Dynamic 31P–MRSI using spiral spectroscopic imaging can map mitochondrial capacity in muscles of the human calf during plantar flexion exercise at 7 T

Abstract Phosphorus MRSI (31P–MRSI) using a spiral‐trajectory readout at 7 T was developed for high temporal resolution mapping of the mitochondrial capacity of exercising human skeletal muscle. The sensitivity and localization accuracy of the method was investigated in phantoms. In vivo performance was assessed in 12 volunteers, who performed a plantar flexion exercise inside a whole‐body 7 T MR scanner using an MR‐compatible ergometer and a surface coil. In five volunteers the knee was flexed (~60°) to shift the major workload from the gastrocnemii to the soleus muscle. Spiral‐encoded MRSI provided 16–25 times faster mapping with a better point spread function than elliptical phase‐encoded MRSI with the same matrix size. The inevitable trade‐off for the increased temporal resolution was a reduced signal‐to‐noise ratio, but this was acceptable. The phosphocreatine (PCr) depletion caused by exercise at 0° knee angulation was significantly higher in both gastrocnemii than in the soleus (i.e. 64.8 ± 19.6% and 65.9 ± 23.6% in gastrocnemius lateralis and medialis versus 15.3 ± 8.4% in the soleus). Spiral‐encoded 31P–MRSI is a powerful tool for dynamic mapping of exercising muscle oxidative metabolism, including localized assessment of PCr concentrations, pH and maximal oxidative flux with high temporal and spatial resolution.

These observations, together with the fact that evaluation of muscle oxidative metabolism provides insight into personal training status, 8,9 have led to a considerable methodological development in medical imaging for non-invasive assessment of muscle energy metabolism.
In particular, phosphorus MRS ( 31 P-MRS) has been established as a powerful tool for studies of energy metabolism. [10][11][12][13][14][15] More specifically, dynamic 31 P-MRS, during exercise and recovery, allows direct estimation of the oxidative adenosine triphosphate (ATP) synthesis rate in challenged muscle, which reflects maximal mitochondrial capacity. 12 Since high temporal resolution (of the order of seconds) is required to map the phosphocreatine (PCr) recovery curve, coarse signal localization restricted only by the sensitive volume of a surface coil is often used to retain sufficient signal-to-noise ratio (SNR) for dynamic 31 P-MRS experiments. 16,17 Such localization cannot distinguish between muscle groups that are recruited differently in the performed exercise (e.g. soleus (SOL) and gastrocnemius during plantar flexion [18][19][20][21][22][23] ).
Single-voxel MRS 24,25 or slab-selective MRS 26,27 have been implemented to overcome this limitation and enable single-muscle localization. However, spatially defined injuries, myopathies, or functional deficits in PAD can be overlooked if only a single predefined muscle location is examined. Thus, actual mapping approaches allowing for coverage of several muscle groups simultaneously are desirable. Frequency-selective phosphorus MRI ( 31 P-MRI) has been shown to provide information on PCr recovery kinetics from several muscles simultaneously, [28][29][30] and was recently extended to provide information about pH dynamics during exercise. 31 So far, these 31 P-MRI techniques do not provide the same amount of information as 31 P-MRS; e.g., there are no data on ATP signal intensity typically used for concentration quantification, or on other 31 P metabolites. The temporal resolution of phosphorus MRSI ( 31 P-MRSI) with Cartesian phase encoding is, however, insufficient for estimating mitochondrial capacity with high spatial resolution unless a dedicated exercise protocol (i.e. gated MRSI 32,33 ) is applied, which considerably complicates and prolongs the examination and may impose limitations, such as the requirement of only mild pH changes.
In this context, our aim was to develop and test a 31 P-MRSI sequence using spiral readout trajectories with high temporal resolution for spatially resolved quantification of maximal oxidative ATPsynthase flux in the muscles of the human calf during plantar flexion exercise. The performance of the proposed sequence was tested in a localization phantom and in healthy volunteers.

| Sequence design
To accelerate the acquisition and hence increase the temporal resolution of our dynamic 31 P-MRSI scans, we implemented a constant-density spiral spectroscopic readout. 34,35 Following each slice-selective excitation (achieved by a Hamming filtered SINC pulse with 600 μs duration and 6.4 kHz bandwidth), we played out consecutive and identical spiral gradient waveforms (n = 512 divided by the number of temporal interleaves) in the read (x) and phase (y) gradient directions that fully covered the k-t space. The spiral trajectories for all excitations were identical. Since the duration of the spiral trajectories for the given voxel size was longer than the temporal sampling required for the desired spectral bandwidth, temporal interleaving (i.e. shifting the gradient trajectory for consecutive T R by a fraction of the dwell time) was employed ( Figure 1) (e.g., for five temporal interleaves at 1.45 kHz spectral bandwidth 103 spirals of about 3.4 ms length per spiral were played out per interleave, leading to a total sampling duration of about 353 ms, with each interleave being delayed by 0.69 ms relative to its predecessor). To optimize the SNR, gradient rewinders (i.e. deadtime during readout that is necessary to return to the k-space center) were minimized (<6%). Hence, only temporal interleaves were used and not spatial interleaves. The number of temporal interleaves was adjusted to the targeted matrix size, making sure that the spectral bandwidth remained between 1.4 and 1.45 kHz (i.e. covering a range of at least 12 ppm from P i to γ-ATP resonances). The achieved spectral resolution, i.e. the spectral bandwidth over the number of acquired spirals, was therefore always 2.7-2.8 Hz. The entire spiral trajectory calculation and data reconstruction were implemented on the MR scanner.
The following four steps were performed within the online processing pipeline: (i) gradient delays between the ADC readout and the x/y gradients of 8 μs were corrected by shifting the sampled data inside the array; (ii) the acquired data were gridded two-dimensionally to a twofold oversampled Cartesian matrix with a Kaiser-Bessel kernel, (iii) a fast Fourier transform (FFT) was applied in the x/y dimension, and then (iv) an FFT was used in the frequency dimension.

| Phantom experiments
The point spread function (PSF) of the proposed MRSI sequence was measured in a two-compartment phantom. The outer compartment (a cylinder with a diameter of 13 cm) was filled with tap water, and the inner compartment (a cube with 9 mm inner side length) was filled with a P i solution (concentration = 1 mol/L). The cube was fixed in the center of the cylinder, 3 cm from its base. Three 2D-MRSI datasets

| In vivo measurements
To test the potential temporal and spatial resolution of the proposed sequence in an in vivo situation, one healthy male volunteer underwent repeated measurements of the calf muscle. The volunteer lay supine on the MR table and the RF coil was placed under the right gastrocnemius muscle. The matrix sizes used and corresponding numbers of required temporal interleaves are listed in Table 1 Twelve young, healthy individuals (nine males/three females, age (mean ± standard deviation) 28.7 ± 4.1 years, BMI (body mass index) 23.2 ± 2.6 kg/m 2 , no professional athletes) agreed to participate in the dynamic part of this study and signed a consent form approved by the institutional ethical board. Each volunteer lay supine on the ergometer, inside the MR system, with the RF coil strapped below their right calf.
The knee of the volunteers was fully extended during the dynamic examination (2 min rest, 6 min exercise and 6 min recovery) to ensure a major involvement of the gastrocnemius muscles and only a minor contribution of the SOL muscle to the exercise performed. [20][21][22] The volunteers performed plantar flexions at a workload set to about 25-35% of the maximal voluntary contraction force, once every T R (2 s). The exercise was synchronized with the data acquisition based on an audio signal, so that the MRSI data were acquired when the calf muscle was relaxed. In addition, five of the recruited male volunteers underwent a second dynamic examination with the knee flexed at about 60°. In this leg position the SOL muscle is expected to be involved more than the two gastrocnemii. 20 This second examination was performed at least 20 min after the first one, to ensure sufficient metabolic recovery. 36 Two additional spiral-MRSI measurements were performed at rest in two of these subjects in order to acquire representative flip angle maps 37

| Data analysis
All acquired MRSI data were interpolated to 16 × 16 matrixes, and voxels with SNR of the PCr signal above 8 in the resting state before exercise (no k-space filtering was applied prior to data analysis) were TABLE 1 The relation between the matrix size (i.e. spatial resolution) and the number of temporal interleaves required (i.e. temporal resolution). For comparison, the temporal resolution of an elliptically phase-encoded MRSI (ePE) is also given. Note that the increase in temporal resolution comes at the cost of SNR, which is, however, comparable once the acquisition time is matched and the differences in PSF between spiral and elliptical encoding are corrected for In-plane constant density spiral readout for FOV 200 × 200 mm 2 and 14 × 14 matrix with temporal interleaving. The slice-selective excitation pulse is followed by the spiral gradient modulations (only x -direction shown). These spiral trajectories are played out repeatedly (512 times; only three shown for illustration) to cover the whole free induction decay in the time domain. As the duration of a spiral is too long to allow a sufficiently short spectral dwell time, temporal interleaves (five temporal interleaves are shown here for illustration) were acquired. Each temporal interleave is acquired after a separate excitation, and identical spiral gradients are played out with a predefined delay. This delay determines the actual dwell time and hence the spectral readout bandwidth. The number of temporal interleaves used in the sequence was derived as the minimum number required to cover the desired spectral bandwidth of 1.4 kHz pre-selected for quantification of dynamic in vivo data. Custom software written in IDL (Exelis Visual Information Solutions, Boulder, CO, USA) was used for pre-selection of these voxels. All selected spectra were analyzed using the jMRUI software (Version 5.0) with the AMARES (advanced method for accurate, robust, and efficient spectral fitting) time domain fitting routine. 39 The γ-ATP resonance was used as an internal concentration reference, assuming a stable cellular ATP concentration of 8.2 mM. 40 To improve the SNR of the γ-ATP peak for quantification purposes, the γ-ATP signal intensity was averaged over the last six measurements (1 min) of the recovery period. For the saturation correction, the actual flip angle was calculated for each muscle group as the average of the measured datasets, and the previ- The SNR was calculated based on the magnitude of the signal from the voxel covering the cubic phantom for the phantom experiments, comparing the SNR of elliptical and spiral encodings matched for acquisition time, and similarly by using the magnitude of PCr signal in voxels within a 5 × 3 area covering the skeletal muscle tissue for the in vivo experiment that compared the SNR for different spatial resolutions.
The standard deviation of noise evaluated from 100 points of the spectra far from the metabolite signals was used for SNR calculation.
To compare the oxidative metabolism between the three muscle groups of interest-gastrocnemius medialis (GM), gastrocnemius lateralis (GL) and SOL-the muscles were manually segmented using 1 H localizer images. Each segmented volume of interest contained 3-5 voxels, leaving at least one voxel free between the adjoining mus- for the fully encoded k-space. The results of the phantom PSF experiments are depicted in Figure 2.
The SNR comparison between different matrix sizes and temporal resolutions measured in vivo at rest is given in and height equal to the slice thickness) and temporal (10 s) resolution with sufficient SNR.
Representative spectra acquired at rest and at the end of exercise from each investigated muscle group are depicted in Figure 3. To demonstrate the importance of 31 P signal localization in dynamic experiments, a voxel containing a mixture of GM and SOL tissue is also visualized (green). Note that in such voxels of mixed tissue splitting of the P i signal, which corresponds to two compartments with different pH values, can be observed.
The time evolution of PCr and P i signals-in GM, GL and SOLduring plantar flexion exercise with a straightened knee is depicted in Figure 4 (top panel). The time evolution of pH in these muscles is also included in Figure 4 (bottom panel  Table 3. the SOL muscle is the one with the highest PCr depletion. The difference in exercise-induced drop in PCr signal between the two dynamic experiments was found to be statistically significant (p < 0.05) for all three muscle groups (i.e. lower for both gastrocnemii and higher for SOL in the second exercise). Significantly shorter τ PCr and higher Q max were calculated for the SOL muscle in the second experiment; however, there were no statistical differences in these parameters found between the two experiments for either GM or GL. Table 4 summarizes the direct comparison of the measured and interpreted measures of mitochondrial function using these two exercise protocols.

| DISCUSSION
In our study, we propose dynamic spiral-accelerated 31  The conventional approach to dynamic 31 P-MRS of using the sensitive volume of the RF coil for signal localization 16 24,25,45 On the other hand, 31 P-MRI techniques aim to map oxidative metabolism over the whole FOV simultaneously. [28][29][30][31]47 Single-voxel spectroscopy (SVS) provides an accurate localization of a cuboid volume as long as selective RF-pulses with broad bandwidth are applied. 48 However, SVS typically targets only a single muscle at a time. An interleaved technique providing information from two voxels within one dynamic experiment was suggested recently, 23 but this still lacks the high spatial resolution of our MRSI approach.
Furthermore, accurate spatial selection of SVS at 7 T requires relatively long T E , thus reducing sensitivity for important 31 P metabolites such as ATP. 25 The proposed MRSI approach is FID based, and therefore does not require such long T E . 31 P-MRI techniques, recently proposed for mapping of muscle oxidative metabolism, [28][29][30][31]47     temporal resolution. 30 Greenman and Smithline reported 2D PCr imaging with a 20 × 20 matrix (5.6 mL nominal spatial resolution) and 6 s temporal resolution at 3 T. 28 Our spectral-spatial encoding approach via spiral spectroscopic imaging, therefore, merges the spectral specificity of 31 P-MRS and spatial selectivity of 31 P-MRI.
In particular, our spiral-MRSI sequence: (i) provides full signal intensity detection for all metabolites within the spectral bandwidth via direct acquisition of the FID; (ii) features the same high spectral resolution as conventional non-localized 31 P-MRS sequences; and (iii) provides accelerated spatial encoding similar to 31 P-MRI for metabolic mapping.
Spectral bandwidth and temporal resolution can be balanced as required, while maintaining the full SNR per unit time (SNR/t).
Theoretically, the use of rewinder gradients (i.e. gradients that are necessary to return to the center of k space) can reduce SNR/t efficiency.
However, we have minimized this source of SNR loss by maximizing the number of spectral interleaves and eliminating the need for spatial interleaves. Thus, the necessary rewinder is very short, which restricts the SNR/t loss to well below 5%. Our phantom measurements also validate that the SNR/t values for elliptically phase-encoded and spiralencoded MRSI were nearly identical. The entire image reconstruction is implemented online. Thus, spectra could be directly inspected/ processed on the MR scanner. was not found to be significantly different between the measurements for either of these muscle groups.    imaging when combined with frequency-selective MEGA-editing pulses. 55 With a recently suggested approach it might be possible to use interleaved 1 H navigators also for 31 P-MRSI on common MRI systems. 56 The spiral MRSI readout proposed in our study could potentially lead to small artifacts when the changes in metabolite concentrations occurring during the dynamic protocol happen in between the acquisitions of individual temporal interleaves. These would originate from the largest signal in the spectrum, which is in our case PCr. However, we did not observe any during our test measurements in vivo, thus these theoretically present artifacts seem to be at or below the level of noise. Nevertheless, the selected bandwidth and number of temporal interleaves should ensure that, even if present, they would not overlap with any visible 31 P resonances. Another potential source of artifacts relates to the narrow acquisition bandwidth used. Metabolite signals that are outside the acquisition bandwidth of the spiral MRSI sequence, but are excited by the excitation pulse, such as α-ATP, could be aliased into the acquired spectra. However, these aliased signals would have only a fraction of the original signal amplitude, due to PSF blurring of signals from outside the spectral width, 57 and therefore were not observed in our in vivo data.
We conclude that spiral-encoded 31 P-MRSI is a powerful tool for dynamic mapping of the muscle oxidative metabolism, including localized assessment of PCr concentration, pH and ATP reference concentration with a high temporal and spatial resolution. This not only allows the assessment of muscle-specific mitochondrial capacity for all muscles within a single slice in physiological studies, but has also great potential for identifying small, i.e. early staged, localized pathologic changes in injuries, myopathies or PAD.