Ultrasound Shear Wave Elasticity Imaging Quantifies Coronary Perfusion Pressure Effect on Cardiac Compliance

Abstract

Diastolic heart failure (DHF) is a major source of cardiac related morbidity and mortality in the world today. A major contributor to, or indicator of DHF is a change in cardiac compliance. Currently, there is no accepted clinical method to evaluate the compliance of cardiac tissue in diastolic dysfunction. Shear wave elasticity imaging (SWEI) is a novel ultrasound-based elastography technique that provides a measure of tissue stiffness. Coronary perfusion pressure affects cardiac stiffness during diastole; we sought to characterize the relationship between these two parameters using the SWEI technique. In this work, we demonstrate how changes in coronary perfusion pressure are reflected in a local SWEI measurement of stiffness during diastole. Eight Langendorff perfused isolated rabbit hearts were used in this study. Coronary perfusion pressure was changed in a randomized order (0–90 mmHg range) and SWEI measurements were recorded during diastole with each change. Coronary perfusion pressure and the SWEI measurement of stiffness had a positive linear correlation with the 95% confidence interval (CI) for the slope of 0.009–0.011 m/s/mmHg (R² = 0.88). Furthermore, shear modulus was linearly correlated to the coronary perfusion pressure with the 95% CI of this slope of 0.035–0.042 kPa/mmHg (R² = 0.83). In conclusion, diastolic SWEI measurements of stiffness can be used to characterize factors affecting cardiac compliance specifically the mechanical interaction (cross-talk) between perfusion pressure in the coronary vasculature and cardiac muscle. This relationship was found to be linear over the range of pressures tested.

I. Introduction

HEART failure (HF) is one of the leading causes of death in the world. HF is broadly divided into systolic and diastolic heart failure (SHF and DHF, respectively). DHF accounts for more than 50% of all heart failure [1]. In DHF, it is thought that myocardial damage affects the tissue mechanical properties and alters the compliance or stiffness of the cardiac tissue [2], [3]. DHF is difficult to diagnose because there is no widely accepted clinical method to evaluate the compliance of the cardiac tissue.

Physiological compliance refers to a mechanical property of organs that measures the tendency of the tissue to resist returning to its original state after an applied force is removed. In cardiac mechanics, compliance is defined as the change in volume divided by the change in pressure (dV/dP) during diastole. This definition or similar ones have been broadly used for cardiac compliance. For many years, pressure-volume (PV) loops were the only available measurement of cardiac compliance. This method, however, suffers from significant limitations. Recording PV loops, with the associated change in preload needed to measure compliance, requires an invasive pressure catheter, and the value measured is a global and indirect measure of cardiac compliance. These limitations have prevented the technique from becoming a routine clinical procedure.

Elasticity imaging (elastography) has grown in use in recent years and could provide a noninvasive measure of cardiac compliance. This technique can be thought of as a “virtual touch.” It enables physicians to palpate tissues remotely from outside the body. Elastography methods excite the tissue mechanically, and observe the response. These techniques have been reviewed in papers by Nightingale, Doherty et al., and Greenleaf et al. [4]–[6]. Shear wave elasticity imaging (SWEI) is a technique that can provide a quantitative measure of tissue stiffness [7]. Acoustic radiation force (ARF) is used as the mechanical excitation. A long ultrasound pulse is delivered to the tissue that results in shear waves propagating in directions perpendicular to the impulse. These waves are tracked as they propagate and their velocity calculated.

Myocardium is considered a nonlinear, viscoelastic and anisotropic material and calculating material properties from the speed of propagation is complex. In a simplified linear, isotropic and elastic medium, the speed of shear waves, C_t (m/s), can be related to the shear modulus, μ (kPa), and to Young's modulus, E (kPa), through the following equation, where ν is Poisson's ratio and ρ (Kg/m³) is the density of the tissue

$$C_{\mathrm{t}}=\sqrt{\frac{\mu }{\rho }}=\sqrt{\frac{E}{2(1+\nu )\rho }}.$$ (1)

Using shear wave imaging, it has been shown that the stiffness of the myocardium varies throughout the cardiac cycle [8]–[14]. During systole, the stiffness increases dramatically as the heart actively contracts. During this phase of the cycle, LV pressure and the active properties of the tissue are likely to dominate measurements of tissue stiffness. During diastole, as the heart relaxes, passive properties are likely to dominate. In late diastole, the preload (LA pressure) plays a significant role [8], [15]; The effect of coronary perfusion pressure on the cardiac stiffness can be more significant in early diastole, as the empty chamber begins to fill. When characterizing diastolic compliance with PV loops, typically the end diastolic pressure- volume relationship (EDPVR) is calculated at the end of diastole. Studying the cardiac stiffness throughout diastole has been challenging in the past, but can now be done with SWEI technique, as has been demonstrated in open-chest, intracardiac and transthoracic scanning configurations [12], [16], [17]. Panel A in Fig. 1 shows SWEI measurements of stiffness through the cardiac cycle in a Langendorff isolated rabbit heart. Panel B shows the simultaneous ECG signal.

Fig. 1.

Panel A shows SWEI measurements (35 Hz sampling rate) through the cardiac cycle in an isolated rabbit heart model. Panel B shows the ECG signal over the same time period. Right Panel: B-mode image of one of the isolated rabbit hearts. Thick-walled circular shape is the left ventricle and the thin wall at the bottom of the image is the right ventricular free wall. Probe is imaging from the top. Cyan rectangle is the region used to track the shear waves. Red arrow represents the axial push direction; the shear waves were tracked in lateral dimension as they propagated to the right as depicted by the yellow arrow.

In Pressure Volume loop measurements, diastolic chamber stiffness is defined as dP/dV (the reciprocal of compliance dV/dP) at end diastole. This corresponds to the slope of EDPVR, which is typically found by varying end-diastolic volume (Panel A, Fig. 2). Researchers have shown that the EDPVR is nonlinear and have typically fit the curve with an exponential function [18]. The derivative corresponding to chamber stiffness (dP/dV) is linear with respect to preload pressure changes as shown in the following formulas (Panel B, Fig. 2) [18]

$$P=A+B{e}^{\alpha V}$$ (2)

$$\frac{dP}{dV}=\alpha (P-A).$$ (3)

Fig. 2.

Panel A shows an example of pressure-volume loops and the exponential curve fit of the EDPVR relationship. Each PV loop is recorded at a different end-diastolic preload pressure. Panel B shows the linear relationship between stiffness defined as dP/dV (the derivative of the EDPVR curve) and intra-ventricular pressure.

Mirsky et al., using a spherical mechanical model of the heart, predicted that wall stiffness is a linear function of mid-wall stress, where E_m is the wall stiffness and σ_m is the mid-wall stress [19]

$$E_{\mathrm{m}}=K{\sigma }_{\mathrm{m}}+C.$$ (4)

The model assumed that late diastolic mid-wall stress is dominated by preload pressure. This model was verified by Kolipaka et al. by varying preload pressure in a spherical phantom and measuring the shear modulus of stiffness using a magnetic resonance elastography (MRE) technique [20].

The effect of perfusion pressure on tissue stiffness in liver [21], [22] and kidney [23] has been measured using elastography techniques and found to be linearly correlated. In the heart, it has been shown that an increase in coronary perfusion pressure shifts pressure-volume loops upward and to the left, indicating that the tissue has become stiffer or less compliant. This has been shown in isolated hearts, in in vivo animal and human experiments, and in isolated cardiac tissue using PV loops, indentation, and stress-strain measurements [24]–[29]. This phenomenon has been termed the “erectile,” “turgor,” “garden hose,” and “Salisbury” effect in the literature [25], [30]. Furthermore, this effect has been verified by mechanical modeling of cardiac vasculature and tissue using a porous model [31].

As discussed above, stiffness changes through the cardiac cycle are mainly a function of contraction, preload condition, and coronary vasculature. We predict that in the absence of contraction and preload effects (in a Langendorff preparation during diastole) coronary perfusion pressure will dominate the mid-wall stress. Therefore, we expect the stiffness of the heart in the Langendorff preparation measured by SWEI to be a linear function of the coronary perfusion pressure. In this study, we characterized the relationship between coronary perfusion pressure and SWEI and found a strong linear correlation between these variables. This finding suggests that changes in cardiac compliance are reflected in changes in ultrasound-measured cardiac stiffness, and that perfusion pressure is an important component of stiffness in the early phase of diastole.

As shown above, it is possible to calculate shear and Young's moduli from shear wave velocity. However, this calculation assumes that the tissue is linear, elastic, isotropic, and homogeneous. Clearly, cardiac tissue does not have these ideal characteristics. So technically we find it more correct to report shear wave velocity for these investigations. For this reason we have primarily reported SWEI in this paper. We included the final shear modulus results for comparison with other investigators' results. Although the calculated slope has units of pressure(kPa)/pressure(mmHg), (shear modulus /perfusion pressure), we did not convert the values to make a unit-less coefficient. This was done to emphasize that the slope is a relationship and not a ratio or fixed quantity.

II. Methods

A. Experimental Setup

Eight White New Zealand rabbits were used in this protocol with an average body weight of 3.93 ± 0.28 kg. The study was performed according to the Institutional Animal Care and Use Committee (IACUC) at Duke University and conformed to the Guide for the Care and Use of Laboratory Animals [32]. A Langendorff preparation was built using a combination of Radnoti (Radnoti LLC, Monrovia, CA, USA) glassware and several custom parts designed to make the preparation suitable for ultrasound imaging.

Tyrode solution was made fresh on the day of experiment. The solution was oxygenated by Carbogen (95% O₂ and 5% CO₂) to reach a pH in the range of 7.35–7.45 and oxygen saturation of 100% with partial pressure of (P_O2 > 300 mmHg). Calcium was added after oxygenation to prevent precipitation and the solution was filtered to 5 µm. O₂ saturation, pH and concentrations of Na, K, Ca were confirmed to be in the normal range before starting the experiment [33].

To prevent blood coagulation in the heart and coronary vasculature during the procedure, the rabbits were heparinized 2 min before anaesthesia. The rabbits were anaesthetized with an initial IM dose of Ketamine 35 mg/Kg and Xylazine 10 mg/Kg followed by IV doses of Ketamine from a 35 mg/Kg initial dose and then the 10 mg/Kg steps until the reflexes disappeared. A bilateral thoracotomy was performed and the heart isolated and placed immediately in Tyrode solution at 0 °C to 4 °C. The aorta was dissected, cannulated and the heart mounted on the Langendorff apparatus. The aorta was perfused retrogradely under constant flow conditions (25–35 mL/min, 70–80 mmHg), with the perfusate maintained at 37 °C to 38 °C with double walled tubing and a heated reservoir. The heart was allowed to beat at its intrinsic rate. A vent was placed in the left ventricle through the left atrium to prevent accumulation of fluid.

The heart and ultrasound transducer were submerged in a saline bath maintained at 37 °C to 38 °C. The bath was lined with sound absorbing material to reduce reflections. The ECG was acquired using electrodes placed in the bath in proximity to the heart. Perfusion pressure was measured using a fluid-filled pressure sensor and a bridge amplifier. Pressure, ECG and temperature data were continuously recorded using PowerLab/ Labchart data acquisition system (ADInstruments, Colorado Springs, CO, USA).

B. Imaging System

Imaging was performed using a Siemens Sonoline Antares ultrasound scanner (Siemens Healthcare, Ultrasound Business Unit, Mountain View, CA, USA). Acoustic Radiation Force impulses were used to induce shear waves. Imaging sequences were developed to record both SWEI and B-mode data. The push impulse was created using 300 cycles of 5.7 MHz excitation, and subsequent tissue tracking was made at 4.3 KHz Pulse Repetition Frequency (PRF). The transmit focus was set at 1.6 cm and a push F-number of 1.5 and tracking F-number of 2 were used. A VF10-5 linear array (192-element) ultrasound transducer was attached to an arm capable of rotating in different angles for imaging the desired locations of the heart. Hydrophone measurement of the peak negative and peak positive pressure of the push pulse yielded values of −4.5 to 10 MPa, respectively. As the shear wave propagates through a viscoelastic medium, its velocity can be affected by dispersion [13], [34]. We performed 2-D Fourier analysis of wave propagation at normal perfusion pressure in diastole. In all of the subjects, a bimodal peaked spectrum was observed. In two of the subjects, the higher frequency (around 390 Hz) peak had the highest amplitude. In the remainder of the subjects, the lower frequency peak (140–180 Hz) was dominant. The ultrasound probe was fixed to show a short axis view 10–15 mm from the epicardial surface of the left ventricular free wall. The probe remained stationary for the duration of the experiment. By maintaining a constant measurement location the effect of fiber orientation on shear wave velocity was minimized.

The Loupas phase estimation method was used to calculate the displacement [35]. Data was filtered by a quadratic motion filter to remove the heart's intrinsic motion [36]. The SWEI sequence was repeated at 35 Hz throughout the cardiac cycle for 1.2 s. The velocity of the shear wave was estimated using the Radon sum transformation algorithm discussed by Rouze et al. [37]. Data analysis was done on a Linux Cluster and using the MATLAB (The MathWorks, Natick, MA, USA) environment. Shear waves were tracked in the sub-epicardium for 5 mm in the lateral dimension (with 0.3 mm beam spacing) and 1 mm in the axial dimension. A typical tracked region is shown as the blue rectangle in the right panel of Fig. 1. A correlation calculation between 0.188 µs kernels of RF-echo data from two subsequent pulses was used to remove noisy data from the displacement estimation and the calculation of velocity. Average correlation coefficients were 0.9931 ± 0.0012. Measurements with a correlation coefficient less than 0.9000 were removed from the data. This happened on one occasion out of 88 acquired data sets. Shear waves are attenuated as they propagate through the tissue. The amount of attenuation depends upon several factors including the viscoelastic properties of the medium and the frequency of the shear waves. To provide an example, in one of the subjects, the shear wave amplitude decreased from 9.25 to 1.47 µm over 2.3 mm of lateral distance at 75 mmHg of coronary perfusion pressure in diastole. At zero perfusion pressure during diastole, the amplitude changed from 28.1 to 0.7 µm over 4.2 mm of lateral distance. The average peak shear wave amplitude for all the measurement steps was about 12 µm. Acquisitions that contained a premature ventricular contraction were dropped and the measurement repeated.

To measure the effect of coronary perfusion pressure on the stiffness of cardiac tissue, the perfusion system was set to constant pressure mode and a randomized pattern of perfusion pressure steps was established according to panel A, Fig. 3. All animals were subjected to this same sequence of steps, with each step lasting under 10 min. SWEI data measurements were taken as soon as possible after the change (typically around 1 min). The pressure was returned to normal (75 mmHg) between each tested step. The change in coronary perfusion pressure at each step was achieved by altering the height of the perfusion chamber. The ECG and an output signal indicating the timing of the SWEI imaging sequence were recorded by Labchart software.

Fig. 3.

Panel A: Randomized coronary perfusion pressure steps in mmHg. Each perfusion pressure step was achieved by changing the height of the perfusion chamber. After each step, perfusion pressure was returned back to normal. Panel B: Mean shear wave velocity in m/s measured in all rabbits at each step. Error bars show the average standard deviation of measurements at each step within all the subjects.

Late diastole was defined as the peak of the P-wave and the three SWEI frames acquired closest to this time were selected for analysis, these frames were designated at −29, 0, +29 ms [15]. Six unique SWEI measurements of stiffness were made over two beats at each pressure step in each animal. At the end of the experiment the hearts were perfused with Tetrazolium stain and dissected to check for infarcts.

The velocity data and the calculated Young's modulus from all of the subjects was pooled together and modeled with a multivariate linear regression. Shear wave velocity was modeled as a linear function of perfusion pressure, rabbit subject, measurement time with respect to the peak of the P-wave (−29, 0, +29 ms) and beat number (1 or 2). The last two variables were found to be not statistically significant (p > 0.5), so the model was reduced to use only perfusion pressure and rabbit subjects. Statistical analysis was done in MATLAB and R (R Foundation).

III. Results

Panel A in Fig. 3 shows the randomized perfusion pressure steps. Panel B of Fig. 3 shows the average shear wave velocity in m/s of all the isolated rabbit hearts at the corresponding pressure steps. The pattern shows that the shear wave velocity returned to near normal during the intervening normal pressure steps. The shear wave velocity measurements for each isolated heart at different pressure steps are shown in Figs. 4 and 5. For each rabbit, six measurements were recorded during diastole at each step. The slope of the linear regression and the R² value for each subject is reported on each plot.

Fig. 4.

Each panel shows the shear wave velocity in m/s versus perfusion pressure in isolated rabbit hearts one through four. “S” indicates the linear regression slope in m/s/mmHg. R² values are indicated on each plot.

Fig. 5.

Each panel shows the shear wave velocity in m/s versus perfusion pressure in isolated rabbit hearts five through eight. “S” indicates the linear regression slope in m/s/mmHg. R² values are indicated on each plot.

The multivariate linear regression model for all of the subjects pooled together showed a value of less than 0.05. The 95% Confidence Interval (CI) was calculated for the slope to be 0.009–0.011 m/s/mmHg with R² = 0.88. Panel B in Fig. 6 shows the predicted values of shear wave velocity from the statistical model versus the observed values of SWEI in all of the measurements. The 95% CI for the perfusion pressure versus shear modulus of stiffness in kPa for all of the rabbits based on the multivariate linear regression was found to be 0.035–0.042 kPa/mmHg with R² = 0.83.

Fig. 6.

Panel A: -axis shows the perfusion pressure steps and -axis shows the shear wave velocity and standard deviations in all rabbits at each step. Panel B: X-axis shows the predicted values from the multivariate linear regression model analysis. Variables were defined as subjects and perfusion pressure. -axis shows the shear wave velocity in m/s. Plot includes data from all hearts. The R² value for the linear model is 0.88.

In one subject, after the first sequence of pressure steps, a second set of measurements was taken with a different order of steps. Panel A in Fig. 7 shows the perfusion pressure steps and panel B shows the corresponding shear wave velocity in m/s. A linear regression of this data showed similar results with a slope of 0.011 m/s/mmHg with an R² = 0.88. In addition, in two subjects, the sequence of pressure steps was repeated and SWEI data was recorded. This was done to check for the repeatability of the measurements in a total of three subjects. The linear regression remained very close to the pooled results with a slope for these measurements of 0.011 m/s/mmHg and 0.010 m/s/mmHg with R² values of 0.75 and 0.96, respectively. These data are shown in panels C and D of Fig. 7.

Fig. 7.

Panel A: Randomized coronary perfusion pressure steps in mmHg with different order. Each perfusion pressure step was achieved by changing the height of the perfusion chamber. After each step, perfusion pressure was returned back to normal. Panel B: shear wave velocity in m/s versus perfusion pressure in mmHg in one isolated rabbit heart with the change in order of the steps shown in panel A. Panels C and D show shear wave velocity in m/s versus perfusion pressure in mmHg done for the second time in two isolated rabbit hearts. “S” indicates the linear regression slope in m/s/mmHg. R² values are indicated on each plot.

IV. Discussion

Our results indicate that as the coronary perfusion pressure increased, the SWEI measurement of stiffness increased indicating that the heart became stiffer. These results are similar to what other researchers have found in the heart using pressure- volume loop measurements [25]. In our experiments, shear wave velocity showed a strong linear correlation with coronary perfusion pressure. This relationship can be written as

$$C_{\mathrm{t}}=m\times P+n.$$ (5)

where “C_t” is the shear velocity, “m” is the slope of regression, “P” is the coronary perfusion pressure and “n” is the intercept at zero pressure. We propose that the C_t value at zero pressure (“n”) is the major cardiac tissue stiffness component excluding loading and contractility components, and can be used as an index of compliance. Using (1) and (5), we can derive the relationship between shear modulus and perfusion pressure

$$\mu ={(mP+n)}^2=mP(mP+2n)+n^2.$$ (6)

This equation predicts that shear modulus is a quadratic function of pressure. Since the value for the slope “m” (0.010 m/s) multiplied by pressure is several times smaller than the intercept value “n” (1.209 m/s) multiplied by 2, we can conclude that the quadratic term over the range of pressures tested is small. Hence, the relationship between shear modulus and pressure could be fit with a linear curve. In our results the mean R² value of linear regression for shear velocity versus pressure was found to be 0.88. This was very close to the mean R² value for shear modulus versus pressure, found to be 0.85. The difference between these two fits was not significant.

Allaart et al. developed a model of cardiac muscle to measure stiffness changes of the cardiac tissue at different perfusion pressures in rats [26]. Using the data in their paper, we extracted and calculated the slope of stiffness versus perfusion pressure in terms of shear modulus and also shear wave velocity to compare them with our results. The perfusion steps they used for their model were: 12, 37, 60, and 82 mmHg. Through the stress and strain curves, assuming a linear elastic isotropic model, we calculated the Young's modulus as the slope of the linear regression using the following formula:

$$\sigma =E\epsilon .$$ (7)

where “σ” is stress, “ε” is strain, and “E” is the Young's modulus. Shear modulus was calculated as E/3 and shear wave velocity as the square root of the shear modulus. Shear wave velocity was related to the perfusion pressure with a linear regression slope of 0.015 m/s/mmHg and R² of 0.95. These results are close to our results using the SWEI technique, and the small difference could be due to the difference in species.

Additionally, Livingston et al. evaluated the slope of stiffness versus coronary perfusion pressure in diastole in isolated canine cardiac tissue using indentation techniques. They found the slope equal to 0.007 g·mm⁻²/mmHg or 0.069 kPa/mmHg. As explained above, after dividing by 3, the shear modulus value is calculated as 0.023 kPa/mmHg [27]. This value for the slope is the same order of magnitude as the value we found in this experiment. The difference in slopes could come from the difference in species or preparations.

In this study, for the first time, we studied the garden hose effect with an elastography technique in cardiac tissue. This study demonstrated two important findings. First, it demonstrated that local measurements of tissue stiffness do reflect global factors of compliance; second, it demonstrated that this particular factor, coronary perfusion pressure, is reflected in diastole and that over an extended pressure range it correlates linearly with tissue stiffness.

This work shows the ability of SWEI to detect changes in cardiac compliance in response to changes in coronary perfusion pressure where coronary perfusion pressure serves as the known factor that changes cardiac stiffness. The measurements were obtained using ultrasound based excitation and imaging, requiring no cardiac interventions or independent mechanical excitation. The experiment was conducted in an isolated preparation under ideal imaging conditions; nonetheless, the results demonstrate that quantitative information about the compliance of the beating heart can be obtained using the SWEI technique. Using this technique, investigators could further characterize the factors affecting stiffness including pre-load, and after-load. By identifying the constituent components of the stiffness waveform, it may be possible to identify an independent component based on material properties alone. Such a material index would be important in the diagnosis of diseases that alter the material properties of the myocardium, including DHF.

The use of a Langendorff preparation for this study had several important benefits. First, the heart could be imaged from any desired angle and the left ventricular free wall was easily accessible. Second, the perfusion pressure of the coronary arteries could be adjusted easily and accurately. Third, the neuro-hormonal reflexes of the body, that could affect the compliance, were removed. One difference between the Langendorff perfused heart and a working or normal heart is that the ventricle does not fill. This helped us to isolate the effect of the coronary perfusion pressure on cardiac compliance independent of preload pressure. Coronary vascular space accounts for 10%–15% of the ventricular wall volume [25]. In a working heart, coronary perfusion pressure contribution to wall stiffness is expected to be dominant at the end of isovolumic relaxation. In the event of coronary occlusion, the perfusion pressure could drop from about 80 mmHg (aortic diastolic pressure) to near zero in the affected tissue, therefore, SWEI might be able to detect acute hypo-perfusion at the end of isovolumic relaxation.

One major concern was that the hypo-perfusion of the coronary vasculature would cause ischemia and affect the subsequent measurements. According to Apstein et al., the increase in cardiac compliance due to hypo-perfusion of coronaries is an acute phenomenon; but if the decrease in coronary perfusion is prolonged then the cardiac compliance starts to decrease. With coronary ligation, which causes a regional supply ischemia, a minimum of 6 h is needed for the cardiac compliance to reverse its pattern. This time is much shorter for global ischemia in isolated hearts. The reversal time varies across species; in rabbits the reversal time is about 30 min [25]. In all our measurements, we kept the hypo-perfusion time under 10 min. Additionally, to make sure that our procedure did not induce ischemia in the heart, we stained the heart with Tetrazolium. We also repeated the perfusion pressure steps a second time in two of the hearts with the same order of steps to investigate any possible effect on the relationship caused by transient hypo-perfusion. We were unable to measure a significant effect.

Another issue to consider is that in addition to shear waves, Lamb waves and surface waves could be produced in the myocardium depending on the tissue thickness, the wave frequency, the characteristics of the push and the location of measurements. Nenadic et al. investigated the relationship between the velocity of these waves and the factors affecting them and have shown that the velocity of Lamb-Rayleigh waves is related to the shear wave velocity. [38] We assume that the propagating waves in this experiment are shear waves. However, even if they are one of other types, the velocity results would remain valid. We believe this to be the case because our measurement location within the myocardial wall and the imaging parameters used were constant within each subject and were similar across subjects.

One of the complications in cardiac elastography measurements is the anisotropy of the cardiac tissue. It is well known that fiber orientation has a significant effect on mechanical wave propagation speed in cardiac tissue. Previous research has shown that cardiac shear wave velocity measurement varies through the depth of the cardiac wall between 0.4 to 2.5 m/s [10], [16], [39]. To minimize this effect, we fixed the probe at one location throughout the study and took measurements from the same location and with the same orientation of cardiac fibers in each experiment. The variance of SWEI measurements between subjects at a single pressure step could be due to slightly different fiber orientations in different subjects. As shown in panel A of Fig. 6, there is variation between the subjects at each perfusion pressure step. Fiber orientation differences were treated as a “between subjects” effect in the statistical model. The coefficients of variation at each step of: 0, 25, 50, 75, and 92 mmHg were: 0.219, 0.177, 0.191, 0.177, and 0.181 indicating a consistency in the fraction of variation at each step.

These variations are also seen in Table I that shows the average of the SWEI measurements at the normal perfusion pressure steps (75 mmHg) for each subject. We repeated the perfusion steps in three of the subjects for a second time (two of them with the same order and one with a different order of steps) as discussed in the methods and results section. The average shear wave velocity for each of these subjects, for the first and second measurements, at normal perfusion pressure steps, was respectively: (2.491 and 2.567), (1.588 and 1.835), and (2.196 and 2.187) m/s, which shows consistency across measurements in each rabbit due to the constant position of the probe. This suggests that the variations could be either due to subtle differences in fiber orientation for each subject or due to some other inherent characteristic of each subject. When we used just the perfusion pressure as the variable for our linear model, the value was reduced to 0.46. Thus, the absolute stiffness value varies by about 20% of the mean across animals at any one pressure: however we found the slope of the perfusion pressure versus velocity measurement curve across animals to be remarkably consistent. Further investigations are needed to understand the cause of the 20% variance in SWEI measurements.

TABLE I.

Mean and Standard Deviation of Shear Wave Velocity in (m/s) For All Normal Pressure Steps (at 75 mmHg) in Each Subject

	Subject 1	Subject 2	Subject 3	Subject 4	Subject 5	Subject 6	Subject 7	Subject 8
Velocity Mean (m/s)	1.821	2.613	2.007	2.034	2.491	1.470	1.558	2.196
Velocity SD (m/s)	0.179	0.140	0.159	0.216	0.100	0.084	0.140	0.259

V. Conclusion

SWEI has opened a door for cardiovascular researchers to measure the local mechanical properties of cardiac tissue precisely. This study shows promising results indicating that SWEI might be used to evaluate the compliance of the heart when it is damaged by various cardiac disorders including coronary artery diseases, diastolic heart failure, transplant rejection or cardiotoxicity caused by anti-cancer drugs. Moreover, SWEI stiffness measurements might be used to accurately investigate the mechanical physiology of the heart and the relative contributions of the coronary vasculature, the myocardium and extracellular tissue to the underlying mechanics.