Four-angle saturation transfer (FAST) method for measuring creatine kinase reaction rates in vivo

Abstract

A new fast method of measuring kinetic reaction rates for two-site chemical exchange is described. The method employs saturation transfer magnetic resonance spectroscopy (MRS) and acquisition of only four spectra under partially saturated, high signal-to-noise ratio (SNR) conditions. In two acquisitions one of the exchanging species is saturated; the other two employ a control saturation. Each pair of acquisitions is applied with two different flip angles, and the equilibrium magnetization, relaxation times, and reaction rates are calculated therefrom. This four-angle saturation transfer (FAST) method is validated theoretically using the Bloch equations modified for two-state chemical exchange. Potential errors in the rate measurements due to the effects of exchange are evaluated for creatine kinase (CK) metabolism modeled for skeletal and heart muscle, and are found to be < 5% for forward CK flux rates of 0.05 < or = k(f) < or = 1.0 s(-1), and up to a 90% depletion of phosphocreatine (PCr). The effect of too much or too little saturating irradiation on FAST appears to be comparable to that of the conventional saturation transfer method, although the relative performance deteriorates when spillover irradiation cuts the PCr signal by 50% or more. "FASTer" and " FASTest" protocols are introduced for dynamic CK studies wherein [PCr] and/or k(f) changes. These protocols permit the omission of one or two of the four acquisitions in repeat experiments, and the missing information is recreated from initial data via a new iterative algorithm. The FAST method is validated empirically in phosphorus ((31)P) MRS studies of human calf muscle at 1.5 T. FAST measurements of 10 normal volunteers yielded the same CK reaction rates measured by the conventional method (0.29 +/- 0.06 s(-1)) in the same subjects, but an average of seven times faster. Application of the FASTer algorithm to these data correctly restored missing information within seven iterations. Finally, the FAST method was combined with 1D spatially localized (31)P MRS in a study of six volunteers, yielding the same k(f) values independent of depth, in total acquisition times of 17-39 min. These timesaving FAST methods are enabling because they permit localized measurements of metabolic flux, which were previously impractical due to intolerably long scan times.

FIG. 1

Comparison of values of k_f measured by the FAST method with true values in model skeletal muscle (a and b) and heart muscle (c) over a 10-fold variation in [PCr] and the range 0.05 ≤ k_f ≤ 1.0 s⁻¹. The curves were calculated by iteration of the Bloch equations for two-site exchange in the Appendix for a 15T static magnetic field and a selective RF pulse power of 15 Hz (0.87 μT). a: The curves for 10%, 20%, 30%, 40%, 50%, 60%, 70%, 80%, 90%, and 100% of a PCr concentration of 28 mmol/kg wet wt overlie each other and are indistinguishable from the line of identity. Contour plots of the fractional error in k_f measured by FAST compared to the true value are shown as a function of k_f and [PCr] or PCr/ATP in parts b and c, with grayscale shown at right. Model parameters were: ${T_{1A}}^{\ast }=T_1^{\ast }(\text{PCr})=6.7\hspace{0.17em}\text{s},\hspace{0.17em}{T_{1B}}^{\ast }=T_1^{\ast }(\gamma -\text{ATP})=2.3\hspace{0.17em}\text{s}$, [PCr] ≤ 28 μmol/g wet wt, [ATP] = 4.5 μmol/g wet wt, TR = 1 s, T₂(PCr) = 0.1 s and T₂(ATP) = 0.05 s for skeletal muscle; and for heart, T_1A* = 6 s, T_1B* = 2 s, PCr/ATP ≤ 1.5, and the same values of TR and T₂.

FIG. 2

a: The apparent value of T₁ observed by a dual-angle measurement performed at TR = 1 s (solid lines) and at TR = 2 s (dashed) as a function of k_f, calculated from the exchange-modified Bloch equations for the model muscle tissue with [PCr] = 28, 21, 14, and 7 mmol/kg wet wt, as labeled on the right side. Changes in [PCr] during dynamic studies can cause changes in the value of T₁, used to calculate M₀ from the FAST method via Eq. [6] which is derived from Eqs. [4] and [5]. b: The error in M₀ that results from neglecting these T₁ changes for the different [PCr] depletions, as a function of k_f. The error is what would be expected if the control 15° acquisition were omitted from a repeat experiment during a dynamic study in which PCr is depleted and the original T₁ is assumed, if k_f remains constant.

FIG. 3

Schematic diagram of the FASTer algorithm. The algorithm permits calculation of T₁′ and M₀′ from the values of the intrinsic T₁, $T_1^{\ast }$, determined in an initial experiment from a dynamic study. This permits omission of the 15° γ-ATP saturated acquisitions in subsequent experiments. Eq, Equation, as numbered in text.

FIG. 4

The absolute error (in s⁻¹) between the true value of k_f and the value that results from applying the FASTer algorithm and the FAST method to calculate T₁′ and M₀′ for an experiment in which M₀(PCr) changes by 10-fold for (a) model skeletal muscle and (b) model heart muscle. The absolute error in k_f does not exceed 0.02 s⁻¹ over the range 0.05 ≤ k_f ≤ 1.0 s⁻¹. The plots are computed from 800 FAST experiments simulated with the exchange-modified Bloch equations in the Appendix. The result of each experiment was iterated with the FASTer algorithm using the start values indicated by arrows. Spillover irradiation and incomplete γ-ATP saturation were minimized by assuming a 15 T static magnetic field and a saturating field strength of 15 Hz.

FIG. 5

Comparison of the accuracy of (a–c) the standard saturation transfer method with (d–f) the FAST method for measuring k_f in the presence of spillover irradiation of PCr and incomplete saturation of γ-ATP, as computed for model skeletal muscle from the chemical-exchange modified Bloch equations in the Appendix. The vertical axis is the measured value of k_f; the horizontal axis is the true value. Curves are calculated for on-resonance saturating field strengths of 2.5 Hz or Q = 0.94–0.99 (a and d), 5 Hz or Q = 0.77–0.91 (b and e), and 10 Hz or Q = 0.47–0.72 (c and f) with 1.5 T chemical shift dispersions. Observed k_f values were calculated from Eq. [1] (solid square symbols), or Eq. [9] (circles). The line of equality is dashed.

FIG. 6

Comparison of the accuracy of (a–c) the standard saturation transfer method with (d–f) the FAST method for measuring k_f in the presence of spillover irradiation of PCr and incomplete saturation of γ-ATP, as computed for model heart muscle from the chemical-exchange modified Bloch equations in the Appendix. The vertical axis is the measured value of k_f; the horizontal axis is the true value. Curves are calculated for on-resonance saturating field strengths of 2.5 Hz or Q = 0.94–0.99 (a and d), 5 Hz or Q = 0.77–0.91 (b and e), and 10 Hz or Q = 0.47–0.72 (c and f) with 1.5 T chemical shift dispersions. Observed k_f values were calculated from Eq. [1] (solid square symbols), or Eq. [9] (circles). The line of equality is dashed.

FIG. 7

Comparison of complete unlocalized data sets acquired by the conventional saturation transfer method (a–c), and by the FAST method (d and e) from the same leg during the same session with comparable SNR. For the conventional method, part b depicts a series of spectra acquired at TR values of 0.6–16 s (NEX = 64, 32, 32, 24, 24, 16, 12, 12) with chemically-selective saturation of γ-ATP (arrows), for measuring T₁′. M₀′ is determined from the fully-relaxed spectrum at TR = 16 s (NEX = 12). Part a shows the peak PCr signals from part b, fitted to Eq. [10] to obtain a T₁′ value. For the FAST method, part d shows two spectra acquired at TR = 1 s with γ-ATP saturated and 15° (lower spectra; NEX = 64) and 60° (upper spectra; NEX = 32) flip angles. e: The two corresponding spectra with control irradiation. Adiabatic BIRP pulses were used for the 90°, 60°, and 15° pulses. Steady-state conditions were assumed after applying pulses for ~16 s.

FIG. 8

Conventional transaxial gradient-echo ¹H image of (a) a human leg, showing the location of a ³¹P MRS detector coil (lower white line) and a series of 1D localized coronal sections (other lines) responsible for a set of spatially-localized FAST ³¹P spectra shown in b–e. The four sets of spectra are plotted vertically as a function of depth at 1-cm intervals from the coil. Parts b and d were acquired with control irradiation (vertical arrow), with 15° and 60° adiabatic excitation, respectively. Parts c and e were acquired with γ-ATP saturated (vertical arrow), with 15° and 60° pulses, respectively. Each ³¹P data set was acquired in 4.3 min (NEX = 8; 32 phase-encoding steps) for a total acquisition time of 17 min.

FIG. 9

Mean k_f (filled circles) calculated from Eq. [1] as a function of depth through the calf muscle in the six subjects studied with localized FAST. Error bars are ±1 standard error.

FIG. 10

Convergence of the FASTer algorithm for calculating correct values of (a) M₀′ and (b) T₁′, as tested on the unlocalized human calf muscle spectra from 10 subjects. The γ-ATP-saturated 15° acquisitions were omitted from the data, and M₀′ and T₁′ were calculated from $T_1^{\ast }$ using the algorithm in Fig. 3. M₀′ and T₁′ converge to within 1% within seven iterations in all cases.