Hyperpolarized [1-13C]-acetate Renal Metabolic Clearance Rate Mapping

11C-acetate is a positron emission tomography (PET) tracer of oxidative metabolism, whereas hyperpolarized 13C-acetate can be used in magnetic resonance imaging (MRI) for investigating specific metabolic processes. The aims of this study were to examine if the kinetic formalism of 11C-acetate PET in the kidneys is comparable to that of 13C-acetate MRI, and to compare the dynamic metabolic information of hyperpolarized 13C-acetate MRI with that obtained with 11C-acetate PET. Rats were examined with dynamic hyperpolarized 13C-acetate MRI or 11C-acetate PET before and after intravenous injection of furosemide, a loop diuretic known to alter both the hemodynamics and oxygen consumption in the kidney. The metabolic clearance rates (MCR) were estimated and compared between the two modalities experimentally in vivo and in simulations. There was a clear dependency on the mean transit time and MCR for both 13C-acetate and 11C-acetate following furosemide administration, while no dependencies on the apparent renal perfusion were observed. This study demonstrated that hyperpolarized 13C-acetate MRI is feasible for measurements of the intrarenal energetic demand via the MCR, and that the quantitative measures are correlated with those measured by 11C-acetate PET, even though the temporal window is more than 30 times longer with 11C-acetate.

Renal oxygen consumption is closely correlated with tubular sodium reabsorption 1,2 and is altered by several pathophysiological conditions, including acute kidney disease, ischemic and diabetic nephropathy, and hypertension 3,4 . Dynamic Nuclear Polarization (DNP) magnetic resonance imaging (MRI) is based on the very strong MR-signal from hyperpolarized carbon-13 nuclei inserted in biological molecules. DNP MRI has recently been established as a suitable method for measuring important renal metabolites in various pathophysiological conditions, including diabetes [5][6][7][8][9][10][11][12] , acute kidney injury [13][14][15] , and acute functional changes [16][17][18] . Hyperpolarized 13 C-acetate MRI has been applied to examinations of both rodents and porcine models [19][20][21][22][23] ; however, the acquisition and subsequent quantification is challenging at clinical field strengths due to the small chemical shift difference between acetate and the downstream products [24][25][26] . It is important to note that hyperpolarized 13 C metabolic flux analysis is currently not fully quantitative and is therefore said to be apparent in nature, thereby limiting the quantitative information available and highlighting the need for new quantitative analysis methods to improve the diagnostic capabilities of the method 27 .
A highly successful clinical metabolic imaging modality, positron emission tomography (PET), similarly relies on the isotopic labeling of biological molecules and allows quantifiable perfusion, uptake, and metabolism 28 . Several metabolically inactive 13 C-biomarkers, such as 13 C-urea, have been shown to be particularly useful in perfusion studies, which enable quantitative evaluation 11,14,18,29 and are analogous to PET perfusion assessment with molecules such as 15 O-water PET and 13 N-ammonia PET, although the signal decay is several orders of magnitude faster with hyperpolarized MRI 30,31 . Moreover, in PET, metabolically active molecules rely solely on signal changes associated with the injected compound to quantify various metabolic alterations in vivo, as opposed to hyperpolarized 13 C, where the downstream metabolic conversion is directly detected. One metric, which has been = RBF RBV MTT (1) where RBV is the renal blood volume and MTT is the mean transit time in the renal parenchyma. Once inside the cell, 11 C-acetate will be metabolized via acetyl-CoA synthetase to acetyl-CoA, which enters the tri-carboxylic acid (TCA) cycle, a reaction that has been shown to be proportional to the oxidative rate of the cycle 30 .
Juillard et al. 34 demonstrated that the renal 11 C-acetate MCR, mono-exponential clearance, was significantly correlated with renal oxygen consumption using 11 C-acetate PET. It was concluded that renal 11 C-acetate MCR would be of value in monitoring the effects of interventions and in understanding the pathophysiology of chronic renal diseases. MCR, denoted K (in units min −1 ) in 11 C-acetate PET, estimated from the decay/removal (signal leaving the compartment in question and/or metabolic conversion), is considered to be a quantitative measure of oxidative metabolism 30,32,33 . The clearance rate is then determined by fitting the tissue dynamic curve with a one-compartment model, single-exponential fit. Alternatively, a novel method, which utilizes the relationship between the mean transit time and the MCR, has been proposed to allow similar quantitative clearance rate mapping 30,35 : Denoted hereafter as K MTT . Analogously to 11 C-acetate, we investigated [1-13 C]-acetate hyperpolarized MRI as a novel method for measuring renal oxygen metabolism solely using the [1-13 C]-acetate signal, rather than separating the metabolic by-products as typically performed with hyperpolarized MRI, by utilizing this simple MTT relationship.
The aims of this study were to investigate the feasibility of hyperpolarized 13 C-acetate MRI for measuring the MCR in the kidneys before and after administration of a diuretic, and to compare the findings with 11 C-acetate MCR PET findings 35 , in vivo and in simulations.

Methods and Materials
Simulations. In order to investigate the accuracy of the proposed formalisms in determining K, we simulated 11 C and 13 C acetate metabolic conversion. We assumed that 11 C-acetate accurately describes the oxidative renal metabolism, and that 11 C and 13 C labelled acetate share common pharmacokinetic information, although the radioactivity decay and longitudinal relaxation are significantly different. A two compartment, unidirectional kinetic simulation of 11 C-acetate and 13 C-acetate kinetic conversion was performed using MATLAB (MATLAB 2016a, The MathWorks Inc., Natick, MA, USA), with the approximately achieved values in vivo: K = 0.15 min −1 , 11 C-acetate decay = 20.4 min, 13 C-acetate relaxation time = 14 s at 3 Tesla 24 , and flip angle = 10 degrees, showing a markedly increased conversion over 90 min compared with 3 min (Fig. 1A,B). In order to simulate the in vivo situation, a radiofrequency field (RF) inhomogeneity of 50% and T 1 variation of 29% in concern with a noise level of 5% was used to identify the relationship between the actual MCR (ranging from 0.05-1.0) and the proposed formalism derived K MTT (Fig. 1C,D). Each MCR point represents 90 iterations with 5% noise, covering the RF and T 1 variation ranges.
Animals. Eleven healthy rats were included in this study. All animals were anaesthetized with 3% sevoflurane in 2 L/min air as breathing gas. Blood glucose levels were measured from tail capillary blood with a Contour blood glucose meter (Bayer Diabetes Care, Copenhagen, Denmark). Tail vein catheterization (G 24) was performed for administration of hyperpolarized [1-13 C]-acetate and a diuretic (furosemide). All catheters were flushed with heparinized saline water. Temperature was maintained at 37 °C (SA Instruments, Stony Brook, NY, USA). The experiments complied with the Guidelines for the Use and Care of Laboratory Animals, and were approved by the Danish Inspectorate of Animal Experiments (J.nr. 2014-15-0201-00327).
Hyperpolarized 13 C-Acetate MRI. Six healthy female Wistar rats (258 ± 8 g) were scanned in a 3 Tesla GE HDx MRI system equipped with a hydrogen/carbon-RF quadrature transmit/receive-coil (GE Healthcare, Milwaukee, WI, USA). [1-13 C]-acetate was polarized in a SpinLab system (GE Healthcare). The kidneys were localized by a standard gradient-echo sequence, and a slice covering both kidneys was shimmed automatically. An axial oblique slice-selective (10 mm) 13 C-dynamic single shot spiral (field of view = 80 × 80, matrix = 32 × 32) sequence (120 sec, one image/sec) was initiated at the start of injection. A volume of 1.5 mL [1-13 C]-acetate was injected into the tail vein over a period of 15 sec. Twenty minutes after a furosemide injection (10 mg/kg), a second dynamic 13 C-MRI was repeated following an [1-13 C]-acetate injection (with similar concentration and injection rate). In order to verify the used in vivo effective T 1 time for correction of the in vivo data. Whole blood was extracted from two healthy rats into sodium heparin vacuum tubes. The blood was stored at 5 °C. Prior to the experiment the blood was heated and maintained at 37 °C. A volume of 4.5 mL blood was mixed with hyperpolarized 13 C-acetate (0.5 ml) prior to placement in the scanner. The MR experiment was acquired over 120 s (120 acquisitions), with a constant flip angle of 10°. The single exponential decay was fitted in MATLAB and corrected for RF depletion. Data were corrected for random coincidence events using a delayed coincidence window, and further corrected for dead time and decay. Images were corrected for attenuation and scatter using 18-min long 3D MR gradient echo sequences (TR 2.0 ms, TE 2.1 ms, flip angle 25°, 0.5 mm slice thickness, and horizontal orientation). In summary, the renal 13 C-acetate and 11 C-acetate distribution was measured under baseline physiological conditions, and again after a furosemide induced reduction of the active oxygen-dependent sodium transport in the ascending loop of Henle.
Analysis. MRI/PET data were imported to the Osirix software (Pixmeo, Geneva, Switzerland), and regions-of-interests on the left and right kidney parenchyma were manually segmented in order to measure the mean renal activity-curve. In the hyperpolarized 13 C-acetate study, an additional region-of-interest was drawn inside the abdominal aorta to obtain the arterial input function.
PET MCR. Two methods were used to estimate the MCR using 11 C-acetate: (1) a single exponential fit of the first 10-12 min after the inflow to the cortical tissue, denoted as K mono 34 , and (2) an analogous estimated K MTT , using the inverse of the mean transit time (MTT) in the tissue, estimated from the first-order moment: MTT ROI ROI 0 0 With t being the acquisition intervals and 11 C-acetate concentration (C ROI ) in the region-of-interest.  Hct). In order to account for the depolarization of the hyperpolarized signal (T 1 and RF depletion), a parametric relationship has previously been demonstrated 29 : where depolarization factor β is defined as: With MTT' being the measured (uncorrected) MTT and T 1 being the relaxation time of the hyperpolarized 13 C-acetate signal (here assumed to be 14 s 24 ).
Statistics. Normality was assessed with quantile-quantile plots. A P-value below 0.05 was considered statistically significant. Statistical analysis was performed using GraphPad Prism (GraphPad Software, La Jolla, CA, USA). A paired student's t-test with equal standard deviation was used for statistical analysis of the pre/ post experiments and an unpaired student's t-test with equal standard deviation was used to test the difference between the perfusion measurements.

Results
The simulated single 11 C-acetate compartment response was found to correlate well with the inverse MTT derived MCR 11 C-K MTT both with (P < 0.0001, R = 0.99) and without (P < 0.0001, R = 0.99) decay correction (data not shown). The 13 C-acetate compartment response was found to correlate similarly well without both relaxation and RF depletion (P < 0.0001, R = 0.99), although an offset was observed between the K input in the simulation and the estimated 13 C-K MTT . A similar offset correlation was recorded taking into account relaxation, RF depletion, and inhomogeneity, as well as experimental variation (P < 0.0001, R 2 = 0.2; Fig. 1). The linear relationship between the simulated input K value and the estimated noise simulations identified an offset of approximately 1 in the estimated 13 C-K MTT compared with the K input in the simulation. All rats were scanned in the fed state, and blood glucose levels were 7.3 ± 0.8 (±SD) mmol/L. Hyperpolarized [1-13 C]-acetate showed accumulation in both kidneys following arterial filling (Fig. 2). The 13 C-acetate RBF did not differ statistically between pre (476 ± 97 ml/100 ml/min) and post administration of furosemide (501 ± 127 (±SD) ml/100 ml/min; paired t-test: P = 0.63; Fig. 3). Furthermore, we found a significantly different 13 C-acetate MTT of 26 ± 8.1 (±SD) sec at baseline compared with 33.4 ± 10.1 (±SD) sec post furosemide administration (paired t-test: P = 0.05). Similarly, there was a significant difference in the 13 C-K MTT between baseline 2.5 ± 0.8 (±SD) min −1 and post furosemide administration 1.9 ± 0.5 (±SD) min −1 (paired t-test: P = 0.03) (Fig. 3). In order to confirm the in vivo effective T 1 , an ex vivo experiment on whole blood was performed. A whole blood 13 C-acetate T 1 of 18 ± 0.2 (±SD) was found. In order to verify the relationship between 11 C-K mono and 11 C-K MTT , in vivo 11 C-acetate dynamic PET images were acquired over 90 min prior to and post furosemide administration (Fig. 4). We observed a statistically significant decrease of 29% (paired t-test: P = 0.01) for 11 C-K MTT estimated from the MTT, and a similar numerical decrease of 27% for 11 C-K mono , although the difference was not significant (paired t-test: P = 0.21) in vivo (Fig. 5). Furthermore, a positive correlation was observed between 11 C-PET K mono and 11 C-K MTT (P = 0.01, R 2 = 0.84) (Fig. 5). No significant difference was observed in the fractional reduction of 13 C-K MTT (30 ± 16%) and 11 C-K MTT (22 ± 16%) (paired t-test: P = 0.46) (Fig. 5).

Discussion
This study investigated the feasibility of hyperpolarized 13 C-acetate MRI for measuring the MCR in kidneys before and after administration of a diuretic, and compared the findings with those of 11 C-acetate MCR PET in vivo and in simulations. The main finding of this study was that it was possible to measure the renal MCR changes  associated with furosemide treatment using hyperpolarized 13 C-acetate, and that these changes correlated with the values reported for quantitative 11 C-acetate PET 34 . The method is based only on the injected 13 C-acetate signal itself, without the need to sample the downstream metabolic products.
Our findings support the use of 11 C-acetate mono-exponential decay analysis in the investigation of renal oxidative alterations associated with changes in sodium reabsorption induced by furosemide, and show that the MCR can be accurately estimated using the 11 C-acetate transit time in the renal parenchyma. Similarly, the hyperpolarized 13 C-acetate is able to show a similar relationship, although there is an offset due to the short temporal window, and fast decaying signal due to RF depletion and signal relaxation decay.
The renal perfusion estimated with 13 C-acetate hyperpolarization was similar to previously reported values with dynamic contrast enhanced imaging in rats 37 and with hyperpolarized 13 C-2-hydroxyethylacrylate 38 . Comparing 13 C-acetate perfusion and MTT to the metabolically inactive hyperpolarized 13 C-urea under similar conditions (see Supplemental Fig. 1) results in similar perfusion characteristics pre and post furosemide administration, while no change is seen in the 13 C-MTT between baseline and furosemide challenge for 13 C-urea 11 , supporting metabolic conversion of 13 C-acetate to be the origin of the changes seen in this study. Previous studies have demonstrated time-dependent renal perfusion alterations following administration of furosemide [39][40][41] . In the present study, no alterations in renal perfusion post furosemide were observed. This could be due to the timing or the low spatial resolution, making spatial localization difficult. An increased RBF post furosemide administration would be expected to limit the renal oxygen consumption measurements and therefore potentially mask the altered oxygen consumption.
The model-free deconvolution has previously been applied in hyperpolarized experiments, yielding accurate 13 C-MTT maps with a minor deviation originating from the relaxation decay of the tracer 29 . These results are further supported by the recent hyperpolarized water perfusion in the porcine kidney 42 , demonstrating that the accurate use of formalism can determine the perfusion of the kidney.
The increased conversion rate of [1-13 C]-acetate observed following furosemide administration supports the view that this diuretic drug increased the filling of the cortical space, while the overall energetic demand was reduced due to the reduced sodium reabsorption induced by furosemide treatment. This finding is consistent with a previous experiment performed with hyperpolarized 13 C-urea in the porcine kidney 16 . The hyperpolarized signal had a significantly shorter decay compared with 11 C-acetate.
The in vivo 13 C-acetate MCR (prior to offset correction) in this study was two orders of magnitude larger than that reported with radioactive 11 C-acetate in the porcine kidney 34 and the in vivo 11 C-acetate MCR values reported in this study. This discrepancy may be explained by the large difference in signal decay, which was more than twenty times longer for 11 C-acetate compared with 13 C-acetate, and the RF depletion following repetitive excitations, showing a similar offset to the estimated 13 C-K MTT . This was supported by the simulations, showing a remarkable consistency with the in vivo results. Additionally, arterial input function and renal perfusion are expected to affect the hyperpolarized signal to a large degree due to the short time frame of the investigation.
Bi-exponential 11 C-acetate PET MCR has previously been described in the myocardium, with the fast decaying component correlating with myocardial oxygen consumption 30 . This is in contrast to the findings of the present study and the study by Juillard et al. 34 , showing a single exponential dependency and an approximately 10 times lower MCR. One contributing factor to this difference could partly originate from the difference in renal and myocardial metabolism, which is supported by the two-fold increase in the acetate-to-acetylcarnitine in rat heart compared with the kidney 24 . While MCR intra-species differences were expected, similar 11 C-acetate MCR have been reported among porcine, rabbit, and rat studies 34,43 . The reason for this intra-species similarity in MCR is currently unknown.
A potential limitation of the 13 C-acetate interpretation was the relaxation decay, which is fast and difficult to measure in vivo because the different cellular compartments exhibit variations in relaxation properties 44 . Furthermore, intra-renal 13 C relaxation differences have been demonstrated in the rodent kidney, both intra-voxel and across the kidney, indicating further improvements in the quantification by adequately accounting for these intra-renal relaxation differences 9,17,45,46 . In the present study, we utilized a simple parametric relationship to correct for the T 1 relaxation (here a simple single component), allowing already existing software packages to be utilized without any modifications 36,37 . The 13 C-acetate T 1 relaxation time (estimated renal T 1 relaxation time 24 ) used for the correction was similar to previously reported values at 3 T in vivo 21,24,47 and largely similar to the whole blood 13 C-acetate T 1 at 3 T (using the whole blood T 1 for correction will results in a slightly underestimated perfusion assessment, see Supplemental Fig. 2). A similar fast in vivo relaxation have been demonstrated at 9.4 T 48 , although it is important to note that reported values in solution is typically more than 40 s and even longer at lower fields 47,[49][50][51] . This is likely due to tissue specific effects on the in vivo T 1 , compared to ex vivo blood. It's unlikely that the T 1 relaxation of the 13 C-acetate metabolic breakdown products affects the MCR found here, as 13 C-acetate metabolic observable signal at 3 T is very small 24 . This can easily be solved by separating the different metabolic components by either selective excitation or spectroscopic separation and thus improving both the MCR and T 1 relaxation estimations 52,53 .
An offset in the estimated MCR originating from the shorter imaging window (offsetting the accurate determination of K MTT ) with hyperpolarized 13 C compared with 11 C PET, was observed in the 13 C-acetate simulations and in vivo 13 C-acetate experiments. Using a simple offset correction, the 13 C-K MTT results in a similar MCR value, thus supporting the inter-relationship of 11 C and 13 C, although the time span was significantly different. This supports the use of 11 C-PET for improving the quantification of 13 C hyperpolarized MRI examinations. Using a similar offset found in the simulations, an overestimation of the in vivo results was identified using hyperpolarized 13 C. This could be due to the difference in input function, T 1 relaxation, animal gender, and strain, in combination with the fact that the estimation was performed independently, indicating that simultaneous hyperpolarized MR and PET examinations are needed to describe the inter-relationship of 11 C and 13 C.

Conclusion
This study introduced a novel hyperpolarized 13 C-acetate MRI method for the investigation of renal MCR, which is a potential surrogate marker of oxidative metabolism. Furthermore, we found that the prior developed formalism for renal imaging with PET tracers allowed for simple and intuitive processing of 13 C single metabolite concentration curves. The formalism is not limited to 13 C-acetate imaging as such and can easily be extended to cover the more typical hyperpolarized biomarkers such as [1-13 C]-pyruvate. This study suggests a link between the metabolic information obtained with PET and hyperpolarized MRI. However, further investigations are needed to fully determine the relationship between the MCR determined with 11 C-PET and 13 C-hyperpolarized MRI.