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INNOVATIVE METHODOLOGY
1Department of Radiology and Radiological Sciences, Vanderbilt University, Nashville, Tennessee 37232; and 2Department of Exercise Science, University of Massachusetts at Amherst, Amherst, Massachusetts, 01003
Submitted 20 February 2003 ; accepted in final form 20 May 2003
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ABSTRACT |
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 TOP ABSTRACT METHODSRESULTSDISCUSSIONDISCLOSURESACKNOWLEDGMENTSREFERENCES |
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transverse relaxation time constant; image processing; time series; exercise; dorsiflexors
Multiexponential relaxation analysis has shown that the major contribution
to signal intensity (SI) changes in mfMRI is made by the increase in the
transverse relaxation time constant (T2) of intracellular water protons
(4,
22,
23). Proposed explanations for
intracellular T2 increases include the accumulation of end products of
cellular energy metabolism, which cause water to move into the cell
(4,
21), decreased intracellular
pH (4,
8), and water shifts from an
intracellular compartment possessing a short T2 (
20 ms) to a second
intracellular compartment having a longer T2 (40 ms)
(22,
23). Any of these possible
explanations, acting alone or in concert with the others, suggests that the
intracellular T2 increase results from changes in the chemical behavior of
water resulting from increased flux through energy metabolism pathways. In
keeping with the long time required for flux through these pathways to reach a
steady rate (2-3 min), these changes make up a slowly evolving,
large-magnitude component of the mfMRI response
(14).
Changes in the extracellular space also affect the SI in mfMRI. Increases in interstitial volume [such as those caused by exercise (24) or leg negative pressure (18)] increase SI in T2-weighted images (6, 18), although the low interstitial volume fraction diminishes the importance of these changes (4, 18). Recently, Hu et al. (12) showed through the injection of an extracellular contrast agent that postexercise hyperemia affects SI in T2-weighted images as well. Finally, changes in blood oxygenation during exercise (11) will alter the T2 of blood (27). Changes in the relaxation of these tissue water fractions will not affect the intracellular T2 unless there is rapid exchange between them and the intracellular space (15) or unless the magnetic susceptibility gradients around capillaries affect diffusing intracellular spins. Otherwise, the quantitative importance of extracellular changes to SI in mfMRI will depend on the pulse sequence and timings and the intercompartmental exchange rates.
Exercise-induced changes in energy metabolism, intracellular and interstitial volumes, and blood volume and oxygenation have different time courses; the result is a complex temporal pattern of SI changes in serially obtained echo-planar images (2, 14, 19). Jenner et al. (14) reported an approximately exponential rise in SI during isotonic dorsiflexion exercise. Others (2, 19) have shown a more complex pattern to the SI changes during and after exercise, with (sometimes) an abrupt initial rise, a dip (possibly below baseline), a secondary rise, and continued increases after exercise. In addition to differences in the shape of the response over time, the magnitude of the response may be heterogeneous.
These differences in shape and magnitude can exist between or within individual muscles (2). Traditionally, these differences have been analyzed by using regions of interest (ROIs) drawn around individual muscles according to an a priori model. One assumption of traditional analysis is that the SI time course within each ROI is homogeneous. However, if this assumption were invalid, then traditional analysis would mask heterogeneities that exist on a smaller scale. Furthermore, traditional mfMRI analysis implicitly assumes a common regional organization of neural activation, perfusion, and/or other systemic variables, an assumption that is physiologically unlikely. Therefore, the purpose of this study was to develop and apply a model-independent method for organizing heterogeneous mfMRI data into clusters whose members behave similarly to each other but distinctly from members of other clusters. Such a method would be useful in identifying regionally varying patterns in the mfMRI SI time course that would otherwise be missed and would allow the temporal and spatial correlation of SI changes with other physiological and biophysical parameters altered by exercise.
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METHODS |
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TOPABSTRACTMETHODSRESULTSDISCUSSIONDISCLOSURESACKNOWLEDGMENTSREFERENCES |
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The following considerations apply to simulated or actual spin-echo, T2-weighted echo-planar images of exercising muscle obtained serially during sustained exercise. For any image voxel i within an activated region of muscle, we assume that there exists a SI time course similar to one of those shown in Fig. 1. For any adjacent voxel j, we assume that the time course will have a similar magnitude and shape to that of i if the two regions of muscle are similar with respect to their metabolic characteristics, blood supply and oxygenation, and neural activation; otherwise, the magnitude and/or shape will differ. These concepts are illustrated in Fig. 1: curves A and B (and A and C) have similar shapes and are well correlated but differ in magnitude, curves B and C have similar shapes and magnitudes, and curve D differs from curves A-C in shape and magnitude. Nonphysiological sources for differences in the curves, such as noise, motion artifacts, partial volume effects, and inhomogeneous distributions of the radio frequency field and the quality factor of the coil, may also exist.
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To quantify the similarity between i and j, we calculate
a similarity index (Sij) that considers
differences in shape and magnitude. First, a time series (such as the exercise
or postexercise period) containing imaging data is specified. Then,
differences in the shapes of the two time series are quantified by calculating
the Pearson's product-moment correlation (Rij)
between them; negative values of Rij are set to
zero. Because Rij alone cannot distinguish
between time series A and B in
Fig. 1, the magnitude
difference between the time series is also quantified, using the mean
Euclidean distance (Mij) between the two time
series
 | (1) |
 | (2) |
1) The eight voxels neighboring the voxel i are found. A planar ROI is defined within the image. 2) The similarity S between i and each of its neighbors is calculated. 3) Values of S lower than a threshold (T) are set to zero. 4) Up to K neighboring voxels are found whose non-zero simularities are greatest. 5) These voxels are grouped together into a cluster. This procedure is repeated for each voxel in the ROI. There are no limits to the size or number of individual clusters, except that provided by the definition of the ROI.
The resulting clusters can be classified as small (<5 voxels) or large
(
5 voxels). As stated above, the assignment of two voxels to separate
clusters is assumed to reflect primarily a physiological difference between
those two areas of muscle. It is also possible that noise could result in
misassignment of a voxel. However, the algorithm employs several strategies
for reducing the effects of noise. First, before S is calculated, the
data from each voxel are filtered at 0.0625 Hz with a fifth-order low-pass
Butterworth filter, which filters out high-frequency noise and preserves the
low-frequency mfMRI data. Second, after the initial cluster assignment, small
clusters are merged into adjacent clusters if the mean SI time courses from
the clusters are sufficiently similar. The merging procedure is carried out as
follows.
1) Cluster C is characterized as large or small. 2A) If C is large, S is calculated between C and each adjacent small cluster. If S > T, the clusters together are merged together. 2B) If C is small, S is claculated between C and all adjacent clusters. For any comparison in which S > T, the clusters are merged together. 3) These steps are repeated for all clusters in the data set, beginning with the smallest cluster and ending with the largest. This procedure is repeated for each voxel in the ROI. There are no limits to the size or number of individual clusters, except these provided by the defination of the ROI.
Simulation Studies
To test the algorithm and identify appropriate values of T and K, simulated data sets were tested by using MATLAB (The Mathworks, Natick, MA). Each data set contained 34 pages of 12 x 22 matrix; each page represented a different point in time (Fig. 2). In each page, the central 200 elements were organized into eight regions, with noise at the boundaries. There were four inactive (IR1-4) and four active (AR1-4) regions, each of size 5 x 5. The inactive regions had unit SI in all 34 matrix pages. In AR1-4, the first four matrix pages simulated inactive muscle and the remaining 30 contained simulated mfMRI SI time series. AR1 and AR2 had SI time series similar to curve D in Fig. 1, whereas the time series in AR3 and AR4 were similar to curves A-C in Fig. 1. The simulated time series were generated by fitting typical experimentally obtained SI time series to third-order polynomials and solving for exercise durations of 4-120 s, in increments of 4 s. The third-order polynomial was chosen because it fit the data well and does not imply a specific mechanism for SI changes in mfMRI. Gaussian noise was added to the time series to generate signal-to-noise ratios (SNRs) of 150, 200, or 250. These SNR levels are similar to those in experimental data (mean of 195, range of 155-237).
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To optimize T for experimental studies, repeated simulations were
run. T was increased from 0.5 (in steps of 0.05) until 90%
classification accuracy (CA) was attained in each of six independent trials.
The CA was calculated as
 | (3) |
Experimental Studies
Subjects. The studies were conducted at the Yale University MRI facility. The Institutional Review Boards of the University of Massachusetts at Amherst and the Yale University School of Medicine approved these studies. The subjects were seven apparently healthy, untrained male volunteers. Each subject provided written, informed consent before participating in the study. In one of the subjects, excessive leg movement during exercise precluded cluster analysis. The presentation and discussion of the data are restricted to the remaining six subjects (age = 22.6 ± 0.9 yr, height = 180.0 ± 2.0 cm, mass = 76.1 ± 3.1 kg).
Exercise protocol. The subjects sustained a 2-min isometric
contraction of the right dorsiflexors at 40% of maximum voluntary contraction
(MVC). The subjects lay supine on the patient bed of the imager with their
right foot in an exercise apparatus. The leg was fully extended, and the foot
was held in 30° of plantar flexion. The exercise apparatus consisted
of an aluminum plate, to which a load cell (model SSM-AJ-250, Interface,
Scottsdale, AZ) was attached. The subjects pulled against a Velcro strap that
was secured to the foot-plate. The plate and load cell were held within a
wooden frame secured to the patient bed. The signals from the load cell were
amplified (model SGA, Interface), digitized at 500 Hz by an analog-to-digital
converter (DAQPAD-6020E, National Instruments, Austin, TX), and recorded on an
IBM-compatible laptop computer using LabView version 5.1 (National
Instruments). An output from LabView, proportional to relative contraction
intensity, was displayed on an LED panel and enabled the subjects to maintain
the desired contraction intensity.
Earlier in the test session, the subjects performed a series of procedures in which perfusion-sensitive images were obtained. The procedures included a single-cuff occlusion protocol in which a blood pressure cuff placed proximal to the knee was inflated to 220 mmHg for 5 min, two 10-s contractions to determine MVC, and ten 10-s submaximal contractions (two each at 10, 30, 50, 70, and 90% of MVC). These contractions were followed by another MVC to evaluate the possibility of fatigue. There were 5 min of rest between each of these procedures and before the 2-min contraction described above.
MR measurements. Imaging was performed on a 1.5-T whole-body Signa (GE Medical Systems, Milwaukee, WI) MR imager. Before exercise, contiguous multislice gradient-echo localizer scans were acquired in three planes and used to locate the maximum cross-sectional area of the anterior compartment. Subsequent imaging was performed with single-slice axial acquisitions at this location. A high-resolution, T1-weighted conventional spin-echo image, used to define ROIs in the traditional mfMRI analysis (see below), was acquired by using repetition time (TR)/echo time (TE) = 600/14 ms, field of view = 20 cm, matrix = 256 x 256, slice thickness = 10 mm, and one excitation. mfMRI used T2-weighted, spin-echo axial echo-planar images acquired with TR/TE = 4,000/35 ms, field of view = 20 cm, matrix = 64 x 64, slice thickness = 10 mm, one excitation, and a 62.5-kHz bandwidth. Seventy mfMRI images were acquired: 4 before, 30 during, and 36 after exercise.
Image analysis. Image analysis was performed in MATLAB. To compensate partially for potential artifacts such as inhomogeneous distributions of the radio frequency field and quality factor of the coil, each voxel's SI time course was divided by the mean SI for that voxel in the four preexercise images. Cluster analysis was restricted to the superficial and deep compartments of the anterior tibialis muscle (AT/S and AT/D, respectively) and the extensor digitorum longus (EDL) muscle. As discussed above, when calculating Mij, the difference in SI between the two voxels being compared was scaled to the range of muscle SIs encountered. To set the boundaries for this analysis, the user set a lower threshold that eliminated voxels containing only noise or in which there was incomplete fat suppression by the EPI sequence and an upper threshold that eliminated voxels containing blood vessels. Cluster analysis was performed with T = 0.75 and K = 4. For simplicity, the presentation and discussion of results is restricted to large clusters.
Traditional mfMRI analyses were also performed. SI was measured in ROIs
drawn around the AT/S, AT/D, EDL, and soleus (Sol) muscles as a function of
exercise or postexercise duration. The ROIs were defined by using of the
high-resolution anatomic images; data from the functional images were obtained
by converting the indexes into the image matrices from 256 x 256 image
space to 64 x 64 image space. Registration errors were corrected by
manually aligning the image mask of the mfMRI images with the anatomic images.
The relative SI changes and the contrast-to-noise ratio (CNR) were calculated.
CNR was calculated according to
 | (4) |
Statistical Analysis
Statistical calculations were made with Microsoft Excel 97. To test for persistent effects of the prior exercise on muscle T2, the mean raw preexercise SI in the AT/S, AT/D, EDL, and Sol ROIs were compared by using a one-way ANOVA. To test for fatigue resulting from the prior exercise, the mean MVC values recorded before and after the perfusion imaging protocol were compared with a paired Student's t-test. To test for acute effects of the 2-min sustained dorsiflexion exercise on muscle T2, the relative change in SI was calculated between the first preexercise image and final exercise image and between the first preexercise image and the image in which the peak postexercise SI occurred. The mean relative SI changes were compared with a two-way ANOVA (muscle by time point), with repeated measures on time point, followed by Tukey's post hoc test. Mean and SE were calculated for all data. Statistical comparisons were considered significant at P < 0.05.
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RESULTS |
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TOPABSTRACTMETHODSRESULTSDISCUSSIONDISCLOSURESACKNOWLEDGMENTSREFERENCES |
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In all, 90 independent simulation trials were executed.
Figure 3A shows the CA
values for each condition; in 13 of 15 cases, the CA was 100% on each trial.
In the other two conditions, the CA was 95%.
Figure 3B shows the
values of T required to produce these CA values. In general, setting
T to 0.60 allowed correct discrimination between clusters. However,
it was necessary to raise T for conditions A, D150, and
E (see Fig. 3). In all
cases, lower-than-optimum values of T produced clusters that were
fewer in number and larger in size than programmed; the converse was true when
T is set too high.
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The algorithm was insensitive to values of K > 2, producing
100% CA for each of these trials. Values of K 
2 produced too
many clusters, each smaller in size than the programmed regions (i.e., <25
voxels). Where possible, the merging procedure was implemented for these
clusters. However, in most cases, the clusters were characterized as large
(5 voxels) and therefore ineligible for the merging procedure.
Experimental Studies
Force production. The mean MVC before the perfusion-sensitive imaging protocol was 175.5 ± 25.4 N; this did not differ significantly from the mean MVC (174.3 ± 15.3 N) recorded after the submaximal exercise protocol (P > 0.05). All subjects were able to maintain the specified contraction intensity of 40% MVC for 2 min.
Traditional mfMRI analysis. Before the 2-min sustained dorsiflexion exercise, there were no statistically significant differences in mean raw SI among the AT/S, AT/D, EDL, and Sol ROIs (P > 0.05). In the final exercise image, there were increases in normalized SI of 5.6 ± 1.3, 6.5 ± 0.9, and 5.1 ± 1.4% in the ROIs drawn around the AT/S, AT/D, and EDL muscles (P < 0.01), which did not differ from each other. All differed from the Sol muscle (P < 0.01), in which the relative SI change (-0.9 ± 0.5%) was not significantly different from zero. After exercise, the peak relative increases in mean normalized SI in the AT/S, AT/D, and EDL ROIs were 14.1 ± 2.0, 13.6 ± 1.9, and 10.5 ± 3.9%, respectively. These values did not differ from each other but were greater (P < 0.01) than the corresponding values for these ROIs at the end of exercise. The SI in the Sol remained unchanged (P > 0.05).
Clustering results: exercise. The clustering algorithm was implemented on the six subjects having acceptable data (i.e., free of visually apparent registration errors from image-to-image). Figure 4 shows an example exercise clustering result. Four clusters were identified in this subject: one in the EDL, one in the AT/D, and two in the AT/S. The filtered mean SI time courses of each cluster are shown in the insets and illustrate the two general patterns described earlier (Fig. 1). Each cluster in the AT had an abrupt initial rise of varying magnitude followed by an early dip (like curves A-C in Fig. 1), whereas the cluster in the EDL had an early dip without an abrupt initial rise (like curve D in Fig. 1).
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Exercise clustering results and the ROI data from the traditional mfMRI analysis are summarized for all subjects in Table 2. In 16 cases, there were relative SI changes in the user-defined ROIs that represented a CNR (relative to the preexercise images) > 5. In 14 of these cases, one or more clusters were found. Eleven of the clusters were located in the AT and five were located in the EDL. The initial rise was absent in four of the five clusters in EDL and present in 12 of 13 clusters in the AT.
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Clustering results: postexercise. The clustering algorithm was implemented in all subjects; an example clustering result from the postexercise data is shown in Fig. 5. In this subject, there was a single postexercise cluster that extended over the AT and EDL muscles.
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Table 3 shows the postexercise cluster data for all of the subjects and reveals that, in five of six subjects, there was only one cluster. Table 3 also shows that in 15 of 16 cases in which the pre- to postexercise CNR was >5, a corresponding cluster was found. In all cases, the SI time courses were similar in shape to the inset to Fig. 5, although the time of the postexercise peak SI varied considerably from subject to subject (range of 28-116 s, mean of 79.3 ± 13.6 s).
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DISCUSSION |
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TOPABSTRACTMETHODSRESULTSDISCUSSIONDISCLOSURESACKNOWLEDGMENTSREFERENCES |
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30%; Ref.
16) changes in SI that occur
during and after exercise are intensity dependent
(14) and relate directly to
electromyographic measures of motor unit activation
(1). The inherent spatial
localization capability of MRI means that muscle utilization can be evaluated
in both superficial and deep muscles with in-plane resolutions of <10
mm2 by using EPI or <5 mm2 by using conventional
spin-echo imaging. However, the dynamic and complex changes in the volumes and
the inherent T2 values of the three major tissue water compartments
(intracellular, interstitial, and vascular), and possibly the rates of
exchange between them, produce a complicated and incompletely understood SI
time course. To investigate how this time course is produced and to use the data in functional studies, it is necessary to organize the SI time courses from the many voxels in an ROI into a small number of groups. One approach is to make a series of a priori hypotheses about the functional organization of the active muscles; the user then draws ROIs according to the proposed organization scheme. An alternative is to build ROIs out of voxels whose SI time courses are similar to each other, reducing the number of prior hypotheses about anatomic or functional compartmentation.
Model-independent analytic approaches, such as principal component analysis (7) and fuzzy C-means clustering (3, 17), have been applied previously to brain functional MRI data. However, we know of only one prior implementation of model-independent activation detection that used mfMRI data (28). That study presented a method for detecting activated muscle based on histogram analysis and morphological processing; no fine partitioning of the activated muscles into different compartments was performed. The algorithm that we present in this work employs a hierarchical clustering technique to group mfMRI data into clusters on the basis of similarity in adjacent voxels. It is model independent and does not require the number of clusters to be known a priori, the latter being a typical requirement of fuzzy C-means clustering. The similarity calculation uses standard arithmetic and statistical calculations (ratio, mean, and Pearson product-moment correlation) and can be executed quickly (<5 min per subject, including interactive steps). We have used this method to demonstrate a functional separation in one or more of the contributors to the SI time course in mfMRI.
There Were No Persistent Effects of the Prior Exercise
Before subjects performed the 2-min isometric dorsiflexion exercise that was used for testing the clustering algorithm, the subjects had performed a series of exercise and cuff occlusion protocols during which perfusion-sensitive images were acquired. Although the contractions were brief (10 s each) and there was a 5-min period of rest between each of them, it is still possible that these contractions fatigued the muscles or increased the T2 of the active muscles. In either case, it could influence the interpretation of the mfMRI data. However, there was no evidence that the prior exercise protocol affected the T2 of the AT and EDL or caused them to fatigue.
Traditional mfMRI Analysis Reveals General Patterns of Muscle Utilization
We observed that the changes in end-exercise SI of 6% in the AT/S,
AT/D, and EDL muscles did not differ significantly from each other. This
finding is similar to that of Price et al.
(20) who observed that, during
isotonic dorsiflexion exercise performed with a resistance equal to 25% MVC,
the SI change in the EDL does not differ significantly from that in the AT.
The findings of our traditional mfMRI analysis differ from those of Akima et
al. (2) who found that, during
isotonic dorsiflexion exercise performed with a resistance equivalent to 60%
MVC, the SI change in the AT/S muscle is significantly greater than that of
the AT/D muscle. After exercise, the SI increased to 12% above the
preexercise SI, which is similar to that observed in other studies
(2,
5,
15,
19). The peak postexercise SI
occurred 80 s after exercise in the present study, slightly longer than
in previous reports (60 s to 75 s; Refs.
2,
5,
15,
19). Overall, the results of
our traditional mfMRI analysis agree generally with those of previous studies,
although different exercise types (isotonic vs. isometric) and exercise
intensities preclude a strict quantitative comparison.
The specific physiological meaning that should be ascribed to these changes is still open for debate. However, one conclusion to be drawn from our traditional mfMRI analysis is that there were no functional differences among the three regions of the anterior compartment measured. The clustering algorithm that we employed, however, indicates otherwise.
Clustering Algorithm Distinguishes Between Regions Whose SI Time Courses Differ
In experimental studies, we encountered two qualitatively different types of SI time courses and heterogeneity in the relative changes in SI at end exercise. To test the clustering algorithm realistically, these characteristics were replicated in the simulated data sets. In particular, the spatial distribution of the regions allowed each active region to border at least one voxel from the other three active regions and two the inactive regions. Therefore, within each data set, all possible combinations of magnitude and shape variation were tested. The CNRs between active and inactive regions ranged from 3.7 to 37.5, whereas the CNR between active regions ranged from zero (for adjacent regions having identical end-exercise SI changes but different SI time courses) to 31.3. In all cases, the algorithm performed with a mean CA of 95% or better. CA of 100% was attained on all trials with CNRs of 6.25 or higher.
To attain this level of accuracy, T and K must be set
appropriately. When the CNR between the regions that one wishes to
discriminate is greater than 7.5, setting T to 0.60 is indicated
(Fig. 3B). However,
when the anticipated CNR falls below this level, T must be raised
(0.70 or higher; Fig.
3B) to avoid erroneous cluster connections due to noise.
The algorithm is insensitive to values of K larger than 2 and has a
low sensitivity to Gaussian noise. Filtering, merging small clusters into
large clusters if their mean SI time courses are sufficiently similar, and/or
raising T ameliorate the effects of low SNR. The algorithm is
sensitive to misregistration errors caused by bulk tissue motion; however,
this is true of traditional mfMRI analysis as well.
In the simulated data sets, the algorithm distinguished between inactive regions and active regions with great facility: in no case was a voxel from an inactive region of the simulated data set assigned to an active cluster. The reason for this is that the only SI variations in the inactive regions were those due to random noise, whereas those in the active regions underwent systematic variation according to the polynomial functions. The correlation coefficient in this case will be zero or close to zero. Thus, although the magnitudes of two SI time courses may be quite similar (as is the case when an inactive voxel borders a marginally active voxel), their low value for Rij2 will cause Sij to fall below the clustering threshold. As a result, the inactive voxel will be excluded from the cluster.
The other purpose that incorporating the R2 term into S serves is to act together with M in discriminating between regions that have similar end-exercise SI changes but very different behaviors in the early portion of the time course. Changing how S is calculated can alter the relative importance of this term. Using R3 instead of R2 will increase the dynamic range of S and increase its importance relative to the magnitude calculation; using R instead of R2 has opposite effects on dynamic range and relative importance. In those cases, the optimized values of T reported in Fig. 3B will no longer hold. In both the simulated and experimental data sets, the ability to discriminate between different SI time course shapes was critical to the separation of functionally distinct clusters.
Clustering Algorithm Makes Fine Distinctions Between Neighboring Active Regions
There are two a priori hypotheses included in the implementation of the
algorithm. The first is explicit and results from restricting the cluster
analysis to a user-defined region. This requires that the user select those
regions of the image in which activation is visually apparent. Expanding the
ROI to intentionally include inactive regions would not significantly impact
the results, because in several subjects there were regions with zero or
near-zero changes in SI in both the exercise and postexercise data (Tables
2 and
3). In none of these regions
was a cluster found. This restriction is therefore not an essential element of
the method; it could be removed, at the cost of increased computational time
(40-fold for these data sets). Alternatively, clustering could be
combined with the automatic activation detection method described by Warfield
et al. (28) to eliminate the
need for this restriction altogether.
The second assumption is implicit and involves how T is set. Because the understanding of the mfMRI time course is still incomplete, a "physiologically appropriate" value for T is unknown. However, we note that an important use of the algorithm will be in future mechanistic mfMRI studies, where it will be used to identify regionally varying SI time courses in muscle. This will allow spatial correlation of the SI time course with other regionally variant physiological parameters altered during exercise. For this purpose, setting T to 0.75 is appropriate because it made very subtle distinctions in SI time series (for examples, clusters 1 and 2 in Fig. 4).
The clusters that resulted from the exercise data tended to follow anatomic boundaries: in most subjects, one or two clusters were found in the AT/S, one cluster was found in the AT/D, and one cluster was found in the EDL. In general, clusters were identified in regions having CNR > 5 in the traditional mfMRI analysis. The failure of clusters to appear in some cases of CNR > 5 may have resulted from bulk tissue motion or a value of T that was set too high for the noise level; however, the overall agreement was excellent.
However, the two methods disagreed with respect to the existence of functional differences between the regions: the cluster analysis suggests that such differences exist (in most subjects, there were three or four unique clusters identified in the anterior compartment), whereas the traditional analysis suggested the opposite (the relative end-exercise SI changes were not significantly different among the regions). The major source of this discrepancy is the sensitivity (cluster analysis) or lack of sensitivity (traditional analysis) to the initial rise and other elements of the early SI time course (<60 s). The sensitivity of the clustering algorithm to the entire time series, as well as the ability to identify regionally varying time series in a model-independent manner, indicates that cluster analysis may be a more useful approach to identifying the mechanism of the mfMRI response than traditional analysis.
Regional Functional Differences Are Not Seen in the Postexercise Data
With regard to the postexercise data, when comparing the existence of clusters in regions that had CNR > 5 in the traditional mfMRI analysis, the agreement between the two methods was also excellent. In this case, the methods agreed further with regard to the apparent absence of functional differences between the regions: traditional analysis found no significant differences between the mean SI changes in the AT/S, AT/D, and EDL. Similarly, in five of six subjects, cluster analysis of postexercise data identified only a single cluster. (In aside, the existence of a single cluster in postexercise data that encompassed the AT/S, AT/D, and EDL indicates that the cluster distinctions observed during exercise did not arise from partial volume artifacts caused by muscle boundaries.)
There are two possible explanations for the difference between the cluster analysis of exercise and postexercise data. One is that there are new physiological determinants of SI in mfMRI that emerge after exercise or determinants that are active during exercise are absent afterward. The other possibility is that the identities of physiological determinants of SI are the same during and after exercise but that the relative contributions differ during these two time periods. In either case, the implications of the data are twofold: first, they suggest that, after moderate-intensity isometric contractions, SI in mfMRI may be dominated by a single contributor that is regulated globally across previously active muscles, such as postexercise hyperemia (12). Second, they indicate that analyzing exercise vs. postexercise data could yield different conclusions about functional distinctions between and within individual muscles.
What Does the Cluster Differentiation Mean?
Above, we noted that, in both simulated and experimental data sets, an important source of cluster discrimination came from the early part of the SI time course. In particular, the magnitudes (and even the existence) of the initial rise and the early dip were quite variable between clusters. To evaluate what functional significance this may hold, we first discuss the possible meanings of these portions of the early mfMRI SI time course.
With regard to the initial rise, it is noteworthy that we used a
single-slice acquisition with a TR that was insufficient for full recovery of
longitudinal magnetization. Under these conditions, the spins inside the
imaged volume will be partially saturated and those outside of it will be
essentially unsaturated, and muscle shortening would contribute to the initial
rise. Muscle shortening occurs even in isometric muscle contractions
(13), and the resulting
introduction of unsaturated spins into the slice plane would immediately
increase the signal by up to 4% (for a T1 of 1.2 s and muscle
shortening equal to or greater than the slice thickness).
Dips in SI of 1% have also been reported in the early portion of the
brain functional MRI time course and have been attributed to local oxygen
consumption that exceeds oxygen supply
(29,
30). The oxygen supply-demand
mismatch causes early elevations in microvascular deoxyhemoglobin
concentration, which have been observed with optical spectroscopy
(10); these changes decrease
the blood T2 (27). In muscle,
optical spectroscopy has shown that, during sustained isometric dorsiflexion
exercise at 30% MVC, there is a rapid increase in oxygen extraction, with
blood oxygenation reaching a plateau at an exercise duration of 45 s
(11). A local minimum in the
mfMRI time course occurs at an exercise duration of 20-30 s
(Fig. 4; Refs.
2,
19). The lack of full temporal
correspondence between blood oxygenation changes and the early dip in SI in
mfMRI may result from the simultaneous, large-magnitude increase in the T2 of
the tissue parenchyma.
If muscle shortening and oxygen extraction do contribute to the initial rise and subsequent dip, respectively, then these portions of the mfMRI SI time course should be considered when attempting to discriminate between functionally distinct regions of muscle. One specific implication of the cluster data is that, if the hypothesis concerning the role of shortening in the initial rise is correct, then the characteristic appearance of the initial rise in the AT but not the EDL muscle would indicate that the AT muscle was shortening (and, presumably, producing force) significantly, whereas the EDL was not. This proposal is consistent with the AT muscles' role as the prime mover in dorsiflexion (26). The meaning of the cluster differentiation with regard to later elements of the SI time course is unclear because they are likely generated by multiple, unmeasured physiological quantities (such as perfusion, oxygen extraction, and metabolic characteristics) whose relative contributions are unknown.
Overall, the fact that cluster analysis distinguished between the AT/S and the AT/D means that our data tend to agree with the conclusions of Akima et al. (2) concerning recruitment plasticity in the AT. However, the only conclusion that we can make with confidence is that the SI time courses of each cluster differ. Other conclusions based on the proposed contributions of muscle shortening, blood oxygenation changes, and energy metabolism to the SI time course are speculative. As noted above, presently, the main value of the algorithm is that it will be a useful tool for testing these hypotheses.
Summary and Conclusions
In this study, we have presented a method for detecting functionally distinct clusters of mfMRI data that require no a priori model of neuromuscular organization. The method was tested in simulated data sets and applied to experimental data obtained during and after isometric dorsiflexion exercise. The clustering algorithm made distinctions between anatomically, and possibly functionally, distinct regions of the leg's anterior compartment that were not seen in traditional mfMRI analysis. The increase in sensitivity in the cluster analysis results from its use of more data (the full SI time course) in its functional classifications. Both types of analysis showed that, under these experimental conditions, the major determinants of mfMRI SI after exercise are similar in the AT and EDL muscles. These analyses further suggest that mfMRI data obtained after exercise, rather than during exercise, may lack information that could be used to identify contributions to the mfMRI response.
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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.
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