Magnetic Resonance in Medicine 55:498 –505 (2006)
T1 Measurement of 31P Metabolites at Rest and during Steady-State Dynamic Exercise Using a Clinical Nuclear Magnetic Resonance Scanner V. Cettolo, C. Piorico, and M. P. Francescato* This article illustrates some problems and possible solutions to determine the apparent spin–lattice relaxation time (T1) of the muscular 31P metabolites at rest and during dynamic steadystate exercise using a clinical 1.5 T NMR scanner and a surface coil. T1 was first estimated on a phosphates solution (phantom) using four different acquisition protocols, all based on the multiple-point “progressive saturation” method, and by fitting each data set with two different mathematical models. Subsequently, two of the four protocols and both models were used to estimate T1 both at rest and during exercise on the calf muscles of 10 healthy volunteers. Experimental results obtained on the phantom showed that T1 is greatly affected by the longest nominal explored repetition time (P < 0.001) and by the mathematical model (P < 0.001), ranging from 0.65 ⴞ 0.10 to 8.4 ⴞ 0.8 s. The two acquisition protocols applied on volunteers yielded significantly different T1 (P < 0.001), which were also rather different from the literature values for the same metabolites. Nevertheless, independently of the acquisition protocol and/or the fitting procedure, T1 of all muscular phosphagens did not change statistically from rest to steady-state aerobic exercise. Magn Reson Med 55:498 –505, 2006. © 2006 WileyLiss, Inc. Key words: T1 time constant; human calf muscles; aerobic exercise; 31P-MRS; spin–lattice relaxations
The availability of phosphorus magnetic resonance spectroscopy (31P-MRS) on standard clinical units enabled researchers to assess high-energy phosphates noninvasively in human skeletal muscles under different experimental conditions (i.e., at rest, during steady-state exercise, or during rest-to-work or work-to-rest transients) (1–9). To maximize the signal-to-noise ratio per unit time of the experiment, data are usually collected under partially saturated conditions, applying the same acquisition protocol regardless of the different metabolic states. This is considered sufficient to guarantee that the change in the MRS peak intensity of the different metabolites is strictly proportional to their concentration changes only and thus no correction is made when the relative change in concentration is calculated. It also follows that when an absolute quantification must be performed, a single saturation factor, determined during the control state, is commonly ap-
plied to scale up the signal intensities to completely relaxed conditions. Different metabolic conditions of the tissue, however, may correspond to different apparent T1 spin–lattice relaxation times of the species under consideration, which include the effects of the different chemical exchange and of the intrinsic T1. If this is true, a single proportionality constant between signal intensity and concentration no longer applies. Thus, to calculate relative changes in concentration and/or their absolute values, specific saturation factors would be needed for each different metabolic status. Alternatively, the knowledge of the apparent T1 would allow an estimate of the saturation factors, provided the experimental acquisition parameters are also known. The apparent T1 of 31P metabolites have been investigated both in animal models (10 –13) and in humans, for which data are available mainly for resting conditions (14 –20). During dynamic exercise, the phosphocreatine (PC) T1 values are sometimes a by-product of investigations concerning the mechanism of creatine phosphokinase reaction (21,22). These works indicate that, both in forearm and in calf muscles, PC T1 does not change significantly during exercise. More recently, Newcomer and Boska (23), using a 1.5 T NMR unit, have attempted to elucidate the possible changes in T1 of all the most important 31P metabolites during voluntary submaximal isometric plantar flexion compared to rest. In contrast with previous data obtained during dynamic exercise, the results of these authors show that the PC T1 changes significantly. Variations in pH and/or net rate of PC breakdown associated with exercise are indicated as the main determinants. The assumption of a constant value of the high-energy phosphates T1 in different metabolic conditions seems thus rather questionable. The aim of the present study was to determine, on a standard clinical NMR unit, the apparent T1 (T1) of the main 31P muscle metabolites (Pi, PC, ␣ATP, ␥ATP, ATP) during rhythmic steady-state plantar flexion of well-controlled intensity, applying acquisition protocols similar to those usually used to study physiologic phenomena. MATERIALS AND METHODS
Dipartimento di Scienze e Tecnologie Biomediche and M.A.T.I. Centre of Excellence, Universita` degli Studi di Udine, Udine, Italy. *Correspondence to: Maria Pia Francescato, Dipartimento di Scienze e Tecnologie Biomediche, Universita` degli Studi di Udine, P.le Kolbe 4, 33100 Udine, Italy. E-mail:
[email protected] Received 24 January 2005; revised 1 October 2005; accepted 2 November 2005 DOI 10.1002/mrm.20803 Published online 31 January 2006 in Wiley InterScience (www.interscience. wiley.com). © 2006 Wiley-Liss, Inc.
All experiments were performed on a standard wholebody Magnetom SP 4000, 1.5 T scanner (Siemens, Erlangen, D), located at the Radiology Unit of the School of Medicine of the University of Udine (Italy). The unit was equipped with a double tuned (1H–31P) 5 cm diameter transmitter and receiver surface coil and a spectroscopy sequence (24) provided by the manufacturer. Excitation consisted of a 500 s rectangular radiofrequency (RF) pulse; acquisition of free induction decay
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TABLE 1 Specific Acquisition Parameters Used for the Four Different PS Protocols Acquisition parameter NTR TR (ms)
nm nacq nps TAtot (min)
Protocol LA
Protocol LB
Protocol SA
Protocol SB
15 601, 801, 1201, 1601, 2001, 2601, 4601, 6601, 8601, 10601, 12601, 14601, 16601, 18601, 20000 1
15 601, 801, 1001, 1201, 1601, 2601, 4601, 6601, 8601, 10601, 12601, 14601, 16601, 18601, 20000 10, 9, 9, 8, 8, 7, 7, 7, 6, 6, 6, 6, 6, 6, 6 3 0
6 601, 801, 1201, 2001, 3601, 6801
7 601, 701, 801, 901, 1001, 1101, 1201
1
10, 10, 9, 9, 9, 9, 9
16 25, 19, 12, 7, 4, 2
3 0
54.07
5.92
6.31
16 25, 19, 12, 9, 7, 6, 4, 3, 3, 2, 2, 2, 2, 1, 1 40.02
Note. NTR, ⫽ number of investigated TR (each with a separate spectral collection); TR ⫽ time intervals used; nm ⫽ number of spectra collected for the corresponding TR ⫽ nacq, number of accumulated FIDs; nps ⫽ number of dummy scans applied for the corresponding TR; TAtot ⫽ estimated total time spent to complete once the protocol.
(FID), in 2048 complex data points, started 250 s after the end of the RF pulse and was performed with a dwell time of 250 s. The sequence allows the investigator to collect automatically a series of nm spectra with the same acquisition parameters. Each spectrum corresponds to the sum of nacq FID acquisitions, separated by the same time interval TR; prior to the start of accumulation, a series of nps dummy scans can be applied, while an initial TR time interval and a final waiting interval (⌬) amounting to 1.25 s are always introduced. Thus, the time necessary to acquire each spectrum amounts to: T m⫽TR䡠(1⫹n ps⫹n acq)⫹⌬
[1]
and, to collect automatically the nm different spectra, the overall time (TA) amounts to: TA⫽n m䡠T m ,
[2]
to which the time required to transfer and store the data (about 1 s for each spectrum) must be added. To acquire spectra with different TR, nps, and/or nacq it is necessary to run the sequence again. Experimental data were obtained first on a phosphate solution (phantom) and subsequently on a group of volunteers. The global shimming procedure on the proton signal of water was performed before each experimental session until the peak was approximately Lorentzian in shape. The final mean peak width at one-half maximum was 8.2 ⫾ 3.2 Hz (mean ⫾ SD) for the phantom studies and 17.6 ⫾ 3.2 Hz (mean ⫾ SD) for the human cases. After switching to 31P, one of four acquisition protocols based on the progressive saturation (PS) technique (25) was applied to estimate the apparent T1. According to this technique, several spectra with different time intervals TR were recorded and the peak areas of the resonances were then plotted against TR. A monoexponential fit of these data allowed us to calculate T1.
Phantom Studies The phantom was provided by the NMR unit manufacturer and consisted of a cylindrical Plexiglas bottle containing 5.88 g of sodium chloride (NaCl), 1 cm3 85% weight of phosphoric acid (H3PO4), and 7.58 g of sodium phosphate dodecahydrate (Na3PO4 䡠 12H2O) dissolved in 1 kg distilled water. Four variants of the PS method were applied (i.e., acquisition protocols LA, LB, SA, and SB). Each protocol consisted of a series of subsequent spectral collections, each with a different TR, the number of which is indicated in Table 1. In turn, each spectral collection was performed after having set the appropriate parameters, which are also detailed in Table 1. Each protocol yielded a complete PS data set. The partial saturation condition was ensured for all protocols by disregarding an initial time interval lasting about three times the expected T1 (⬃6 s), i.e., dummy scans were applied in protocols LA and SA, while the first collected spectra were discarded in protocols LB and SB, for which only the last six collected spectra were subsequently averaged off-line (see Data Treatment). Each acquisition protocol was completed six times in different days, yielding six complete PS data sets for each protocol. Actual overall time spent to complete the specific protocol was checked by means of a stopwatch. Protocols LA and LB aimed at estimating with good accuracy the T1 on the phantom. Thus, the whole available TR range (i.e., 601–20000 ms) was explored. A rather high number of short TR values was used to obtain more information on the saturation phenomena under these conditions. Protocols SA and SB were designed to collect all the data needed to estimate T1 within one entire exercise cycle for a volunteer (described further), i.e., in a time interval of about 7 min, which corresponds to the duration of a constant intensity calf exercise in humans (e.g., see Refs. 4, 8, 9). Two other constraints for protocols SA and SB were as follows: (1) In the allotted time window (7 min), each protocol had to contain the largest possible number of TRs. In the case of protocol SA the duration of each individual
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TR increased exponentially (see Table 1), whereas in protocol SB, each individual TR increased by 100 ms over the preceding one, i.e., the most commonly used TRs in physiologic studies were applied. (2) For each TR value, the obtained spectrum had to be composed of at least 16 FID acquisitions, either accumulated by the system or averaged during postprocessing. Human Studies Ten healthy adults (9 males and 1 female of mean (⫾ SD) age 24.7 ⫾ 3.7 years) volunteered to be subjects after having been thoroughly informed about the aims and methods of the protocol. Average (⫾ SD) height and body mass of the subjects was 1.79 ⫾ 0.05 m and 72.1 ⫾ 8.0 kg, respectively. All subjects were healthy and moderately active, but none was highly trained. The local ethics committee approved the study. During the same experimental session, each volunteer repeated three times the trial lying in a supine position on a specially designed nonferromagnetic calf ergometer, described in detail in a previous paper (26). In turn, each trial consisted of about 7 min rest followed by about 7 min steady-state rhythmic exercise. A waiting interval of at least 5 min separated the trials. The three repeated exercise periods were kept at moderate intensity and consisted of repeated synchronous plantar flexions (about 30°) of both feet against the same resistance, with the knee extended, at a frequency of 0.83 Hz (imposed by a metronome). Subjects monitored the amplitude of plantar flexion on a LED bar fixed at eye level and were asked to control carefully amplitude and frequency of movement. Adjustable straps and belts maintained subjects’ feet and body in the appropriate position on the pedals and on the main frame, thus minimizing unwanted movements and muscle contractions. Actual mechanical power was calculated from the outputs of the force and displacement transducers of the ergometer (26). 31 P-MR spectra were acquired from the triceps surae, positioning the surface coil on the middle of the belly of the gastrocnemius medialis muscle of the right leg. The 10 subjects were divided randomly into two groups, composed of 6 or 4 volunteers, respectively. Protocol SA was applied on the first group in all three trials, whereas the second group underwent protocol SB in all three trials. During each trial, all the spectral collections of the appropriate protocol (SA or SB) were performed one after the other twice, once at rest, and once during the exercise period. Thus, overall, six complete PS data sets were obtained for each subject (three at rest and three during exercise). During exercise the spectroscopy sequence was started at least 10 s after the onset of exercise. The repetition of the trials allowed us to increase the total number of PS data sets available to estimate the corresponding T1. Data Treatment Off-line, prior to further data treatment, the average spectrum of the last six spectra collected with the same TR during the same repetition was calculated for protocols LB and SB, resulting in a series of new spectra each composed of more than 16 acquisitions. Subsequently, spectroscopy
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data were analyzed with the MRUI software (27). Peak areas (S) and spectral peak positions were determined by means of the time-domain VARPRO/minpack fitting program, using the appropriate starting values. The unique peak of inorganic phosphate was estimated for the spectra acquired on the phantom, without any prior knowledge. For the spectra collected on volunteers, the five main peaks (Pi, PC, ␥ATP, ␣ATP, and ATP) were considered. No constraints were imposed to Pi and PC peaks, whereas the classic constraints for a 1.5 T spectrometer were applied for the three ATP peaks; in detail, line widths, Jcoupling constants, and phases of all ATP peaks were linked to each other and peak intensities were constrained to the ratios reported by the MRUI Manual (28). Intracellular pH, when appropriate, was calculated from the equation (29, 30):
pH⫽6.75⫹Log
冉
冊
␦⫺3.27 , 5.69⫺␦
[3]
where ␦ equals the chemical shift of the Pi spectral peak relative to PC (in parts per million). Two models were fitted to the S values of the PS data sets as a function of the TR values. The first time the fitting procedure had three free parameters (T1, S0, and b; compensated exponential model, CeM), whereas the second time only two parameters were free (b was set equal to 1 and a simple exponential model, SeM, was used). For protocols LA and SA the following equation was applied:
冉
冊
TR
S(TR)⫽S0 䡠 1⫺b 䡠 e⫺ T 1 .
[4]
Each spectrum collected with protocols LB and SB was made up by the sum of three consecutive acquisitions, the first of which was separated from the last acquisition of the preceding spectrum by a time interval amounting to 2 TR ⫹ ⌬ (see Eq. [1]), while the last two acquisitions were separated by only one TR. Therefore, the fitting was performed with a modified equation, as follows:
冉
冊
2TR⫹⌬ T1
S(TR)⫽S0 䡠 1⫺b 䡠 e⫺
冉
冊
TR
⫹2S0 䡠 1⫺b 䡠 e⫺ T 1 .
[5]
Chi-square fitting was applied to determine the best fit for all models. Custom software, based on the algorithms reported by Numerical Recipes (31), was used. Chi-square (2) was calculated using for each data point the SD obtained with the VARPRO spectral analysis program. The statistical probability level of 2, for the appropriate degrees of freedom (number of data couples minus number of estimated parameters), was determined. Only fittings with Q ⬎ 0.05 were considered for subsequent analyses. Statistics were performed using a commercially available statistical package (SPSS, SPSS, Inc., Chicago, IL, USA). Multivariate analysis of variance (MANOVA), followed, if appropriate, by specific contrasts and two-tailed Student’s t test, was applied; a value of P ⬍ 0.05 was assumed as the significance level. All values are expressed as means ⫾ SD.
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1.22 s fitting the data obtained by means of protocol LA with SeM and CeM, respectively, while the fittings of the data obtained by means of protocol LB yielded an average T1 of 3.99 ⫾ 0.36 and 8.42 ⫾ 0.81 s applying SeM and CeM, respectively. Average T1 values obtained by means of the two short acquisition protocols (i.e., SA and SB) amounted to 1.77 ⫾ 0.10 and 0.65 ⫾ 0.10 s and to 4.42 ⫾ 0.51 and 5.98 ⫾ 0.51 s, applying SeM and CeM, respectively. Analysis of variance showed that the four acquisition protocols provided significantly different results (MANOVA, Protocol effect, F ⫽ 45.6, P ⬍ 0.001), with values estimated with CeM being significantly higher than those obtained with SeM (MANOVA, Model effect, F ⫽ 1132, P ⬍ 0.001). The values of the parameter b were not significantly different when estimated from the data acquired with the four different acquisition protocols (ANOVA, F ⫽ 0.14, P ⫽ 0.93), amounting on average to 0.79 ⫾ 0.02 (n ⫽ 6 ⫻ 4). Figure 2 illustrates, as a function of the maximal TR set on the console, the T1 values calculated on partial data sets of the protocols LA and LB (obtained by discarding progressively the data corresponding to the highest TR value considered for the previous estimate). Figure 2 shows that the estimated T1 increases with the maximal TR used (MANOVA, TR effect, F ⫽ 76.8, P ⬍ 0.001) and that the partial estimates of protocol LB, for the same maximal TR, yield greater T1 values compared to LA (MANOVA, Protocol effect, F ⫽ 71.2, P ⬍ 0.001). The b value obtained for the partial data sets was not influenced by the highest TR considered (MANOVA, TR effect, F ⫽ 0.05, P ⫽ 0.88). FIG. 1. Average signal intensities obtained for different TR values on the phantom by means of the two long acquisition protocols (LA and LB in a and b, respectively). The curves were drawn by inserting the appropriate average values of the parameters into the fitting equations. For protocol LA, they amounted to T1 ⫽ 3.37 s, S0 ⫽ 284.4 a.u., and b ⫽ 1 applying SeM and to T1 ⫽ 7.05 s, S0 ⫽ 318.7 a.u., and b ⫽ 0.788 using CeM; for protocol LB they amounted to T1 ⫽ 3.99 s, S0 ⫽ 19.6 a.u., b ⫽ 1 and to T1 ⫽ 8.42 s, S0 ⫽ 21.8 a.u., and b ⫽ 0.786 applying SeM and CeM, respectively. Bars are SD.
Human Studies Mechanical power was not statistically different for the subjects who underwent the two acquisition protocols (MANOVA, Protocol effect, F ⫽ 2.42, P ⫽ 0.16), nor were the three trials significantly different from each other (MANOVA, Trial effect, F ⫽ 0.45, P ⫽ 0.65). Average mechanical power of all the repeated exercises amounted to 5.63 ⫾ 1.52 W (sum of both limbs).
A post hoc analysis has demonstrated that, for an ␣ probability level of 0.05, the selected sample sizes for both phantom and human studies yielded a power greater than 0.8. RESULTS Phantom Studies The fitting procedure, applying both mathematical models, was statistically significant for all the data sets obtained on the phantom independently of the acquisition protocol. The average 2 calculated fitting the data with CeM was lower than that obtained with SeM (MANOVA, Model effect, F ⫽ 112, P ⬍ 0.001), indicating that, in all cases, CeM better fits experimental data. Figure 1 shows the average signal intensities corresponding to the different TR values of the two longer protocols (i.e., LA and LB); the curves were drawn, inserting the appropriate average values of the parameters T1, b, and S0 into the fitting equations. Average T1 amounted to 3.37 ⫾ 0.49 and 7.05 ⫾
FIG. 2. Average T1 values obtained on the phantom by means of the two different mathematical models considering only partially the data sets of both protocol LA (full symbols) and protocol LB (open symbols). Data are plotted as a function of the greatest TR considered. Bars are SD. Dots: model CeM; T1 estimates for ⱖ5 data points. Diamonds: model SeM; T1 estimates for ⱖ4 data points.
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A preliminary analysis of variance for repeated measures was carried out independently for the two protocols (SA and SB) on the pH data, since the two acquisition protocols provided, for each metabolic condition, a different number of spectra (i.e., 6 versus 7). For both protocols, pH was not affected by the TR used to acquire the spectra (MANOVA, TR effect, F ⫽ 2.02, P ⫽ 0.11, and F ⫽ 1.75, P ⫽ 0.17, respectively). Thus, for each volunteer, pH data obtained in the same trial and in the same metabolic condition (i.e., rest or exercise) were averaged. A subsequent analysis of variance demonstrated that mean intracellular pH was not affected by the acquisition protocol (MANOVA, Protocol effect, F ⫽ 2.43, P ⫽ 0.16), by the repeated trials (MANOVA, Trial effect, F ⫽ 2.92, P ⫽ 0.08), or by the exercise (MANOVA, Exercise effect, F ⫽ 0.34, P ⫽ 0.58). Average pH amounted to 7.05 ⫾ 0.05 at rest and to 7.07 ⫾ 0.07 during steady-state exercise. Figure 3 shows, for a typical subject, the spectra acquired with the different TR values applying acquisition protocol SA during one of the three trials at rest (Fig. 3a) or during exercise (Fig. 3b). The small inserts of each panel illustrate the peak intensities of PC, Pi, and ATP of the same subject and repetition as a function of the TR used to collect the different spectra. Curves were drawn inserting the appropriate values of the parameters T1, b, and S0 in Eq. [4]. Table 2 summarizes, for each considered phosphagen, the average T1 and b values, calculated by applying the fitting equations with b ⫽ free (CeM) to the data sets obtained both at rest and during exercise with the acquisition procedures SA and SB, respectively. Independently of the acquisition protocol, the T1 values estimated by means of SeM (data not shown) were significantly lower than those obtained by means of CeM (MANOVA, Model effect, F ⫽ 154, P ⬍ 0.001). The five investigated phosphagens show significantly different T1 values (MANOVA, Peak effect, F ⫽ 4.68, P ⬍ 0.001). The two acquisition protocols led to significantly different results (MANOVA, Protocol effect, F ⫽ 60.4, P ⬍ 0.001), but the T1 did not change significantly during exercise (MANOVA, Exercise effect, F ⫽ 1.48, P ⫽ 0.23). Parameter b was significantly different among the five investigated phosphagens (ANOVA, Peak effect, F ⫽ 6.28, P ⬍ 0.001), while it did not change significantly during exercise (ANOVA, Exercise effect, F ⫽ 1.06, P ⫽ 0.30). Overall, the two different acquisition protocols yielded statistically significant different b values (ANOVA, Protocol effect, F ⫽ 6.29, P ⬍ 0.02) but analyzing separately the different peaks, no significant differences were observed (unpaired t test, P ⬎ 0.90 for all the peaks). DISCUSSION The aim of the present study was to estimate, in a time interval of at most 7 min, the apparent T1 relaxation times of the main 31P muscle metabolites (Pi, PC, ␣ATP, ␥ATP, ATP) at rest and during steady-state exercise (rhythmic plantar flexion of the ankle) using a clinical NMR unit. From a theoretical point of view, an inversion recovery sequence would be the best acquisition scheme for accurate T1 measurements. However, this method requires full relaxation of the magnetization before each scan; thus, it is
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FIG. 3. The spectra acquired with the different TR values during one of the three trials are illustrated for a typical subject participating to protocol SA. (a) The data acquired at rest; (b) refers to exercise conditions. The small inserts of each panel illustrate the peak intensities of PC, Pi, and ATP of the same subject and trial as a function of the TR used to obtain the spectrum. The SD of peak intensities lie within the symbols. Curves were drawn by inserting the appropriate values of the parameters T1, b, and S0 in Eq. [4]. Q amounted to 0.98 and 0.62 for PC, 0.30 and 0.60 for Pi, and 0.05 and 0.27 for ATP at rest and during exercise, respectively. For display purposes, the spectra were processed with the following parameters: 6 Hz exponential filter, phase-corrected and baseline-corrected.
not feasible in vivo, in particular when the time spent for acquisition is a crucial factor. The more time-efficient progressive saturation technique (25) was thus applied, in particular since most of the published physiologic studies (1–9) have used similar spectroscopy sequences. Nevertheless, the reader should also bear in mind that the parameter T1 obtained by means of the PS technique is not the “true” or intrinsic longitudinal relaxation time, but it rather represents the “apparent” relaxation time (25). T1 literature values were mainly obtained at rest, often employing more than half an hour, even using more suitable experimental protocols and instrumentations (14,15,17,19,23). However, it is not clear whether the soobtained T1 values can be safely applied to estimate actual
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TABLE 2 T1 Time Constants and b Values Obtained by Applying the Compensated Exponential Models (CeM) on the Data Sets Obtained by Means of the Two Acquisition Protocols (i.e., SA and SB) both at Rest and during Exercise on the Same Volunteers Rest
Exercise
Metabolite Protocol SA Pi PC ␥ATP ␣ATP ATP Protocol SB Pi PC ␥ATP ␣ATP ATP
n
T1
b
n
T1
b
9 18 14 12 16
1.73 ⫾ 0.29 2.70 ⫾ 0.87 2.08 ⫾ 1.08 1.83 ⫾ 0.87 3.03 ⫾ 1.34
0.84 ⫾ 0.12 0.81 ⫾ 0.09 0.85 ⫾ 0.14 0.94 ⫾ 0.07 0.83 ⫾ 0.11
15 18 11 16 17
2.25 ⫾ 1.20 3.11 ⫾ 0.89 2.58 ⫾ 1.60 2.10 ⫾ 0.77 2.93 ⫾ 1.51
0.82 ⫾ 0.12 0.77 ⫾ 0.11 0.83 ⫾ 0.13 0.84 ⫾ 0.14 0.84 ⫾ 0.15
6 12 8 7 11
3.42 ⫾ 0.39 4.18 ⫾ 1.03 4.22 ⫾ 1.18 4.37 ⫾ 1.07 3.25 ⫾ 0.91
0.88 ⫾ 0.08 0.84 ⫾ 0.04 0.94 ⫾ 0.07 0.97 ⫾ 0.03 0.90 ⫾ 0.08
9 12 9 10 7
3.39 ⫾ 0.43 4.08 ⫾ 0.58 4.50 ⫾ 0.83 4.79 ⫾ 1.54 3.33 ⫾ 0.91
0.89 ⫾ 0.08 0.83 ⫾ 0.07 0.93 ⫾ 0.09 0.86 ⫾ 0.11 0.83 ⫾ 0.07
Note. Data are means ⫾ SD; n ⫽ number of statistically significant fits.
concentrations from the data obtained in vivo using different protocols, characterized by short repetition times with multiple FID acquisitions (to enhance the signal-to-noise ratio). Thus, in the present study an acquisition protocol similar to those usually adopted to study the kinetics of PC splitting/resynthesis was also used. Mathematical Models to Estimate the T1 Constant The changes of the spectroscopy peak intensity as a function of the time between two consecutive excitations is described in the literature by means of various models and interpretations (25), the easiest of which is a simple exponential function. However, when a surface coil is employed, to compensate the nonuniform irradiation of the investigated sample, the increase in signal intensity S is usually described by means of an exponential function including a correction coefficient “b” (see Eqs. [4] and [5]), which ranges from 0 to 1 (23). Mathematically, a value of “b” lower than 0 leads to a decreasing function (in contrast with the definition of the T1 time constant in the NMR theory), whereas a value of “b” greater than 1 implies that the estimated absolute signal, for TR tending to zero, becomes negative, i.e., as such, nonsensical. Thus, the estimated value of b yields also some insights if the raw data make sense. The average values of “b” estimated in the present investigation were compliant with the above considerations and turned out to be in the predicted under all the investigated conditions. Moreover, the dashed lines of Fig. 1 and the lower 2 values obtained on all the data sets suggest that CeM describes better the studied phenomena. In fact, the simple exponential model underestimates the T1 value depending on the discrepancy between 1 and the actual value of b, and thus the b value calculated by the CeM model gives an estimate of the accuracy of the SeM model. Nevertheless, the use of the T1 estimated by means of CeM to scale up data acquired under partially saturated conditions to fully relaxed conditions cannot neglect the appropriate value of the parameter b, which, however, is rarely reported by the literature.
Estimate of the Apparent T1 Constant on Phantoms Independently of the mathematical model considered, protocol LB yielded longer T1 values (Fig. 2). This result can be explained by the different parameters applied to collect the spectra; as a matter of fact, as already explained under Methods, protocol LB sums up the signals of three consecutive acquisitions, the first of which is separated from the last acquisition of the preceding spectrum by a time interval amounting to 2TR ⫹ ⌬. As a result, the average time interval between the three excitations making up each spectrum is longer than the TR on the NMR console. Nevertheless, the T1 obtained by fitting the nominal TR values is very likely the correct time constant to use when scaling up to actual concentrations data acquired using acquisition protocols of similar structure, even if it does not correspond to the T1 according to its classic definition. In addition, it can be mathematically demonstrated that the ⌬ factor has a slowing effect on the T1. In most cases, time to acquire a complete data-set is limited; thus, the longest TR used may not allow for complete recovery of signal between measurements, as was certainly the case for the two short protocols (SA and SB) of the present investigation. Even so, it is commonly believed that the limited number of spectra collected is sufficient to estimate correctly T1. In contrast, the present work clearly shows that the estimated T1 increases with the maximal TR used (Fig. 2). The acquisition parameters used for protocols SA and SB (Table 1) allowed us to explore the maximum number of TR values during the predetermined time interval. In both protocols a good signal-to-noise ratio was obtained and the saturation condition was reached. Therefore, both protocols were considered adequate to estimate in vivo the T1 time constant, even if protocol SB explored a rather restricted range of TR (i.e., 601–1201 ms). This protocol, however, was designed in order to use acquisition parameters very similar to those commonly adopted when studying PC splitting kinetics, even though actual time spent to collect each spectrum was greater than fourfold the TR set on the console (Eq. [1]) and thus the maximal allowed time
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window of about 7 min was quickly reached. Data sets acquired with protocols SA and SB led to shorter T1 values compared to those obtained by means of the corresponding longer protocol and model, as could be expected from the maximal TR effect discussed above and illustrated in Fig. 2. Human Studies The experimental protocols adopted on humans were meant to evaluate the T1 of phosphagens both at rest and during moderate steady-state dynamic plantar flexion exercise, below the anaerobic threshold. This goal was achieved, since no change in intracellular pH was observed between rest and exercise (7.05 ⫾ 0.05 versus 7.07 ⫾ 0.07). Moreover, mechanical power developed with both limbs by volunteers (5.63 ⫾ 1.52 W) was lower than twice the values reported in the literature as the “one leg” intramuscular (i.m.) lactate threshold (i.e., 4.6 – 4.8 W) (9,33). For these exercise intensities, PC concentration decreases monoexponentially with a time constant of about 20 s (4,5,8,32), thereafter remaining constant (2,4,7–9). The applied dummy scans or the discarded spectra, together with the 10 s delay before the start of the spectroscopy sequence, allowed us to reach a reasonable steady-state PC concentration, which, in turn, is an essential condition to assess the T1 in working muscles. The muscles involved in the plantar flexion, even during heavy exercise, are the gastrocnemius medialis and the gastrocnemius lateralis, while the soleus is not activated (9). Thus, to look at the active muscle masses, surface coils ranging from 2.5 to 6 cm in diameter (4,7,8,22,32,33) are usually considered adequate. Table 2 summarizes, for the two acquisition protocols, the T1 of all the investigated phosphagens, both at rest and during exercise. Some PS data sets had to be discarded, since the fitting procedure was not statistically significant, particularly so for Pi at rest, a condition that yields low signal intensities. Nevertheless, the T1, as estimated in the present investigation, did not change statistically from rest to moderate steady-state rhythmic exercise for any of the phosphagens, independently of the acquisition protocol. This result confirms also that no chemical or ionic exchanges are specifically associated with this kind of exercise, since no changes in pH or in the phosphagens concentration have been reported for these conditions (2,4, 7–9). As shown also by other authors (23), b values obtained in the present investigation differed significantly among the five investigated compounds. The b values obtained for the two different acquisition protocols were significantly different, maybe because of the longer TR values explored with protocol SA. Indeed, the use of relatively long TR values leads to a poorer description of the earliest part of the exponential function, which was reflected in a rather high variability of the estimated b factor (Table 2). The T1 of phosphagens determined for calf muscles in humans with the present investigation was obtained with a restricted range of TR in order to reduce the time volunteers had to stay in the NMR unit. To estimate the T1 exploring a wide range of TR values (“ideal” conditions, for example, applying protocols LA or LB) the overall time
Cettolo et al. TABLE 3 Theoretical Average (Rest and Exercise) Estimated T1 Relaxation Times (s) of the 13P Metabolites under “Ideal” Conditions Metabolite
Protocol SA
Protocol SB
Pi PC ␥ATP ␣ATP ATP
3.23 4.63 3.67 3.87 4.75
4.79 5.83 6.10 6.45 4.60
Note. Data of both acquisition protocols are reported. See text for details.
would be longer than 1 h and a half, too long even for resting conditions. However, assuming that the same systematic errors affected the different acquisition protocols and data analyses, both in phantoms and in volunteers, theoretical values for ideal conditions were calculated. So, the ratio between the T1 values obtained on the phantom applying the long and the corresponding short acquisition protocol (i.e., LA and SA or LB and SB) was applied to “correct” the T1 values obtained for the different phosphagens (average of rest and exercise). These figures are summarized in Table 3. Values obtained with acquisition protocol SA are somewhat lower than the literature values (19), whereas protocol SB yields T1 values that agree quite well with the values obtained in other laboratories at 1.5 T (19). In particular, the T1 of PC, as calculated, amounts to 5.83 s, a value not far from that reported for the same compound by Newcomer et al. (i.e., 5.6 s) (23), obtained at rest under similar acquisition conditions. Lower T1 values can be found in the literature (18), but they were estimated applying a two parameters model (i.e., with b ⫽ 1). CONCLUSIONS In the present work different acquisition protocols and mathematical models to estimate T1 have been compared. Results obtained on the phantom show that different experimental protocols yield different T1 values, mainly because of the longest explored TR and/or the mathematical model used. Results obtained on humans, despite the numerous limits of the study, indicate that the apparent T1 time constants of all the muscular phosphagens do not change statistically from rest to steady-state aerobic exercise, independently of the acquisition protocol and/or the fitting procedure. ACKNOWLEDGMENTS We thank Prof. P.E. di Prampero, Prof. G. Esposito, and Dr. F. Fogolari for many helpful discussions. REFERENCES 1. Walter G, Vandenborne K, McCully KK, Leigh JS. Noninvasive measurement of phosphocreatine recovery kinetics in single human muscles. Am J Physiol 1997;272:C525–C534. 2. Whipp BJ, Rossiter HB, Ward SA, Avery D, Doyle VL, Howe FA, Griffiths JR. Simultaneous determination of muscle 31P and O2 uptake kinetics during whole body NMR spectroscopy. J Appl Physiol 1999; 86:742–747.
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P Metabolites during Dynamic Exercise
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