Corrections for off-resonance effects and incomplete saturation in conventional (two-site) saturation-transfer kinetic measurements

Rapid, B 1 -insensitive, dual-band quasi-adiabatic saturation transfer with optimal control for complete quantification of myocardial ATP flux

PURPOSE

Phosphorus saturation-transfer experiments can quantify metabolic fluxes noninvasively. Typically, the forward flux through the creatine kinase reaction is investigated by observing the decrease in phosphocreatine (PCr) after saturation of γ-ATP. The quantification of total ATP utilization is currently underexplored, as it requires simultaneous saturation of inorganic phosphate ( P i ) and PCr. This is challenging, as currently available saturation pulses reduce the already-low γ-ATP signal present.

METHODS

Using a hybrid optimal-control and Shinnar-Le Roux method, a quasi-adiabatic RF pulse was designed for the dual saturation of PCr and P i to enable determination of total ATP utilization. The pulses were evaluated in Bloch equation simulations, compared with a conventional hard-cosine DANTE saturation sequence, before being applied to perfused rat hearts at 11.7 T.

RESULTS

The quasi-adiabatic pulse was insensitive to a >2.5-fold variation in B 1 , producing equivalent saturation with a 53% reduction in delivered pulse power and a 33-fold reduction in spillover at the minimum effective B 1 . This enabled the complete quantification of the synthesis and degradation fluxes for ATP in 30-45 minutes in the perfused rat heart. While the net synthesis flux (4.24 ± 0.8 mM/s, SEM) was not significantly different from degradation flux (6.88 ± 2 mM/s, P = .06) and both measures are consistent with prior work, nonlinear error analysis highlights uncertainties in the P_i -to-ATP measurement that may explain a trend suggesting a possible imbalance.

CONCLUSIONS

This work demonstrates a novel quasi-adiabatic dual-saturation RF pulse with significantly improved performance that can be used to measure ATP turnover in the heart in vivo.

Quantification of creatine kinase reaction rate in mouse hindlimb using phosphorus-31 magnetic resonance spectroscopic fingerprinting

The goal of this study was to evaluate the accuracy, reproducibility, and efficiency of a 31 P magnetic resonance spectroscopic fingerprinting (31 P-MRSF) method for fast quantification of the forward rate constant of creatine kinase (CK) in mouse hindlimb. The 31 P-MRSF method acquired spectroscopic fingerprints using interleaved acquisition of phosphocreatine (PCr) and γATP with ramped flip angles and a saturation scheme sensitive to chemical exchange between PCr and γATP. Parameter estimation was performed by matching the acquired fingerprints to a dictionary of simulated fingerprints generated from the Bloch-McConnell model. The accuracy of 31 P-MRSF measurements was compared with the magnetization transfer (MT-MRS) method in mouse hindlimb at 9.4 T (n = 8). The reproducibility of 31 P-MRSF was also assessed by repeated measurements. Estimation of the CK rate constant using 31 P-MRSF (0.39 ± 0.03 s-1 ) showed a strong agreement with that using MT-MRS measurements (0.40 ± 0.05 s-1 ). Variations less than 10% were achieved with 2 min acquisition of 31 P-MRSF data. Application of the 31 P-MRSF method to mice subjected to an electrical stimulation protocol detected an increase in CK rate constant in response to stimulation-induced muscle contraction. These results demonstrated the potential of the 31 P-MRSF framework for rapid, accurate, and reproducible quantification of the chemical exchange rate of CK in vivo.

Characterization of Carbonic Anhydrase In Vivo Using Magnetic Resonance Spectroscopy

Carbonic anhydrase is a ubiquitous metalloenzyme that catalyzes the reversible interconversion of CO2/HCO3-. Equilibrium of these species is maintained by the action of carbonic anhydrase. Recent advances in magnetic resonance spectroscopy have allowed, for the first time, in vivo characterization of carbonic anhydrase in the human brain. In this article, we review the theories and techniques of in vivo 13C magnetization (saturation) transfer magnetic resonance spectroscopy as they are applied to measuring the rate of exchange between CO2 and HCO3- catalyzed by carbonic anhydrase. Inhibitors of carbonic anhydrase have a wide range of therapeutic applications. Role of carbonic anhydrases and their inhibitors in many diseases are also reviewed to illustrate future applications of in vivo carbonic anhydrase assessment by magnetic resonance spectroscopy.

31 P magnetic resonance fingerprinting for rapid quantification of creatine kinase reaction rate in vivo

The purpose of this work was to develop a 31 P spectroscopic magnetic resonance fingerprinting (MRF) method for fast quantification of the chemical exchange rate between phosphocreatine (PCr) and adenosine triphosphate (ATP) via creatine kinase (CK). A 31 P MRF sequence (CK-MRF) was developed to quantify the forward rate constant of ATP synthesis via CK ( kfCK), the T1 relaxation time of PCr ( T1PCr), and the PCr-to-ATP concentration ratio ( MRPCr). The CK-MRF sequence used a balanced steady-state free precession (bSSFP)-type excitation with ramped flip angles and a unique saturation scheme sensitive to the exchange between PCr and γATP. Parameter estimation was accomplished by matching the acquired signals to a dictionary generated using the Bloch-McConnell equation. Simulation studies were performed to examine the susceptibility of the CK-MRF method to several potential error sources. The accuracy of nonlocalized CK-MRF measurements before and after an ischemia-reperfusion (IR) protocol was compared with the magnetization transfer (MT-MRS) method in rat hindlimb at 9.4 T (n = 14). The reproducibility of CK-MRF was also assessed by comparing CK-MRF measurements with both MT-MRS (n = 17) and four angle saturation transfer (FAST) (n = 7). Simulation results showed that CK-MRF quantification of kfCK was robust, with less than 5% error in the presence of model inaccuracies including dictionary resolution, metabolite T2 values, inorganic phosphate metabolism, and B1 miscalibration. Estimation of kfCK by CK-MRF (0.38 ± 0.02 s-1 at baseline and 0.42 ± 0.03 s-1 post-IR) showed strong agreement with MT-MRS (0.39 ± 0.03 s-1 at baseline and 0.44 ± 0.04 s-1 post-IR). kfCK estimation was also similar between CK-MRF and FAST (0.38 ± 0.02 s-1 for CK-MRF and 0.38 ± 0.11 s-1 for FAST). The coefficient of variation from 20 s CK-MRF quantification of kfCK was 42% of that by 150 s MT-MRS acquisition and was 12% of that by 20 s FAST acquisition. This study demonstrates the potential of a 31 P spectroscopic MRF framework for rapid, accurate and reproducible quantification of chemical exchange rate of CK in vivo.

In-vivo31P-MRS of skeletal muscle and liver: A way for non-invasive assessment of their metabolism

In addition to direct assessment of high energy phosphorus containing metabolite content within tissues, phosphorus magnetic resonance spectroscopy (³¹P-MRS) provides options to measure phospholipid metabolites and cellular pH, as well as the kinetics of chemical reactions of energy metabolism in vivo. Even though the great potential of ³¹P-MR was recognized over 30 years ago, modern MR systems, as well as new, dedicated hardware and measurement techniques provide further opportunities for research of human biochemistry. This paper presents a methodological overview of the ³¹P-MR techniques that can be used for basic, physiological, or clinical research of human skeletal muscle and liver in vivo. Practical issues of ³¹P-MRS experiments and examples of potential applications are also provided. As signal localization is essential for liver ³¹P-MRS and is important for dynamic muscle examinations as well, typical localization strategies for ³¹P-MR are also described.

A simple approach to evaluate the kinetic rate constant for ATP synthesis in resting human skeletal muscle at 7 T

Inversion transfer (IT) is a well-established technique with multiple attractive features for analysis of kinetics. However, its application in measurement of ATP synthesis rate in vivo has lagged behind the more common saturation transfer (ST) techniques. One well-recognized issue with IT is the complexity of data analysis in comparison with much simpler analysis by ST. This complexity arises, in part, because the γ-ATP spin is involved in multiple chemical reactions and magnetization exchanges, whereas Pi is involved in a single reaction, Pi → γ-ATP. By considering the reactions involving γ-ATP only as a lumped constant, the rate constant for the reaction of physiological interest, kPi→γATP , can be determined. Here, we present a new IT data analysis method to evaluate kPi→γATP using data collected from resting human skeletal muscle at 7 T. The method is based on the basic Bloch-McConnell equation, which relates kPi→γATP to m˙Pi, the rate of Pi magnetization change. The kPi→γATP value is accessed from m˙Pi data by more familiar linear correlation approaches. For a group of human subjects (n = 15), the kPi→γATP value derived for resting calf muscle was 0.066 ± 0.017 s(-1) , in agreement with literature-reported values. In this study we also explored possible time-saving strategies to speed up data acquisition for kPi→γATP evaluation using simulations. The analysis indicates that it is feasible to carry out a (31) P IT experiment in about 10 min or less at 7 T with reasonable outcome in kPi→γATP variance for measurement of ATP synthesis in resting human skeletal muscle. We believe that this new IT data analysis approach will facilitate the wide acceptance of IT to evaluate ATP synthesis rate in vivo. Copyright © 2015 John Wiley & Sons, Ltd.

Amplification of the effects of magnetization exchange by (31) P band inversion for measuring adenosine triphosphate synthesis rates in human skeletal muscle

PURPOSE

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

METHODS

The strategy works by simultaneously inverting the (31) P resonances of phosphocreatine (PCr) and ATP using a wide bandwidth, adiabatic inversion radiofrequency pulse followed by observing dynamic changes in intensity of the noninverted Pi signal versus the delay time between the inversion and observation pulses. This band inversion technique significantly delays recovery of γ-ATP magnetization; 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 two-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 two-site exchange model.

(31)P-MRS of healthy human brain: ATP synthesis, metabolite concentrations, pH, and T1 relaxation times

The conventional method for measuring brain ATP synthesis is (31)P saturation transfer (ST), a technique typically dependent on prolonged pre-saturation with γ-ATP. In this study, ATP synthesis rate in resting human brain is evaluated using EBIT (exchange kinetics by band inversion transfer), a technique based on slow recovery of γ-ATP magnetization in the absence of B1 field following co-inversion of PCr and ATP resonances with a short adiabatic pulse. The unidirectional rate constant for the Pi → γ-ATP reaction is 0.21 ± 0.04 s(-1) and the ATP synthesis rate is 9.9 ± 2.1 mmol min(-1)  kg(-1) in human brain (n = 12 subjects), consistent with the results by ST. Therefore, EBIT could be a useful alternative to ST in studying brain energy metabolism in normal physiology and under pathological conditions. In addition to ATP synthesis, all detectable (31)P signals are analyzed to determine the brain concentration of phosphorus metabolites, including UDPG at around 10 ppm, a previously reported resonance in liver tissues and now confirmed in human brain. Inversion recovery measurements indicate that UDPG, like its diphosphate analogue NAD, has apparent T1 shorter than that of monophosphates (Pi, PMEs, and PDEs) but longer than that of triphosphate ATP, highlighting the significance of the (31)P-(31)P dipolar mechanism in T1 relaxation of polyphosphates. Another interesting finding is the observation of approximately 40% shorter T1 for intracellular Pi relative to extracellular Pi, attributed to the modulation by the intracellular phosphoryl exchange reaction Pi ↔ γ-ATP. The sufficiently separated intra- and extracellular Pi signals also permit the distinction of pH between intra- and extracellular environments (pH 7.0 versus pH 7.4). In summary, quantitative (31)P MRS in combination with ATP synthesis, pH, and T1 relaxation measurements may offer a promising tool to detect biochemical alterations at early stages of brain dysfunctions and diseases.

Two repetition time saturation transfer (TwiST) with spill-over correction to measure creatine kinase reaction rates in human hearts

BACKGROUND

Phosphorus saturation transfer (ST) magnetic resonance spectroscopy can measure the rate of ATP generated from phosphocreatine (PCr) via creatine kinase (CK) in the human heart. Recently, the triple-repetition time ST (TRiST) method was introduced to measure the CK pseudo-first-order rate constant kf in three acquisitions. In TRiST, the longitudinal relaxation time of PCr while γ-ATP is saturated, T1`, is measured for each subject, but suffers from low SNR because the PCr signal is reduced due to exchange with saturated γ-ATP, and the short repetition time of one of the acquisitions. Here, a two-repetition time ST (TwiST) method is presented. In TwiST, the acquisition with γ-ATP saturation and short repetition time is dropped. Instead of measuring T1`, an intrinsic relaxation time T1 for PCr, T1 (intrinsic), is assumed. The objective was to validate TwiST measurements of CK kinetics in healthy subjects and patients with heart failure (HF).

METHODS

Bloch equation simulations that included the effect of spillover irradiation on PCr were used to derive formulae for T1 (intrinsic) and kf measured by both TRiST and TwiST methods. Spillover was quantified from an unsaturated PCr measurement used in the current protocol for determining PCr and ATP concentrations. Cardiac TRiST and TwiST data were acquired at 3 T from 12 healthy and 17 HF patients.

RESULTS

Simulations showed that both kf measured by TwiST and T1 (intrinsic) require spill-over corrections. In human heart at 3 T, the spill-over corrected T1 (intrinsic) = 8.4 ± 1.4 s (mean ± SD) independent of study group. TwiST and TRiST kf measurements were the same, but TwiST was 9 min faster. Spill-over corrected TwiST kf was 0.33 ± 0.08 s(-1) vs. 0.20 ± 0.06 s(-1) in healthy vs HF hearts, respectively (p < 0.0001).

CONCLUSION

TwiST was validated against TRiST in the human heart at 3 T, generating the same results 9 min faster. TwiST detected significant reductions in CK kf in HF compared to healthy subjects, consistent with prior 1.5 T studies using different methodology.

Exchange kinetics by inversion transfer: integrated analysis of the phosphorus metabolite kinetic exchanges in resting human skeletal muscle at 7 T

PURPOSE

To develop an inversion pulse-based, chemical exchange saturation transfer-like method for detection of (31) P magnetization exchanges among all nuclear magnetic resonance visible metabolites suitable for providing an integrated kinetic analysis of phosphorus exchange reactions in vivo.

METHODS

The exchange kinetics by inversion transfer (EKIT) sequence includes application of a frequency-selective inversion pulse arrayed over the range of relevant (31) P frequencies, followed by a constant delay and a hard readout pulse. A series of EKIT spectra, each given by a plot of Z-magnetization for each metabolite of interest versus frequency of the inversion pulse, can be generated from this single data set.

RESULTS

EKIT spectra reflect chemical exchange due to known biochemical reactions, cross-relaxation effects, and relayed magnetization transfers due to both processes. The rate constants derived from EKIT data collected on resting human skeletal muscle were: ATP synthesis via ATP synthase (0.050 ± 0.016 s(-1) ), ATP synthesis via creatine kinase (0.264 ± 0.023 s(-1) ), and cross-relaxation between neighboring spin pairs within ATP (0.164 ± 0.022 s(-1) ).

CONCLUSION

EKIT provides a simple, alternative method to detect chemical exchange, cross relaxation, and relayed magnetization transfer effects in human skeletal muscle at 7 T.

One-dimensional image-selected in vivo spectroscopy localized phosphorus saturation transfer at 7T

PURPOSE

To evaluate the feasibility of a one-dimensional image-selected in vivo spectroscopy (1D-ISIS) saturation transfer (ST) sequence at 7T for localized in vivo measurements of energy metabolism in different tissues in clinically reasonable examination times.

METHODS

The performance of a gradient offset independent adiabacity-based 1D-ISIS localization was tested on phantom and the localized ST sequence was compared with the nonlocalized version in vivo. We performed localized measurements of basal metabolism of human liver and different muscle groups of the calf. Localized ST experiments took 15-25 minutes.

RESULTS

The selectivity of the 1D-ISIS sequence was 81.63% and the outer volume suppression was 97.57%. The ST parameters acquired with the 1D-ISIS sequence and with the nonlocalized acquisition in the muscle were not statistically different. The forward rate constants for phosphocreatine (PCr)-adenosine triphosphate (ATP) and inorganic phosphate (Pi)-ATP exchange reactions were measured in the soleus (kCK  = 0.30 ± 0.06 s(-1) and kATP  = 0.11 ± 0.02 s(-1) , respectively) and in the medial gastrocnemius (kCK  = 0.27 ± 0.06 s(-1) and kATP  = 0.09 ± 0.03s(-1) , respectively) in 15 minutes per muscle group. The corresponding fluxes were FCK  = 6.26 ± 1.28 μmol/g/s, FATP  = 0.22 ± 0.05 μmol/g/s and FCK  = 6.29 ± 1.66 μmol/g/s, FATP  = 0.21 ± 0.07 μmol/g/s, for soleus and gastrocnemius, respectively. The hepatic ATP synthesis measurement was feasible in 24 minutes.

CONCLUSION

The fast assessment of PCr-ATP and Pi-ATP exchange rates at 7T makes the 1D-ISIS ST sequence a promising tool for examining local resting-state metabolism in clinically acceptable measurement times.

Assessment of in vivo mitochondrial metabolism by magnetic resonance spectroscopy

Magnetic resonance spectroscopy (MRS), a companion technique to the more familiar MRI scan, has emerged as a powerful technique for studying metabolism noninvasively in a variety of tissues. In this article, we review two techniques that we have developed which take advantage of the unique characteristics of (31)P and (13)C MRS to investigate two distinct parameters of muscle mitochondrial metabolism; ATP production can be estimated by using the (31)P saturation-transfer technique, and oxidation via the TCA cycle can be modeled from (13)C MRS data obtained during the metabolism of a (13)C-labeled substrate. We will also examine applications of the techniques to investigate how these parameters of muscle mitochondrial metabolism are modulated in insulin resistant and endurance trained individuals.

Correcting reaction rates measured by saturation-transfer magnetic resonance spectroscopy

Off-resonance or spillover irradiation and incomplete saturation can introduce significant errors in the estimates of chemical rate constants measured by saturation-transfer magnetic resonance spectroscopy (MRS). Existing methods of correction are effective only over a limited parameter range. Here, a general approach of numerically solving the Bloch-McConnell equations to calculate exchange rates, relaxation times and concentrations for the saturation-transfer experiment is investigated, but found to require more measurements and higher signal-to-noise ratios than in vivo studies can practically afford. As an alternative, correction formulae for the reaction rate are provided which account for the expected parameter ranges and limited measurements available in vivo. The correction term is a quadratic function of experimental measurements. In computer simulations, the new formulae showed negligible bias and reduced the maximum error in the rate constants by about 3-fold compared to traditional formulae, and the error scatter by about 4-fold, over a wide range of parameters for conventional saturation transfer employing progressive saturation, and for the four-angle saturation-transfer method applied to the creatine kinase (CK) reaction in the human heart at 1.5 T. In normal in vivo spectra affected by spillover, the correction increases the mean calculated forward CK reaction rate by 6-16% over traditional and prior correction formulae.

Inverse polarization transfer for detecting in vivo 13C magnetization transfer effect of specific enzyme reactions in 1H spectra

The wide chemical shift dispersion and long T(1) of (13)C have allowed determination of in vivo magnetization transfer effects caused by aspartate aminotransferase and lactate dehydrogenase reactions using (13)C magnetic resonance spectroscopy. In this report, we demonstrate that these effects can be observed in the proton spectra by transferring the equilibrium magnetization of (13)C via the one-bond scalar coupling between (13)C and (1)H using an inverse insensitive nuclei enhanced by polarization transfer-based heteronuclear polarization transfer method. This inverse method allows a combination of the advantages of the long (13)C T(1) for maximum magnetization transfer and the high sensitivity of proton detection. The feasibility of this in vivo inverse polarization transfer approach was evaluated for detecting the (13)C magnetization transfer effect of aspartate aminotransferase and lactate dehydrogenase reactions from a 72.5-microl voxel in the rat brain at 11.7 T.

Measurement of spin-lattice relaxation times and chemical exchange rates in multiple-site systems using progressive saturation

A new method for measuring spin-lattice relaxation times and chemical exchange (CE) rate constants in multiple-site exchanging systems is described. The method, chemical exchange and T(1) measurement using progressive saturation (CUPS), was applied to determine T(1)s and analyze phosphorus exchange among phosphocreatine (PCr), ATP, and inorganic phosphate (Pi), mediated by creatine kinase (CK) and ATP synthase, using (31)P-MRS. Two-site exchange was analyzed in vitro and in the rat leg, and three-site exchange was analyzed in the rat heart. Data were fitted to a model of progressive saturation incorporating T(1) relaxation and CE. For the in vitro system at 8.45 T, we found T(1)(PCr)=2.86 s and T(1)(gamma-ATP)=1.72 s. For the rat gastrocnemius at 1.9T, we found T(1)(PCr) = 6.60 s and T(1)(gamma-ATP) = 2.06 s. For the rat heart at 9.4 T, we found T(1)(PCr)=3.35 s, T(1)(gamma-ATP)=0.69 s, and T(1)(Pi=1.83 s. All of these values were within 20% of literature values. Similarly, the determined exchange rates were in the same range as published values. Using simulations, we compared CUPS with transient saturation transfer as a method for measuring T(1)s and rates. The two methods showed similar sensitivity to noise. We conclude that CUPS is a viable alternative for measuring T(1)s and CE rates in exchanging systems.

Quantifying exchange rates in chemical exchange saturation transfer agents using the saturation time and saturation power dependencies of the magnetization transfer effect on the magnetic resonance imaging signal (QUEST and QUESP): Ph calibration for poly-L-lysine and a starburst dendrimer

The ability to measure proton exchange rates in tissue using MRI would be very useful for quantitative assessment of magnetization transfer properties, both in conventional MT imaging and in the more recent chemical exchange saturation transfer (CEST) approach. CEST is a new MR contrast mechanism that depends on several factors, including the exchange rate of labile protons in the agent in a pH-dependent manner. Two new methods to monitor local exchange rate based on CEST are introduced. The two MRI-compatible approaches to measure exchange are quantifying exchange using saturation time (QUEST) dependence and quantifying exchange using saturation power (QUESP) dependence. These techniques were applied to poly-L-lysine (PLL) and a generation-5 polyamidoamine dendrimer (SPD-5) to measure the pH dependence of amide proton exchange rates in the physiologic range. Data were fit both to an analytical expression and to numerical solutions to the Bloch equations. Results were validated by comparison with exchange rates determined by two established spectroscopic methods. The exchange rates determined using the four methods were pooled for the pH-calibration curve of the agents consisting of contributions from spontaneous (k0) acid catalyzed (ka), and base catalyzed (kb) exchange rate constants. These constants were k0 = 68.9 Hz, ka = 1.21 Hz, kb = 1.92 x 10(9) Hz, and k0 = 106.4 Hz, ka = 25.8 Hz, kb = 5.45 x 10(8) Hz for PLL and SPD-5, respectively, showing the expected predominance of base-catalyzed exchange for these amide protons.

Theoretical analysis of carbon-13 magnetization transfer for in vivo exchange between alpha-ketoglutarate and glutamate

Many enzymes catalyze fast exchange between a small pool and a large pool in vivo. For example, aspartate aminotransferase catalyzes fast exchanges between alpha-ketoglutarate and glutamate and between oxaloacetate and aspartate, which can be detected using in vivo(13)C MRS while saturating alpha-carbons of the keto acids. Unlike in the traditional saturation transfer experiments studied using (31)P MRS, the tricarboxylic acid cycle intermediates alpha-ketoglutarate and oxaloacetate are below the detection limit of in vivo NMR. In this work, a theoretical analysis of the saturation transfer between alpha-ketoglutarate and glutamate catalyzed by aspartate aminotransferase was presented to examine the requirements for complete saturation of the rapidly turning over alpha-ketoglutarate pool without affecting the longitudinal magnetization of glutamate. The fast turnover of the small alpha-ketoglutarate pool also allows a quasi-steady-state approximation of its dynamic longitudinal relaxation. The theoretical analysis provides a useful guide for designing experimental methods to characterize saturation transfer processes associated with fast turning over small pools in vivo.

Optimization of the irradiation power in chemical exchange dependent saturation transfer experiments

In chemical exchange dependent saturation transfer imaging experiments, exchangeable solute protons are saturated and the transfer of saturation to water is subsequently detected. When the applied irradiation power is comparable to the resonance frequency difference between the water protons and saturated solute protons, the proton transfer (PT) efficiency is reduced due to concomitant direct saturation effects. In this study, the PT process is modeled using a two-pool system. An empirical general proton transfer ratio (PTR) equation for arbitrary RF irradiation power is derived, and its optimal power to maximize the PTR is analyzed. The results are confirmed experimentally on 4.7 T using a poly-L-lysine solution. The theory provides a useful tool for optimizing the irradiation power of the PT sequences in the presence of direct saturation effects.

Quantitative description of proton exchange processes between water and endogenous and exogenous agents for WEX, CEST, and APT experiments

The proton exchange processes between water and solutes containing exchangeable protons have recently become of interest for monitoring pH effects, detecting cellular mobile proteins and peptides, and enhancing the detection sensitivity of various low-concentration endogenous and exogenous species. In this work, the analytic expressions for water exchange (WEX) filter spectroscopy, chemical exchange-dependent saturation transfer (CEST), and amide proton transfer (APT) experiments are derived by the use of Bloch equations with exchange terms. The effects of the initial states for the system, the difference between a steady state and a saturation state, and the relative contributions of the forward and backward exchange processes are discussed. The theory, in combination with numerical calculations, provides a useful tool for designing experimental schemes and assessing magnetization transfer (MT) processes between water protons and solvent-exchangeable protons. As an example, the case of endogenous amide proton exchange in the rat brain at 4.7 T is analyzed in detail.

Quantitative magnetization transfer imaging of pre-lesional white-matter changes in multiple sclerosis

OBJECTIVE

Previous magnetization transfer (MT) studies in multiple sclerosis (MS) suggest a reduction of the MT ratio (MTR) precedes new lesion development. To gain further insight into pre-lesional tissue abnormalities, we investigated the time course of additional quantitative MT parameters.

METHODS

Serial magnetic resonance imaging (MRI), including a gadolinium-enhanced T1 scan and MT imaging by means of a FastPACE sequence, was performed on 12 patients (4 males, 8 females) with relapsing-remitting MS. Quantitative MT values including the magnetization exchange rate (kfor) and the native relaxation time (T1free were analysed in the six months prior to the appearance of 44 enhancing lesions and in 88 control regions of persistently normal-appearing white matter (NAWM).

RESULTS

Appearance of new active lesions was preceded by a significant decrease of the MTR (F7,166=91.5; p<0.0001) and of kfor (F7,166=105.2; p<0.0001), and by an increase of T1free (F7,166=57.3; p<0.0001). The drop of kfor was the most pronounced pre-lesional change and together with the MTR was statistically significant already four months before the appearance of new lesion. The observed increase of T1free was relatively small. MT variables of reactivated lesions were always different from NAWM but showed no characteristic time course.

CONCLUSIONS

Multiparametric MT measurements suggest both a reduction of macromolecular material and a focal increase of free water to occur several months before the appearance of an active lesion. Reduction of the magnetization exchange rate, which may result from primary damage to myelin, appears to be the leading event

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

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.

Correcting for incomplete saturation and off-resonance effects in multiple-site saturation-transfer kinetic measurements

The effects of incomplete saturation and off-resonance irradiation on nuclear magnetic resonance saturation-transfer measurements of three-site chemical-exchange rates are discussed. A new method that uses double-saturation measurements is compared with two published methods, one that uses single-saturation measurements and one that uses a single-saturation measurement and a double-saturation measurement. Several formulas are compared for measuring the exchange rate constant k(DE) for exchange from a detected spin D to an exchanging spin E in the presence of exchange from spin D to a competing spin C. For each method, formulas are derived with corrections for incomplete saturation or off-resonance effects, with both corrections, and with neither correction. Exact formulas are available for three exchanging sites with incomplete saturation if there are no off-resonance effects. Off-resonance corrections are imperfect even with complete saturation.