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INNOVATIVE METHODOLOGY
1Applied Physiology Research Group, School of Sport and Exercise Sciences, University of Birmingham; and 2Institute for Biophysical and Clinical Research into Human Movement, Manchester Metropolitan University, Alsager, United Kingdom
Submitted 27 September 2005 ; accepted in final form 1 December 2005
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ABSTRACT |
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 TOP ABSTRACT METHODSRESULTSDISCUSSIONACKNOWLEDGMENTSREFERENCES |
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ultrasonography; muscle; contractile element
Most measurements of contractile length have been made by studying reduced animal muscle preparations in vitro or by studying animal muscle in vivo using invasive techniques. There are four main techniques for measuring changes in contractile length in vivo in a living animal. 1) Sonomicrometry is used to measure the length of the muscle by surgically implanting a piezoelectric ultrasound transmitter and receiver into both ends of the muscle and has been used, for example, on rats, dogs, and turkeys (4, 6, 7). This provides good spatial (<1% rest length, <0.1 mm) and temporal resolution measurements, although a surgical procedure is required to implant the piezoelectric crystals. 2) Real-time and cine-phase contrast magnetic resonance imaging have recently been used to study human muscle motion by measuring the velocity of tissue contraction (2, 22, 24). This technique measures velocity directly and is most suited to measuring high-velocity contractions. Contractile velocities as low as 2 cm/s have been successfully measured, and typically images are sampled at 6 frames/s (2). This technique is noninvasive, although the main constraint is that the subject has to remain within the scanner. 3) X-ray scanning has been used to track radio opaque markers inserted proximally and distally into the human biceps muscle (1). With this technique, there was a limit on the dose and therefore duration of the experiment. This technique produced 50 frames/s and resolved movements to <1 mm. Clearly, this technique is invasive. 4) The most common approach is to measure joint angle by using a goniometer and either assume that joint angle, or the distance between origin and insertion, describes muscle contractile length or to use a model of the joint geometry and tendon compliance to calculate muscle contractile length (3, 9). This method is the easiest to use, although it is better for estimating combined muscle-tendon length and is less accurate for measuring contractile length alone because, for example, of the complex effects of tendon compliance.
Ultrasound (Fig. 1) has previously been used for measuring relatively static changes in tendon, aponeurosis, and muscle fascicle length (10, 11, 18, 19). Usually, the position of visually distinctive features, such as the intersection of an echogenic collagen fascicle with an echogenic aponeurosis, has been located manually, and changes in position have been calculated by comparing two or more frames (17, 21). This technique has allowed tendon strain and aponeurosis strain to be studied in vivo while step changes in load are applied. These methods are limited in spatial resolution to several hundred micrometers and are too labor intensive to provide a continuous measure of changes in position. More recently, a technique for automating this process has been published using the Lukas-Kanade feature tracking algorithm (20). This technique successfully tracked movements, frame by frame, of the gastrocnemius aponeurosis and free tendon over several millimeters to an accuracy of ±0.2 mm.
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The verification problem can be refined into several issues. First is the biological correlation: Do the changes in contractile length measured from the sonograph images correlate in size and timing with other biological and biomechanical signals? Second is the biological accuracy and validity: Even if the scanner produces high-quality images and the tracking algorithm works perfectly, do the two-dimensional (2D) images of moving muscle correspond to actual contraction and lengthening along the line of action of the muscle? Third is the intrinsic accuracy, resolution, and frequency response of the ultrasound scanner and tracking algorithm: Does the ultrasound scanner and tracking procedure faithfully record the movements of an object that is moving in a known way? This can be tested in a controlled, nonbiological experiment.
Previously, our laboratory compared changes in contractile length with surface EMG and found good correlations that gave us confidence in the tracking procedure (14). We also used a simple model to predict changes in contractile length from the changes in ankle torque and ankle angle, and this also gave us confidence in the tracking procedure (14, 15). We also applied the tracking algorithm to 16 markers for each muscle and gauged reliability from the consistency of the marker movements.
Here, we subject the tracking procedure to more stringent and definitive tests. First, we test the spatial and temporal resolution of the technique in the tracking of small changes in contractile length of the soleus and gastrocnemius muscles. When sudden rotations are applied to the ankle joint, one would expect the soleus and gastrocnemius muscles to be stretched. By applying short-duration, 200-ms, square-pulse rotations, we test whether the tracking procedure reveals the expected synchronous change in contractile length. By varying the size of the rotation, we test whether the tracking procedure reveals a credible, corresponding scaling in the size of the muscle stretches. Second, we test the ability of the technique to track a wire oscillating in water with a known amplitude and frequency. By measuring the gain and phase transfer function, we establish the accuracy of the technique for a range of movements from 1 µm to 8 mm and for a frequency range of 0.1 to 8 Hz. If the measurement technique were perfect, there would be a gain of unity and a phase lag of zero after correction for the time delay of the scanner.
The purpose of this paper is 1) to explain the tracking algorithm, 2) to test the spatial and temporal resolution and consistency with which biologically meaningful measurements of contractile length can be made, and 3) to measure the intrinsic, instrument-limited amplitude and frequency range of the technique.
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METHODS |
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TOPABSTRACTMETHODSRESULTSDISCUSSIONACKNOWLEDGMENTSREFERENCES |
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Automated, offline analysis of images. The ultrasound scanner produced a movie file containing a sequence of image frames (30 frames/s, pixel dimension 185 x 185 µm) that were saved for subsequent analysis. On a typical sonograph (Fig. 2), the pennate structure of the contractile element is revealed by the white streaks of collagen. The central, distal, and peripheral proximal aponeurosis are also visual as continuous white streaks of collagen. When the muscle shortens, the distal and peripheral aponeuroses move in opposite directions and also move apart if the muscle thickens (see supplemental data that shows real-time leg flexions at http://jap.physiology.org/cgi/content/full/01229.2005/DC1). Visual inspection confirms that relative motion between these structures can be used to estimate the changes in length (and thickness) of the contractile element. We identify structures in the image whose motion we wish to observe, we mark the position of those structures and the tracking algorithm measures the change in position of each marker for the duration of the movie (14). Our aim is to measure series or longitudinal changes in contractile length along the line of the muscle-tendon unit. So we place makers on or close to the proximal and distal aponeuroses and calculate the component of differential inter-aponeurosis movement along the direction of the central, distal aponeurosis which is continuous with the Achilles tendon. An important feature of the technique is that because we are measuring differential marker motion, motion of the probe relative to the muscle does not interfere with the result. Motion of the probe relative to both proximal and distal markers is subtracted out. Because we are not measuring changes in fascicle length we do not need to see both ends of the same fascicle (10), but we do need to see the relative motion between the proximal and distal aponeuroses.
In outline, the tracking procedure works in an iterative manner. The first pass of the algorithm measures the position of each marker relative to its position on a common frame selected as the base frame. Subsequent iterations work on the expectation that the markers are arranged in groups and that these markers should move as a group. Non-group motion is regarded as a possible source of error, and such marker movements are identified and recalculated in subsequent iterations. When the procedure is complete, the extent to which all markers in a group move as a group provides an assessment of the consistency of the estimate. The algorithm uses spatial, 2D cross correlation to calculate the movement of markers. This technique ideally requires that the feature surrounding a marker changes position but does not change shape, orientation, or composition. Changes in the feature contribute error to the procedure.
Absolute method: tracking relative to a common base frame. A single frame, e.g., the first frame in the movie, is selected as a base frame. Markers are placed, and a square of certain size is centered on each marker (Fig. 2, sonograph). This square defines the correlation area. For each marker on each comparison frame, the square of pixels that best correlates with the square of pixels on the base frame is calculated as defining the position of each marker on the comparison frame (Fig. 3A). In all methods, this 2D cross correlation is performed using the MATLAB function cpcorr in the Image Processing Toolbox (MathWorks). The function was modified to allow a variation of square size. This function calculates the 2D cross correlation for integer shifts in pixel position and uses 2D quadratic interpolation around the maximum to provide subpixel estimation of the position of peak correlation.
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This cross-correlation procedure can fail for a number of reasons. Mainly, if the image feature within the correlation square is not similar in the base frame and comparison frame, a high correlation cannot be made and an accurate change in position of the feature cannot be calculated.
If the feature, the location of maximum correlation, lies outside the search area, the correct correlation cannot be made. In these cases, the size of the search area can be increased.
A false-positive correlation may be made with a feature that is similar (possibly more similar) to the original feature in the base image than the displaced feature being tracked. The solution here is to reduce the search area and center the search more precisely with a more accurately chosen predicted marker position.
Relative method: tracking relative to the preceding frame. When markers on a comparison frame are compared with markers on a base frame, an accurate cross correlation can be made provided the feature within the correlation square is similar in the two frames. As the muscle shortens and lengthens, the feature changes in shape, orientation, and composition, and thus accurate cross correlation is more prone to error for larger changes in contractile length (see Fig. 3A). From one frame to the next, the change in image is usually smaller than from one single base frame to another arbitrary frame. So, a second method is to compute changes in marker position from one frame to the next and to accumulate the changes throughout the frames to provide the continuous change in marker position (Fig. 3B). The preceding frame is always used as the base frame for the comparison frame. This method can successfully follow cumulative changes in feature from frame to frame. While solving one problem, this procedure introduces a second problem, namely that there is no common reference frame for all the comparison frames. Each calculation of the shift in feature position between frames contains a random error (noise). Calculating shift successively from frame to frame accumulates this error, introducing cumulative drift (Fig. 3B), such that markers wander substantially from the original image position to regions where the muscle features may be moving in different ways. (Unlike aponeurosis strain, where the drift would be ordered with marker and related to displacement from the mean position, this drift is random with respect to marker and is cumulative through time.)
If correlation between successive frames is not possible because the feature has changed too much, then the technique fails irretrievably. This is likely to happen in cases where the contractile length changes greatly in a short time interval.
Relative stepping method. This procedure combines the previous two. Base frames are selected at regular intervals and provide steps between which the record can be constructed. Changes in marker position of comparison frames are computed relative to the nearest base frame. Changes are computed relative to the preceding base frame, and successive interbase frame records are joined together. This compromise method combines ability to record changes in feature from frame to frame and reduces the longer term drift by using a smaller number of base frames. This method is still susceptible to drift but takes longer for the drift to accumulate (Fig. 3C). The step size can be varied to trade off frame-to-frame accuracy vs. drift inaccuracy.
Tracking algorithm. First, all frames should be cross correlated relative to a single base frame. Then, absolute tracking method should be applied to each marker (Fig. 3A). Second, individual markers that have wandered should be tidied up. For a group of markers, the marker that deviates most from the mean should be identified, as well as the regions where that 2D deviation is greater than a certain level (0.5 pixels), the relative stepping method (step size 5 frames) should be applied to each region and the recalculated positions joined for each region at each end to the marker position whose deviation from the mean is small (< 0.5 pixels). Repeat for all markers in that group in descending order of deviance from the mean. Repeat for all groups.
For a single group of markers, the result is illustrated in Fig. 3D.
Calculation of changes in contractile length. For each muscle, for each frame relative to the single base frame, for each distal-proximal marker pair, the component of vector displacement should be calculated along the direction of the central aponeurosis, as well as the mean and standard deviation values. This basic algorithm can be adapted depending on the muscle movements studied. For example, step 2 can be iterated with a variety of deviation levels and stepping sizes.
Note that the algorithm does not constrain markers to move as a group. It simply identifies regions where the markers do not move as a group and recalculates the movements using the relative stepping method. The second method accepts greater accumulation of error to compare frames that are temporally closer. If the markers exhibit non-group motion, this will be recorded. Experience shows that non-group motion is random among the markers, resulting from image change (Fig. 3A), and is not systematic with marker order resulting from aponeurosis strain.
The optimum size of square used for cross correlation depends on the size of the features that are being tracked. If the square size is too small, the cross correlations are more affected by small scale changes in the feature rather than movement of gross features, and the result is a noisier record with greater variance between group markers. If the square size is too large, it includes differing movements of different structures, and the changes in position will reflect an average of these different motions. For example, markers either side of the central aponeurosis can be moving in opposite directions, and longitudinal relative motion between proximal and distal markers decreases in the center of the muscle. Also, as the square size increases, the computation time increases as the square of the square size in accord with the number of pixels included in the calculation. We find that a square side length of 30–50 pixels (
6–10 mm) works well while being computationally manageable.
The number of markers that one can use in a group depends on the square size. Essentially, for maximum statistical estimation of the mean, one requires as many independent, nonoverlapping markers as possible that can be fitted on the structure that moves as a whole. We tend to use eight markers on each structure, and this number allows us to keep markers away from the edge of the image.
Perturbation experiments.
Eight healthy subjects, four women and four men, aged 21–49 yr, stood quietly while strapped securely around the hips to a vertical supporting board (Fig. 4). Subjects stood on two footplates with the center of their ankles 22 cm apart. Their ankles were positioned to be coaxial with the axis of rotation of the footplates. The right footplate was locked in the horizontal position. With the use of a pneumatic actuator, square pulse ankle rotations of 0.2-s duration were delivered approximately every second to the left ankle (Fig. 4A). A trial lasted 40 s, and each subject participated in five trials in which the size of rotation varied from 0.03 to 0.6°. The subject was aware of the rotations from the noise and size of ankle rotation. Because subjects were supported, only minimal activity in the calf muscles was required, and subjects were asked to maintain constant minimal ankle torque in each ankle using their ankle torque displayed on an oscilloscope for guidance. The mean left ankle torque for all subjects was 5 ± 1 N·m (mean ± SD). For demonstration purposes, each subject was unstrapped from the vertical board and performed an additional trial in which they flexed their knees and allowed their back to slide down and up the backboard several times. The purpose was to create a record in which the monoarticular soleus muscle was lengthening while the biarticular gastrocnemius muscle was shortening and vice versa. The subjects gave informed consent to these simple noninvasive experiments, and the study was approved by the local human ethics committee and conformed to the principles of the Declaration of Helsinki.
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For each individual rotation, the step change in footplate angle, true ankle angle, gastrocnemius length, and soleus length was calculated as the maximum increase in the period 0.06–0.18 s after rotation onset. This was the period within which the footplate settled at its step position after an initial overshoot, and all subjects displayed maximum change in contractile length and ankle angle. For each trial, the coefficient of variation (CV = SD/mean) was calculated for change in gastrocnemius length, the change in soleus length, and change in true ankle angle. Values for gastrocnemius and soleus were averaged to calculate a CV of muscle stretch. For each trial, the following ratio was calculated: relative CV = CV of change in contractile length/CV of change in true ankle angle.
Oscillating wire experiment.
A vertical wire was suspended in water in a plastic beaker from a horizontal beam (Fig. 5). At one end, the beam was hinged by fine needle bearings. The free end of the beam was suspended by a thread from a pulley mounted on a position servomotor and was maintained in tension by a stiff spring pulling the beam to the ground. By applying a sinusoidal waveform to the servomotor, the beam could be made to oscillate faithfully with amplitudes of 0.75 µm to 4 mm (1.5 µm to 8 mm peak to peak) at the wire tip across the frequency range of 0.1–8 Hz. A laser range finder (YP05MGVL80, Wenglor Sensoric, Germany) with a resolution of <2 µm and a response time of 5 ms was mounted vertically above the beam close to the wire to measure vertical deflection of the beam. Our contactless variable reluctance displacement sensor (model 502-F, NS020, EMIC) with a sensitivity of 1 mV/µm and response time of <0.1 ms was also mounted vertically above the beam to corroborate the vertical displacement of the beam. Angular displacement of the beam (
) was calculated using = arctan (y/L) where y is the vertical displacement of the beam and L is the horizontal distance of the vertical laser beam or variable reluctance sensor from the beam hinge. The ultrasound probe (5–10 MHz probe, DIASUS) was mounted in a vertical plane, strapped to the beaker, such that movements of the wire tip occurred in the plane of the beam. Given the shape of the wire edge, horizontal movements of the wire tip were tracked more consistently by the tracking algorithm than vertical movements. Horizontal movements of the wire (x) were calculated from angular movements of the beam using the formula x = L2 sin() – L1[1 – cos()], where L1 is the length of the beam from the hinge to the wire and L2 is the length of the wire. Because the laser signal was recorded electrically on the data logging computer and the ultrasound frames were recorded as a movie file on the DIASUS computer, there was no possibility of crosstalk between the laser measurements and measurements derived from analysis of the ultrasound images.
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RESULTS |
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TOPABSTRACTMETHODSRESULTSDISCUSSIONACKNOWLEDGMENTSREFERENCES |
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= 200 ms) after a delay of 36 ms. One can see how the shortening of the gastrocnemius muscle corresponds with rises in gastrocnemius EMG (time = 3 and 23 s) and not soleus EMG.
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70 and 50–70 ms, respectively, after the onset of footplate rotation. For these subjects, the maximum muscle stretch, particularly soleus, is slightly less than the three subjects who showed no sign of stretch reflexes (Fig. 8, A and B). For the reflexive subjects, the maximum muscle stretches were achieved on average 70 ms after the onset of footplate rotation.
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For all subjects, the smallest muscle stretches of 5–20 µm were tracked with considerable consistency (Fig. 8, D and E), showing a mean interquartile range of 10 µm for gastrocnemius and 17 µm for soleus. This shows that the tracking technique is capable of resolving changes in contractile length as low as 5 µm.
The variation in the size of muscle stretches is comparable to the variation in the size of individual ankle rotations (Fig. 8F). For all subjects and all stretch sizes, the ratio CV of muscle stretch to CV of true ankle rotation had a median value of 1.6. Thus, in general, the ultrasound tracking procedure provided a measure of contractile length that was comparable in consistency to a high quality biomechanical measurement of ankle rotation using a laser range finder and variable reluctance transducer.
Accuracy and frequency response when tracking an oscillating wire. The accuracy of the ultrasound tracking procedure was assessed by measuring the movements of a wire oscillating in water. Accuracy is quantified as the ratio of ultrasound measured movement to laser measured movement. The ultrasound scanner and tracking procedure has an intrinsic root mean square noise level of 0.6 µm (0.003 pixels) and is capable of measuring oscillations with a peak-to-peak amplitude of 1.5 µm (Fig. 9, A and B) to 8 mm (Fig. 9, C and D). The accuracy of the tracking procedure is best at low frequencies, is close to unity (>97%) in the range 0–1.6 Hz, decreases to 90% at 3.2 Hz, and 81% at 4.5 Hz, and decreases markedly above 4.5 Hz (Fig. 9E). The 3-dB point for accuracy occurs at 5.8 Hz. The plateau frequency error (0.1–1.6 Hz) is <20% at the smallest amplitudes of 1.5 and 3 µm, <10% error at amplitudes >10 µm, and <5% at amplitudes >100 µm (Fig. 9F). The ultrasound measurements have a phase delay that increases linearly with frequency at a best-fit mean rate of 0.632 radians per Hz, which indicates a mean ultrasound scanner time delay of 101 ms (Fig. 9G). The results reported above pertain to the DIASUS scanner, probe, and settings used. Clearly, the specific values for other equipment would need to be determined by experiment.
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DISCUSSION |
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TOPABSTRACTMETHODSRESULTSDISCUSSIONACKNOWLEDGMENTSREFERENCES |
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Tracking algorithm. The tracking algorithm uses a simple image registration technique of spatial cross correlation to measure the movement of features on sonograph images. The algorithm has been customized to study relatively small movements of the muscles soleus and gastrocnemius, although in principle it can be applied to track the movements of any feature or structure on a series of images.
The cross-correlation technique has an in-principle limitation that is that the same feature of interest must be present in similar form in the two frames between which a change in position of the feature is calculated. The procedure is subject to error or fails when the same feature is not present in both images separated in time (Fig. 3A). When pennate muscle such as soleus and gastrocnemius is tracked, changes in contractile length are associated with a change in angle of pennation. Thus the orientation of the white collagen fascicles changes. Also, with large joint movements and large muscle contractions, the muscle movement cannot be assumed to be perfectly planar. The plane of white collagen fascicles that is in the narrow planar beam of the probe and thus in view in one image may not be in view in a different image. These are two reasons why the feature being tracked can change.
Our algorithm used absolute tracking, comparing all frames with a single base frame to ensure a consistent reference for a single trial (Fig. 3, A and E). Our algorithm then used relative tracking, comparing frames with successive base frames to measure regions where the image features had evolved from that presented in the single base frame (Fig. 3, B–D). If the regions to which relative tracking is applied are not bounded by regions that are well correlated with the single base frame, then uncertainty in estimating contractile length may grow so large as to render the estimate useless (Fig. 3, B and C). In such cases, manual identification of a few key boundary frames might provide a method for anchoring the relative tacking sections.
So far, our fully automated technique has been successfully applied to large, exaggerated, slow voluntary forward and backward sways (16) to tiny muscle movements under postural conditions (14, 15) and to slow leg flexion/extension movements of 10° at the ankle joint (Fig. 6). This example of slow leg flexion/extensions (Fig. 6) illustrates the ability to resolve differential movement between soleus and gastrocnemius in close proximity across the central aponeurosis. So far, we have applied this technique to small or slow medium-size movements. It has yet to be demonstrated whether this or a similar technique can be applied successfully to measuring changes in contractile length during large, fast limb movements.
Temporal and spatial resolution under biological conditions. Under biological conditions, the ultrasound tracking technique is capable of resolving rapid (0.1 s), individual, unaveraged changes in muscle contractile length as small as 5 µm (0.03 pixels) and in these experiments measured abrupt contractile stretches as large as 400 µm (2.2 pixels) (Figs. 7 and 8). These individually measured changes in contractile length are credible for the following reasons.
First, the tracked stretches occur repeatedly in response to repeated identical applied rotations of the foot (Fig. 7). Unlike the unpredictable background variation in contractile length, we know that contractile length should be changing in a square-pulse manner of width 200 ms and constant height simultaneously with the ankle rotations. Whether the tracking procedure "sees" these stretches and reproduces the applied waveform is a powerful test of its spatial and temporal resolution.
Second, the consistency of the individual stretch measurements is virtually as reliable as biomechanical measurements of the actual ankle rotation (Fig. 8, D–F). The CV is 1.6 times that produced by laser measurement of ankle rotation, and the CV is better than the laser measurements for the smallest movements.
Third, the size of the measured stretch correlates with the size of the applied rotation (Fig. 8, A–C). The muscles show signs of being more compliant with larger ankle rotations, which accords with the known fact that short-range muscle stiffness is greater than long-range muscle stiffness (12, 23).
Fourth, 50% or more of the true ankle rotation is seen by the series elastic component rather than the contractile component, which is consistent with recent measurements on relaxed calf muscles (10) (Fig. 8, A and B).
Thus the tracking procedure has a reliable spatial and temporal resolution of 5 µm and better than 0.1 s, respectively, under biological conditions. Observation of Fig. 7, H–J, suggests that, with sufficient averaging to reduce the background variation in contractile length, even smaller applied stretches may be resolvable. The remaining issue untested by this procedure is whether there was a systematic error in the size of the measured stretches even though the applied ankle rotation waveform was tracked reliably.
Intrinsic accuracy and frequency response of the ultrasound tracking technique. Under nonbiological laboratory conditions, the ultrasound tracking technique is capable of faithfully resolving movements of peak-to-peak amplitude 1.5 µm (0.008 pixels) (Fig. 9A). It is clear from Fig. 9A that with smoothing or averaging to reduce the background noise of 0.6 µm (0.003 pixels) smaller movements still may be resolvable. The biological measurement of changes in contractile length requires difference in motion between two features (two ends of the muscle) and thus is intrinsically subject to twice the error measured in the laboratory oscillating wire experiment. Even so, the resolution of 5 µm achieved under biological conditions is well within the intrinsic capabilities of the technique.
The high accuracy of low-frequency measurements (Fig. 9, E and F) even at the smallest amplitudes of motion confirms that there is no intrinsic systematic error in the measurement technique. This gives confidence that 5-µm movement measured under biological conditions represent 5 µm of actual movement recorded by the probe.
The accuracy of tracked movements decreases progressively with frequency. This low-pass characteristic is easily explained by an effective sampling frequency that is less than the frame rate. For example, if an oscillation is sampled once in every half cycle, then the amplitude measured would depend on when the measurement was made during the half cycle. If the movement was sampled at its extremes, the accuracy would be 100%, but the accuracy would be less if the motion was sampled elsewhere. On average, one might expect the accuracy to be 63% if the sampling points were randomly chosen (mean, abs, sin, theta = 0.63), and since the accuracy is 63% at 6 Hz (Fig. 9E), this indicates that the effective sampling frequency is 12 Hz and the independent temporal resolution is 83 ms.
During the most rapid large movements (amplitude > 2 mm, frequency > 4.5 Hz), frames were produced where the wire appeared at two or three distinct locations. This illustrates that each frame produced by the scanner is a composite of the two or three most recent frames and explains why the effective sampling frequency of 12 Hz is less than the actual frame rate of 30 frames/s. The tracking algorithm in its current form produced false-positive correlations with the ghost images and particularly preferred ghosts that were close to the orientation of the base frame rather than stronger images at a different orientation. Manual tracking has confirmed that the decreases in accuracy of the largest movements below the main trend is a consequence of tracking algorithm limitations and not the ultrasound scanner.
Given that the pixel resolution is 185 µm, it may be surprising to discover that movements of a few micrometers can be registered by the scanner. This demonstrated fact is possible because of spatial averaging and spatial consistency of the feature displacement. The spatial cross-correlation calculation is averaging information from two squares each of 31 x 31 = 961 pixels. The resulting 2D correlation function, which is sampled at pixel intervals, has a peak whose location can be estimated by subpixel interpolation. In effect, the feature displacement is independently estimated many times, increasing the likelihood that the mean estimate is accurate. The spatial sharpness and smoothness of the peak depends on the extent to which the shape and orientation of the feature is preserved while only its position changes. This latter condition is best met for small movements.
The accuracy of our technique can be compared with the automated algorithm of Magnusson et al. (20). As a test, these authors tracked a needle sliding 10 mm through gel along the probe surface with an accuracy of <0.2 mm or <2%. This provides a comparable test to our oscillating wire experiment. For low-frequency movements of 0.8–8 mm peak-to-peak amplitude, we also observed a mean accuracy of <2% (Fig. 9F). Thus, for movements of up to 1 cm, the two techniques have similar accuracy.
Biological validity of the ultrasound measurements. The tests presented in this paper assess the ability of the ultrasound technique to reliably and accurately measure movement recorded by the probe. The remaining question is the extent to which movements of the distal and proximal aponeuroses recorded on the sonographs correspond to actual movements of the contractile portion of a whole muscle. This is a complex issue because the probe only sees a thin slice of muscle tissue typically comprising 5 x 5 x 0.24 cm (near field 0- to 5-cm depth, Medical Devices Agency report, MDA/99/61, DIASUS). Errors will be introduced for the following reasons.
First, muscle movement perpendicular to the slice cannot be seen. Most muscles do not shorten precisely along a plane, and the gastrocnemius and soleus muscles do not have identical lines of action. Perpendicular muscle movement is less of a problem than might be imagined. We are measuring changes in contractile length along the line of the muscle-tendon unit and changes perpendicular to this are not of concern. We actually observe changes perpendicular to the central aponeurosis in the plane of the probe (changes in muscle thickness), and we discard this information.
Misalignment of the slice with the line of action of the muscle is the source of error. Off-plane observations will underestimate contractile movements and introduce a geometrical error of 1 – cos where is the angular disparity between the probe plane and line of muscle-tendon action. The extent of this error can be estimated from the anatomy of the muscles. Between insertion and origin, the muscles make an angle of <10° medially or posteriorally to the leg. If the probe has been aligned to the leg and not manually adjusted to provide a longitudinal view the maximum error would be 10°. Aligning the probe will reduce the error. Assuming a worst case of 20° error, changes in contractile length would be underestimated by 6%.
Second, if the muscle does not shorten uniformly along its length and in all planes, then the shortening measured in the observed region may not represent the shortening of the whole contractile element. We measured changes in contractile length along the line of the muscle-tendon complex, and we assumed that the proximal and distal aponeuroses move relative to each other as nondeformable objects. This is thought to be a good assumption (20). We see 5 cm of muscle belly, 1/4 and 1/6 of gastrocnemius and soleus, respectively, and have not found evidence of aponeurosis strain.
The representative example of leg flexion/extension movements (Fig. 6) reveals excellent correlation (r = 0.993) between the contractile length of the monoarticular soleus muscle and ankle joint angle. This gives confidence that what the probe sees is a measure of whole muscle behavior, although it does not rule out any systematic errors in the measurement of contractile length. The good correlation between biarticular gastrocnemius and EMG (r = –0.71) also gives confidence that what is seen by the probe reflects whole muscle activity and again does not rule out systematic errors in contractile length.
Evaluation of the ultrasound tracking technique. For high accuracy, this technique is most suitable for measuring features that move in the low-frequency range of 0–4 Hz. Higher frequency movements can be studied, but they will be attenuated by the low-pass filtering effect of the ultrasound scanner. Within these limits, high accuracy is possible for moderately large movements of 8 mm down to small biological movements of 5 µm.
This technique has the advantage of allowing noninvasive in vivo measurements to be made on human subjects, whereas invasive techniques such as sonomicrometry (4, 6–8) and X-ray scanning (1) are unattractive for human subjects. Modern real-time and cine-phase contrast magnetic resonance imaging scanning techniques (2, 22, 24) may be more suitable for making accurate noninvasive measurements on human subjects of rapid muscle contractions, although the opportunities for movement are limited when subjects are inside the magnetic resonance imaging scanner and the limb under observation has to be kept relatively still. For slower, muscle movements and particularly for moderate to small muscle movements, the ultrasound scanning technique has a clear advantage in accuracy and allowed freedom of natural movement by the subject. With higher effective frame rates, it is possible that this technique could track muscle movements in walking, running, and jumping.
What physiological and biomechanical reasons are there for studying muscle contractile length? Muscle contractile length is largely determined by neural stimulus (EMG) and joint angle (origin to insertion distance). When the tendon is relatively compliant, contractile length and joint angle are not the same thing, and each quantity needs to be measured independently. This is particularly the case for the calf muscles where the compliant Achilles tendon has interesting consequences for the neural control of balance (5, 13–16). Our measurements of contractile length have demonstrated the compliance of the Achilles tendon and the consequent paradoxical muscle movements that occur in normal stance. When the tendon is compliant, contractile length is independent of joint angle and provides a view of muscle activity and neuromotor output that is complementary to surface EMG. Contractile length is similar to integrated EMG (14) and less ambiguous in its interpretation. Namely, it is possible to know which muscle you are studying and you can distinguish between the activity of anatomically close muscles. Moreover, as a signal, contractile length is less noisy than EMG (15). Ultrasound tracking has the potential to study muscle activity and neuromotor output in small muscles and muscles close together where surface EMG cannot resolve the activity of individual muscles.
Judging by the number of muscle spindles in the body, contractile component length is a quantity of major sensory interest to the nervous system. By measuring contractile length directly, physiologists have closer access to information that the nervous system is interested in, and this is particularly relevant in the study of stretch reflexes.
The soleus and gastrocnemius muscles are pennate muscles. The aponeuroses at both ends of the muscle fibers can be seen simultaneously since the proximal and distal aponeuroses interdigitate. For fusiform and strap muscles, it will probably not be possible to view both ends of the contractile portion simultaneously, although it may be possible to measure contractile thickness (11). It will still be possible to measure movement in sections of muscle, although the relationship to whole muscle activity may be more ambiguous. Also, fusiform muscles are more likely to have higher contraction velocities than pennate muscles, and this may require a different tracking algorithm to analyze the ultrasound images.
In conclusion, here, we have demonstrated a technique for tracking changes in contractile length of soleus and gastrocnemius. With the scanner used, the technique is sensitive to changes of 1 µm and can reliably measure changes of 5 µm with a temporal resolution of 80 ms. Using applied ankle rotations, we have demonstrated that the reliability of these measurements is as good as laser measurements of ankle angle. The ultrasound scanner has a low-pass filter effect in that it attenuates higher frequencies with a 3-dB attenuation at 6 Hz. For low frequencies under 3 Hz, the intrinsic accuracy of this technique is close to unity. Intrinsic error increases for the smallest length changes but is still <10% for movements larger than 10 µm. This technique is particularly suitable for noninvasive tracking of pennate muscles, tendons, and aponeuroses and is suitable for studying muscle motion in the frequency range of voluntarily controlled movements.
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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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