Research article Received: 13 November 2014,

Revised: 12 March 2015,

Accepted: 12 March 2015,

Published online in Wiley Online Library: 24 April 2015

(wileyonlinelibrary.com) DOI: 10.1002/nbm.3301

Comparison of acquisition schemes for hyperpolarised 13C imaging Markus Dursta†, Ulrich Koellischa*†, Annette Frankb, Giaime Rancanb, Concetta V. Gringerib, Vincent Karasc, Florian Wiesingerc, Marion I. Menzelc, Markus Schwaigerb, Axel Haasea and Rolf F. Schultec The aim of this study was to characterise and compare widely used acquisition strategies for hyperpolarised 13C imaging. Free induction decay chemical shift imaging (FIDCSI), echo-planar spectroscopic imaging (EPSI), IDEAL spiral chemical shift imaging (ISPCSI) and spiral chemical shift imaging (SPCSI) sequences were designed for two different regimes of spatial resolution. Their characteristics were studied in simulations and in tumour-bearing rats after injection of hyperpolarised [1-13C]pyruvate on a clinical 3-T scanner. Two or three different sequences were used on the same rat in random order for direct comparison. The experimentally obtained lactate signal-to-noise ratio (SNR) in the tumour matched the simulations. Differences between the sequences were mainly found in the encoding efficiency, gradient demand and artefact behaviour. Although ISPCSI and SPCSI offer high encoding efficiencies, these non-Cartesian trajectories are more prone than EPSI and FIDCSI to artefacts from various sources. If the encoding efficiency is sufficient for the desired application, EPSI has been proven to be a robust choice. Otherwise, faster spiral acquisition schemes are recommended. The conclusions found in this work can be applied directly to clinical applications. Copyright © 2015 John Wiley & Sons, Ltd. Keywords: hyperpolarised

13

C; pyruvate; tumour; metabolic imaging

INTRODUCTION

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* Correspondence to: U. Köllisch, Technische Universität München, Institute of Medical Engineering, Boltzmannstraße 11, 85748 Garching b. München, Germany. E-mail: [email protected] a M. Durst, U. Koellisch, A. Haase Technische Universität München, Institute of Medical Engineering, Munich, Germany b A. Frank, G. Rancan, C. V. Gringeri, M. Schwaiger Nuklearmedizinische Klinik und Poliklinik, Klinikum rechts der Isar, Technische Universität München, Munich, Germany c V. Karas, F. Wiesinger, M. I. Menzel, R. F. Schulte GE Global Research, Munich, Germany †

These authors contributed equally to this work. Abbreviations used: CSI, chemical shift imaging; ECG, electrocardiogram; EPSI, echo-planar spectroscopic imaging; FFT, fast Fourier transform; FID, free induction decay; FOV, field of view; FRFES, fast-recovery fast spin-echo; FWHM, full width at half-maximum; ISPCSI, IDEAL spiral chemical shift imaging; Na-EDTA, sodium ethylenediaminetetraacetate; NUFFT, non-uniform fast Fourier transform; PSF, point spread function; RF, radiofrequency; ROI, region of interest; SNR, signal-to-noise ratio; SPCSI, spiral chemical shift imaging; SSFP, steady-state free precession; VFA, variable flip angle.

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Dynamic nuclear polarisation with subsequent dissolution (1) has enabled real-time studies with endogenous biomarkers (2,3), providing new methods to investigate and characterise various disease states. Among the most promising hyperpolarised substrates to date is [1-13C]pyruvate, which is being used in preclinical trials to study the cellular energy metabolism of diseases such as cancer (4–6) and ischaemia (7–9). Although the technique is currently being translated to clinical applications (10), the evaluation and optimisation of different imaging sequences still represent a highly active field of research (11,12). The nonrenewable, rapidly decaying signal and low signal-to-noise ratio (SNR) regime of in vivo hyperpolarisation experiments require fast and time-efficient sampling strategies to obtain sufficient image quality. Typically, multidimensional data, including chemical shift information, metabolic conversion and spatial localisation need to be encoded within a few minutes. In the past few years, many different approaches have been reported, most having been adapted from 1H MRSI sequences, such as free induction decay chemical shift imaging (FIDCSI) (5,13–17), echo-planar spectroscopic imaging (EPSI) (12,18–21), spiral chemical shift imaging (SPCSI) (22–27), strategies based on multi-echo chemical shift species separation [e.g. IDEAL spiral chemical shift imaging (ISPCSI) (28–31)], spin-echo (19,32) and steady-state free precession (SSFP) (33–36) methods. As a result of this variety, a complete and comprehensive overview is not practical. Instead, an indepth comparison of exemplary sequence types is presented in order to derive general conclusions on hyperpolarised imaging strategies.

Currently, the sequences that are used most often rely on a simple pulse-and-acquire scheme in which a slice-selective pulse is combined with a specific gradient readout to encode the spectral and spatial dimensions. Such approaches can be split into two general types. The static acquisition schemes focus on encoding only one or a few images within the time window provided by the hyperpolarised agent, and therefore have low encoding efficiency requirements. There are also dynamic

M. DURST ET AL. approaches, which aim at encoding the time curve of a hyperpolarised substrate and its metabolites in real time in order to be able to quantify the enzymatic reaction. To do so, a high encoding efficiency, which means a high temporal resolution, is required. The selection of sequences for the comparison was based on several criteria. First, the sequence needs to be well established and tested in the literature, showing certain potential for use in clinical studies and also allowing us to use the most optimised choice of parameters. Furthermore, the sequence needs to be widely used, judging by the number of reported studies, in order to be of relevance to the majority of readers. Last, we tried to include a great variety of acquisition speeds and gradient encoding patterns, so that many possible applications are covered. Four exemplary sequence types were chosen for the comparison: FIDCSI (5,13–17), EPSI (12,18–21), ISPCSI (28–31) and SPCSI (22–27). An extensive theoretical treatment is provided, together with simulations, to characterise the behaviour of the sequences and illustrate their potential advantages and disadvantages. These strategies were then compared directly for the first time in vivo using tumour-bearing rats after the injection of hyperpolarised [1-13C]pyruvate. The goals of this work are to facilitate the selection of optimal imaging parameters for a specific purpose and to provide a basis for the identification of potential candidates for clinical applications.

THEORY SNR properties of hyperpolarised acquisitions

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The SNR of a hyperpolarised acquisition is influenced by several sequence-related parameters. For static acquisitions, the starting time of the scan is crucial. To maximise metabolite SNR and minimise artefacts caused by rapid signal change, the expected range of the conversion rate constants can be used to calculate the optimal starting point. A real-time bolus-tracking approach can help to overcome problems with varying levels of perfusion (37). Dynamic acquisitions can be started at the beginning of the injection if the bolus characteristics are of interest. The SNR of hyperpolarised acquisitions does not depend solely on the total readout time, but the maximum obtainable SNR is dependent on the time window of the acquisition. The optimal repetition time and flip angle in order to obtain the maximum SNR of the metabolite or to extract the conversion rate constant can be calculated by considering the expected ranges of the metabolic conversion and relaxation processes (37,38). An important factor when designing the spatial readout is the SNR gradient encoding efficiency, which is determined by the uniformity of the trajectory. A non-uniform k-space density leads to an SNR penalty as a result of noise amplification (39,40). For EPSI, this applies to the ramp part of the gradient lobes, whereas, for spiral trajectories, gradient slew rate constraints can cause a non-uniform k-space sampling density at the beginning of the trajectory. The SNR gradient encoding efficiency can be defined mathematically as: ffi vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi uX 2 u d u j j ε¼t X 2 n j dj

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where d is the density compensation of the trajectory and n is the number of trajectory points. In general, the point spread function (PSF) of a k-space sampling scheme is determined by the Fourier transform of its shape. The real resolution can be described by the full width at half-maximum (FWHM) of the main lobe. Neglecting T2* decay, it can be expressed as: θ¼μ

FOV npix

where FOV is the field of view, npix is the nominal resolution in pixels and μ is a factor resulting from the shape of the PSF. For a rectangular sampling scheme (as used for EPSI), μ ≈ 1.22 and the PSF is sinc-shaped (41). For a circular sampling pattern (FIDCSI, ISPCSI, SPCSI), μ ≈ 1.40 and the PSF is jinc-shaped (41). For SPCSI and even more for ISPCSI, T2* decay will act as a natural apodisation and can cause significant broadening of the PSF. [For this case, see ref. (42) for a detailed theoretical treatment.] Filtering can be used to improve the shape of the PSF, e.g. minimise sidelobes. Furthermore, filtering is necessary to optimise the SNR in the presence of T2* decay during the long readouts; however, the SNR optimal filter depends on the properties of the measured sample. For FIDCSI, EPSI and SPCSI, the decay occurs mainly along the spectral dimension, whereas, for ISPCSI, it affects mainly the spatial k-space domain. As the T2* value and the signal distribution in k-space are not known exactly, assumptions must be made which affect the final SNR. In this work, a 15-Hz Gaussian filter (corresponding to T2* = 20 ms) was chosen for all acquisitions, which previous studies have shown to be a reasonable choice for the optimisation of SNR and minimisation of PSF broadening (43). Sequences FIDCSI FIDCSI represents the gold standard for 1H chemical shift imaging (CSI). It consists simply of free induction decay (FID) acquisitions with a preceding phase encoding gradient to scan k-space pointwise with multiple excitations. As a result of this inefficient encoding scheme, typically only one or a few images can be acquired before the hyperpolarised signal has decayed. A variable flip angle (VFA) scheme (44,45) can be used to obtain equal signals for each excitation in the presence of a decaying polarisation to avoid signal inconsistencies. For the same reason, the starting time needs to be chosen carefully in order to avoid the initial bolus phase. Usually, a Cartesian encoding scheme is used, so that reconstruction can be performed by taking fast Fourier transforms (FFTs) along the spectral and spatial k-space dimensions. A spatially resolved spectrum can be obtained at an arbitrary sampling rate and sampling time, which provides maximum flexibility for all kinds of chemical shift distributions. A circular sampling pattern (Fig. 1) can be used to obtain isotropic resolution and to reduce the scan time. EPSI EPSI samples a single line in k-space repeatedly after one radiofrequency (RF) excitation in order to acquire both spatial and spectral information simultaneously. Thus, it provides a significantly increased encoding efficiency relative to FIDCSI, so that biochemical pathways can be sampled dynamically with a time

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COMPARISON OF ACQUISITION SCHEMES FOR HYPERPOLARISED 13C IMAGING

Figure 1. Two-dimensional spatial k-space trajectories of the investigated sequences for the lower (a) and higher (b) resolution. CSI, chemical shift imaging; EPSI, echo-planar spectroscopic imaging; FIDCSI, free induction decay chemical shift imaging.

resolution of a few seconds. As the spectral bandwidth is determined by the time it takes to return to the same k-space point, in general, EPSI has a high gradient demand, and the spectral and spatial resolution are limited by the maximum available gradient amplitude and slew rate. This is even more critical for 13C than for 1H because of the lower gyromagnetic ratio. Usually, a flyback design is chosen for the trajectory (Fig. 1), and only the plateau parts are used for reconstruction. This increases the gradient hardware requirements and lowers the SNR efficiency, but also reduces artefacts. If the ramp parts are included in a gridding reconstruction, the lost SNR efficiency can be partially recovered. ISPCSI ISPCSI uses a single-shot spiral trajectory to encode the two spatial dimensions after RF excitation. To cover the spectral domain, this trajectory is repeated in separate excitations with a specific increase in TE tailored to the expected 13C frequency shifts. The TE shift must be chosen carefully in order to minimise noise amplification (28,46). A least-squares algorithm (IDEAL) (46) is then used to separate the different metabolic species based on their chemical shift frequencies, which are required as prior knowledge. Usually, slice-selective FIDs are acquired alongside the images to obtain the frequency profile. IDEAL exploits the sparsity of the in vivo 13C spectra, which typically do not have background signals. This ensures a high encoding efficiency as, for n metabolites, only n echoes are required. Moreover, the design constraints are low because the spatial and spectral domains are acquired independently. One of the drawbacks to this method is that no full spectrum is obtained, and the spiral trajectory is therefore vulnerable to off-resonance effects. SPCSI

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METHODS Sequence design All sequences were designed for a FOV of 8 × 8 cm2, a maximum gradient amplitude of 40 mT/m and a maximum slew rate of 150 T/m/s. Two groups of sequences were created: the first consisted of FIDCSI, EPSI and SPCSI trajectories with a low resolution of about 8 × 8 pixels, and the second of FIDCSI, EPSI and ISPCSI trajectories with a resolution of about 16 × 16 pixels. The rats were divided into two subgroups to test the two spatial resolutions. For each animal, two or three of the sequences were then tested in random order. A 10-mm slice containing the tumour and, in some cases, the kidneys was selected for hyperpolarised 13C imaging. The time between dissolution and the start of the injection was kept fixed at 24 s in order to obtain comparable levels of polarisation. All measurements were started at the beginning of the injection, except for FIDCSI, which was delayed by 15 s in order to obtain a good metabolite signal. For EPSI, ISPCSI and SPCSI, a constant flip angle was chosen, so that an equal 10% portion of the magnetisation was used to

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As in EPSI, spectral and spatial information are obtained simultaneously during readout in SPCSI by repeatedly scanning a spiral

trajectory after RF excitation. The spectral width of this approach is thus determined by the duration of a single spiral including the rewinder. To increase the spectral width, additional excitations with a time-shifted trajectory can be acquired, or the k-space sampling can be split into multiple spiral interleaves. In principle, this approach has the highest sampling efficiency as two-dimensional spatial and spectral information can be obtained from a single excitation. However, this implies severe timing constraints for the trajectory design, resulting in a very high gradient demand. In addition, the non-Cartesian spiral trajectory is sensitive to gradient imperfections, and artefacts can occur if there are deviations along the spiral sampling train. If the spatial information is acquired in multiple spiral interleaves, signal inconsistencies can be another source of error.

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encode one image within 4 s, and a 5° slice-selective FID was appended to each image for control purposes. A VFA scheme with an estimated T1 of 20 s was used for FIDCSI (44,45). For each animal, a B0 field map was calculated from the phase development of four respiratory-gated gradient-echo images (slice thickness 3 mm) with increasing TEs (ΔTE = 2 ms) for each acquisition. Fast-recovery fast spin-echo (FRFSE) 1H images with a slice thickness of 3 mm were acquired to provide anatomical overlay. The automatic shim from a proton prescan was used for the 13C experiments. For FIDCSI, phase encodes were created with the maximum slew rate and amplitude. k-space was sampled in centric order, starting from the inner points and going outwards; 256 points were sampled with a readout bandwidth of 5000 Hz, amounting to a total readout time of 51.2 ms and a spectral resolution of 19.5 Hz. The high-resolution sequence was created with a nominal resolution of 16 × 16 pixels consisting of 208 excitations, and the low-resolution sequence was created with a nominal resolution of 8 × 8 pixels consisting of 52 excitations. As there are no active gradients during encoding, the SNR gradient encoding efficiency was 100%. For EPSI, a flyback approach was chosen because of its robustness to phase errors. A trapezoidal gradient shape using maximum gradient slew rate and amplitude was employed to rewind the phase after the actual readout lobe. The highresolution trajectory has a nominal resolution of 16 × 16 pixels including ramps, and a plateau ratio of 43%, resulting in an pffiffiffiffiffiffiffiffiffiffiffiffiffi SNR readout efficiency of ð0:43Þ ¼ 66%: The low-resolution trajectory has a nominal resolution of 8 × 8 pixels including ramps, and a plateau ratio of 67%, translating to an SNR readout pffiffiffiffiffiffiffiffiffiffiffiffiffi efficiency of ð0:67Þ ¼ 82% . Both trajectories were designed with a spectral width of 581 Hz and consisted of 37 individual readout lobes, amounting to a total sampling time of about 64 ms. The y-axis phase encodes were created centre-out and corresponded to the nominal resolution of the x-axis readout. The SNR gradient encoding efficiency was 94% for the lowresolution trajectory and 92% for the high-resolution trajectory; both were designed with a maximum gradient amplitude of 40 mT/m and a maximum gradient slew rate of 150 T/m/s. The high- and low-resolution images were acquired with flip angles of 6.6° and 9.4°, respectively. The ISPCSI trajectory was created with uniform density and a nominal resolution of 32 × 32 pixels which, assuming a T2* decay of about 20 ms and a Gaussian filter of equal magnitude, translates to a real resolution of 16 × 16 pixels (42). The spiral trajectory was designed using the variable density spiral generation script by Hargreaves (47). The total readout time was 45 ms. For pyruvate and its metabolites, seven echoes with a TE shift increase of 1.12 ms were acquired with a flip angle of 10°. This waiting time translates to an SNR readout efficiency of 92% for an assumed T2* of 20 ms. The SNR efficiency regarding chemical shift separation with this TE shift was calculated to have a mean value of 91% for pyruvate, lactate and alanine with an assumed Gaussian line broadening as a result of B0 inhomogeneity of 20 Hz. The SNR gradient encoding efficiency was 99% with a maximum gradient amplitude of 22 mT/m and a maximum gradient slew rate of 73 T/m/s. The SPCSI trajectory consisted of two spatial interleaves and one additional TE shift, so that four excitations are necessary for one image (Fig. 1); therefore, a flip angle of 13.3° was used. The spiral trajectories were calculated with the variable density

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spiral generation script (47), and then a rewinder was calculated using trapezoidal gradient shapes. The individual interleaves were arranged into a train of 18 consecutive interleaves. A single SPCSI readout had a spectral width of 294 Hz and, with the TE shift of 1.7 ms in a separate excitation, a final spectral width of 581 Hz was obtained. The nominal spatial resolution was 11.4 × 11.4 pixels, translating to a real resolution of about 8 × 8 when assuming a T2* value of 20 ms (42). The ratio of data collection to the rewinder was 76%, resulting in an SNR readout efficiency of pffiffiffiffiffiffiffiffiffiffiffiffiffi ð0:76Þ ¼ 87%. The SNR gradient encoding efficiency (excluding the rewinder) was 95% with a maximum gradient amplitude of 40 mT/m and a maximum gradient slew rate of 150 T/m/s. Simulations An extensive simulation framework was created using MATLAB (MathWorks, Inc., Natick, MA, USA) to compare the performances of the four sequence types. A phantom consisting of multiple circular areas with lactate, pyruvate hydrate, alanine and pyruvate (0, –125, –215 and –392 Hz at 3 T, equal concentrations) was simulated using the forward signal encoding matrix with the respective parameters. After reconstruction, a region of interest (ROI) in the lactate map was selected to quantify the relative SNR. The phantom was smoothed using a Gaussian filter to mitigate PSF effects. Moreover, the spatial PSFs were simulated for all acquisition schemes by sampling a constant k-space signal (corresponding to a delta function in the image domain) for the same metabolites. Off-resonance effects were simulated by changing the signal frequency (offset 10 and 30 Hz). Eddy current-induced gradient errors were simulated by weighting the positive and negative gradient lobes differently, introducing an error in the zero-order gradient moment (1% discrepancy between the positive and negative gradient parts, with the PSF located at a distance from the centre equal to 50% of the FOV along x and y). Movement was simulated by changing the position of the point source between the excitations (using a shift equal to 10% of the FOV along the x and y axes during a full image encoding). For quantification, the PSF was integrated over the FOV and normalised to its maximum. The ratios between the corrupted and non-corrupted PSF values were used to determine the extent of the artefacts in the image domain. To determine the error in the spectral domain, the ratio of lactate to pyruvate was formed at the maximum of the PSF for both corrupted and non-corrupted PSF. These simulations were carried out for a thermal magnetisation to derive general conclusions. In addition, a two-site model (5) was used to illustrate the effects of enzymatic conversion and decaying magnetisation on SNR and PSF. Typical parameters of a hyperpolarised pyruvate measurement in tumour tissue were chosen: kPyr→Lac = 0.1 s–1; T1 = 20 s; inflow rate, 0.2 s–1; duration of inflow, 5 s. In vivo experiments The previously described sequences were tested in 11 male Fisher F344 rats (Charles River, Sulzfeld, Germany) bearing a subcutaneous Mat BIII tumour in the kidney region. [1-13C] Pyruvic acid doped with 15 mM Trityl OX063 radical and 1 mM Dotarem was polarised in a HyperSense dynamic nuclear polariser (Oxford Instruments, Abingdon, Oxfordshire, UK). After 1 h, the samples were rapidly dissolved by flushing with a hot aqueous solution containing 80 mM Trizma buffer, 80 mM NaOH and 0.1 g/L sodium ethylenediaminetetraacetate (Na-EDTA), leading

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COMPARISON OF ACQUISITION SCHEMES FOR HYPERPOLARISED 13C IMAGING to an 80 mM pyruvate solution with physiological pH, osmolarity and temperature. The liquid-state polarisation measured in n = 19 samples in a 1-T spectrometer (Bruker Minispec, Bruker, Karlsruhe, Germany) was 25.0 ± 2.1%. After dissolution, 2.5 mL/kg of this solution was injected into the tail veins of the tumourbearing rats (average weight, 152 ± 7 g; injection time, ≈5 s), which were anaesthetised with 1–3% isoflurane inhalation gas. The animals were monitored for electrocardiogram (ECG), breathing, oxygen saturation and temperature, and were kept warm on a heating pad with circulating warm water. The experiments were carried out on a 3-T HDx scanner (GE Healthcare, Milwaukee, WI, USA) with a maximum gradient amplitude of 40 mT/m and a maximum slew rate of 150 T/m/s. A dual-tuned 13C–1H birdcage volume coil (diameter: 8 cm) was used for RF transmission and reception (48). The animal study was approved by the local governmental committee for animal protection and welfare (Tierschutzbehörde, Regierung von Oberbayern).

Reconstruction FIDCSI A 15-Hz Gaussian filter was applied along the readout dimension before the data were sorted into a zero-filled three-dimensional matrix. The FFT was applied along all three dimensions.

EPSI Data were sorted into a zero-filled three-dimensional matrix, and a 15-Hz Gaussian filter was applied along the spectral dimension. The FFT was computed along the spectral dimension, and the phase along the readout dimension was corrected to compensate for the spatial shift for each frequency. Subsequently, the FFT was applied along the spatial dimensions. For comparison, the full trajectory was reconstructed using the non-uniform fast

Figure 2. Two-dimensional spatial point spread functions of the investigated sequences for the lower (a) and higher (b) resolution. CSI, chemical shift imaging; EPSI, echo-planar spectroscopic imaging; EPSI full, EPSI reconstruction including ramps and rewinder; FIDCSI, free induction decay chemical shift imaging. Results illustrating effects of motion and off-resonance can be found at http://nmr-wiki.imetum.tum.de/13C/

Table 1. Simulated signal-to-noise ratio (SNR), point spread function (PSF) full width at half-maximum (FWHM) and theoretical parameters for the compared sequences Sequence

SNR SNR normalised PSF FWHM to voxel size along x (mm)

FIDCSI 8 × 8 EPSI 8 × 8 EPSI full 8×8 SPCSI 8 × 8 FIDCSI 16 × 16 EPSI 16 × 16 EPSI full 16 × 16 ISPCSI 16 × 16

1.0 0.8 0.88 0.46 0.25 0.17 0.19 0.20

1.0 0.77 0.89 0.99 0.98 0.67 0.92 1.20

13.84 14.37 13.78 9.41 6.91 7.59 6.37 5.58

SNR gradient SNR readout SNR chemical Number of efficiency (%) shift separation encoding excitations/total efficiency (%) acquisition time (ms) efficiency (%) 52/2662 8/512 8/512 4/245 208/10650 16/1024 16/1024 7/315

100 100 94 95 100 100 92 99

100 82 100 87 100 66 100 92

100 100 100 100 100 100 100 91

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EPSI, echo-planar spectroscopic imaging; EPSI full, EPSI reconstruction including ramps and rewinder; FIDCSI, free induction decay chemical shift imaging; ISPCSI, IDEAL spiral chemical shift imaging; SPCSI, spiral chemical shift imaging. SNR gradient encoding efficiency, efficiency considering the noise amplification as a result of non-Cartesian encoding; SNR readout efficiency, SNR efficiency based on the fraction of the sampled data which is actually used for reconstruction; SNR chemical shift separation efficiency, SNR efficiency describing the noise amplification during the process of separation of the chemical species.

M. DURST ET AL. Table 2. Simulated point spread function (PSF) for IDEAL spiral chemical shift imaging (ISPCSI) with off-resonance effects Sequence

FWHM along x (normalised)

ISPCSI 16 × 16, 0 Hz off-resonance ISPCSI 16 × 16, 10 Hz off-resonance ISPCSI 16 × 16, 30 Hz off-resonance

1.00 1.09 2.25

Software MATLAB (MathWorks, Inc.) was used to implement the waveform design, simulations and reconstructions. All related code, as well as the raw data files, can be found at http://nmr-wiki.imetum. tum.de/13C/. All software was run on a standard notebook with 16 GB of RAM and an Intel Core i5-4200M processor.

RESULTS

FWHM, full width at half-maximum.

Simulation

Fourier transform (NUFFT) code by Fessler (49), where the gradient waveform itself was used for density compensation. ISPCSI A 15-Hz Gaussian filter was applied along the readout dimension. Image reconstruction was performed using least squares fitting to separate the individual metabolites (46). A phase correction for the chemical shift evolution was applied for each metabolite. The NUFFT algorithm was used to reconstruct the spiral data on a Cartesian grid (49). Density compensation was obtained according to (50). SPCSI Data were sorted into a two-dimensional matrix and a 15-Hz Gaussian filter was applied following the FFT along the spectral dimension. The phase along the readout dimension was corrected to compensate for the chemical shift for each frequency. Subsequently, Cartesian images were reconstructed using NUFFT (49) along the spatial readout dimension. Density compensation was obtained according to (50). SNR comparison To summarise the results over different animals, the total lactate SNR was calculated in a tumour ROI for each dataset, starting from the third time point including all points with an SNR higher than three. For comparison, the SNR values were normalised to the SNR of the EPSI reconstruction including ramps and rewinder (EPSI full).

The spatial PSFs are depicted in Figure 2, and their FWHM values are provided in Table 1. For FIDCSI and EPSI, the PSFs show notable truncation artefacts, which could be diminished by additional filtering at the cost of resolution. In the presence of offresonance effects, the PSF of ISPCSI is considerably blurred, resulting in a 9% lower resolution for 10 Hz and a 125% lower resolution for 30 Hz off-resonance (Table 2). The non-Cartesian spiral sequences show a strong sensitivity to motion artefacts, as well as to gradient errors (see Table 3). The relative SNR of the simulated test phantom is given in Table 1. In addition to the absolute values, the SNR was normalised to the FWHM of the PSF along both spatial dimensions. For the 16 × 16 acquisitions, FIDCSI scored the highest SNR, followed by ISPCSI and EPSI. Among the lower resolution acquisitions, FIDCSI also performed the best, followed by EPSI and SPCSI, where SPCSI has a significantly lower SNR because of the higher resolution. When including enzymatic conversion and decay, the simulations show a different impact on the sequences (see Table 4). For FIDCSI, a variable flip angle scheme is used which targets equal magnetisation for each excitation. As this considers only decay and not enzymatic conversion, there is an overweight of the outer k-space points for the metabolite signal, resulting in lower SNR and narrower PSF compared with a constant magnetisation. For dynamic acquisitions with constant flip angle, the (relative) SNR and PSF will vary slightly in each time frame because the signal will increase or decrease in the successive excitations of the same image frame. This effect was observed to be strongest for EPSI as the spatial

Table 3. Simulated point spread function (PSF) artefact ratio for motion [where the shift is 10% of the field of view (FOV) distance along the x and y directions within one image encoding] and gradient error (1% deviation between positive and negative gradient lobes). The artefact ratio is defined as the ratio of the integral of the corrupted PSF and the non-corrupted PSF, each normalised to its maximum. Quantification error lactate/pyruvate is taken from the ratio of the maximum of the PSF from corrupted and noncorrupted PSF Sequence

FIDCSI 16 × 16 EPSI 16 × 16 EPSI full 16 × 16 ISPCSI 16 × 16 FIDCSI 8 × 8 EPSI 8 × 8 EPSI full 8 × 8 SPCSI 8 × 8

Artefact ratio (motion)

Quantification error lactate/pyruvate (motion)

Artefact ratio (gradient error)

Quantification error lactate/pyruvate (gradient error)

1.21 1.30 1.36 3.15 1.05 1.11 1.11 1.50

1.0 0.99 0.97 1.12 1.0 1.01 1.02 1.03

1.00 1.01 1.01 1.68 1.00 1.00 1.00 1.22

1.0 1.01 1.01 1.0 1.0 1.01 1.01 0.97

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EPSI, echo-planar spectroscopic imaging; EPSI full, EPSI reconstruction including ramps and rewinder; FIDCSI, free induction decay chemical shift imaging; ISPCSI, IDEAL spiral chemical shift imaging; SPCSI, spiral chemical shift imaging.

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COMPARISON OF ACQUISITION SCHEMES FOR HYPERPOLARISED 13C IMAGING Table 4. Influence of inflow, enzymatic conversion and decaying magnetisation (labelled ‘hyp’) compared with thermal signal-tonoise ratio (SNR) and point spread function (PSF) (labelled ‘therm’). Assumed values for the two-site model: kPyr→Lac = 0.1 s–1; T1 = 20 s; inflow rate 0.2 s–1; duration of inflow 5 s. Values shown are for lactate; PSF is taken along y (phase encoding direction for EPSI) Sequence

Average SNRhyp/SNRtherm

SNRhyp/SNRtherm steepest rise/decline

Average PSFhyp/PSFtherm

PSFhyp/PSFtherm steepest rise/decline

0.77 0.99 0.98 1.01 0.42 1.00 1.02 0.99

Not applicable 0.62/1.05 0.64/1.02 0.94/1.00 Not applicable 0.56/1.12 0.58/1.09 0.93/0.99

0.93 1.0 1.0 1.0 0.92 1.0 1.0 1.0

Not applicable 0.85/1.03 0.85/1.03 1.00/1.00 Not applicable 0.87/1.03 0.87/1.03 1.01/1.00

FIDCSI 8 × 8 EPSI 8 × 8 EPSI full 8 × 8 SPCSI 8 × 8 FIDCSI 16 × 16 EPSI 16 × 16 EPSI full 16 × 16 ISPCSI 16 × 16

EPSI, echo-planar spectroscopic imaging; EPSI full, EPSI reconstruction including ramps and rewinder; FIDCSI, free induction decay chemical shift imaging; ISPCSI, IDEAL spiral chemical shift imaging; SPCSI, spiral chemical shift imaging.

encoding is split up into many phase encodes, whereas it seems to have a minor effect on the spiral sequences. For the average SNR and PSF, these fluctuations will cancel out.

Experiment High-resolution images Visual assessment of the acquisition methods in the same animal reveals some of the basic characteristics of each method. In

Figure 3a, the sums over the images of 15 time points acquired with the higher (16 × 16) resolution are illustrated. Figure 4a shows the time evolution of lactate SNR in the tumour ROI under the dynamic techniques. The tumour can be easily distinguished from healthy tissue, and it appears that it is even possible to resolve tumour inhomogeneities (see Fig. 3a). The IDEAL spiral images show blurring, particularly in the tumour area, where the image quality is impaired by off-resonance effects. The structures are considerably broadened in comparison with the other imaging modalities, which is clearly visible in a one-dimensional

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Figure 3. Pyruvate and lactate maps acquired with the sequences investigated. Sequences with the higher (16 × 16) resolution (a) and lower (8 × 8) resolution (b). The proton reference images show the tumour (T) and kidney (K) regions of interest (ROIs). The field maps illustrate the off-resonance for 13 C in hertz. EPSI, echo-planar spectroscopic imaging; EPSI full, EPSI reconstruction including ramps and rewinder; FIDCSI, free induction decay chemical shift imaging; GRE, gradient-echo; ISPCSI, IDEAL spiral chemical shift imaging; SPCSI, spiral chemical shift imaging. Time-resolved images can be found at http://nmr-wiki.imetum.tum.de/13C/

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Figure 4. The lactate signal-to-noise ratio (SNR) time course for the investigated techniques in the tumour region of interest (ROI) for the higher resolution (a) and the lower resolution (b).

Figure 5. One-dimensional cut through the lactate map in the tumour for the higher (16 × 16) resolution (a, b) and the lower (8 × 8) resolution (c, d).

cross-section through the tumour (Fig. 5). Field inhomogeneities of about 20–30 Hz over the tumour were observed (see the fieldmap in Fig. 3a). The EPSI image appears to be slightly sharper in the tumour region; the reconstruction including the ramp (‘EPSI full’) has a minor effect on the image quality, but increases slightly the SNR of the images (Fig. 4a). In the FIDCSI image (Fig. 3a), Gibbs ringing is present in the lactate map. Low-resolution images

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The results of a low-resolution dataset (where each image is the sum over 18 time points) are illustrated in Figure 3b, and the evolution of the SNR is shown in Figure 4b. As predicted by the PSF simulation, SPCSI has a higher resolution; therefore, the SNR is significantly lower. The image quality obtained with the other techniques is similar. The tumour can still be distinguished

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from the healthy tissue at these lower resolutions, although there seems to be some signal bleeding from the bowel area.

SNR comparison The values of the mean and standard deviation for tumour and kidney ROIs are presented in Table 5. The average signal of ISPCSI is lower than the simulated value. Likewise, FIDCSI has a lower SNR than predicted by the simulation, yet only few datasets could be obtained. NUFFT reconstruction of the full flyback gradient for EPSI leads to an SNR enhancement of about 11%, which matches the predictions of the simulations. The relative SNR for the kidney region is very stable. For the low-resolution datasets, the relative SPCSI SNR (54 ± 15%) is in agreement with the predicted value. NUFFT reconstruction of the EPSI data acquired during the ramps and rewinder

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COMPARISON OF ACQUISITION SCHEMES FOR HYPERPOLARISED 13C IMAGING Table 5. Measured total lactate signal-to-noise ratio (SNR) in the tumour and kidney regions of interest (ROIs) relative to ‘EPSI full’ (EPSI reconstruction including ramps and rewinder) Sequence

Tumour SNR/SNR(EPSI full)

FIDCSI 16 × 16 EPSI 16 × 16 EPSI full 16 × 16 ISPCSI 16 × 16 FIDCSI 8 × 8 EPSI 8 × 8 EPSI full 8 × 8 SPCSI 8 × 8

0.71 ± 0.08 (n 0.90 ± 0.11 (n 1 (n 0.83 ± 0.17 (n 1.62 (n 0.97 ± 0.03 (n 1 (n 0.54 ± 0.15 (n

= = = = = = = =

2) 5) 5) 5) 1) 4) 4) 4)

Kidney SNR/SNR(EPSI full) 0.94 (n = 0.87 ± 0.02 (n = 1 (n = 0.73 ± 0.02 (n = n.a. n.a. n.a. n.a.

1) 3) 3) 3)

EPSI, echo-planar spectroscopic imaging; EPSI full, EPSI reconstruction including ramps and rewinder; FIDCSI, free induction decay chemical shift imaging; ISPCSI, IDEAL spiral chemical shift imaging; n.a., not available; SPCSI, spiral chemical shift imaging.

had a minor effect, as the reconstruction without NUFFT has an SNR that is not significantly lower (97 ± 3%).

DISCUSSION AND CONCLUSIONS

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This work focuses on the characterisation and comparison of different acquisition strategies for hyperpolarised 13C metabolic imaging. Although FIDCSI delivered adequate image quality compared with its competitors, its low encoding efficiency prevents dynamic or multi-slice imaging, which would be of particular interest for clinical applications. An overestimation or underestimation of certain parts of k-space, leading to Gibbs ringing artefacts, was observed. The applied VFA scheme compensates only for the monoexponential signal decay during the acquisition, which is a valid approximation for the total magnetisation. However, lactate magnetisation accumulating during the acquisition leads to an overestimation of high k-space frequencies, as kspace is sampled in a centric order. The main advantages of FIDCSI are its robustness and benign artefact behaviour, as there is no active gradient encoding during readout, which makes it stable against gradient errors, as well as motion and flow artefacts. As a full spectrum is acquired, it is inherently stable against off-resonance effects. For dynamic acquisitions, no general recommendation for a certain strategy can be given; rather, the correct approach depends on the desired application. EPSI showed a solid performance for both 16 × 16 and 8 × 8 acquisitions, with a better SNR efficiency for the lower resolution because of lower gradient demands. As a full spectrum is obtained, it is stable against offresonance effects, and the Cartesian sampling scheme reduces errors caused by gradient imperfections. Its rectangular sampling pattern results in an anisotropic PSF, which could be modified using filters at the cost of resolution. However, it showed a stronger susceptibility to signal change caused by enzymatic conversion and decay. ISPCSI and SPCSI can theoretically achieve slightly higher SNR values. The major advantage of these techniques is their high encoding efficiencies, allowing to scan more slices or a whole three-dimensional volume. However, non-Cartesian encoding has a poorer artefact behaviour in respect to both off-resonance effects and gradient imperfections. In particular, for ISPCSI, offresonance effects impair the image quality with blurring

artefacts. This is also most likely the reason why the experimental SNR in the tumour is lower than predicted by simulation, which is also supported by the corresponding B0 map. In order to reduce off-resonance effects, one could apply a proper shimming method or a correction for the B0 inhomogeneity in the reconstruction. For other imaging methods, such as spin echo or balanced SSFP, this artefact behaviour should be similar if they rely on the same gradient encoding pattern; however, a detailed discussion is beyond the scope of this article. All three techniques used for the lower (8 × 8) resolution acquire a full spectrum at each k-space position, and so there is no off-resonance distortion in the images. The images show that it is feasible to quantify tumour metabolism with this resolution, if the tumour heterogeneity is of minor interest. The reproducibility of the lactate conversion of the tumour in all three injections, leading to very similar shapes of the SNR curves, is remarkable. The lactate curves in the kidney are even more stable across different animals, which could be caused by the lower metabolic variance of healthy tissue compared with the tumour region during anaesthesia. With regard to clinical applications, the SNR will very probably be the major limiting factor for most applications. The substrate concentration in tissue must be lower for reasons of patient safety. Furthermore, the quality assurance process leads to a longer duration between dissolution and injection, resulting in a lower polarisation level of the injected solution. In addition, perfusion is slower in humans than in rats or mice. Therefore, the achievable spatial resolution will be severely limited by sensitivity, as can be observed in the first published studies (10). With regard to sequence design, this will also result in lower gradient demands. Under these conditions, EPSI and SPCSI are the appropriate choices for the reasons mentioned above. For applications in which an entire organ needs to be scanned, multi-slice or phase-encoded three-dimensional imaging will be desirable. Therefore, efficient encoding techniques, such as SPCSI and ISPCSI, are favourable. In conclusion, our comparison did not yield major weaknesses for any of the compared acquisition strategies, given that they are used with appropriate parameters. It was demonstrated in simulations and in tumour-bearing rats that comparable SNR and image quality can be achieved with all of the examined sequences. The choice therefore depends on secondary parameters, such as encoding efficiency and artefact behaviour. If acquisition time is not critical, EPSI is a robust choice for many

M. DURST ET AL. applications. If multiple slices are to be acquired, or a high time resolution is needed, ISPCSI or SPCSI should be considered. FIDCSI is only an option for static acquisition where no time resolution is needed. This article can only present a limited number of possible aspects relevant for hyperpolarised 13C sequence design; however, the entire source code and raw data are provided (see Software section), and the reader is invited to study other details of interest.

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Acknowledgements This work was supported by a grant from the German Bundesministerium für Bildung und Forschung (BMBF FKZ 13EZ1114), DFG grant SFB 824, and the Technische Universität München – Institute for Advanced Study, funded by the German Excellence Initiative.

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