Background
Phosphorus (
31P) 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 high-energy phosphates between the mitochondria, where ATP is created, and the myofibrils, where it is used. The pseudo-first-order rate constant (k
f) for CK indexes the fractional rate of ATP generation from phosphocreatine (PCr).
31P 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 pseudo-first-order rate constant can be determined with:
$$ {k}_f=\frac{1}{T_1\hbox{'}}\left(1-\frac{M_0\hbox{'}}{M_0}\right), $$
(1)
where T
1` and M
0` are the longitudinal relaxation time and the equilibrium magnetization of PCr measured while the exchanging γ-ATP resonance at −2.5 ppm is selectively saturated (signified by primes); and M
0 is the equilibrium magnetization of PCr measured without γ-ATP 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 signal-to-noise ratio (SNR). Using TRiST, T
1` and M
0` are measured by the dual-repetition time (TR) method [
8] with a short TR (M`(TR
short); TR
short = 2 heart beats, cardiac-gated) and a long TR (M`(TR
long); TR
long ~10 s, cardiac-gated) both while the exchanging γ-ATP resonance is saturated. A third cardiac-gated acquisition at a TR of ~ 16 s is performed to measure M
0. To compensate for the effects of spill-over irradiation on PCr during γ-ATP 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:
$$ {k}_f^{TRiST}=\frac{1}{T_1\hbox{'}}\left(1-\frac{M_0\hbox{'}}{M_0^{control}}\right). $$
(2)
Spill-over irradiation is caused by imperfect frequency-selective saturation of γ-ATP that can partially saturate the nearby PCr resonance. A measure of the spill-over effect is provided by the ratio
$$ Q=\frac{M_0^{control}}{M_0}, $$
(3)
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 spill-over 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 spill-over, 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 two-repetition time ST (TwiST) method for measuring k
f. TwiST is based on prior knowledge of the so-called “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]:
$$ {T}_1^{intrinsic}={T}_1\hbox{'}\left(\frac{M_0^{control}}{M_0\hbox{'}}\right). $$
(4)
If T
1
intrinsic is known and is similar among groups studied, then k
f is determinable from just two fully-relaxed 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]:
$$ {k}_f^{TwiST}=\frac{1}{T_1^{intrinsic}}\left(\frac{M_0^{control}}{M_0\hbox{'}}-1\right), $$
(5)
The pre-requisite 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 spill-over ratio, Q, on measurements of T
1
intrinsic, k
f
TRiST, and k
f
TwiST are evaluated by Bloch equation analysis. Spill-over 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].
Discussion
We present a new, faster method called TwiST for measuring the forward CK rate-constant in human heart. The method is validated by Bloch equation analysis and by comparison with the previously validated TRiST method in
31P 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 reaction-rates 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 T1
intrinsic, or a range of T1
intrinsic for the Q-corrected TwiST, is assumed instead of measuring T1`. In TRiST, T1` is determined from two measurements: M`(TRlong) and M`(TRshort). Compared to TRiST, TwiST does not measure M`(TRshort). M`(TRshort) is the acquisition with the lowest PCr signal in TRiST because of the short TR and its chemical exchange with the saturated γ-ATP. The combination of low signal for M`(TRshort) and the inherently low SNR in clinical cardiac 31P MRS settings, makes the determination of T1` critical to the accuracy of TRiST kf 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 spill-over 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 Q-corrected T
1
intrinsic and TRiST/TwiST k
f formulae. For the Monte Carlo simulations without spill-over 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 Q-corrections (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 spill-over 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,
$$ {k}_f^{Q- TwiST}\left(Q=1\right)=\frac{1}{8.13}\left(\frac{M_0^{control}}{M\hbox{'}\left(T{R}_{long}\right)}-1.03\right), $$
(9)
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
Q-TwiST can be determined from Fig.
5. Apart from this, the coefficients in Table
2 for the spill-over corrected formulae for T
1
Q-intrinsic, k
f
Q-TRiST and k
f
Q-TwiST 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 spill-over 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 γ-ATP saturation. In practice, Q values larger than 0.95 can occur because of low saturation power (leading to both reduced spill-over saturation of PCr and incomplete γ-ATP resonance saturation) or because of noise in the acquired spectra. The former can be assessed in the spectra by noting any residual γ-ATP resonance. We attributed Q > 1 to noise and rounded Q to 1 in the Q-corrected 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 Q-corrected 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 time-dependent 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 Q-corrected T
1
Q-intrinsic = 8.4 ± 1.4 s presented here. Xiong et al. published a very fast ST method applied to
in vivo swine hearts at ultra-high 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 Q-corrected 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 re-test 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 31P MRS.
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.