Amplification of the Effects of Magnetization Exchange by ³¹P Band Inversion for Measuring ATP Synthesis Rates in Human Skeletal Muscle

Abstract

Purpose

The goal was to amplify the effects of magnetization exchange between γ-ATP and inorganic phosphate (Pi) for evaluation of ATP synthesis rates in human skeletal muscle.

Methods

The strategy works by simultaneously inverting the ³¹P resonances of PCr and ATP using a wide bandwidth, adiabatic inversion RF pulse followed by observing dynamic changes in intensity of the non-inverted Pi signal versus the delay time between the inversion and observation pulses. This band inversion technique significantly delays recovery of γ-ATP magnetization and consequently the exchange reaction, Pi ↔ γ-ATP, is readily detected and easily analyzed.

Results

The ATP synthesis rate measured from high-quality spectral data using this method was 0.073 ± 0.011 s⁻¹ in resting human skeletal muscle (N = 10). The T₁ of Pi was 6.93 ± 1.90 s, consistent with the intrinsic T₁ of Pi at this field. The apparent T₁ of γ-ATP was 4.07 ± 0.32 s, about 2-fold longer than its intrinsic T₁ due to storage of magnetization in PCr.

Conclusion

Band inversion provides an effective method to amplify the effects of magnetization transfer between γ-ATP and Pi. The resulting data can be easily analyzed to obtain the ATP synthesis rate using a 2-site exchange model.

INTRODUCTION

There is long-standing interest in measuring ATP synthesis rates in vivo by use of ³¹P magnetization transfer methods (1–6). Recent studies using ³¹P saturation transfer (ST), one subset of magnetization transfer methods, suggest that the inorganic phosphate (Pi) ↔ ATP exchange may be sensitive to age, insulin resistance, type 2 diabetes and other metabolic disorders in skeletal muscle (7–13). ST operates by irradiation of γ-ATP with a frequency-selective RF pulse or pulse train resulting in a reduced Pi signal through chemical exchange mediated by ATPase (2). Since the Pi ↔ ATP exchange rate is relatively slow in vivo, prolonged irradiation of γ-ATP is essential to detect significant changes in Pi using ST. Some have expressed concerns that the unidirectional Pi → ATP rate measured by ST is too large when compared to rates estimated by other complimentary methods (see reviews (1,2,14) and the references therein). This disparity has been attributed to contributions from Pi ↔ ATP exchange reactions other than oxidative phosphorylation (1,14) and added effects due to small metabolite pools hidden under the ATP signals (15) that may be activated by prolonged ST pulses. To clarify this issue, an alternative method is needed that is sensitive to the slow exchange rate but insensitive to potential contaminations from exchanges that may be occurring among smaller NMR invisible pools.

Recently, we reported an approach termed exchange kinetics by inversion transfer (EKIT) that used frequency-selective inversion pulses rather than prolonged saturation pulses (16). In resting human skeletal muscle, we observed magnetization transfer between Pi and γ-ATP as expected, but surprisingly we also observed exchanges between Pi and phosphocreatine (PCr). This observation was not anticipated since the phosphate group of PCr does not exchange with Pi directly. The phenomenon was attributed to a relayed magnetization transfer effect due to sequential exchanges mediated by creatine kinase (CK) and ATPase. This suggests that PCr, a metabolite present in skeletal muscle at much higher concentrations and with a longer T₁ than γ-ATP, can temporarily store the inverted magnetization and transfer it to γ-ATP. Furthermore, quite significant exchanges attributed to cross relaxation were detected between γ-ATP and the other phosphates of ATP (16). Together, these observations suggest that the small but physiologically important magnetization transfer effect between γ-ATP and Pi could potentially be amplified by co-inversion of PCr and all ATP resonances.

To test this concept, we used a trapezoid-shaped adiabatic pulse for inversion of all ATP resonances plus PCr without exciting Pi or the phosphodiesters (PDE). This technique termed “exchange kinetics by band inversion transfer” or EBIT, was applied to evaluate ATP synthesis rates in resting human skeletal muscle at 7T. The kinetic rate constant k_Pi→γATP was extracted from the ³¹P MRS data using a 2-site exchange model involving Pi and γ-ATP (Figure 1). The magnetization transfer effect between Pi and γ-ATP is amplified multiple times upon co-inversion of PCr and all phosphates of ATP, as compared to selective inversion of γ-ATP.

FIG. 1.

Possible ³¹P magnetization transfer pathways in skeletal muscle. (a) A simplified 2-site exchange model for evaluation of the ATP synthesis reaction Pi → γ-ATP using EBIT sequence with co-inversion of PCr and ATP spins. Through chemical exchange or NOE, all inverted spins contribute to the apparent exchange between Pi and γ-ATP. (b) A 7T ³¹P MR spectrum acquired from human calf muscle using the EBIT sequence for band inversion of PCr and ATP signals showing the pathways of magnetization transfer between inverted and non-inverted ³¹P signals. Abbreviation: Pi, Inorganic phosphate; PCr, phosphocreatine; ATP, adenosine triphosphate; Ad, adenosine. Chemical exchange, marked as solid arrows; dipolar cross-relaxation (NOE), marked as dashed arrows.

METHODS

Theory

For any given spin system, in the absence of an applied B₁ field, the time-dependent Z-magnetization M_z (for clarity, the subscript “z” is omitted hereafter) is described by:

$$\frac{d(M(t)-M^o)}{dt}=A(M(t)-M^o)$$ [1]

in which M^o denotes the Z-magnetization at Boltzmann thermal equilibrium at t → ∞; A is a n-by-n matrix describing the NMR properties of spin relaxation and exchange of the n-spin system. Assume the spin system undergoes a perturbation at t = 0 with an initial Z-magnetization M(0) then the magnetization of the system evolves with t by

$$M(t)=M^o-e^{At}(M^o-M(0))$$ [2]

For a two spin system comprised of Pi and γ-ATP in chemical exchange:

$$\underset{a}{Pi}\hspace{1em}\stackrel{k}{\leftrightarrow }\hspace{1em}\underset{b}{\gamma ATP}$$ [3]

the 2 × 2 spin matrix A is given by:

$$A=\left[\begin{array}{cc}\hfill -1/T_{1,a}-k_{ab}\hfill & \hfill k_{ba}\hfill \\ \hfill k_{ab}\hfill & \hfill -1/T_{1,b}-k_{ba}\hfill \end{array}\right]$$ [4]

For a five spin system comprised of Pi, PCr, α-, β- and γ-ATP with multiple magnetization exchange pathways (including both chemical exchanges and cross-relaxation (NOE)), one must also include equation [5],

$$\underset{c}{PCr}\hspace{1em}\stackrel{k}{\leftrightarrow }\hspace{1em}\underset{b}{\gamma ATP}\hspace{1em}\stackrel{\sigma }{\leftrightarrow }\hspace{1em}\underset{d}{\beta ATP}\hspace{1em}\stackrel{\sigma }{\leftrightarrow }\hspace{1em}\underset{e}{\alpha ATP}$$ [5]

so the 5 × 5 spin matrix A can be described by:

$$A=\left[\begin{array}{ccccc}\hfill -1/T_{1,a}-k_{ab}\hfill & \hfill k_{ba}\hfill & \hfill 0\hfill & \hfill 0\hfill & \hfill 0\hfill \\ \hfill k_{ab}\hfill & \hfill -1/T_{1,b}-k_{ba}-k_{bc}\hfill & \hfill k_{cb}\hfill & \hfill {\sigma }_{db}\hfill & \hfill 0\hfill \\ \hfill 0\hfill & \hfill k_{bc}\hfill & \hfill -1/T_{1,c}-k_{cb}\hfill & \hfill 0\hfill & \hfill 0\hfill \\ \hfill 0\hfill & \hfill {\sigma }_{bd}\hfill & \hfill 0\hfill & \hfill -1/T_{1,d}\hfill & \hfill {\sigma }_{ed}\hfill \\ \hfill 0\hfill & \hfill 0\hfill & \hfill 0\hfill & \hfill {\sigma }_{de}\hfill & \hfill -1/T_{1,e}\hfill \end{array}\right]$$ [6]

in which the forward and reverse pseudo first-order rate constants k (chemical exchange) and σ (cross-relaxation) are related by

$$k_{ji}=k_{ij}\frac{M_i^o}{M_j^o}\hspace{1em}\hspace{1em}(i,j=a,b\text{ or }b,c)$$ [7]

and

$${\sigma }_{ji}={\sigma }_{ij}\frac{M_i^o}{M_j^o}\hspace{1em}\hspace{1em}(i,j=b,d\text{ or }d,e)$$ [8]

If one considers this spin system after applying an inversion-recovery pulse sequence (180° – t_D – 90° – τ), in which t_D is the delay time after the inversion pulse and τ is the duration of magnetization recovery following the 90° readout pulse, then the Z-magnetization for each spin immediately following the inversion pulse is given by:

$$M_i(0)=f_i{M}_i^o\hspace{1em}\hspace{1em}(i=a-e)$$ [9]

where f_i is the coefficient of the fractional inversion (−1 ≤ f ≤ 1; f = −1 for full inversion, and f = 1 if a given spin is not affected by the inversion).

Following inversion, the Z-magnetization evolves with the delay time (t_D), and equation [2] becomes equation [10]:

$$M(t_D)=M^o-e^{A{t}_D}(M^o-f{M}^o)$$ [10]

M(t_D) is detected by applying a non-selective readout pulse at the end of the t_D period.

Thus, for a non-inverted spin, any deviation of M(t_D) from M^o reflects the exchange effects that is developed in t_D period due to inversion of other spins. In this study, the normalized signal of Pi (M(t_D)/M^o or m_z(t_D)) is plotted against the delay time t_D to detect exchanges between Pi and γ-ATP after band inversion of PCr, α- β- and γ-ATP. To calculate the exchange rate constant, k_Pi→γ-ATP, from the m_z(t_D) versus t_D data, a 2-site exchange model for Pi and γ-ATP was used (equations [3,4]). This was compared to the results from fitting the m_z(t_D) versus t_D data acquired for Pi, PCr, α- β- and γ-ATP using a 5-site exchange model (Equations [5,6]).

Human Subjects

The protocol was approved by the Institutional Review Board of the University of Texas Southwestern Medical Center. Prior to the MRS study, informed written consent was obtained from all participants. Ten subjects (6 male and 4 female), aged 28 ± 4 yr and BMI 24 ± 2, participated the study. All subjects were in good general health with no history of peripheral vascular, systemic or myopathic diseases. To avoid possible exercise-associated physiological variations among subjects, all subjects were asked to refrain from any physical activity of moderate or high intensity for 24 hours prior to the study, and subjects sat at rest for 20 minutes prior to the scan. Heart rate and blood oxygen saturation levels were monitored during the scan. The study was well-tolerated by all subjects.

MRS Protocol

All subjects were positioned feet-first and supine in the MRI scanner (7T Achieva, Philips Healthcare, Cleveland, OH), with the right calf muscle positioned parallel to the magnetic field and directly on the detection coil (Philips Healthcare, Cleveland, OH). The coil was a partial volume, double-tuned ¹H/³¹P quadrature TR coil consisting of two tilted, partially overlapping 10 cm loops for ³¹P detection. The center of the coil was positioned approximately 1/3 of the distance along the leg from the knee to the heel. Axial, coronal, and sagittal T2-weighted turbo spin echo images were acquired for voxel planning. Typical imaging parameters included field-of-view 180 × 180 mm (FOV), repetition time (t_R) 2 s, echo time (TE) 75 ms, turbo factor 16, in-plane spatial resolution 0.6 × 0.7 mm², slice thickness 4 mm, gap 2 mm, bandwidth 517 Hz, number of acquisitions (NA) one, and acquisition time 1.2 min. 2^nd order ¹H-based automatic volume shimming was applied prior to ³¹P spectral acquisitions.

The EBIT sequence (180° – t_D – 90° – τ) consisted of an adiabatic inversion pulse (Figure 2a) followed by a variable post-inversion delay time t_D, a hard 90° readout pulse, and a recovery period τ, beginning with FID sampling. FID-based ³¹P spectra were acquired from calf muscle for each subject with a constant t_R of 30 sec, 4 averages, 4 K sampling points zero-filled to 8 K prior to FT, and at 12 delay times (t_D = 30, 626, 1253, 1923, 2641, 3414, 4252, 5167, 6174, 7294, 8556 and 10000 msec). The total data acquisition time for the t_D series was 24 min. A fully-relaxed ³¹P NMR spectrum was also acquired using a single pulse without inversion for $M_z^o$ measurements, from which the concentration of each ³¹P metabolites was evaluated using the area of γ-ATP signal as an internal reference (5.5 mmol/kg wet weight). Intra-session data reproducibility was tested on two subjects by repeating the same EBIT sequence after re-entry into the scanner during the same scan session.

FIG. 2.

Illustration of the EBIT inversion pulse and its inversion profile. Panel (a) shows a trapezoid-shaped adiabatic pulse with inversion bandwidth Δf and center frequency f_o. Panel (b) illustrates the measured excitation profile with inversion bandwidth Δf = 2500 Hz, data acquired with frequency step 100 Hz from a phosphate phantom sample in aqueous solution. In panel (c) a ³¹P MR spectrum acquired at 7T from human calf muscle illustrates the spectral coverage of the inversion profile. Note that PCr and ATP signals are within the inversion window while Pi and PDE signals are excluded. Abbreviation: freq, frequency; amp, amplitude; Pi, Inorganic phosphate; PCr, phosphocreatine; ATP, adenosine triphosphate; PDE, phosphodiester.

The band-inversion pulse was a short trapezoid-shaped adiabatic pulse (pulse width pw = 42 msec, including 7 msec of pre- and post-ramp time), maximal B₁ 11.5 µT, inversion bandwidth of 2500 Hz, and centered at 150 Hz upfield from α-ATP at −7.5 ppm. The excitation profile of the band-inversion pulse was pre-determined using a methyl phosphate phantom in aqueous solution (volume 3 liters, cylinder-shaped, 2 g/L), by stepwise shifting the center (f_o) of the inversion band (bandwidth Δf = 2500 Hz) across a broad frequency region (± 3600 Hz) in 100 Hz step. A short crusher pulse (3 ms) was applied at the end of the t_D period prior to the readout pulse to eliminate residual transverse magnetization. The readout pulse was 0.22 ms rectangular-shaped pulse with a nominal B₁ of 59 µT, with the transmitter frequency centered at 700 Hz upfield from the resonance of PCr.

To investigate the effect of inversion bandwidth on the magnetization exchange effect between Pi and γ-ATP, a separate experiment was also conducted on two subjects by applying the same shaped inversion pulse but with varied pw and B₁ level so that inversion band width Δf was changed from 2500 Hz (inverting PCr and ATP) to 700 Hz (to invert both PCr and γ-ATP) to to 400 Hz (to invert just γ-ATP). For inversion band widths of Δf 400 and 700 Hz, the B₁ level was 1.85 and 3.24 µT, and the corresponding pw value was 270 and 153 ms, respectively. The center frequency was adjusted accordingly. Again, a total of 12 spectra were collected from each subject with the inversion delay time varied within a 10 sec range. The chemical shifts of all ³¹P metabolites were referenced to PCr at 0 ppm. Gaussian apodization (6 Hz) was applied to each FID prior to Fourier transformation using the scanner software (SpectroView, Philips Healthcare) and the kinetic data were analyzed using Matlab (Mathworks) routines.

³¹P Spectral Analysis

Signal post-processing, curve fitting of m(t_D) ~ t_D data, and statistics were done in Matlab (The Mathworks, Natick, MA). The ³¹P NMR data acquired at each of the 12 delay times were fitted to two different models: 1) a two-site exchange model that included only Pi and γ-ATP with k_Pi→ATP and T₁ relaxation time of Pi and γ-ATP as unknowns; 2) a five-site model including all five spins (Pi, PCr, ATP α-, β- and γ spins) with the following unknowns k_Pi→ATP, k_PCr→ATP, σ_α↔βATP, σ_β↔γATP and T₁ relaxation times for Pi, PCr, ATP α-, β- and γ spins. The fitting was based on Equation [10] using an exponential matrix algorithm and a nonlinear least-squares algorithm (Matlab function lsqcurvefit) to minimize the sum of squared difference between experimental and calculated Z-magnetizations, m(t_D).

The delay time $t_D^{\mathit{\text{min}}}$ at which Pi signal reaches a minimum due to exchange from γ-ATP, together with the corresponding normalized magnetization $m(t_D^{\mathit{\text{min}}})$ for Pi and γ-ATP, were evaluated from the 2×2 matrix form of Equation [10] (Matlab function fminsearch). The fractional inversion coefficient f for the band inversion adiabatic pulse was determined from the m(t_D) ~ t_D curve extrapolated to t_D = 0 (see Equation [10], Theory Section): −0.86 ± 0.04 (PCr), −0.65 ± 0.05 (γ-ATP), −0.60 ± 0.05 (α-ATP) and −0.48 ± 0.03 (β-ATP).

Statistical Analysis

All data are reported as mean ± standard deviation, calculated using Excel. The coefficient of variations (CV) in T_1,Pi and k_Pi→γ-ATP were evaluated by σ(T₁)/T₁ and σ(k)/k, respectively.

RESULTS

Inversion profile and spectrum by EBIT sequence

The trapezoid-shaped inversion pulse using in the EBIT sequence (illustrated in Figure 2) provides a uniform inversion pulse that spans 2500 Hz. This bandwidth proved suitable for inverting all ³¹P resonances from PCr to β-ATP (~ 2000 Hz at 7T) leaving the downfield Pi and phosphodiester (PDE) signals out of the inversion window (Figure 2c and Figure 3). There was no measurable difference in the intensity of Pi signal at 4.9 ppm before and immediately after the band inversion, unless the inversion delay time t_D was increased (Figure 3). A typical ³¹P MR spectral series acquired using the EBIT sequence shown in Figure 4 was collected from resting calf muscle of a healthy male (27-year old, BMI 25 kg/m²). The Pi signal at 4.9 ppm was sensitive to the delay time t_D exactly as anticipated from a classical inversion transfer experiment (Figure 4). A minimum in the intensity of Pi signal occurred with t_D ~ 3.4 – 4.2 s, with a m_z(t_D) value of ~82%, relative to M^o (Figure 4). In contrast, the nearby PDE signal at 2.9 ppm, which is also outside of the inversion window, was constant and independent of t_D (Figures 4 and 5). These spectral features were observed for all subjects in the group (N = 10, Figure 5a) with high intra-session reproducibility (Figure 5b). Unlike the ³¹P signals of Pi and PDE, each of the inverted signals (PCr, α-, β- and γ-ATP) recovered exponentially with t_D (Figure 6). Among these ³¹P resonances, the α- and β-ATP signals recovered the fastest (m_z(t_D): ≥ 97% at t_D = 10 s), while the recovery of γ-ATP and PCr signal was considerably slower (m_z(t_D): < 84% at t_D = 10 s). Importantly, the recovery curves for γ-ATP and PCr were similar, in sharp contrast to their large differences in intrinsic T₁ relaxation times (1.7 s for γ-ATP vs. 5.3 s for PCr, ref [16]).

FIG. 3.

Representative ³¹P MR spectra acquired from resting human calf muscle at 7 T using a single pulse without inversion (blue trace) and using EBIT sequence with delay time t_D at 30 ms (red trace) and at 4249 ms (black trace). All spectra were collected with TR = 30 sec and NA = 4 with identical y-scale.

FIG. 4.

A typical ³¹P MR spectral series acquired with EBIT using various delay times t_D. The insets show the individual stacked plots of Pi, PDE, PCr, α-, β- and γ-ATP. Note the characteristic pattern of Pi signal change versus t_D upon inversion recovery of PCr, α-, β- and γ-ATP. The evolution of the Pi signal is in sharp contrast to the PDE signal which remains constant for all values of t_D. The data were collected from resting calf muscle of a healthy male (27-year old, BMI 25 kg/m²). All inset signals were enlarged 4 times vertically except for PCr which was reduced twofold for easy comparison. Inversion delay times t_D = 30, 626, 1253, 1923, 2641, 3414, 4252, 5167, 6174, 7294, 8556 and 10000 msec. Abbreviation: Pi, Inorganic phosphate; PCr, phosphocreatine; ATP, adenosine triphosphate; PDE, phosphodiester.

FIG. 5.

Variability in the intensity of Pi between subjects. Panel (a) shows the variation of EBIT data among all 10 subjects. After scaling to the baseline Pi signal, there was some variability in PDE among subjects. At a t_D of ~ 3.4 seconds, the Pi signal was substantially reduced in all subjects with no detectable effect on PDE. Panel (b) shows one example of intra-session reproducibility of EBIT data acquisition during a repeated scans (red and blue traces) for the same subject. Inversion delay time t_D = 30, 626, 1253, 1923, 2641, 3414, 4252, 5167, 6174, 7294, 8556 and 10000 msec. Abbreviation: Pi, Inorganic phosphate; PCr, phosphocreatine; ATP, adenosine triphosphate; PDE, phosphodiester.

FIG. 6.

Normalized Z-magnetizations versus delay time t_D. Data are shown for Pi, PCr and ATP metabolites in resting human muscle (averaged for 10 subjects). The solid curves in the plots represent the data fitting using the 2-site model for the exchange reaction Pi ↔ γ-ATP; the dotted curves represent the fitting results using 5-site exchange model including Pi, PCr, α-, β- and γ-ATP. The recovery of γ-ATP is similar to PCr rather than to the recovery curves for α- and β-ATP. The dashed lines mark the maximum MT effect, occurring at delay time t_D^min = 4.07 s. Abbreviation: Pi, Inorganic phosphate; PCr, phosphocreatine; ATP, adenosine triphosphate.

EBIT data fitting

To evaluate the rate constant, k_Pi→γ-ATP, each dynamic data set was fitted using a 2-site exchange model (Equations [3,4]). The fitted curves agree well with the experimental data for both Pi and γ-ATP (solid curves, Figure 6). In comparison, each EBIT data set was also fit using the 5-site exchange model including Pi, PCr, α-, β- and γ-ATP (dotted curves, Figure 6). The derived kinetic and NMR parameters for the two models are summarized in Table 1. For the group of subjects studied (N = 10 subjects), on average there is virtually no difference in k_Pi→γ-ATP between these two models (k_Pi→γ-ATP = 0.073 ± 0.011 s⁻¹ for 2-site model vs 0.071 ± 0.010 s⁻¹ for 5-site model). The fitted T₁ relaxation times obtained for the two models were similar for Pi (6.93 ± 1.90 by 2-site model vs 6.55 ± 1.46 by 5-site model) but was significantly different for γ-ATP (4.07 ± 0.12 s by 2-site model vs 1.97 ± 0.14 s by 5-site model). The intra- and inter-subject variability in k_Pi→γ-ATP and T_1,Pi as measured by coefficient of variation (CV) were comparable between these two models (2-site vs 5-site model: 0.12 vs 0.11 for intraCV(k); 0.15 vs 0.14 for interCV(k); 0.14 vs 0.11 for intraCV(T₁), and 0.27 vs 0.22 for interCV(T₁)). The maximal magnetization exchange effect by EBIT was 18.3 ± 2.0%, corresponding to a t_D^min value of 4.07 ± 0.37 s by 2-site model or 3.96 ± 0.39 s by 5-site model (N = 10 subjects).

Table 1.

Rate of chemical exchange (k, s⁻¹) and cross-relaxation (σ, s⁻¹) and ³¹P T₁ relaxation times (s) in resting human calf muscle by band inversion at 7T (N = 10)

	Band Inversion
	2-pool Model	5-pool Model
kPi→γ-ATP	0.073 ± 0.011	0.071 ± 0.010
kPCr→γ-ATP	-	0.138 ± 0.062
σγ↔β-ATP	-	0.208 ± 0.047
σα↔β-ATP	-	0.210 ± 0.051
T1 (Pi)	6.93 ± 1.90	6.55 ± 1.46
T1 (PCr)	-	4.63 ± 0.35
T1 (γ-ATP)	4.07 ± 0.32	1.97 ± 0.14
T1 (α-ATP)	-	1.34 ± 0.07
T1 (β-ATP)	-	1.02 ± 0.05

Narrowband vs wideband inversion

To examine the effect of inversion bandwidth on magnetization exchange (ME) between Pi and γ-ATP, the resonance of γ-ATP was inverted using three different bandwidths, Δf = 400, 700 and 2500 Hz, respectively. As shown in Figures 7 and 8, with an increase in Δf, both the magnitude of the γ-ATP fractional inversion coefficient f and ME at Pi increased (f = ~ 0%, −30% and −68%; and maximal (1 − m_pi) = 3%, 8% and 16% for this particular subject). Furthermore, compared to γ-ATP inversion using narrowband (Δf = 400 Hz), the co-inversion of PCr and γ-ATP using wideband (Δf = 700 and 2500 Hz) dramatically slowed the recovery of γ-ATP (the apparent T₁ = 0.66 ± 0.01 sec for Δf = 400 Hz versus 3.82 ± 0.08 sec and 3.57 ± 0.06 sec for Δf = 700 and 2500 Hz, respectively, under assumption of a mono-exponential recovery; N = 2 subjects). For the wideband inversion, the inclusion of α- and β-ATP in the inversion led to a delayed occurrence of the maximal magnetization exchange effect at Pi (t_D^min = 2.6 sec for Δf = 700 Hz versus t_D^min = 3.4 sec for Δf =2500 Hz, Figure 8).

FIG. 7.

The effect of the inversion bandwidth on magnetization exchange between Pi and γ-ATP at varying inversion delay times with the inversion band set to invert (a) only γ-ATP; (b) both PCr and γ-ATP; and (c) PCr, α-, β- and γ-ATP. The insets show the stacked plots of Pi, and the Pi intensity data are plotted against inversion delay time in Figure 8. Abbreviation: Pi, Inorganic phosphate; PCr, phosphocreatine; ATP, adenosine triphosphate.

FIG. 8.

(a) The stacked plots of Pi at various delay times showing the effect of the inversion bandwidth on the inversion recovery of the γ-ATP signal. (b) A comparison of ME observed at Pi upon inversion of γ-ATP (bottom) at three different inversion bandwidths. Note the much smaller magnetization exchange occurring in Pi using the narrower bandwidth (inverting only α-, β- and γ-ATP) in comparison to that using the wider bandwidths (inverting PCr and γ-ATP), and the more efficient inversion of γ-ATP when the α- and β-ATP spins are included in the wide band inversion. The raw data are from spectra in Figure 7.

DISCUSSION

Exchange-kinetics by band inversion transfer (EBIT) is presented here as a strategy to amplify the magnetization exchange effects between Pi and γ-ATP by capitalizing on the large PCr pool that is in active exchange with ATP in skeletal muscle (16,17). By simultaneous co-inversion of PCr with γ-ATP, the effect of EBIT is to slow the apparent relaxation of γ-ATP, thereby lengthening the time for buildup of ME between γ-ATP and Pi (Figures 4–8). As a tool for measuring energy metabolism, EBIT has three technically appealing features: 1) it is based on a T₁ sequence readily available in clinical scanners; 2) data analysis for evaluation of the rate of ATP synthesis can be done using a simple model based on 2-site exchange between Pi and γ-ATP, circumventing the more complex 5-spin system which includes multiple exchange pathways (Figure 1); and 3) it utilizes the large pool of PCr as a magnetization buffer for γ-ATP instead of resorting to continuous RF saturation (ST), thereby lowering the SAR exposure and avoiding potential “spillover” artifacts which could gradually accumulate during a longer saturation period (18,19). Consequently, there is no need to collect control spectra with the inversion band centered on the opposite side of Pi signal as in ST. The readily-detectable ³¹P signal of PDE, an inert metabolite not actively involved in exchange with other high energy phosphates, provides a reliable internal reference for the effects of inversion (Figures 3–5) since the center of the band inversion is further away from Pi (4.9 ppm) than from PDE (2.9 ppm).

Moreover, as a subset of inversion transfer methods, an inherent advantage of EBIT is its larger dynamic range in Z-magnetization (theoretically M^o → -M^o for inversion transfer versus M^o → 0 for ST). In practice, the use of shaped pulses in vivo leads to a reduced inversion efficacy. Under the current experimental condition, the inversion efficacy was found to be spin-dependent, even though the inversion profile is uniform for a given spin (Figure 2). In particular, for the trapezoid-shaped adiabatic pulse with an inversion bandwidth of 2500 Hz, the order of inversion efficacy is 86% for PCr, 65% for γ-ATP, 60% for α-ATP and 48% for β-ATP (Figure 5). This suggests that inversion efficacy parallels the T₂ of each spin (20), as noted previously using a hyperbolic secant-shaped inversion pulse with a narrow bandwidth of 150 Hz (16).

It has been challenging to generate a sizable reduction in Pi signal by pulsing selectively at γ-ATP (15,16,21,22) because the kinetic rate constant for conversion of Pi → γ-ATP is much slower than that for PCr → γ-ATP and the relaxation rate of Pi (1/T_1,Pi) is relatively fast (~2 fold faster than k_Pi→γATP, Table 1). Strategies for measuring exchange between Pi → γ-ATP are quite limited, often relying on long duration (typically, 5–8 s), high power saturation pulses. In recent years, more ³¹P studies performed at high and ultra-high magnetic fields with the advantages of both high S/N and wide chemical shift dispersion (4,16,23–25). The longer T₁ of Pi at high fields is an advantage for measuring chemical exchanges with γ-ATP. However, this is partially negated by the shorter T₁ and T₂ values of γ-ATP due to a larger contribution from chemical shift anisotropy (20), implying that an increased B₁ power may be needed for full saturation of γ-ATP. As illustrated here, co-inversion of PCr and γ-ATP provides an effective way for EBIT to overcome the T₁ shortening of γ-ATP thereby lengthen the period for the magnetization to exchange between Pi and γ-ATP.

Quantitatively, when co-inverted with PCr, γ-ATP relaxes 2.4-fold slower than its intrinsic T₁ (1.70 s, ref(16)), and ~ 5–6-fold slower in comparison to when γ-ATP is selectively inverted (Figures 7 and 8). This increase in the apparent T₁ of γ-ATP contributes to the observed ~ 5–6-fold enhancement in ME between γ-ATP and Pi (~ 16 – 18 % by wide-band inversion of PCr and ATP, Figures 4 – 6) as compared to the narrow-band inversion of only γ-ATP (~ 3 %, Figure 8). Conceptually, the co-inverted PCr serves as a buffer to replenish the smaller pool of inverted γ-ATP. In effect, co-inversion serves the same purpose as continuous irradiation of γ-ATP in ST, except that in ST, an external RF source is employed to continuously reduce the M_z of γ-ATP. Both α- and β-ATP spins are included with PCr and γ-ATP in band inversion. There is a strong ³¹P cross-relaxation effect within ATP (16,26) so inclusion of α- and β-ATP permits more efficient inversion of γ-ATP (the magnitude of fractional inversion coefficient f was increased from 30% to 68%, Figures 7 and 8), providing additional time for ME to buildup between Pi and γ-ATP (t_D^min was increased by 0.8 sec, Figure 8).

Interestingly, although co-inversion of PCr, γ-ATP, α-ATP and β-ATP are critical for maximizing ME between γ-ATP and Pi, it is not obligatory to include all the inverted magnetizations in the formula for evaluation of the exchange rate constant k_Pi→γATP. The fitting results (Figure 6 and Table 1) demonstrate that the 2-site exchange model provides nearly identical results as the more inclusive 5-site model for measurement of k_Pi→γATP. This is not surprising since in the 2-site model, the effect of the three “hidden” pools (PCr, α- and β-ATP) is taken into account by the apparent T₁ relaxation time of γ-ATP. As a result of this simplification, the T₁ of γ-ATP obtained by fitting the data to the 2-site kinetic model (Equation [4]) represents apparent T₁ rather than intrinsic T₁ (4.07 s from the 2-site model vs 1.97 s from the 5-site model, Table 1). It should be noted that, for a classic 2-site inversion recovery exchange model, an analytical solution is available for the inverted and undisturbed magnetizations (27) but the mathematical expressions are rather complicated and generally nonlinear least-squares fitting of these equations must be used to evaluate the rate constant k, as demonstrated by Malloy et al. (28) and Dagani et al. (29). The present work adopted a matrix approach due to its simplicity in expression (Equations [2] and [4]), which can be solved numerically in Matlab.

With a typical S/N of 50:1 for the Pi signal, the scan time for an EBIT experiment at 7T is 24 min (for acquisition of 12 data points at varying t_D’s with 4 averages), as compared to 55 min using the recently reported EKIT technique at 7T (14) and ~ 1 hr for the most widely used ST techniques (under varying acquisition conditions, ref (2)). Lengthy data acquisition times can be a limiting factor in measuring exchange kinetics in vivo (30), and efforts toward rapid collection of exchange data have been reported in vivo and in phantoms (4,30–32). Conventional steady-state ST is an alternative technique for measuring k_Pi→γ-ATP using two spectra (an on-resonance plus an off-resonance control) but it requires a separate measure of the T₁ of Pi (2), a parameter with a relative large variation. The relatively long scan time of 30 s was used here allow for nearly full recovery of the ³¹P signals. Potentially, the scan time for EBIT data acquisition can be reduced, especially for those data points with short t_Ds. Fewer data points and/or number of averages can also shorten scan time. However, for reliable quantification of the rate of ATP synthesis and to discern small variations in k_Pi→γATP among different patient populations, it is essential to acquire quality data with high S/N.

The reliability and sensitivity of the EBIT approach in measurement of ME is reflected by the high reproducibility of the t_D-dependent ME (Figure 5) and the significant ME effects relative to the low spectral background noise (Figures 3, 4 and 5). Admittedly, as an experiment that is based on multiple data points for evaluation of both k_Pi→γ-ATP and T_1,Pi, EBIT likely takes more time than a typical steady-state ST experiment using two spectral data (provided that the T₁ of Pi is known). In terms of variability in k_Pi→γ-ATP and T_1,Pi, the results derived from EBIT data were similar to those reported for human calf muscle using a steady-state ST method at 7T (4). Using EBIT, a ME of ~18 % was observed in resting human skeletal muscle, comparable to a typical ST result (~ 20%) as reported by Befroy et al in their recent review (2). A more than 30% reduction of Pi signal was observed by Valkovic et al at 7T using steady-state ST (4,25). Importantly, for the group of 10 subjects studied, both the 2- and 5-site models yielded newly identical k_Pi→γ-ATP values (0.073 ± 0.011 s⁻¹ by 2-site model vs 0.071 ± 0.010 s⁻¹ by 5-site model). Similar rate constants have been reported for resting skeletal muscle by us using frequency-selective EKIT at 7T (0.05 s⁻¹, ref(14)) and by others using ST (for example, 0.059 s⁻¹ (soleus) and 0.057 s⁻¹ (gastrocnemius) by Befroy et al (2)). A k_Pi→γ-ATP value of 0.11 s⁻¹ was derived by Valkovič et al at 7T using steady-state ST (4,25), falling at the high end of the k_Pi→γ-ATP range (0.04–0.12 s⁻¹) by ST as summarized by Kemp and Brindle (1) for muscle studies. Using the resultant kinetic constant k_Pi→γ-ATP and Pi concentration (2.10 mmol/kg ww), an ATP synthesis rate of 9.1 mmol/kg ww/min is derived for the reaction Pi → γ-ATP in resting human calf muscle, in agreement with the measurements reported using ST (1,3,7). Therefore, despite the fundamental difference in the mechanism by which ME is generated, both methods appear to be consistent.

It should be emphasized that the primary objective of this study was technical development of a robust IR method for measurement of the unidirectional rate of Pi → γ-ATP in vivo. The current EBIT approach is not optimized to probe both Pi ↔ γ-ATP and PCr ↔ γ-ATP reactions, since ME for this later reaction is blended with PCr T₁ relaxation and therefore not as easily identified compared to ME between Pi and γ-ATP. Thus the k_PCr→γATP value can only be analyzed non-intuitively by a more complex 5-site exchange model (Table 1). Furthermore, as pointed out by From and Ugurbil (14) and Kemp and Brindle (1), the resultant rate constant measured by EBIT (and by ST) may have contributions from both mitochondrial oxidative phosphorylation (through ATPase) and glycolysis (through exchanges occurring at GAPDH/phosphoglycerokinase and PFK/fructose-bis-phosphatase). Such glycolytic reactions likely contribute to the measured rate for conversion of Pi → γ-ATP because carbohydrates are known to contribute roughly 50% of total ATP energy demand for humans at rest (33). One might anticipate for muscle at rest, the contribution from glycolysis to the ³¹P NMR-measured Pi → γ-ATP rate would be quite low in comparison to the rate of mitochondrial ATP production (assuming O₂ is not limiting). However, we observed ¹H signals from both lactate and acetyl-carnitine (at 4.1 ppm and 2.12 ppm, respectively, refs (34,35)) in resting soleus muscle of normal healthy subjects (population averaged data with N = 80, ref (36)), suggesting that glycolysis compensates for limited mitochondrial oxidation perhaps due to inadequate oxygenation in mitochondrial microenvironment. This finding supports the view that the ³¹P NMR-measured Pi → γ-ATP rate in resting muscle exceeds estimates obtained from oxygen consumption and TCA turnover rate using tracer ¹³C MR methods (1,14,37). Indeed, the ATP production rate by EBIT in this study (9.1 mmol/min/kg ww) is nearly 3-fold higher than that estimated from the rate of acetyl disposal in resting human soleus muscle after moderate exercise using ¹H NMR (3.2 mmol/min/kg ww, derived from data in ref (35)).

In addition to contributions from glycolytic ATP production, Balaban and Koretsky (15) suggested that small pools of metabolites, invisible in the ³¹P NMR spectrum due to binding to large enzyme complexes or residing in space-restricted compartments with dense protein and rich paramagnetic species, may contribute to the ST-measured Pi → γ-ATP rate due to augmentation effect of the prolonged ST irradiation. Since such species are characterized by short T₂’s, they are unlikely inverted to a significant extent due to the use of the adiabatic pulse for inversion. Additionally, different from ST, there is no augment effect for small pools in EBIT since the magnetization exchanges occur in the post-inversion delay period in the absence of any applied B₁ field (15). Therefore, one can expect that the EBIT-measured Pi → γ-ATP rate is essentially free from potential contamination of small NMR-invisible pools.

Under current experimental conditions, the EBIT inversion pulse is set to invert only PCr and ATP spins while leaving the downfield Pi and phosphodiester (PDE) signals out of the inversion window. This makes it possible for a reliable assignment of the t_D-dependent Pi signal reduction to magnetization exchange between Pi and γ-ATP, rather than a “spillover” effect. In case the inversion pulse is felt by the Pi signal, then one could easily correct this “spillover” effect by using the f-factor as defined in Equation [9], without the need to performing a separate experiment with the band-inversion centered on the opposite of Pi, as typically required by ST.

In summary, the ATP synthesis reaction, Pi → γ-ATP, was studied in resting human skeletal muscle at 7T using a simple band-inversion pulse sequence. The resultant high-quality ³¹P MR spectral data with enhanced exchange effect between Pi and γ-ATP can be easily analyzed using simple 2-site exchange model. Given its good sensitivity and simplicity, it is therefore expected that EBIT could become a useful tool for studying energy metabolism in clinic settings or sports medicine with potential applications extendable to other organs such as brain and heart where abnormal ATP synthesis may be important in characterizing a disease.