the development of the dissolution dynamic nuclear polarization ( dnp ) method has allowed hyperpolarized metabolites to probe new frontiers in biomedical research and medical imaging ( 1 ) . hyperpolarized [ 1-c]pyruvate has been used extensively in vivo to probe cardiac metabolism in basic research ( 25 ) , and is transitioning to use as a clinical tool that can provide functional information in pathologies where metabolic dysregulation is prevalent , such as heart disease ( 1 ) and cancer ( 6 ) . while originally dynamic nuclear polarization with [ 1-c]pyruvate was used to provide non - localized spectroscopic information about metabolism at the whole organ level , diseases where metabolic dysregulation is implicated are often spatially localized , such as cancer and myocardial ischaemia .
this issue has lead to a variety of strategies to image metabolism following the injection of hyperpolarized [ 1-c]pyruvate .
hyperpolarized cardiac imaging has to overcome at least three key challenges : ( a ) the heart moves , and this motion is difficult to retrospectively correct for as the observed signal is inherently a function of time , independent of cardiac motion ; ( b ) the paramagnetic nature of blood produces local magnetic field inhomogeneities that make single - shot imaging techniques more challenging to apply owing to b0 inhomogeneities , a decrease in t2 , and flow artifacts ; and ( c ) any imaging sequence has to be maximally  magnetization efficient ,  to avoid destroying the spin structure that dynamic nuclear polarization creates , for example , by an errant 90 pulse . like any other form of mri ,
hyperpolarized imaging is fundamentally a trade off between spectral , spatial , and temporal resolution .
commonly , two - dimensional spectroscopic imaging methods are used that either provide a single time - point image ( e.g. with a 12-s acquisition window and a 12  12 matrix ( 6 ) ) or significantly undersample the spectral domain and take an accelerated k - space trajectory to improve spatial resolution ( 7 ) .
excitation with two - dimensional spectral - spatial radiofrequency pulses may be thought of as representing the limit of spectral undersampling , as only a spectral region defined a priori is excited for subsequent imaging .
there has been much interest in using single or multiple - slice spectral - spatial excitation pulses for hyperpolarized imaging , and their utility has been shown extensively in the pig heart ( 8) , for saturation - recovery rate mapping in rat tumor models ( 9 ) , and in mice ( 10 ) . the inverse relationship between radiofrequency ( rf )
pulse length and excitation bandwidth necessitates that most proposed spectral - spatial pulses are relatively long and , as noted by sigfridsson et al ( 11 ) , this puts strenuous requirements on both the maximum strength and slew rate of the gradient set used for imaging . at high field
, these requirements effectively preclude the excitation of thin slices . to pursue higher resolution imaging , sigfridsson et al
propose a different multiband approach , in which a temporally short spectral - spatial pulse excites multiple metabolites with different flip angles and a multiecho readout chain is used for multiple metabolite imaging .
the shorter pulse allows for the excitation of a slice whose thickness would not be achievable with conventional pass / stopband single - excitation pulses .
however , as noted by sigfridsson et al ( 11 ) , this scheme fails if b0 is not homogeneous and requires accurate knowledge of the centre frequency of the arriving pyruvate bolus . on account of the oscillatory excitation profile ,
a small error in this frequency translates into a large error in the flip angle that each metabolite experiences .
pass / stop - band spectral - spatial pulses are more tolerant of off - resonance effects and b0 inhomogeneity , which improves their utility in vivo . in this work
, we have developed a centric ordered fully three - dimensional pass / stopband spectral - spatial echo - planar imaging ( epi ) sequence that enables the imaging of hyperpolarized metabolites with a spatial resolution of 2  2  3.8 mm , and a ( duty - cycle limited ) maximum temporal resolution of 780 ms/3d image . to minimize the effects of gradient infidelity ,
a fly - back pulse has been used , whereby rf is only transmitted on the positive lobes of the underlying slice selection gradient .
the pulse excites a comparatively large slab ( 45.5 mm ) , with subsequent phase encoding in the z - direction trading time for z - resolution .
an epi readout train then follows , with a phase encoding direction that flips on alternate acquisitions to allow for the post hoc correction of frequency shifts and , theoretically , ( 12 ) flow and susceptibility artefacts in the resulting cardiac images .
the sequence was prospectively cardiac gated and timestamped by a custom hardware device , which prevents an error in the time axis arising from variability in the r 
this gating reduces the temporal resolution from 780 ms to ~1.8 s/3d image , although the resulting tr is not constant . to demonstrate the sensitivity of the technique
, we have used this sequence to image rodents whose metabolic flux through pyruvate dehydrogenase ( pdh ) has been modulated by being fed , fasted , and dosed with the pyruvate dehydrogenase kinase ( pdk ) inhibitor dichloroacetate ( dca ) . a significant difference in apparent pdh flux was observed in these three circumstances , in accordance with the known biochemistry .
we propose that this sequence is a good compromise between spatial and temporal resolutions , and demonstrate that it can effectively image metabolic dynamics in the rodent heart .
as shown in figure 1a , a 9 ms long pulse was designed under the rf excitation k - space formalism with zipper correction as described previously ( 8) .
subpulses under a gaussian envelope were designed with the shinnar  le - roux algorithm ( 13 ) , with a time - bandwidth product of 3 in the spectral domain and 9 in the spatial domain , and zero amplitude on negative gradient lobes to produce a fly - back pulse .
the scheme was slew - rate ( smax ) limited rather than gmax limited , as we found that waveforms played at smax were reproduced with significantly better fidelity than those at gmax , when measured by the method proposed by duyn et al ( 14 ) .
the pulse had a sublobe duration of 246 s and 37 sublobes , corresponding to an excitation bandwidth of 240 hz , and a stop - band of ~2 khz .
as shown , this was sufficient at 7 t to avoid every resonance in the spectrum of hyperpolarized [ 1-c]pyruvate , denoted as white vertical lines in figure 1b , and the excitation bandwidth was sufficiently large ( 3 ppm ) to provide relative immunity to transmitting off - resonance and b0 inhomogeneity , improving in vivo utility .
the minimum excitation slab thickness was obtained when operating at smax , which corresponded to gz = 10 g / cm and a slab thickness of 45.5 mm .
the spectral excitation profile of the pulse was measured on a spherical phantom under the designed conditions ; the implementation matched the design ( fig .
the above spectral - spatial pulse excited a 45.5 mm slab of magnetization in the z - direction .
phase encoding with centric - ordered shots was then used to trade temporal resolution for z - resolution , and an epi readout with three navigators followed in plane ( fig .
the matrix size was 32  32  12 with a field of view ( fov ) of 64  64  45.5 mm , for an acquisition resolution of 2  2  3.8 mm ; te = 16.34 ms ; minimum tr = 70 ms ( duty cycle limited ; sequence length 31.48 ms ) .
as illustrated in figure 3 , excitation was performed sequentially across metabolites in the order 
 x111,x121,  ,x1n1,x212,  ,x2n2,x313,  ,x3n3,x114 ,  
 where xij denotes time - point j and phase encoding step i = 1 
n for metabolite x . here , { 1x , 2x , 3x } = [ pyr , bic , lac ] , and n = 12 .
the sequence was electrocardiogram ( ecg)-gated , and the polarity of the in - plane phase encoding ( y ) axis was alternated on successive acquisitions of the same metabolite .
the flip angle per shot was chosen to be  = 3 for x = pyr , and  = 20 for x  pyr , such that the overall flip angle for each 3d image is  = arccos(cos ) = 17 for x = pyr and 61 for x  pyr .
a thermally polarized 5 m c urea phantom was included next to the animal to provide a carbon frequency reference .
three - dimensional , cardiac - gated volume shimming was performed using the previously mapped behavior of the magnet s shim set and a spherical harmonic cardiac autoshimming algorithm as described previously ( 15 ) .
multiecho cardiac gated gradient echo b0 maps were acquired ( 48  48 matrix ; 70  70 mm fov ; 1.2 mm slice ; tr 100 ms ; te = 3.06 , 3.56 ms ; tread = 1 ms ; total scan time 60 s ) to verify homogeneity over the whole volume of acquisition ( 15 ) .
the c centre frequency transmit was set by identifying the frequency of the urea phantom urea , and compensating for any small measured b0 variation between the urea phantom and the heart b0 as transmit = urea + b0c/h .
anatomical images were acquired with a gradient echo cine sequence described previously ( 16 ) , with the same slice thickness and fov as the hyperpolarized data ( tr = 4.6 , te = 1.41 ms , 28 frames , fa = 25 ) .
experiments were performed on a varian 7 t ddr system with gmax = 17.5 g / cm , smax = 87.5 g / cm / ms , with an actively detuned transmit / surface receive setup consisting of a 72 mm dual - tuned h / c proton / carbon birdcage volume coil with a 40 mm two - channel c surface receive array with an integrated preamp ( rapid biomedical gmbh , rimpar , germany ) . a home - made combined rf shield and animal handling system
the volume coil c flip - angle calibration was performed on a cylindrical reference phantom consisting of 500 ml of 1 m natural abundance urea with thermal equilibrium slice - selective spectroscopy .
it was found that the position and width of the resonant frequency of the volume coil did not change appreciably between loading with the phantom and with a rat , indicating that the delivered carbon flip angle was as calibrated .
the b1 + homogeneity of the volume coil was assessed by acquiring a multiple flip angle b1 map on the urea phantom with tr at least 5t1 .
we found that the spatial variation of flip angle was 8% , which is believed to be dominated by noise in the acquired data . to allow for the reconstruction of an accurate time axis , it was necessary to create a simple hardware device that recorded when each ecg - gated scan occurred to a resolution of 10 s .
this high temporal resolution ensured that the error on recording the time at which each shot occurs could be neglected .
scans were gated to the r - wave using a threshold - based detection device described previously ( 16 ) .
respiratory gating was not performed , as no artefacts were observed that were believed to be due to respiratory motion .
the period of respiratory motion ( c. ~ 1.52 s in the anaesthetized rat ) was comparable to the duration of each acquisition .
all experiments were performed in accordance with relevant uk legislation ( with personal , project and institutional licenses granted under the animals ( scientific procedures ) act 1986 ) , and were subject to local ethical review and an independent cost - benefit analysis .
approximately 40 mg of [ 1-c]pyruvate doped with 15 mm ox063 trityl radical and 3 l of a 1 in 50 dilution of dotarem ( guerbet laboratories ltd ) gadolinium chelate was polarized and dissoluted in a prototype polarizer as described previously ( 17 ) .
the estimated liquid state polarization was ~32% after dissolution , 2 ml of the resulting 80 mm pyruvate solution were injected manually over a 20 s period through a previously placed tail vein cannula in anaesthetized male wistar rats ( 2% isoflurane in 90% o2 , 10% n2o ; n = 4 ; body weight 410  70 g ) .
pyruvate was injected approximately 10 s after dissolution , and its ph was measured after each dissolution to ensure correct neutralization in all experiments .
animals were housed in a custom handling system within the magnet bore that regulated their temperature and provided rf shielded electrical connections for ecg triggering and the rf coils .
four rats were scanned on three separate occasions with at least two days as a recovery period between scans .
animals were imaged three times : ( a ) in the fed state after being allowed food and water ad libitum ; ( b ) after being fasted for at least 8 h prior to imaging ; and ( c ) following injection with the pdk inhibitor , dca , in the fed state .
rats were dosed with dca at approximately 30 mg / kg as previously proposed ( 18 ) , 30 min before hyperpolarized imaging . to minimize the total volume of injected agents , dca was administered as a 100 l bolus
data were regridded appropriately in matlab , and linear phase correction performed in - plane on the epi readout .
alternate lines of k - space were then fourier transformed independently , and added in magnitude in image space ; halving the fov and eliminating the ghost .
the noise decorrelation matrix for the two - channel array was calculated following the method of kellmen and mcveigh ( 19 ) , and the data prewhitened .
images were combined and coil sensitivities calculated following the method of mckenzie ( 20 ) . following the method of cunningham et al ( 21 ) ,
blip - reversed epi data were spatially corrected by a mutual information maximization method , to compensate for small spatial shifts caused by being off - resonance .
the resulting five - dimensional image stacks were zero - filled by a factor of two in all spatial directions , producing an image stack with a final in - plane resolution of 1  1  1.9 mm .
a manually segmented roi was drawn in the lumen ( pyruvate ) or myocardium ( bicarbonate , lactate ) and the ratio of maximum bicarbonate to maximum pyruvate computed after subtracting the mean noise as measured from the last 10 time points of the experiment .
as shown in figure 1a , a 9 ms long pulse was designed under the rf excitation k - space formalism with zipper correction as described previously ( 8) .
subpulses under a gaussian envelope were designed with the shinnar  le - roux algorithm ( 13 ) , with a time - bandwidth product of 3 in the spectral domain and 9 in the spatial domain , and zero amplitude on negative gradient lobes to produce a fly - back pulse .
the scheme was slew - rate ( smax ) limited rather than gmax limited , as we found that waveforms played at smax were reproduced with significantly better fidelity than those at gmax , when measured by the method proposed by duyn et al ( 14 ) .
the pulse had a sublobe duration of 246 s and 37 sublobes , corresponding to an excitation bandwidth of 240 hz , and a stop - band of ~2 khz .
as shown , this was sufficient at 7 t to avoid every resonance in the spectrum of hyperpolarized [ 1-c]pyruvate , denoted as white vertical lines in figure 1b , and the excitation bandwidth was sufficiently large ( 3 ppm ) to provide relative immunity to transmitting off - resonance and b0 inhomogeneity , improving in vivo utility .
the minimum excitation slab thickness was obtained when operating at smax , which corresponded to gz = 10 g / cm and a slab thickness of 45.5 mm .
the spectral excitation profile of the pulse was measured on a spherical phantom under the designed conditions ; the implementation matched the design ( fig .
the above spectral - spatial pulse excited a 45.5 mm slab of magnetization in the z - direction .
phase encoding with centric - ordered shots was then used to trade temporal resolution for z - resolution , and an epi readout with three navigators followed in plane ( fig .
the matrix size was 32  32  12 with a field of view ( fov ) of 64  64  45.5 mm , for an acquisition resolution of 2  2  3.8 mm ; te = 16.34 ms ; minimum tr = 70 ms ( duty cycle limited ; sequence length 31.48 ms ) .
as illustrated in figure 3 , excitation was performed sequentially across metabolites in the order 
 x111,x121,  ,x1n1,x212,  ,x2n2,x313,  ,x3n3,x114 ,  
 where xij denotes time - point j and phase encoding step i = 1 
n for metabolite x . here , { 1x , 2x , 3x } = [ pyr , bic , lac ] , and n = 12 .
the sequence was electrocardiogram ( ecg)-gated , and the polarity of the in - plane phase encoding ( y ) axis was alternated on successive acquisitions of the same metabolite .
the flip angle per shot was chosen to be  = 3 for x = pyr , and  = 20 for x  pyr , such that the overall flip angle for each 3d image is  = arccos(cos ) = 17 for x = pyr and 61 for x  pyr .
a thermally polarized 5 m c urea phantom was included next to the animal to provide a carbon frequency reference .
three - dimensional , cardiac - gated volume shimming was performed using the previously mapped behavior of the magnet s shim set and a spherical harmonic cardiac autoshimming algorithm as described previously ( 15 ) .
multiecho cardiac gated gradient echo b0 maps were acquired ( 48  48 matrix ; 70  70 mm fov ; 1.2 mm slice ; tr 100 ms ; te = 3.06 , 3.56 ms ; tread = 1 ms ; total scan time 60 s ) to verify homogeneity over the whole volume of acquisition ( 15 ) .
the c centre frequency transmit was set by identifying the frequency of the urea phantom urea , and compensating for any small measured b0 variation between the urea phantom and the heart b0 as transmit = urea + b0c/h .
anatomical images were acquired with a gradient echo cine sequence described previously ( 16 ) , with the same slice thickness and fov as the hyperpolarized data ( tr = 4.6 , te = 1.41 ms , 28 frames , fa = 25 ) .
experiments were performed on a varian 7 t ddr system with gmax = 17.5 g / cm , smax = 87.5 g / cm / ms , with an actively detuned transmit / surface receive setup consisting of a 72 mm dual - tuned h / c proton / carbon birdcage volume coil with a 40 mm two - channel c surface receive array with an integrated preamp ( rapid biomedical gmbh , rimpar , germany ) . a home - made combined rf shield and animal handling system
the volume coil c flip - angle calibration was performed on a cylindrical reference phantom consisting of 500 ml of 1 m natural abundance urea with thermal equilibrium slice - selective spectroscopy .
it was found that the position and width of the resonant frequency of the volume coil did not change appreciably between loading with the phantom and with a rat , indicating that the delivered carbon flip angle was as calibrated .
the b1 + homogeneity of the volume coil was assessed by acquiring a multiple flip angle b1 map on the urea phantom with tr at least 5t1 .
we found that the spatial variation of flip angle was 8% , which is believed to be dominated by noise in the acquired data . to allow for the reconstruction of an accurate time axis , it was necessary to create a simple hardware device that recorded when each ecg - gated scan occurred to a resolution of 10 s .
this high temporal resolution ensured that the error on recording the time at which each shot occurs could be neglected .
scans were gated to the r - wave using a threshold - based detection device described previously ( 16 ) .
respiratory gating was not performed , as no artefacts were observed that were believed to be due to respiratory motion .
the period of respiratory motion ( c. ~ 1.52 s in the anaesthetized rat ) was comparable to the duration of each acquisition .
all experiments were performed in accordance with relevant uk legislation ( with personal , project and institutional licenses granted under the animals ( scientific procedures ) act 1986 ) , and were subject to local ethical review and an independent cost - benefit analysis .
approximately 40 mg of [ 1-c]pyruvate doped with 15 mm ox063 trityl radical and 3 l of a 1 in 50 dilution of dotarem ( guerbet laboratories ltd ) gadolinium chelate was polarized and dissoluted in a prototype polarizer as described previously ( 17 ) .
the estimated liquid state polarization was ~32% after dissolution , 2 ml of the resulting 80 mm pyruvate solution were injected manually over a 20 s period through a previously placed tail vein cannula in anaesthetized male wistar rats ( 2% isoflurane in 90% o2 , 10% n2o ; n = 4 ; body weight 410  70 g ) .
pyruvate was injected approximately 10 s after dissolution , and its ph was measured after each dissolution to ensure correct neutralization in all experiments .
animals were housed in a custom handling system within the magnet bore that regulated their temperature and provided rf shielded electrical connections for ecg triggering and the rf coils .
four rats were scanned on three separate occasions with at least two days as a recovery period between scans .
animals were imaged three times : ( a ) in the fed state after being allowed food and water ad libitum ; ( b ) after being fasted for at least 8 h prior to imaging ; and ( c ) following injection with the pdk inhibitor , dca , in the fed state .
rats were dosed with dca at approximately 30 mg / kg as previously proposed ( 18 ) , 30 min before hyperpolarized imaging . to minimize the total volume of injected agents , dca was administered as a 100 l bolus
data were regridded appropriately in matlab , and linear phase correction performed in - plane on the epi readout .
alternate lines of k - space were then fourier transformed independently , and added in magnitude in image space ; halving the fov and eliminating the ghost .
the noise decorrelation matrix for the two - channel array was calculated following the method of kellmen and mcveigh ( 19 ) , and the data prewhitened .
images were combined and coil sensitivities calculated following the method of mckenzie ( 20 ) . following the method of cunningham et al ( 21 ) ,
blip - reversed epi data were spatially corrected by a mutual information maximization method , to compensate for small spatial shifts caused by being off - resonance .
the resulting five - dimensional image stacks were zero - filled by a factor of two in all spatial directions , producing an image stack with a final in - plane resolution of 1  1  1.9 mm .
a manually segmented roi was drawn in the lumen ( pyruvate ) or myocardium ( bicarbonate , lactate ) and the ratio of maximum bicarbonate to maximum pyruvate computed after subtracting the mean noise as measured from the last 10 time points of the experiment .
we were able to resolve the metabolism of prepolarized [ 1-c]pyruvate in the in vivo rat heart with a reconstructed spatiotemporal resolution of 1  1  1.9 mm and ~1.8 s. the three - dimensional sequence reports on hyperpolarized metabolism in a 64  64  45.5 mm fov , which was sufficient to encompass the whole heart and the liver .
the large field of view was advantageous as we obtained information from multiple organs at the same point in time .
the data were five - dimensional and an example maximum intensity projection ( summed over time ) showing the acquisition volume is illustrated in figure 4 . alternating the epi blip direction allowed for the accurate correction of bulk frequency shifts , and the data overlay with anatomical cine images , illustrating myocardial metabolism ( cf .
the time - courses of these data are available as supplementary videos s13 , which are representative examples from each group of rats scanned .
the b1 homogeneity arising from the volume transmit / surface receive hardware used was sufficient to ensure a uniform excitation across the volume of interest .
this homogeneity should be contrasted to the spatially nonuniform flip angle arising from a surface transmit / receive coil . however , due to the sensitivity profile of the surface receive coil used , it was not always possible to resolve segments of the myocardium distal from the chest wall . across the 12 scans ,
the distal wall was completely resolved twice , partially resolved four times , and not resolved six times .
the temporal resolution of the technique was sufficient to resolve metabolic dynamics following injection of hyperpolarized [ 1-c]pyruvate in a single voxel .
concomitantly with the known anatomy , pyruvate was observed perfusing the great vessels at early times , before arriving in the right and then left ventricles .
summing the data acquired in a manually segmented roi over the heart allowed for the reconstruction of metabolic dynamic time - courses ( fig .
6 ) , as expected . reflecting the known modulation of pdk by both dca and fasting , significant differences in the ratio of the summed myocardial maximum bicarbonate to maximum pyruvate
; student s t - test p = 0.03 between fasted and fed , and fed and dca ; p = 0.0008 between fasted and dca ) .
the administration of dca serves to approximately double this ratio compared to the fed animals , and quadruple it compared to fasted animals ( dca to fed : 1.6  0.3 , dca to fasted : 3.9  2.8 ; values ratio means  s.e.m .
this doubling of pdh flux between fed animals and those dosed with dca is the same as that obtained when this experiment was performed by simple unlocalized c spectroscopy following hyperpolarized [ 1-c]pyruvate injection ( 18 ) . a slight distribution of acquisition trs
r interval and a small number of shots at 2  r  r interval , reflecting a number of missed triggers that we conjecture are due to respiratory motion .
it was noted that the tr of the experiment was not constant , and that the distribution of 3d image trs was well described by a gamma distribution ( fig .
the mean of this distribution was not equal to the number of z phase encodes , n  the r 
the observed coefficient of variation of tr / image was 40.411.4% ( distribution /  s.e.m .
we are confident that this effect is biological in origin and not an experimental artefact ; the variability vanished when a signal generator was used to provide an input comparable to an ecg into our cardiac triggering hardware .
we note that the correct time axis is fundamentally important in hyperpolarized imaging , as it is desirable to create quantitative maps of metabolic rate constants of interest .
we have developed a novel sequence for the spectroscopic imaging of hyperpolarized [ 1-c]pyruvate and its downstream metabolites in the in vivo rat heart .
the proposed sequence was robust in the sense that ( a ) the flyback 3d spectral - spatial excitation reduces gradient demands , and was replayed with better fidelity than pulses that excite a thin slab , ( b ) the excitation bandwidth of the pulse was relatively large ( 3 ppm ) , minimising sensitivity to b0 inhomogeneity , and ( c ) bulk frequency shifts on the order of 30 hz that arose from uncertainty of the pyruvate frequency a priori could be corrected for with the alternating epi readout .
our hardware produced accurate information about the acquisition time of each image , which was used to compensate for the variability of the heartbeat of the anaesthetized rat .
cardiac small animal imaging is challenging , as the required resolution and rapid heart rate increases both gradient hardware and snr demands .
nevertheless , it is desirable to image small rodents as they form the predominant animal model of choice for cardiovascular research , and unlike large animals , mice ( and increasingly rats ) can be readily genetically manipulated to further probe the genetic basis of disease ( 22 ) .
therefore , while small animal imaging is challenging , it is of considerable utility owing to the large number of different conditions that could be investigated .
it is also a central tenant of ethical animal experimentation to minimize the degree of discomfort experienced using a less sentient model species if one is available ( 23 ) .
scenario for human imaging , as the required spatial and temporal resolutions are in excess of those required for human use .
as the total magnetization available for hyperpolarized imaging is independent of the scanner hardware ( instead depending on the polarizer used and the quantity of visible carbon injected ) , the ultimate snr limited resolution for a given sequence and a given quantity of visible carbon will also be largely independent of subject and hardware .
for the reasons outlined above , it is therefore desirable to develop the best possible imaging sequence for capturing hyperpolarized metabolism in the rodent heart , even though scaling arguments predict that this is more challenging than imaging larger animals , including humans .
the proposed sequence is a good compromise between spectral , spatial , and temporal resolution .
as shown , we were able to spatially resolve metabolism within the myocardium and liver with temporal resolution sufficient to capture metabolic dynamics of interest .
the flyback spectral - spatial excitation effectively represents the limit of spectral undersampling and reduces demands on gradient hardware .
we could record metabolism in multiple organs simultaneously , with an acquisition resolution of 2  2  3.8 mm in a comparatively large fov that ensures whole heart coverage .
moreover , the large excitation slab reduced flow artefacts that can occur due to pyruvate in the blood flowing into ( and out of ) a thin excitation slab for 2d multislice imaging approaches .
we do not observe any in - plane flow ghosting artefacts , reflecting the comparatively short readout train as epi readouts are known to be particularly prone to these distortions ( 24 ) .
the resolution of this sequence compares favorably to other approaches , such as multiband , ( 11 ) ideal csi ( 25 ) , high resolution accelerated spiral csi ( 26 ) , spectral - spatial excitation followed by a multislice spiral readout ( 8) , or k - t undersampling following spectral - spatial excitation with an epi readout ( 27 ) , for which the reported resolutions are 2  2  4 mm 4.4
 4.4  10 mm 2.7  2.7  10 mm , 8.8  8.8  10 mm , and 1  1  8 mm , respectively .
while these sequences have been developed on a variety of hardware with different limitations , and utilized on a variety of different animal models of disease , they all fundamentally encounter the snr limitations of pyruvate m0 generated in a 3 t preclinical hyperpolarizer .
an argument can , therefore , be made that the ultimate achievable resolution of hyperpolarized pyruvate imaging depends on the quantity of visible carbon injected , which is approximately constant , and the compromises made in the design of sequences to image it .
we accordingly believe that the proposed sequence represents an acceptable compromise between spatial , spectral and temporal resolution that will be generally applicable to those wishing to image hyperpolarized metabolism in any organism .
the scanner used is a common preclinical system , and is not state - of - the - art .
we have found that the fly - back pulse running at smax produces a waveform whose biggest distortion is a constant time offset , which can be corrected by the introduction of a small delay between the rf relative to the gradient waveform , and whose effect otherwise is to slightly degrade the slice profile .
this should be contrasted to non - fly - back spectral - spatial pulses , where infidelities cause spurious excitation at 0 hz , producing unwanted mixed metabolic excitation .
the duration of the fly - back pulse is chosen to have a narrow spectral passband and a large stopband , that is , to avoid exciting pyruvate hydrate and lactate at the same time .
reducing the slab thickness increases resolution at the cost of gradient requirements and snr ; increasing it reduces either the spatial or temporal resolution with associated snr and gradient requirement benefits .
as expected , the sensitivity to metabolism of this hyperpolarized imaging strategy was confirmed by modulating the metabolic state of the rodents imaged , whereupon significant differences in pdh flux were observed between animals that were fasted , fed , and fed and given the pdk inhibitor dca . the fact that the relative increase in apparent pdh flux was the same as when the same experiment was performed spectroscopically validated the technique .
three dimensional hyperpolarized imaging strategies need to be designed to take into account the effect of the depletion of the longitudinal magnetization by each phase encode on the resulting image .
the relative snr efficiency of 3d pulses for hyperpolarized imaging is well documented ( 28,29 ) , and can be approximated by the ratio 
 snr2dsnr3d = sin2dnsin3d 
 where n is the number of z phase encodes .
here n = 12 , 2d = 17 or 61 , and 3d = 3 or 20. this predicts an approximately equal snr efficiency for pyruvate imaging ( 2d/3d ratio = 0.993 ) , and a ~25% snr benefit for metabolites other than pyruvate ( ratio = 0.743 ) .
this snr improvement from exciting a large volume comes at a cost , as noted by wild et al , as the effect of the depletion of the longitudinal magnetization is to apply a filter in kz that serves to blur the image through the z direction .
the size of this effect is related to 1  ( cos  ) , the acquisition scheme , and the ratio tr / t1 that together determine the full width half max ( fwhm ) of the filter .
the quantity 1  ( cos ) here is small ( ~0.02 ) for pyruvate and  1/2 for metabolites other than pyruvate . to quantify the effect of this proposed acquisition scheme , the kz filter h(z ) as defined by wild et al
was numerically calculated for the 3d sequence described here ( i.e. with n = 12 centric ordered shots ) , and fourier transformed to find the point spread function . the resulting kz filter had a fwhm of 1.012 for pyruvate , and 1.176 for metabolites other than pyruvate .
we consider a subvoxel blurring in the slice direction to be outweighed by the ~25% snr gain resulting from the three - dimensional approach .
the error in gated scan timing , here defined as the difference between actual and  expected 
( n  r - r interval ) scan time , became progressively worse over time ( fig .
the mean of this distribution was not equal to n  r  r interval ; and it was broad : the coefficient of variation of tr / image was 40.411.4% ( distribution /  s.e.m . over 16 scans ) .
as shown in figure 8 , the observed distribution of tr s were well - described by the two - parameter gamma distribution 
 f(x;k,)=xk1exk(k)forx>0andk,>0 
 where (k ) is the gamma function (k)=0xk1exdx , and k and  are the shape and scale parameters that were fit to the acquired data .
as the ecg can be considered a stochastic time - series that is a sum of underlying fundamental processes ( 30,31 ) , the scan counts are positive semidefinite , and the distribution of increment times , that is , trs , are gamma distributed , the number of gated scans at a given time can be considered a gamma process , a type of generalized poisson process ( 32 ) .
this fact implies that dynamic techniques which neglect this information will have a skewed time axis that becomes progressively distorted as time increases , despite the relatively small distribution in the r - r interval itself .
system independent  quantities of interest such as rate constants or perfusion values , which fundamentally depend on an accurate time axis , are therefore liable to be biased if data is not time - stamped accurately .
we note that the majority of preclinical scanners do not record the exact time at which a shot occurs .
future work might be able to exploit the distribution of repetition times in this acquisition with sequences inspired by stochastic nmr ( 33 ) .
owing to the fact that z - phase encoding is centric ordered , we propose that the effective timepoint for each 3d volume acquired is defined as the echo time of the first shot , when the centre slab of z k - space is acquired .
we note that this definition might be contentious , but the use of an accurate timestamping device allows for the post hoc reconstruction of the time axis as required ; here , the axis was defined as above .
the acquisition strategy spans several orders of magnitude in time , with the pulse length (= 31.48 ms ) short in comparison to the cardiac cycle ( ~ 150 ms ) and respiratory motion ( ~ 1.5  2 s ) .
we did not observe any artefacts that could be ascribed to respiratory motion , but a separate acquisition showed that cardiac triggering was still required to avoid motion artefacts in the myocardium .
first , the snr benefit and the width of the kz filter arising from the 3d approach is highly dependent on the actual flip angle delivered , and therefore requires good b1 + homogeneity . in this study
, a volume transmit coil was used that was homogeneous over the region of interest .
it is likely that this acquisition strategy will be challenging with a surface transmit / receive coil , where the flip angle delivered is inherently a function of space .
we would expect the resulting images to have a significant degree of interslice blurring arising from the large flip angle close to the surface of the coil .
however , if these effects can be ameliorated by ensuring homogeneous b1 + ( as they have been here ) , the 3d approach can fundamentally deliver better snr .
second , hyperpolarized imaging sequences that use phase encoding effectively apply a blurring filter in the phase encoding direction , here z , due to the depletion by each shot of the initial magnetization .
this effect is proportional to 1  cos( ) , which grows quickly with  and n. however , the snr benefit grows only as n sin , which is approximately linearly at small  , and slowly with n. there are , therefore , several regions of  and n where this approach is inferior to 2d imaging with multiple slices , for example , as   90 , where the slice resolution approaches the fov , and at very low flip angles and small n , where the 2d approach has better snr . as demonstrated , we have chosen values of  and n such that this effect was ameliorated , and a substantial snr benefit was obtained at the cost of a modest trade - off in slice resolution .
third , one would expect that the high slew - rate requirements of the fly - back pulse would introduce nonlinear distortions that serve to degrade the excitation profile of the pulse .
1c ) , despite the prediction of a slight problem with pre - emphasis from the measured gradient impulse response function for this pulse .
fourth , the 3d sequence is relatively robust to flow artefacts , as the large excitation slab thickness ensures that excited spins will be read out irrespective of their motion .
however , we have not quantified the effect of flow over the 12 rr intervals that each volume is acquired over , and it is likely that different parts of kz correspond to flowing spins in different positions , which could result in a flow artefact .
we expect two types of artefact to arise from flow ; ghosting in the phase encoding direction arising from in - plane motion during the epi readout ( 24 ) , and linear shift in z arising from through - plane motion during the 3d readout .
this last effect arises as the kz gradient blips can serve to act as velocity encoding gradients , creating a phase ramp on spins through z. in the proposed sequence , the largest blip is 328 s long , and 7.51 g in amplitude .
this corresponds to a large velocity encoding moment ; spins flowing at 23 m / s would be shifted by one voxel in z. this artefact is correspondingly negligible in the rat heart .
it is also appropriate to consider the effect of metabolism on the resulting images , as the c label is transferred to downstream metabolites during the acquisition period of the 3d volume .
this effect is analogous to modulating the t1 of the compound imaged , as the net effect of the ( dis)appearance of a small quantity of hyperpolarized metabolite in bulk will be analogous to the increase or decrease in t1 for that compound .
accordingly , the effect on the image is a slight blurring or sharpening through kz , as the nonrenewable magnetization is depleted or slightly replenished between phase encodes .
we do not observe any appreciable through - plane blurring , indicating that this effect is small . finally ,
the first - order phase correction method used did not always remove the nyquist ghost arising from the epi readout train used .
owing to the large acquisition fov of the technique , we elected to recombine odd and even lines separately in every case , halving the fov and eliminating the ghost .
however , in general it is possible to perform a 2d phase correction to remove the distortion ( 34 ) .
unfortunately , the dynamic nature of hyperpolarized imaging means that many standard algorithms will not work  out - of - the box  and instead a manual in - plane phase map has to be created and applied for each acquisition , estimated from high snr images that cover as large a volume as possible , including both ventricles and the myocardium .
this is a potentially challenging and time - consuming step that might drive a desire to perform fly - back epi .
first , the snr benefit and the width of the kz filter arising from the 3d approach is highly dependent on the actual flip angle delivered , and therefore requires good b1 + homogeneity . in this study
, a volume transmit coil was used that was homogeneous over the region of interest .
it is likely that this acquisition strategy will be challenging with a surface transmit / receive coil , where the flip angle delivered is inherently a function of space .
we would expect the resulting images to have a significant degree of interslice blurring arising from the large flip angle close to the surface of the coil .
however , if these effects can be ameliorated by ensuring homogeneous b1 + ( as they have been here ) , the 3d approach can fundamentally deliver better snr .
second , hyperpolarized imaging sequences that use phase encoding effectively apply a blurring filter in the phase encoding direction , here z , due to the depletion by each shot of the initial magnetization .
this effect is proportional to 1  cos( ) , which grows quickly with  and n. however , the snr benefit grows only as n sin , which is approximately linearly at small  , and slowly with n. there are , therefore , several regions of  and n where this approach is inferior to 2d imaging with multiple slices , for example , as   90 , where the slice resolution approaches the fov , and at very low flip angles and small n , where the 2d approach has better snr . as demonstrated , we have chosen values of  and n such that this effect was ameliorated , and a substantial snr benefit was obtained at the cost of a modest trade - off in slice resolution .
third , one would expect that the high slew - rate requirements of the fly - back pulse would introduce nonlinear distortions that serve to degrade the excitation profile of the pulse .
1c ) , despite the prediction of a slight problem with pre - emphasis from the measured gradient impulse response function for this pulse .
fourth , the 3d sequence is relatively robust to flow artefacts , as the large excitation slab thickness ensures that excited spins will be read out irrespective of their motion .
however , we have not quantified the effect of flow over the 12 rr intervals that each volume is acquired over , and it is likely that different parts of kz correspond to flowing spins in different positions , which could result in a flow artefact .
we expect two types of artefact to arise from flow ; ghosting in the phase encoding direction arising from in - plane motion during the epi readout ( 24 ) , and linear shift in z arising from through - plane motion during the 3d readout .
this last effect arises as the kz gradient blips can serve to act as velocity encoding gradients , creating a phase ramp on spins through z. in the proposed sequence , the largest blip is 328 s long , and 7.51 g in amplitude .
this corresponds to a large velocity encoding moment ; spins flowing at 23 m / s would be shifted by one voxel in z. this artefact is correspondingly negligible in the rat heart .
it is also appropriate to consider the effect of metabolism on the resulting images , as the c label is transferred to downstream metabolites during the acquisition period of the 3d volume .
this effect is analogous to modulating the t1 of the compound imaged , as the net effect of the ( dis)appearance of a small quantity of hyperpolarized metabolite in bulk will be analogous to the increase or decrease in t1 for that compound .
accordingly , the effect on the image is a slight blurring or sharpening through kz , as the nonrenewable magnetization is depleted or slightly replenished between phase encodes
. we do not observe any appreciable through - plane blurring , indicating that this effect is small .
finally , the first - order phase correction method used did not always remove the nyquist ghost arising from the epi readout train used .
owing to the large acquisition fov of the technique , we elected to recombine odd and even lines separately in every case , halving the fov and eliminating the ghost .
however , in general it is possible to perform a 2d phase correction to remove the distortion ( 34 ) .
unfortunately , the dynamic nature of hyperpolarized imaging means that many standard algorithms will not work  out - of - the box  and instead a manual in - plane phase map has to be created and applied for each acquisition , estimated from high snr images that cover as large a volume as possible , including both ventricles and the myocardium .
this is a potentially challenging and time - consuming step that might drive a desire to perform fly - back epi .
we have developed a novel ecg - gated three - dimensional pulse sequence for the cardiac spectroscopic imaging of hyperpolarized [ 1-c]pyruvate and its downstream metabolites in vivo .
the sensitivity of the developed sequence to metabolism has been confirmed by manipulating the metabolic state of the rodents imaged .
the 3d spectral - spatial excitation is relatively immune to b0 inhomogeneity , and does not place unphysical demands on gradient hardware to image at high spatiotemporal resolution .
a simple argument is presented to support the hypothesis that three - dimensional hyperpolarized imaging is more snr efficient than multislice approaches , at the cost of a slight blurring in the slice direction .
we have further shown that cardiac time - stamping is important when imaging dynamic processes because of the stochastic nature of cardiac gating , a fact that is often overlooked .
this work allows the spectrally efficient metabolic imaging of cardiac metabolism in small animals at high spatiotemporal resolution .
this is of utility for preclinical research into both cardiovascular disease and more broadly diseases where metabolism is dysregulated .
supplementary video 1 : representative mid - ventricular single - slice time - resolved data overlaid on anatomical reference images .
shown here are the three metabolites , from left to right , pyruvate , bicarbonate and lactate in a fasted rat .
the color axis for each of the three images is scaled relative to the maximum pyruvate .
supplementary video 2 : representative mid - ventricular single - slice time - resolved data overlaid on anatomical reference images . shown here
are the three metabolites , from left to right , pyruvate , bicarbonate and lactate in a fed rat .
the color axis for each of the three images is scaled relative to the maximum pyruvate .
supplementary video 3 : representative mid - ventricular single - slice time - resolved data overlaid on anatomical reference images . shown here
are the three metabolites , from left to right , pyruvate , bicarbonate and lactate in a fed rat administered the pdk inhibitor dca .
the color axis for each of the three images is scaled relative to the maximum pyruvate .
 purposehyperpolarized metabolic imaging has the potential to revolutionize the diagnosis and management of diseases where metabolism is dysregulated , such as heart disease . 
 we investigated the feasibility of imaging rodent myocardial metabolism at high resolution at 7 t.methodswe present here a fly - back spectral - spatial radiofrequency pulse that sidestepped maximum gradient strength requirements and enabled high resolution metabolic imaging of the rodent myocardium . 
 a 3d echo - planar imaging readout followed , with centric ordered z - phase encoding . 
 the cardiac gated sequence was used to image metabolism in rodents whose metabolic state had been manipulated by being fasted , fed , or fed and given the pyruvate dehydrogenase kinase inhibitor dichloroacetate.resultswe imaged hyperpolarized metabolites with a spatial resolution of 2  2  3.8 mm3 and a temporal resolution of 1.8 s in the rat heart at 7 t. significant differences in myocardial pyruvate dehydrogenase flux were observed between the three groups of animals , concomitant with the known biochemistry.conclusionthe proposed sequence was able to image in vivo metabolism with excellent spatial resolution in the rat heart . 
 the field of view enabled the simultaneous multi - organ acquisition of metabolic information from the rat , which is of great utility for preclinical research in cardiovascular disease . 
INTRODUCTION
METHODS
Spectral-Spatial Pulse Design
Pulse Sequence
Hardware
Animal Handling and Dosing
Reconstruction
RESULTS
DISCUSSION
Limitations
CONCLUSIONS
Supplementary Material