for capturing and processing ultrasonic Doppler signals and blood pressure signals at pre-programmed intervals is described. The Doppler signals are Fourier transformed and a composite maximum frequency envelope extracted from the spectral data. The frequency envelope is split into individual cardiac cycles and a number of Doppler parameters calculated. All Doppler and blood pressure results are stored on disc, and the most important may be displayed in the form of trend graphs on a computer screen. The system has been used to study variations in middle cerebral artery blood flow velocity and systemic blood pressure in neonates over periods of several hours.

Real-time digital processing of Doppler ultrasound signals and calculation of flow parameters.

Vascular diseases and their complications are responsible for around 27% of deaths in Brazil. Doppler ultrasound is a non-invasive technique that has been used to study blood flow in intact blood vessels since Satomura first reported the potential of the technique in 1959. Because it is non-invasive it makes sequential studies and those in normals feasible. Whereas in contrast angiography only vessel anatomy is displayed, Doppler ultrasound produces dynamic information on blood-flow. It may be used to estimate flow-rates, to image regions of blood flow (colour Doppler), and to help in locating sites of arterial disease, thus complementing X-ray examinations. This paper describes a system based on a Digital Signal Processor for real-time spectrum analysis of Doppler ultrasound signals, real-time display of sonograms, and calculation and analysis of three parameters of clinical interest derived from the Doppler signal. The system comprises a TMS320C25 development board, which acquires the signal and performs spectrum analysis, and a microcomputer, which reads the spectral estimates, displays them as a sonogram in real-time and calculates a set of spectral parameters proposed in the literature. The system permits a maximum sampling frequency of 40.96 kHz, and in the sonogram, 80 power spectra per second (each with 128 frequency bins) are displayed. In a preliminary study, the stability of the haemodynamic parameters and their dependence on a user-defined threshold value is investigated.