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Circ Res. Author manuscript; available in PMC 2012 March 18.

Published in final edited form as:

Published online 2011 February 3. doi: 10.1161/CIRCRESAHA.110.231456

PMCID: PMC3090083

NIHMSID: NIHMS275520

Xiong -- T_{1}^{nom} method for superfast enzyme kinetic study

Qiang Xiong,^{*,}^{1,}^{2} Fei Du,^{*,}^{2,}^{3} Xiaohong Zhu,^{2} Pengyuan Zhang,^{1} Piradeep Suntharalingam,^{1} Joseph Ippolito,^{1,}^{2} Forum D. Kamdar,^{1} Wei Chen,^{†,}^{2} and Jianyi Zhang^{†,}^{1,}^{2}

^{31}P magnetization saturation transfer (MST) experiment is the most widely used method to study ATP metabolism kinetics. However, its lengthy data acquisition time greatly limits the wide biomedical applications *in vivo*, especially for studies requiring high spatial and temporal resolutions. We aim to develop a novel superfast MST method that can accurately quantify ATP production rate constants (k_{f}) through creatine kinase (CK) or ATP synthase (ATPase) with two spectra.

The T_{1}^{nom} (T_{1} nominal) method utilizes a correction factor to compensate the partially relaxed MST experiments, thus allowing measurement of enzyme kinetics with an ** arbitrary** repetition time and flip angle, which consequently reduces the data acquisition time of a transmurally differentiated CK k

A novel MST method for superfast examination of enzyme kinetics *in vivo* has been developed and verified theoretically and experimentally. In the *in vivo* normal heart, redundant multiple supporting systems of myocardial ATP production, transportation, and utilization exist, such that inhibition of one mechanism, does not impair the normal LV contractile performance.

The adenosine triphosphate (ATP) metabolism in a living organ is characterized by a chemical exchange network among phosphocreatine (PCr), ATP, and inorganic phosphate (Pi), which is largely controlled by the enzymes creatine kinase (CK, catalyzing PCr↔ATP) and ATP synthase (ATPase, catalyzing Pi↔ATP): ^{1, 2}

$$\mathrm{PCr}\underset{{k}_{\mathrm{r},\mathrm{CK}}}{\overset{{k}_{\mathrm{f},\mathrm{CK}}}{\rightleftarrows}}\mathrm{ATP}\underset{{k}_{\mathrm{f},\mathrm{ATPase}}}{\overset{{k}_{\mathrm{r},\mathrm{ATPase}}}{\rightleftarrows}}\mathrm{Pi}$$

where k_{f} and k_{r} are the pseudo-first-order forward and reverse rate constants for CK and ATPase reactions. Under most *in vivo* circumstances, a steady-state condition is established, resulting in equal forward and reverse fluxes for both CK and ATPase reactions ^{1, 2}. Therefore, the kinetics of PCr↔ATP↔Pi chemical exchange can be characterized by two forward pseudo-first-order rate constants (k_{f,CK} for PCr→ATP and k_{f,ATPase} for Pi→ATP), and studied by ^{31}P magnetization saturation transfer (MST) experiment where ATPγ resonance is selectively saturated ^{1, 2}.

The exchange rates of CK and ATPase reactions have been extensively studied on various organs, such as heart, brain, and skeletal muscle ^{3-5}. Previous studies have suggested that the kinetics of the PCr↔ATP↔Pi exchange network may be associated with the pathological status of the organ. For example, significantly lowered ATP production rates via CK have been observed in association with various heart diseases in both large animal models ^{4, 5} and patients ^{6-8}. The cerebral ATP metabolic rate through ATPase has been demonstrated to be tightly coupled to brain activity level in a rat model ^{9}. In addition, the CK activity in the visual cortex of human brain was increased during visual simulation ^{10}. In contrast, in heart it was found that CK forward flux rate was independent from the increase of cardiac workloads in response to catecholamine stimulations ^{5}.

In order to compensate the lengthy data acquisition time imposed by conventional MST technique, Dr. Bottomley *et al*. proposed a four-angle saturation transfer (FAST) method, allowing rapid *in vivo* measurement of CK reaction rates with four short-repetition time (TR) spectra ^{11}. This method was later employed by Dr. Weiss *et al*. in patients to examine the myocardial CK reaction kinetics ^{11}. We have recently reported an improved MST method for measuring CK kinetics with as few as three spectra ^{12}, the method focused on minimizing the saturation time by optimizing the pre-saturation delay, which resulted in a significant reduction of repetition time.

In the present study, we demonstrate a novel steady-state MST method (T_{1}^{nom}) for performing extremely rapid measurements of CK and ATPase kinetics with ** arbitrary** repetition time and flip angle (FA). The accurate quantification of k

The evolution of spin magnetizations in the coupled CK and ATPase reactions can be characterized by the modified Bloch-McConnell equations ^{14, 15} shown as below:

$$\frac{d{M}_{\mathrm{PCr}}\left(t\right)}{dt}=\frac{{M}_{0,\mathrm{PCr}}-{M}_{\mathrm{PCr}}\left(t\right)}{{T}_{1,\mathrm{PCr}}^{\mathrm{int}}}-{k}_{\mathrm{f},\mathrm{CK}}{M}_{\mathrm{PCr}}\left(t\right)+{k}_{\mathrm{r},\mathrm{CK}}{M}_{\mathrm{ATP}\gamma}\left(t\right)$$

[1]

$$\frac{d{M}_{\mathrm{Pi}}\left(t\right)}{dt}=\frac{{M}_{0,\mathrm{Pi}}-{M}_{\mathrm{Pi}}\left(t\right)}{{T}_{1,\mathrm{Pi}}^{\mathrm{int}}}-{k}_{\mathrm{f},\mathrm{ATPase}}{M}_{\mathrm{Pi}}\left(t\right)+{k}_{\mathrm{r},\mathrm{ATPase}}{M}_{\mathrm{ATP}\gamma}\left(t\right)$$

[2]

$$\frac{d{M}_{\mathrm{ATP}\gamma}\left(t\right)}{dt}=\frac{{M}_{0,\mathrm{ATP}\gamma}-{M}_{\mathrm{ATP}\gamma}\left(t\right)}{{T}_{1,\mathrm{ATP}\gamma}^{\mathrm{int}}}+{k}_{\mathrm{f},\mathrm{CK}}{M}_{\mathrm{PCr}}\left(t\right)+{k}_{\mathrm{f},\mathrm{ATPase}}{M}_{\mathrm{Pi}}\left(t\right)-({k}_{\mathrm{r},\mathrm{CK}}+{k}_{\mathrm{r},\mathrm{ATPase}}){M}_{\mathrm{ATP}\gamma}\left(t\right)$$

[3]

When ATPγ is selectively saturated as applied in MST experiments, Equations [1] to [3] change to:

$$\frac{d{M}_{\mathrm{PCr}}\left(t\right)}{dt}=\frac{{M}_{0,\mathrm{PCr}}-{M}_{\mathrm{PCr}}\left(t\right)}{{T}_{1,\mathrm{PCr}}^{\mathrm{int}}}-{k}_{\mathrm{f},\mathrm{CK}}{M}_{\mathrm{PCr}}\left(t\right)$$

[4]

$$\frac{d{M}_{\mathrm{Pi}}\left(t\right)}{dt}=\frac{{M}_{0,\mathrm{Pi}}-{M}_{\mathrm{Pi}}\left(t\right)}{{T}_{1,\mathrm{Pi}}^{\mathrm{int}}}-{k}_{\mathrm{f},\mathrm{ATPase}}{M}_{\mathrm{Pi}}\left(t\right)$$

[5]

$${M}_{\mathrm{ATP}\gamma}\left(t\right)=0$$

[6]

Equation [4] and [5] are mathematically equivalent, therefore CK and ATPase reactions are treated together using the same equations in the following discussion. The extent of the reduction of PCr and Pi magnetizations in response to ATPγ saturation is proportional to the forward rate constants:

$${k}_{\mathrm{f},\mathrm{CK}\left(\mathrm{ATPase}\right)}=\left(\frac{{M}_{0,\mathrm{PCr}\left(\mathrm{Pi}\right)}-{M}_{\mathrm{ss},\mathrm{PCr}\left(\mathrm{Pi}\right)}}{{M}_{\mathrm{ss},\mathrm{PCr}\left(\mathrm{Pi}\right)}}\right)/{T}_{1,\mathrm{PCr}\left(\mathrm{Pi}\right)}^{\mathrm{int}}$$

[7]

where M_{ss} and M_{0} represent the fully relaxed magnetizations with and without saturation on ATPγ and T_{1}^{int} is the intrinsic longitudinal relaxation time constant. k_{f} calculation using Equation [7] is called conventional steady-state MST experiment, which requires measurement of two fully relaxed spectra (M_{0} and M_{ss}) ^{14, 15}. The validity of steady-state MST experiment has been confirmed by the fact that the intrinsic T_{1} is constant among subjects with different physiological and pathologic conditions ^{1, 4, 5, 9, 16-18} and even, in some case, among different species ^{19}. The reliable intrinsic T_{1} can be measured using conventional progressive MST experiment, which employs multiple data acquisitions with progressively prolonged saturation time on ATPγ and thus extremely time consuming (Online Supplemental Materials).

The conventional steady-state MST experiment is inefficient in terms of signal to noise (SNR) per unit acquisition time due to full relaxation prerequisite for both M_{0} and M_{ss} measurements. In addition, full relaxation requirement results in very long TR since the T_{1}s of the ^{31}P metabolites are characteristically long ^{20}, which leads to a prohibitively lengthy total acquisition time for studies requiring higher spatial or temporal discrimination.

Preferably such experiments should be performed with a short TR and an appropriate FA to maximize the SNR per unit acquisition time. The pulse sequence employed is illustrated in Figure 1. For the reason of simplicity, we chose to utilize the same TR and FA for both saturated and control spectra. Two new steady-state measurements would be obtained from spectra obtained without (M_{c}) and with (M_{s}) saturation on ATPγ as compared to M_{0} and M_{ss} in conventional steady-state MST experiment (Figure 2). In this case, Equation [7] no longer holds for k_{f} calculation due to extra saturation factor from partial relaxation. The new relationship between k_{f} value and the extent of magnetization reduction in response to ATPγ saturation can be elucidated by numerical simulation with various k_{f} values and acquisition parameters (Figure 3). The simulation results suggest an approximately linear relationship between M_{c}/M_{s} ratio and k_{f} values under various acquisition conditions. Therefore, based on a simple linear regression, Equation [7] can be re-formulated into the following equation for k_{f} quantification under partial relaxation conditions:

$$\frac{{M}_{\mathrm{c},\mathrm{PCr}\left(\mathrm{Pi}\right)}}{{M}_{\mathrm{s},\mathrm{PCr}\left(\mathrm{Pi}\right)}}\approx \beta +{T}_{1,\mathrm{PCr}\left(\mathrm{Pi}\right)}^{\mathrm{nom}}\cdot {k}_{\mathrm{f},\mathrm{CK}\left(\mathrm{ATPase}\right)}$$

[8]

where β is the intercept (usually within ±5% of 1) and T_{1}^{nom} is the slope of the line obtained by linear regression of the simulated M_{c}/M_{s} vs k_{f} plot. Equation [8] is similar to the following equation which is the rearrangement of Equation [7] (dashed lines in Figure 3):

$$\frac{{M}_{0,\mathrm{PCr}\left(\mathrm{Pi}\right)}}{{M}_{\mathrm{ss},\mathrm{PCr}\left(\mathrm{Pi}\right)}}=1+{T}_{1,\mathrm{PCr}\left(\mathrm{Pi}\right)}^{\mathrm{int}}{k}_{\mathrm{f},\mathrm{CK}\left(\mathrm{ATPase}\right)}$$

[9]

Equation [8] indicates that, the partial relaxation effects can be largely accounted for by one empirical parameter T_{1}^{nom} (means nominal T_{1} in contrast to intrinsic T_{1} as in Equation [9]). In general, T_{1}^{nom} is a function of both spin system parameters (T_{1}^{int} and pool size ratios of metabolites, such as PCr/ATP or Pi/ATP ratio), and acquisition parameters (TR and FA) and it approaches to T_{1}^{int} as TR increases and/or FA decreases:

$${T}_{1}^{\mathrm{nom}}=f\left({T}_{1}^{\mathrm{nom}},\text{pool size ratio};\mathit{TR},\mathit{FA}\right)$$

[10]

There is no general analytical expression for Equation [10], however, the value of T_{1}^{nom} can be obtained with linear regression of simulated M_{c}/M_{s} vs k_{f} plot based on Equation [1] to [6]. In practice T_{1}^{nom} and β can be empirically determined for specific experimental setup, and then k_{f} value can be readily calculated with M_{c} and M_{s} measurements according to Equation [8].

Schematic view of pulse sequence used in steady-state magnetization saturation transfer experiment. For control spectrum, the saturation pulse train is replaced by a simple delay (or changed to a symmetrically opposite frequency for correcting spillover **...**

T_{1}^{nom} method allows k_{f} calculation with arbitrary repetition time and flip angle. However, the best experimental condition (optimal TR and FA) remains unclear. Here we provide an optimization strategy to generate the best TR/FA range for T_{1}^{nom}-based k_{f} measurement and quantification. The goal of optimization is to have the smallest relative k_{f} calculation error for a given data acquisition time. Three types of k_{f} error have been considered in this section. Analytical expression for each type is provided followed by a demonstration of parameter optimization using human brain studies at 7 Tesla ^{16}.

M_{c}/M_{s} vs k_{f} plot in Figure 3 are not perfectly straight lines. The relative k_{f} calculation error due to non-linearity is defined as below:

$${\left(\frac{\delta {k}_{\mathrm{f}}}{{k}_{\mathrm{f}}}\right)}_{\mathrm{NLIN}}=\frac{\mid {k}_{\mathrm{f}}^{\text{real}}-{k}_{\mathrm{f}}^{\mathrm{cal}}\mid}{{k}_{\mathrm{f}}^{\text{real}}}$$

[11]

where k_{f}^{real} and k_{f}^{cal} stand for actual k_{f} and k_{f} calculated from Equation [8], respectively. The deviation due to nonlinearity is acquisition condition dependent, thus the optimization can be performed such that the type 1 error is minimized.

k_{f} calculation is based on two measurements from control (M_{c}) and saturated (M_{s}) spectra (Equation [8]), each of which is subject to sampling error due to finite spectral SNR. The measurement error of each spectrum would in turn contribute to the final k_{f} calculation error following error propagation theory.

Assuming a constant total acquisition time (t) and intrinsic scanner noise level (σ), the final k_{f} relative error due to spectral SNR can be expressed as:

$${\left(\frac{\delta {k}_{\mathrm{f}}}{{k}_{\mathrm{f}}}\right)}_{\mathrm{SNR}}=\frac{{M}_{c}\u2215{M}_{s}}{{M}_{c}\u2215{M}_{s}-\beta}\sqrt{1+{\left(\frac{{M}_{c}}{{M}_{s}}\right)}^{2}}\frac{\sqrt{\mathit{TR}}}{{M}_{c}}\frac{R\sqrt{t}}{\sigma}$$

[12]

Equation [12] (see deduction in Online Supplemental Materials) takes into account both the SNR of each spectrum (M_{c} and M_{s}) and the sensitivity level of k_{f} calculation towards spectral errors (T_{1}^{nom} value). A normalized type 2 error (K_{SNR}) can be introduced from Equation [12]:

$${K}_{\mathrm{SNR}}={\left(\frac{\delta {k}_{\mathrm{f}}}{{k}_{\mathrm{f}}}\right)}_{\mathrm{SNR}}/\frac{\sqrt{t}}{\sigma}\frac{{M}_{c}\u2215{M}_{s}}{{M}_{c}\u2215{M}_{s}-\beta}\sqrt{1+{\left(\frac{{M}_{c}}{{M}_{s}}\right)}^{2}}\frac{\sqrt{\mathit{TR}}}{{M}_{c}}$$

[13]

Due to lack of extra information on MR system performance or total data acquisition time, the optimization strategy is based on minimizing K_{SNR} level.

Flip angle can vary spatially due to B_{1} field inhomogeneity, especially in the case of surface coil and ultra-high magnetic field. Such variation can be greatly minimized by using adiabatic pulses (such as BIR4 pulse as employed in the present study ^{21}). Therefore, the accuracy of k_{f} calculation based on T_{1}^{nom} method would be affected by flip angle variation. The relative k_{f} calculation error due to flip angle inaccuracy can be expressed by the following equation (See detailed deduction in Online Supplemental Materials):

$${K}_{\text{flip}}=-{\left(\frac{\delta {k}_{\mathrm{f}}}{{k}_{\mathrm{f}}}\right)}_{\text{flip}}/\frac{\delta \mathit{FA}}{\mathit{FA}}\approx \frac{\partial {T}_{1}^{\mathrm{nom}}}{\partial \mathit{FA}}\frac{\mathit{FA}}{{T}_{1}^{\mathrm{nom}}}$$

[14]

K_{flip} is a non-dimensional parameter that characterizes the sensitivity level of k_{f} error due to flip angle error, i.e., a smaller absolute K_{flip} value means the k_{f} calculation is more robust against flip angle variation. The negative sign in Equation [14] indicates that an underestimation of flip angle would result in overestimation of k_{f} and vice versa. The optimization strategy hereby is to find the acquisition conditions that lead to a K_{flip} value below an arbitrary level.

As a demonstration, numerical simulation for each type of k_{f} error (Equations [11], [13] and [14]) have been carried out based on human brain data at 7 Tesla ^{16} and the results are shown in Figure 4a-f. By setting arbitrary cutoff criteria for each type of k_{f} error, the overall optimized TR and FA range for the T_{1}^{nom} experiment can be obtained (Figure 4g-h, shadowed regions).

All experiments were performed in accordance with the animal use guidelines of the University of Minnesota, and the experimental protocol was approved by the University of Minnesota Research Animal Resources Committee. The investigation conformed to the “Guide for the care and use of laboratory animals” published by the National Institutes of Health (NIH publication No 85-23.).

Validation of T_{1}^{nom} method was performed with a creatine kinase inhibition experiment by iodoacetamide (IAA), an irreversible CK inhibitor ^{22}. Young female Yorkshire swine (~30 kg, n=8) were employed for the study. Iodoacetamide solution (450 mmol/L) was administrated (1 mL/kg/hr iv), and a complete CK activity inhibition (as evidenced by M_{0,PCr} = M_{ss,PCr}) was usually achieved with a total dose of 0.45 mmol/kg iv. Infusion was paused every 10 min, and steady-state MST experiments were performed in both fully and partially relaxed conditions, with interleaved acquisition. Dummy scans were employed to enforce steady state for MST experiments with partial relaxation. 5 more pigs received an extra catecholamine intervention (dopamine/dobutamine, each of 10 μg/kg/min iv) after complete inhibition of CK. Details of the open-chest surgery preparation and ^{31}P MRS have been described previously ^{5} and are included in the Online Supplemental Materials.

T_{1}^{nom} method was further employed to measure myocardial CK activity with transmural differentiation on female Yorkshire pigs (~40 kg, n=4). The spatially localized measurement was achieved with one dimensional chemical shift imaging (1D-CSI) sequence. Detailed methods are included in the Online Supplemental Materials.

To examine whether the LV contractile function can be maintained when the CK system is completely inhibited, additional 6 swine were employed for the cardiac MRI study on a clinical 1.5 Tesla scanner. LV chamber function was measured throughout the process of CK inhibition via iodoacetamide infusion at both basal and high cardiac workload conditions. Detailed cardiac MRI methods are included in the Online Supplemental Materials.

Male Sprague-Dawley rats (n=5) were employed for brain studies. Details of rat preparation as well as MRS data acquisition have been published previously (Online Supplemental Materials) ^{9}.

Intrinsic T_{1} measurements before and after complete CK inhibition yielded the same results for PCr (3.2±0.2 vs 3.1±0.2 s, p=NS, see in Figure 5), suggesting that T_{1}^{int} value is independent of CK activity and thus it is feasible to apply T_{1}^{nom} method to calculate the CK activity based on a constant T_{1}^{int} value.

Measurement of intrinsic T_{1} using (a) progressive magnetization saturation transfer before CK inhibition and (b) inversion recovery after CK inhibition. NEX=8 for each spectrum. Calculation of intrinsic T_{1} is performed by fitting the PCr or ATPγ **...**

Figure 6 illustrates the representative spectra from steady-state MST experiments with various acquisition conditions throughout the CK inhibition process. ATPγ saturation was achieved by BISTRO saturation pulse train ^{23}, which has been shown to have negligible spillover effects on the neighboring PCr peak ^{12}. As CK gets completely inhibited (top to bottom), the PCr magnetization in saturated spectra (Sat.) all approaches to that of control spectra (Ctrl.) regardless of acquisition conditions, in agreement with Equation [8] that when k_{f} equals 0, M_{c}/M_{s} ratio equals 1.

Representative spectra from steady-state MST experiments before, during and after CK inhibition. Each steady-state MST experiment consisted of two spectra, with saturation pulse set at ATPγ frequency (Sat.) or symmetrically opposite site (Ctrl.), **...**

PCr signals measured with partially relaxed conditions (Figure 6b-d) throughout the CK inhibition process were quantified, and the ratio of PCr signals in control and saturated spectra was plotted against the CK k_{f} value as measured by conventional steady-state MST experiments (Figure 7). The plot indicates a linear relationship between PCr signal ratios and k_{f} values, with a slope depending on the acquisition parameters. Also included in Figure 7 (solid lines) are the simulation results with the same parameters as utilized by the experiment. The experimental results matched the simulation, indicating the validity of T_{1}^{nom} method. Notably, the steady-state MST experiments in condition d produced the least k_{f} measurement error as compared to conditions b and c, consistent with the prediction based on the simulation results using the optimization strategy.

Quantification of steady-state MST results from the MRS data used in Figure 6. PCr signal ratio from conditions b-d were plotted against k_{f} value which was calculated according to Equation [7] from condition a. The solid lines were generated from simulation **...**

Figure 8 illustrates a typical set of transmurally differentiated measurement of creatine kinase forward flux rate constant (k_{f,CK}) using T_{1}^{nom} method in combination of 1D-CSI sequence. The 1D-CSI spectra (Figure 8, panel b) displayed a typical “column” along the phase encoding direction perpendicular to the surface coil plane, as demonstrated by the minimal overlap of the characteristic resonances representing different depths away from the surface coil. Namely, signals are from compounds of: localization phantom (Na_{3}PO_{4}), coil, myocardium characterized by high levels of PCr and ATP, and erythrocytes from the LV cavity blood characterized by 2,3-DPG peaks. The particular setup generated a T_{1}^{nom} of 1.8 sec, which was utilized for k_{f} calculation according to Equation [8]. Panel c illustrates the reconstructed spectra demonstrating the spatially localized k_{f} measurements from the subepi- and the subendo- layers of LV anterior wall. Based on 4 swine studies, the corresponding k_{f} values are 0.36±0.03 sec^{−1} and 0.40±0.03 sec^{−1} for subepi- and subendo- myocardial layers, respectively.

The hemodynamic and myocardial energetic data in response to CK inhibition via iodoacetamide infusion are summarized in Online Table II and III, respectively. Iodoacetamide infusion significantly increased the heart rate (p<0.05 vs baseline). However, within an observation window of 30 min, both the LV systolic pressure (LVSP) and the high energy phosphate PCr/ATP ratio are maintained despite of complete inhibition of CK activity. In respond to catecholamine stimulation, both the heart rate and LV systolic pressure increased significantly (Online Table III, p<0.05 vs IAA).

The LV contractile functions measured by cardiac MRI during baseline and high cardiac workload states with or without creatine kinase inhibition are summarized in the Online Supplemental Materials. Representative movies of LV short-axis cine imaging on one heart are also included in the Online Supplemental Materials. The LV contractile functions in terms of ejection fraction and systolic thickening fraction were not impaired during CK inhibition. Moreover, despite of CK inhibition, the heart can respond to catecholamine stimulation with an increased ejection fraction as non-inhibited hearts do (p<0.05 vs IAA, Online Figure I).

Taken together, these data demonstrate that LV contractile performance is maintained when the ATP production rate via CK is inhibited, suggesting existence of multiple and redundant ATP production systems in supporting the chemical energy need of the contractile apparatus.

The non-invasive T_{1}^{nom} method is further verified on rat brain at 9.4 Tesla with measurements of the CK and ATPase activities at rest condition (Online Figure II). There is no statistically significant difference between the k_{f} values measured by conventional (TR=9 sec, FA=90°) and T_{1}^{nom} (TR=3 sec, FA=45°) methods (k_{f,CK}: 0.26±0.04 sec^{−1} vs 0.24±0.03 sec^{−1}, p=NS; k_{f,ATPase}: 0.17±0.06 sec^{−1} vs 0.15±0.08 sec^{−1}, p=NS).

The present work demonstrated a novel and simple method (T_{1}^{nom}) to quantify k_{f} under partial relaxation conditions, allowing steady-state MST experiments to be performed with arbitrary repetition time and flip angle. The T_{1}^{nom} method features with extremely fast k_{f} measurement yet simple linear algorithm (Equation [8]) for quantification. In addition, the optimization strategy would significantly enhance the performance of T_{1}^{nom} method by minimizing the final k_{f} errors. By necessity, the T_{1}^{nom} method together with the optimization strategy can greatly facilitate the *in vivo* enzyme kinetic studies that demand high spatial and temporal resolution.

The linear relationship between M_{c}/M_{s} ratio and k_{f} is well maintained throughout a large range of simulated acquisition parameters (Figure 3). More extensive simulation suggested that this linear relationship holds in general regardless of pool size ratio or intrinsic T_{1} values, suggesting T_{1}^{nom} method a versatile tool for kinetic studies independent of experimental setup.

In the present study, the T_{1}^{nom} method is theoretically demonstrated based on the human brain study at 7 Tesla (three-site exchange model, PCr↔ATP↔Pi) and further experimentally verified on an *in vivo* swine heart model for measuring myocardial CK forward reaction rate constant at 9.4 Tesla (two-site model, PCr↔ATP). The two-site model is preferably employed for myocardial bioenergetic studies since the Pi resonance is largely overlapped by the 2,3-diphosphoglycerate peaks from blood and thus difficult to quantify unless spatial localization is employed ^{24}. When applied to the two-site exchange model, ATP↔Pi reaction (corresponding to Equations [3] and [6]) was ignored during the numerical simulation process (M_{c}/M_{s} vs k_{f}, Figure 3) for finding the T_{1}^{nom} value. Therefore, the T_{1}^{nom} method-based k_{f} calculation is readily applicable to both two- and three-site models as supported by the good agreement between experimental and simulation results shown in Figure Figure77 and and88.

The T_{1}^{nom} method can be considered as an improved version of conventional steady-state MST technique. The extensive previous studies on CK and ATPase kinetics have suggested that the intrinsic T_{1} is constant among subjects regardless of physiological and pathologic conditions ^{1, 4, 5, 9, 16-18}. This is consistent with the observation in the present study that T_{1,PCr}^{int} is a constant among subjects and independent of reaction rate change throughout CK inhibition process. The Intrinsic T_{1} (T_{1}^{int}) characterizes the relaxation process of a spin population to re-establish the thermal equilibrium distribution (spin-lattice relaxation) ^{25}. Therefore, in a defined magnetic field of a given organ of interest, the T_{1}^{int} of a compound is a constant, which should only reflect its characteristic molecular tumbling rate ^{25}. However, the reported T_{1}^{int} value does vary due to different magnetic fields, species, organs, pulse and pulse sequences, and acquisition parameters. Therefore, it is always recommended to be cautious when using the T_{1}^{int} value from literature. In a rare case where a biological system has no prior report of its T_{1}^{int}, a direct T_{1}^{int} measurement of a few healthy subjects should be performed prior to the application of T_{1}^{nom} method.

The T_{1}^{nom} method is highly robust to the variation of pool size ratio of metabolites, such as PCr/ATP ratio for CK reaction and Pi/ATP ratio for ATPase reaction. For the acquisition parameters within the optimized region as shown in Figure 4g-h, the relative k_{f} measurement error due to a variation of pool size ratios of metabolite is less than 1/8 of the variation level itself, i.e., a change of PCr/ATP ratio of 40% would result only a 5% of k_{f} measurement error using the T_{1}^{nom} method. Finally, in case of large change of pool size ratios of metabolites, an iteration approach can be employed to correct for the originally assumed pool size ratio based on M_{c} measurement (Online Figure III). The iteration approach is based on the assumption that the change in pool size ratio is proportionally reflected in the magnetization (M_{c}) ratio measured in control spectra as long as the intrinsic T_{1}s in the two statuses are the same:

$$\frac{{\phantom{\mid}{\mathrm{M}}_{0,\mathrm{PCr}}:{\mathrm{M}}_{0,\mathrm{ATP}\gamma}:{\mathrm{M}}_{0,\mathrm{Pi}}\mid}_{\text{status}1}}{{\phantom{\mid}{\mathrm{M}}_{0,\mathrm{PCr}}^{\prime}:{\mathrm{M}}_{0,\mathrm{ATP}\gamma}^{\prime}:{\mathrm{M}}_{0,\mathrm{Pi}}^{\prime}\mid}_{\text{status}2}}\approx \frac{{\phantom{\mid}{\mathrm{M}}_{\mathrm{c},\mathrm{PCr}}:{\mathrm{M}}_{\mathrm{c},\mathrm{ATP}\gamma}:{\mathrm{M}}_{\mathrm{c},\mathrm{Pi}}\mid}_{\text{status}1}}{{\phantom{\mid}{\mathrm{M}}_{\mathrm{c},\mathrm{PCr}}^{\prime}:{\mathrm{M}}_{\mathrm{c},\mathrm{ATP}\gamma}^{\prime}:{\mathrm{M}}_{\mathrm{c},\mathrm{Pi}}^{\prime}\mid}_{\text{status}2}}$$

[15]

Numerical simulation suggested a correction precision of >95% for Equation [15] with wide range of parameters (CK study of human brain at 7 Tesla 16, k_{f,CK}=0.15~0.6 sec^{−1}, TR=0.4~8 sec, FA=5~90°). Equation [15] is useful for obtaining the metabolites’ pool size ratio in the absence of fully relaxed measurements, which is highly valuable since the pool size ratio such as PCr/ATP has been widely accepted as a useful index for the bioenergetic status ^{26, 27}. Therefore, based on Equation [8] and [15], a complete energetic study of both pool size ratio of metabolites and enzyme activity level can be performed without fully relaxed measurements.

The performance of k_{f} measurement using the T_{1}^{nom} method would be greatly enhanced by the optimization strategy, which is based on the k_{f} error analysis to generate the best acquisition parameter range (TR and FA, that are most relevant to the longitudinal relaxation processing).

Type 1 error as defined by Equation [11] represents the accuracy of k_{f} calculation using the T_{1}^{nom} method. As shown in Figure 4a-b, the type 1 error for human brain studies at 7 Tesla is below 1% for most acquisition conditions. Similar type 1 error levels were observed from numerical simulations with parameters that are characteristic of heart and skeletal muscle. Those simulation results again demonstrated the versatility of T_{1}^{nom} method for measuring enzyme kinetics on various organs.

The type 2 error specifically addresses the spectral SNR issue. For MR experiment with partial relaxation, the spectral SNR per unit acquisition time would be maximized if the flip angle is chosen at the Ernst angle that is determined by TR and spin’s longitudinal relaxation time. When chemical exchange is involved, the Ernst angle also depends on the reaction rate. Therefore, the Ernst angle for control and saturated spectrum would be different. However, applying different flip angles for M_{c} and M_{s} measurements would render the spectrum comparison less intuitive and the k_{f} calculation more prone to flip angle inaccuracy. In current approach, instead, both spectra are acquired with a same flip angle that is globally optimized according to error propagation theory (Equation [13]). Since the acquisition parameters are identical for both M_{c} and M_{s} spectra, any measurement error due to flip angle variation would be cancelled out in Equation [8] for k_{f} calculation and the only residual effect would be the change of T_{1}^{nom} value, which is taken into account as the type 3 error. Even though none of the M_{c} or M_{s} measurements is acquired exactly at its Ernst angle, the overall performance from this globally optimized flip angle is still substantially better than the conventional steady-state MST. Taking human brain studies at 7 Tesla for instance (same parameter as used in Figure 4), the T_{1}^{nom} method can easily achieve a level of <1% type 1 error. The same type 1 error level would require a TR of 16 sec for the conventional MST methods (99% full relaxation, FA=90°). Should such an experiment be performed under an optimized condition using the T_{1}^{nom} method (e.g. TR=2 sec, FA=45°), an 88% reduction of total acquisition time could be achieved assuming a same number of signal averaging (NEX).

Type 3 error deals with the residual effects of flip angle inaccuracy on the final k_{f} calculation error. As demonstrated in Figure 4e-f, the spin system becomes more robust against flip angle variation as flip angle decreases or TR increases. This result is consistent with the previous simulation results showing that T_{1}^{nom} approaches to T_{1}^{int} as flip angle decreases or TR increases (Figure 3). Therefore, based on the analysis of type 3 error (Figure 4e-f) we can compensate the impact of flip angle variation to an arbitrary level at an expense of reduced SNR per unit time. This is advantageous over some other rapid saturation transfer methods which employ multiple flip angles for calculating the k_{f} and thus more vulnerable to flip angle variation, such as FAST method ^{11}.

The superior performance of the T_{1}^{nom} method is demonstrated by the transmurally differentiated measurement of k_{f,CK} (Figure 8). The total data acquisition time using T_{1}^{nom} method in combination of 1D-CSI sequence (2 sets of spectra, 17 phase encoding steps, NEX=8, TR=3 sec) is 13.6 minutes. In contrast, a similar transmurally differentiated k_{f,CK} measurement performed by Robitaille PM *et al*. using a conventional saturation transfer method took 153.6 min (8 sets of spectra, 18 phase encoding steps, NEX=8 and TR=8 sec) to accomplish the data acquisition ^{13}. Therefore, the present study demonstrates that using T_{1}^{nom} method results in a reduction of data acquisition time by 91.2% as compared to the conventional saturation transfer method.

Upon inhibition of creatine kinase via iodoacetamide infusion, the LV function and systemic hemodynamic did not change within an observation window of 30 min (Online Tables), the high energy phosphate PCr/ATP ratio was preserved (Online Table III), and the inorganic phosphate (Pi) level did not increase (Figure 6). Collectively, the present study demonstrate for the first time that a normal LV chamber contractile function can be maintained in the presence of complete inhibition of CK activity in normal *in vivo* heart under basal and high cardiac workstates. This finding is surprising, and raises a significant question of what a significant role CK plays in the cascade of ATP production, transportation and utilization. In the normal *in vivo* heart, the ATP production rate via creatine kinase exceeds that of the mitochondria ATPase by an order of magnitude ^{4}. Therefore, it is possible that a small amount of residual CK activity may be sufficient to support normal LV function in a relatively short term. In the present study, it is possible that a residual undetectable creatine kinase activity of 5% (or less) remained at 30 minutes after the IAA infusion initiation. Based on the signal to noise ratio (Figure 6), a 5% of residual CK activity could be at noise level. This small fraction of residual creatine kinase-derived ATP, along with other ATP sources, could be sufficient in supporting cardiac contractile function in the short term.

The severity of CK kinetics change is related to the chronic cardiac pathologic changes such as severity of the LV hypertrophy or LV dysfunction ^{4-8}. However, the mechanisms of these relationships are still unknown. The results of the present study demonstrate that an acute severe inhibition of ATP production rate via CK does not impair the LV regional or global contractile function. The finding of normal LV chamber function with complete inhibition of CK activity in the present study is in agreement with the previous observation using engineered mice, which demonstrated a normal growth and LV chamber function in mice with double knockout of the muscle and mitochondrial isoforms (M/MtCK-/- mice) ^{28}. Taken together, these data suggest that in normal heart under *in vivo* conditions, redundant supporting systems exist to maintain an important organ function. These data also suggest that in the failing hearts that are usually severely hypertrophied, the redundant supporting systems such as CK, mitochondrial electron transport system and ATPase, may all be impaired. Consequently, the severity of the alterations of each of these systems is related to the severity of the LV dysfunction such as being observed earlier ^{6, 7, 29-31}.

In summary, we have demonstrated a novel steady-state magnetization saturation transfer method (T_{1}^{nom}) together with an optimization strategy that allows accurate k_{f} quantification under partially relaxed acquisition conditions. The new method features an unprecedented fast k_{f} measurement yet simple linear algorithm for quantification. This method enables broad applications for *in vivo* enzyme kinetic studies that require high spatial or temporal resolution. Using this novel NMR methods and an established swine model, these data demonstrate that acute inhibition of CK activity does not limit LV chamber function in the *in vivo* heart.

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**SOURCES OF FUNDING** These works were supported by National Institutes of Health grants: HL50470, HL 67828, HL 95077, HL 100407, NS041262, NS057560, NS070839, P41 RR008079, P30 NS057091; and Keck Foundation.

**DISCLOSURES** None.

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