Accurate phosphorus metabolite images of the human heart by 3D acquisition-weighted CSI



Fourier imaging modalities suffer from significant signal contamination between adjacent voxels, especially when the spatial resolution is comparable to the size of the anatomical structures. This contamination can be positive or negative, depending on the spatial response function and the geometry of the object. Such a situation arises in human cardiac 31P chemical shift imaging (CSI). Acquisition-weighted CSI reduces this contamination substantially, which is demonstrated by comparing conventional CSI to Hanning-weighted 3D 31P-CSI experiments in 13 healthy volunteers at 2 T. The nominal spatial resolution and the total number of scans were identical for both experiments. The improved spatial response function of the acquisition-weighted experiment led to a significantly (P < 0.0001) higher myocardial PCr/ATP ratio (2.05 ± 0.31, mean ± SD, N = 33, corrected for saturation and blood contribution) compared to the conventional CSI experiment (1.60 ± 0.46). This is explained by the absence of negative contamination from skeletal muscle, which also resulted in an increase of the observed SNR (from 5.4 ± 1.4 to 7.2 ± 1.4 for ATP). With acquisition-weighted CSI, metabolic images with a nominal resolution of 16 ml could be obtained in a measurement time of 30 min. After correction for the inhomogeneous B1 field of the surface coil, these images show uniform ATP distribution in the entire myocardium, including the posterior wall. Magn Reson Med 45:817–826, 2001. © 2001 Wiley-Liss, Inc.

Phosphorus NMR spectroscopy of the heart has been shown to be potentially useful in many clinical examinations (1). Studies have found possible applications in cases of dilated cardiomyopathy (2) and coronary artery disease (3). Furthermore, 31P spectroscopy may be useful to distinguish between viable and nonviable myocardial tissue (4) or to detect rejection after heart transplantation (5). Chemical-shift imaging (CSI) (6–8) has recently become the most widely used method for examining the metabolism of the human heart (9–16). It allows the acquisition of spatially resolved 31P spectra of the heart with a sufficient signal-to-noise ratio (SNR) in an acceptable time. However, the low concentration of the observed metabolites and the low sensitivity of the 31P nucleus require large voxel sizes and the use of high-sensitivity surface coils. Until today, only measurements in anterior regions of the heart have been reported. The results (mostly expressed as the metabolite ratio PCr:ATP) reported in the literature (2, 3, 9–22) show a high variability, especially when different measurement modalities are used.

The quality of CSI experiments is often impaired by the inconvenient shape of its spatial response function (SRF), which is due to the small fraction of k-space covered in the experiment. This effect is particularly pronounced in situations where the spatial resolution is comparable to the size of the anatomical structures, and may cause severe contamination of the spectrum of a voxel by signal from surrounding tissue. Depending on how the positive or negative lobes of the SRF coincide with anatomical regions having low or high metabolic concentration, the signal contamination from adjacent regions can be additive or subtractive, and thus the observed signal amplitude can change significantly.

It is well known that the shape of the SRF can be improved by applying a k-space filter, which gives more weight to the phase-encode steps at the center of k-space than to those in the outer regions. Such a filter substantially reduces the sidelobes of the SRF, and consequently the contamination originating from adjacent tissue. Numerical filtering of the raw data in a post-processing step, however, affects the spatial resolution. It also modifies the noise properties of the experiment: at fixed spatial resolution and experimental duration, an improvement of the SRF solely by numerical filtering necessarily decreases the sensitivity, i.e., the SNR obtained from within the voxel per unit time (23–25). This sensitivity loss is avoided when applying k-space weighting during the data acquisition, accumulating a different number of averages for every phase-encode step (26, 27). A similar effect can also be obtained by varying the excitation angle depending on the k-space position (28). At identical spatial resolution and total experimental duration, these “acquisition-weighted” approaches provide an intrinsic sensitivity equal to conventional, nonweighted experiments. At the same time, they offer the advantage of an improved SRF shape (29).

Despite these advantages, acquisition weighting has only rarely been used to enhance the quality of 31P spectroscopic experiments of the human heart, mainly because of the limited availability of this technique on clinical scanners. Some studies have used ISIS localization combined with 1D acquisition-weighted CSI (13, 14). A 1D version of acquisition-weighted CSI is available on Philips systems. We know of only one work that describes acquisition weighting in all three spatial dimensions at 4.1 T (11). We have conducted both conventional and acquisition-weighted experiments on 13 human volunteers at 2 T to assess the performance gain of acquisition-weighted CSI under the particular circumstances of human cardiac 31P spectroscopy. The formulas for appropriate weighting functions that ensure identical spatial resolution of the experiments have been established. The improved performance of this method has allowed us to generate metabolic maps of the high-energy phosphates in the human heart.


The fundamental principles of acquisition-weighted CSI are well understood (26). In the following section, we concentrate on the issue of spatial resolution in acquisition-weighted experiments. To adequately compare different imaging experiments, it is imperative that their spatial resolution be strictly identical. Therefore, we first attempt to clarify the somewhat obscure notion of “spatial resolution,” and define “nominal spatial resolution.” Then, formulas are given for 1D, 2D, and 3D experiments, which allow one to adjust a Hanning weighting function accurately to the desired spatial resolution and experimental duration. These formulas are of high practical value, and to our knowledge have not been published previously. Finally, the ramifications of the modified shape of the spatial response function are discussed in terms of sensitivity, contamination, and observed SNR.

The resolving power of optical instruments is most commonly calculated using the Rayleigh criterion (30). This criterion is a measure for the minimal distance between two infinitely small objects to be discriminated by an observation through the optical apparatus. The limit of resolution, as defined by the Rayleigh criterion, is reached when the observed intensity maximum of one object occurs at the location of the first minimum of the diffraction pattern of the second object. The diffraction pattern is due to the inevitably limited aperture of the optical instrument. A very similar situation presents itself in Fourier imaging, particularly in conventional CSI experiments. The limited aperture of the optical instrument corresponds closely to the limited k-space area covered in the MR experiment, and the diffraction pattern of the former translates to the pointspread function (PSF) in the latter. Therefore, it is attractive to apply the well established and generally accepted Rayleigh criterion to assess the spatial resolution of MRI experiments (31).

When the Rayleigh criterion is applied to Fourier imaging with conventional, Cartesian k-space sampling, it has been shown that it indicates a spatial resolution which is identical to the “nominal spatial resolution,” i.e., the field of view (FOV) divided by the number of k-space samples (31). This appears to be very reasonable at first glance, but it also raises a number of issues. First of all, one should be aware of the critical view that Lord Rayleigh himself held of his criterion (30): “This rule is convenient on account of its simplicity and it is sufficiently accurate in view of the necessary uncertainty as to what exactly is meant by resolution.” Indeed, the Rayleigh criterion can only be an indication for the order of magnitude of the resolving power, but it does not set a sharp limit. To accurately assess the resolving power of some experiment, one has to take into account all aspects of the PSF. In optical instruments, the aperture is usually a binary system: light passes within the aperture, and there is no light path outside. Thus, the diffraction pattern has always the same shape (a sinc-type function), which then can be fully characterized by the Rayleigh criterion alone. The situation is different in acquisition-weighted MR experiments, where the weight of various k-space samples can be adjusted and the shape of the PSF thus can be influenced. Under these circumstances, the nominal spatial resolution (as indicated by the Rayleigh criterion) is still an adequate measure for the width of the main lobe of the PSF, but it provides no information at all about its sidelobes, and consequently no information about the signal contamination between adjacent voxels.

Last but not least, the Rayleigh analogy highlights the issue of digital resolution in MRI. According to the criterion, two objects at a distance of the nominal resolution should be distinguishable. Yet, after Fourier transformation they are represented as identical gray values in adjacent pixels of the image. From this image, one can not tell whether the two pixels represent a single large object or two smaller objects. If the digital resolution is increased (by Fourier interpolation or zero-filling), an intensity dip will appear between the two objects. Only then the resolving power of the experiment is fully exploited. Increasing the digital resolution can render visible all the information that is contained in the original data. Nevertheless, the nominal spatial resolution is an inherent property of the data-acquisition procedure, which is by no means influenced by zero-filling or by other approaches that modify the digital resolution.

In the following analysis, the SRF is used rather than the PSF. While the PSF describes how signal from one point x in the object propagates across all pixels of the entire image, the SRF indicates for one pixel in the spectroscopic image the weight of contribution for all locations in the object. The SRF thus provides a more intuitive understanding of the spatial origin of a localized spectrum, and allows one to directly assess possible locations of signal contamination. If k-space is sampled symmetrically at kn = [n – (N + 1)/2] · Δk, n = 1, 2,…, N, the 1D SRF of a conventional imaging experiment is given by:

equation image(1)

In these equations, the k-space increment Δk is determined from the FOV: Δk = 1/FOV, N is the number of phase-encoding steps, and Δx is the nominal spatial resolution: Δx = FOV/N.

The coverage of k-space and the corresponding SRF for a conventional, 1D experiment with eight phase-encoding steps is depicted by the dashed lines in Fig. 1. Three fundamental properties of the experiment can be derived from this figure. First, the inherent spatial resolution of the experiment, given both by the Rayleigh criterion and by FOV/N, is indicated by the 64% level of the SRF. Second, the sensitivity of the experiment is given by the amplitude of the SRF within the voxel-of-interest (VOI). Third, potential signal contamination from adjacent regions is caused by the sidelobes of the SRF outside the VOI. An equivalent, acquisition-weighted experiment must have identical spatial resolution and sensitivity, but should have less contamination, i.e., smaller sidelobes.

Figure 1.

The (a) k-space weighting function and (b) SRF of a 1D, nonweighted CSI experiment with eight phase-encode steps (solid line), compared to an acquisition-weighted experiment with identical spatial resolution and duration (dashed line). Within the VOI, both SRFs are essentially the same. The sidelobes of the SRF, however, are efficiently suppressed in the weighted sequence. Since the number of accumulations per phase-encode step has to be an integer, the actual values used in the experiments differ from the ideal weighting function. The thin step-shaped line in the left graph shows these deviations for an example in which the nonweighted experiment is averaged four times.

Mareci et al. (23) have shown that a good compromise between localization and sensitivity is obtained by weighting k-space with a Hanning function. For a 1D experiment, the weight w given by a Hanning function to the k-space sample kn is:

equation image(2)

In this equation, we have introduced the coefficients α and β, which allow an accurate adjustment of the inherent spatial resolution, sensitivity, and total duration for the acquisition-weighted experiment. The solid lines in Fig. 1 show the weighting function and the corresponding SRF for a 1D Hanning-weighted experiment. Within the VOI, the two SRF are virtually identical; their difference lies mainly in the sidelobes. For experiments with two or three spatial dimensions, radial weighting of k-space should be employed. Consequently, the variable kn in Eq. [2] then must be replaced by the length of the nthk-space vector |kn|.

The width of the acquisition-weighted SRF can be adjusted with the coefficient α. Two independent criteria need to be fulfilled within the VOI: for equivalent spatial resolution, the 64% level of the SRF should correspond to the desired spatial resolution Δx; for equivalent sensitivity, the integral over the SRF within the VOI should be the same as for the nonweighted experiment. By iterative calculation of the SRF and numerical optimization, the appropriate values of the coefficient α were obtained. Because of the slightly different shape of the conventional and acquisition-weighted SRFs, the surface (volume) of the SRF at the 64% level was used as a criterion for spatial resolution in the 2D and 3D cases, respectively. The two aforementioned conflicting criteria for spatial resolution and sensitivity yield values for α that differ by only 1% or less. The mean values for α arising from the two criteria are given in Table 1. With these coefficients, the central lobe of the Hanning-weighted SRF can be closely matched to that of a conventional experiment. In the 1D case, the desired spatial resolution Δx is obtained for α1D = 1.61. As can be seen in Fig. 1, a correspondingly larger section of k-space needs to be covered in the acquisition-weighted experiment.

Table 1. Hanning-Coefficients α and β
Spatial dimensionsαβ
  1. Appropriate values for the coefficients α and β in Eq. [2], for acquisition-weighted experiments with one, two or three spatial dimensions. The coefficient α controls the width of the spatial-response-function, β the total duration of the experiment.


The other condition for equivalent imaging experiments is identical total duration. For acquisition-weighted experiments, this can be expressed as the area under the weighting curve, which needs to be the same as in the nonweighted situation. Having obtained the coefficients α, the coefficients β can be computed by numerical integration of Eq. [2], and by setting the integral equal to the area under the nonweighted function. The resulting coefficients β for 1D, 2D, and 3D experiments are also listed in Table 1.

In spectroscopic imaging, a straightforward way to accomplish acquisition weighting is to vary the number of accumulations for each phase-encoding step. In this case, the weighting function can only be approximated by its nearest integer value. The number of accumulations NA(kn) to be performed for phase-encoding step kn thus can be calculated as:

equation image(3)

with NAtot the total number of scans for the experiment, “round” the mathematical function that finds the nearest integer, and w(|kn|) computed from Eq. [2]. The square brackets in this equation indicate optional terms for 2D or 3D experiments. As the ideal weighting function is only approximated by the number of averages, the SRF can be somewhat improved in a post-processing step, multiplying the signal acquired for each phase-encoding step kn with the corresponding correction factor w(|kn|)/NA(|kn|). This hardly affects the noise properties of the experiment because the correction is small, and the mean value of the correction factors is close to unity.

As an example, let us assume a conventional CSI experiment with three spatial dimensions, with Nx = Ny = Nz = 8 phase-encode steps in each direction. If four accumulations are performed at each phase-encode step, the total number of scans is NAtot = 2048. The number of accumulations for an equivalent acquisition-weighted experiment, resulting from Eqs. [2] and [3], is given in Fig. 2. There are 840 different phase-encoding steps in the weighted experiment (compared to 83 = 512 in the original experiment); the total number of scans is 1912. Because of the rounding, the total numbers of scans obtained from Eq. [3] can differ somewhat from the desired NAtot, especially if NAtot is small. In this case, a brief iteration on β can provide a better approximation of NAtot. Although the weighted acquisition covers a larger fraction of k-space, and has a higher number of averages in its center, the total duration of both experiments is very similar. Furthermore, the central lobe of their SRF is, in essence, identical, indicating that both experiments have the same nominal spatial resolution and sensitivity.

Figure 2.

Number of accumulations per phase-encoding step, calculated from Eq. [3], for a 3D CSI experiment with a nominal resolution of Δx/FOV = 1/8, and with a total number of NAtot = 2048 scans. Fully symmetric sampling of k-space with an even number of phase-encoding steps has been assumed. Only the positive quadrant of k-space is shown. In this case, acquisition weighting leads to 840 different phase-encoding steps.

The difference between the conventional and the acquisition-weighted experiment is the significant attenuation of the sidelobes of the SRF in the latter. Thus, contamination arising from tissue in the region of the sidelobes can to a large extent be avoided. While this does not affect the sensitivity of the experiment (i.e., the signal amplitude originating from within the nominal VOI), this can nevertheless have significant repercussions on the observed signal amplitude. To illustrate this point, we have calculated the integral of the SRF over the entire FOV. This integral corresponds to the total signal that would appear after reconstruction in a voxel if a homogeneous sample covering the FOV were used. Although the main lobes of the SRF with and without acquisition weighting are very similar, the integral over the FOV is indeed quite different. In the nonweighted experiment, the first negative sidelobe of the sinc-function is larger than the next positive lobe, and so forth. The overall contamination from the sidelobes hence leads to signal attenuation. For this reason, the integral of the 1D acquisition-weighted SRF is 1.35 times larger than that of the nonweighted SRF. For more-dimensional experiments, this difference becomes even more distinct: for two dimensions and a resolution of 8 × 8 voxels, the integral over the acquisition-weighted SRF is 1.72-fold larger than the nonweighted one; for 3D experiments it is 2.22-fold larger. In the latter case, the contamination would reduce the signal observed in the reconstructed spectra by more than one half!


Acquisition weighting is particularly advantageous when the size of the voxels is of the same order as the structures in the examined object, since in that case, contamination is especially pronounced. A very interesting application is in 31P-CSI of the human heart, where the low sensitivity and low concentration of the observed metabolites allow only for a very low spatial resolution, close to the thickness of the myocardium. To assess the improvement obtained by acquisition weighting, we compared the performance of conventional CSI experiments to acquisition-weighted ones on 13 healthy volunteers.

All experiments were performed on a 2 T Bruker whole-body system, equipped with a Siemens 31P/1H-surface coil that was retuned for 2 T. This coil included a larger, double-tuned coil (27.5 cm in diameter), which was used for 1H-transmit and -receive and for 31P-transmit. The 31P signal is received by a smaller quadrature coil, which consisted of a 12-cm × 14-cm rectangular coil and a figure-eight-shaped 24-cm × 14-cm coil. Preamplifiers integrated in the coil casing amplified both channels.

For spectroscopy, a straightforward “pulse/phase-encode/acquire” measurement protocol was used (RF pulse: 300 μs, triangular gradient pulse: 1.2 msec, sweep width 2500 Hz, 512 complex data points). The conventional CSI sequence had an FOV of 20 × 20 × 32 cm3 with eight phase-encoding steps in each direction, leading to a nominal voxel size of 2.5 × 2.5 × 4 cm3 (25 ml). Fully symmetric sampling of k-space was employed. To accumulate sufficient signal, the whole experiment was averaged four times. The results of this experiment were compared to those of an acquisition-weighted sequence with identical nominal spatial resolution and total duration. To sample the center of k-space (which provides a global spectrum that is helpful in determining the parameters for phase correction) and still cover k-space symmetrically, an odd number of phase-encoding steps was applied. With the above formulas, these conditions yielded up to 13 phase-encode steps per k-space direction, and six averages in the center of k-space. The coefficient β was slightly adjusted to provide 2048 scans.

To compare the properties of the two experiments, the SRF was measured by applying the protocol to a point source (a small sphere filled with phosphorus acid). The reconstructed signal of such a source yields the point-spread function, which has the same shape as the SRF. The point-spread functions measured for both sequences are shown in Fig. 3. The high amplitude of the sidelobes of the unweighted sequence (left panel) obviously can lead to substantial contamination, which can be positive or negative, depending on the actual geometry of the studied object. In the weighted sequence (right panel), the sidelobes of the SRF are very efficiently suppressed. The 64% volume of the central peak of the SRF of the weighted experiment was measured to be only 3.5% larger than that of the nonweighted experiment. Thus the nominal spatial resolution of both sequences is virtually identical.

Figure 3.

Experimentally determined SRFs of the CSI experiments used on the 2 T instrument for the volunteer study, measured on a small sphere containing phosphorus acid. To better visualize the amplitude of the sidelobes, the results here are shown in magnitude mode (all spectra in the other figures are in absorption mode after phase correction). These measurements demonstrate the significant attenuation of the sidelobes in the acquisition-weighted experiment. The 64% volume of the weighted SRF has been measured to be 3.5% larger than the nonweighted one. The nominal spatial resolution of both experiments thus is essentially the same.

Volunteers were connected to ECG, which supplied the synchronization signal in all experiments, and were placed prone on the coil. Since the results are to be corrected for the different saturation of the metabolites, the flip angle over the whole FOV has to be known. For this reason, a small vial was attached at the back of the coil, which was filled with phenylphosphonic acid doped with chromium acetylacetonate. Its chemical shift is 20 ppm downfield of PCr, well away from all metabolite resonances in the heart. The flip angle at the location of this vial was determined by the acquisition of global spectra with nine different flip angles. Having computed the B1-field distribution of the transmitter coil using the law of Biot-Savart, this calibration allowed us to calculate the local flip angle in every voxel of the spectroscopic image.

Next, the optimal orientation for the spectroscopic experiments was determined. Due to the geometry of the thin, long myocardium, a double-oblique orientation in the short-axis direction of the heart was chosen. This reduces partial volume effects for voxels that are longer in the direction of the long axis of the heart. A multislice CINE 1H-image of the entire heart was acquired in this orientation in order to visualize the anatomic origin of the spectroscopic signals. Collecting eight phase-encode steps for each of six images (typically) per heartbeat, we acquired 20 slices in about 3–5 min, using the inflow effect to obtain good contrast between blood and cardiac tissue. After 1H imaging and 31P-B1-field calibration, the two spectroscopic examinations were conducted. Both experiments consisted of 2048 excitations and took 25–40 min, depending on the heart rate of the volunteer. Including shimming, 1H imaging and the two spectroscopic experiments, the whole protocol took about 90 min. An examination with only one CSI measurement can thus be performed in less than an hour.

The data acquired in the acquisition-weighted experiments were first corrected for the rounding errors of the weighting function, as mentioned after Eq. [3]. The data of both types of experiments were zero-filled to 64 points in the spatial directions, exponentially filtered in the spectral dimension (line-broadening 8 Hz) and Fourier transformed. A linear phase correction calculated from theory was applied in the spatial dimensions; the global spectrum acquired at k-space origin provided the coefficients for zero- and first-order phase corrections in the spectral dimension. The relatively strong first-order phase correction in the spectral dimension, necessary because of the missing initial data points during the phase-encoding gradients, leads to a rolling baseline in the spectra, particularly about the PCr-resonance. This baseline undulation somewhat impedes the generation of metabolic maps by a simple visualization of the spatial distribution of resonance amplitudes.

For spectral quantification, the missing data points were accounted for by an initial dead time in a time-domain-fitting algorithm. Spectra were quantified using the AMARES algorithm (32), which is included in the MRUI package (33). From the noise contained in the spectra, AMARES also computes the SNR of each resonance. For each voxel, the excitation flip angle was calculated from the flip angle measured at the location of the reference vial and from the B1-field map. The flip angle in the heart was typically about 45°. This local flip angle, together with the actual repetition time (dependent on the heart rate) and values for T1 relaxation from the literature (34), served to correct the PCr:ATP ratio for partial saturation. The contribution from blood to the ATP signal was compensated for using the method described by Hardy et al. (35).


Thirteen healthy male volunteers were examined using the above protocol. For each, both an acquisition-weighted and a nonweighted CSI experiment were performed in the same session without changing the position of the volunteer or the setup of the experiment. Results acquired with both sequences for one volunteer can be seen in Fig. 4. For both experiments, localized spectra centered at exactly the same position are shown. It can be seen that the observed SNR of the PCr resonance is significantly higher for the weighted than for the nonweighted spectra. Since the adjustment of the SRF of both experiments ensures that the nominal resolution, and consequently the signal amplitude originating from within the voxels, is identical in both experiments; since the noise amplitude is not influenced by the weighting, this difference is due to spatial contamination. For the nonweighted experiment, the overall signal contribution from outside of the voxel is mainly negative, which leads to the observed reduction of SNR.

Figure 4.

Results of (a) the nonweighted and (b) the acquisition-weighted CSI experiment of a healthy volunteer. For both experiments, four spectra from the same voxel positions are shown. Nominal voxel size was 2.5 × 2.5 × 4.0 cm3, and each experiment consisted of 2048 scans synchronized to the heart beat. The indicated SNR has been computed by the time-domain-fitting algorithm AMARES. The spectra acquired with acquisition weighting show a considerably higher PCr:ATP ratio and a higher SNR for the PCr and ATP signals.

A total of 33 spectra from 11 volunteers (two had to be rejected because of too-large linewidths) from different regions of the heart were statistically evaluated. The results for all volunteers and for both methods are summarized in Fig. 5. The PCr:ATP ratio of the left-ventricular myocardium shows a distinct discrepancy between the two experiments: for acquisition-weighted CSI, we found a PCr:ATP ratio of 2.05 ± 0.31 (mean ± SD, N = 33), but only 1.60 ± 0.46 for the nonweighted sequence. Figure 5 also shows a comparison of the SNR of the PCr and ATP resonances in the reconstructed spectra obtained with both sequences. For conventional CSI, the average SNR of the PCr peak is 7.6 ± 2.4; for the acquisition-weighted sequence it is 11.6 ± 3.0. Since noise amplitude and voxel size are equal in both sequences, voxels in the weighted sequence appear to contain on average 53% more PCr than in the nonweighted sequence. In some voxels, we even observed a more than twofold SNR increase. The amplitude of the β-ATP resonance increased on average by 37%. The differences between both sequences for the ATP:PCr ratios and for the SNRs of PCr and ATP are statistically highly significant, according to Student's paired t-test, with P < 0.0001 for all tests. Avoiding the destructive interference caused by spatial contamination, the acquisition-weighted sequence in many cases even provided reasonable spectra from the posterior wall (Fig. 4).

Figure 5.

Summary of results for conventional and acquisition-weighted CSI experiments from 33 spectra obtained in 11 volunteers. The bars mark the mean value and the standard deviation of (a) the PCr:ATP ratio and (b) the measured SNR of the PCr and ATP resonances. The acquisition-weighted experiments yield a considerably higher PCr:ATP ratio with a smaller standard deviation (2.05 ± 0.31) compared to the conventional experiment (1.60 ± 0.46). The measured SNR of both the PCr and ATP peaks are also significantly higher in the weighted sequence (11.6 ± 3.0 and 7.2 ± 1.4, respectively) than in the conventional experiment (7.6 ± 2.4 and 5.4 ± 1.4). All differences are statistically highly significant (P < 0.0001).

An explanation for these unexpectedly high differences in the amplitude of the metabolite peaks in the reconstructed spectra is given in Fig. 6. It displays the SRF of the nonweighted CSI experiment for a voxel located in the anterior wall of the left-ventricular myocardium, overlaid unto the morphologic image. Obviously, large negative contributions to the signal originate in the chest muscle. Since this region lies in a much more sensitive region of the surface coil, this negative signal contribution is even stronger. It thus causes a large reduction in the observed amplitude of the metabolite signals, which is avoided when using acquisition weighting. In voxels for which the negative lobes of the SRF do not fall inside the chest muscle, the difference is less drastic. This effect also accounts for the different PCr:ATP ratios observed with both sequences. Since the breast muscle contains much more PCr than ATP, the destructive influence on the PCr peak of the myocardial spectra is higher than for the ATP peak, causing the observation of too small a PCr:ATP ratio in the nonweighted spectra. The magnitude of the negative contamination depends strongly on the location of the negative lobes of the SRF, and thus on the exact geometry and voxel position. Consequently, both the observed signal amplitude and the PCr:ATP ratio depend strongly on individual morphology, experimental parameters such as orientation or voxel shape, and the position of the voxel. These effects are probably an important element in explaining the wide variability of the PCr:ATP ratios found in the literature. A striking example was given by Kolem et al. (9), in which measurements with different orientations resulted in strong variations of the observed PCr:ATP ratio. This influence of geometrical factors is significantly reduced by acquisition weighting, thereby providing better reproducibility of results.

Figure 6.

The SRF of a conventional CSI experiment causes errors in the PCr:ATP ratio and the metabolite concentrations: for a voxel positioned in the left myocardium, the contours of the main positive and first negative lobes of the SRF are overlaid onto a 1H image of the heart. A region of strong negative contribution lies in the breast muscle, which, in addition, is in a much more sensitive region of the surface coil than the voxel itself. This strong negative interference reduces the signal amplitude and distorts the measured PCr:ATP ratio observed for this voxel. Acquisition weighting of k-space can suppress these effects, with no penalty in sensitivity or spatial resolution.

Because of the better localization properties of the weighted experiments, it was possible to reduce the voxel size to 2.0 × 2.0 × 4.0 cm3 (16 ml) without changing the total duration of the experiment. The FOV was increased in the third direction to 20 × 20 × 40 cm3. These parameters lead to a sequence with up to 15 phase-encode steps per k-space direction, with three averages at the k-space center. This experiment was performed on six healthy volunteers. Nuclear Overhauser enhancement (NOE) was used to enhance the SNR, by applying two to four 2-msec 1H pulses between the phosphorus pulses, depending on the heart rate. Spectra from one volunteer are shown in Fig. 7. The SNR is still sufficient over a large part of the heart for observing the typical metabolic pattern.

Figure 7.

Metabolic images from two volunteers, gathered using acquisition-weighted CSI with a nominal voxel size of only 2.0 × 2.0 × 4.0 cm3 (16 ml). In these experiments, NOE enhancement was applied to increase the SNR. For (a) the first volunteer, three spectra from different locations of the myocardium are shown, which still have an adequate SNR. For both volunteers, the metabolite images (b,c) display the distribution of β-ATP and DPG. Theses images were constructed by numerical integration of a small region in the real part of the phased spectra, and were corrected for the B1 inhomogeneity of the surface coil. Contours from the 1H image were overlaid onto the DPG maps.

Because of the improved resolution, the high SNR, and the low contamination of the acquisition-weighted protocol, it is possible to display the spatial distribution of the metabolites in the heart. Figure 7 shows the distribution of β-ATP and DPG observed in two volunteers. The images were reconstructed from an acquisition-weighted CSI experiment, as described in the previous paragraph, after zero-filling to 64 × 64 points in the spatial dimensions. The ATP and DPG images were obtained by summing over a small spectral range (∼ 0.3 ppm) about the desired resonance, and visualizing the spatial distribution of this amplitude. These images were also corrected for the B1 inhomogeneity of the surface coil. The ATP image clearly shows the entire circle of the left-ventricular myocardium. In the DPG image, which displays the distribution of blood, the left and right ventricles, and the liver, can be discerned. The missing initial data points lead to a baseline distortion that is particularly pronounced about the PCr resonance. This artifact strongly affects the numerical summation about this resonance and hindered the reconstruction of PCr images. A more sophisticated reconstruction procedure that circumvents the issue of the missing data points, such as an algorithm based on time-domain fitting, possibly could generate adequate PCr images.


An acquisition-weighted technique for gathering metabolite images has many advantages. In a situation such as 31P-MRS of the human heart, which is characterized by large voxel sizes, an experimental duration governed by low sensitivity, and by the use of inhomogeneous surface coils, acquisition weighting significantly reduces the spatial cross-talk between adjacent voxels. At identical sensitivity, the sidelobes of the SRF are substantially attenuated, and the reduced spatial contamination improves the experimental reproducibility. Finally, acquisition weighting can significantly influence the observed SNR, which results from an interaction of the SRF and the particular morphologic geometry. In the particular case of 31P-MRS of the human heart, where the size of the voxels is similar to the thickness of the myocardial wall, destructive interference with signals from skeletal chest muscle can attenuate the observed signal amplitudes, and can even alter the measured metabolite ratios. The actual degree of spatial interference in a particular study of course depends on the spatial resolution of the experiment and on the orientation of the image plane, which both influence the interaction between anatomy and SRF.

When implementing an acquisition-weighted protocol, the low sensitivity makes it mandatory to accurately control the spatial resolution inherent to the experiment. After presenting a definition for the nominal spatial resolution, which was derived from the well-established Rayleigh criterion in optics, the appropriate coefficients for a Hanning weighting function were given. These allowed adjusting both the width of the SRF and the total duration of the spectroscopic examination. The properties of conventional and acquisition-weighted CSI with identical spatial resolution and total duration were then compared by 31P-metabolite imaging in the human heart.

Measurements in 13 volunteers at 2 T revealed a higher observed SNR and a higher PCr:ATP ratio, both of which can be explained by reduced destructive interference with signals originating in the breast muscle. The reduced contamination in acquisition-weighted CSI made it possible to obtain spectra from the posterior wall of the left ventricle. The corresponding spectra from nonweighted CSI were severely degraded due to the contamination from tissue that is closer to the coil and thus is in a more sensitive region.

Reliable 31P-metabolite images may be useful in clinical practice since they allow the detection of regions of ATP depletion, and the location of anomalies in metabolism. Up to now, however, only very few 31P metabolite images (from the calf muscle (36, 37) and heart (11, 38)) have been published. The reduced contamination and improved resolution of acquisition-weighted CSI now makes it possible to obtain images showing the distribution of ATP over the entire heart. These results indicate that 31P-CSI may become feasible even for diagnostic applications.


We are grateful to Dr. Wolfgang Renz (Siemens, Erlangen) for the adjustment of the coil to our field strength, and we thank Prof. A. Haase for making measurement time available on his instrument.