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Chapter 26 Introduction to speckle tracking in cardiac ultrasound imaging Damien Garcia1, Pierre Lantelme1,2 and E´ ric Saloux3 In this chapter, we will first recall some basic principles of speckle tracking. The fundamentals of speckle tracking in a wider context are essentially described in Chapter 13. We will then treat speckle-tracking echocardiography and echo- cardiographic particle image velocimetry (echo-PIV) and indicate a number of clinical applications in the context of evaluation of cardiac function. We will then briefly introduce color Doppler approaches complementary to speckle tracking. We will finally present how speckle-tracking techniques could benefit from high- frame-rate echocardiography (also called ‘‘ultrafast echocardiography’’). We will conclude with the expected contribution of high-frame-rate ultrasound for speckle tracking in three-dimensional (3-D) echocardiography. 26.1 Speckle formation and speckle tracking The word ‘‘speckle’’ refers to the granular appearance of an image generated by a coherent imaging system, such as laser, optical coherence tomography, and ultra- sound. As explained in detail in Chapter 2, speckles appear when a random col- lection of scatterers is illuminated by waves whose wavelength is larger than the size of the individual scatterers. The grainy aspect of a speckle pattern is produced by the multiple backscattered signals of similar frequency that interfere con- structively and destructively, depending on their relative phases and amplitudes (Figure 26.1). In medical ultrasound imaging, as soft tissues contain many scat- terers, the ultrasound waveforms detected by the transducer are the combination (interference) of the different wave reflections induced by the distinct scatterers. The resulting speckles are visible in the unfiltered gray-level (B-mode) images as dark and bright specks. 1INSERM. CREATIS, UMR 5220, U1206, Universite´de Lyon, INSA-Lyon, Universite´Claude Bernard Lyon 1, UJM-Saint E´ tienne, France 2Fe´de´ration de Cardiologie Croix-Rousse, Lyon-Sud, Hospices Civils de Lyon, Universite´ de Lyon, France 3Department of Cardiology, CHU de Caen. EA 4650, SEILIRM, Universite´de Normandie, France Loizou-6990339 29 November 2017; 12:16:26 572 Handbook of speckle filtering and tracking Figure 26.1 Speckle formation. Left: interferences produced by two scatterers. Right: speckles produced by the interference of backscattered waves generated by randomly distributed scatterers (white dots) When the individual contributions of the scatterers are independent, the speckle patterns can be accurately modeled by various statistical distributions whose phy- sical meanings have been thoroughly discussed in [1]. Chapter 3 also provides an overview of the statistical models introduced since the pioneering work of Burc- khardt in 1978 [2]. Because medical ultrasound images are made exclusively of speckles, they can significantly affect visualization quality or postprocessing tasks, and in turn negatively impact the diagnostic potential of medical ultrasound [3]. Despeckling can thus be a necessary task in some specific imaging situations. This angle is a main theme of this handbook and is largely addressed in the chapters devoted to speckle filtering (i.e., part II). On the contrary, in the present chapter, we consider the speckle patterns as intrinsic signatures of the insonated medium. In such a case, these distinctive imprints must be sufficiently preserved from one frame to the next one to allow analysis of tissue dynamics through speckle tracking. Speckle tracking for ultrasound imaging has been introduced by Trahey et al. [4], from Duke University, North Carolina, United States, to produce a blood flow velocity vector field in a human vein (Figure 26.2, left). Although it does not appear in the paper’s references, it is likely that Trahey et al.’s approach has been influ- enced by two-dimensional (2-D) speckle velocimetry, a former speckle photography technique to measure 2-D velocity fields in unsteady flows [6]. Since then, speckle tracking in medical ultrasound imaging has been the subject of a yearly increasing number of investigations (Figure 26.3), mainly in the field of myocardial strain imaging (deformation imaging of the cardiac muscle). Another strong interest for speckle tracking later emerged in contrast echocardiography (cardiac ultrasound imaging with contrast agents) to display 2-D blood velocity vector fields in the cardiac left ventricular cavity, a technique often called ‘‘echocardiographic particle image velocimetry’’ (or echo-PIV). The following paragraphs will describe these two common applications of speckle tracking in cardiac ultrasound imaging. Although strain imaging and echo-PIV are also of interest in ultrasound vascular imaging, the vascular field will not be discussed in the present chapter. We invite the Loizou-6990339 29 November 2017; 12:16:26 Speckle tracking echocardiography 573 Blood flow Myocardial motion Trahey et al., 1987 Mailloux et al., 1987 Figure 26.2 First applications of speckle tracking. Left: Venous blood velocity profile obtained with a cross-correlation-based block-matching approach [4]. Right: Myocardial motion from a global Horn– Schunck optical flow method [5] Occurrence of “speckle tracking” 600 in MEDLINE (title/abstract) 500 400 300 200 100 1 1991 1995 2000 2005 2010 2015 Figure 26.3 Yearly occurrence of ‘‘speckle tracking’’ in abstracts and/or titles of MEDLINE-referred papers. The first occurrence of ‘‘speckle tracking’’ is in [7] Loizou-6990339 29 November 2017; 12:16:29 574 Handbook of speckle filtering and tracking interested reader to refer to the chapters that address these specific topics. One of the reasons for focusing on cardiac imaging is that speckle tracking is mostly used clinically in the context of cardiac evaluation. In summary—Speckles are issued from the interference of the wave reflections induced by the tissue scatterers. Although considered as noise in some imaging applications, speckle patterns also represent local signatures of the insonified tissues. These speckles can be tracked to determine frame-to-frame motion. 26.2 Basic principles of speckle tracking As explained earlier, speckles can be considered as acoustic markers of the inso- nified tissues. In a time series of ultrasound images, these markers are sufficiently preserved from one frame to the next if the frame rate is high enough. In this latter condition, it is therefore possible to locally track the speckle patterns and thus deduce the local tissue displacements with a frame-wise approach as explained in detail in Part III. For example, in the current clinical practice, a frame rate of 50–80 frames/s is recommended to obtain optimal conditions for speckle tracking in the resting heart [8]. Ultrasound speckles can be tracked frame to frame by various approaches, such as differential optical-flow methods [9,10] or block-matching algorithms [10–12]. A block-matching algorithm is a method used to estimate motion in a video sequence by locating similar blocks between two successive images. It is generally well adapted to retrieve relatively large frame-to-frame displacements. A simple though standard block-matching method is to compare the intensities of the pixels using the sum of absolute/squared differences measure [13]. Among a number of similarity criteria, the normalized cross-correlation was his- torically the first [7], and is still one of the most applied methods, in medical ultrasound imaging [14–17]. In the following, although different similarity criteria can be used, we thus focus on the normalized cross-correlation without loss of generality. The normalized cross-correlation can be evaluated directly in the spatial domain by using small subwindows in one frame, and search areas of larger size in a subsequent frame [18]. Another possibility is to calculate the normalized cross- correlation in the Fourier domain (Figure 26.4), a consequence of the Wiener– Khinchin theorem [19]. The latter approach is often called ‘‘phase correlation’’ [20]. The peak location of the normalized cross-correlation corresponds to the local displacement with a pixel precision. A subpixel precision can be returned from 2-D fitting of the correlation peak [19]. In its simplest form, speckle tracking by cross- correlation can be summed up by the following three-step process: (1) division of two successive B-mode images into small subwindows, (2) normalized cross-cor- relation of the subwindow pairs, and (3) peak fitting and estimation of the dis- placements. In the Fourier domain (phase correlation), it boils down to the following steps (see also Figure 26.4): Let I1 and I2 represent two successive gray-level B-mode images. These two  k images are both subdivided into evenly-spaced subwindows of size (m n), w1 and Loizou-6990339 29 November 2017; 12:16:30 Speckle tracking echocardiography 575 k w1 w k W k 1 FFT 1 k k W1 W2 B-mode image #1 Subwindowing FFT –1 k k W1 W2 k w2 Normalized Displacement FFT k cross-correlation W2 k w2 B-mode image #2 Figure 26.4 Speckle tracking using the normalized cross-correlation implemented in the Fourier domain. This block-matching scheme can be generalized with other similarity criteria, such as the SAD or SSD (sum of absolute/squared differences) k ¼ w2, with k 1...M, M denoting the total number of subwindows. Size and overlap of the subwindows must be adapted to adjust the precision/accuracy compromise,ÀÁ as W k ¼ F k well as theÀÁ resolution of the output displacement field. Let 1 w1 and W k ¼ F k 1 w1 be the 2-D Fourier transforms of two paired subwindows. The Fast Fourier Transform (FFT)-based normalized cross-correlation for each subwindow k is given by ! wk wk NCCk ¼ FÀ1 1 2 : jwkwk j 1 2 The inverse Fourier transform is denoted by FÀ1, and the overbar denotes the complex conjugate. The divisions and multiplications are elementwise. The relative D k D k k k translation ( i , j ) between the two subwindows w1 and w2 is given by the location of the peak in NCCk: ÀÁ ÀÁ k k k Di ; Dj ¼ arg maxðÞi;j NCC To determine the translation with subpixel accuracy, a simple and robust method is to fit the correlation peak to some function, such as a paraboloid or Gaussian sur- face [19].

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