Ultrasound Frame Rate Requirements for Cardiac Elastography: Experimental and in Vivo Results

Ultrasonics 49 (2009) 98–111

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Ultrasonics

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Ultrasound frame rate requirements for cardiac elastography: Experimental and in vivo results

Hao Chen a,c, Tomy Varghese a,*, Peter S. Rahko b, J.A. Zagzebski a a Department of Medical Physics, University of Wisconsin-Madison, 1300 University Avenue, 1530 MSC, Madison, WI 53706, USA b Cardiovascular Medicine, UW Hospital and Clinics, University of Wisconsin-Madison, 1300 University Avenue, 1530 MSC, Madison, WI 53706, USA c Department of Electrical and Computer Engineering, University of Wisconsin-Madison, 1300 University Avenue, 1530 MSC, Madison, WI 53706, USA article info abstract

Article history: Cardiac elastography using radiofrequency echo signals can provide improved 2D strain information Received 28 February 2008 compared to B-mode image data, provided data are acquired at sufﬁcient frame rates. In this paper, Received in revised form 15 May 2008 we evaluate ultrasound frame rate requirements for unbiased and robust estimation of tissue displace- Accepted 31 May 2008 ments and strain. Both tissue-mimicking phantoms under cyclic compressions at rates that mimic the Available online 20 June 2008 contractions of the heart and in vivo results are presented. Sinusoidal compressions were applied to the phantom at frequencies ranging from 0.5 to 3.5 cycles/sec, with a maximum deformation of 5% of Keywords: the phantom height. Local displacements and strains were estimated using both a two-step one-dimen- Cardiac imaging sional and hybrid two-dimensional cross-correlation method. Accuracy and repeatability of local strains Displacement Echocardiography were assessed as a function of the ultrasound frame rate based on signal-to-noise ratio values. Elastography The maximum signal-to-noise ratio obtained in a uniformly elastic phantom is 20 dB for both a 1.26 Hz Elastogram and a 2 Hz compression frequency when the radiofrequency echo acquisition is at least 12 Hz and 20 Hz Elasticity respectively. However, for compression frequencies of 2.8 Hz and 4 Hz the maximum signal-to-noise Elasticity imaging ratio obtained is around 16 dB even for a 40 Hz frame rate. Our results indicate that unbiased estimation Strain of displacements and strain require ultrasound frame rates greater than ten times the compression fre- Cardiac deformation quency, although a frame rate of about two times the compression frequency is sufﬁcient to estimate the Ultrasound compression frequency imparted to the tissue-mimicking phantom. In vivo results derived from short- axis views of the heart acquired from normal human volunteers also demonstrate this frame rate requirement for elastography. Ó 2008 Elsevier B.V. All rights reserved.

1. Introduction ing is observed in the lateral direction and shortening is observed as the base moves towards the apex. Thickening and shortening of Echocardiography has been routinely used for assessment of re- the wall muscle during the cardiac cycle may be characterized by gional myocardial function, left ventricular size, and ventricular local tissue displacements and accompanying wall strain, suggest- structure since it provides real-time information, is portable, and ing that strain imaging could be a very useful indicator of myocar- is readily available. Conventional two-dimensional (2D) B-mode dial performance [2]. imaging along with M-mode recordings are well suited to define Doppler techniques, originally applied to analysis of blood flow global and regional functional changes in left ventricular perfor- across valves, have evolved to provide information about global mance. However, this type of analysis is limited because it provides and regional left ventricular and right ventricular performance. Tis- semi-quantitative information on cardiac wall movement abnor- sue Doppler imaging (TDI), also called tissue velocity imaging, esti- malities. As a consequence, there is considerable variation among mates local tissue velocities and tracks heart wall motion. [3,4]. TDI interpreters of echocardiograms, limiting the usefulness of such is most commonly derived from pulsed Doppler imaging of local- evaluations [1]. ized regions. Resultant signals may be displayed by color-coding During systole short-axis echo images of the left ventricle (LV) and superimposing TDI velocity estimates on a B-scan image, sim- show wall thickening in the radial direction and shortening in ilar to color-flow imaging. However, TDI does not differentiate be- the circumferential direction, while in the long-axis view thicken- tween active contraction and simple rotation or translation of the heart wall, nor does it differentiate passively following tissue from active contraction. Fleming et al. [5] used the spatial gradient of the * Corresponding author. Tel.: +1 608 265 8797; fax: +1 608 262 2413. TDI derived velocities to measure relative changes in wall thick- E-mail address: [email protected] (T. Varghese). ness, or strain-rate (definitions of the strain and strain-rate are

0041-624X/$ - see front matter Ó 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.ultras.2008.05.007 H. Chen et al. / Ultrasonics 49 (2009) 98–111 99 provided in Appendix A), to overcome this problem. However, as imaging performance. A TM phantom was subjected to cyclic com- velocities decrease toward the apex, the Doppler signal-to-noise pressions using the apparatus shown in Fig. 1. The phantom is sup- ratio decreases, limiting TDI’s usefulness in the apical part of the ported between two plates, which are mounted on cylindrical ventricle. Strain-rate plots using cross-correlation also have been slides as shown in the figure. The top plate is held stationary but reported on M-mode data [6]. Strain and strain-rate measurements its location can be adjusted to accommodate different sized phan- based on TDI have been compared to three-dimensional myocar- toms. This plate has a fixture and a rectangular channel that holds dial strain using tagged magnetic resonance imaging methods [7]. an ultrasound transducer. The transducer can be translated linearly Because of limitations in Doppler-derived velocity and strain within the channel. The bottom of the channel is sealed using a indices, there has been renewed interest in B-mode based strain poly-methyl pentene (PMP) strip that is flush with the bottom sur- and strain-rate measurements for assessing cardiac muscle perfor- face of the plate. Madsen et al. [13] have described this material mance [8–11]. B-mode based calculations of strain have the con- and shown that ultrasound can be transmitted readily through siderable advantage of not being directionally limited. Thus, the PMP material. This enables the use of a coupling medium such limitations from Doppler imaging, such as an inability to differen- as water or ultrasound gel within the translation channel. tiate between active contraction, simple rotation, and translational The bottom compression plate is connected using ball bearings motion of the heart wall are no longer significant issues. Further- to cylindrical slides to minimize friction during applied compres- more, B-mode related techniques such as speckle tracking have al- sions. This plate is driven by a variable speed direct current (DC) lowed new strain methodologies to be used in the left ventricle. motor (Cole-Parmer Instruments, Chicago IL) whose shaft rotates Local strain along the long-axis is now being estimated, along with between 1 and 10 cycles/s. The motor speed is adjusted using an rotational and radial indices of strain and strain-rate. analog controller to vary the current. The shaft is connected to Both General Electric Medical Systems (GEMS) (GE Healthcare, the plate in a slightly eccentric manner, with multiple connectors Milwaukee, WI, USA) and Siemens (Siemens Ultrasound, Mountain to enable the introduction of variations in the stroke amplitude. View, CA, USA) have introduced 2D speckle tracking for strain The moving compression plate supports the TM phantom and is imaging on their cardiac ultrasound systems. GEMS’s strain imag- larger than the phantom surface, providing a uniform compression. ing is based on processing ultrasound B-mode data loops. [8–10]. The phantom is placed in a small concave groove in the compres- Reisner et al. [10] utilized the entire U-shaped length of the LV sion plate to minimize horizontal slippage. The US transducer to estimate global peak longitudinal strain (GLS) and strain-rate placed on the top plate is utilized to collect RF data during com- (GLSR) in 4 patients after myocardial infarction (MI) and 3 controls. pressions. In this study, echo data were acquired for different Their results show that the average GLS and GLSR differ signifi- strain-rates by varying the amplitude and frequency of the cyclic cantly between patients who have suffered myocardial infarction compressions. The maximum compressional displacement applied (MI) and normal control subjects. Korinek et al. [8] compared by the DC motor was approximately 4 mm. Compression frequen- strains measured in vitro using sonomicrometry and in vivo using cies in the range of 0.6 Hz to 4 Hz were used as these are similar to the GEMS EchoPAC software package. Becker et al. [9] collected the human heart beat frequency. data over 64 patients and showed that tracking strain and strain- rate using B-mode image data enables improved analysis of regional systolic LV function. Their study provides an excellent analysis of regional strain for wall motion. Cardiac elastography using radiofrequency echo signals can provide improved 2D strain information over that obtained from B-mode image data [12], provided data are acquired at sufficient frame rates. The frame rate of current medical ultrasound systems, though high, may not be sufficient to characterize the quasi-periodic compression, relaxation, and rotation of the myocardium during the cardiac cycle for unbiased and robust cardiac displacement and strain imaging. In this paper, we present a relationship between the frame rate of an ultrasound system and the quality of computed strain images for a uniformly elastic tissue-mimicking phantom undergoing cyclic compressions. Image quality is quantified using the strain signal-to-noise ratio (SNRe) for various ratios of the compression frequency to the ultrasound system frame rate. In addition, displacement and strain estimates are obtained from in vivo strain images for short-axis views of the heart. The relative phase between strains measured in different locations of the myocardium is determined as a function of ultrasound system frame rates, which is varied by skipping radiofrequency (RF) data frames for which strains are computed.

2. Materials and method

2.1. Cyclic compression system

Since LV wall movements and velocities during the cardiac cycle can be assumed to vary in a quasi-periodic manner, a combined tissue-mimicking (TM) phantom and cyclic compression system was Fig. 1. Schematic diagram of the cyclic compression apparatus used to apply the developed to evaluate tradeoffs between frame rate and strain sinusoidal compression force to the uniform TM phantom. 100 H. Chen et al. / Ultrasonics 49 (2009) 98–111

2.2. Tissue-Mimicking phantom and ultrasound system 2.3. In vivo data acquisition

The TM phantom has dimensions of 90 90 90 mm. The Five healthy volunteers were scanned with the GE Vingmed Vi- Young’s modulus of the TM material is 30 KPa as measured using vid 7 Ultrasound system (GEMS Inc., USA), using the same 2.5 MHz an ELF 3200 mechanical testing system (EnduraTEC, Minnetonka, phased array transducer. Both B-mode and radiofrequency data MN)14. The ultrasound system is a GE Vingmed Vivid 7 Cardiovas- along the short-axis view at the mid papillary muscle level were cular machine (GEMS Inc., USA), equipped with a 2.5 MHz phased acquired with the patient lying on the left side, using the paraster- array transducer having an approximate 60% bandwidth. A single nal window to image the heart over several cardiac cycles. For the transmit focus was applied, set at a depth of 55 mm, and dynamic human data the transducer provided 114 A-lines over a RF data focusing was used on receive. The maximum RF acquisition frame frame covering a 75° sector angle. A single transmit focus was rate for the 60 degree sector (95 A-lines per RF data frame) and again applied, this time set at a depth of 100 mm. This system pro- 80 cm depth setting utilized was 43.7 Hz or frames per second duced RF data over a depth of 150 mm at a 20 MHz sampling rate (FPS). Frame rates were effectively reduced by skipping frames and frame rate of 34.1 frames per second (FPS). In this case each during analysis, yielding frame rates of 43.7, 21.8, 10.9, 5.5 and data set contained 201 frames of RF data, which were stored in a 2.2 Hz respectively (downsampling by a factor of 2). personal computer for off-line analysis. Data acquisition on human For each experiment, an initial pre-compression of 3% was ap- volunteers was performed at the University of Wisconsin-Madison plied to the phantom to ensure proper contact between the top Hospitals and Clinics, under a protocol approved by the UW-Mad- plate and the phantom surface. Then data were recorded as the ison Institutional review board (IRB) for data acquisition on human phantom underwent cyclic compressions. RF data sets for 10 differ- subjects. Each volunteer provided written consent to participate in ent compression frequencies, ranging from 0.9 to 3.5 Hz were ac- the study. quired. Each resultant data set at a ﬁxed compression rate and displacement amplitude contained 175 frames of RF data, Signals 2.4. Multi step 2D cross-correlation algorithms were stored in a personal computer for off-line analysis. Normalized 1D cross-correlation analysis [14] is the most commonly used method for measuring tissue displacements during strain imaging. The shift in the peak of the cross-correlation function is utilized to track tissue deformation. However, for 1D strain estimations we require a window length of at least 10 wavelengths (independent of the transducer center frequency) to obtain unbiased and precise displacement and strain estimates [15]. This pre- cludes the use of smaller gated window lengths that would enable acceptable axial resolution in cardiac strain images, which often

Fig. 3. Displacement along the axial direction obtained using the two-step cross- correlation method. Displacements and strains within the 2 ROI shown within the white boundaries are tracked over all the data frames to evaluate accuracy in the tracking of the displacement and strain due to the cyclic compression.

Fig. 2. (a) M-mode image showing the periodic sinusoidal displacement of the TM phantom due to the cyclic compression force applied to the phantom. (b) Corresponding normalized power spectrum computed from the M-mode data provides the exact cyclic compression frequency estimated from the fundamental Fig. 4. Relationship between the direction of ultrasound insoniﬁcation and the z- frequency component. axis location of the ROI at the different positions in the phantom. H. Chen et al. / Ultrasonics 49 (2009) 98–111 101

Frame Rate : 43.68 Hz Frame Rate : 43.68 Hz 0.03 1.5 0.02 1 0.01 0.5

0 0 Strain -0.5 -0.01 Displacement (mm) -1 -0.02

-1.5 -0.03 2 3 4 5 2 3 4 5 Time (s) Time (s)

Frame Rate : 21.84 Hz Frame Rate : 21.84 Hz 0.03 1.5 0.02 1 0.01 0.5

0 0 Strain -0.5 -0.01 Displacement (mm) -1 -0.02 -1.5 -0.03 2 3 4 5 2 3 4 5 Time (s) Time (s)

Frame Rate : 10.92 Hz Frame Rate : 10.92 Hz 0.03 1.5 0.02 1 0.01 0.5

0 0 Strain -0.5 -0.01 Displacement (mm) -1 -0.02 -1.5 -0.03 2 3 4 5 2 3 4 5 Time (s) Time (s)

Frame Rate : 5.46 Hz Frame Rate : 5.46 Hz 0.03 1.5 0.02 1

0.5 0.01

0 0 Strain -0.5 -0.01 Displacement (mm) -1 -0.02 -1.5 -0.03 2 3 4 5 2 3 4 5 Time (s) Time (s) Frame Rate : 2.18 Hz Frame Rate : 2.18 Hz 0.03 1.5 0.02 1

0.5 0.01

0 0 Strain -0.5 -0.01 Displacement (mm) -1 -0.02 -1.5 -0.03 2 3 4 5 2 3 4 5 Time (s) Time (s)

Fig. 5. The mean displacement (left) and strain (right) estimates along with the standard deviation plotted as errorbars for the 0.98 Hz cyclic compression frequency. The two curves correspond to the two ROI shown in Fig. 3. The ﬁgures from top to bottom denote results starting with a frame rate of 43.7, 10.9, 5.5 and 2.18 Hz respectively. The left column is the periodic displacement function. The right column is the periodic strain function. 102 H. Chen et al. / Ultrasonics 49 (2009) 98–111

Frame Rate : 43.68 Hz Frame Rate : 43.68 Hz 0.03 1.5 0.02 1 0.01 0.5

0 0 Strain

-0.5 -0.01 Displacement (mm) -1 -0.02

-1.5 -0.03 2 3 4 5 2 3 4 5 Time (s) Time (s)

Frame Rate : 21.84 Hz Frame Rate : 21.84 Hz 0.03 1.5 0.02 1

0.5 0.01

0 0 Strain -0.5 -0.01 Displacement (mm) -1 -0.02 -1.5 -0.03 2 3 4 5 2 3 4 5 Time (s) Time (s)

Frame Rate : 10.92 Hz Frame Rate : 10.92 Hz 0.03 1.5 0.02 1

0.5 0.01

0 0 Strain -0.5 -0.01 Displacement (mm) -1 -0.02 -1.5 -0.03 2 3 4 5 2 3 4 5 Time (s) Time (s)

Frame Rate : 5.46 Hz Frame Rate : 5.46 Hz 0.03 1.5 0.02 1

0.5 0.01

0 0 Strain -0.5 -0.01 Displacement (mm) -1 -0.02 -1.5 -0.03 2 3 4 5 2 3 4 5 Time (s) Time (s)

Frame Rate : 2.18 Hz Frame Rate : 2.18 Hz 0.03 1.5 0.02 1

0.5 0.01

0 0 Strain -0.5 -0.01 Displacement (mm) -1 -0.02 -1.5 -0.03 2 3 4 5 2 3 4 5 Time (s) Time (s)

Fig. 6. The mean displacement (left) and strain (right) estimates along with the standard deviation (STD) plotted as errorbars for the 1.67 Hz cyclic compression frequency. The two curves correspond to the two ROI shown in Fig. 3. The figures from top to bottom denote results starting with a frame rate of 43.7, 21.8, 10.9, 5.5 and 2.18 Hz respectively. The left column is the periodic displacement function. The right column is the periodic strain function. H. Chen et al. / Ultrasonics 49 (2009) 98–111 103 must be applied to tissue segments only a few mm thick. In fact, (x-axis) directions for two regions of interest (ROI) at different Righetti et al.[16], demonstrated that the ultimate axial resolution locations in the displacement image are indicated in Fig. 4. One in elastography is only limited by and directly proportional to the ROI is close to the geometric center of the image and the other is wavelength (i.e. inversely proportional to the fractional band- near the edge of the image. Phantom material within the ROI at width) of the ultrasound system. the edge of the image underwent greater lateral motion during To enable the use of small window lengths, we have developed compression than material in the ROI near the center because a pyramidal search algorithm [17] that utilizes multiple processing the phantom is not fixed at the sides, resulting in lateral expansion steps to carry out a coarse to fine displacement estimation. The during compression. coarse displacements are utilized to guide high resolution steps, Local strains were estimated using a least squares strain estima- where the final axial window lengths are on the order of 1–2 wave- tor applied to the displacement data [19]. Displacements and lengths. Both 1D [15] and 2D [17] cross-correlation based methods strains for both ROI’s marked on the displacement image were have been developed for linear array [15,17] and phased array tracked over the entire 175 frames (4 s) to evaluate the tracking transducers [18]. In this paper we utilized a 2D kernel for the TM accuracy for different cyclic compression frequencies. The two- phantom data and a hybrid 2D algorithm for in vivo data. The hy- step cross-correlation method was applied to each data set to track brid, cross-correlation based 2D search algorithm is combined with the z-axis displacement and strain within the ROI. a 2D surface fitting routine using phased array-grid co-ordinates Fig. 5 presents z-axis displacements and strains within the two [18] to provide fast, and precise displacement estimations. ROI’s for different frame rates with a cyclic compression frequency of 0.98 Hz. Displacement curves in both ROI’s demonstrate sinusoidal motion when tracked with the highest frame rate, 43.7 Hz. 3. Experimental TM phantom results However, as the frame rate is reduced to 10.9 Hz we observe devi- ations from the smooth displacement curves. The sinusoidal shape 3.1. Estimation of the compression frequency of the displacement curve is lost when the frame rate is reduced to 2.2 Hz. The local strain curves demonstrate a similar trend in that The analog controller on the compression system adjusts the for the lower frame rates the deformation pattern deviates from electric current to the variable speed DC motor to control the mo- the sinusoidal curve. The strain data appears noisier than the dis- tor speed and thereby the cyclic compression frequency. We utilized M-mode ultrasound data to obtain a precise measure of the cyclic compression frequency in our experiment. Prior to each RF data recording, M-mode data were also collected using the same 2.5 MHz phased array transducer, transmit focal properties and field of view discussed previously. We acquired M-mode data for an 80 mm depth at 634 A-lines per second. Each M-mode trace de- picts 5.73 s of data, which were stored in a personal computer for off-line analysis. Fig. 2a presents a sample M-mode trace acquired with a cyclic compression frequency of approximately 1 Hz. The high data rate obtained using M-mode traces enables precise com- putations of the cyclic compression frequency. The top of the phantom and transducer scanning window are fixed as shown in Fig. 1. Thus, shallow regions on the M-mode trace do not exhibit large displacements because the compression is applied from the bottom of the phantom. We used the M-mode data over a 3 cm to 8 cm range to measure the compression frequency during each experiment. The Fourier spectrum of each line of the M-mode data at a different depth was calculated after removing the DC component or detrending the data. Finally the power spectrum was obtained as an average of the individual Fourier spectra. Fig. 2b presents the normalized power spectrum for a frequency range of 0–2.5 Hz, exhibiting a peak at 1.4 Hz. The same procedure was used to compute other compression frequencies used in the experiment.

3.2. Displacement and strain estimation

A reference RF data frame was first selected near the center of the acquired 175 frame data loop. Displacement and strain images of the reference data frame with respect to the data frames imme- diately before and after this frame were then obtained using the two-step cross-correlation method [15]. The first correlation step used windows that have a 28 wavelength axial length, 7 A-lines in the lateral direction, and a 50% overlap. The second step used 75% overlapping windows with a 3 wavelength axial length and a 5 A-line width in the lateral direction. Strains along the z-axis, i.e., the direction of the applied compression, were computed for Fig. 7. Plots of the SNR variation in the averaged strain image over 2 compression both steps. e cycles versus the frame rate for different cyclic compression frequencies. The plots Fig. 3 presents an image depicting local z-axis displacements. present the a) mean SNRe value and the b) standard deviation of the SNRe from 10 The relationship between the acoustic scan lines and the z-axis independent data sets. 104 H. Chen et al. / Ultrasonics 49 (2009) 98–111 placement data, even for the highest frame rate, which is expected eral frame rates. In general the displacement data and the strain since the strain is obtained by computing the gradient of the dis- data demonstrate similar performance in the cyclic frequency esti- placement. The relative errorbars (standard deviation) on the mation. Larger cyclic compression frequencies require increased strain curves are therefore larger than those for the displacement frame rates in the RF data, as expected. We found that accurate curves. estimation of the cyclic compression frequency requires a frame Fig. 6 presents z-axis displacements and strains for the two rate that is on the order of two times the cyclic compression fre- ROI’s at different analysis frame rates for a cyclic compression frequency which forms the minimum requirement for both displace- quency of 1.67 Hz. For a given frame rate, the shapes of the dis- ment and strain imaging. placement and strain curves deviate more from a sine wave than those in Fig. 5. Displacement and strain introduced by increased 4. In vivo cardiac elastography results compression frequencies therefore require higher frame rates to accurately represent their sinusoidal characteristics. A hybrid 2D algorithm was utilized to compute strains for Quantitative evaluation of the performance of strain estima- in vivo data to avoid anticipated frame-to-frame signal decorrela- tions at different frame rates was obtained from a SNRe parameter. tion resulting from cardiac motion. For this algorithm, B-Mode im- The SNRe of averaged strain images over two compression cycles age data were used in an initial first cross-correlation step to was calculated from the ROI using SNRe =S1/r1 where S1 is the estimate coarse displacements. The analysis window size was 28 mean strain over the ROI and r1 is the standard deviation. Fig. 7 wavelengths (axial) by 7 A-lines (lateral), with a 50% overlap be- presents the (a) mean SNRe value and (b) standard deviation of tween successive windows. A second correlation step using 2 the SNRe vs. the frame rate for compression frequencies ranging wavelength 5 A-line windows having a 75% overlap provided from 1.26–4.08 Hz. Results in Fig. 7a demonstrates that frame rates fine displacement measurements. on the order of ten times the compression frequency provide con- sistent signal-to-noise ratio estimates, as illustrated in all four 4.1. Compensation for the drift in the displacement curves. When the frame rate is reduced or decimated to values lower than 10 times the compression frequency, the SNRe in the In order to calculate local strains within small ROI’s, it was nec- averaged strain image decreases. Note from Fig. 7b that the stan- essary to first accumulate local displacements over consecutive dard deviation is high at the lower frame rates and decreases as frames. However, as shown in Fig. 10a local displacement esti- the frame rate increases, similar to the trend shown by the mean mates exhibit a drift when taken over multiple cardiac cycles. This SNRe value in Fig. 7a. drift error was corrected [20] before the time-integration step uti- We also evaluated the lowest frame rate required for accurate lized prior to the application of the least squares estimation to ob- estimations of the cyclic compression frequency in the phantom tain local strain estimates. It was compensated for by assuming from displacement and strain data. This frequency was determined that at the end of each cardiac cycle, the heart wall should have from the spectrum of the displacement and strain data shown in zero accumulated displacement because the heart muscle should Figs. 5 and 6. Fig. 8 presents the estimated cyclic compression force return to its initial position and shape after a complete cardiac cy- frequency versus the actual cyclic compression frequency for sev- cle. Thus, using this boundary condition and assuming that the bias

(i) 3.5 Frame Rate 43.7 Hz 3.5 Frame Rate 43.7 Hz Frame Rate 21.8 Hz Frame Rate 21.8 Hz 3 Frame Rate 10.9 Hz 3 Frame Rate 10.9 Hz Frame Rate 5.5 Hz Frame Rate 5.5 Hz 2.5 Frame Rate 2.2 Hz 2.5 Frame Rate 2.2 Hz

2 2

1.5 1.5

1 1 Estimated Frequency (Hz) Estimated Frequency (Hz) 0.5 0.5

0 0 1 1.5 2 2.5 3 3.5 1 1.5 2 2.5 3 3.5 (a) Compression Frequency (Hz) (b) Compression Frequency (Hz)

(ii) 3.5 Frame Rate 43.7 Hz 3.5 Frame Rate 43.7 Hz Frame Rate 21.8 Hz Frame Rate 21.8 Hz 3 Frame Rate 10.9 Hz 3 Frame Rate 10.9 Hz Frame Rate 5.5 Hz Frame Rate 5.5 Hz 2.5 Frame Rate 2.2 Hz 2.5 Frame Rate 2.2 Hz

2 2

1.5 1.5

1 1 Estimated Frequency (Hz) Estimated Frequency (Hz) 0.5 0.5

0 0 1 1.5 2 2.5 3 3.5 1 1.5 2 2.5 3 3.5 (a) Compression Frequency (Hz) (b) Compression Frequency (Hz)

Fig. 8. The cyclic compression frequency estimated from the i) displacement for a) center ROI and b) ROI on the right and ii) strain curves for a) center ROI and b) ROI on the right versus the actual compression frequency for the different frame rates. H. Chen et al. / Ultrasonics 49 (2009) 98–111 105 introduced is not dependent on the heart wall position within the tal end of the myocardium) than for the ROI at the proximal or top heart cycle, the displacement drift can be accounted for within of the myocardium in Fig. 11a. Observe also the change in the each heart cycle, as illustrated in Fig. 10b. shape of the displacement curve and the small lag in the displacement between these two regions. In a similar manner Fig. 11b plots 4.2. Displacement and strain estimation the displacements for the ROI for the left and right regions of the myocardium indicated in Fig. 9. Here the displacements are of sim- Four ROI’s were selected within the short-axis B-mode images ilar magnitudes and appear to be in phase. of the heart to evaluate relative phases among their strain wave- The corresponding local strain curves are shown in Fig. 12a and forms and study effects of frame rate on these data. The ROI’s were b for the same ROI’s as in Fig. 11a and b. The local strain curves at the top, bottom, right and left regions within the myocardium, demonstrate a similar trend as the displacement data, such that depicted as the white regions in Fig. 9. Fig. 11 presents the esti- for the lower frame rates ﬁner details in the strain curves are lost. mates of the local displacement vs. time for each ROI. The curves Similar to that displayed on the displacement curves, two strain shown in Fig. 11a correspond to the ROI’s at the top and bottom peaks are observed in each cardiac cycle when the frame rate is of the B-mode image, while those shown in Fig. 11b correspond higher than 11.35 Hz, while the smaller strain peak is lost in some to the ROI’s in the left and right regions of the myocardium. The of the cardiac cycles when the frame rate is reduced to 8.52 Hz. Fi- displacements curves in Fig. 11 present the tracked motion of small nally, only one of the local strain peaks is observed in most cardiac sections of the heart wall. These are recorded using the full frame cycles when the frame rate is 6.81 Hz or lower. Observe that the lo- rate of 34.06 Hz, and decimated frame rates of 17.03, 11.35, 8.52, cal strain values are roughly the same for the ROI at the top and 6.81 and 5.68 Hz from the left to right and top to bottom respec- bottom of the myocardium (Fig. 12a) even though the local dis- tively. The heat rate was 0.92 Hz, estimated from the B-mode data. placements at the bottom ROI were signiﬁcantly lower than the Two displacement peaks can be observed over each cardiac cy- top ROI (Fig. 11a). However, note that the lag observed in the dis- cle for the highest frame rate (Fig. 11a and b). However, as the placement curves is also present in the local strain curves. In a sim- frame rate is reduced to 8.52 Hz, the smallest displacement peak ilar manner, the local strains in the ROI on the left and right regions partially disappears, and only one displacement peak remains of the myocardium are shown in Fig. 12b. Here the strain is roughly when the frame rate is reduced to 6.81 Hz or lower. Note also that the same and no lag is observed in either the displacement or the estimated displacement is lower for the ROI at the bottom (dis- strain curves (comparing Figs. 11b and Fig. 12b).

Fig. 9. B-mode cardiac image of the heart along a short-axis view (a), axial displacement (b) and the axial strain image (c). The displacements and strain in the heart wall are illustrated in the images. Four ROI’s are selected at the top, bottom, right and left as the white regions on the B-mode images. 106 H. Chen et al. / Ultrasonics 49 (2009) 98–111

muscle. In addition, we also present in vivo results acquired from short-axis displacement and strain images from a normal volunteer. Local displacements and strains were computed at different frame rates using a two-step 1D cross-correlation algorithm for the TM phantom data. Processing for the displacement and strain was performed starting at the highest frame rate provided by the system, and then decimating the frame rate by factors of 2 by leav- ing out one frame at a time. As expected, as the frame rate drops below the Nyquist sampling rate, the cyclic shape of compression curves are not reproduced in the displacement and strain data. Two parameters were measured after processing the RF data at the different frame rates. The ﬁrst parameter was the cyclic compression frequency from the displacement and strain data. Our results in Fig. 8, demonstrate that when the frame rate is greater than two times the compression frequency, an accurate estimate of the cyclic compression frequency is obtained from the displacement or strain data. The second parameter is related to the quality of the strain information obtained at the different frame rates, quantiﬁed

using the signal-to-noise ratio (SNRe) parameter. Fig. 7, shows that the maximum SNRe obtained is around 20 dB for both the 1.26 and 2 Hz compression frequencies at frame rates of 12 and 20 Hz respectively. However, for higher compression frequencies of 2.8

and 4 Hz the maximum SNRe obtained is around 16 dB for a 40 Hz frame rate. It was seen that the standard deviation of the

SNRe estimated converge as frame rate was increased (1.5– 1 dB) indicating that the precision of the results improves with the frame rate, as would be expected. Summarizing we ﬁnd that for frame rate that are 10 times the

cyclic compression frequency, the SNRe remains high and constant for the different cyclic compression frequencies. The SNRe decreases when the frame rate is reduced to be less than 10 times

the compression frequency, although the drop-off in the SNRe is not very large. Variations in the normalized cross-correlation coef- ﬁcient values were not presented as a quality measure, since the local strain between frames would also vary when we perform the frame rate decimation procedure. The correlation coefﬁcient would depend both on the local strain and the variation in the

frame rate. The SNRe estimate, therefore, provides the best indica- Fig. 10. The drift in the local displacement (a) for a small region-of-interest within tor of the performance of cardiac elastography under different the heart wall over several cardiac cycles. Compensated displacement curve frame rates. The variation in the SNR at different mechanical com- (b) using the physical boundary condition where the tissue displacement at the e ends of each cardiac cycle should be zero. pression frequencies, however, shows a significant drop-off with an increase in the cyclic compression frequency. This result is clearly observed for cyclic compression frequencies greater than 5. Discussion and conclusions 1.26 Hz. This is due to the increased generation of shear waves in the TM phantom with an increase in the cyclic compression fre- Strain and strain-rate imaging, as adjuncts to traditional echo- quency. This result was also verified using in vivo cardiac RF data cardiography, are developing into techniques that provide new from healthy volunteers. When the frame rate with in vivo cardiac information for evaluation of regional myocardial function. Clinical data is less than 10 times the heart beat, the displacement and diagnosis using echocardiography is based on visually assessed strain curves lose detail regarding the information of the move- wall motion scoring, which is semi quantitative and heavily depen- ment of the heart wall. dent on operator experience and expertise. Cardiac strain imaging The in vivo results on the local variations in the displacements methods using either tissue Doppler or elastography have been and strain estimates over small regions of interest are also pre- found to provide important diagnostic information for the mea- sented in this paper. These curves are very useful in depicting local surement and quantification of mechanical dyssynchrony in pa- variations in displacements and strain amplitudes and synchrony tients with advanced heart failure [21], and for patients with between small ROI in different sections of the myocardium. The myocardial infarction [8–11]. timing of the displacements and strains over the cardiac cycle In this paper we evaluate the ultrasound frame rate require- may also provide useful information, since certain types of cardio- ments for accurate estimation of tissue displacements and strain myopathies have significant abnormalities in timing of contraction in cardiac elastography. The frame rate as mentioned in the intro- that reduce ventricular performance that can be analyzed by these duction is one of the important issues related to the displacement techniques. and strain estimation performance in cardiac elastography. We uti- lize a uniformly elastic TM phantom that undergoes cyclic com- Acknowledgements pressions at compression frequencies ranging from 0.5 to 3.5 cycles/sec with a maximum deformation of 5% of the phantom This work is supported in part by a grant from the UW-Madison height simulating the compression and relaxation of the heart Graduate School. H. Chen et al. / Ultrasonics 49 (2009) 98–111 107

Fig. 11. Drift compensated axial displacement estimates within the four ROI’s within the heart wall with a heart beat rate of 0.92 Hz. The ﬁgures from the top to bottom and left to right denote displacement results obtained starting with a frame rate of 34.06, 17.03, 11.35, 8.52, 6.81 and 5.68 Hz respectively. The curves shown in (a) correspond to the ROI at the top (red ) and bottom (black ), while the curves shown in (b) correspond to ROI on the left (red ), and right (black ) of the short-axis B-mode image of the heart. (For interpretation of the references to colour in this ﬁgure legend, the reader is referred to the web version of this article.) 108 H. Chen et al. / Ultrasonics 49 (2009) 98–111

Fig. 11 (continued) H. Chen et al. / Ultrasonics 49 (2009) 98–111 109

Fig. 12. Drift compensated axial strain in the heart wall for the displacements plotted in Fig. 11. The heart beat rate is 0.92 Hz. The ﬁgures from the top to bottom and left to right denote local strain results obtained starting with a frame rate of 34.06, 17.03, 11.35, 8.52, 6.81 and 5.68 Hz respectively. The curves shown in (a) correspond to the ROI at the top (red ) and bottom (black ), while the curves shown in (b) correspond to ROI on the left (red ), and right (black ) of the short-axis B-mode image of the heart. (For interpretation of the references to colour in this ﬁgure legend, the reader is referred to the web version of this article.) 110 H. Chen et al. / Ultrasonics 49 (2009) 98–111

Fig. 12 (continued) H. Chen et al. / Ultrasonics 49 (2009) 98–111 111

Appendix A. Deﬁnition of strain and strain-rate References

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The strain tensors are to quantify dyssynchrony and predict response to cardiac resynchronization obtained from the gradient of the displacement at that point: therapy, Circulation 113 (7) (2006) 960–968. Epub 2006 Feb 13. [12] T. Varghese, J. Ophir, Characterization of elastographic noise using the envelope of echo signals, Ultrasound Med. Biol. 24 (4) (1998) 543–555. odz strainzðz; xÞ¼ezðz; xÞ¼ o ð3Þ [13] E.L. Madsen, J.A. Zagzebski, I.R. Medina, G.R. Frank, Performance testing of z transrectal US scanners, Radiology 190 (1) (1994) 77–80. od [14] J. Ophir, I. Cespedes, H. Ponnekanti, Y. Yazdi, X. Li, Elastography: a quantitative strain ðz; xÞ¼e ðz; xÞ¼ x ð4Þ x x ox method for imaging the elasticity of biological tissues, Ultrason Imaging 13 (2) (1991) 111–134. The unstressed length-based definition of strain, for example the [15] H. Chen, H. Shi, T. 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