ATP Production Rate via Creatine Kinase or ATP Synthase In VivoNovelty and Significance
A Novel Superfast Magnetization Saturation Transfer Method
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Abstract
Rationale: ^{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.
Objective: We aimed 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 2 spectra.
Methods and Results: The T_{1}^{nom} (T_{1} nominal) method uses 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_{f} measurement by 91% as compared with the conventional method with spatial localization. The novel T_{1}^{nom} method is validated theoretically with numeric simulation, and further verified with in vivo swine hearts, as well as CK and ATPase activities in rat brain at 9.4 Tesla. Importantly, the in vivo data from swine hearts demonstrate, for the first time, that within an observation window of 30 minutes, the inhibition of CK activity by iodoacetamide does not limit left ventricular chamber contractile function.
Conclusions: 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 left ventricular 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}
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}
To compensate the lengthy data acquisition time imposed by conventional MST technique, Bottomley et al proposed a fourangle saturation transfer (FAST) method, allowing rapid in vivo measurement of CK reaction rates with 4 shortrepetition time (TR) spectra.^{11} This method was later used by 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 3 spectra,^{12} the method focused on minimizing the saturation time by optimizing the presaturation delay, which resulted in a significant reduction of repetition time.
In the present study, we demonstrate a novel steadystate 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_{f} under such partial relaxation conditions requires only 2 spectra. The T_{1}^{nom} method is theoretically validated based on numeric simulation of modified Bloch–McConnell equations that govern the evolution of spin magnetizations during MST experiment. In addition, an optimization strategy for finding the best acquisition parameter range (TR and FA) used in the T_{1}^{nom} method is provided. The new method is verified experimentally with in vivo measurements of: (1) k_{f}_{,CK} on swine heart model during the process of CK inhibition by iodoacetamide (IAA) infusion; and (2) both k_{f}_{,CK} and k_{f}_{,ATPase} on rat brain model at rest condition. Finally, the T_{1}^{nom} method was used to measure the myocardial CK forward rate constant with transmural differentiation, demonstrating a reduction of data acquisition time by 91% as compared with a similar study using conventional saturation transfer method.^{13}
Detailed descriptions of different types of T_{1} are included in the Online Data Supplement, available at http://circres.ahajournals.org.
Theory
k_{f} Calculation of Conventional SteadyState MST Experiment
The evolution of spin magnetizations in the coupled CK and ATPase reactions can be characterized by the modified Bloch–McConnell equations,^{14,15} as shown below:
When ATPγ is selectively saturated as applied in MST experiments, Equations 1 through 3 change to:
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:
T_{1}^{nom} Method for Extremely Rapid k_{f} Measurement and Quantification
The conventional steadystate MST experiment is inefficient in terms of signal to noise (SNR) per unit acquisition time because of the full relaxation prerequisite for both M_{0} and M_{ss} measurements. In addition, full relaxation requirement results in very long TR because 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 used is illustrated inFigure 1. For the sake of simplicity, we chose to use the same TR and FA for both saturated and control spectra. Two new steadystate measurements would be obtained from spectra obtained without (M_{c}) and with (M_{s}) saturation on ATPγ as compared with M_{0} and M_{ss} in conventional steadystate MST experiment (Figure 2). In this case, Equation 7 no longer holds for k_{f} calculation because of 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 numeric 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 reformulated into the following equation for k_{f} quantification under partial relaxation conditions:
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} versus k_{f} plot. Equation 8 is similar to the following equation which is the rearrangement of Equation 7 (dashed lines in Figure 3):
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:
There is no general analytic expression for Equation 10; however, the value of T_{1}^{nom} can be obtained with linear regression of simulated M_{c}/M_{s} versus k_{f} plot based on Equation 1 through 6. In practice T_{1}^{nom} and β can be empirically determined for specific experimental setup, and then the k_{f} value can be readily calculated with M_{c} and M_{s} measurements according to Equation 8.
Optimization Strategy for T_{1}^{nom} Method
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. Analytic expression for each type is provided followed by a demonstration of parameter optimization using human brain studies at 7 Tesla.^{16}
Type 1 Error: M_{c}/M_{s} Versus k_{f} Nonlinearity
M_{c}/M_{s} versus k_{f} plot in Figure 3 are not perfectly straight lines. The relative k_{f} calculation error attributable to nonlinearity is defined as below:
Type 2 Error: Spectral SNR
k_{f} calculation is based on 2 measurements from control (M_{c}) and saturated (M_{s}) spectra (Equation 8), each of which is subject to sampling error attributable 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 attributable to spectral SNR can be expressed as:
Equation 12 (see deduction in the Online Data Supplement) takes into account both the SNR of each spectrum (M_{c} and M_{s}) and the sensitivity level of k_{f} calculation toward spectral errors (T_{1}^{nom} value). A normalized type 2 error (K_{SNR}) can be introduced from Equation 13:
Because of the lack of extra information on MR system performance or total data acquisition time, the optimization strategy is based on minimizing K_{SNR} level.
Type 3 Error: Flip Angle Inaccuracy
Flip angle can vary spatially because of B_{1} field inhomogeneity, especially in the case of surface coil and ultrahigh magnetic field. Such variation can be greatly minimized by using adiabatic pulses (such as BIR4 pulse as used in the present study^{21}). Therefore, the accuracy of k_{f} calculation based on the T_{1}^{nom} method would be affected by flip angle variation. The relative k_{f} calculation error attributable to flip angle inaccuracy can be expressed by the following equation (see detailed deduction in the Online Data Supplement):
K_{flip} is a nondimensional parameter that characterizes the sensitivity level of k_{f} error attributable to flip angle error, ie, 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 thereby is to find the acquisition conditions that lead to a K_{flip} value below an arbitrary level.
As a demonstration, numeric 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 through 4f. 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 and 4h, shadowed regions).
Methods
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 NIH Guide for the Care and Use of Laboratory Animals (NIH publication No 8523.).
In Vivo Swine Heart Studies
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 used for the study. Iodoacetamide solution (450 mmol/L) was administrated (1 mL/kg per hour, 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 minutes, and steadystate MST experiments were performed in both fully and partially relaxed conditions, with interleaved acquisition. Dummy scans were used to enforce steady state for MST experiments with partial relaxation. Five more pigs received an extra catecholamine intervention (dopamine/dobutamine, each of 10 μg/kg/min IV) after complete inhibition of CK. Details of the openchest surgery preparation and ^{31}P MRS have been described previously^{5} and are included in the Online Data Supplement.
The T_{1}^{nom} method was further used to measure myocardial CK activity with transmural differentiation on female Yorkshire pigs (≈40 kg, n=4). The spatially localized measurement was achieved with 1D chemical shift imaging (1DCSI) sequence. Detailed methods are included in the Online Data Supplement.
To examine whether the left ventricular (LV) contractile function can be maintained when the CK system is completely inhibited, additional 6 swine were used 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 Data Supplement.
In Vivo Rat Brain Studies
Male Sprague–Dawley rats (n=5) were used for brain studies. Details of rat preparation as well as MRS data acquisition have been published previously (Online Data Supplement).^{9}
Results
Cardiovascular Physiological Studies Using a Swine Model
^{31}P MR Spectroscopy Data
Intrinsic T_{1} measurements before and after complete CK inhibition yielded the same results for PCr (3.2±0.2 versus 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.
Figure 6 illustrates the representative spectra from steadystate 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 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.
PCr signals measured with partially relaxed conditions (Figure 6b through 6d) 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 steadystate 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 used by the experiment. The experimental results matched the simulation, indicating the validity of the T_{1}^{nom} method. Notably, the steadystate MST experiments in condition d produced the least k_{f} measurement error as compared with conditions b and c, consistent with the prediction based on the simulation results using the optimization strategy.
Figure 8 illustrates a typical set of transmurally differentiated measurement of creatine kinase forward flux rate constant (k_{f}_{,CK}) using the T_{1}^{nom} method in combination of 1DCSI sequence. The 1DCSI spectra (Figure 8b) 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 2,3DPG peaks. The particular setup generated a T_{1}^{nom} of 1.8 seconds, which was used for k_{f} calculation according to Equation 8.Figure 8c 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 and 0.40±0.03 sec^{−1} for subepi and subendomyocardial layers, respectively.
Hemodynamic, Myocardial Energetics, and MRI Data in Response to CK Inhibition
The hemodynamic and myocardial energetic data in response to CK inhibition via iodoacetamide infusion are summarized in Online Tables II and III, respectively. Iodoacetamide infusion significantly increased the heart rate (P<0.05 versus baseline). However, within an observation window of 30 minutes, 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 versus 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 Data Supplement. Representative movies of LV shortaxis cine imaging on one heart are also included in the Online Data Supplement. 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 noninhibited hearts do (P<0.05 versus 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.
In Vivo Rat Brain Studies
The noninvasive 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 seconds, FA=90^{o}) and T_{1}^{nom} (TR=3 seconds, FA=45^{o}) methods (k_{f}_{,CK}: 0.26±0.04 versus 0.24±0.03 sec^{−1}, P=NS; k_{f}_{,ATPase}: 0.17±0.06 versus 0.15±0.08 sec^{−1}, P=NS).
Discussion
The present work demonstrated a novel and simple method (T_{1}^{nom}) to quantify k_{f} under partial relaxation conditions, allowing steadystate 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 the 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.
Versatility of the T_{1}^{nom} Method
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 the T_{1}^{nom} method as 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 (3site 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 (2site model, PCr↔ATP). The 2site model is preferably used for myocardial bioenergetic studies because the Pi resonance is largely overlapped by the 2,3diphosphoglycerate peaks from blood and thus difficult to quantify unless spatial localization is used.^{24} When applied to the 2site exchange model, ATP↔Pi reaction (corresponding to Equations 3 and 6) was ignored during the numeric simulation process (M_{c}/M_{s} versus 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 threesite models, as supported by the good agreement between experimental and simulation results shown in Figures 7 and Online Figure II.
Validity of the Methodology
The T_{1}^{nom} method can be considered as an improved version of conventional steadystate 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 pathological 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 reestablish 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 because of 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 before the application of the 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 and 4h, the relative k_{f} measurement error attributable to a variation of pool size ratios of metabolite is less than oneeighth of the variation level itself, ie, a change of PCr/ATP ratio of 40% would result in only a 5% of k_{f} measurement error using the T_{1}^{nom} method. Finally, in the case of large change of pool size ratios of metabolites, an iteration approach can be used 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 2 statuses are the same:
Numeric 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 seconds, FA=5–90^{o}). Equation 15 is useful for obtaining the pool size ratio of the metabolites in the absence of fully relaxed measurements, which is highly valuable because 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 Equations 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.
Enhanced Performance From Optimization Strategy
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 and 4b, 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 numeric simulations with parameters that are characteristic of heart and skeletal muscle. Those simulation results again demonstrated the versatility of the 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 the longitudinal relaxation time of spin. 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 the present approach, instead, both spectra are acquired with a same flip angle that is globally optimized according to error propagation theory (Equation 13). Because the acquisition parameters are identical for both M_{c} and M_{s} spectra, any measurement error attributable 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 steadystate 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 seconds for the conventional MST methods (99% full relaxation, FA=90^{o}). Should such an experiment be performed under an optimized condition using the T_{1}^{nom} method (eg, TR=2 seconds, FA=45^{o}), 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 and 4f, 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 and 4f), 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 use 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 the T_{1}^{nom} method in combination of 1DCSI sequence (2 sets of spectra, 17 phase encoding steps, NEX=8, TR=3 seconds) is 13.6 minutes. In contrast, a similar transmurally differentiated k_{f}_{,CK} measurement performed by Robitaille et al using a conventional saturation transfer method took 153.6 minutes (8 sets of spectra, 18 phase encoding steps, NEX=8 and TR=8 seconds) to accomplish the data acquisition.^{13} Therefore, the present study demonstrates that using the T_{1}^{nom} method results in a reduction of data acquisition time by 91.2% as compared with the conventional saturation transfer method.
LV Contractile Function in Relation to CK Inhibition in the In Vivo Heart
On inhibition of creatine kinase via iodoacetamide infusion, the LV function and systemic hemodynamic did not change within an observation window of 30 minutes (Online Tables), the high energy phosphate PCr/ATP ratio was preserved (Online Table III), and the 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 work states. 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 kinasederived 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 pathological 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 steadystate MST 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.
Sources of Funding
These work was supported by NIH grants HL50470, HL 67828, HL 95077, HL 100407, NS041262, NS057560, NS070839, P41 RR008079, and P30 NS057091; and the Keck Foundation.
Disclosures
None.
Footnotes

In December 2010, the average time from submission to first decision for all original research papers submitted to Circulation Research was 14.5 days.
Nonstandard Abbreviations and Acronyms
 β
 intercept of linear regression of simulated M_{c}/M_{s} vs k_{f} data curves (Equation 8)
 σ
 intrinsic MR system noise level (Equation 13)
 CK
 creatine kinase
 d_{1}
 total time in MST experiment when ATPγ is not saturated
 FA
 flip angle of excitation pulse
 k_{f}
 pseudo–firstorder forward rate constant of enzyme reactions
 k_{r}
 pseudo–firstorder reverse rate constant of enzyme reactions
 K_{flip}
 normalized relative k_{f} error attributable to flip angle inaccuracy
 K_{SNR}
 normalized relative k_{f} error attributable to spectral SNR
 LV
 left ventricular
 M_{0}
 steadystate magnetization in control spectrum obtained under fully relaxed condition
 M_{c}
 steadystate magnetization in control spectrum obtained under partially relaxed condition
 M_{ss}
 steadystate magnetization in saturated spectrum obtained under fully relaxed condition
 M_{s}
 steadystate magnetization in saturated spectrum obtained under partially relaxed condition
 MST
 magnetization saturation transfer
 NEX
 number of excitations for signal averaging
 Pi
 inorganic phosphate
 t
 total scan time (Equation 13)
 t_{sat}
 duration of saturation pulse in the MST experiment
 T_{1}^{app}
 apparent longitudinal relaxation time when ATPγ is continuously saturated
 T_{1}^{int}
 intrinsic longitudinal (spinlattice) relaxation time constant
 T_{1}^{mix}
 approximate longitudinal relaxation time constant when chemical exchange is involved
 T_{1}^{nom}
 nominal T_{1}, defined as the slope of linear regression of simulated M_{c}/M_{s} vs k_{f} data curves (Equation 8)
 TR
 repetition time of MST experiment
 Received August 27, 2010.
 Revision received January 6, 2011.
 Accepted January 21, 2010.
 © 2011 American Heart Association, Inc.
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 Garwood M,
 Schleich T,
 Ross BD,
 Matson GB,
 Winters WD
Novelty and Significance
What Is Known?
The mechanisms and relationships between the alterations of myocardial creatine kinase (CK) and left ventricular (LV) contractile dysfunction in failing heart remain undefined.
Although the ^{31}P MRbased magnetization saturation transfer (MST) can measure the activity of the 2 most important energetic enzymes: CK and ATP synthase (ATPase), the conventional MST technique suffers from the lengthy acquisition time such that an in vivo transmurally differentiated enzyme activity measurement could not be obtained in the in vivo failing hearts.
What New Information Does This Article Contribute?
A novel MST method was established theoretically with mathematical and numeric simulation and was verified with in vivo measurements of CK activity of swine hearts, as well as CK and ATPase activities of rat brain at 9.4 Tesla magnetic field.
This novel MST method enables in vivo transmural differentiation studies to examine the CK activity with an unprecedented short data acquisition time.
The in vivo swine study demonstrates that the acute inhibition of CK activity does not limit LV chamber function, suggesting that redundant multiple supporting systems of myocardial ATP production, transportation, and utilization exist in the heart.
This study describes a novel MST method that enables noninvasive in vivo studies for superfast measurements of enzyme kinetics in vivo. By applying this method to an in vivo swine model of myocardial CK inhibition by iodoacetamide, it was found that the acute inhibition of CK activity does not limit LV chamber function, suggesting that there are redundant multiple supporting systems of myocardial ATP production, transportation, and utilization in the heart, such that inhibition of one mechanism does not impair normal LV contractile performance.
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 ATP Production Rate via Creatine Kinase or ATP Synthase In VivoNovelty and SignificanceQiang Xiong, Fei Du, Xiaohong Zhu, Pengyuan Zhang, Piradeep Suntharalingam, Joseph Ippolito, Forum D. Kamdar, Wei Chen and Jianyi ZhangCirculation Research. 2011;108:653663, originally published March 17, 2011https://doi.org/10.1161/CIRCRESAHA.110.231456
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 ATP Production Rate via Creatine Kinase or ATP Synthase In VivoNovelty and SignificanceQiang Xiong, Fei Du, Xiaohong Zhu, Pengyuan Zhang, Piradeep Suntharalingam, Joseph Ippolito, Forum D. Kamdar, Wei Chen and Jianyi ZhangCirculation Research. 2011;108:653663, originally published March 17, 2011https://doi.org/10.1161/CIRCRESAHA.110.231456