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Two repetition time saturation transfer (TwiST) with spillover correction to measure creatine kinase reaction rates in human hearts
Journal of Cardiovascular Magnetic Resonancevolume 17, Article number: 70 (2015)
Abstract
Background
Phosphorus saturation transfer (ST) magnetic resonance spectroscopy can measure the rate of ATP generated from phosphocreatine (PCr) via creatine kinase (CK) in the human heart. Recently, the triplerepetition time ST (TRiST) method was introduced to measure the CK pseudofirstorder rate constant k_{f} in three acquisitions. In TRiST, the longitudinal relaxation time of PCr while γATP is saturated, T_{1}`, is measured for each subject, but suffers from low SNR because the PCr signal is reduced due to exchange with saturated γATP, and the short repetition time of one of the acquisitions. Here, a tworepetition time ST (TwiST) method is presented. In TwiST, the acquisition with γATP saturation and short repetition time is dropped. Instead of measuring T_{1}`, an intrinsic relaxation time T_{1} for PCr, T_{1} ^{intrinsic}, is assumed. The objective was to validate TwiST measurements of CK kinetics in healthy subjects and patients with heart failure (HF).
Methods
Bloch equation simulations that included the effect of spillover irradiation on PCr were used to derive formulae for T_{1} ^{intrinsic} and k_{f} measured by both TRiST and TwiST methods. Spillover was quantified from an unsaturated PCr measurement used in the current protocol for determining PCr and ATP concentrations. Cardiac TRiST and TwiST data were acquired at 3 T from 12 healthy and 17 HF patients.
Results
Simulations showed that both k_{f} measured by TwiST and T_{1} ^{intrinsic} require spillover corrections. In human heart at 3 T, the spillover corrected T_{1} ^{intrinsic} = 8.4 ± 1.4 s (mean ± SD) independent of study group. TwiST and TRiST k_{f} measurements were the same, but TwiST was 9 min faster. Spillover corrected TwiST k_{f} was 0.33 ± 0.08 s^{−1} vs. 0.20 ± 0.06 s^{−1} in healthy vs HF hearts, respectively (p < 0.0001).
Conclusion
TwiST was validated against TRiST in the human heart at 3 T, generating the same results 9 min faster. TwiST detected significant reductions in CK k_{f} in HF compared to healthy subjects, consistent with prior 1.5 T studies using different methodology.
Background
Phosphorus (^{31}P) saturation transfer (ST) magnetic resonance spectroscopy (MRS) enables the in vivo study of adenosine triphosphate (ATP) kinetics including those through the creatine kinase (CK) reaction [1, 2]. In muscle, the CK reaction serves as the prime energy reserve and a putative shuttle, transporting highenergy phosphates between the mitochondria, where ATP is created, and the myofibrils, where it is used. The pseudofirstorder rate constant (k_{f}) for CK indexes the fractional rate of ATP generation from phosphocreatine (PCr). ^{31}P ST MRS using the Four Angle Saturation Transfer (FAST; [3]) protocol at 1.5 T enabled human cardiac CK kinetic studies for the first time and identified significant reductions in cardiac k_{f} in patients with heart failure (HF). These findings and others indicated that reduced CK energy supply occurs in human HF, may play a role in the associated contractile dysfunction [4, 5], and is an independent predictor of subsequent clinical HF events [6].
In a ST experiment, the pseudofirstorder rate constant can be determined with:
where T_{1}` and M_{0}` are the longitudinal relaxation time and the equilibrium magnetization of PCr measured while the exchanging γATP resonance at −2.5 ppm is selectively saturated (signified by primes); and M_{0} is the equilibrium magnetization of PCr measured without γATP saturation. Recently, the Triple Repetition time ST (TRiST) protocol was introduced to more efficiently measure k_{f} in the human heart at 3 T [7]. TRiST only requires three acquisitions to determine k_{f}. Each of the three acquisitions takes between 8 and 22 min as they employ chemical shift imaging (CSI) for localization and multiple averages for sufficient signaltonoise ratio (SNR). Using TRiST, T_{1}` and M_{0}` are measured by the dualrepetition time (TR) method [8] with a short TR (M`(TR_{short}); TR_{short} = 2 heart beats, cardiacgated) and a long TR (M`(TR_{long}); TR_{long} ~10 s, cardiacgated) both while the exchanging γATP resonance is saturated. A third cardiacgated acquisition at a TR of ~ 16 s is performed to measure M_{0}. To compensate for the effects of spillover irradiation on PCr during γATP saturation, this third acquisition is performed while applying saturation at +2.5 ppm–termed “control saturation”, yielding M_{0} ^{control}. Equation [1] is then written as:
Spillover irradiation is caused by imperfect frequencyselective saturation of γATP that can partially saturate the nearby PCr resonance. A measure of the spillover effect is provided by the ratio
of the PCr signal acquired with control saturation, to the PCr signal acquired without any saturation [3, 9]. The control saturation experiment does not fully compensate for the effect of spillover on the observed k_{f}, and several methods have been presented to correct for the residual errors [9, 10]. Nevertheless, the rate constant measured with TRiST appears relatively robust to varying levels of spillover, as evidenced, for example, by essentially constant leg k_{f} measurements at 3 T over regions wherein Q varied from 0.5 to 0.9 [7].
The goal of the present work is to introduce and validate an even more efficient tworepetition time ST (TwiST) method for measuring k_{f}. TwiST is based on prior knowledge of the socalled “intrinsic T_{1}” of PCr (T_{1} ^{intrinsic}) which is independent of the chemical exchange processes implicit in Eqs [1] and [2]. The intrinsic T_{1} was introduced long ago as the hypothetical T_{1} that would occur if there were no chemical exchange, and is given by [1, 11]:
If T_{1} ^{intrinsic} is known and is similar among groups studied, then k_{f} is determinable from just two fullyrelaxed measurements of M_{0} and M_{0}` [11, 12]. These two measurements comprise the TwiST experiment. In this case, k_{f} is given by [13]:
The prerequisite for performing TwiST is prior knowledge of T_{1} ^{intrinsic}. Here, T_{1} ^{intrinsic} is determined from equation [4] and based on experimental data acquired from the hearts of healthy subjects and patients with HF. The effects of variations in the spillover ratio, Q, on measurements of T_{1} ^{intrinsic}, k_{f} ^{TRiST}, and k_{f} ^{TwiST} are evaluated by Bloch equation analysis. Spillover correction for T_{1} ^{intrinsic}, k_{f} ^{TRiST}, and k_{f} ^{TwiST} is derived analogous to the method described in [9]. If needed, this correction uses an unsaturated acquisition that is routinely recorded for determining PCr and ATP concentrations, and for measuring CK flux, (k_{f} x [PCr]), in standard patient protocols [4–6, 14–18].
Methods
Monte Carlo simulations without spillover effects
Analogous to [7], Monte Carlo simulations were performed using Python 2.7 software (www.python.org) to determine the effect of low ^{31}P SNR on k_{f} ^{TwiST} for 0.1 ≤ k_{f} ≤ 0.4 s^{−1} [4, 5], and 5 ≤ T_{1} ^{intrinsic} ≤ 9 s. These ranges were based on measured values for human heart, including an observed T_{1} of PCr, T_{1,PCr}, of 5.8 s [8] which sets a lower limit to T_{1} ^{intrinsic} because chemical exchange with ATP reduces T_{1,PCr} [19]. Gaussian noise with a standard deviation (SD) of σ = 0.16 M_{0} per acquisition was added 2000 times to the two TWiST acquisitions, M`(TR_{long}) and M_{0} ^{control}(TR_{control}). k_{f} ^{TwiST} was calculated from Eq. [5]. For estimating error, the SD of k_{f} ^{TwiST} was calculated from the 2000 runs, and then averaged for the different k_{f} and T_{1} ^{intrinsic}. Fiftynine different combinations of averages and cardiacgated TRs that resulted in a fixed total scan time of ~30 min for the two acquisitions were evaluated. For each TR combination, the number of averages leading to the lowest error was selected. Bias was determined for each sequence combination with a midrange T_{1} ^{intrinsic} = 7 s only.
Bloch equation calculation of spillover effects
In the prior TRiST protocol [7], a surface coil was used for RF transmission, producing an inhomogeneous excitation field with high intensity close to the coil and a gradual decline moving away from it. An adiabatic excitation pulse was used to generate a homogeneous flipangle (FA) over the region of interest, and a modulated DANTE pulse train was used for saturating the exchanging γATP moiety. The DANTE pulses are subject to inhomogeneity in the transmit field, and were set to provide sufficient saturation at the depth of the heart. This causes spillover saturation of PCr closer to the coil, which is quantified by the variable Q in Eq. 3. Its effects on the measured T_{1} ^{intrinsic}, k_{f} ^{TRiST} and k_{f} ^{TwiST} are determined here by numerical analysis of the Bloch–McConnell equations modified for twosite chemical exchange in matrix form [3, 20] implemented on a graphical programming interface (GPI) [21].
The PCr signals, M_{0}(TR = 16 s), without any saturation; M_{0} ^{control}(TR = 16 s) with control saturation at +130 Hz; and M`_{PCr}(TR = 10 s) and M`_{PCr}(TR = 1.7 s) with γATP saturated at −130 Hz, were all determined for the TRiST and TwiST experiments. The saturation of γATP by the amplitudemodulated DANTE scheme described in Eq. 5 of [7] was simulated with parameters used in human studies (m = 5 suppression bands; δ = 9 Hz separation between bands; β = 0.9° FA per band as expected 10 cm from the coil [8]; τ = 0.91 ms between hard subpulses of 100μs duration).
To simulate a range of spillover strengths, β was varied from 0.1° to 6.0°. Other parameters were: T_{1} ^{intrinsic} = 7900 ms; T_{1,ATP} ^{intrinsic} = 2200 ms for the T_{1} ^{intrinsic} of ATP; with corresponding spinspin relaxation times (T_{2}), T_{2,PCr} = 250 ms and T_{2,ATP} = 50 ms chosen somewhat shorter than values measured in calf muscle [22]. To simulate the effect of static magnetic field inhomogeneity, the calculations were performed 9 times with the saturation frequency offset by −20 to +20 Hz in steps of 5 Hz. Results from the 9 runs were weighted with a 20 Hz fullwidthhalfmaximum Gaussian function and averaged. Based on the four calculated M_{0} and M` PCr signals, simulated values of T_{1} ^{intrinsic}, k_{f} ^{TRiST}, and k_{f} ^{TwiST} were determined from equations [4], [2], and [5], respectively. Two different “true” k_{f}s of 0.21 s^{−1} and 0.32 s^{−1} were assumed, reflecting previous rates measured at 1.5 T for HF patients and healthy subjects, respectively [4].
Spillover corrections for intrinsic T_{1}, TRiST and TwiST
Spillover corrected T_{1} ^{intrinsic}, TRiST and TwiST formulae were determined using the approach of Gabr et al. [9]. The Bloch–McConnell equations [20] were numerically solved for the range of parameters listed in Table 1, with the range of saturation power limited to Q ≤ 0.96 to ensure sufficient saturation of γATP (see Discussion). A minimum sumofthesquared fractional differences algorithm was applied to fit the calculated data to linear spillover corrected formulae with an affine dependence on the measured parameters. The corrected intrinsic T_{1}, T_{1} ^{Qintrinsic}, had the form:
The Qcorrected TRiST, k_{f} ^{QTRiST} was:
And the Qcorrected TwiST, k_{f} ^{QTwiST} was formulated as:
where an are fitting coefficients.
These new spillover corrected formulae were applied to the simulated PCr signals generated from the previous section.
Human studies
Human studies were approved by the Institutional Review Board of the Johns Hopkins University School of Medicine, with all participants providing written informed consent. TRiST data, that included TwiST data as a subset, were acquired on a 3 T broadband Achieva scanner (Philips Healthcare, Best, the Netherlands) from twelve healthy subjects (7 men, 5 women, mean age of 36 ± 15 years) with no history of hypertension, diabetes, or heart disease; and in seventeen HF patients (8 men, 9 women, mean age of 48 ± 15 years) with a clinical history of HF (New York Heart Association class I (2), class II (8), and class III (7)), a left ventricular ejection fraction <40 %, and no significant coronary disease.
Both TwiST and reference TRiST data were acquired from a single TRiST protocol described in [7]. Guided by scout MRI, participants were oriented prone with the heart centered above a custom built ^{31}P coil set with dual loop 17/11cm diameter transmit and 8cm receive coils [8] that had a fiducial marker at its center (Fig. 1). Localized 2^{nd}order shimming was performed based on acquired field mapping [23]. Axial balanced steadystate free precession cine images were acquired during free breathing to determine the trigger delay for MRS acquisition at endsystole, which was chosen to minimize motion and maximize the amount of cardiac tissue close to the coil. Cardiactriggered, 1D CSI data were acquired with sixteen phase encodes from a 16cm fieldofview using frequencysweepcycled adiabatic halfpassage [8] excitation. A first data set was acquired without saturation at TR ≥ 16 s and 2 averages to measure M_{0}. This data set was used to center the saturation frequency on the cardiac γATP resonance and to determine the spillover ratio Q; it can also be used to determine metabolite concentrations [14](not reported here). Next, three TRiST data sets were acquired: the first, M_{0} ^{control}, with control saturation applied (TR_{control} ≥ 16 s; 2 averages); the second, M`(TR_{long}), with γATP saturated (TR_{long} ≥ 10 s; 8 averages); and the third, M`(TR_{short}) also with γATP saturated (TR_{short} = 2 heart beats; 18 averages). The third acquisition was not used in the TwiST analysis. The average TR of each triggered acquisition was determined from the scanner’s physiological log.
Spectra from the anterior myocardium were analyzed as described in [7]. A semiautomatic tool (IDL 6.3, Exelis Visual Information Solutions, Boulder, Colorado) was used to measure PCr signals from peak heights after subtracting the baseline (Fig. 2). Peak height instead of area is used because signal ratios are determined from acquisitions with identical shim settings. User interactions were limited to the selection of cardiac slices (including quarter or half slice Fourier shift) and zero order phasing. Identical phasing is used for all four acquisitions. The baseline is determined automatically by averaging values around the minimum points of the peak of interest. T_{1}` and M_{0}` were determined from M`(TR_{short}) and M`(TR_{long}) using the dualTR method [8]. To perform spillover corrections, Q was determined for all cardiac spectra using Eq. [3]. Q values larger than one (due to SNR fluctuations) were set equal to 1.0.
T_{1} ^{intrinsic} and spillover corrected T_{1} ^{Qintrinsic} were calculated for each cardiac slice using Eq. [4] and [6], respectively, and averaged for each participant. The mean and SD of T_{1} ^{intrinsic} and T_{1} ^{Qintrinsic} were determined for the healthy and the HF groups, and the two groups compared using an unpaired Student’s ttest. Uncorrected and Qcorrected intrinsic T_{1} values were compared with a paired Student’s ttest.
k_{f} ^{TRiST} and k_{f} ^{TwiST} were determined for all cardiac slices using Eq. [2] and [5], respectively. For k_{f} ^{TwiST}, T_{1} ^{intrinsic} = 7.9 s was used. Spillover corrected k_{f} ^{QTRiST} and k_{f} ^{QTwiST} were determined using Eq. [7] and [8]. All cardiac values were averaged for each participant. TRiST and TwiST k_{f} values were compared with and without Qcorrections using paired Student’s ttesting, linear regression, and BlandAltman analysis. The mean and SD of Qcorrected k_{f} ^{QTwiST} were determined for the healthy and HF groups, and the two cohorts compared by unpaired Student’s ttesting. A p < 0.05 was considered significant for all statistical testing.
Results
Simulations
Figure 3 shows the results of the Monte Carlo simulations without spillover effects. Figure 3a and b can be compared directly to that of TRiST in Fig. 3 of [7]. The average SD (Fig. 3a) of TwiST is lower and varies less for different TRs than the TRiST result [7]. The expected noiseinduced SD at the TRs used in the present study is 8.3 % compared to 13.4 % for TRiST [7]. Unlike TRiST, the bias error in TwiST (Fig. 3b) depends strongly on TR_{long}. For TR_{long} < 8 s the negative bias error grows rapidly. The currently applied TR_{long} of 10 s is in the flat part of the graph and therefore a reasonable choice. In this regime, the bias error increases slightly when decreasing TR_{control}, and TR_{control} =16 s remains a reasonable choice.
The effects of spillover as determined by the Bloch equation simulations are shown in Fig. 4. The T_{1} ^{intrinsic} (Fig. 4a and b, blue lines) determined in the presence of spillover underestimates the true value in proportion to the amount of spillover, as indexed by declining Q. The underestimation of T_{1} ^{intrinsic} is independent of k_{f} at 0.21 s^{−1} (Fig. 4a) vs. 0.32 s^{−1} (Fig. 4b). Figure 4c and d show the deviation in k_{f} ^{TRiST} (blue lines) from the true values (black, dashed lines) vs. Q for the TRiST method. The error stays within about 10 % for Q > 0.6 but increases with higher spillover (Q < 0.6). For the TwiST method, k_{f} ^{TwiST} varies more strongly with Q (blue lines in Fig. 4e and f). At high levels of spillover (Q ~ 0.4), k_{f} ^{TwiST} is underestimated by ~50 %, and a spillover correction is required over most of the range.
The coefficients of the spillover corrected formulas for T_{1} ^{Qintrinsic} (Eq. [6]), k_{f} ^{QTRiST} (Eq. [7]) and k_{f} ^{QTwiST} (Eq. [8]) are listed in Table 2. The calculated relative errors of T_{1} ^{intrinsic}, k_{f} ^{TRiST} and k_{f} ^{TwiST} over the simulated range of parameters (Table 1) before and after spillover correction are shown in Table 3. Spillover correction removes the bias error and moderately reduces the error range, which includes the effect of a varying T_{1} ^{intrinsic} in accordance with Eq. 5. The relative error of k_{f} ^{QTwiST} for the same parameter range is plotted in Fig. 5 versus the T_{1} ^{intrinsic} used in the simulations. As expected, the bias error for T_{1} ^{intrinsic} outside of 8–8.5 s is proportional to the actual T_{1} ^{intrinsic}. Applied to the simulations shown in Fig. 4, the spillover correction (red lines) improves the determined intrinsic T_{1}, (Fig. 4a and b) and TwiST k_{f} (Fig. 4e and f) for a wide range of Q, and TRiST k_{f} for Q < 0.6 (Fig. 4c and d).
Experiments
The total acquisition time including repositioning and scout MRI at the beginning of each study to optimally position the coil for cardiac TRiST was 84 ± 10 min (mean ± SD) for all participants. This included the 9 min to acquire the unsaturated M_{0} data set with no saturation used for the Q corrections and metabolite quantification. The duration of the three TRiST acquisitions was 40 ± 1 min. Omitting the M`(TR_{short}) acquisition, which is no longer needed for TwiST, reduces the effective acquisition time by 9 ± 1 min, for a 23 % efficiency improvement for TwiST.
Cardiac PCr T_{1} ^{intrinsic} are shown in Fig. 6, both with and without Qcorrection. T_{1} ^{intrinsic} with and without Qcorrection does not differ significantly between patients and healthy controls. However, spillover correction significantly increases the intrinsic T_{1}. With Qcorrection, T_{1} ^{Qintrinsic} = 8.2 ± 1.3 s in healthy subjects vs. 8.5 ± 1.5 s in HF (p = 0.6). The average spillover corrected T_{1} ^{Qintrinsic} in all participants is 8.4 ± 1.4 s. The Q values were the same in both groups at 0.84 ± 0.13 in healthy subjects and 0.85 ± 0.11 in HF (p = 0.8).
TwiST k_{f} measurements are compared to the previously validated TRiST k_{f} in Fig. 7. Linear regression (Fig. 7a and b) reveals a significant correlation between k_{f} ^{TRiST} and k_{f} ^{TwiST} calculated both without (R^{2} = 0.53) and with (R^{2} = 0.73) Qcorrections (p < 0.0001 for both). Corresponding BlandAltman plots in Fig 7c and d show that the Qcorrection reduces scatter.
Figure 8 presents box plots for k_{f} determined with spillover Qcorrected TRiST and TwiST methods for healthy and HF patients measured at 3 T. K_{f} ^{QTwiST} are the same as k_{f} ^{QTRiST} values for both healthy subjects (p = 0.2) and HF patients (p = 0.8). The TwiST CK rate constant in HF patients was 0.20 ± 0.06 s^{−1} (mean ± SD), significantly lower than that in the healthy group at 0.33 ± 0.08 s^{−1} (p = 0.00001). Results of the previously published TRiST analysis without Qcorrection are compared to the ones with Qcorrection in an additional figure [see Additional file 1].
Discussion
We present a new, faster method called TwiST for measuring the forward CK rateconstant in human heart. The method is validated by Bloch equation analysis and by comparison with the previously validated TRiST method in ^{31}P MRS studies of healthy and failing human hearts performed at 3 T. The TwiST method is faster than the TRiST method, requiring one less acquisition and saving 9 min from the present protocol, or a 23 % efficiency improvement vs. the three TRiST acquisitions. The number of acquisitions required for measuring CK reaction rates has thus now been reduced from four [3] or three [7] to two, resulting in proportionate improvements in efficiency for the ST portion of the protocol. Although the timesaving is not large relative to the entire protocol, it does shorten a long exam, making it more tolerable for patients with cardiovascular disease without introducing significant error.
This study also presented the first 3 T measurements of cardiac CK kinetics in patients with heart failure. The results show significant reductions in cardiac CK reactionrates that are in quantitative agreement (both mean values and errors) with prior measurements obtained at 1.5 T, where k_{f} was 0.21 ± 0.07 s^{−1} in HF patients compared to 0.32 ± 0.07 s^{−1} in healthy subjects [3]. The new measurements obtained by both TRiST and TwiST methods and at a different field strength of 3 T, provide further independent evidence that CK energy supply is reduced in the failing human heart. A paired comparison of data acquired by the different methods at 1.5 T and 3 T from the same subjects was not performed here, as the original 1.5 T scanner is no longer available. Such studies could help elucidate whether the residual scatter has biologic or instrumental origins.
The Monte Carlo simulations show that the expected scatter for a given SNR decreases to 8.3 % in TwiST measurements compared to 13.4 % with TRiST. This is because in TwiST a T_{1} ^{intrinsic}, or a range of T_{1} ^{intrinsic} for the Qcorrected TwiST, is assumed instead of measuring T_{1}`. In TRiST, T_{1}` is determined from two measurements: M`(TR_{long}) and M`(TR_{short}). Compared to TRiST, TwiST does not measure M`(TR_{short}). M`(TR_{short}) is the acquisition with the lowest PCr signal in TRiST because of the short TR and its chemical exchange with the saturated γATP. The combination of low signal for M`(TR_{short}) and the inherently low SNR in clinical cardiac ^{31}P MRS settings, makes the determination of T_{1}` critical to the accuracy of TRiST k_{f} determinations.
Bloch equation simulations showed that T_{1} ^{intrinsic} measured with the TRiST sequence underestimates the true value to an extent that depends strongly on the spillover ratio Q. This can confound its determination. For example, assuming an input T_{1} ^{intrinsic} of 7.9 s, the simulations predict apparent T_{1} ^{intrinsic} values of 4 to 7 s as Q varies from 0.5 to 1 (Fig. 4a and b). In the present study, the measured T_{1} ^{intrinsic} varied from 3.4 to 10.7 s. We therefore assumed a range in the actual intrinsic T_{1} from 6.5 to 9.5 s for computing the Qcorrected T_{1} ^{intrinsic} and TRiST/TwiST k_{f} formulae. For the Monte Carlo simulations without spillover corrections, T_{1} ^{intrinsic} = 7 s was chosen to be consistent with simulations performed in [7], and to enable a comparison of the findings. In the present study, there were no significant differences in T_{1} ^{intrinsic} between healthy subjects and HF patients, whether calculated with or without Qcorrections (Fig. 6). This suggests that the same T_{1} ^{intrinsic} can be assumed for TwiST studies of k_{f} in HF patients and healthy subjects. The overall average value pooling the HF patients and healthy subjects was 8.4 ± 1.4 s. That T_{1} ^{intrinsic} is the same, is also consistent with the notion that T_{1} ^{intrinsic} for PCr is a measure of T_{1} independent of any exchange effects or differences therein in healthy and HF populations.
The proposed formula for spillover corrected TwiST, Eq. [8], does not explicitly include T_{1} ^{intrinsic}. Nevertheless, the coefficients in Table 2 depend on the range of T_{1} ^{intrinsic} assumed for their determination. For Q = 1, Eq. 8 can be transformed into an equation similar to Eq. 5,
with an equivalent T_{1} ^{intrinsic} of 8.13 s very close to the value measured in this study. Hence, T_{1} ^{intrinsic} is absorbed into coefficients l and n of Eq. 8. The effect of varying T_{1} ^{intrinsic} on k_{f} ^{QTwiST} can be determined from Fig. 5. Apart from this, the coefficients in Table 2 for the spillover corrected formulae for T_{1} ^{Qintrinsic}, k_{f} ^{QTRiST} and k_{f} ^{QTwiST} are only applicable for data acquired with the sequence parameters used in the present study to measure cardiac CK exchange rates at 3 T with the expected parameter range as given in Table 1. Deviations would in general require determination of a new set of coefficients based on adapted simulations.
The Bloch equation simulation results in Fig. 4 suggest that for Q > 0.95 spillover effects lead to a dip of T_{1} ^{intrinsic} and both the TRiST and TwiST k_{f} measurements. Q values larger than 0.95 only occur for very low saturation power and the dip in T_{1} ^{intrinsic} and TRiST/TwiST k_{f} for Q values larger than 0.95 is caused by incomplete γATP saturation. In practice, Q values larger than 0.95 can occur because of low saturation power (leading to both reduced spillover saturation of PCr and incomplete γATP resonance saturation) or because of noise in the acquired spectra. The former can be assessed in the spectra by noting any residual γATP resonance. We attributed Q > 1 to noise and rounded Q to 1 in the Qcorrected formulae. Based on Eq. [3], the error in Q is the root of the sum of the squared errors in M _{ 0 } and M _{ 0 } ^{control}. In the determination of the Qcorrected formulae the range of saturation power was limited to keep Q below 0.96 to ensure that the dip was not included in the fitting coefficients.
Recently, Bashir et al. presented a timedependent ST approach to measure CK k_{f} values in the human heart at 3 Tesla [24]. Their reported k_{f} = 0.32 ± 0.05 s^{−1} agrees well with k_{f} values of the present work, whereas their PCr T_{1} ^{intrinsic} = 7.36 ± 1.79 s is somewhat smaller than the Qcorrected T_{1} ^{Qintrinsic} = 8.4 ± 1.4 s presented here. Xiong et al. published a very fast ST method applied to in vivo swine hearts at ultrahigh field strength (4.7 T  9.4 T) [25, 26]. Their fastest 1D CSI localized T_{1} ^{nom} method acquires the ST protocols in less than 14 min. This compares to ~40 min for our Qcorrected TwiST protocol that includes a third acquisition for measuring metabolite concentrations and Q. The T_{1} ^{nom} method has yet to be translated to human heart studies or combined with concentration measurements. Also it is not compensated for spillover which may be more problematic at lower fields where chemical shift dispersions are proportionately smaller.
Limitations
Test retest reproducibility of these methods remains to be studied in the future. The transmit/receive coil and pulse sequences used in this study have been specially designed and built by our research team for cardiac ^{31}P MRS.
Conclusions
In conclusion, the spillover Qcorrected TwiST method can be used to measure the CK pseudofirstorder rateconstant k_{f} in the human heart at 3 Tesla with one fewer acquisition compared to the previously presented TRiST method. Instead, a range of PCr T_{1} ^{intrinsic} is assumed. It is shown that T_{1} ^{intrinsic} is the same in healthy subjects and in heart failure patients. The values of k_{f} measured with Qcorrected TwiST closely agree with earlier measurements at 1.5 Tesla, and demonstrate a significant reduction in failing, compared to healthy hearts.
Abbreviations
 1D CSI:

Onedimensional chemical shift imaging
 ^{31}P:

Phosphorus
 ATP:

Adenosine triphosphate
 CK:

Creatine kinase
 DANTE:

Delays alternating with nutations for tailored excitation
 HF:

Heart failure
 PCr:

Creatine phosphate
 Q:

Spill over ratio, see equation 3
 SD:

Standard deviation
 ST:

Saturation transfer
 TRiST:

Triple Repetition time Saturation Transfer
 TwiST:

Two Repetition time Saturation Transfer
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Acknowledgements
NIH: R01 HL56882, R01 HL61912, R01 HL63030; AHA grant #13GRNT17050100
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Competing interests
MS was an employee of Philips Healthcare until May 2014, the manufacturer of equipment used in this study.
Authors’ contributions
MS made substantial contributions to conception and design, the acquisition, analysis and interpretation of data; performed part of the simulations, and drafted and revised the manuscript. RG made substantial contributions to interpretation of data; performed part of the simulations, and critically revised the manuscript for important intellectual content. AE made substantial contributions to conception and design, the acquisition and interpretation of data, and critically revised the manuscript for important intellectual content. AS made substantial contributions to the acquisition of data, and critically revised the manuscript for important intellectual content. PB made substantial contributions to conception and design, the interpretation of data, and critically revised the manuscript for important intellectual content. RW made substantial contributions to conception and design, the acquisition and interpretation of data, and critically revised the manuscript for important intellectual content. All authors read and approved the final manuscript.
Additional file
Additional file 1:
Boxplot of cardiac CK pseudofirstorder rate constant k _{ f } determined with TRiST, spillover Qcorrected TRiST, and spillover Qcorrected TwiST for healthy and heart failure patients. k_{f} measured with TRiST, with Qcorrected TRiST, and with Qcorrected TwiST are the same in both healthy and HF patients. Cardiac CK k_{f} in HF is significantly reduced compared to that in normal subjects. (PDF 60 kb)
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Keywords
 Saturation transfer
 Human heart
 Metabolism
 Reaction rate
 Highenergy phosphate
 Heart failure
 3 Tesla
 Creatinekinase
 TwiST