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Determination of Tissue Motion Velocity by Correlation Interpolation of Pulsed Ultrasonic Echo Signals
Abstract
Correlation interpolation is introduced as a method to determine the displacement of moving biological tissue on the basis of a sequence of ultrasonic echo signals. The echo signal is sampled along the echo depth with approximately 4 samples per average high frequency period. Sampling in time occurs with the pulse repetition frequency. The necessary information is extracted from a crosscorrelation function between successive signals, which is modelled using four parameters. The parameters are estimated from five calculated correlation sums and the shift with maximum correlation is determined. In contrast to existing techniques, the performance of this method is determined mainly by the number of samples used, while the ratio of the number of samples in depth and time is irrelevant. Using 64 samples at a signal-to-noise power ratio of 10, the standard deviation of the error in the determination of the shift in depth is 0.08 sampling intervals. As in many other methods, the width of the aliasing interval equals the mean frequency period.
... The cosine fit was used to interpolate three points of the cross correlation function: the maximum, y(0), and the two closest points to the maximum, y(−1) and y(1). Therefore, the equations presented below were used to estimate the time delay [10,37,38]: ...
... According to Céspedes et al. [10], this method estimates the time delay with less bias and dispersion than parabolic interpolation. However, this method presents aliasing for speeds that exceed the Nyquist limit [38]. ...
... The majority of the work found in the literature sought to compare the processing methods using a window length of echo/backscattered signals smaller than 1 μs [10,11,27,31,37,38]. However, in this study, the window length was 20 μs owing to the thickness of the material. ...
Although few studies on ultrasonic materials characterization present the expanded uncertainty, it is very important to quantify the final quality of the result. In addition, many of these studies do not mention the method used to estimate time delay, which is employed to calculate the longitudinal phase velocity (vTS). Therefore, the purpose of this study is to estimate the uncertainties of vTS values obtained by different time-delay estimation methods based on cross-correlation. In addition, computational simulation was used to validate the experimental results. The results of the computational simulation showed that when the sampling frequency is 50 MHz, the bias phase velocity was greater than 1.2 m·s⁻¹ for almost all time-delay estimation methods. Therefore, it is not advisable to use a sampling frequency less than or equal to 50 MHz. In all cases, the expanded uncertainty was below 3.5 m·s⁻¹. The statistical test results indicated a significant difference between the values of the longitudinal phase velocity estimated with a given method, as a function of the sampling frequency and the estimated velocity with each method as a function of the received bandwidth of transducer. The expanded uncertainty for phase velocity is intrinsically dependent on accurate speed of ultrasound estimation in the reference medium. The speed of ultrasound and temperature are correlated, therefore, precise estimation of the reference medium temperature is important to maintain the overall precision of the method employed in this study. The novelty of this work resides in the comparison of different time-delay estimation using measurement uncertainty as parameter. Furthermore, after the detailed step by step assessment of uncertainties for the dissimilar computational methods, one can easily estimate the uncertainty by his own using this paper as guidance.
... • Cosine interpolation estimator [18], [20], [21] This method uses a cosine function to interpolate around the peak of the DC interpolation. The estimated time delay is ...
... Although the performance of these interpolation estimators is much higher than sampling interval, they always suffer relatively high bias problem [18]. When it is inconsist between real curve and interpolation curve, those methods are biased obviously. ...
... The Lagrange interpolation [17] and LS fitting are the common methods of interpolation. Cosine interpolation and triangular interpolation representing the algorithms can be found in [18] and [22]. As shown in the figure, the RMSEs of all the 6 algorithms also decrease as the SNR increases. ...
Considering the obvious bias of the traditional interpolation method, a novel time delay estimation (TDE) interpolation method with sub-sample accuracy is presented in this paper. The proposed method uses a generalized extended approximation method to obtain the objection function. Then the optimized interpolation curve is generated by Second-order Cone programming (SOCP). Finally the optimal TDE can be obtained by interpolation curve. The delay estimate of proposed method is not forced to lie on discrete samples and the sample points need not to be on the interpolation curve. In the condition of the acceptable computation complexity, computer simulation results clearly indicate that the proposed method is less biased and outperforms the other interpolation algorithms in terms of estimation accuracy.
... ANNEXES voir la figure 7.17 où sont illustrés l'utilisation d'une parabole [119], d'une gaussienne [120] ou encore d'un cosinus [121,122]. Après ajustement de l'une de ces fonctions paramétriques au voisinage du maximum de la corrélation croisée, la position estimée du maximum de la f parabole (t) = at 2 + bt + c, (7.17) ...
... Ainsi, l'ajustement par une gaussienne de la fonction xcorr{x, y} autour des points Ajustement par un cosinus. Une autre méthode d'interpolation à 3 points est l'utilisation d'un cosinus [121,122] : ...
Ce travail de thèse traite du développement d’une antenne microphonique compacte et d’une chaîne de traitement du signal dédiée, pour la reconnaissance et la localisation angulaire de cibles aériennes. L’approche globale proposée consiste en une détection initiale de cible potentielle, la localisation et le suivi de la cible, et une détection affinée par un filtrage spatial adaptatif informé par la localisation de la cible. Un algorithme original de localisation goniométrique est proposé. Il utilise l’algorithme RANSAC sur des données pression-vitesse large bande [100 Hz - 10 kHz], estimées en temps réel, dans le domaine temporel, par des différences et sommes finies avec des doublets de microphones à espacements inter-microphoniques adaptés à la fréquence. L’extension de la bande passante de l’antenne en hautes fréquences est rendue possible par l’utilisation de différences finies d’ordre élevé, ou de variantes de la méthode PAGE (Phase and Amplitude Gradient Estimation) adaptées à l’antenne développée. L’antenne acoustique compacte ainsi développée utilise 32 microphones MEMS numériques répartis dans le plan horizontal sur une zone de 7.5 centimètres, selon une géométrie d’antenne adaptée aux l’algorithmes de localisation et de filtrage spatial employés. Des essais expérimentaux de localisation et de suivi de trajectoire contrôlée par une sphère de spatialisation dans le domaine ambisonique ont montré une erreur de localisation moyenne de 4 degrés. Une base de données de signatures acoustiques de drones en vol a été créée, avec connaissance de la position du drone par rapport à l’antenne microphonique apportée par des mesures GPS. L’augmentation des données par bruitage artificiel, et la sélection dedescripteurs acoustiques par des algorithmes évolutionnistes, ont permis de détecter un drone inconnu dans un environnement sonore inconnu jusqu’à 200 mètres avec le classifieur JRip. Afin de faciliter la détection et d’en augmenter la portée, l’étape de détection initiale est précédée d’une formation de voies différentielle dans 4 directions principales (nord, sud, est, ouest), et l’étape de détection affinée est précédée d’une formation de voies de Capon informée par la localisation et le suivi de la cible à identifier.
... Several curve-fitting methods have been applied in the postinterpolation problem, such as triangular interpolation and Lagrange interpolation. (Benedetto & Giunta., 2011;Jong et al., 1990;Taylor., 2017;Tjahjono, Sudiharto, & Anggriawan, 2016). Although above these methods can achieve sub-sample accuracy, they cannot be obtained simultaneously. ...
... Motivated by this drawback, surface interpolation methods are used to the pattern CAF (Li et al., 2013;Salemi, Nelson, & Staum, 2016;Tao., 2008;Yaou & Chang, 1994). But these interpolation ways always suffer relatively high estimation variance problem (De Jong et al., 1990) and not combine the advantages of fitting and interpolation. The Cramér-Rao lower bound (CRLB) cannot be attained at high signal-to-noise ratio (SNR) conditions. ...
Considering the low estimation accuracy of the traditional interpolation method, this paper, on the basis of second-order cone programming (SOCP), proposes a novel joint time difference of arrival (TDOA) and frequency difference of arrival (FDOA) estimation interpolation method, which can attain the sub-sample precision. The proposed method uses several discrete samples produced by cross ambiguity function (CAF) to structure the convex optimization models with regard to the interpolation surface. Then, the SOCP is utilized to obtain the interpolation surface which matches the discrete surface of CAF well. Finally, the method achieves the precision superior to the traditional TDOA and FDOA estimation directly through the search for the maximum of the continuous approximate surface. This method decreases the computational load without loss of precision and can efficiently reduce the limitation of finite sampling interval and sampling time in estimation precision. Numerical simulations show that the method in this paper is efficient and outperforms existing interpolation algorithms about estimation precision.
... So the TDOA and FDOA estimation accuracies are no longer forced to lie on discrete samples and sampling time respectively. Several methods have been described to apply the post-interpolation problem, such as Lagrange interpolation [5], parabolic interpolation [6], cosine interpolation estimator [7], et al. These plane interpolation methods can only estimate TDOA and FDOA separately. ...
... We plot curves of RMSEs corresponding to SNR using different interpolation methods, as well as the CRLB [2]. The plane interpolation method denotes the method in [7], whereas the surface fitting and moving least square method represents the algorithm in [8] and [9] respectively. It can be observed that the RMSEs of all the algorithms also decrease as the SNR increases but the estimation precision of the proposed method is much closer than that of the plane interpolation methods and surface interpolation methods especially in high SNR. ...
... The Correlation Interpolation Algorithm, or Cross-Correlation Model (CCM), [24], [44] is based on the notion that a given spectral power distribution will produce a cross-correlation (or 2-D auto-correlation) function of known shape and offers a number of advantages over the RF cross-correlation algorithm. This signal model allows the velocity to be expressed in terms of the 2-D auto-correlation function evaluated at five fixed points as opposed to the 2N − 1 (where N denotes the length in samples of one cycle of the transmit pulse) estimates required by the RF cross-correlation algorithm. ...
... 24 shows a longer section of the relevant filter outputs corresponding to an uncoded pulse, the Golay pair of length 16 and a chirp with a time-bandwidth product of 16. It is evident that Golay envelopes correspond very closely to that of the uncoded sequence, apart from the difference in their noise floors. ...
Ultrasound is a well-established tool for medical imaging. It is non-invasive and relatively
inexpensive, but the severe attenuation caused by propagation through tissue limits its effectiveness
for deep imaging. In recent years, the ready availability of fast, inexpensive computer
hardware has facilitated the adoption of signal coding and compression techniques to counteract
the effects of attenuation. Despite widespread investigation of the topic, published opinions
vary as to the relative suitability of discrete-phase-modulated and frequency-modulated (or
continuous-phase-modulated) signals for ultrasonic imaging applications. This thesis compares
the performance of discrete binary-phase coded pulses to that of frequency-modulated pulses
at the higher imaging frequencies at which the effects of attenuation are most severe.
The performance of linear and non-linear frequency modulated pulses with optimal side-lobe
characteristics is compared to that of complementary binary-phase coded pulses by simulation
and experiment. Binary-phase coded pulses are shown to be more robust to the affects of attenuation
and non-ideal transducers. The comparatively poor performance of frequency-modulated
pulses is explained in terms of the spectral characteristics of the signals and filters required to
reduce side-lobes to levels acceptable for imaging purposes.
In theory, complementary code sets like bi-phase Golay pairs offer optimum side-lobe performance
at the expense of a reduction in frame rate. In practice, misalignment caused by
motion in the medium can have a severe impact on imaging performance. A novel motioncompensated
imaging algorithm designed to reduce the occurrence of motion artefacts and
eliminate the reduction in frame-rate associated with complementary-coding is presented. This
is initially applied to conventional sequential-scan B-mode imaging then adapted for use in
synthetic aperture B-mode imaging. Simulation results are presented comparing the performance
of the motion-compensated sequential-scan and synthetic aperture systems with that of
simulated systems using uncoded and frequency-modulated excitation pulses.
... They are used for instance in the field of elastography [7], in the field of strain and strain rate imaging of the heart [6], for tissue motions estimation [90,91], or for acoustic radiation force microscopy (ARFI) applications [89]. For all these applications, time-shift based estimators and most particularly normalised crosscorrelation, have gained a widespread acceptance. ...
... The necessary interpolation of the crosscorrelation peak can introduce a systematic error in the crosscorrelation estimates. One of the simplest solutions is the parabola fitting method, as introduced in Eq. 5.7, but some other methods have also been considered and studied [90,110,111]. ...
Doppler ultrasound imaging modalities arguably represent one of the most complex task performed
(usually in real time) by ultrasound scanners. At the heart of these techniques lies the
ability to detect and estimate soft tissues or blood motion within the human body. As they
have become an invaluable tool in a wide range of clinical applications, these techniques have
fostered an intensive effort of research in the field of signal processing for more than thirty
years, with a push towards more accurate velocity or displacement estimation. Coded excitation
has recently received a growing interest in the medical ultrasound community. The use of
these techniques, originally developed in the radar field, makes it possible to increase the depth
of penetration in B-mode imaging, while complying with safety standards. These standards
impose strict limits on the peak acoustic intensity which can be transmitted into the body. Similar
solutions were proposed in the early developments of Doppler flow-meters to improve the
resolution / sensitivity trade-off from which typical pulsed Doppler systems suffer.
This work discusses the potential improvements in resolution, sensitivity and accuracy achievable
in the context of modern Doppler ultrasound imaging modalities (taken in its broadest
sense, that is, all the techniques involving the estimation of displacements, or velocities). A
theoretical framework is provided for discussing this potential improvements, along with simulations
for a more quantitative assessment. Colour Flow Imaging (CFI) modalities are taken
as the main reference technique for discussion, due to their historical importance, and their
relevance in many clinical applications. The potential achievable improvement in accuracy is
studied in the context of modern velocity estimation strategies, which can be broadly classified
into narrowband estimators (such as the “Kasai” estimator still widely used in CFI) and time
shift based wideband strategies (normalised crosscorrelation estimator used, for instance, in
applications like strain or strain rate estimation, elastography, etc.). Finally, simulations and
theoretical results are compared to experimental data obtained with a simple custom-designed
experimental set-up, using a single-element transducer.
... Due to the limited sampling intervals, some proven techniques have been used to reduce these estimated errors. These techniques can be classified into the following types: up-sampling from the original signals [1,2], curve-or parabola-fitting on the original signals [3,4], and curve-or parabola-fitting on the cross-correlation functions [5][6][7]. ...
... It should be noted that curve-or parabola-fitting on the cross-correlation function has already replaced the aforementioned two methods, and has been broadly applied in the sub-sample displacement estimations. In ultrasound elastography, curve-fitting techniques are generally used for the estimation of sub-sample displacement along one direction, such as the parabola-fitting [6], cosine-fitting [7], and spline-fitting [2] under one-dimensional (1D) conditions , or for the multi-dimension polynomial fitting displacement estimation [8]. In spite of its efficient computation and favorable precision, the calculated sub-sample displacement by curve fitting is often the optimal solution of the function composed of several cross-correlation coefficients. ...
Ultrasound elastography has been widely applied in clinical diagnosis. To produce high-quality elastograms, displacement estimation is important to generate ne displacement map from the original ratio-frequency signals. Traditional displacement estimation methods are based on the local information of signals pair, such as cross-correlation method, phase zero estimation. However, the tissue movement is nonlocal during realistic elasticity process due to the compression coming from the surface. Recently, regularized cost functions have been broadly used in ultrasound elastography. In this paper, we tested the using of analytic minimization of adaptive regularized cost function, a combination of different regularized cost functions, to correct the displacement estimation calculated by cross-correlation method directly or by lateral displacement guidance. We have demonstrated that the proposed method exhibit obvious advantages in terms of imaging quality with higher levels of elastographic signal-to-noise ratio and elastographic contrast-to-noise ratio in the simulation and phantom experiments respectively.
... It is well known that it is possible to obtain subsample time precision through coherence measurements. In our study, we employed a cosine fitting method to estimate subsample delay time in the time domain [De Jong et al., 1990; Cespedes et al., 1995]. ...
... [7] It is well known that it is possible to obtain subsample time precision through coherence measurements. In our study, we employed a cosine fitting method to estimate subsample delay time in the time domain [De Jong et al., 1990; Cespedes et al., 1995]. Given the largest sample of the correlation function, CC(0), and its two neighbors CC(-1) and CC(1), the estimated subsample shift is given by ...
1] We have applied a waveform cross correlation technique to study the similarity and the repeatability of more than 21,000 microearthquakes (0 < M < 4.5) in the aftershock zone of the 1984 western Nagano earthquake in central Japan. We find that the seismicity in this particular intraplate fault essentially consists of no repeating earthquakes that occurred on the same patch of the fault in a quasiperiodic manner in the study period between 1995 and 2001. On the other hand, we identify a total of 278 doublets and 62 multiplets (807 events) that occurred consecutively within seconds to days. On the basis of the relative arrival times of the P and S waves, we have obtained precise relative locations of these consecutive events with an error between several meters to a few tens of meters. There is a clear lower bound on the distances measured between these consecutive events and the lower bound appears to be proportional to the size of the first events. This feature is consistent with what Rubin and Gillard [2000] have observed near the San Juan Bautista section of the San Andreas Fault. Shear stress increases at the edge of an earthquake rupture, and the rupture edge becomes the most likely place where the second events are initiated. The observed minimum distance thus reflects the rupture size of the first events. The minimum distance corresponds to the rupture size calculated from a circular fault model with a stress drop of 10 MPa. We found that using different time windows results in a slight difference in the delay time estimates and the subsequent projection locations, which may reflect the finite size nature of earthquake ruptures.
... Hence, the lateral position of the wall was considered constant. First, the Eulerian axial velocity field was computed using beamformed radio frequency cross-correlation (56) with cosine interpolation (57). V E (z E , x E , t), with (z E , x E ) being the constant spatial coordinates of the IQ pixels and t the frame index. ...
Blood pressure measurement is the most widely performed clinical exam to predict mortality risk. The gold standard for its noninvasive assessment is the auscultatory method, which relies on listening to the so-called “Korotkoff sounds” in a stethoscope placed at the outlet of a pneumatic arm cuff. However, more than a century after their discovery, the origin of these sounds is still debated, which implies a number of clinical limitations. We imaged the Korotkoff sound generation in vivo at thousands of images per second using ultrafast ultrasound. We showed with both experience and theory that Korotkoff sounds are paradoxically not sound waves emerging from the brachial artery but rather shear vibrations conveyed in surrounding tissues by the nonlinear pulse wave propagation. When these shear vibrations reached the stethoscope, they were synchronous, correlated, and comparable in intensity with the Korotkoff sounds. Understanding this mechanism could ultimately improve blood pressure measurement and provide additional understanding of arterial mechanical properties.
... OF measurements can be challenging when it comes to measuring the time elapse between two fast signals at speeds greater than 10m/s. One of the most widely used methods here is the classical normalized cross-correlation (NCC) method [9,2,8,1,11]. A reference window is defined on the first signal and compared with windows in the second signal delayed by a fixed time lag: a cross-correlation coefficient is then determined between the two windows. ...
The fast normalized cross-correlation (NCC) calculation method presented here features low computational requirements, which makes it suitable for being implemented in real time onboard micro-controllers with very few computational resources. This method was adapted for making distance measurements, using a high speed optic flow sensor operating at 20m∕s. An application of this study is to develop a proof of concept of an innovative optic flow sensor fixed at the tip of an helicopter’s blade (from Airbus Helicopter) to measure the distance to various obstacles (wall, cliff...) in the azimuthal plane (rotor plane) during hovering flight. Due to its small size, this sensor developed in this paper can also be also adapted for Micro aerial vehicles (MAVs). This method of calculation requires less memory than the reference method, at the expense of some extra arithmetical operations, but it is still significantly lighter than the classical NCC method. An algorithm for implementing this method in real-time robotic applications is presented. Experimental results confirm the efficiency of this highly time-saving method.
... Compared with other available imaging methods, it is a quick, radiation-free, and relatively inexpensive method of visualizing the arterial wall in vivo [11]. In the past decade, three main ultrasonic imaging methods were used for measuring displacements of an arterial wall: echo tracking [12,13], B-mode [14,15], and M-mode [7,16]. Among them, the echo-tracking imaging method has a high resolution and thus has been widely adopted. ...
Estimating the motions of the common carotid artery wall plays a very important role in early diagnosis of the carotid atherosclerotic disease. However, the disturbances caused by either the instability of the probe operator or the breathing of subjects degrade the estimation accuracy of arterial wall motion when performing speckle tracking on the B-mode ultrasound images. In this paper, we propose a global registration method to suppress external disturbances before motion estimation. The local vector images, transformed from B-mode images, were used for registration. To take advantage of both the structural information from the local phase and the geometric information from the local orientation, we proposed a confidence coefficient to combine them two. Furthermore, we altered the speckle reducing anisotropic diffusion filter to improve the performance of disturbance suppression. We compared this method with schemes of extracting wall displacement directly from B-mode or phase images. The results show that this scheme can effectively suppress the disturbances and significantly improve the estimation accuracy.
... La position du sommet de cette parabole donne alors une estimation non-biaisée du délai entre nos deux signaux. Sous les bonnes hypothèses, il a été montré que la précision de cette méthode est, in fine, limitée par le rapport signal à bruit des signaux et peut être inférieure à 5% du temps d'échantillonnage (Carter, 1987;De Jong et al., 1990;Sandrin et al., 1999;Walker and Trahey, 1994). Nous allons donc procéder à cette mesure sur des signaux issus du cortex visuel, colliculus supérieur et LGN. ...
Ces travaux de thèse portent sur les récents progrès de l’imagerie fonctionnelle par ultrasons et ses nouvelles applications en ophtalmologie. Dans le cadre d’un projet mêlant physique des ondes, imagerie, neurosciences et ophtalmologie, nous avons appliqué cette technologie à l’imagerie du système visuel et à l’étude préclinique de thérapies le ciblant. Au cours de ce projet, nous avons accompagné nos études précliniques de progrès constants dans notre imagerie.Un dispositif permettant l’imagerie du cerveau en 3 dimensions a été conçu. Cette imagerie a été réalisée en temps réel, ou à une fréquence ultrasonore de 30 MHz grâce au procédé d’entrelacement. Grâce à une connaissance a priori de l’architecture vasculaire cérébrale et de l’effet Doppler, il est possible de réaliser une décomposition spectrale des écoulements sanguins cérébraux selon leurs vitesses et de leurs orientations.Ceci a permis une étude des fonctions visuelles du rat et du primate non-humain. Nous avons imagé la rétine du primate en Doppler de puissance, mais sa forte mobilité en fait un organe délicat à imager en imagerie fonctionnelle. En revanche, nous avons réalisé une imagerie fonctionnelle de la rétine de rat à 30 MHz. Nous avons caractérisé en détail le système visuel cérébral de ce rongeur. Nous avons mis en évidence ses principales structures et redémontré leurs caractéristiques les plus connues, comme leur organisation rétinotopique ou leur différence de temps de réponse neurovasculaire à un stimulus. Des animaux traités par des thérapies de restauration visuelle a été imagée. La première imagerie de primates non-humains anesthésiés puis éveillés et exécutant une tâche comportementale, et la détection de variations de flux sanguins dues à des erreurs uniques ont été réalisées. Enfin, une étude préclinique aiguë et une étude chronique de traitements ayant des effets neurovasculaires ont été menées grâce au suivi du flux sanguin par nos procédés.
... While in the dynamic method, a localized and impulsive mechanical strain is induced remotely by an external force (commonly, a focusing ultrasound transducer is employed for inducing remote mechanical excitation) 12 and reconstruction of elastic property distribution is carried out through evaluation-employing iterative numerical method for solving the governing mechanical problem-of motion pattern induced by externally applied stress, i.e., distribution of elastic property is evaluated through examination of relative motion of tissue elements. 108,109 Several USE methods-Doppler effect-based velocity measurements, [110][111][112] cross-correlation methods [113][114][115][116] to quantify motions (induced internally or externally), visual inspection of M-and/or Bmodes images, [117][118][119] and Fourier-based methods 120,121 -were reported 6 and have already been integrated in conventional (clinical) US scanners. Studies for an absolute estimate of tissue stiffness based on the variation of measurement of speeds of wave propagation (faster in stiffer tissues) were also reported. ...
Elastography imaging is a promising tool-in both research and clinical settings-for diagnosis, staging, and therapeutic treatments of various life-threatening diseases (including brain tumors, breast cancers, prostate cancers, and Alzheimer's disease). Large variation in the physical (elastic) properties of tissue, from normal to diseased stages, enables highly sensitive characterization of pathophysiological states of the diseases. On the other hand, over the last decade or so, photoacoustic (PA) imaging-an imaging modality that combines the advantageous features of two separate imaging modalities, i.e., high spatial resolution and high contrast obtainable, respectively, from ultrasound- and optical-based modalities-has been emerging and widely studied. Recently, recovery of elastic properties of soft biological tissues-in addition to prior reported recovery of vital tissue physiological information (Hb, HbO2, SO, and total Hb), noninvasively and nondestructively, with unprecedented spatial resolution (μm) at penetration depth (cm)-has been reported. Studies demonstrating that combined recovery of mechanical tissue properties and physiological information-by a single (PA) imaging unit-pave a promising platform in clinical diagnosis and therapeutic treatments. We offer a comprehensive review of PA imaging technology, focusing on recent advances in relation to elastography. Our review draws out technological challenges pertaining to PA elastography (PAE) imaging, and viable approaches. Currently, PAE imaging is in the nurture stage of its development, where the technology is limited to qualitative study. The prevailing challenges (specifically, quantitative measurements) may be addressed in a similar way by which ultrasound elastography and optical coherence elastography were accredited for quantitative measurements.
... This constitutes an unbiased estimator of the delay between two correlated band-limited signals. Previous reports have shown a typical precision below 5% of the sampling time which is ultimately limited by the SNR of the signals (Carter, 1987;DEJONG et al., 1990;Sandrin et al., 1999;Walker and Trahey, 1994). ...
3D functional imaging of the whole brain activity during visual task is a challenging task in rodents due to the complex tri-dimensional shape of involved brain regions and the fine spatial and temporal resolutions required to reveal the visual tract. By coupling functional ultrasound (fUS) imaging with a translational motorized stage and an episodic visual stimulation device, we managed to accurately map and to recover the activity of the visual cortices, the Superior Colliculus (SC) and the Lateral Geniculate Nuclei (LGN) in 3D. Cerebral Blood Volume (CBV) responses during visual stimuli were found to be highly correlated with the visual stimulus time profile in visual cortices (r = 0.6), SC (r = 0.7) and LGN (r = 0.7). These responses were found dependent on flickering frequency and contrast, and optimal stimulus parameters for largest CBV increases were obtained. In particular, increasing the flickering frequency higher than 7Hz revealed a decrease of visual cortices response while the SC response was preserved. Finally, cross-correlation between CBV signals exhibited significant delays (d = 0.35s +/− 0.1s) between blood volume response in SC and visual cortices in response to our visual stimulus. These results emphasize the interest of fUS imaging as a whole brain neuroimaging modality for brain vision studies in rodent models.
... Given that R NCC only contained integer lags interpolation is necessary to improve the estimation accuracy. A cosine function was selected to fit to the three points (τ = −1,0, 1) [46] and thus, to estimate the axial wall displacements (d PWI ) in parallel for all the windows in all the lines of all the frames the following calculations were made: ...
Pulse wave velocity (PWV) is a surrogate marker of arterial stiffness linked to cardiovascular morbidity. Pulse wave imaging (PWI) is a technique developed by our group for imaging the pulse wave propagation in vivo. PWI requires high temporal and spatial resolution, which conventional ultrasonic imaging is unable to simultaneously provide. Coherent compounding is known to address this tradeoff and provides full aperture images at high frame rates. This study aims to implement PWI using coherent compounding within a GPU-accelerated framework. The results of the implemented method were validated using a silicone phantom against static mechanical testing. Reproducibility of the measured PWVs was assessed in the right common carotid of six healthy subjects (n = 6) approximately 10–15 mm before the bifurcation during two cardiac cycles over the course of 1–3 d. Good agreement of the measured PWVs (3.97 ± 1.21 m s⁻¹, 4.08 ± 1.15 m s⁻¹, p = 0.74) was obtained. The effects of frame rate, transmission angle and number of compounded plane waves on PWI performance were investigated in the six healthy volunteers. Performance metrics such as the reproducibility of the PWVs, the coefficient of determination (r ²), the SNR of the PWI axial wall velocities () and the percentage of lateral positions where the pulse wave appears to arrive at the same time-point, indicating inadequacy of the temporal resolution (i.e. temporal resolution misses) were used to evaluate the effect of each parameter. Compounding plane waves transmitted at 1° increments with a linear array yielded optimal performance, generating significantly higher r ² and values (p ≤ 0.05). Higher frame rates (≥1667 Hz) produced improvements with significant gains in the r ² coefficient (p ≤ 0.05) and significant increase in both r ² and from single plane wave imaging to 3-plane wave compounding (p ≤ 0.05). Optimal performance was established at 2778 Hz with 3 plane waves and at 1667 Hz with 5 plane waves.
... This approach does not restrict the time-delay estimates to be an integer multiple of the sampling period. A number of interpolation techniques have been described in the literature which include, but not limited to, cosine-curve fitting [28], paraboliccurve fitting [29,30], grid slope [31,32], and spline fitting [33]. ...
... These methods determine the velocity of the wave inside the media by using high frequency ultrasound. Wilson and Robinson ([23]) used a phase method to determine human tissue characteristics; Tristam et al. ([20]) developed a correlation method for determining kinetic characteristics of human tissues, and de Jong et al. ( [3]) introduced a correlation interpolation of pulsed ultrasonic signal for determination of tissue motion velocity. In this research, these methods were applied and tested for the specific application of noninvasive estimation of temperature. ...
Noninvasive thermometry is one of the greatest challenges for hyperthermia treatment and ultrasound thermometry is one of the most attractive techniques used for this purpose. In this chapter, four time-delay estimation methods, which relate temperature changes inside tissue replica (phantom) with time shifts in ultrasound echo-signals, were tested and their results were comparatively evaluated. These methods were tested, for temperatures ranging from 30 • C to 50 • C and for both experimental and simulated echo-signals. Simulated signals were obtained from a numerical phantom which is proposed in this chapter, and experimental signals were acquired from a specially developed agar phantom with uniformly distributed scatterers. Regression coefficients obtained for each method and percentage errors are presented. In order to select the best method for delay estimation in hyperthermia context, a multi-index criterion for evaluation and comparison, which considers a) their suitability for simulated signals and for experimental signals, b) their associated processing time and c) their robustness under noisy conditions, is also proposed.
... There has been a long-standing scientific interest in evaluating the biomechanical properties of soft tissues, and initial work was mostly done on ex vivo tissue specimens [3,4,7,13,57,77,[80][81][82][83]. Many ultrasound-based imaging techniques have been used to measure tissue response to static or quasi-static stress [5,6,8,9,12,14,16,18,78,84,85], and these methods paved the way for newer imaging modalities such as MRI for assessment of the tissue response. ...
... Some results, obtained with this technique, are here compared in well-controlled multipulse echo patterns, with other results obtained using an approach based on one of the previous alternative techniques conventionally used for artery analysis, the basic time cross-correlations (TCC) of ultrasonic echoes coming from wall interfaces in distinct cycle points. There are a number of works that successfully use the crosscorrelation operator to detect moving reflectors or internal properties into biological tissues [4,5,7,9,26,29]. And other works related directly to this arterial problem use this same TCC time operator in an elastographic context [12,[23][24][25]. ...
By locally measuring changes on arterial wall thickness as a function of pressure, the related Young modulus can be evaluated. This physical magnitude has shown to be an important predictive factor for cardiovascular diseases. For evaluating those changes, imaging segmentation or time correlations of ultrasonic echoes, coming from wall interfaces, are usually employed. In this paper, an alternative low-cost technique is proposed to locally evaluate variations on arterial walls, which are dynamically measured with an improved high-resolution calculation of power spectral densities in echo-traces of the wall interfaces, by using a parametric autoregressive processing. Certain wall deformations are finely detected by evaluating the echoes overtones peaks with power spectral estimations that implement Burg and Yule Walker algorithms. Results of this spectral approach are compared with a classical cross-correlation operator, in a tube phantom and "in vitro" carotid tissue. A circulating loop, mimicking heart periods and blood pressure changes, is employed to dynamically inspect each sample with a broadband ultrasonic probe, acquiring multiple A-Scans which are windowed to isolate echo-traces packets coming from distinct walls. Then the new technique and cross-correlation operator are applied to evaluate changing parietal deformations from the detection of displacements registered on the wall faces under periodic regime.
... These methods determine the velocity of the wave inside the media by using high frequency ultrasound. Wilson and Robinson ([23]) used a phase method to determine human tissue characteristics; Tristam et al. ([20]) developed a correlation method for determining kinetic characteristics of human tissues, and de Jong et al. ( [3]) introduced a correlation interpolation of pulsed ultrasonic signal for determination of tissue motion velocity. In this research, these methods were applied and tested for the specific application of noninvasive estimation of temperature. ...
Noninvasive thermometry is one of the greatest challenges for hyperthermia treatment and ultrasound thermometry is one of the most attractive techniques used for this purpose. In this chapter, four time-delay estimation methods, which relate temperature changes inside tissue replica (phantom) with time shifts in ultrasound echo-signals, were tested and their results were comparatively evaluated. These methods were tested, for temperatures ranging from 30 • C to 50 • C and for both experimental and simulated echo-signals. Simulated signals were obtained from a numerical phantom which is proposed in this chapter, and experimental signals were acquired from a specially developed agar phantom with uniformly distributed scatterers. Regression coefficients obtained for each method and percentage errors are presented. In order to select the best method for delay estimation in hyperthermia context, a multi-index criterion for evaluation and comparison, which considers a) their suitability for simulated signals and for experimental signals, b) their associated processing time and c) their robustness under noisy conditions, is also proposed.
... The first one is the cross-correlation algorithm. The peak-searching algorithm identifies the peak of the discrete function of the cross-correlation using Cosine interpolation algorithm [6] , Gaussian interpolation algorithm [7] or Parabolic interpolation algorithm. The second one is the sample tracking algorithm. ...
How to estimate the differential time of flight accurately is a challenging problem in the area of ultrasonic flow measurement. High time resolution is necessary, especially in a small inner diameter, short sound path measurement environment, since sound velocity in the liquid is quite fast and the order of magnitude is nanosecond. A newer method to obtain the differential time of flight is a Spline-Based algorithm. Although the calculation accuracy of a Spline-Based algorithm is higher than the common method, cross-correlation algorithm, the calculated quantity of this algorithm is huge. For this reason, an improved Spline-based algorithm is proposed to reduce the computational cost while keeping the accuracy. In addition, installation location of transducers is one of the most important factors affecting the measurement accuracy of ultrasonic flowmeter. This paper also analyzes the affection of the differential separation distance between transducers. Experiments have shown that the improved algorithm is effective and the separation distance affects the result seriously.
... There has been a long-standing scientific interest in evaluating the biomechanical properties of soft tissues, and initial work was mostly done on ex vivo tissue specimens [3,4,7,13,57,77,[80][81][82][83]. Many ultrasound-based imaging techniques have been used to measure tissue response to static or quasi-static stress [5,6,8,9,12,14,16,18,78,84,85], and these methods paved the way for newer imaging modalities such as MRI for assessment of the tissue response. ...
A newly developed magnetic resonance imaging technique can directly visualize propagating acoustic strain waves in tissue-like materials. By estimating the local wavelength of the acoustic wave pattern, quantitative values of shear modulus can be calculated and images generated that depict tissue elasticity or stiffness. Since tumors are significantly stiffer than normal tissue (the basis of their detection by palpation), this technique may have potential for 'palpation by imaging,' with possible application to the detection of tumors in breast, liver, kidney, and prostate. We describe the local wavelength estimation algorithm, study its properties, and show a variety of sample results.
... We then computed the cross correlation between the first seismogram of each of the repeating-earthquake series and explosion pair with each subsequent seismogram in the corresponding sequence or pair to obtain the delay times of the P arrivals between events of the sequences and explosions. We further used a cosine fitting method to estimate the subsample delay times that were not included from the cross-correlation method (De Jong et al., 1990;Cespedes et al., 1995). Given the largest sample of the correlation function C
0 and its two neighbors C
1 and C
1, the estimated subsample delay time is given by the following expression: ...
Time-lapse seismic imaging (4D) is a new and rapidly-evolving technology. It has attracted wide attention in recent years, because accurate imaging of the evolving subsurface structure has significant applications in resource exploration and environmental monitoring. To apply this technology to monitor the time-varying stress field associated with earthquakes, one needs highly-repeatable powerful sources that can propagate through tens of kilometers to generate similar waveform data that allows for investigating temporal changes in the crustal velocity structure at seismogenic depth. One natural source is repeating earthquakes, which are believed to occur at nearly the same location with the same source mechanism. As such, they produce virtually identical seismograms at a given station. Yet, there are subtle differences in these records that can result, in principle, from either temporal changes in the medium, or from slight differences in source parameters, or both, assuming the signal to noise ratio is high. Approaches such as using differential seismograms or making differential seismic images potentially suffer from the systematic bias introduced by changes in source parameters. For example, variations in source location can be significant when natural sources are used since changes in the medium are typically very small. In order to minimize this bias, we adopt the so-called coda wave interferometry technique. To quantify the difference between seismograms in a repeating earthquake cluster, we compute the cross correlation between the first seismogram and each subsequent seismogram within a moving time window. The lag time tau(t) is obtained when the maximum cross correlation, Cm(t), is reached, and a decorrelation index D(t) is defined as 1- Cm(t). We find that temporal changes in source location, background velocity and the scattered wave field have very different influences on the two functions, and can thus be separated on this basis. Uniform changes in the background velocity, for example, results in a monotonic increase or decrease of lag time as a function of elapsed time on the seismogram, and consequently these changes can be estimated from the slope of lag time function tau(t). Our finite difference synthetic simulations demonstrated that these various influences are distinguishable by migrating the decorrelation index D(t). We are able to image localized changes in scattering field from waveform data that substantial changes in location and the background velocity are presented. Our technique of imaging scatterer migration thus can be applied to broad regions where relatively loosely defined clusters are available.
... and is equivalent to fitting a parabola to the logarithm of the data. A final method is to fit a cosine to the three points [11] [12]: ...
A common problem in radar, ultrasound, acoustic and other fields is that of determining the delay between two signals. In many situations, it is possible to determine the delay of a sampled signal to an accuracy better than the sample period. This paper presents a comparison of a number of methods of estimating this subsample delay, with special attention to the case of periodic signals. The authors also suggest two methods, which perform better than previous methods in some situations.
... We have tested three different crosscorrelation-based algorithms: (1) cosine fitting, (2) seismogram interpolation, and (3) cross-correlation interpolation. Cosine curve fitting (method 1) has been used extensively in the past in interpolating the discrete correlation function to estimate subsample delay time (de Jong et al., 1990de Jong et al., , 1991 Cespedes et al., 1995). In algorithm (2) we calculate the Fourier transform of a time series, pad the frequency spectrum with zeros, and calculate the inverse Fourier transform. ...
We have conducted a series of cross-well experiments to continuously measure in situ temporal variations in seismic velocity at two test sites: building 64 (B64) and Richmond Field Station (RFS) of the Lawrence Berkeley National Laboratory in California. A piezoelectric source was used to generate highly repeat- able signals, and a string of 24 hydrophones was used to record the signals. The B64 experiment was conducted utilizing two boreholes 17 m deep and 3 m apart for � 160 h. At RFS, we collected a 36-day continuous record in a cross-borehole facility using two 70-m-deep holes separated by 30 m. With signal enhancement techniques we were able to achieve a precision of � 6.0 nsec and � 10 nsec in delay-time esti- mation from stacking of 1-hr records during the � 7- and � 35-day observation pe- riods at the B64 and RFS sites, which correspond to 3 and 0.5 ppm of their travel times, respectively. Delay time measured at B64 has a variation of � 2 lsec in the 160-hr period and shows a strong and positive correlation with the barometric pres- sure change at the site. At RFS, after removal of a linear trend, we find a delay-time variation of � 2.5 lsec, which exhibits a significant negative correlation with baro- metric pressure. We attribute the observed correlations to stress sensitivity of seismic velocity known from laboratory studies. The positive and negative sign observed in the correlation is likely related to the expected near- and far-field effects of this stress dependence in a poroelastic medium. The stress sensitivity is estimated to be � 106/ Pa and � 107/Pa at the B64 and RFS site, respectively.
... In this study, we employed a cosine fitting method to estimate subsample delay time in the time domain [Cespedes et al, 1995;De Jong et al, 1990]. Given the largest sample of the correlation function, cc(0), and its two neighbours cc(-l) and cc(l), the estimated subsample shift is given by following expression: r = a/arctan(^^), ...
The time-varying stress field of fault systems at seismogenic depths plays the mort important role in controlling the sequencing and nucleation of seismic events. Using seismic observations from repeating earthquakes, controlled active sources and seismic ambient noise, five studies at four different fault systems across North America, Central Japan, North and mid-West China are presented to describe our efforts to measure such time dependent structural properties. Repeating and similar earthquakes are hunted and analyzed to study the post-seismic fault relaxation at the aftershock zone of the 1984 M 6.8 western Nagano and the 1976 M 7.8 Tangshan earthquakes. The lack of observed repeating earthquakes at western Nagano is attributed to the absence of a well developed weak fault zone, suggesting that the fault damage zone has been almost completely healed. In contrast, the high percentage of similar and repeating events found at Tangshan suggest the existence of mature fault zones characterized by stable creep under steady tectonic loading. At the Parkfield region of the San Andreas Fault, repeating earthquake clusters and chemical explosions are used to construct a scatterer migration image based on the observation of systematic temporal variations in the seismic waveforms across the occurrence time of the 2004 M 6 Parkfield earthquake. Coseismic fluid charge or discharge in fractures caused by the Parkfield earthquake is used to explain the observed seismic scattering properties change at depth. In the same region, a controlled source cross-well experiment conducted at SAFOD pilot and main holes documents two large excursions in the travel time required for a shear wave to travel through the rock along a fixed pathway shortly before two rupture events, suggesting that they may be related to pre-rupture stress induced changes in crack properties. At central China, a tomographic inversion based on the theory of seismic ambient noise and coda wave interferometry clearly reveals a coseismic velocity decrease region with the strike and length strikingly matching the fault zone of the 2008 M 7.9 Wenchuan earthquake at depth. We speculate the imaged decrease velocity region resulted from decreased crustal stress around the fault zone at upper crust.
Harmonic Motion Imaging (HMI) is an ultrasound elastography technique that estimates the viscoelastic properties of tissues by inducing localized oscillatory motion using focused ultrasound. The resulting displacement, assumed to be inversely proportional to the tissue local stiffness, is estimated using an imaging array based on RF speckle tracking. In conventional HMI, this is accomplished with plane wave (PW) imaging, which inherently suffers from low lateral resolution. Coherent PW compounding (PWC) leverages spatial and temporal resolution using synthetic focusing in transmit. In this study, we introduced focused imaging with parallel tracking in HMI and compared parallel tracking of various transmit F-numbers (F/2.6, 3, 4, 5) qualitatively and quantitatively with PW and PWC imaging at various compounded angle ranges (6°, 12°, 18°). An
in silico
model of a 56-kPa spherical inclusion (diameter: 3.6 mm) embedded in a 5.3-kPa background and a 5.3-kPa elastic phantom with cylindrical inclusions (Young’s moduli: 22 to 56 kPa, diameters: 2.0 to 8.6 mm) were imaged to assess different tracking beam sequences. Speckle biasing in displacement estimation associated with parallel tracking was also investigated and concluded to be negligible in HMI. Parallel tracking in receive resulted in 2-7% and 8-12% increase compared to PW imaging (p<0.05) in HMI contrast and contrast-to-noise ratio
in silico
and phantoms. Focused imaging with parallel tracking in receive was concluded to be most robust among PW and PWC imaging for displacement estimation, and its preclinical feasibility was demonstrated in post-surgical human cancerous breast tissue specimens and
in vivo
murine models of breast cancer.
Current ultrasound methods for recognition and motion-tracking of arterial walls are suited for image-based B-mode or M-mode scans but not adequately robust for single-line image-free scans. We introduce a time-warping-based technique to address this need. Its performance was validated through simulations and in-vivo trials on 21 subjects. The method recognized wall locations with 100% precision for simulated frames (SNR > 10 dB). Clustering detections for multiple frames achieved sensitivity > 98%, while it was ∼90% without clustering. The absence of arterial walls was predicted with 100% specificity. In-vivo results corroborated the performance outcomes yielding a sensitivity ≥ 94%, precision ≥ 98%, and specificity ≥ 98% using the clustering scheme. Further, excellent frame-to-frame tracking accuracy (absolute error < 3%, RMSE < 2 μm) was demonstrated. Image-free measurements of peak arterial distension agreed with the image-based ones, within an error of 1.08 ± 3.65 % and RMSE of 38 μm. The method discerned the presence of arterial walls in A-mode frames, robustly localized, and tracked them even when they were proximal to hyperechoic regions or slow-moving tissue structures. Unification of delineation techniques with the proposed methods facilitates a complete image-free framework for measuring arterial dynamics and the development of reliable A-mode devices.
Ultrasound systems are widely used to visualize in real-time internal structures and blood flow velocity distributions. The latter are estimated from the received ultrasound radio frequency (RF) signals backscattered from moving red blood cells, using a mean frequency estimator. Since RF-signals contain not only scattering, but also reflections, reverberations and noise it is necessary to suppress the power of the reflections and/or reverberations (clutter removal) to estimate the temporal mean frequency of the signal component induced by scattering. Normally this is done with a static high-pass filter acting in the temporal direction with a fixed cut-off frequency. However, by using such a filter the time dependent aspect of the reflections is ignored. A more selective way is to use a band stop filter which adapts its rejection range to the mean frequency of the clutter. A great advantage of this adaptive filter (ADP-f) method is that the rejection range can be kept small.
In medicine, pulsed ultrasound is a widespread noninvasive technique that measures motion in the direction of the ultrasound beam, i.e., axial motion. The magnitude of the actual motion can be determined only if the angle between the ultrasound beam and the direction of motion (transducer-to-motion angle) is known. For blood flow measurements, current pulsed ultrasound systems assume this angle to be equal to the angle between the ultrasound beam and the longitudinal direction of the vessel, as can be estimated from a two-dimensional brightness-mode (B-mode) image that is obtained prior to the blood flow measurement. For tissue motion measurements, current pulsed ultrasound systems are mostly unable to determine the transducer-to-motion angle. Recently, a model has been derived for the correlation of(analytic) radiofrequency (rf) signals, assessed with a circularshaped ultrasound transducer along the same line of observation. In the present paper, this model is used to derive estimators, requiring only the calculation of a few correlation coefficients, for the motion components (axial, lateral and actual) and for some of the signal parameters (center frequency, bandwidth and signal-to-noise ratio) of the assessed rf signals, The transducer-to-motion angle can be derived from the estimated motion components. For the evaluation of the estimators, rf signals were acquired with a motion-controlled experimental arrangement. The results of the evaluation study show that the transducer-to-motion angle can be estimated with a mean standard deviation of less than 2 degrees.
In order to measure the small change of velocity before rock fracture, the velocity measurement precision must be improved, the methods including digital wave form, the wave stacking, cross correlation and Subsample delay time estimate were used, the precision of time and velocity reached to 0.001 micro second and 1 m/s respectively. The delay time was measured as the stress increase with the interval of 0.17 MPa, then the rule of velocity as stress increase was obtained. Experimental results showed the velocity had the maximum value at the rock strength of 0.98, after that the velocity decreased about 30 m/s to fracture. The power of wave at main frequency was calculated and had the same characteristic with velocity, it was considered the changes may be caused by rock dilation. The square error of delay time was discussed by using the fluctuation model.
The walls of arteries move due to the changes in blood pressure and flow during the cardiac cycle. The largest and most obvious component of motion is radial, in that the diameter increases and decreases during the cardiac cycle. However, there are other important components of motion. It is increasingly apparent that arteries move longitudinally to some degree, and there is flexion and extension of the carotid arteries due to movement of the skeleton.
Various relationships are suggested in the literature to qualify the elastic behavior of (a segment of) an artery as a function of measurable parameters.
Time Delay Estimation is a basic technique used for locating and tracking radiating acoustic source. TDE process is common for studying signal-to-noise ratio, input signals and systems that are common in process industry. The delay estimate is acquired using the generalized cross-correlation function applied between the original and the time-lagged filtered version of the received signal. In recent years ultrasound elastography proved as a successful alternative of the invasive biopsy. The fundamental necessity lies in estimating the strain for which time delay estimation is a pre-requisite step. Taking the phase of the complex envelope of the pre and post compression RF echo signals it is possible to successfully compute the time delay between them. The ultimate target of an Elastographic process is the noiseless Elastogram which is used to identify the suspected nodules embedded into the deep of tissue column. In this paper the strain information acquired from the phase of complex envelope and the same is used to analyze the quality of Elastograms studying mainly two parameters strain and sampling frequency.
Due to their low-power levels, GPS signals are very susceptible to interference from either intentional or unintentional sources. This vulnerability is further aggravated by the increased reliance of the civilian infrastructure on GPS for time synchronization. This brings about the pressing need for detection and localisation of the interferers in real-time to prevent disturbance to everyday operation of this infrastructure. This paper details the upgrades to one such system, GNSS Environmental Monitoring System (GEMS) which consists of a number of sensor stations connected to a central processing unit, to achieve real-time interference localisation. The paper describes the GEMS environment and details and compares performance of various time and frequency domain Time Difference of Arrival (TDOA) estimation approaches.
The aim of this study was to evaluate tracking performance when an extra reference block is added to a basic block-matching method, where the two reference blocks originate from two consecutive ultrasound frames. The use of an extra reference block was evaluated for two putative benefits: (i) an increase in tracking performance while maintaining the size of the reference blocks, evaluated using in silico and phantom cine loops; (ii) a reduction in the size of the reference blocks while maintaining the tracking performance, evaluated using in vivo cine loops of the common carotid artery where the longitudinal movement of the wall was estimated. The results indicated that tracking accuracy improved (mean = 48%, p < 0.005 [in silico]; mean = 43%, p < 0.01 [phantom]), and there was a reduction in size of the reference blocks while maintaining tracking performance (mean = 19%, p < 0.01 [in vivo]). This novel method will facilitate further exploration of the longitudinal movement of the arterial wall.
Most cardiac diseases are related to non-uniformities in contractile function. Such regional non- uniformities can be recognized
conventionally, but transmural gradients in mechanical function cannot be determined that easily. We propose a method to assess
transmural differences in myofiber shortening, using MRI- tagging of the heart. Midwall motion of 5 short-axis slices of the
left ventricle was determined non-invasively. Using a model of cardiac motion, the transmural distribution of deformation
of the left ventricular wall was determined. On the basis of remodeling rules, the transmural course of myofiber orientation
was estimated. From deformation and fiber orientation data transmural differences in myofiber shortening were calculated.
The method appears sensitive to distinguish patients with aortic stenosis from healthy volunteers.
Prostate tumors can have a higher mechanical hardness than the surrounding tissue. During the digital rectal exam this can be used not only to detect the hypertrophy but also localized hardenings. The examination by digital palpation is inaccurate and even in combination with PSA-value and a transrectal ultrasonic examination the result is often not reliable. Ultrasound strain imaging is able to measure and visualize the elastic properties of a tissue region and hence is an adequate supplement for commonly used diagnostic procedures. We have developed a real time system for elastographic prostate diagnosis which can be used for the first time during the transrectal ultrasonic examination for navigation and diagnosis. During the examination a sequence of ultrasonic images is acquired while the organ is slightly compressed by the ultrasound probe. Using a numerical analysis of image pairs of the acquired sequence the tissue strain is calculated which represents the spatial elasticity distribution of a specific cross-section of the organ and which are able to distinguish hard areas in the tissue. We present results from several patients which show, that real time strain imaging is able to detect tumor-like areas which are inconspicuous in the b-mode image. The results correspond to the histological specimens. Furthermore we found that in 24 of 26 patients the tumor location and extend was correctly predicted (prospective study) using real time strain imaging.
Digital image correlation techniques are commonly used to evaluate deformation gradients from image sets by cross correlating pixel intensities. Recently, Bayesian framework based texture correlation technique have gained greater acceptance to study soft tissue deformation due to its ability to model noisy image data. Besides cross correlation, this probability based technique weighs regions of potential matches by radial distance from center of search region thereby eliminating large improbable displacements. Simple tension tests on soft tissue using magnetic resonance and ultrasound imaging modalities are presented. This initial study revealed encouraging results from ultrasound images compared to MR due to better a priori incremental image data. Having established a suitable imaging modality, plane strain tension and indentation tests were carried out on homogeneous (breast phantom) and non-homogeneous (muscle tissue) specimens and validated using optical images with surface markers. The specimens were deformed up to 10 mm in tension and indentation modes. The root mean square (RMS) error between the strain values from texture correlation and optical images varied from 6 to 10% for breast phantom compared to 2 to 7% for muscle tissue. As expected, the errors appeared to increase with larger deformation to suggest the limited scope of dependable estimates. The displacement estimates evaluated for square block sizes in muscle tissue, revealed acceptable RMS error range at 6 to 7 mm for tension and indentation test. The block sizes are significantly lower for homogeneous specimen due to better texture and dynamic range compared to muscle tissue. The indentation tests show the Bayesian texture correlation technique's ability to predict regions of non-homogenous deformation. Further studies must aim at analyzing image data with varying signal to noise ratios and identifying a measure of filter to remove questionable displacements.
In color Doppler systems the received RF signal is multiplied by a reference signal and subsequently averaged over a short depth range to obtain a sample of Doppler signal. The mean frequency of the Doppler signal, reflecting the mean velocity of the scatterers moving through the depth range, is obtained by a time-domain autocorrelator. An alternative is to evaluate the time shift of range-gated RF signals over subsequent A-lines, and then give the velocity of the scatterers. This paper presents a frequency-domain autocorrelator to estimate the time shift associated with a high-pass filter for removing small time shift components. It has the same mathematical expression as that for the time-domain autocorrelator, and most of the hardware of the conventional color Doppler systems can be used for its implementation. The first results of computer simulations show that the new estimator is superior to the conventional Doppler technique.
Young's Modulus of soft tissue is a key index to evaluate the biomechanical features of the soft tissue; it has a close relationship to the force and deformation of the soft tissue. In order to measure the force and the deformation of soft tissue, a specially designed device is used to link ultrasound and force transducers by mounting them in series. The combined transducers can simultaneously sense the compressive force and the deformation of the soft tissue. The measurement system is calibrated, before it is used, to collect the data. Based on the measured force and the measured deformation of the soft tissue, the analytics biomechanical model of the soft tissue can be obtained by data fitting.
In this paper, the biomechanical model of the soft tissue is assumed to be linear and possess viscous elasticity; when the model of the soft tissue is a linear model, the derived Young's Modulus of the soft tissue is a constant; when the model of the soft tissue is a viscoelastic model, the derived Young's Modulus is a function of the deformation of the tissue. Calibration data show that the maximal error of the measurement system is less than 1.9 µm, non‐linearity error γT is ±0.06%, and the static error band γ is ±0.07%. The measurement system can be used to diagnose the pathology of soft tissue.
A specially designed device is used to link ultrasound and force transducers by mounting them in series. The combined transducers can simultaneously sense the deformation and compression force in the soft tissue. In this system, the method for obtaining the exact strain of the soft tissue during compression is very important. In this paper, six different algorithms to estimate the strain of the tissue are compared: Normalized Correlation (NC), Direct Correlation (DC), Sum Absolute Differences (SAD), Sum Squared Differences (SSD), Hybrid‐sign Correlation (HC), and Maximum algorithm. In order to evaluate the results of the six algorithms, a calibration system is setup in which the grating transducer and ultrasound sensor are connected in series. The strain of the soft tissue analyzed by six methods is compared. The results show that the estimating accuracy of tissue strain by the NC, DC, and SSD algorithms are completely the same, and there is no distinct difference in estimating accuracy between the SAD and NC (or DC and SSD) algorithms (α=0.05). The standard deviation and maximal deviation of the delay time obtained by the HC and Maximum algorithms is unstable, and the delay time estimated by these two algorithms also shows false peaks. The time to run the SAD algorithm is more than the time to run the DC and SSD algorithms (α=0.05), while there is no distinct difference in the time to run the DC and SSD algorithms. For systems with limited hardware resources, the DC and SSD algorithms are suitable.
Accurate subsample displacement estimation is necessary for ultrasound elastography because of the small deformations that occur and the subsequent application of a derivative operation on local displacements. Many of the commonly used subsample estimation techniques introduce significant bias errors. This article addresses a reduced bias approach to subsample displacement estimations that consists of a two-dimensional windowed-sinc interpolation with numerical optimization. It is shown that a Welch or Lanczos window with a Nelder-Mead simplex or regular-step gradient-descent optimization is well suited for this purpose. Little improvement results from a sinc window radius greater than four data samples. The strain signal-to-noise ratio (SNR) obtained in a uniformly elastic phantom is compared with other parabolic and cosine interpolation methods; it is found that the strain SNR ratio is improved over parabolic interpolation from 11.0 to 13.6 in the axial direction and 0.7 to 1.1 in the lateral direction for an applied 1% axial deformation. The improvement was most significant for small strains and displacement tracking in the lateral direction. This approach does not rely on special properties of the image or similarity function, which is demonstrated by its effectiveness with the application of a previously described regularization technique.
The purpose of this work is to develop and test a new kind of imaging system that the authors call "palpation imaging." They have demonstrated that palpation imaging can be a useful tool for improving the discrimination between benign and malignant breast tumors. They implemented their algorithm for imaging tissue elasticity on a commercial ultrasound imaging system and tested the new imaging system on phantoms and in vivo breasts. Palpation images are produced at substantially real-time frame rates with normal ultrasound B-mode and strain images displayed side-by-side. The algorithms are fully integrated into the commercial system and require no system modifications. Breast exams performed on volunteers have shown that palpation imaging techniques are almost identical to the standard clinical breast ultrasound exam. ROC analysis of elasticity image information demonstrates that the diagnostic confidence of breast radiologists is improved when elasticity information is added to standard ultrasound images. Further increases in observer performance will come through improved training, observer tools (automated segmentation), and image quality improvements.
The field of imaging the elastic properties of tissue has grown to an impressive variety of techniques and applications, some of which are currently in clinical trials. This review focuses on the specific role of vibration sonoelastography, beginning with the first images of tissue “hardness, through the development of real time scanning techniques, 3D reconstructions, and applications to major disease categories, especially the detection of prostate cancer.
We present a three-dimensional tracking routine for nondiffraction-limited particles, which significantly reduces pixel bias. Our technique allows for increased resolution compared to that of previous methods, especially at low magnification or at high signal/noise ratio. This enables tracking with nanometer accuracy in a wide field of view and tracking of many particles. To reduce bias induced by pixelation, the tracking algorithm uses interpolation of the image on a circular grid to determine the x-, y-, and z-positions. We evaluate the proposed algorithm by tracking simulated images and compare it to well-known center-of-mass and cross-correlation methods. The final resolution of the described method improves up to an order of magnitude in three dimensions compared to conventional tracking methods. We show that errors in x,y-tracking can seriously affect z-tracking if interpolation is not used. We validate our results with experimental data obtained for conditions matching those used in the simulations. Finally, we show that the increased performance of the proposed algorithm uniquely enables it to extract accurate data for the persistence length and end-to-end distance of 107 DNA tethers in a single experiment.
The spatial resolution of a pulsed Doppler system heavily depends on both the characteristics of the ultrasound transducer and the processing circuitry. The local characteristics of the ultrasound beam give the lateral sample function while the way the signals are processed affects the axial shape of the sample volume. A simple way to explore the size of the sample volume is the employment of a running string target. However, the detected Doppler signals will be the sum of all the Doppler signals returned by the string along its course through the sample volume. Therefore, it will be complicated to separate the axial and lateral contribution to the actual size of the sample volume. A scanning system capable of visualizing the cross-sectional distribution of the ultrasound intensity allows the assessment of the sample sensitivity in lateral direction. A single vibrating point target enables the exploration of both the axial and lateral sampling function. The latter approach is especially suited to evaluate routinely the spatial performance of pulsed Doppler systems in clinical practice.
A new type of pulse-Doppler is described and results illustrating in vivo operation presented. The system uses a phase detection principle to produce an output proportional to the velocity of moving structures continously as a function of depth into the tissue, similar to an A-mode display. It employs only a single processing channel consisting of double delay line canceller and delay line phase-detector. Operation is equivalent to a parallel processing multiple-gate Doppler having a very large number of gates. This relatively simple system has promise in making true Doppler imaging available with B-mode imaging systems as well as for investigating velocity profiles and diameter of peripheral arteries.
The temporal correlation properties of ultrasonic echoes from contracting myocardium are investigated theoretically. Myocar- dium is modeled as a dense suspension of moving particles, with time- varying scattering amplitudes. Single scattering is assumed. Echoes from different particles are added coherently. The variance of particle velocity is proposed as an indicator of contractile performance. It is shown how this parameter may be extracted from the average corre- lation of pairs of echoes arising from separate ultrasound pulses. An experiment is performed in which a manufactured target with known motion characteristics is interrogated using a commercial medical ul- trasound scanner. The experimental results are found to be in good agreement with theory. Finally, practical considerations for perform- ing and interpreting these measurements in human myocardium are discussed. EVERAL INVESTIGATIONS have demonstrated that it may be possible to evaluate cardiac contractile per- formance accurately with ultrasound. One technique in- volves the measurement of the frequency average of the intensity of ultrasonic echoes emanating from myocar- dium. Echo intensity has been found to vary throughout the cardiac cycle in normal canine myocardium, with the maximum level occurring at end-diastole and the mini- mum at end-systole ( l), (2). In addition, the magnitude of this effect has a regional dependence throughout the heart, with areas of greater contractile activity exhibiting greater amplitudes of variation (3). The extent of the cyclic variation of echo intensity has also been observed to drop significantly in canine myocardium making a tran- sition from normal to ischemic 141. Thus the magnitude of cyclic variation may be interpreted as a measure of contractile performance. A second technique entails quantitative analysis of video images of the heart produced by ultrasound scan-
A discrete-time Doppler system is described which features: (a) simultaneous processing of the velocity information for 128 data points or more; (b) sampled time domain frequency analysis; and (c) basic fast response elements for next generation ″real time″ two dimensional flow imaging scanners. The frequency detector measures the instantaneous phase of the echo signal by a dedicated high speed hardware processor. The phase increment between two subsequent transmit/receive cycles is a direct measure of the instantaneous frequency. This parameter is then used to calculate the mean and variance of the detected velocity. A computer simulation study, generating time signals off a given spectrum, has been used to verify the performance of the new processor, such as linearity, adequacy of dynamic range, transient response and noise sensitivity. Experimental, as well as clinical results obtained with a prototype instrument are presented.
Based on the cross correlation of two signals, the speed measurement method presented in this paper is to be used on materials whose structure is stable (railway, papersheet, etc.) or not (turbulent flows). There is not only a time delay between the signals, but more generally a filtering effect which may be regarded as linear. In these conditions, the theoretical characteristics (bias, variance) of the estimation are given. They are compared with simulation results. The influence of the computational rapidity of the electronic circuit on the quality of the estimation is studied.
A new image processing method is developed to process two-dimensional ultrasound B-scan echo images which makes possible the delineation of the displacement of cardiac boundaries for the precise assessment of infarcted/ischemic regions. An economic image processing system is designed for the purpose. An algorithm to compute the direction and amplitude of the displacement vector at any point in the cardiac image, given two frames of the image at two different time instants, is developed. The performance of the algorithm is examined with synthesized images. Displacement amplitudes along the boundaries of the left ventricle are plotted and compared for normal and diseased conditions.
The purpose of this study was to assess the ability of two-dimensional echocardiograms of complete heart cycles in closed-chest dogs to discriminate between normal and infarcted myocardium. Six mongrel dogs, two with normal hearts and four with instilled infarcts, were used in the study. Ultrasonic markers, inserted into the endocardium of the left ventricle of each dog, were used to correlate the ultrasound images with the pathologic slices which were made from the excised hearts. Two-dimensional echocardiograms of short axis views of the left ventricle in regions adjacent to the markers were videotaped, and selected sequences of frames comprising one heart cycle were digitized and analyzed. Histogram moment and autocorrelation values for normal and infarcted regions were calculated for the temporally changing images allowing any cyclic variations in the echo-amplitude information to be detected. The results show that the two lowest order histogram moment parameters, mean and variance, are greater in infarcted tissue and can quantitatively distinguish between normal and infacted regions with significance levels of P< 0.0001. The manner in which the mean varies over the cardiac cycle is also a good indicator of the state of the myocardium. The infarcted areas yield regions of higher intensity throughout the cardiac cycle, and the mean demonstrates greater variability in infarcted regions. Copyright © 1985 by The Institute of Electrical and Electronics Engineers, Inc.
In multigate pulsed Doppler systems with serial processing the Doppler signals are retained in their sampled form. The time-discrete nature of the Doppler signals affects the procedure to estimate the average frequency of the Doppler signal. Based on computer simulation studies it is demonstrated that a time-discrete frequency estimator based on either the density of zero-crossings or the time average of the instantaneous frequency exhibit a large relative error under poor signal-to-noise conditions or in the case of relatively wide band signals. Especially, the frequency estimator based on the instantaneous frequency functions poorly for average Doppler frequencies close to the Nyquist frequency. However, restricting the detected instantaneous frequency to a specific interval around its average improves the estimator performance considerably, while it allows tracking of center frequencies beyond the Nyquist frequency. A hardware realization of this modified estimator as incorporated in a high-resolution multigate pulsed Doppler system is described. In vitro and in vivo registrations as assessed with this system demonstrate the ability of the system to track frequencies close to and beyond the Nyquist frequency.
It holds: Ryy (QO) = T (So + No) RyyfAx 0) = T (So + No)cos(oc Ax) RyyfO~Af~ = T Socos(-co, v At) Ryy@W) = T so cos(w, Ax -oc v At) Ryy(-Ax,At) = 2 so cos (-wc Ax -wc v At) (1 W (1 Ob) (1 w (1 W (1 W This set of five equations contains four solvable unknowns
- According
According to Eqs. (8) and (9) Ryy(X,T) is written in terms of the parameters Ob, o,, SO, No and v. It holds: Ryy (QO) = T (So + No) RyyfAx 0) = T (So + No)cos(oc Ax) RyyfO~Af~ = T Socos(-co, v At) Ryy@W) = T so cos(w, Ax -oc v At) Ryy(-Ax,At) = 2 so cos (-wc Ax -wc v At) (1 W (1 Ob) (1 w (1 W (1 W This set of five equations contains four solvable unknowns. In order to solve pa-rameter v, we have used the following calculation scheme. Using Eqs. (10a) and
oc Ax) sin (wc v At) = [Ryy(Ax,At) -Ryfi-Ax,At)]/2 (12) The factor sin(oCAx) is calculated using the result of Eq Using Eqs
- T So
T SO si n(oc Ax) sin (wc v At) = [Ryy(Ax,At) -Ryfi-Ax,At)]/2 (12) The factor sin(oCAx) is calculated using the result of Eq. (11). Using Eqs. (12) and