Simultaneous Myocardial Strain and Dark-Blood Perfusion Imaging Using a Displacement-Encoded MRI Pulse Sequence

Abstract

The purpose of this study is to develop and evaluate a displacement-encoded pulse sequence for simultaneous perfusion and strain imaging.

Displacement-encoded images in 2–3 myocardial slices were repeatedly acquired using a single shot pulse sequence for 3 to 4 minutes, which covers a bolus infusion of Gd. The magnitudes of the images were T₁ weighted and provided quantitative measures of perfusion, while the phase maps yielded strain measurements. In an acute coronary occlusion swine protocol (n=9), segmental perfusion measurements were validated against microsphere reference standard with a linear regression (slope 0.986, R² = 0.765, Bland-Altman standard deviation = 0.15 ml/min/g). In a group of ST-elevation myocardial infarction(STEMI) patients (n=11), the scan success rate was 76%. Short-term contrast washout rate and perfusion are highly correlated (R²=0.72), and the pixel-wise relationship between circumferential strain and perfusion was better described with a sigmoidal Hill curve than linear functions.

This study demonstrates the feasibility of measuring strain and perfusion from a single set of images.

Introduction

Regional contractile function and perfusion are two key indices in the diagnosis and prognosis of ischemic heart disease. Magnetic resonance imaging can accurately assess myocardial wall motion and strain through several techniques including tagged MRI(1–4), velocity-encoded MRI(5) and displacement-encoded MRI(6–8). Contrast-enhanced imaging, including first-pass(9–15) and delayed hyper-enhancement (DHE) MRI(16–21), provide information on the perfusion and viability status of the myocardial tissue. Whether the clinical situation is to assess the efficacy of reperfusion strategy with greater accuracy or to recognize patients that would require further therapy, the knowledge of both regional myocardial function and perfusion is helpful in differentiating among the various scenarios.

An MRI pulse sequence capable of measuring myocardial perfusion and strain in a single data set, which thus far has not been generally possible in humans, would save scan time and facilitate perfusion-function correlation by eliminating the problem of registration. Imaging techniques that combine myocardial strain and DHE imaging have been reported by several groups(22,23). However, these techniques employed interleaved acquisition of multiple images, which are combined into single strain and DHE images; therefore they are not suited for first-pass perfusion imaging due to the time constraints.

The purpose of this study is to develop a pulse sequence for simultaneous perfusion and strain imaging, to validate the perfusion measurement in a swine model, and to assess its performance in a group of acute myocardial-infarction patients.

The pulse sequence is a single-shot, multi-slice displacement-encoded (DENSE)(7) sequence. It was used to collect displacement-encoded images in every other heartbeat over several minutes covering the first-pass and initial washout of the contrast agent(24,25). An arterial input function (AIF) slice was acquired concurrently. This approach differs from current saturation-recovery perfusion sequences in that the DENSE images are positively T₁ weighted, meaning that the signal intensity decreases with shortened T₁. As a result, the myocardial tissue that receives the contrast agent becomes dark, while the ischemic segments remain bright. Additionally, the ventricular cavities are dark due to rapid blood flow and high contrast agent concentration(7).

Methods

Animal Protocol

The protocol was approved by NIH Animal Care and Use Committee. Yorkshire farm pigs (n = 9, weight 28–86 kg, all males) were maintained under anesthesia with isoflurane (2–3%) and monitored by their heart rate, blood pressure and pCO₂ level during the entire experiment. In 6 pigs left side thoracotomy exposed either the LAD or LCX arteries and these were ligated to effect total occlusion. One co-author is an interventional cardiologist and was available to perform percutaneous LAD occlusion with balloon occluders in the other 3 pigs. MR imaging was performed immediately after the occlusion, followed by the injection of fluorescent microspheres (NuFlow®, IMT Laboratories, Irvine, CA, USA or FluoSpheres®, Invitrogen, Carlsbad, CA, USA) into the left atrium. Concurrent arterial blood samples were taken from the femoral artery for calibration of the microsphere counts. The animal was then euthanized and the heart was excised and embedded in agarose gel. The gelled samples were oriented in accordance with the MRI short-axis scan planes in vivo using a two-axis gimbal mount(26). Five of the nine hearts were sliced into 4–5 mm slices, sectioned into tissue samples according to the American Heart Association (AHA) segmentation scheme(27) and sent to IMT (Irvine, CA, USA) for flow measurement. The rest four hearts were sent to Barlow Scientific (Olympia, WA, USA) for 3D microsphere imaging and flow measurement.

Patients

Between April, 2, 2008 and July, 18, 2008, 13 patients who presented with first acute ST-elevation myocardial infarction (STEMI) (11 men, 2 women, age range 39–82) were recruited as part of a Health Insurance Portability and Accountability Act (HIPAA)–compliant Institutional Review Board–approved protocol. Inclusion criteria were presence of a complete occlusion (TIMI 0) of a single culprit coronary artery, successful angioplasty with a patent infarct-related artery with a final TIMI of 3 (within 6 hours of symptom onset), and presence of no-reflow segments in the myocardial wall based on DHE images. MRI was performed at 2 days after angioplasty. Informed consent was given by all patients. The data from two patients were excluded due to failure of ECG triggering (a 52-year-old male) and misplacement of the AIF slice (a 67-year-old female), respectively (Fig. 1). In our institution the cardiac patients that were most available for this study were STEMI post-angioplasty patients who were stable enough to allow an MRI evaluation of the reperfusion treatment. In these patients cardiac MRI exam provided comprehensive and high quality prognostic information.

Figure 1.

Patient flow chart.

MRI protocol

All MR scans were performed on a clinical 1.5T scanner (Siemens MAGNETOM Avanto, Erlangen, Germany). Three to four short-axis slices were acquired in every other heartbeat and repeated 90 times (3 encoding directions ×30 repetitions) over a period of 3 to 4 minutes or 180 hearts beat. The imaging sequence (Fig. 2) was a multi-slice single-shot DENSE sequence(7) with true-FISP readout (6,28,29) detailed below.

Figure 2.

Pulse sequence and ECG triggering scheme. The displacement-encoding section starts immediately after the QRS trigger. This is then followed by the single-shot acquisition of the arterial-input-function slice using an fGRE readout. Starting at 150 ms after the encoding segment, the 3 DENSE slices are acquired sequentially using single-shot ramped-flip angle true-FISP readout. Each slice takes 100 ms to acquire. At the very end of the exam, a proton-density reference for the AIF slice was acquired by turning off the displacement-encoding segment.

The three displacement-encoding gradients were combinations of in-plane and through-slice moments of Y+Z, −Y+Z and X+Z respectively, where X, Y and Z are the readout, phase-encode and through-slice directions(28). The same through-slice encoding moment was applied to all three images while the in-plane encoding gradients varied amongst them. The uniform through-slice encoding served to suppress the unwanted T1 recovery and conjugate echoes in all 3 images. In post-processing the three phase maps were linearly recombined to produce X by 2(X+Z)−(Y+Z)−(−Y+Z) and Y by (Y+Z)−(−Y+Z) encoded phase maps and remove any phase errors from off-resonance, RF and other systematic factors(28). The X and Y encoding moments were 0.38 rad/mm in pigs and 0.27 rad/mm in patients. The Z encoding moment was 4.8 radians per slice thickness. This value was found to be sufficient to suppress the free induction decay (FID) and conjugate echo signals(8,30). Additionally the uniform through-slice encoding moment meant that the image intensity would not be affected by the encoding directions, and only varied with the influx of the contrast agent.

Other imaging parameters included tFISP echo spacing of 2.5 ms, matrix size of 128 × 40 with inner-volume excitation equivalent to 128 × 96 and 3/4 phase-encode FOV, in-plane resolution of 2.5 mm in pigs and 3.5 mm in patients, and slice thickness of 6–8 mm. Ramped-flip-angle (30°–75°)readout(31) was also implemented to equalize the echo train amplitude.

Figure 2 shows the events in a heartbeat: the displacement-encoding segment was placed immediately after the QRS trigger, followed by the acquisition of the saturation-recovery arterial-input-function image, and then sequential acquisitions of the 2 to 3 displacement-encoded slices. The AIF slice was positioned at the LV base and acquired with fast gradient-recalled-echo (fGRE) readout of TE of 1.2ms without refocusing the displacement-encoding moments. The DENSE slices were positioned to cover the territory of the occluded artery. At the end of an exam a proton-density image of the AIF slice was also acquired for the purpose of calibration.

The saturation-recovery time of the AIF slice was 50 ms. The mixing time (T₁ weighting) of the DENSE slices were from 200 ms for the first slice to 400 ms for the third slice. The acquisition time of each slice was 100 ms. In all, a data set contained 270–360 images of 3–4(slices) × 3(encoding directions) × 30(repetitions). At 30 seconds after the start of scan, Gd contrast was given intravenously at a dose of 0.1 mmol/kg and a rate of 2.0 ml/sec in the pigs, and at a higher infusion rate of 4.0 ml/sec in patients. The different infusion rates were scaled according to the total amount of contrast. The swine study was carried out in the US and used Gd-DTPA (Magnevist, Bayer HealthCare Pharmaceuticals Inc. Wayne, NJ). The patient study was performed in Lyon, France where Gd-DOTA was the standard contrast agent and used in the study.

Image processing

All DENSE images were warp-registered to correct for respiratory motion(32–34). Perfusion and circumferential strain maps were obtained from the magnitude and phase of the DENSE images, respectively. Circumferential strain was calculated from each set of three encoding directions using a software running in Windows or MAC operating systems (DENSEView)(28). The 30 repetitions yielded 30 strain measurements, and the final strain map was the SNR-weighted average of the 30 measurements(35):

$$\begin{array}{l}\mathit{Ecc}(x,y)=\frac{{\displaystyle \sum _{n=1}^{30}}\left[{\mathit{Ecc}}_n(x,y)I_n^2(x,y)\right]}{{\displaystyle \sum _{n=1}^{30}}{I}_n^2(x,y)},\\ I_n(x,y)=I_{n,1}(x,y)I_{n,2}(x,y)I_{n,3}(x,y),\end{array}$$ (1)

where Ecc(x,y) is final strain value at each location (x,y), Ecc_n(x,y) is the strain calculated using the nth set of images, I_n,1(x,y), I_n,2(x,y) and I_n,3(x,y) are the three images of different encoding directions in the nth image set.

AIF image intensity in the descending aorta or the LV cavity was used to derive the arterial contrast concentration(36,37). Time intensity data of the myocardial pixels were then converted to absolute perfusion F and short-term washout rate k through a Fermi function-based deconvolution using the Marquardt–Levenberg algorithm(10,15). This is detailed in the Appendix A.

The effect of image noise on the perfusion accuracy was investigated with Monte Carlo simulations and described in Appendix B. The results showed that at the current sampling rate of one image every 2 sec, noise levels below 15% of the pre-contrast intensity gave acceptable accuracy in perfusion estimates. This was used as the threshold to exclude highly noisy pixels. The method to estimate the noise level in each pixel is also detailed in Appendix B.

Perfusion measurement validation

DENSE myocardial strain measurements have been validated in other studies. DENSE strain maps acquired during breath-holding has been validated in normal volunteers(38,39). In patients, detection of abnormal wall motion by breath-hold DENSE has been validated against 2D echocardiography (28). Free-breathing data acquisition followed by warp image registration was validated in a normal volunteer study (34). Our swine study focused on the accuracy of the perfusion measurement against microsphere reference standards. The MRI perfusion maps were segmented according to AHA recommendation(27), then MRI and microsphere segmental perfusion values were compared using linear regression and Bland-Altman analysis.

Success rate and image quality in patients

In each patient the DENSE slices were visually scored by one author as ‘0 = failure’, ‘1 = good’ and ‘2 = excellent’ according to the following criteria: a slice containing signal drop-outs in the myocardial wall or apparent errors in image registration due to through-slice motion or other reasons is a failure; a slice that has no signal drop-outs or apparent image registration errors is considered good; a slice that has high signal-to-noise ratio and none of the above errors is rated excellent. The average success rate in all patients and the average score of all successful slices were calculated. The reasons for failures were investigated.

Correlation of short-term contrast washout rate and systolic strain with perfusion

Since the strain, perfusion and washout rate maps came from the same images they were inherently perfectly matched. This allows pixel-by-pixel correlation of different measurements. Pixels in the LV myocardial wall of the successful slices in all patients were pooled for linear regression between perfusion and contrast washout rate.

Similarly pixel values of circumferential strain and perfusion were correlated using linear regression. Here it became necessary to exclude the last one of the three DENSE slices. The reason is that the three slices were acquired at delays of 200 ms, 300 ms and 400 ms after the R-wave trigger, which means that the last slice was outside the end-systole plateau and did not provide end-systolic strain. Strain values in the first two slices were plotted against both the absolute perfusion and the normalized perfusion defined in each patient as the ratio of absolute perfusion over the average of the remote normal area. Since a previous study showed that the relationship between strain and perfusion may be better described by sigmoidal curves(40), both linear and sigmoidal Hill curves were used to fit the strain-perfusion data.

Statistical Analysis

The statistical analysis was performed using Microsoft Excel (Microsoft Corporation) and JMP (SAS Institute Inc.). All numerical results below are presented as mean with 95% confidence interval (CI) unless specified otherwise. Quality of curve fittings was evaluated by their Pearson correlation coefficient (R²) values. Significance of linear regression was assessed with the F-test. Significance of difference between two measurements was assessed with Wilcoxon signed rank test without assuming normal distribution.

Results

Signal intensity curve in DENSE images

Figure 3 shows the image time-intensity curves in normal and ischemic myocardium in a DENSE slice as well as the LV blood pool in the saturation-recovery AIF slice. It can be seen that the intensity of the ischemic segments decreased less than that of the normal segments upon contrast infusion, thereby appearing bright immediately after infusion. The perfusion, strain and washout rate maps of a patient are shown in Fig. 4. The low perfusion areas apparently match the areas of low strain and low washout rate.

Figure 3.

Signal time-intensity curves in a pig heart. (a) Intensity of the LV blood pool in the saturation-recovery AIF image. (b) Intensity of the myocardium in a DENSE slice after Gd infusion. Arrow points to the ischemic segment. Due to the positive T₁ contrast of the image, normally perfused tissue became dark upon contrast arrival while ischemic tissue retained its brightness. Ventricular cavities are dark due to rapid blood flow and high contrast concentration.

Figure 4.

The perfusion, strain and short-term washout rate maps of a patient. (a, b) The perfusion maps in units of ml/min/g; (c, d) Corresponding circumferential strain maps. (e, f) Corresponding short-term contrast washout rate maps in units of s⁻¹.

Perfusion measurement validation

MR perfusion maps and fluorescence microsphere images from a pig heart are shown in Fig. 5. It can be seen that areas of low fluorescence in Fig. 5c and 5d are matched with low MR perfusion in Fig. 5a and 5b. The regression between segmental MRI and microsphere perfusion values of all pigs is shown in Fig. 6. The correlation between the two is R² = 0.765 (P <0.01). The slope is 0.986 (95% CI = [0.88, 1.09]). The intersection is 0.058 (95% CI = [−0.0047, 0.12]), which is not significantly different from zero (P = 0.07).

Figure 5.

(a, b) MRI perfusion maps of the basal and mid-level slices of a pig heart in units of ml/min/g. (c, d) Epi-fluorescence images of the microsphere distribution in the same slices.

Figure 6.

Segment-by-segment regression of perfusion measured by DENSE vs. regional blood flow by microspheres for all pigs. The teal lines show the 95% prediction limit, the lime lines show the 95% confidence limit of the regression.

Figure 7 shows the Bland-Altman plot for the same comparison. The standard deviation of the difference between the two measurements is ±0.15 ml/min/g. The average of the difference is 0.05 ml/min/g, which is statistically not significant by Wilcoxon signed rank test (P = 0.19). The overall range of perfusion was from 0 to 1.2 ml/min/g.

Figure 7.

Bland-Altman plot of perfusion measurement comparison of MR and microspheres. The mean difference (teal line) was 0.05 ml/min/g. The standard deviation of the difference is ±0.15 ml/min/g.

Success rate and image quality assessment in patients

Among all 33 DENSE slices of the 11 patients, 8 slices were deemed failures. These included 1 due to signal drop-outs, and 7 due to errors in image registration. The success rate was 76%, and the average score in successful slices was 1.44, or midway between good and excellent.

Correlation of short-term contrast washout rate and systolic strain with perfusion

Figure 8 shows that the short-term contrast washout rate was strongly correlated with absolute perfusion in patients with R²=0.726 (P<0.01). The slope of linear regression was 0.0336 (95% CI =[0.0324, 0.0348]).

Figure 8.

Correlation of short-term washout rate vs. perfusion in STEMI patients.

Figure 9 shows the strain vs. absolute perfusion data and curve fittings. The sigmoidal Hill fitting yielded a higher correlation (R² = 0.211) than linear regression (R²=0.164, P<0.01). Strain was better correlated with normalized perfusion than absolute perfusion in both linear regression (R²=0.288, P<0.01) and sigmoidal fitting (R²=0.308) (Fig. 10).

Figure 9.

Correlation of circumferential strain vs. perfusion in STEMI patients. Sigmoidal Hill curve fitting (red line) gives higher correlation coefficient than linear regression (black line).

Figure 10.

Correlation of circumferential strain vs. normalized perfusion in STEMI patients. The sigmoidal Hill curve fits the data better than linear function.

The perfusion and circumferential strain from the pig study yielded somewhat higher correlation with R² = 0.496. The normalized perfusion and circumferential strain had a correlation coefficient R² = 0.493.

Discussion and Conclusions

In this study we developed a modified displacement-encoded MRI sequence and demonstrated its ability to measure myocardial perfusion and strain simultaneously. The absolute perfusion measurements matched well with the reference standard microsphere measurements in light of prior validation studies of saturation recovery sequences. For example, in one of the first swine hyperemia studies using a saturation recovery TurboFLASH sequence(11) the correlation between MRI relative perfusion index and microsphere absolute perfusion was R²=0.77 over the flow range of 0 to 4.1 ml/min/g; A later canine study using a multi-slice saturation recovery segmented-EPI sequence achieved R²=0.50 to 0.76 for resting flow(12); In a more recent canine hyperemia study using a double-injection technique and a saturation recovery sequence to quantify absolute flow(41), a high correlation of R²=0.88 was achieved between MR and microsphere measures over the flow range of 0 to 5.0 ml/min/g. The flow range of the present study is 0 to 1.2 ml/min/g. Since given the same measurement error the correlation tends to be tighter with wider ranges of flow, the displacement-encoded sequence was able to yield comparable to better accuracy relative to the saturation recovery sequences.

While contraction in the through-slice direction will slightly reduce the DENSE signal level(7,42), it does not affect the perfusion measurement. This is because perfusion estimation is based on the relative change of signal level pre and post contrast injection. Tissue deformation and other non-contrast related factors are constant throughout the scan and thus do not affect the perfusion estimation.

In the patient study the performance of this approach was primarily determined by errors in image registration, which accounted for 87.5% of the failed slices. Elastic image registration is affected by dynamic image intensity changes during contrast first-pass as well as through-slice motion. This step is therefore the focus of further improvement of this methodology.

The relationship between myocardial perfusion and function has been extensively investigated(40,43–48). In earlier studies, perfusion was usually measured by microspheres while the wall thickening/shortening were quantified with sonomicrometry(40,43–46) or tagged MRI(47). Spatial matching between the two measurements was a persistent technical challenge. It has been stated that(49) “no combination of techniques to measure regional myocardial blood flow and function has the spatial and temporal resolution to quantify the history and thus pathogenesis of a given observed contractile dysfunction and unequivocally either prove or disprove the role of perfusion-contraction matching in the time course of its development.” The current pulse sequence potentially provides a means to resolve this problem.

In our small group of STEMI patients, the correlation between circumferential strain and absolute perfusion at rest was found to be marginal, and was strengthened by normalizing regional perfusion to the mean of the remote normoperfused area. Previous studies in animal models came to the same conclusion(40,44,47,49). This lack of tight correlation is also seen in our pig study. It confirms what previous studies have found (40,43–49) and attributed to a degree of physiological decoupling between perfusion and mechanical function at the basal rest condition. Additionally, the current study focused on myocardial circumferential strain for two reasons. One is that it is closely associated with the active shortening of the muscle fibers and linearly related to ejection fraction(50). The second is that the radial strain contains higher errors from edge effects at the endo and epi-cardial surfaces(28).

The parameter of short-term contrast washout rate is the product of perfusion and contrast extraction across the capillary wall(51,52). In the patient group the high level of correlation between this parameter and absolute perfusion implies that the contrast extraction in the myocardial tissue was relatively unchanged by the pathological condition in these patients(52).

The current methodology has limitations. Only two of the three DENSE slices provided end-systolic strain. This may be remedied with a modified ECG trigger scheme where displacement-encoding occurs in end-systole and image acquisition occurs in late diastole. The trade-off is that automatic determination of systole duration according to established formulas may be inaccurate in some patients. The single-shot data acquisition also limited the strain measurement to a single cardiac phase, and the myocardial slices have different cardiac phases due to the different trigger delay times.

The AIF-based estimation of perfusion makes several assumptions. First is that T₂* effects on the AIF blood pool signal was negligible given the 1.2 ms echo time of the fGRE readout. To verify this point we imaged Gd-DTPA solution phantoms of concentrations up to 10 mM which is higher than the peak of the injection bolus (~5mM). The linearity between ln(1-I/I₀) and [Gd-DTPA] held up well for all concentrations (Fig. 11), showing that the T2* effect in the blood pool was negligible.

Figure 11.

Verification of the saturation recovery relationship between the AIF image intensity and [Gd-DTPA] in solution phantoms of various concentrations. All sequence parameters were the same as the human study.

The second assumption is that the tFISP DENSE image myocardial signal follows a simple T₁ relaxation of I=I₀e^−R₁·Tm, and that the relaxation rate is R₁ = R₁₀ + (Gd-DTPA relaxivity)×[Gd-DTPA], where the same Gd-DTPA relaxivity value governs both this relationship and the AIF image intensities, such that we can quantify absolute perfusion using the AIF-based deconvolution described in Appendix A. This assumption was also validated in phantoms. Several aspects of this assumption is addressed below.

The first is whether the DENSE tFISP image intensity follows a simple exponential decay of I = I₀exp(−a×[Gd-DTPA]) relative to contrast concentration, given the complex T₁ and T₂ dependence of tFISP signal in a transient phase. Klaus Scheffler (53) derived image intensity of a standard tFISP sequence in a transient phase, and showed that it approaches the steady state following an exponential relationship. This was verified experimentally by Wang and coauthors (54) in first pass myocardial diffusion imaging. However these results cannot be directly applied to our experiment for two reasons. The first and basic reason is that the modified tFISP readout in the DENSE image only acquires displacement-encoded magnetization that is not replenished by T₁ relaxation(6,28,29). This spin dynamics differs substantially from the previous two studies. The second difference between the current pulse sequence and the previous studies is that we employed a ramped flip angle scheme to equalize the echo amplitudes in the readout train, which likely further complicates the T₁ and T₂ dependence of the image intensity. For these reasons we determined experimentally the relationship between tFISP DENSE image intensity and [Gd-DTPA] in several agarose gel phantoms doped with Gd-DTPA up to 1.0 mM concentration. This is beyond the peak myocardial concentration(55). Figure 12 shows the linear relationship between ln(I/I₀) and [Gd-DTPA] with R² = 0.990. Therefore, despite the complexity of T₁ and T₂ dependence associated with the tFISP readout, the DENSE signal follows a simple exponential decay relative to [Gd-DTPA] in the range of 0 to 1.0 mM concentration.

Figure 12.

Dependence of the normalized DENSE image intensity on [Gd-DTPA] in several doped agarose gel phantoms. All sequence parameters including Tm times were the same as the human study. It shows that the image intensity follows simple exponential decay relative to contrast concentration.

The second question is whether the apparent decay rate of the tFISP DENSE image intensity is the true R₁, or in terms that are relevant to the perfusion estimation, whether the apparent relaxivity of Gd-DTPA derived from the exponential relationship is the true relaxivity. The slope in Fig. 12 yields an apparent relaxivity of 5.55 mM⁻¹sec⁻¹. Tofts and coauthors measured a relaxivity of 4.5 mM⁻¹sec⁻¹ in agarose gel (56). Therefore, the tFISP images likely overestimate the relaxivity of Gd-DTPA. However, the AIF-based perfusion estimates are valid as long as this apparent relaxivity is the same as the one in the AIF signal.

Therefore, the third and most relevant question is whether the apparent Gd-DTPA relaxivity is the same in the AIF images and the tFISP images. The relationship between the AIF image intensity and [Gd-DTPA] was investigated in several solution phantoms ranging from 0 to 10 mM concentration. As described in the “Methods” section, the AIF image is a saturation recovery image using a Turbo Flash readout. In the phantom study the AIF intensity follows the saturation recovery relationship of ln(1−I/I₀) = a + b×[Gd-DTPA] with high fidelity (Fig. 11). Using the nominal saturation-recovery time of 50 ms which is the interval between spin saturation and the time of the central k-space echo, the Gd-DTPA relaxivity was calculated to be 5.65 mM⁻¹sec⁻¹. This value was 2% above the one from the tFISP DENSE images which would lead to a 2% error in perfusion values. However, by setting the AIF relaxivity equal to the tFISP DENSE image relaxivity, we obtain a calibrated AIF saturation-recovery time of 50.9 ms. This calibrated time can then be used to obtain the correct perfusion levels.

Lastly, dynamic changes of the myocardial resonance frequency during first pass may affect the tFISP image intensity. Ferreira and coauthors (57) measured myocardial frequency shifts during the first pass of Gd-DTPA at the same dose of 0.1 mmol/kg as this study and a higher injection rate. They found that the shifts were within the range of [−69, 85] Hz, and maximal shifts occured in horizontal hearts. They proposed that in the worst case scenario, the maximal shift from Gd-DTPA may combine with the inherent offset from the posterior cardiac vein to reach a level that can cause significant signal loss in tFISP images of 2.5 ms TR. This is a limitation of tFISP based perfusion imaging.

The temporal resolution of image acquisition is limited by the time needed for magnetization recovery. At high flow rates the temporal resolution may need to be substantially higher than the short-term contrast washout rate in order to accurately measure the amplitude of the myocardial intensity drop. Therefore measuring hyperemic flow is a potential limitation of this pulse sequence and will need to be tested experimentally.

In the pig study some had heart rates at or above 100 bpm, and it became necessary to waited 2 heart beats between acquisitions to allow magnetization recovery. In the post-angioplasty STEMI patients the heart rates were all below 80 bpm and some were on beta-blocker medication, so two R-to-R intervals were used for ECG triggers. In general, a better strategy may be to set a low threshold of the interval between acquisitions in the pulse sequence, such that it automatically adjusts the number of heart beats between acquisitions according to heart rates.

The current study protocol did not permit stress testing which potentially yields tighter correlation between flow and function(58). The main constraint in apply this sequence to stress imaging is the high heart rate and short systole and diastole periods. At heart rates of 150 bpm or higher only one of the three DENSE slices will have the correct delay time to provide end-systolic strain. A solution around this limitation may be a rotating order of the trigger delays of the slices in which each slice will be acquired first in turn, and corresponding adaptation of the image processing methods.

In summary, this study shows that a displacement-encoded pulse sequence is able to quantify both myocardial perfusion and strain distributions in a single scan.

Appendix A: Flow estimation by Fermi Model-base deconvolution

To estimate the absolute perfusion level from the dynamic changes of the DENSE image intensities during the passage of the bolus of contrast agent, we followed the constrained deconvolution method using a Fermi function model described by Jerosch-Herold et al.(15,59). Denote the time of the starting of the bolus infusion as t = 0, then the Fermi function model relates the myocardial concentration of contrast agent at time t and location (x, y), c_m(x, y, t), to the arterial blood concentration of contrast agent, c_a(t), through the convolution formula

$$c_m(x,y,t)=F(x,y){\int }_0^t{c}_a(\tau )\frac{1}{exp\{k(x,y)[\tau -{\tau }_d(x,y)]\}+1}d\tau ,$$ (A1)

where the value F is the myocardial perfusion rate, the value τ_d accounts for the time delay between the arterial concentration curve c_a(t) in the aorta and the input at the region of interest in the myocardium, and the value k is the contrast washout rate. To proceed further we need to know the myocardial concentration c_m(x, y, t) for each pixel, as well as the arterial input function (AIF) c_a(t).

The AIF was measured from the aortic blood pool signal in the saturation-recovery AIF slice, which was imaged immediately following the displacement-encoding (DE) block (Fig. 2). It was acquired without refocusing the displacement-encoding gradients, and thus the DE block acted as the saturation prep. The AIF image intensity was

$$I_a(t)=I_0\{1-exp[-T_s·(R_{1b}+\alpha ·c_a(t))]\},$$ (A2)

where I₀ is the image intensity in the absence of the DE block, T_s is the effective saturation recovery (SR) time, R_1b is the native T₁ relaxation rate of blood of 0.67 sec⁻¹ at 1.5 tesla(60), and α is the efficiency of T₁ relaxation of the contrast agent. I₀ was measured with a separate acquisition without the DE block at the end of the scan. The effective SR time T_s was specific to the fGRE acquisition of the AIF slice, and was obtained through a calibration process using several phantoms of known T₁’s:

$$I_n=I_{n0}\{1-exp[-T_s/T_{1n}]\},$$ (A3)

where I_n and I_n0 were the AIF image and proton density image intensities of the nth phantom, and T_1n was the T₁ of the nth phantom. The SR time T_s was obtained through linear regression in the log(1−I_n/I_n0) vs. 1/T_1n plot. Once the SR time was known, the AIF was then derived from eq.(A2) to within the unknown efficiency coefficient α

$$\alpha ·c_a(t)=-\frac{ln[1-I_a(t)/I_0]}{T_s}-R_{1b}.$$ (A4)

We next look at the myocardial contrast concentration c_m(x, y, t) and its effect on the DENSE slices. The three DENSE slices were acquired with single-shot true-FISP readout of sequential k-space coverage. Each slice took 100 ms to acquire. The time delays between the DE block and the centers of the slice acquisitions were, therefore,

$$T_{mj}=(200+100·j)(ms),j=0,1,2.$$ (A5)

The DENSE image signal intensity is influenced by T₁ decay during the time delay in the form

$$I_j(x,y,t)=I_{j0}exp\{-T_{mj}·[R_{1m}+\alpha ·c_{mj}(x,y,t)]\},j=0,1,2,$$ (A6)

where R_1m is the native T₁ relaxation rate of the myocardium, and we assume complete magnetization recovery. Our image acquisition began at 30 seconds before bolus infusion. During the pre-contrast period

$$I_j(x,y,t<0)=I_{j0}exp(-T_{mj}·R_{1m}),j=0,1,2.$$ (A7)

The time average of the images during this period provided the reference images

$$I_{rj}(x,y)={<I_j(x,y,t<0)>}_t,j=0,1,2.$$ (A8)

Combining eq.(A6) and (A8) yielded the myocardial contrast concentration to within the efficiency coefficient α

$$\alpha ·c_{mj}(x,y,t)=-ln[I_j(x,y,t)/I_{rj}(x,y)]/T_{mj},j=0,1,2.$$ (A9)

By using this equation the relative signal intensity change instead of the absolute signal intensity is used for perfusion estimation, so other factors that affect the image signal intensity, such as coil profile, will be removed with no need for additional correction. We then assume that the relaxation efficiency α of the contrast agent is the same in the arterial blood pool as in the myocardium. The AIF from eq.(A4) and the myocardial contrast from eq.(A9) were then input into Fermi function model of eq.(A1). Through the Marquardt–Levenberg nonlinear least squares fitting algorithm (Interactive Data Language, ITT, White Plains, New York), the perfusion F(x,y) and washout rate k(x,y) were estimated for each pixel. If the fitting algorithm failed to converge for a specific pixel, then that pixel was left blank in the resulting perfusion maps and was excluded in the statistical analyses.

Appendix B: Simulation Study on the effect of noise and sampling rate on perfusion estimation

The same Fermi function convolution model of Appendix A was used to simulate myocardial contrast concentration from a known AIF. The AIF is taken from one of the pig experiments after being fitting to gamma-variate function(15):

$$c(t)=C·t^{\nu }·exp(-t/u).$$ (B1)

A series of myocardial signal time-intensity traces were generated according to eq.(A1) with perfusion levels F_real ranging between 0.25–2.5 ml/min/g, and corresponding washout rates k according to the linear relationship between the two. Normally distributed random noise of standard deviation (σ_N) of 10%, 15% and 20% of the pre-contrast signal intensity was added to the time-intensity traces. The resulting noisy signal as well as the AIF were sampled at the rate of once per 2 sec. These were the simulated myocardial image signal. They were input into the flow estimation routine to produce a simulated measurement of perfusion F_est. For each noise level and perfusion level, 1000 simulations were performed. The root-mean-squared error of the estimated flow RMS(F_est) and the normalized error RMS(F_est)/F_real were plotted in Fig. B1.

Figure B1.

Absolute and normalized error of flow estimation vs. real flow for different levels of noise in the image intensity. The dashed lines represent the root-mean-squared error of flow estimation RMS(F_est), and the solid lines represent the normalized error RMS(F_est)/F_real.

The results show that for the noise level of 15%, the relative uncertainty in perfusion measurement is below 30% when the perfusion level is greater than 0.75 ml/min/g, and the uncertainty stays below 0.2 ml/min/g for lower perfusion levels. This was regarded as acceptable in the patient study.

In the patient data the noise level of each pixel was measured by the error of the curve fitting, which is defined as the RMS difference between the actual signal and the fitted values. The simulations showed that the above procedure accurately estimate the true noise levels in the simulated time-intensity curves. In the experimental studies, myocardial pixels with noise levels above 15% were excluded from further processing and left blank in the perfusion maps.