3D ultra-short echo time 31P-MRSI with rosette k-space pattern: Feasibility and comparison with conventional weighted CSI

Phosphorus-31 magnetic resonance spectroscopic imaging (31P-MRSI) provides valuable non-invasive in vivo information on tissue metabolism but is burdened by poor sensitivity and prolonged scan duration. Ultra-short echo time (UTE) acquisitions minimize signal loss when probing signals with relatively short spin-spin relaxation time (T2), while also preventing first-order dephasing. Here, a three-dimensional (3D) UTE sequence with a rosette k-space trajectory is applied to 31P-MRSI at 3T. Conventional chemical shift imaging (CSI) employs highly regular Cartesian k-space sampling, susceptible to substantial artifacts when accelerated via undersampling. In contrast, this novel sequence’s “petal-like” pattern offers incoherent sampling more suitable for compressed sensing (CS). These results showcase the competitive performance of UTE rosette 31P-MRSI against conventional weighted CSI with simulation, phantom, and in vivo leg muscle comparisons.


Introduction
Phosphorous-31 magnetic resonance spectroscopy ( 31 P-MRS), the longest-standing in vivo MRS modality, can be an invaluable tool for probing in vivo metabolites such as phosphocreatine (PCr), inorganic phosphate (Pi), phosphomonoesters (PMEs), phosphodiesters (PDEs), and adenosine triphosphate (ATP) . 1,2As fundamental phospholipids and consitituents of the high-energy phosphate pathway, these 31 P metabolites provide noninvasive measures of tissue pH, lipid metabolism, and oxidative bioenergetics. 3,4Thus, 31 P-MRS possesses versatile diagnostic and prognostic potential.6][7][8][9] Furthermore, 31 P-MRS has been used to assess whole-liver treatment e cacy, monitoring metabolite changes in malignant tissues following therapy. 10Likewise, diminished PCr/ATP ratios and post-exercise PCr recovery rates have been measured in cardiac and skeletal muscles of patients with type 2 diabetes. 11[14][15][16][17][18][19][20] While relevant 1 H-MRS metabolite signals are obscured by background signals such as contaminating fat, water, and macromolecular signals, widely spaced 31 P spectral peaks can be easily elucidated due to the absence of these nuisance signals.However, in contrast to 1 H-MRS, 31 P-MRS is burdened by a lower gyromagnetic ratio and relatively short spin-spin metabolite relaxation times (T 2 ); 21,22 these factors engender extremely poor in vivo relative sensitivity and force a delicate balance between SNR, resolution, and scan duration.Low 31 P-MRS tissue concentrations (approximately 2 mM γ-ATP in liver 23 ) further exacerbate SNR challenges, so that commonly used acquisition delays (T E > 300 µs) with conventional methods result in prolonged acquisition, phase distortions, baseline roll, and subsequent operator errors during metabolite quanti cation.Such complications have been severely limiting factors in the clinical feasibility of 31 P-MRS.Recent advances in coil engineering and the introduction of ultra-high eld (UHF, B 0 > 3T) scanners have assisted in mitigating these limiting factors; one experiment demonstrated a 2.8factor increase in PCr SNR at 7T relative to 3T. 24 Conversely, UHF acquisitions also necessitate larger spectral bandwidth (SBW), with a 40 ppm range requiring approximately 2.0 kHz at 3T but 4.8 kHz at 7T.Still, excessive acquisition durations remain the clear barrier to clinical translation without innovative acceleration.
To address these points, we propose a three-dimensional (3D), ultra-short echo time (UTE) sequence with a novel rosette k-space trajectory (previously validated in ultra-short-T 2 imaging 25,26 and brain iron mapping 27,28 ) for 31 P magnetic resonance spectroscopic imaging (MRSI). 29Compared to conventional CSI Cartesian k-space trajectories, rosette's "petal-like" pattern (Fig. 1) maps 3D k-space far more e ciently.Additionally, rosette's relatively inchorent data sampling allows the possibility of signi cant acceleration through higher undersampling factors and compressed sensing (CS) reconstruction; offering better k-space coverage when compared to radial and spiral trajectories, generalized rosette's curvature affords superior SNR performance under aggressive acceleration. 30Furthermore, UTE acquisitions permit the capture of short-T 2 signals before signi cant transverse signal decay and rst-order dephasing occur, enhancing SNR, simplifying spectral pre-processing, and minimizing operator quanti cation errors.Substantial efforts have been invested towards clinically feasible 31 P-MRSI, experimenting with short repetition times (T R ), measuring multiple k-space points per T R , k-space undersampling, enhanced reconstruction via prior knowledge, and their conceivable combinations. 313D extensions of ISIS have shown promise in UHF preclinical and 3T cardiac studies but remain limited by time resolution and motion artifact sensitivity. 32,33Non-localized or FID acquisitions are often preferred to minimize rapid 31 P T 2 -decay, but also to overcome speci c absorption rate (SAR) limitations at UHFs.Thus, variations of spatial-spectral encoding (SSE) schemes and their synergies with k-space undersampling appear to be the more promising avenue forward; several Cartesian and non-Cartesian acquisition designs offer varying degrees of SNR e ciency, k-space weighting, gradient system demands, and undersampling acceleration potential.
Flyback EPSI has been tested in skeletal calf muscle, 34 offering considerable time savings over conventional phase-encoded when combined with CS acceleration; 35 despite its acceleration potential, EPSI offers lower SNR e ciency and SBW at ne resolutions than other SSE options.Density-weighted concentric ring 36 trajectories (CRTs) offer increased SNR e ciency and SBW limits, enabling faster MRSI even with UHF systems.CRTs boast exibility in weighting and temporal interleaves, allowing tailoring according to acceleration needs and gradient slew rates.Similarly, spiral-encoded 31 P-MRSI has exhibited faster dynamic calf muscle mapping than conventional weighting phase-encoded acquisition. 37Though spirals offer high acceleration, SNR e ciency, and customizable weighting, they are also limited by SBW and gradient system hardware.
Conventional CSI FIDs commonly possess T E on the order of 1-2 ms, which is restricted by the duration of constant excitation pulses and phase encoding gradients to reach the outermost k-space points.This acquisition delay can be decreased using variable pulse widths and amplitudes.Sampling throughout gradient transition periods, or ramp sampling, remains an additional option for minimizing T E .Studies have showcased T E as low as 480 µs and 520 µs for EPSI and radial EPSI, respectively. 35,38Acquisitions using such UTE CSI techniques 39 have achieved T E = 300 µs at 3T and T E = 500 µs at 7T. 40,41 In non-Cartesian center-out k-space trajectories employing ramp sampling, T E is primarily limited by the dead time between coil transmit-receive switching, permitting the shortest possible T E .Despite this possibility, SBW constraints and conventional sequence parameter (T A /FOV) matching have prevented extensive investigation of non-Cartesian UTE 31 P-MRSI.
In this study, we evaluate the 3D UTE 31 P-MRSI with a novel rosette k-space trajectory by comparing its performance to conventional 3D-weighted 31 P CSI in the quadriceps muscle at 3T.We ultimately aim to demonstrate its potential value in clinical spectroscopic acquisitions.

UTE Rosette
General sequence parameters were as follows: T A = 36:00, T R = 350 ms, T E = 65 µs, matrix size = 24x24x24, nominal voxel size = 8 mL, FOV = (480x480x480) mm 3 , SBW = 2083 Hz, spectral time samples = 512.Parameters are summarized in Table 1.As in prior work, 25 3D UTE rosette k-space trajectory (Fig. 1) for 31 P-MRSI was generated with Equations ( 1) and ( 2): Where K max is the maximum extent of k-space, is the frequency of oscillation in the radial direction, is the frequency of rotation in the angular direction, determines the location in the z-axis, and determines the initial phase in the angular direction.For this 31 P-MRSI study, K max = 25/m, was sampled uniformly in the range of [-/2, /2], was sampled uniformly in the range of [0, 2 ], RF pulse duration = 50 µs, readout dwell time = 5 µs, and each rosette petal was designed with 96 points.This leads to  1.

Simulations
To assess the theoretical performance of the 3D UTE rosette relative to weighted CSI, MATLAB (Mathworks, Natick, USA) simulations were run examining side lobes and SNR relative to the spatial response function (SRF).A simple, constant 3D object was placed at the origin of a 48 x 48 x 48 grid (FOV = 480 mm isotropic producing a 1 mL nominal voxel size) with added noise and reconstructed using the non-uniform FFT (NUFFT) method and k-space information for each in vivo acquisition.We use spatial response function (SRF) instead of point spread function (PSF) since the former speci cally estimates side lobes and signal bleed between adjacent voxels, while the latter measures contribution from a single object point to the entire population of voxels.

Experimental comparison
All data acquisition occurred on a 3T MRI system (Prisma, Siemens, Erlangen, Germany) with G max = 80 mT/m and slew rate = 200 mT/m/ms isotropically.Human subject protocols were approved by the Institutional Review Boards of Purdue University, and informed consent was obtained.Sequence parameters are summarized in Table 1.
The rosette and conventional acquisitions were tested with a uniform 2-liter bottle phantom (0.17 mg/mL phosphoric acid) using a dual-tuned 1 H/ 31 P Tx/Rx exible 11-cm surface coil (RAPID Biomedical).For in vivo comparison, ve healthy volunteers (BMI = 26 ± 2 kg/m 2 ; age = 29 ± 5 years; 2 f / 3 m) underwent leg scans with an 8-channel, dual-tuned 1 H/ 31 P Tx/Rx phased array coil 42 (Stark Contrast, Erlangen, Germany).Quadriceps was chosen for its superior PCr SNR and absence of respiratory motion during prolonged scanning.Subjects were positioned feet-rst and supine, with the upper quadriceps tightly surrounded by the coil plates.Following localizer imaging, the adjustment volume was manually positioned (spanning both legs), and linewidth was minimized using a 3D GRE eld map and interactive SIEMENS shimming.Each subject was scanned rst with the conventional weighted Cartesian acquisition followed uninterrupted by the 3D UTE rosette 31 P-MRSI.Sequence parameters are summarized in Table 1.

Post-processing and reconstruction
Raw data les were exported for reconstruction and pre-processing in MATLAB.Gridding and FFT were completed using adjoint NUFFT (regridding), 43 Hanning ltered, and, when necessary, coil-combined using whitened singular value decomposition (wSVD). 44Spectra were zero-order phased by maximizing the integral of the largest peak (PCr, 0 ppm) for the 3D UTE rosette.Spectra from the weighted CSI were zero-order phased and rst-order phased to correct a 2.3 ms delay.

SNR and quanti cation
Spectra were tted within the Oxford Spectroscopy Analysis (OXSA) toolbox 45 using AMARES methods.
Metabolite peak SNRs were calculated according to Eq. ( 3), with noise variance calculated from a residual region lacking metabolite signals.As an additional signal quanti cation metric, "raw SNR" (Eq.( 4)) was estimated by dividing the highest absolute peak point by the noise variance in an offspectrum region; this method carries the advantage of consistently assessing signal strength regardless of any interfering spectral phase.
Data acquisition, reconstruction, processing, and analysis work ow is summarized in Figs. 2 and 3.

RMS off−spectrumnoise
The performance of 3D UTE rosette and weighted CSI in phantom solution and quadriceps muscle were assessed using Pi and PCr metabolite signals, respectively.Quanti cation considered the central, highest signal axial slices within each subject, attempting to quantify every voxel.Only voxels with SNR > 3 and OXSA-AMARES Cramér-Rao lower bound (CRLB) goodness of t smaller than 20% for PCr peak were included in the nal analysis.

Spatial Response Function simulation comparison of UTE Rosette with Weighted CSI
The impact of varying k-space sampling trajectories on image quality can be evaluated via SRF simulations as shown in Fig. 4. FWHMs along the x-axis at the center of the FOV were comparable between rosette (30.7 mm) and weighted CSI (36.1 mm).Both acquisition schemes exhibit noticeable sidelobe noise, albeit with slightly reduced side lobes in the rosette trajectory.

Phantom comparison of UTE Rosette with Weighted CSI
Figure 5 showcases results and setup of phantom experiments with dual-tuned exible surface coil.With approximately matched acquisition times, mean raw SNR (Eq.( 4)) was 69% higher in 3D UTE rosette than in weighted CSI.

In vivo leg comparison of UTE Rosette with Weighted CSI
Figure 6 shows representative 3D UTE rosette and weighted CSI axial PCr maps and spectra in the same volunteer.High-signal muscle regions are clearly distinguishable from low-signal bony femur regions.As expected, PCr predominates the 31 P muscle spectrum alongside smaller Pi and ATP peaks.
Quantitative PCr results for all subjects are given in Fig. 7, highlighting the different SNRs resulting from Equations ( 3) and ( 4) respectively.Tables 2 and 3 summarize these distinctions.While 3D UTE rosette consistently outperformed weighted CSI, the advantage was slightly more prominent in AMARES-tting of the real data at 34% compared to raw SNR of absolute data at 18%.

overview
This study demonstrates the feasibility of using 3D UTE 31 P-MRSI with a novel rosette k-space trajectory to acquire quality in vivo human subject data.Simulations showed the rosette trajectory produced acceptable image quality and SRF characteristics when compared to a conventional 3D weighted CSI acquisition.Experimental phantom scans utilized a uniform Pi bottle solution and the same scanning parameters later applied to in vivo quadriceps subjects.

UTE advantages
The novel acquisition's 70 µs acquisition delay is substantially lower than the 300-500 µs delays in previously published UTE 31 P CSI methods 40,41 , minimizing transverse signal decay and rst-order dephasing.Accurate phasing is key to spectral tting and quanti cation of real spectral data; when tting parameters must be tailored to hundreds of voxels across a large volume, such as for high resolution 3D MRSI, the challenge of avoiding phasing errors is most apparent.As expected, all 3D UTE rosette data were intrinsically devoid of noticeable rst-order phasing, thereby streamlining the quanti cation process.The SNR gap between 3D UTE rosette and weighted CSI acquisitions was narrowed when solely considering absolute data (Eq.( 4)).This distinction might be partially explained by the absence of phase in these magnitude spectra, whereby the 3D UTE rosette (T E = 70 µs) acquisition loses a portion of its advantage over conventional weighted CSI (T E = 2.3 ms).Notably, SDs for 3D UTE rosette SNR were signi cantly higher (50% or more) compared to weighted CSI.This elevated variation is partially explained by the novel acquisition's signi cantly higher SNR; moreover, weighted CSI's wider SRF engenders higher inter-voxel crosstalk, diminishing overall variation among quanti ed voxels.

Acceleration potential
Although these 36-minute acquisitions are quite lengthy, conventional ungated in vivo 3D 31 P-MRSI typically requires a minimum of 20 minutes at 3T.Compared to a weighted Cartesian trajectory, this novel rosette k-space pattern's relative incoherence makes it a very suitable candidate to CS acceleration via undersampling.Applying undersampling factors of 2 to 4, as demonstrated previously in uT 2 brain imaging 25 , could reduce 31 P-MRSI's TA to 9-18 minutes (or less with fewer averages). 46Such an acceleration would allow implementation of 31 P-MRS within realistic clinical constraints, while also being translatable to UHF research systems and higher resolutions.
As with all 31 P-MRS, spectral quality can also see potential improvement via proton decoupling and nuclear Overhauser effect (NOE) enhancement, albeit with implications for SAR and measured metabolite ratios.Furthermore, appropriately applied low-rank approximation and principal component analysis denoising have seen use in heightening SNR of MRSI data sets; [47][48][49] nevertheless, in the absence of ground truths or precise simulation, care must be taken in estimating metabolite concentration uncertainties after denoising.

Resolution and SBW
Many non-Cartesian acquisitions face restrictions in spatial resolution, SBW, and SNR due to available gradient hardware. 31For example, spiral trajectories face reduced SNR while waiting to return to k-space center between spirals; this ine ciency is addressed by closed-loop, out-in trajectories, but these remain impractical outside UHF animal gradient systems. 50Concentric rings can be similarly adjusted to meet needs with temporal interleaves. 36ill, SBW limitations remain a signi cant challenge; while 2.0 kHz might be su cient for 31 P-MRS at 3T, such a SBW would only offer a spectral range of around 17 ppm at 7T.While this rosette acquisition sampled 48 points per petal every 480 µs, the sequence remains highly customizable.By leveraging the second half of each petal (Fig. 1), it is possible to partially satisfy Nyquist criterion at even higher bandwidths and enable ner resolution reconstructions than the relatively coarse 8 mL voxels shown here.Additionally, this permits greater SBW acquisitions, opening the door to 3D UTE rosette 31 P-MRSI at UHF and 1 H MRSI at 3T.However, these petal halves are analogous to odd and even echoes of EPSI MRSI; since the timings between individual N pp are not equidistant, "full-petal" spectra will suffer from some degree of noise ampli cation and aliasing artifact.

Other limitations
Further experimentation is required in exploring the potential and limitations of 3D UTE rosette MRSI.Notably, these quadriceps scans focused on quadriceps muscle with plentiful PCr signal in a healthy volunteer population.However, 31 P-MRSI is frequently applied in measuring diverse brain, cardiac, and liver spectra, where nearby tissues may introduce contaminating metabolite signals.Minimal signal contamination was observed in noisy voxels within bony regions.Nonetheless, due to the relative uniformity of skeletal muscle spectra, it would be di cult to discern the rosette acquisition's relatively incoherent aliasing.Future work will aim to assess accelerated performance in patient populations.

Conclusions
Using the quadriceps of ve healthy volunteers at 3T, we investigated a potential application to 31 P-MRSI using a novel 3D UTE rosette sequence.In comparison to a conventional 3D weighted CSI with matched bandwidth, nominal resolution, and acquisition time, the novel rosette acquisition provided competitive resolution and superior SNR with straightforward quanti cation.As this proof-of-concept study was limited to ve subjects and a relatively homogeneous region of PCr-plentiful muscle, additional testing is required to demonstrate e cacy in differentiating diverse and diseased tissue regions.
Illustration      Un ltered magnitude spectra from each method in the highlighted muscle (red) and bone (green) voxels scaled to the maximum PCr peak amplitude.Stated spectral SNR is for PCr peak.
Measured PCr SNR (mean ± SD) from OXSA-AMARES quanti able voxels across all ve quadriceps subjects using each acquisition scheme and real data (Equation ( 3)).By this quanti cation metric, 3D UTE rosette outperforms weighted CSI by approximately 34% in vivo.(B) Measured raw PCr SNR (mean ± SD) from quanti able voxels across all ve quadriceps subjects and bottle phantom using each acquisition scheme and absolute data (Equation ( 4)).By this quanti cation metric, 3D UTE rosette outperformed weighted CSI by approximately 69% in phantom and 18% in vivo.Detailed results are provided in Tables 2 and 3.
ω 2 = = = 6545rad/s π pointsperpetal (N pp ) *dwelltime π 96 * 5μs as well as and the resulting − 20 to + 20 ppm 3T spectral range is more than su cient for 31 P-MRS.In reconstruction, each petal was downsampled from N pp = 96 points to N pp = 48 by averaging the oversampled points.With a 24x24x24 reconstruction matrix, the required number of petals (N p ) to satisfy Nyquist criterion was calculated as However, due to the rosette's e cient sampling scheme, only 80% coverage (N p = 1444) was de ned as full k-space acquisition.Thus, the acquisition time per average was calculated as or roughly 9 minutes.A complete description including the in uence of trajectory parameters, Nyquist criterion, and the speci c gradient ramp-up of this 3D rosette k-space pattern is provided in earlier work (Shen et al.). 252.1.2Weighted CSI Conventional Cartesian 3D acquisitions used the vendor-provided 31 P CSI FID with k-space weighting and Hanning lter.Sequence parameters were as follows: T A = 36:56, T R = 1000 ms, T E = 2.3 ms, matrix size = 16x16x16, nominal voxel size = 8 mL, FOV = (320x320x320) mm 3 , SBW = 2200 Hz, spectral time samples = 512.Parameters are summarized in Table N p * T R = 1444 * 350ms = 505s of 3D rosette k-space trajectory and gradients.(A-C) Acquisition begins at k-space center for every petal, crossing k-space origin twice at each petal's beginning and end.Petals can be manually separated into two halves, similar to odd and even echoes in EPSI MRSI.(D, E) Varied petal rotations form the rosette pattern, providing su cient k-space coverage.(F) With the closed-loop trajectory, acquisition delay is further minimized by enabling the analog to digital converter (ADC) for sampling during gradient ramp-up.

Figure 2 Work
Figure 2

Figure 4 Results
Figure 4

Figure 5 Results
Figure 5

Table 1 Table of
protocol parameters for conventional 3D weighted CSI, novel 3D UTE rosette MRSI, and additional retrospectively accelerated rosette sequences.Nominal voxel size was matched between methods, with total acquisition time approximately equal between the two full acquisitions.SBWs were matched via interpolation during post-processing.

Table 2
Mean in vivo PCr SNR from quanti able voxels in individual subjects using each method.With matched voxel size and acquisition resolution, 3D UTE rosette consistently outperforms weighted CSI acquisition in measured SNR.

Table 3
Mean PCr SNR from quanti able voxels across all ve quadriceps subjects and bottle phantom using each method.With matched voxel size and acquisition resolution, 3D UTE rosette consistently outperforms weighted CSI acquisition in measured SNR.