Ultrasound frame rate requirements for cardiac elastography: … · 2008. 12. 5. · provide improved 2D strain information over that obtained from B-mode image data [12], provided

Ultrasonics 49 (2009) 98–111

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Ultrasonics

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Ultrasound frame rate requirements for cardiac elastography: Experimental andin 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, USAb Cardiovascular Medicine, UW Hospital and Clinics, University of Wisconsin-Madison, 1300 University Avenue, 1530 MSC, Madison, WI 53706, USAc Department of Electrical and Computer Engineering, University of Wisconsin-Madison, 1300 University Avenue, 1530 MSC, Madison, WI 53706, USA

a r t i c l e i n f o a b s t r a c t

Article history:Received 28 February 2008Received in revised form 15 May 2008Accepted 31 May 2008Available online 20 June 2008

Keywords:Cardiac imagingDisplacementEchocardiographyElastographyElastogramElasticityElasticity imagingStrainCardiac deformationUltrasound

0041-624X/$ - see front matter � 2008 Elsevier B.V.doi:10.1016/j.ultras.2008.05.007

* Corresponding author. Tel.: +1 608 265 8797; faxE-mail address: [email protected] (T. Varghese)

Cardiac elastography using radiofrequency echo signals can provide improved 2D strain informationcompared to B-mode image data, provided data are acquired at sufficient frame rates. In this paper,we evaluate ultrasound frame rate requirements for unbiased and robust estimation of tissue displace-ments and strain. Both tissue-mimicking phantoms under cyclic compressions at rates that mimic thecontractions of the heart and in vivo results are presented. Sinusoidal compressions were applied tothe phantom at frequencies ranging from 0.5 to 3.5 cycles/sec, with a maximum deformation of 5% ofthe phantom height. Local displacements and strains were estimated using both a two-step one-dimen-sional and hybrid two-dimensional cross-correlation method. Accuracy and repeatability of local strainswere assessed as a function of the ultrasound frame rate based on signal-to-noise ratio values.

The maximum signal-to-noise ratio obtained in a uniformly elastic phantom is 20 dB for both a 1.26 Hzand a 2 Hz compression frequency when the radiofrequency echo acquisition is at least 12 Hz and 20 Hzrespectively. However, for compression frequencies of 2.8 Hz and 4 Hz the maximum signal-to-noiseratio obtained is around 16 dB even for a 40 Hz frame rate. Our results indicate that unbiased estimationof displacements and strain require ultrasound frame rates greater than ten times the compression fre-quency, although a frame rate of about two times the compression frequency is sufficient to estimate thecompression 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 require-ment for elastography.

� 2008 Elsevier B.V. All rights reserved.

1. Introduction

Echocardiography has been routinely used for assessment of re-gional myocardial function, left ventricular size, and ventricularstructure since it provides real-time information, is portable, andis readily available. Conventional two-dimensional (2D) B-modeimaging along with M-mode recordings are well suited to defineglobal and regional functional changes in left ventricular perfor-mance. However, this type of analysis is limited because it providessemi-quantitative information on cardiac wall movement abnor-malities. As a consequence, there is considerable variation amonginterpreters of echocardiograms, limiting the usefulness of suchevaluations [1].

During systole short-axis echo images of the left ventricle (LV)show wall thickening in the radial direction and shortening inthe circumferential direction, while in the long-axis view thicken-

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ing is observed in the lateral direction and shortening is observedas the base moves towards the apex. Thickening and shortening ofthe wall muscle during the cardiac cycle may be characterized bylocal tissue displacements and accompanying wall strain, suggest-ing that strain imaging could be a very useful indicator of myocar-dial performance [2].

Doppler techniques, originally applied to analysis of blood flowacross valves, have evolved to provide information about globaland regional left ventricular and right ventricular performance. Tis-sue Doppler imaging (TDI), also called tissue velocity imaging, esti-mates local tissue velocities and tracks heart wall motion. [3,4]. TDIis most commonly derived from pulsed Doppler imaging of local-ized regions. Resultant signals may be displayed by color-codingand superimposing TDI velocity estimates on a B-scan image, sim-ilar to color-flow imaging. However, TDI does not differentiate be-tween active contraction and simple rotation or translation of theheart wall, nor does it differentiate passively following tissue fromactive contraction. Fleming et al. [5] used the spatial gradient of theTDI derived velocities to measure relative changes in wall thick-ness, or strain-rate (definitions of the strain and strain-rate are

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H. Chen et al. / Ultrasonics 49 (2009) 98–111 99

provided in Appendix A), to overcome this problem. However, asvelocities decrease toward the apex, the Doppler signal-to-noiseratio decreases, limiting TDI’s usefulness in the apical part of theventricle. Strain-rate plots using cross-correlation also have beenreported on M-mode data [6]. Strain and strain-rate measurementsbased on TDI have been compared to three-dimensional myocar-dial strain using tagged magnetic resonance imaging methods [7].

Because of limitations in Doppler-derived velocity and strainindices, there has been renewed interest in B-mode based strainand strain-rate measurements for assessing cardiac muscle perfor-mance [8–11]. B-mode based calculations of strain have the con-siderable advantage of not being directionally limited. Thus,limitations from Doppler imaging, such as an inability to differen-tiate between active contraction, simple rotation, and translationalmotion of the heart wall are no longer significant issues. Further-more, B-mode related techniques such as speckle tracking have al-lowed new strain methodologies to be used in the left ventricle.Local strain along the long-axis is now being estimated, along withrotational and radial indices of strain and strain-rate.

Both General Electric Medical Systems (GEMS) (GE Healthcare,Milwaukee, WI, USA) and Siemens (Siemens Ultrasound, MountainView, CA, USA) have introduced 2D speckle tracking for strainimaging on their cardiac ultrasound systems. GEMS’s strain imag-ing is based on processing ultrasound B-mode data loops. [8–10].Reisner et al. [10] utilized the entire U-shaped length of the LVto estimate global peak longitudinal strain (GLS) and strain-rate(GLSR) in 4 patients after myocardial infarction (MI) and 3 controls.Their results show that the average GLS and GLSR differ signifi-cantly between patients who have suffered myocardial infarction(MI) and normal control subjects. Korinek et al. [8] comparedstrains measured in vitro using sonomicrometry and in vivo usingthe GEMS EchoPAC software package. Becker et al. [9] collecteddata over 64 patients and showed that tracking strain and strain-rate using B-mode image data enables improved analysis of regio-nal systolic LV function. Their study provides an excellent analysisof regional strain for wall motion.

Cardiac elastography using radiofrequency echo signals canprovide improved 2D strain information over that obtained fromB-mode image data [12], provided data are acquired at sufficientframe rates. The frame rate of current medical ultrasound systems,though high, may not be sufficient to characterize the quasi-peri-odic compression, relaxation, and rotation of the myocardium dur-ing the cardiac cycle for unbiased and robust cardiac displacementand strain imaging.

In this paper, we present a relationship between the frame rateof an ultrasound system and the quality of computed strain imagesfor a uniformly elastic tissue-mimicking phantom undergoing cyc-lic compressions. Image quality is quantified using the strain sig-nal-to-noise ratio (SNRe) for various ratios of the compressionfrequency to the ultrasound system frame rate. In addition, dis-placement and strain estimates are obtained from in vivo strainimages for short-axis views of the heart. The relative phase be-tween strains measured in different locations of the myocardiumis determined as a function of ultrasound system frame rates,which is varied by skipping radiofrequency (RF) data frames forwhich strains are computed.

Fig. 1. Schematic diagram of the cyclic compression apparatus used to apply thesinusoidal compression force to the uniform TM phantom.

2. Materials and method

2.1. Cyclic compression system

Since LV wall movements and velocities during the cardiac cyclecan be assumed to vary in a quasi-periodic manner, a combined tis-sue-mimicking (TM) phantom and cyclic compression system wasdeveloped to evaluate tradeoffs between frame rate and strain

imaging performance. A TM phantom was subjected to cyclic com-pressions using the apparatus shown in Fig. 1. The phantom is sup-ported between two plates, which are mounted on cylindricalslides as shown in the figure. The top plate is held stationary butits location can be adjusted to accommodate different sized phan-toms. This plate has a fixture and a rectangular channel that holdsan ultrasound transducer. The transducer can be translated linearlywithin the channel. The bottom of the channel is sealed using apoly-methyl pentene (PMP) strip that is flush with the bottom sur-face of the plate. Madsen et al. [13] have described this materialand shown that ultrasound can be transmitted readily throughthe PMP material. This enables the use of a coupling medium suchas water or ultrasound gel within the translation channel.

The bottom compression plate is connected using ball bearingsto cylindrical slides to minimize friction during applied compres-sions. This plate is driven by a variable speed direct current (DC)motor (Cole-Parmer Instruments, Chicago IL) whose shaft rotatesbetween 1 and 10 cycles/s. The motor speed is adjusted using ananalog controller to vary the current. The shaft is connected tothe plate in a slightly eccentric manner, with multiple connectorsto enable the introduction of variations in the stroke amplitude.The moving compression plate supports the TM phantom and islarger than the phantom surface, providing a uniform compression.The phantom is placed in a small concave groove in the compres-sion plate to minimize horizontal slippage. The US transducerplaced on the top plate is utilized to collect RF data during com-pressions. In this study, echo data were acquired for differentstrain-rates by varying the amplitude and frequency of the cycliccompressions. The maximum compressional displacement appliedby the DC motor was approximately 4 mm. Compression frequen-cies in the range of 0.6 Hz to 4 Hz were used as these are similar tothe human heart beat frequency.

100 H. Chen et al. / Ultrasonics 49 (2009) 98–111

2.2. Tissue-Mimicking phantom and ultrasound system

The TM phantom has dimensions of 90 � 90 � 90 mm. TheYoung’s modulus of the TM material is 30 KPa as measured usingan ELF 3200 mechanical testing system (EnduraTEC, Minnetonka,MN)14. The ultrasound system is a GE Vingmed Vivid 7 Cardiovas-cular machine (GEMS Inc., USA), equipped with a 2.5 MHz phasedarray transducer having an approximate 60% bandwidth. A singletransmit focus was applied, set at a depth of 55 mm, and dynamicfocusing was used on receive. The maximum RF acquisition framerate for the 60 degree sector (95 A-lines per RF data frame) and80 cm depth setting utilized was 43.7 Hz or frames per second(FPS). Frame rates were effectively reduced by skipping framesduring analysis, yielding frame rates of 43.7, 21.8, 10.9, 5.5 and2.2 Hz respectively (downsampling by a factor of 2).

For each experiment, an initial pre-compression of 3% was ap-plied to the phantom to ensure proper contact between the topplate and the phantom surface. Then data were recorded as thephantom underwent cyclic compressions. RF data sets for 10 differ-ent compression frequencies, ranging from 0.9 to 3.5 Hz were ac-quired. Each resultant data set at a fixed compression rate anddisplacement amplitude contained 175 frames of RF data, Signalswere stored in a personal computer for off-line analysis.

Fig. 2. (a) M-mode image showing the periodic sinusoidal displacement of the TMphantom due to the cyclic compression force applied to the phantom. (b)Corresponding normalized power spectrum computed from the M-mode dataprovides the exact cyclic compression frequency estimated from the fundamentalfrequency component.

2.3. In vivo data acquisition

Five healthy volunteers were scanned with the GE Vingmed Vi-vid 7 Ultrasound system (GEMS Inc., USA), using the same 2.5 MHzphased array transducer. Both B-mode and radiofrequency dataalong the short-axis view at the mid papillary muscle level wereacquired with the patient lying on the left side, using the paraster-nal window to image the heart over several cardiac cycles. For thehuman data the transducer provided 114 A-lines over a RF dataframe covering a 75� sector angle. A single transmit focus wasagain applied, this time set at a depth of 100 mm. This system pro-duced RF data over a depth of 150 mm at a 20 MHz sampling rateand frame rate of 34.1 frames per second (FPS). In this case eachdata set contained 201 frames of RF data, which were stored in apersonal computer for off-line analysis. Data acquisition on humanvolunteers was performed at the University of Wisconsin-MadisonHospitals and Clinics, under a protocol approved by the UW-Mad-ison Institutional review board (IRB) for data acquisition on humansubjects. Each volunteer provided written consent to participate inthe study.

2.4. Multi step 2D cross-correlation algorithms

Normalized 1D cross-correlation analysis [14] is the most com-monly used method for measuring tissue displacements duringstrain imaging. The shift in the peak of the cross-correlation func-tion is utilized to track tissue deformation. However, for 1D strainestimations we require a window length of at least 10 wavelengths(independent of the transducer center frequency) to obtain unbi-ased and precise displacement and strain estimates [15]. This pre-cludes the use of smaller gated window lengths that would enableacceptable 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 thewhite boundaries are tracked over all the data frames to evaluate accuracy in thetracking of the displacement and strain due to the cyclic compression.

Fig. 4. Relationship between the direction of ultrasound insonification and the z-axis location of the ROI at the different positions in the phantom.

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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 twocurves 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 leftcolumn is the periodic displacement function. The right column is the periodic strain function.


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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 Hzrespectively. The left column is the periodic displacement function. The right column is the periodic strain function.



must be applied to tissue segments only a few mm thick. In fact,Righetti et al.[16], demonstrated that the ultimate axial resolutionin elastography is only limited by and directly proportional to thewavelength (i.e. inversely proportional to the fractional band-width) of the ultrasound system.

To enable the use of small window lengths, we have developeda pyramidal search algorithm [17] that utilizes multiple processingsteps to carry out a coarse to fine displacement estimation. Thecoarse displacements are utilized to guide high resolution steps,where the final axial window lengths are on the order of 1–2 wave-lengths. Both 1D [15] and 2D [17] cross-correlation based methodshave been developed for linear array [15,17] and phased arraytransducers [18]. In this paper we utilized a 2D kernel for the TMphantom data and a hybrid 2D algorithm for in vivo data. The hy-brid, cross-correlation based 2D search algorithm is combined witha 2D surface fitting routine using phased array-grid co-ordinates[18] to provide fast, and precise displacement estimations.

Fig. 7. Plots of the SNRe variation in the averaged strain image over 2 compressioncycles versus the frame rate for different cyclic compression frequencies. The plotspresent the a) mean SNRe value and the b) standard deviation of the SNRe from 10independent data sets.

3. Experimental TM phantom results

3.1. Estimation of the compression frequency

The analog controller on the compression system adjusts theelectric current to the variable speed DC motor to control the mo-tor speed and thereby the cyclic compression frequency. We uti-lized M-mode ultrasound data to obtain a precise measure of thecyclic compression frequency in our experiment. Prior to each RFdata recording, M-mode data were also collected using the same2.5 MHz phased array transducer, transmit focal properties andfield of view discussed previously. We acquired M-mode data foran 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 foroff-line analysis. Fig. 2a presents a sample M-mode trace acquiredwith a cyclic compression frequency of approximately 1 Hz. Thehigh 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 arefixed as shown in Fig. 1. Thus, shallow regions on the M-mode tracedo not exhibit large displacements because the compression is ap-plied from the bottom of the phantom. We used the M-mode dataover a 3 cm to 8 cm range to measure the compression frequencyduring each experiment. The Fourier spectrum of each line of theM-mode data at a different depth was calculated after removingthe DC component or detrending the data. Finally the power spec-trum was obtained as an average of the individual Fourier spectra.Fig. 2b presents the normalized power spectrum for a frequencyrange of 0–2.5 Hz, exhibiting a peak at 1.4 Hz. The same procedurewas used to compute other compression frequencies used in theexperiment.

3.2. Displacement and strain estimation

A reference RF data frame was first selected near the center ofthe acquired 175 frame data loop. Displacement and strain imagesof the reference data frame with respect to the data frames imme-diately before and after this frame were then obtained using thetwo-step cross-correlation method [15]. The first correlation stepused windows that have a 28 wavelength axial length, 7 A-linesin the lateral direction, and a 50% overlap. The second step used75% overlapping windows with a 3 wavelength axial length anda 5 A-line width in the lateral direction. Strains along the z-axis,i.e., the direction of the applied compression, were computed forboth steps.

Fig. 3 presents an image depicting local z-axis displacements.The relationship between the acoustic scan lines and the z-axis

(x-axis) directions for two regions of interest (ROI) at differentlocations in the displacement image are indicated in Fig. 4. OneROI is close to the geometric center of the image and the other isnear the edge of the image. Phantom material within the ROI atthe edge of the image underwent greater lateral motion duringcompression than material in the ROI near the center becausethe phantom is not fixed at the sides, resulting in lateral expansionduring compression.

Local strains were estimated using a least squares strain estima-tor applied to the displacement data [19]. Displacements andstrains for both ROI’s marked on the displacement image weretracked over the entire 175 frames (4 s) to evaluate the trackingaccuracy for different cyclic compression frequencies. The two-step cross-correlation method was applied to each data set to trackthe z-axis displacement and strain within the ROI.

Fig. 5 presents z-axis displacements and strains within the twoROI’s for different frame rates with a cyclic compression frequencyof 0.98 Hz. Displacement curves in both ROI’s demonstrate sinusoi-dal motion when tracked with the highest frame rate, 43.7 Hz.However, as the frame rate is reduced to 10.9 Hz we observe devi-ations from the smooth displacement curves. The sinusoidal shapeof the displacement curve is lost when the frame rate is reduced to2.2 Hz. The local strain curves demonstrate a similar trend in thatfor the lower frame rates the deformation pattern deviates fromthe sinusoidal curve. The strain data appears noisier than the dis-


placement data, even for the highest frame rate, which is expectedsince the strain is obtained by computing the gradient of the dis-placement. The relative errorbars (standard deviation) on thestrain curves are therefore larger than those for the displacementcurves.

Fig. 6 presents z-axis displacements and strains for the twoROI’s at different analysis frame rates for a cyclic compression fre-quency of 1.67 Hz. For a given frame rate, the shapes of the dis-placement and strain curves deviate more from a sine wave thanthose in Fig. 5. Displacement and strain introduced by increasedcompression frequencies therefore require higher frame rates toaccurately represent their sinusoidal characteristics.

Quantitative evaluation of the performance of strain estima-tions at different frame rates was obtained from a SNRe parameter.The SNRe of averaged strain images over two compression cycleswas calculated from the ROI using SNRe = S1/r1 where S1 is themean strain over the ROI and r1 is the standard deviation. Fig. 7presents the (a) mean SNRe value and (b) standard deviation ofthe SNRe vs. the frame rate for compression frequencies rangingfrom 1.26–4.08 Hz. Results in Fig. 7a demonstrates that frame rateson the order of ten times the compression frequency provide con-sistent signal-to-noise ratio estimates, as illustrated in all fourcurves. When the frame rate is reduced or decimated to valueslower than 10 times the compression frequency, the SNRe in theaveraged strain image decreases. Note from Fig. 7b that the stan-dard deviation is high at the lower frame rates and decreases asthe frame rate increases, similar to the trend shown by the meanSNRe value in Fig. 7a.

We also evaluated the lowest frame rate required for accurateestimations of the cyclic compression frequency in the phantomfrom displacement and strain data. This frequency was determinedfrom the spectrum of the displacement and strain data shown inFigs. 5 and 6. Fig. 8 presents the estimated cyclic compression forcefrequency versus the actual cyclic compression frequency for sev-

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eral frame rates. In general the displacement data and the straindata demonstrate similar performance in the cyclic frequency esti-mation. Larger cyclic compression frequencies require increasedframe rates in the RF data, as expected. We found that accurateestimation of the cyclic compression frequency requires a framerate that is on the order of two times the cyclic compression fre-quency which forms the minimum requirement for both displace-ment and strain imaging.

4. In vivo cardiac elastography results

A hybrid 2D algorithm was utilized to compute strains forin vivo data to avoid anticipated frame-to-frame signal decorrela-tion resulting from cardiac motion. For this algorithm, B-Mode im-age data were used in an initial first cross-correlation step toestimate coarse displacements. The analysis window size was 28wavelengths (axial) by 7 A-lines (lateral), with a 50% overlap be-tween successive windows. A second correlation step using 2wavelength � 5 A-line windows having a 75% overlap providedfine displacement measurements.

4.1. Compensation for the drift in the displacement

In order to calculate local strains within small ROI’s, it was nec-essary to first accumulate local displacements over consecutiveframes. However, as shown in Fig. 10a local displacement esti-mates exhibit a drift when taken over multiple cardiac cycles. Thisdrift error was corrected [20] before the time-integration step uti-lized prior to the application of the least squares estimation to ob-tain local strain estimates. It was compensated for by assumingthat at the end of each cardiac cycle, the heart wall should havezero accumulated displacement because the heart muscle shouldreturn to its initial position and shape after a complete cardiac cy-cle. Thus, using this boundary condition and assuming that the bias

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introduced is not dependent on the heart wall position within theheart cycle, the displacement drift can be accounted for withineach heart cycle, as illustrated in Fig. 10b.

4.2. Displacement and strain estimation

Four ROI’s were selected within the short-axis B-mode imagesof the heart to evaluate relative phases among their strain wave-forms and study effects of frame rate on these data. The ROI’s wereat the top, bottom, right and left regions within the myocardium,depicted as the white regions in Fig. 9. Fig. 11 presents the esti-mates of the local displacement vs. time for each ROI. The curvesshown in Fig. 11a correspond to the ROI’s at the top and bottomof the B-mode image, while those shown in Fig. 11b correspondto the ROI’s in the left and right regions of the myocardium. Thedisplacements curves in Fig. 11 present the tracked motion of smallsections of the heart wall. These are recorded using the full framerate of 34.06 Hz, and decimated frame rates of 17.03, 11.35, 8.52,6.81 and 5.68 Hz from the left to right and top to bottom respec-tively. The heat rate was 0.92 Hz, estimated from the B-mode data.

Two displacement peaks can be observed over each cardiac cy-cle for the highest frame rate (Fig. 11a and b). However, as theframe rate is reduced to 8.52 Hz, the smallest displacement peakpartially disappears, and only one displacement peak remainswhen the frame rate is reduced to 6.81 Hz or lower. Note also thatthe estimated displacement is lower for the ROI at the bottom (dis-

Fig. 9. B-mode cardiac image of the heart along a short-axis view (a), axial displacementillustrated in the images. Four ROI’s are selected at the top, bottom, right and left as the

tal end of the myocardium) than for the ROI at the proximal or topof the myocardium in Fig. 11a. Observe also the change in theshape of the displacement curve and the small lag in the displace-ment between these two regions. In a similar manner Fig. 11b plotsthe displacements for the ROI for the left and right regions of themyocardium indicated in Fig. 9. Here the displacements are of sim-ilar magnitudes and appear to be in phase.

The corresponding local strain curves are shown in Fig. 12a andb for the same ROI’s as in Fig. 11a and b. The local strain curvesdemonstrate a similar trend as the displacement data, such thatfor the lower frame rates finer details in the strain curves are lost.Similar to that displayed on the displacement curves, two strainpeaks are observed in each cardiac cycle when the frame rate ishigher than 11.35 Hz, while the smaller strain peak is lost in someof the cardiac cycles when the frame rate is reduced to 8.52 Hz. Fi-nally, only one of the local strain peaks is observed in most cardiaccycles when the frame rate is 6.81 Hz or lower. Observe that the lo-cal strain values are roughly the same for the ROI at the top andbottom of the myocardium (Fig. 12a) even though the local dis-placements at the bottom ROI were significantly lower than thetop ROI (Fig. 11a). However, note that the lag observed in the dis-placement curves is also present in the local strain curves. In a sim-ilar manner, the local strains in the ROI on the left and right regionsof the myocardium are shown in Fig. 12b. Here the strain is roughlythe same and no lag is observed in either the displacement orstrain curves (comparing Figs. 11b and Fig. 12b).

(b) and the axial strain image (c). The displacements and strain in the heart wall arewhite regions on the B-mode images.

Fig. 10. The drift in the local displacement (a) for a small region-of-interest withinthe heart wall over several cardiac cycles. Compensated displacement curve(b) using the physical boundary condition where the tissue displacement at theends of each cardiac cycle should be zero.


5. Discussion and conclusions

Strain and strain-rate imaging, as adjuncts to traditional echo-cardiography, are developing into techniques that provide newinformation for evaluation of regional myocardial function. Clinicaldiagnosis using echocardiography is based on visually assessedwall motion scoring, which is semi quantitative and heavily depen-dent on operator experience and expertise. Cardiac strain imagingmethods using either tissue Doppler or elastography have beenfound to provide important diagnostic information for the mea-surement and quantification of mechanical dyssynchrony in pa-tients with advanced heart failure [21], and for patients withmyocardial infarction [8–11].

In this paper we evaluate the ultrasound frame rate require-ments for accurate estimation of tissue displacements and strainin cardiac elastography. The frame rate as mentioned in the intro-duction is one of the important issues related to the displacementand strain estimation performance in cardiac elastography. We uti-lize a uniformly elastic TM phantom that undergoes cyclic com-pressions at compression frequencies ranging from 0.5 to 3.5cycles/sec with a maximum deformation of 5% of the phantomheight simulating the compression and relaxation of the heart

muscle. In addition, we also present in vivo results acquired fromshort-axis displacement and strain images from a normalvolunteer.

Local displacements and strains were computed at differentframe rates using a two-step 1D cross-correlation algorithm forthe TM phantom data. Processing for the displacement and strainwas performed starting at the highest frame rate provided by thesystem, 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 dropsbelow the Nyquist sampling rate, the cyclic shape of compressioncurves are not reproduced in the displacement and strain data.

Two parameters were measured after processing the RF data atthe different frame rates. The first parameter was the cyclic com-pression frequency from the displacement and strain data. Our re-sults in Fig. 8, demonstrate that when the frame rate is greater thantwo times the compression frequency, an accurate estimate of thecyclic compression frequency is obtained from the displacement orstrain data. The second parameter is related to the quality of thestrain information obtained at the different frame rates, quantifiedusing the signal-to-noise ratio (SNRe) parameter. Fig. 7, shows thatthe maximum SNRe obtained is around 20 dB for both the 1.26 and2 Hz compression frequencies at frame rates of 12 and 20 Hzrespectively. However, for higher compression frequencies of 2.8and 4 Hz the maximum SNRe obtained is around 16 dB for a40 Hz frame rate. It was seen that the standard deviation of theSNRe estimated converge as frame rate was increased (�1.5–1 dB) indicating that the precision of the results improves withthe frame rate, as would be expected.

Summarizing we find that for frame rate that are 10 times thecyclic compression frequency, the SNRe remains high and constantfor the different cyclic compression frequencies. The SNRe de-creases when the frame rate is reduced to be less than 10 timesthe compression frequency, although the drop-off in the SNRe isnot very large. Variations in the normalized cross-correlation coef-ficient values were not presented as a quality measure, since thelocal strain between frames would also vary when we performthe frame rate decimation procedure. The correlation coefficientwould depend both on the local strain and the variation in theframe rate. The SNRe estimate, therefore, provides the best indica-tor of the performance of cardiac elastography under differentframe rates. The variation in the SNRe at different mechanical com-pression frequencies, however, shows a significant drop-off withan increase in the cyclic compression frequency. This result isclearly observed for cyclic compression frequencies greater than1.26 Hz. This is due to the increased generation of shear waves inthe TM phantom with an increase in the cyclic compression fre-quency. This result was also verified using in vivo cardiac RF datafrom healthy volunteers. When the frame rate with in vivo cardiacdata is less than 10 times the heart beat, the displacement andstrain curves lose detail regarding the information of the move-ment of the heart wall.

The in vivo results on the local variations in the displacementsand strain estimates over small regions of interest are also pre-sented in this paper. These curves are very useful in depicting localvariations in displacements and strain amplitudes and synchronybetween small ROI in different sections of the myocardium. Thetiming of the displacements and strains over the cardiac cyclemay also provide useful information, since certain types of cardio-myopathies have significant abnormalities in timing of contractionthat reduce ventricular performance that can be analyzed by thesetechniques.

Acknowledgements

This work is supported in part by a grant from the UW-MadisonGraduate School.

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 andleft 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 tothe 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 ofthe heart. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)


Fig. 11 (continued)


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 toright 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 atthe 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.)


Fig. 12 (continued)



Appendix A. Definition of strain and strain-rate

Strain is defined as the deformation of an object, normalized toits original shape. The original shape could be an n-dimensionalsurface. For two-dimensional strain echocardiography, n is usuallyequal to 2. The deformation of the object could be caused by out-side compressional forces, but in cardiac strain imaging deforma-tion is caused by compression and relaxation of the cardiacmuscle. In most previous applications of elastography, linear arraytransducers were used and the ultrasound beam direction was ta-ken as the z-axis, while the x-axis denoted the orthogonal directionwithin the imaging plane. For a phased array transducer such asused in echocardiography, we specify the z-axis as the directionof the central beam line used to acquire the image.

Consider the deformation of an object, where L is the originallength of the object, and L0 is the length of the object after defor-mation. The z-axis strain that describes the relative deformationis defined as:

strainz ¼ ez ¼L� L0

L0ð1Þ

When continuous, sequential deformation processes are known, theinstantaneous strain during the deformation process can be definedas:

strainzðtÞ ¼ ezðtÞ ¼LðtÞ � L0ðtÞ

L0ðtÞð2Þ

The point O in space is observed using an ultrasound transducer asshown in Fig. 1. The medium at this point undergoes an actual dis-placement, specified by vector �d. The displacement vector �d con-tains two orthogonal components dz and dx. The strain tensors areobtained from the gradient of the displacement at that point:

strainzðz; xÞ ¼ ezðz; xÞ ¼odz

ozð3Þ

strainxðz; xÞ ¼ exðz; xÞ ¼odx

oxð4Þ

The unstressed length-based definition of strain, for example theinformation utilized in echocardiography, is also called theLagrangian strain [22]. For a two-dimensional object the deforma-tion is not limited to lengthening (positive strain) or shortening(negative strain) in one direction, referred to as normal strains,but also shearing strain due to deformation or motion parallel tothe body of the object. Therefore all four strain components haveto be known to completely characterize the deformation of a 2D ob-ject. This deformation can be written in matrix form, referred to as astrain tensor matrix, for an object in the x–y co-ordinate system as:

ez ezx

exz ex

� �ð5Þ

where ez = Dz/z, ex = Dx/x, ezx = Dz/x and exz = Dx/z, where the differ-ent component are identified by their indices.

The strain-rate (SR) measures the time course of deformation,and this is the primary parameter of deformation that is derivedfrom tissue Doppler imaging. Strain-rate is used to describe thespeed at which deformation occurs, and is given by:

strain ratez ¼ez

Tð6Þ

where T is the period over which the deformation occurs.

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