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Departments of 1 Physiology and 3 Radiology, Michigan State University, East Lansing, Michigan 48824; and 2 Department of Exercise Science, Syracuse University, Syracuse, New York 13244
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ABSTRACT |
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This study examined the relationships between muscle
fiber type, metabolism, and blood flow vs. the increase in skeletal muscle 1H-NMR transverse relaxation time (T2) after
stimulation. Triceps surae muscles of anesthetized rats were stimulated
in situ at 1-10 Hz for 6 min, and T2 was calculated from
1H-NMR images acquired at 4.7 T immediately after
stimulation. At low-to-intermediate frequencies (1-5 Hz),
the stimulation-induced T2 increase was greater in the superficial,
fast-twitch white portion of the gastrocnemius muscle compared with the
deeper, more aerobic muscles of the triceps surae group. Although whole triceps muscle area changed in parallel with T2 after stimulation when
blood flow was intact, clamping of the femoral artery during stimulation prevented an increase in muscle area but not an increase in
T2. Partial inhibition of lactic acid production with iodoacetate diminished intracellular acidification (measured by 31P-NMR
spectroscopy) during brief (1.5 min) stimulation but had no significant
effect either on estimated osmolite accumulation or on muscle T2 after
stimulation. Depletion of muscle phosphocreatine content by feeding
rats
-guanidinopropionate decreased both estimated osmolite
accumulation and T2 after 1.5-min stimulation. The results are
consistent with the hypothesis that the T2 increase in stimulated muscle is related to osmotically driven shifts of fluid into an intracellular compartment.
magnetic resonance imaging; muscle functional magnetic resonance imaging; muscle recruitment; transverse relaxation time
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INTRODUCTION |
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THE TRANSVERSE RELAXATION TIME (T2) of human skeletal muscle increases by up to 30% during exercise (13, 14). Because the T2 increase depends, in part, on exercise intensity (9, 18), it is increasingly exploited in functional magnetic resonance imaging (MRI) studies as a noninvasive, semiquantitative index of muscle recruitment during various exercises (e.g., Refs. 15, 17, 29). However, in contrast to the well-known (blood oxygenation level dependent) mechanism, which underlies brain functional MRI (25), the mechanism of the T2 increase underlying muscle functional MRI is still poorly understood. One attractive hypothesis was that the T2 increase is due to increased extracellular fluid volume (2), inasmuch as the intrinsic relaxation rate of extracellular fluid is slow compared with that of intracellular fluid, which contains a dense matrix of myofibrillar proteins. Classic exercise studies supported the idea that extracellular fluid increases during exercise (33), and MRI studies found a good correlation between changes in T2 and total muscle volume during and after exercise (13, 15). However, more recent studies show that the T2 increase during exercise cannot be explained by accumulation of extracellular fluid. Passive manipulation of extracellular fluid volume, either by altered vascular pressure (8) or by decreased interstitial pressure (26), did not mimic the effect of exercise on T2. Furthermore, studies of fluid balance in perfused muscles show that the increase in total muscle volume during stimulation is largely due to intracellular, not extracellular, fluid (37, 38). Therefore, the exercise-induced T2 change must result primarily from altered relaxation within the active muscle cells.
The increase in intracellular fluid during exercise is caused by the
accumulation of small metabolic osmolites such as Pi [from
net phosphocreatine (PCr) hydrolysis] and lactate (37, 38). Therefore, if osmotic expansion of an intracellular fluid compartment is the primary cause of the exercise-induced T2 change, then the T2 change ought to vary with the varying metabolic properties in different muscles. The triceps surae (soleus, plantaris,
gastrocnemius) muscles of the rat lower hindlimb have been extensively
characterized with respect to fiber type and metabolic behavior
(3, 4, 10, 11, 20). The soleus consists of >80% slow
fibers, which have a high mitochondrial content, low glycogenolytic
capacity and PCr content, and low ATPase rate during stimulation. At
the opposite extreme, the lateral superficial portion of the
gastrocnemius consists predominantly of fast fibers with very low
mitochondrial content, high glycogenolytic capacity and PCr content,
and high ATPase rate. Previous studies show that, when these muscles
are stimulated at the same rate, net PCr hydrolysis and lactate
accumulation are much higher in the white gastrocnemius than in the
more aerobic muscles. For example, 3-5 min of stimulation at 5 Hz
results in hydrolysis of >20 µmol PCr/g muscle and accumulation of
30 µmol/g lactate in white gastrocnemius, corresponding to a total
osmotic load of >50 mM (10, 22). In contrast, stimulation
of the soleus at even higher rates results in only a few micromoles per
gram net PCr hydrolysis and lactate accumulation (39). The
other muscles in the triceps surae group (plantaris, deep medial
portions of the gastrocnemius) lie between these extremes, both in
fiber-type profile and metabolite accumulation. The purpose of this
study was to examine whether the T2 increase in these rat muscles
during stimulation varies with these known metabolic differences. In addition, we examined the effect on T2 of three manipulations expected
to alter net metabolite or fluid accumulation: ischemia, partial
inhibition of lactic acid production with iodoacetate (10), and partial depletion of total creatine by feeding
rats the creatine analog
-guanidinopropionate (
-GPA)
(22). The results support the hypothesis that the increase
in T2 of contracting muscle depends on osmotically driven fluid
accumulation within an intracellular compartment.
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MATERIALS AND METHODS |
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Male Sprague-Dawley rats (275-425 g) were anesthetized with pentobarbital sodium (50 mg/kg ip, with supplementary doses of 5 mg/kg as needed) and prepared for in situ stimulation of the triceps surae group via the sciatic nerve essentially as described previously (22), except that the nerve branch innervating the anterior tibialis muscle of the lower leg was cut. The leg was secured in a 3.0-cm-diameter Helmholtz imaging coil within a custom-built imaging/spectroscopy probe. The leg position was fixed by a titanium pin inserted through the femoral condyles and clamped to the coil support, and the Achilles tendon was tied to an aluminum cantilever-beam strain-gauge force transducer. The muscle was stretched to optimize isometric twitch force (passive force, 200-250 g) in response to supramaximal test stimuli (6-10 V, 2-ms duration). Supramaximal stimuli were 50% greater than that which elicited maximum twitch force in response to test stimuli before each stimulation bout. Stimulation voltage was increased by 10-15% near the end of each stimulation bout to ensure that stimuli were still supramaximal. In some studies, the femoral artery was exposed in the inguinal region and placed within a loop of no. 4-0 surgical thread. This enabled the femoral artery to be reversibly clamped within the magnet by sliding a length of PE-100 tubing down the thread against the artery. Muscles were stimulated at 1-10 Hz for 6 min, and peak twitch force was continuously recorded during the stimulation.
Two additional studies examined the effect of chemical modulations of
metabolite production during stimulation on muscle T2. In one study,
lactic acid production was partially inhibited by infusion of a
solution of 32.2 mg/ml sodium iodoacetate at 2.8 ml/min via a carotid
artery catheter for 4 min before stimulation (10). Control
animals were infused with equivalent volumes of 0.9% NaCl. In another
study, muscle total creatine content was depleted by the feeding of rat
chow containing 1%
-GPA for 8-10 wk (22). In both
of these experiments, the stimulation duration was reduced to 1.5 min
rather than 6 min, and muscles were stimulated at 5 or 10 Hz. However,
there was little difference in integrated peak twitch force (i.e., mean
peak twitch force times stimulation rate) or metabolic response to 5- vs. 10-Hz stimulation for 1.5 min; thus results from the two
frequencies were pooled. The briefer stimulation period was chosen to
minimize the extent of lactate and hydrogen ion efflux, thus allowing
net lactate accumulation to be estimated from the observed pH changes
(see Eq. 2). In addition, stimulation of
-GPA-loaded muscles for longer periods resulted in substantial
hydrolysis of the phosphorylated analog.
1H images were acquired at 200 MHz on a 4.7-T General
Electric CSI Omega system equipped with a 20 G/cm gradient insert (free bore 17 cm). A single axial slice across the belly of the
triceps surae group was selected from a set of eight axial scout
images. Images of this slice were collected before and after
stimulation by use of a single-slice [BIR4 refocusing pulses
(35)] multiecho sequence (repetition time = 1,000;
echo time = 20, 40, 60, and 80 ms; 256 × 128 matrix; 3- to
4-cm field of view; 2-mm-thick slice; no. of excitations, 2;
acquisition time, 4.27 min). Despite the use of BIR4 pulses, pulse
imperfections resulted in significant refocusing error on alternate
echoes; therefore, the 40- and 80-ms images were excluded from the
analysis. Raw data was zero-filled to 256 × 256 and Gaussian
filtered, and T2 images were calculated from the 20- and 60-ms images
on a pixel-by-pixel basis from
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(1) |
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Nonlocalized 31P spectra (repetition time = 2,000, 2 kilobytes data, 5,000-Hz sweep width, no. of
excitations = 16, nominal 45° pulse) were acquired from a large
(2.3 × 2.7 cm) saddle-shaped surface coil placed orthogonally
within the imaging coil and centered on the belly of the triceps surae
group. 31P spectra were multiplied by an exponential
corresponding to 10-Hz line broadening, and peaks were integrated and
pH calculated from the chemical shift of the Pi peak, as
described previously (22). Pi and
phosphomonoester (PME) contents (µmol/g) were computed by dividing
each peak integral by the total phosphorus integral and multiplying by
the total phosphorus measured chemically in a previous study [51 and
49 µmol/g for control and
-GPA fed, respectively
(22)]. In the iodoacetate study, phosphorus spectra were
continuously acquired before and immediately after stimulation in
additional animals studied in parallel with the imaging measurements. In the
-GPA study, phosphorus spectra were acquired before and immediately after stimulation in the same muscles from which the images
were acquired.
The change in whole triceps surae osmotic load with stimulation was
estimated from phosphorus spectra acquired before and immediately after
stimulation as follows. The major metabolic changes in muscles
stimulated for short duration are net phosphagen hydrolysis and net
lactic and pyruvic acid production. Net phosphagen hydrolysis
contributes 1 mosM/mM of the reaction, irrespective of whether
the liberated phosphate appears as Pi or as PME. The extent
of lactate plus pyruvate production after brief stimulation can be
estimated from the pH change, the changes in Pi and PME concentrations, and the nonphosphate buffer capacity of rat hindlimb muscle (1)
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(2) |
is the nonphosphate buffer capacity, brackets indicate
concentrations, and
Pi and
PME are
the stoichiometric coefficients for hydrogen ion consumption by net
hydrolysis of PCr to Pi or PME, respectively, i.e.
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(3) |
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(4) |
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(5) |
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(6) |
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RESULTS |
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Figure 2 shows the peak twitch force
during 6 min of stimulation at rates from 1 to 10 Hz. Initial peak
twitch force at the onset of stimulation was 693 ± 34 (SE) g
(n = 27), or 2.3 ± 0.3 g/g body wt, which is
similar to that reported in previous studies (e.g., Refs.
20, 21). As expected from these previous
studies, stimulation at 5 Hz resulted in significant fatigue of the rat triceps surae group within 2 min, which has been attributed to loss of
force development in the less aerobic fast-twitch glycolytic fibers
(23). Compared with 5-Hz stimulation, 10-Hz stimulation resulted in greater fatigue, suggesting that this stimulation rate
exceeded the aerobic capacity of a large fraction of the fibers,
including many of the highly oxidative fast fibers in the triceps
group. As expected, ligation of the femoral artery decreased twitch
force to near zero by the end of 6 min of 5-Hz stimulation.
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Figure 3 shows magnitude and calculated
T2 images acquired before and after stimulation of the triceps surae
group at 5 Hz for 6 min. There is clear variation in signal intensity
and T2 across the stimulated muscle group after exercise, corresponding inversely with the well-known pattern of decreasing aerobic capacity and increasing metabolite accumulation nearer the surface of this muscle group. Table 1 shows the average
T2 of the soleus, plantaris, and the three regions of the gastrocnemius
muscle before and after stimulation. As reported by others
(12), the T2 of rat soleus muscle is significantly greater
than that of the other muscles at rest. This difference may reflect the
higher resting total water content of soleus muscle compared with other
muscles in the hindlimb (6). However, after 5-Hz
stimulation, T2 of the soleus was unchanged, whereas T2 significantly
increased in the other stimulated muscles. The T2 change was greatest
in the superficial white section and progressively less in mixed
gastrocnemius, red gastrocnemius, and plantaris. There was also a small
but significant increase in T2 in the denervated anterior tibialis
muscle, possibly as a result of field stimulation of the cut nerve in
some experiments. Figure 4 shows the time
course of recovery of T2 in the five triceps sections after
stimulation. Compared with the red gastrocnemius and plantaris, T2
recovery was slower in the white gastocnemius, in which T2 was still
significantly elevated above rest after 1 h of recovery. As shown
in Fig. 5, T2 also increased at lower stimulation rates in the white and mixed gastrocnemius compared with
the other muscles. In the red gastrocnemius and plantaris, T2 increased
roughly linearly with stimulation rate over the range examined, similar
to the result obtained in human muscle during voluntary contractions
(18).
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Figure 6 shows the effect of clamping the
femoral artery on the changes in whole triceps surae muscle T2 and
cross-sectional area (which is proportional to muscle volume at fixed
muscle length) after 6 min of stimulation at 5 Hz. Although the femoral
clamp eliminated the 15% increase in muscle area that occurred during stimulation without the clamp, the increase in whole triceps T2 was
only slightly diminished compared with stimulation without the clamp.
However, as shown in Table 2, elimination
of femoral flow did significantly diminish the T2 increase in the white
and mixed gastrocnemius sections. Restoration of flow by release of the
clamp after stimulation was accompanied by a further increase in whole
muscle T2 (Fig. 6), which occurred most markedly in the white section
(Table 2). As expected, the extent of PCr depletion and muscle
acidification was dramatically increased after ischemic compared with
control stimulation (Fig. 7, B
and A, respectively).
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The 31P spectra in Fig. 7, C and D,
illustrate the effects of iodoacetate infusion and depletion of PCr
content by
-GPA feeding on the metabolic changes after stimulation
for 1.5 min. Although iodoacetate infusion did significantly decrease
the extent of muscle acidification and estimated acid production after
1.5 min of stimulation (Table 3),
iodoacetate also significantly increased PME accumulation. Thus the
estimated total osmotic load after stimulation with iodoacetate was
only marginally reduced compared with after saline infusion.
Similarly, iodoacetate infusion only marginally decreased whole muscle
T2 after stimulation. This decrease was statistically significant only
in the white gastrocnemius section. On the other hand, both
poststimulation T2 and estimated osmotic load were significantly
decreased after 1.5 min of stimulation in
-GPA-loaded
compared with control muscles (Table
4). As expected from previous
studies (22), the lower estimated osmotic load after
stimulation of
-GPA-loaded vs. control muscles was due both to
decreased net phosphagen hydrolysis to Pi and to decreased acid production.
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DISCUSSION |
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The results of this study are generally consistent with the
hypothesis that the T2 increase observed in rat muscles after stimulation is related to the uptake of fluid into an intracellular compartment, osmotically driven by the accumulation of intracellular metabolites. First, the magnitude of the increase varied between rat
triceps surae muscles, as expected from their known metabolic profiles.
During stimulation at 5 Hz, the ATPase rate in the superficial fast-twitch white section of rat gastrocnemius muscle is three- to
sixfold greater than the ATPase rate that can be sustained by aerobic
metabolism in these fibers. Thus PCr is rapidly depleted, and lactate
rapidly accumulates in these fibers during 5-Hz stimulation (10). In contrast, 5-Hz stimulation is well within the
maximum aerobic capacity of rat slow-twitch fibers, which have a high mitochondrial content and a threefold lower ATP cost per twitch compared with fast fibers and produce relatively little lactate, even
during ischemic stimulation (39). Thus the soleus muscle can sustain 5-Hz stimulation with relatively little net Pi
or lactate accumulation. Although the mitochondrial content of the highly aerobic fast-twitch fibers in the medial portion of the gastrocnemius is higher than that of slow-twitch fibers, these fast-twitch fibers also have a high ATP cost per twitch. Thus 5-Hz
stimulation results in ATPase rates closer to the maximum aerobic
capacity of these fibers and greater PCr depletion and lactate
accumulation (10). Finally, the rat plantaris is a mixed muscle with lower average mitochondrial content than the red portion of
the gastrocnemius but a higher fraction of low ATPase slow fibers
(3). Thus on balance it falls between the soleus and red
gastrocnemius in metabolic profile. Second, the above considerations also argue that metabolite accumulation, fluid influx, and hence the T2
increase should occur at lower stimulation frequencies in the white
gastrocnemius than in the more aerobic muscles, and this was indeed the
case (Fig. 5). Third, replacement of PCr with the less labile
phosphagen, phosphorylated
-GPA, decreased net osmolite production
during brief stimulation and also diminished the increase in muscle T2.
Finally, partial inhibition of lactate production and muscle
acidification with iodoacetate tended to diminish the T2 increase,
although in this case the effect was insignificant, because iodoacetate
treatment also increased the accumulation of phosphorylated osmolites.
Parenthetically, the iodoacetate result confirms that pH changes per se
are not the dominant cause of the T2 increase during exercise. This was
already suggested by the observation that the recovery of muscle pH
after exercise is faster than the recovery of T2 (7).
Of course, the above interpretation depends on the assumption that supramaximal stimulation of the sciatic nerve results in stimulation of the entire triceps surae group, such that the observed variations in T2 across the muscles or between protocols are not simply the result of variations in stimulation per se. Several features of the data indicate that this was the case, i.e., that the majority of the fibers in the triceps surae were effectively stimulated. First, stimulation after ligation of the femoral artery resulted in nearly complete depletion of PCr (Fig. 7B). In contrast, PCr depletion in nonstimulated, ischemic rat triceps surae muscle takes >60 min (5). Therefore, if a substantial fraction of the fibers were not stimulated, then substantial PCr would have remained after only 6 min of ischemic stimulation. Second, the dependence of peak twitch force on stimulation rate and time (Fig. 2) is entirely consistent with previous studies of this well-characterized mixed muscle. For example, the initial loss of force during the first 2 min of 5-Hz stimulation has been attributed to rapid fatigue in the less aerobic fibers, whereas force development after 3-5 min of 5-Hz stimulation has been attributed to continuing contraction of the more aerobic fibers (23). The fact that force dropped to near zero during ischemic stimulation confirms that force after 3-5 min at 5 Hz does depend on aerobic metabolism. Thus, considered as a whole, the pattern of force development indicates that fibers with both low and high aerobic capacity were effectively stimulated. Finally, the initial peak twitch force in this study is similar to that reported in previous studies of the same preparation. Therefore, if a substantial fraction of the fibers were not stimulated, many other studies of this preparation would have to be reevaluated.
Although this and other studies (27, 30, 31) indicate that the T2 increase during stimulation is related to osmotically driven fluid shifts, the T2 increase clearly does not depend simply on an increase in total water content, because T2 increased substantially even after ischemic stimulation, when total muscle volume did not change (Fig. 6). Similar results were reported in a study of ischemic human muscle (2). It is also unlikely that T2 depends simply on total intracellular water content. Although there may be a shift of water from the extracellular to intracellular compartment during ischemic stimulation, the increase in intracellular volume at the expense of extracellular volume during ischemic stimulation could be only a small fraction of the 15% increase that occurs during intense stimulation with intact flow (37). For example, assuming a closed system with a 5:1 ratio of osmotically active intracellular to extracellular fluid, and assuming a maximum 17% increase in intracellular osmolarity (e.g., from 300 to 350 mosM) due to production of impermeable metabolites, osmotic equilibrium would be reestablished by only a 2.4% increase in intracellular fluid (at the expense of a 12% decrease in extracellular fluid, with a final osmolarity of 341 mosM in both compartments). Therefore, if muscle T2 were simply dependent on total intracellular fluid volume, the T2 increase during ischemic stimulation would be <20% of the maximum observed during stimulation with flow. In fact, even in the white gastrocnemius section, in which the T2 increase was the most attenuated by ischemia, the change during ischemia was still 42% of the largest change observed in this section with flow intact. This result suggests that the relaxation change depends on a shift of fluid into a subcompartment of the intracellular volume rather than on changes in total intracellular volume. During ischemic stimulation, this shift could occur at the expense both of the extracellular fluid and, possibly, of other compartments within the cell. Inasmuch as metabolic osmolites are produced primarily to support the myofibrillar ATPase, the obvious candidate for this compartment is the fluid associated with the myofibrils. Such compartmentation of the intracellular fluid might also explain the observation that incubation of isolated muscles in hypotonic solutions did not change muscle T2, although it did result in increased total muscle water (40).
Kennen et al. (19) showed that shifts of fluid between subcompartments within a muscle cannot change the observed T2 unless the compartments are in slow exchange or unless the relationship between intrinsic relaxation rate and macromolecular concentration within the compartments is not linear. Either of these caveats seems possible considering the complex ultrastructure of muscle cells, with a dense, regular array of myofibrillar proteins and extensive intracellular membrane systems. In particular, Saab et al. (30) recently reported that two large, distinct T2 components at 20 and 40 ms can be resolved within the relaxation decay of water in human muscle, suggesting slow exchange between two large intracellular compartments. Furthermore, there was a shift of amplitude from the 20- to the 40-ms component after exercise (31). Unfortunately, resolution of these relaxation components requires acquisition of high signal-to-noise spectra at several hundred echo times, so those results cannot be directly compared with the conventional imaging results from this study. Nonetheless, both the observations of Saab et al. (30, 31) and of this study suggest that changes within the intracellular fluid play a key role in the T2 increase during contraction.
It should be emphasized that the observation of a T2 increase during ischemic stimulation does not imply that muscle perfusion plays no role in the phenomenon. On the contrary, there was a clear enhancement of the T2 increase when flow was reestablished after ischemic stimulation in this study (Fig. 6), just as in a previous study of human muscle (2). Furthermore, it is well known that the extent of PCr breakdown, lactate production, and hence osmolite accumulation during stimulation depend on perfusion as well as on the intrinsic metabolic properties of muscle fibers. Inasmuch as there is a good correlation between aerobic capacity and perfusion rate during stimulation in the different rat muscles (20), both factors likely played a role in the regional T2 differences observed in this study. Perfusion might be a particularly important factor in the recovery of T2 after stimulation. The recovery of PCr and intracellular pH are faster than the recovery of T2 after exercise in human muscles (7), suggesting that the return of tissue fluid to the state before stimulation does not directly track osmolite removal. Similarly, previous studies of the rat gastrocnemius show that PCr and lactate recover within 30 min after intense stimulation (24), whereas in this study T2 had not recovered in the superficial white section after 60 min. Thus the slower recovery of T2 in the superficial white compared with the more aerobic sections might be due primarily to lower perfusion in this section.
Finally, these results have some obvious practical implications for the application of muscle T2 as an index of muscle recruitment during exercise. First, the results show that the T2 increase depends on muscle fiber type, aerobic capacity, and perfusion, all of which can vary widely among human subjects. Therefore, assuming that these results can be extrapolated to human muscle, differences in muscle T2 among subjects exercising at the same absolute work rate cannot be directly interpreted as a differences in recruitment intensity. Similarly, it may not be appropriate to use muscle T2 changes as a direct index of recruitment changes before and after an exercise training program, because the training program might alter muscle metabolic and/or vascular properties. Furthermore, if different muscles within a subject differ markedly in fiber type and aerobic capacity, it also may not be possible to use T2 measurements to compare the recruitment of different muscles within an individual, for example, to compare the recruitment of limb muscles during different exercises (29). Fortunately, compared with muscles of rodents and other quadrupeds, the fiber types of human muscles are not so dramatically different with respect to phosphagen or mitochondrial contents (34, 36), and the differences in fiber-type distribution among human muscles are not so profound (32). Therefore, in view of the empirical evidence that there is a good correlation between exercise intensity and T2 in various human muscles (9, 18, 28), semiquantitative comparisons among muscles within an individual still seem justified. Finally, the results suggest that the rate of T2 recovery after exercise is somewhat faster in more aerobic muscles. Therefore, muscle functional MRI measurements should be made during or as soon after the exercise as possible.
In summary, the T2 increase after stimulation differs among rat muscles with different metabolic characteristics and varies both with the accumulation of intracellular osmolites and with tissue perfusion. Muscle functional imaging based on T2 increases can be a useful supplement to electromyography, for example to map the precise location of denervation injuries or the effects of muscle stimulation therapy (16). However, because the T2 increase reflects metabolic events, muscle functional MRI cannot replace electromyography as a direct measure of muscle activation.
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ACKNOWLEDGEMENTS |
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This study was supported by National Institute of Arthritis and Musculoskeletal and Skin Diseases Grant AR-43903.
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FOOTNOTES |
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Address for reprint requests and other correspondence: R. A. Meyer, Dept. of Physiology, Giltner Hall, Michigan State Univ., East Lansing, MI 48824 (E-mail: ram{at}pslsun.psl.msu.edu).
The costs of publication of this article were defrayed in part by the payment of page charges. The article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.
Received 23 November 1999; accepted in final form 31 August 2000.
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