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Keywords:

  • cardiac MRI;
  • myocardial tagging;
  • harmonic phase;
  • myocardial strain;
  • left ventricle

Abstract

  1. Top of page
  2. Abstract
  3. THEORY
  4. METHODS
  5. RESULTS
  6. DISCUSSION
  7. CONCLUSION
  8. REFERENCES

Magnetic resonance tagging has proven a valuable tool in the quantification of myocardial deformation. However, time-consuming postprocessing has discouraged the use of this technique in clinical routine. Recently, the harmonic phase (HARP) technique was introduced for automatic calculation of myocardial strain maps from tagged images. In this study, a comparison was made between HARP instantaneous strain maps calculated from single tagged images (SPAMM) and those calculated from subtracted tagged images (CSPAMM). The performance was quantified using simulated images of an incompressible cylinder in the ‘end-systolic’ state with realistic image contrast and noise. The error in the second principal stretch ratio was 0.009 ± 0.032 (mean ± SD) for the SPAMM acquisition, and 0.007 ± 0.016 for CSPAMM at identical contrast-to-noise ratio. Furthermore, differences between the methods were illustrated with in vivo strain maps. Those calculated from CSPAMM images showed fewer artifacts and were less sensitive to the choice of cut-off frequencies in the HARP band-pass filter. A prerequisite for the method to become practical is that the CSPAMM images should be acquired in a single breathhold. Magn Reson Med 46:993–999, 2001. © 2001 Wiley-Liss, Inc.

Since its introduction, MR tissue tagging (1, 2) has been used successfully for the quantification of motion and deformation in both normal and abnormal myocardium. Thus far, however, time-consuming postprocessing has discouraged the use of tagging and strain analysis in clinical routine.

One method that overcomes this limitation is the harmonic phase (HARP) technique (3–8). In the original form, the HARP method uses a narrow band-pass filter to extract the tagging information from the MR image, after which the local frequency of the tag modulation is detected. A key point in the HARP method is the choice of appropriate cut-off frequencies of the band-pass filter. If the filter is too narrow it suppresses the tag modulation in areas with large deformation, while a filter that is too wide introduces artifacts in the strain maps.

In this article, we show that HARP strain maps can be improved by using subtracted tagged images (which we refer to as complementary SPAMM or CSPAMM images [9]). The CSPAMM images are generated by subtraction of a normal SPAMM image and a SPAMM image that has the tagging pattern inverted. As illustrated in Fig. 1, the central part of k-space is cancelled and only the tagging signal remains. As a result, the peaks are better separated, giving more freedom to choose the appropriate band-pass filter. The improvements are illustrated with simulated images and with in vivo MR images.

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Figure 1. a: SPAMM magnitude image of a healthy volunteer with sinusoidal tag modulation in the end-systolic time frame. b: Same image plane with CSPAMM image, calculated by subtracting a SPAMM image with inverted tag lines from the image in a. All the nontagged image content cancels. c:k-space magnitude image of the SPAMM image in a. The central peak contains the ‘nontagged’ image, while the tagging signal resides in the two peaks aside. The dashed vertical line gives an indication of the high-pass filter cut-off frequency. d: In the CSPAMM image, the central peak is cancelled by subtraction of the two SPAMM images, while the side peaks remain. The dashed line again indicates the cut-off frequency.

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THEORY

  1. Top of page
  2. Abstract
  3. THEORY
  4. METHODS
  5. RESULTS
  6. DISCUSSION
  7. CONCLUSION
  8. REFERENCES

The magnitude of an image I1(x, y) with vertical tag lines, acquired immediately after application of a sinusoidal tag profile (two 45° RF tag pulses, 1-1 SPAMM), is described by multiplication of the nontagged MR image magnitude I0(x, y) and a tag-modulation function m1(x):

  • equation image(1)

For the 1-1 SPAMM image, the modulation directly after application of the tag pulses is given by:

  • equation image(2)

where k1 is the spatial frequency of the (vertical) tag lines and φ1 determines the phase at x = 0.

Deformation of the tissue will alter the frequency of the tag lines in the heart wall. Ignoring the tag line fading due to T1 relaxation, we can describe the deformed state by replacing the constant frequency k1 in Eq. [2] with a frequency that depends on the position (x, y):

  • equation image(3)

A fundamental step in the HARP procedure is the application of a Hilbert transformation for detection of the instantaneous (‘local’) frequency of the tagging signal. The Hilbert transform consists of a Fourier transform, application of a band- or high-pass filter that passes positive frequencies only (kx > 0, right half of k-space), and an inverse Fourier transform. The result is a complex signal Hmath image(x, y) of which the real part equals the original (real) signal without the zero-frequency (offset) term, and of which the imaginary part equals the original signal with a 90° phase shift. In the original HARP procedure (6), the band-pass filter is chosen not only to remove the negative frequencies, but it passes only a narrow frequency range around the tagging frequency.

HARP uses the Hilbert transform to determine the angle θmath image(x, y) of the tag signal. The tangent of the angle equals the quotient of the imaginary and real parts:

  • equation image(4)

The angle, wrapped into the range (−π, π), can be calculated from the inverse of the tangent in Eq. [4] by taking into account the sign of the numerator and denominator. This quantity is referred to as the HARP angle ϕmath image(x, y), which equals θmath image(x, y) except for the wrapping artifact.

Instantaneous frequency (10) is defined as the spatial derivative of the angle θmath image(x, y). Therefore, the instantaneous frequency (vector) can be calculated from the HARP angle ϕmath image(x, y) with:

  • equation image(5)

where the asterisk denotes removal of the wrapping artifact from the derivative (3). Note that the calculation of the instantaneous frequency is useful only when the zero-frequency (offset) has been removed in the Hilbert transform. Calculation of the instantaneous frequency is identical to techniques used for demodulation of FM signals in communication theory (11). The tag signal intensity (referred to as the harmonic magnitude) is calculated by taking the magnitude of H′(x, y).

The above procedure also holds for the image with horizontal tag lines, from which the instantaneous frequency kmath image is calculated using the upper half of k-space for the Hilbert transform. Under the condition that the tag frequency of both vertically and horizontally tagged images equals k1, the deformation gradient tensor is calculated with:

  • equation image(6)

The superscript −T stands for inversion of the transposed 2 × 2 matrix built from the two instantaneous frequency vectors. Note that F can be related to a material point in the deformed state only, as the displacement between the undeformed and the deformed state is not known (but may be calculated using a tracking algorithm [3]).

Two-dimensional strain parameters are calculated from F with the usual mathematics. For example, polar decomposition of F separates the rigid body rotation R from the stretch U (12):

  • equation image(7)

The eigenvalues of the stretch tensor U are the principal stretch ratios, λ1 and λ2, with the convention that λ1 ≥ λ2. λ > 1 indicates stretch of the tissue and λ < 1 indicates shortening. The eigenvectors of U give the directions of the principal stretches. In this article, we have focused on the eigenvalues of the stretch tensor U for evaluation of the HARP method. The eigenvalues are independent of the referenced coordinate system. The functional map of a stretch ratio will be referred to as ‘strain map.’

METHODS

  1. Top of page
  2. Abstract
  3. THEORY
  4. METHODS
  5. RESULTS
  6. DISCUSSION
  7. CONCLUSION
  8. REFERENCES

HARP

In this article, a CSPAMM image is defined as the subtraction of two SPAMM magnitude images, one of which has inverted tag lines. The HARP technique can be applied to both SPAMM and CSPAMM images. In k-space, the SPAMM image consists of three peaks (Fig. 1c). During the cardiac cycle, the magnitude of the central peak (nontagged image) increases while the magnitude of the side-peaks (tag peaks) decreases. If the central peak is not removed by the band-pass filter during the Hilbert transform, it will cause artifacts in the strain maps. In the CSPAMM image, the central peak in k-space is inherently canceled by the subtraction, and therefore only two peaks in k-space remain (Fig. 1d). In theory, this allows all positive frequencies to be used in the Hilbert transform. In practice, the use of such wide band-pass filters is associated with a decrease in the SNR. We applied a median filter (5 × 5 kernel) to the instantaneous frequency maps in order to improve SNR, while preserving sharp gradients in strain.

In our implementation of HARP, the band-pass filter was a simple high-pass filter with a cut-off frequency νx. Frequencies above νx remained unaffected, while frequencies equal to and below νx (including all negative frequencies) were put to zero prior to the inverse Fourier transform. The cut-off frequency of the high-pass filter will be reported for the image with vertical tag lines in terms of νx = (kx/2π) · FOVx. Using this definition, νx equals the number of cycles in the FOV, as well as the number of pixels in the frequency domain. Our tag distance of 7 mm corresponds to νx = 300 mm/7 mm = 43 in both the human and the synthetic images. The image with the horizontal tag lines is treated with a rotated version of the high-pass filter.

Analytical Test Case

To investigate the errors in the HARP method, we simulated SPAMM and CSPAMM line-tagged images of a deforming cylinder with normally distributed noise added. The displacement in this cylinder is given by an analytical expression, which allowed for comparison of the ‘measured’ instantaneous strain with the ‘true’ analytical strain. Only the deformation in the end-systolic state was simulated.

The 3D analytical displacement field was defined in cylindrical coordinates. The displacement field relates the position of a myocardial point in the deformed state p′(r, θ, z) to its position in the undeformed state p(R, Θ, Z). The displacement field in an incompressible cylinder without longitudinal shear strains and torsion is given by the following equations (13, 14):

  • equation image(8)

The function r(R) is dictated by the incompressibility of the myocardium:

  • equation image(9)

where Ri and ri are the inner radii of the cylinder before and after deformation, respectively.

The deformation parameters were chosen similar to Young and Axel (14) to exaggerate the motion of the human heart: Ri = 15.0 mm, ri = 10.0 mm, initial outer radius 33.0 mm, R-Θ shear ϕ = 0.33°/mm, rigid body rotation ε = 9.2°, and longitudinal contraction λ = 0.8. The thickness of the cylinder wall was 18.0 mm in the undeformed state. The resulting ejection fraction was 65%. The deformation gradient tensor (with reference to the position in the undeformed state) of this analytical displacement field is given by (13):

  • equation image(10)

Polar decomposition (Eq. [7]) was then applied to the top-left 2 × 2 submatrix of F and the ‘true’ principal stretch ratios were calculated.

The synthetic MR image was a basic simulation of a tagged image in the RΘ-plane. The tagged image was simulated using Eq. [1]. I0(x, y) equaled 1 within the cylinder wall and 0 elsewhere. Tag line fading was simulated by introduction of an additional parameter s ∈ [0, 1] in the modulation function:

  • equation image(11)

The CSPAMM image is a subtraction of two 1-1 SPAMM images, one of which has the tag lines inverted, and thus the modulation function for a CSPAMM image is given by:

  • equation image(12)

The synthetic image of the deformed state was created by setting the intensity of a pixel at position p′ in the deformed image Imath image equal to the intensity in the undeformed image I1 at p.

An image pair I2(x, y) and Imath image(x, y) with horizontal tag lines was created analogously. Imaging parameters were similar to the in vivo images: the FOV was 300 × 300 mm2, the image matrix was 2562, and the tag line distance was 7 mm (6 pixels). The contrast-to-noise ratio (CNR) and the tag line fading parameter s were estimated from the end-systolic in vivo images. The CNR was estimated using the approach outlined by Henkelman (15), where we defined contrast as the difference between the center of the black lines and the center of the white lines. Both SPAMM and CSPAMM images were simulated with the same CNR. Thus, the SPAMM images simulated two averaged SPAMM acquisitions, which, in the real world, have an acquisition time equal to that of the CSPAMM image.

Human MR Images

One healthy volunteer was subjected to MR imaging in a 1.5T scanner (Magnetom Vision, Siemens, Erlangen, Germany). Informed consent was obtained from the volunteer. The in vivo dataset consisted of four single breathhold acquisitions at the midventricular level in the short-axis plane. Two 55° nonselective RF pulses separated by magnetic field gradients in the frequency-encoding direction applied a sinusoidal modulation of the tissue magnetization (2) immediately after triggering on the ECG R-wave. The period of the sine (tag line distance) was 7 mm. The tagging pulses were followed by a fast low angle shot (FLASH) cine imaging sequence. Fifteen frames were imaged with a temporal resolution of 50 ms. A 80 × 256 matrix was acquired in 16 heartbeats (segmented k-space with 5 ky-lines per heartbeat, linear phase encoding ordering). Other imaging parameters were: FOV 300 × 300 mm2, echo time 4.8 ms, excitation angle 15°, slice thickness 6 mm.

The first acquisition out of four produced an image with ‘vertical’ tag lines. For the second acquisition the tagging pattern was inverted (or shifted over half a tag-period) by adding a 180° phase shift to the second nonselective RF pulse. After reconstruction, the magnitude images of both acquisitions were subtracted. This procedure was repeated with swapped frequency- and phase-encoding directions, thus producing ‘horizontal’ tag lines.

In the analysis, we focused on the end-systolic state because the deformation of the heart wall reaches a maximum at end systole. Therefore, the peak of the tag signal has a maximum spread in the frequency domain.

RESULTS

  1. Top of page
  2. Abstract
  3. THEORY
  4. METHODS
  5. RESULTS
  6. DISCUSSION
  7. CONCLUSION
  8. REFERENCES

Analytical Test Case

From the end-systolic in vivo SPAMM images, the CNR was estimated at 11 and s was estimated at 0.7. Because of the subtraction of two SPAMM images, the CNR in the CSPAMM image improved with a factor √2 to 15. Both SPAMM and CSPAMM images were generated with a CNR of 15.

The calculated strain maps of the analytical test case are presented in Fig. 2, with only the center of the image shown. The harmonic magnitude image in the right column was used for masking. Both the λ1 and the λ2 strain maps of SPAMM and high-pass filter ν > 20 (top row) showed faint artificial stripes. Furthermore, the strains at the edges of the cylinder were not correctly estimated, as illustrated by black spots at the inner edge of the λ1 map and the dark spots at the outer edge of the λ2 map.

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Figure 2. Functional map of the principal stretch ratios (in short: ‘strain maps’) of the analytic test case. Only the center of the image is shown here, and the strain maps are given in the geometry of the deformed state; therefore, the cylinder wall appears relatively thick. The scale is identical for all λ1 maps (left column) and for all λ2 maps (middle column). The rightmost column shows the harmonic magnitude image calculated from the corresponding tagged image with vertical lines, providing a mask for the strain maps. The masking color equals zero deformation (λ = 1) in all strain maps. a–c: Results for SPAMM images and a high-pass filter with a cut-off frequency ν = 20. The arrow in a indicates one of the faint artificial stripes (see Results). d–f: Results for SPAMM images and a high-pass filter with a cut-off frequency ν = 30. The arrows in f indicate the regions with a decreased magnitude of the tag signal as a result of the applied filter. g–i: Results for CSPAMM images and a high-pass filter with a cut-off frequency ν = 20.

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The middle row in Fig. 2 shows the results of a SPAMM image with high-pass filter ν > 30. This filter reduced the artificial stripes in the strain maps somewhat (although this effect was more obvious in the in vivo data, see below). However, this filter removed some of the lower frequencies in the tagging signal (associated with large stretch), as illustrated in the harmonic magnitude image in Fig. 2f. The strain maps calculated from the CSPAMM images (Fig. 2g, h) also showed errors in the strain near the edges, but the stripe-artifact was absent.

The stretch ratio in the cylinder wall, as a function of the radius, is plotted as a solid line in Fig. 3a, b. The stretch ratio as calculated with HARP from the CSPAMM image is also plotted (n = 2484 pixels). Clearly, λ1 was systematically underestimated near the edges of the cylinder. Therefore, we excluded a circle of two pixels thick at the inner and outer boundary of the cylinder from the statistical analysis (n = 1920 pixels remaining). Figure 3c–h shows the error plots corresponding to the strain maps in Fig. 2. These plots show that the error in stretch increased with larger magnitudes of stretching and that λ1 was underestimated for the large stretches at the inner part of the cylinder.

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Figure 3. Plots of the analytical test case. a,b: Principal stretch ratio in the cylinder as a function of the radius. The solid line gives the true strain, whereas the crosses give strain we computed with HARP for the CSPAMM image. Each marker corresponds to one pixel in Fig. 2g or 2h. The vertical dashed lines at r = 12.3 and r = 32.1 mm indicate the boundaries of the region included in the statistical analysis. c–h: Error plot for each of the strain maps shown in Fig. 2. The solid line corresponds to the mean error, and the dashed lines indicate the ±2 SD boundaries. Only pixels between r = 12.3 and r = 32.1 mm are shown.

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The mean error and the standard deviation (SD) of the error are listed in Table 1. Overall, λ2 is better estimated than λ1. The error in λ1 was similar for the SPAMM and CSPAMM, as it was mainly determined by the underestimation of large stretches at the inner part of the cylinder. λ1 calculated from a SPAMM image using a cut-off frequency of ν = 30 considerably underestimated the true strain (mean error −0.07), and had a large SD (0.08). λ2 was estimated with a reasonably small mean error in all cases. The SD of the error in λ2 was comparable for both cut-off frequencies with the SPAMM images (0.032 and 0.029). The SD of the error in λ2 was only half as large for the CSPAMM image (0.016).

Table 1. Error in Analytical Test Case
AcquisitionFilter cut-off frequencyλ1aλ2a
  • a

    Values are mean ± SD of measured strain minus true strain. Two pixels off inner and outer boundary of cylinder are excluded (12.3 < r < 32.1 mm, n = 1920 pixels), tag line fading parameter s = 0.7, CNR = 15 for both the SPAMM and CSPAMM images, instantaneous frequency map filtered with 5 × 5 median filter.

SPAMMν = 200.01 ± 0.060.009 ± 0.032
SPAMMν = 30−0.07 ± 0.080.004 ± 0.029
CSPAMMν = 20−0.01 ± 0.060.007 ± 0.016

In Vivo Strain Maps

The strain maps and harmonic magnitude images calculated from the in vivo data are shown in Fig. 4. The same filter cut-off frequencies were used as with the analytical test case in Fig. 2. The strain maps calculated from SPAMM images using a cut-off frequency of ν = 20 show a striping artifact, which is best observed in the chest wall but may also be observed in the heart wall. This artifact was reduced by increasing the cut-off frequency to ν = 30, as shown in the middle row. The harmonic magnitude image shows that the tag modulation was reduced by this filter in regions with large stretch, as indicated by the arrows.

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Figure 4. Strain maps calculated from in vivo data. The image has been cropped to 130 × 111 pixels. Type of images and filters used are identical to the strain maps of the analytical test case shown in Fig. 2. a–c: Results for SPAMM images and a high-pass filter with a cut-off frequency ν = 20. The chest wall clearly shows artificial stripes. d–f: Results for SPAMM images and a high-pass filter with a cut-off frequency ν = 30. The arrows in Fig. 2f indicate the regions with a decreased magnitude of the tag signal as a result of the applied filter. g–i: Results for CSPAMM images and a high-pass filter with a cut-off frequency ν = 20.

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The results for the CSPAMM images are shown in the bottom row. The artificial stripes were absent in both the λ1 and λ2 map. The harmonic magnitude image (Fig. 4i) had good contrast and provided a good mask for the strain maps. The λ1 map shows that the largest stretch occurred in the posterolateral segment of the LV wall. The λ2 map reveals a transmural gradient, with more shortening (darker in strain map) occurring at the subendocardium compared with the subepicardium.

DISCUSSION

  1. Top of page
  2. Abstract
  3. THEORY
  4. METHODS
  5. RESULTS
  6. DISCUSSION
  7. CONCLUSION
  8. REFERENCES

In this article, we have used an analytical test case to estimate the performance of the HARP method using a high-pass filter to suppress the central peak in k-space. Strain maps that were calculated from an in vivo dataset were shown to have similar artifacts as the analytical test case.

The analytical test case has a strong gradient in λ1 in the inner part of the cylinder wall, which was systematically underestimated in the strain maps. However, in this respect the cylinder is not likely to be a realistic model of LV heart wall. Approximately the inner 1/3 of the heart wall consists of spongy myocardium, from which blood is ejected into the LV cavity during systole. Therefore the stretch in the subendocardial layers is lower than we modeled with the incompressible cylinder. The systematic underestimation of λ1 near the inner part of the cylinder thus represents a ‘worst case’ scenario, and may not be as severe for the in vivo data as the results of our analytical test case suggest.

Comparing the λ1 error plot in Fig. 3c (SPAMM) with the plot in Fig. 3g (CSPAMM), it may be observed that the CSPAMM error plot has a cloud which is narrower than that of the SPAMM error plot. This better performance of the CSPAMM data is not represented in the SD of the error in Table 1 because the SD is primarily determined by the systematic underestimation of the steep gradient in the inner layers of the cylinder. To quantify this difference, we also computed the SD of the error using only the pixels with a true λ1 < 1.5. The error using SPAMM then equals 0.014 ± 0.054 vs. −0.003 ± 0.039 for the CSPAMM data.

The λ1 maps do not give a reliable estimate of the deformation near the edge of the cylinder wall. This is probably caused by the tag lines suddenly being cut off at the edges with the instantaneous frequency vector k′ orthogonal to the cylinder wall. Thus, the tag modulation suddenly stops in the ‘direction’ in which the frequency of the tag modulation is detected. Cutting the modulation gives a semirandom phase jump at the edge, which results in a high or low instantaneous frequency at the edge. In our approach, the edge-zone was made as small as possible by using a wide band-pass filter. The median filter we applied to the instantaneous frequency maps eliminated the outliers at the edge. The pixels at the edge are less problematic in the λ2 maps, which are mainly determined by tag lines orthogonal to the heart wall.

Comparing the in vivo strain maps with earlier reports, the results appear credible. For example, the transmural gradient in λ2 is in agreement with the results of Waldman et al. (16) and Moore et al. (17). Also, the largest stretch may be expected to occur in the lateral free wall, as confirmed by the λ1 map. Furthermore, the stretch ratio in the papillary muscle near the lateral wall is almost 1 (no deformation) in both maps, which agrees with this muscle contracting mainly in the longitudinal direction.

A general drawback of the instantaneous HARP method is that the rigid body displacement cannot be calculated from the instantaneous frequency maps. Thus, the strain can be mapped only onto the deformed heart, while it cannot be mapped onto the undeformed heart. This drawback is overcome by the application of HARP-tracking (3). Provided that the tracking algorithm performs correctly, the errors for the tracking method are expected to be equal to the errors in the instantaneous strain maps.

Filter Cut-off Frequency

A key point in the HARP method is the choice of an appropriate filter to isolate the tagging peak in k-space from the central peak. In this article, we have given examples of strain maps produced with a high-pass filter to suppress the central peak. The cut-off frequency of ν = 20 was established by evaluation of strain maps calculated from simulated and in vivo CSPAMM images, using a range of cut-off frequencies between ν = 0 and ν = 40. For the simulated images, all strain maps with cut-off frequency ν < 25 were equal. Choosing a low cut-off frequency of ν = 10 resulted in light artifacts in the in vivo end-systolic strain maps. These artifacts are due to imperfect cancellation of the central peak in the CSPAMM image, occurring if the SPAMM image is not exactly reproduced with inverted tag lines in the second SPAMM image.

The artificial stripes in the strain maps in Fig. 4a,b arise from overlap in the peaks in k-space in the SPAMM images. A low filter cut-off frequency passes the tail of the central peak, causing the striping artifact. In the analytical test case, the striping artifact is less visible because the central peak is less spread out in k-space compared to the in vivo data. Increasing the cut-off frequency reduces the striping artifact, but also filters out the tag signal in areas with large stretch, as it rejects the lowest tag frequencies (see Fig. 2f and 4f). Using CSPAMM images provides a solution to this problem: the resulting strain maps are less sensitive to small alterations in the filter cut-off frequency.

SPAMM vs. CSPAMM Acquisition

The strain maps calculated from the SPAMM acquisition (requiring half the acquisition time of the CSPAMM acquisition) display either artificial lines (cut-off at ν = 20) or underestimate the first principal strain (cut-off at ν = 30). HARP does allow correct estimation of the second principal strain from SPAMM images. Note that we simulated the SPAMM images with the CNR of a double acquisition (requiring the same acquisition time as the CSPAMM acquisition). In practice, however, one would use just a single acquisition, which would increase the noise in the strain map compared to our analytical test case.

The CSPAMM method requires two SPAMM acquisitions. Subtraction of the SPAMM images is sensible only if the two single breathhold acquisitions are identical (except for the sign in the tag modulation). The drawback is that there can be substantial variation in position between breathholds. The consequence is that images in two different breathholds often do not match, resulting in large gradients in image intensity at the edges of the heart wall. These gradients interfere with the tag signal and affect the estimated strain near the edges of the heart wall.

The CSPAMM-HARP method therefore seems practical only if both acquisitions can be measured in one single breathhold (19).

CONCLUSION

  1. Top of page
  2. Abstract
  3. THEORY
  4. METHODS
  5. RESULTS
  6. DISCUSSION
  7. CONCLUSION
  8. REFERENCES

An analytical test case was used to quantify the error in the HARP instantaneous myocardial strain maps from SPAMM and CSPAMM images with sinusoidal modulation using a wide band-pass filter in the Hilbert transform. Best results were obtained with the CSPAMM images. A major advantage of the CSPAMM acquisition is that the central peak in k-space is effectively suppressed, resulting in more accurate strain maps that are less sensitive to the choice of the HARP band-pass filter.

The drawback of CSPAMM acquisition is the double acquisition time compared to the SPAMM acquisition. A prerequisite for the method to become practical is that the CSPAMM images should be acquired in one single breathhold. Fast imaging techniques, such as segmented echo planar imaging, should bring this within reach (19).

REFERENCES

  1. Top of page
  2. Abstract
  3. THEORY
  4. METHODS
  5. RESULTS
  6. DISCUSSION
  7. CONCLUSION
  8. REFERENCES