Asymmetric deformation of contracting human gastrocnemius muscle

Abstract

Muscle fiber deformation is related to its cellular structure, as well as its architectural arrangement within the musculoskeletal system. While playing an important role in aponeurosis displacement, and efficiency of force transmission to the tendon, such deformation also provides important clues about the underlying mechanical structure of the muscle. We hypothesized that muscle fiber cross section would deform asymmetrically to satisfy the observed constant volume of muscle during a contraction. Velocity-encoded, phase-contrast, and morphological magnetic resonance imaging techniques were used to measure changes in fascicle length, pinnation angle, and aponeurosis separation of the human gastrocnemius muscle during passive and active eccentric ankle joint movements. These parameters were then used to subsequently calculate the in-plane muscle area subtended by the two aponeuroses and fascicles and to calculate the in-plane (dividing area by fascicle length), and through-plane (dividing muscle volume by area) thicknesses. Constant-volume considerations of the whole-muscle geometry require that, as fascicle length increases, the muscle fiber cross-sectional area must decrease in proportion to the length change. Our empirical findings confirm the definition of a constant-volume rule that dictates that changes in the dimension perpendicular to the plane, i.e., through-plane thickness, (−6.0% for passive, −3.3% for eccentric) equate to the reciprocal of the changes in area (6.8% for passive, 3.7% for eccentric) for both exercise paradigms. The asymmetry in fascicle cross-section deformation for both passive and active muscle fibers is established in this study with a ∼22% in-plane and ∼6% through-plane fascicle thickness change. These fiber deformations have functional relevance, not only because they affect the force production of the muscle itself, but also because they affect the characteristics of adjacent muscles by deflecting their line of pull.

a rarely discussed topic in muscle physiology is how the cross-sectional area of the fiber changes with changes in fiber length. Although the ratio of muscle fascicle length change to the aponeurosis displacement, conventionally termed the “gear ratio”, can vary, depending on the relative magnitude of muscle deformation in the direction orthogonal to the muscle's line of action (3), the significance of dynamic changes in muscle shape has been overlooked in most classic models of pinnate muscle (1). Furthermore, patterns of deformation provide important measures of muscle properties, which must be accounted for in accurate models of muscle mechanical actions. While attention to this topic has been intermittent, it has enjoyed a long history, dating back to the 17th century when Stensen recorded his observation that the length and separation of the aponeuroses of contracting muscles remained constant, implying that the plane described by these measures retained a constant area as a muscle changed length (cited in Ref. 7). One significant conclusion from this constant-volume observation is that the muscle dimension perpendicular to the plane must also remain constant to maintain the constant volume of the muscle. The described plane is ideally a plane consisting of a single layer of muscle fibers, thus implying that the deformation of a muscle fiber cross section is not symmetric as the fiber length changes (16, 19, 20). Such observations stimulated a long history of theoretical concepts assuming a constant aponeurosis separation (i.e., the distance between aponeuroses), with relative small changes in aponeurosis length (i.e., the length of attachment) often simplified to a parallelogram-like structure with a constant area (5, 13, 18, 20). However, recent experimental findings have created some uncertainty as to whether the area defined by the length of the aponeuroses and their separation actually remain constant. A pair of papers by the same authors have indicated no significant differences in area of rat gastrocnemius over a muscle length (l₀) range of −5 mm to +1 mm (19), but an area decrease of 25% as the muscle shortened from l₀ + 3 mm to l₀ − 6 mm (20). Other investigators have reported an 11% decrease in area as the rat medial gastrocnemius (MG) muscle contracts isometrically, with very little effect of length between l₀ − 4 mm and l₀ + 3 mm (16). In addition, we have shown a relative large aponeurosis length change (up to 10%) in an isometric plantar flexion of 40% maximum voluntary contraction (MVC) in humans (8). Another apparent finding was that the aponeurosis of the two sides behaved differently (8, 14). Thus the area of the muscle plane may vary as the muscle fiber length changes, and such variation may be dependent on muscle length, possibly even dependent on individual muscle architecture (9, 10). Nevertheless, a consequence of the muscle constant volume is that muscle fiber cross-sectional deformations must remain within measurable geometrical constraints, relating the area of the plane in which the fibers lie to their thickness in the through-plane direction. Thus measurable changes in the area of the plane can be used to measure through-plane changes and thus determine any asymmetry in the deformation of muscle fiber cross section (2, 16).

To test this hypothesis, we used velocity-encoded, phase-contrast (VE-PC) and morphological magnetic resonance imaging (MRI) to measure the area of a number of subregions of the muscle bounded by fascicles and the aponeuroses they contact in one oblique-sagittal plane of the muscle. We also measured the overall lengths of the muscle and aponeurosis, and aponeurosis separation. We selected the MG muscle because its aponeuroses lie on the surfaces of the muscle, and because the intramuscular region has a relatively uniform structure devoid of large, load-transmitting tendinous structures. A combination of VE-PC and morphological MRI offers an advantage of being able to accurately track fascicle orientation and its behavior as the muscle length changes. We compared the deformations of the MG between passive and active eccentric movements to determine whether there are significant differences between the deformations of active and passive muscle fibers during length changes and to determine the validity of using submaximal contraction levels of whole muscle to draw conclusions about this property of active portions of muscle.

METHODS

Experiment I

Eleven (9 men) healthy subjects (age 29 ± 10 yr, height 1.71 ± 0.08 m, weight 74 ± 15 kg) were recruited to participate in this study. The study was carried out under the approval of the Medical Research Ethics Board of University of California San Diego and conformed to all standards for the use of human subjects in research as outlined in the Declaration of Helsinki on the use of human subjects in research. All subjects gave informed consent before participating in the study.

Deformations of the MG muscle were measured using VE-PC imaging as the foot was dorsiflexed with a hydraulically operated foot pedal. The details of this technique have been previously described (6, 8, 14, 15). The pedal was programmed to complete a rotational cycle of 45°, from 120° (most plantar flexed position) to 75° (most dorsiflexed position) with the cyclic period of 2.86 s (21 cycles/min). The complete acquisition of VE-PC images required ∼70 identical ankle joint rotations. Ankle torque was measured with an optical strain gauge (Fiberscan 2000, Luna Innovations, Blacksburg, VA) glued to the foot plate. The force signal, along with a target force level, was projected onto the face of the scanner to provide feedback to the subject (14). An MVC value was determined by asking the subject to perform three voluntary maximum ankle plantar flexions with the ankle in 90° plantar flexed position. The highest peak value was used as the MVC (6). For the eccentric contraction, the subject performed 40% of the MVC during the dorsiflexion phase of the ankle rotation cycle, thereby activating the plantar flexors under the stretching effect of the dorsiflexion. A 40% MVC was about the maximum resistance at which the subject could complete the requisite number of phase-encoding cycles required to acquire a magnetic resonance (MR) image without fatigue. For the passive condition and plantar flexed phase during active eccentric contraction, the subject was instructed to fully relax the leg while the foot rotation was driven by the testing apparatus. The order of testing for the two exercise paradigms was randomized across subjects.

MR imaging.

All morphological and VE-PC images were acquired using a 1.5-Tesla Signa HDx MR scanner (GE Medical Systems, Milwaukee, WI). The subject lay supine on the MR scanner, and the foot of the dominant leg was positioned on the foot pedal of the testing apparatus (14). Morphological images were obtained with the ankle in the extreme plantar flexed position (120°) using a water-saturated spin echo sequence [2,000-ms repetition time (TR), 12.9 ms echo time (TE), 90° flip angle (FA), 192 × 320 image matrix, 300 × 180-mm field of view (FOV), 3-mm slice thickness, 244-Hz/pixel bandwidth, 3 excitations, 1 slice, and 2:30 scan time]. These images were used to visualize the structural orientation of fatty layers running parallel to fascicles, facilitating the selection of regions of interest (ROIs) along the direction of fibers over the entire length of the MG muscle (Fig. 1, A–C). The orientation of oblique sagittal images was adjusted to provide a section showing in-plane muscle fibers, identified as the plane in which visibility of fascicle lengths was maximized. All subsequent sagittal images were obtained in this orientation. With similar ankle angle position, other morphological images were acquired in the axial plane from the origin to the MG insertion by using axial slices acquired with a fast gradient echo sequence (371-ms TR, 2.4-ms TE, 45° FA, 256 × 192-image matrix, 180 × 135-mm FOV, 5-mm slice thickness, 10-mm slice interval, bandwidth 244 Hz/pixel, 1 excitation, 25–35 slices, and 1:38 scan time). The fascicle behavior during passive and eccentric modes of the contraction was measured by a VE-PC sequence (16.5-ms TR, 7.7-ms TE, 20° FA, 122-Hz/pixel bandwidth, 10 cm/s velocity encoding in three directions, 4 views per segment, 22 phases, 2 excitations, 154 × 256-mm image matrix, 300 × 180-mm FOV, 1 slice, and 1:53 scan time). See Supplemental Video Clips S1 and S2. (The online version of this article contains supplemental data.)

Fig. 1.

A: water-saturated imaging was used to elucidate the structural orientation of fatty layers running parallel to muscle fascicles. Oblique sagittal section from one typical subject is shown. B and C: the T1-weighted image was used to determine the ends of the fascicles (whose positions were defined by superposition of the fascicle position from the water-saturated images in A), as shown by the red dots during passive condition (B) and active eccentric contraction (C). For B and C, left side shows ankle plantar flexed position (phase 1 in a time phase of E), and right side shows ankle-most dorsiflexed position (phase 11 in a time phase of E). See Supplemental Video Clips S1 (passive condition) and S2 (active eccentric contraction). D: the white filled portion identifies area, defined by the two aponeuroses (ad and bc) and two fascicles (ab and cd). E: the time course of the exerted torque and ankle angle during passive condition and 40% maximum voluntary contraction (MVC) eccentric contraction.

Data analysis.

ROIs along the superficial and deep aponeuroses were used to define the orientation and deformation of the fascicle-aponeurosis complex using an indigenous program written using MATLAB (The Mathworks, Natick, MA). A registration between the morphological image and the corresponding VE-PC image was used to translate the location of ROIs selected on the morphological image onto the VE-PC image using another indigenously developed image registration algorithm. Muscle fascicles were identified as orientated parallel to the fatty layers, which were first identified using the morphological images, as described above. The fascicular movements were characterized by tracking ROIs arranged between their origins (superficial aponeurosis) and insertions (deep aponeurosis) along the fascicular length. There were no ROIs between origin and insertion of the fascicle, since the trajectories of the fascicles in the MG appear mostly linear (14). Segments of the image plane bounded by the aponeuroses and between two muscle fascicles defined the area occupied by a group of in-plane muscle fascicles (Fig. 1D), and these were tracked throughout the ankle rotation cycle. The muscle area in the image plane was calculated by multiplying the sum of the all of those muscle segments. The overall length of muscle, superficial, and deep aponeurosis was manually measured as the distance between the most proximal and distal ends of the muscle and each aponeurosis in the oblique-sagittal magnitude image with ImageJ (National Institutes of Health, Bethesda, MD), in which MG was identifiable. The aponeurosis separation was also measured in each segment as the perpendicular distance between the aponeuroses (Fig. 1D) and averaged over all of those segments to generate a mean aponeurosis separation. Strain ([l − l₀]/l₀) was calculated by using the distance between two tracked ROIs in the VE-PC images (l) and the resting length at a plantar flexed position (l₀).

The in-plane cross sectional dimension of the fascicle was calculated by dividing the area by the fascicle length. The through-plane dimension, perpendicular to the plane of the image, or “thickness” was calculated by dividing the muscle volume by the area. It should be pointed out that, while the through-plane direction would have coincided with the mediolateral direction, if the imaging plane were a straight sagittal, in the present case, since the imaging was an oblique sagittal plane, the through-plane direction, i.e., the normal, to the imaging plane was tilted away from the mediolateral axis. The volume of the muscle was calculated by multiplying the sum of the cross-sectional areas by the distance between axial slices.

For the purpose of confirming that the typical velocities (and therefore displacements) along the through-plane axis are minimal, which implies that fascicles remain mainly in plane throughout the contraction cycle, a large rectangular ROI was located in the middle portion of the MG for each subject (8). The size of the ROI, width ∼13.2 mm × height ∼52.2 mm, was varied to best fit each subject's anatomy. The larger side of the ROI was aligned with the superior-inferior direction of the leg. The pixels within the ROI were averaged to generate a mean velocity, which was then used to calculate the velocity of the ROI in the three orthogonal directions: anterior-posterior, right-left, and superior-inferior. The filtration method described above was used to minimize discrepancy in pixel locations that would have occurred if a single pixel were used as the ROI.

Experiment II

Five (four men) volunteers (age 27 ± 8 yr, height 1.74 ± 0.10 m, weight 70 ± 13 kg) participated in an additional experiment. MVC and lower limb volume tests were conducted before and immediately after a 64-repetitive passive condition and 40% MVC eccentric contractions. An MVC measurement and 64-repetitive exercise's protocol were exactly similar to the main experiment (experiment I) in the present study. A lower limb volume was measured by a volumeter that was filled with water up to the level of an extended lip through which excess or displaced water flowed. Subjects placed their calf in the volumeter, and displaced water from the volumeter was collected in a beaker and measured on a scale.

Statistics

Values are presented as means and SD. The dependent variables for the area, fascicle length, and in-plane and through-plane thicknesses were compared with a two-factor ANOVA (2 exercise paradigms × 22 time points) with repeated measures. The dependent variables for the overall muscle length, aponeurosis length, and aponeurosis separation were compared with a two-factor ANOVA (2 exercise paradigms × 2 conditions). The dependent variable for the strain was compared with a one-factor ANOVA (2 exercise paradigms). The dependent variables for the MVC and lower limb volume were compared with a two-factor ANOVA (2 exercise paradigms × 2 conditions) with repeated measures. The Newman-Keuls or Scheffé tests were used for post hoc analysis where appropriate. The level of statistical significance was set at P < 0.05.

RESULTS

The area bounded by the aponeurosis and a pair of identified fascicles did not change significantly during an eccentric contraction (3.5 ± 2.5% in the most dorsiflexed position compared with the initial plantar flexed position, Fig. 2A). The corresponding area measured during a passive ankle dorsiflexion over the same excursion increased significantly (P < 0.05, main effect of time point in a 2-factor ANOVA with repeated measures) (6.8 ± 3.6% in the most dorsiflexed position compared with the initial plantar flexed position). The area differed significantly between passive condition and active eccentric contraction in the 10th and 11th time phases (P < 0.05, main effect of exercise paradigm in a 2-factor ANOVA). There was no interaction for the area between the exercise paradigm × time point. The initial fascicle length was 34 ± 7 mm in the plantar flexed position (Fig. 2B). During dorsiflexion, the muscle fascicle length increased by ∼10 mm (29%) to 45 ± 9 mm for passive condition and 43 ± 3 mm for active eccentric contraction (P < 0.05, main effect of time point in a 2-factor ANOVA with repeated measures). There was no significant difference in the fascicle length change between passive condition and active eccentric contraction. There was no interaction for the fascicle length between the exercise paradigm × time point. The findings of the in-plane and through-plane thicknesses are described into the discussion. There were no interactions for the in-plane and through-plane thicknesses between the exercise paradigm × time point.

Fig. 2.

A: changes in the area (y-axis) bounded by the fascicles is plotted as lines with open circles (passive condition) and solid circles (active eccentric contraction) with the x-axis of the graphs representing the 22 cine-MRI frames throughout the ankle dorsiflexion-plantar flexion cycle. B: change in fascicle length and in-plane and through-plane thicknesses of the fascicle during passive (top) and active eccentric (bottom) ankle dorsiflexion-plantar flexion cycle. Values are means and SD. *P < 0.05 vs. first time phase. #P < 0.05, passive condition vs. active eccentric contraction.

The relationship between torque and fascicle length change for the passive condition and active eccentric contraction is shown in Fig. 3. The torque-length curves traveled in a clockwise direction for both passive condition and active eccentric contraction. The torque increased significantly in the initial lengthening (dorsiflexed) phase, and then remained nearly constant in the late lengthening phase. The active eccentric torque was greatest in the lengthening (dorsiflexed) phase. The greatest fascicle length change was observed in the most dorsiflexed position for both passive condition and active eccentric contraction. There was no interaction for the fascicle length between the exercise paradigm × time point.

Fig. 3.

Relationship between torque and fascicle length change of the 22 cine-MRI frames throughout dorsiflexion-plantar flexion movements with the passive condition (open circles) and active eccentric contraction (solid circles). Arrows are drawn as a guide to the direction of dorsiflexion-plantar flexion movements. Shaded circle indicates the most dorsiflexed position for both the passive condition and active eccentric contraction, respectively. One data point is represented as a mean of 11 subjects.

The overall muscle length increased 8.5 ± 4.7% for the passive condition and 5.7 ± 2.7% for the active eccentric contractions as the ankle dorsiflexed (P < 0.05, main effect of condition in a 2-factor ANOVA, Table 1). The aponeuroses were lengthened 7.4 ± 4.1% (superficial aponeurosis) and 9.7 ± 4.2% (deep aponeurosis) for the passive condition and 5.3 ± 2.3% (superficial aponeurosis) and 5.7 ± 4.1% (deep aponeurosis) for the eccentric contraction as the muscle lengthened (P < 0.05, main effect of condition in a 2-factor ANOVA). There were no interactions for the overall muscle and aponeurosis lengths between the exercise paradigm × condition. The strains of the muscle and deep aponeurosis were greater for the passive condition than the eccentric contraction (P < 0.05, main effect of exercise paradigm in a 1-factor ANOVA).

Table 1.

Changes in dimensional properties of the muscle and aponeurosis

	Passive Condition			Active Eccentric Contraction
Condition	Rest (initial plantar flexed), mm	Rest (most dorsiflexed), mm	Strain, %	Rest (initial plantar flexed), mm	Active (most dorsiflexed), mm	Strain, %
Muscle length	183.0 ± 31.7	198.1 ± 33.1*	8.5 ± 4.7†	181.8 ± 33.0	192.2 ± 36.1*	5.7 ± 2.7
Superifical aponeurosis length	189.5 ± 31.9	203.4 ± 35.2*	7.4 ± 4.1	188.8 ± 34.7	198.7 ± 36.3*	5.3 ± 2.3
Deep aponeurosis length	162.6 ± 23.6	178.0 ± 24.6*	9.7 ± 4.2†	159.8 ± 20.4	168.9 ± 22.6*	5.7 ± 4.1
Aponeurosis separation	7.5 ± 1.2	7.4 ± 1.2	−1.5 ± 3.4	7.5 ± 1.5	7.3 ± 1.4*	−2.3 ± 3.1

Value are means ± SD. Muscle and aponeurosis lengths are a longitudinal distance between proximal and distal ends. Aponeurosis separation is a transverse distance between two aponeuroses.

^*P < 0.05 vs. initial plantar flexed position.

^†P < 0.05 vs. active eccentric contraction.

Aponeurosis separation decreased for both passive condition (−1.5 ± 3.4%) and active eccentric contraction (−2.3 ± 3.1%). Statistical significance was observed in aponeurosis separation only for active eccentric contraction between rest (initial plantar flexed position) and active (most dorsiflexed position) modes (P < 0.05, main effect of condition in a 2-factor ANOVA). There was no interaction for the aponeurosis separation between the exercise paradigm × condition.

Movement of the muscle was evaluated along the three orthogonal directions (Fig. 4). Velocity vs. time phase curves of the muscle revealed relatively high velocities in the superior-inferior direction during passive condition and active eccentric contraction, while the velocities in right-left direction were near zero. These findings indicate that the velocities and, therefore, displacements of the fascicles along the through-plane axis are minimal. From these data, we concluded that fascicles movement remains mainly in-plane during joint movement.

Fig. 4.

Representative velocity-encoded, phase-contrast (VE-PC) images that are used for calculation of velocity distribution and displacement of tissue points within the medial gastrocnemius muscle. A: VE-PC MRI provide both magnitude (leftmost) and three velocity images. Anatomical location of the rectangle region of interest can be chosen from the magnitude image. Three sagittal velocity images with velocities encoded in the anterior-posterior (A-P), right-left (R-L), and superior-inferior (S-I) axes, acquired during passive contraction at an angle corresponding to a dorsiflexed position (phase 6 in a time phase of B), are shown on the three images on the right-hand side, respectively. In the velocity images, the gray-scale values represent velocities, with white indicating maximum inferior to superior, and dark indicating maximum velocity in the opposite direction. B: velocity vs. time phase curves during passive (top) and active eccentric (bottom) ankle dorsiflexion-plantar flexion cycle. The positive velocities represent movement toward the posterior side for A-P axis, left side for R-L axis, and inferior side for S-I axis, respectively. Each graph is represented as a mean of 11 subjects. The images, as well as the curves, indicate substantially higher S-I and, to a lesser degree, A-P velocities than through-plane R-L velocities.

For experiment II, both MVC and lower limb volume remained unchanged between before and immediately after passive condition (2.0 ± 2.5% for the MVC and 0.5 ± 1.0% for the lower limb volume immediately after exercise compared with before exercise) and active eccentric contraction (2.1 ± 2.8% for the MVC and 0.7 ± 1.3% for the lower limb volume immediately after exercise compared with before exercise). There were no interactions for the MVC and lower limb volume between the exercise paradigm and time point.

DISCUSSION

The experimental data presented here clearly provide new physiological findings regarding fiber deformation concomitant with fiber length changes. A long history of experimental data emphasize that muscle volume remains constant during contraction (7). Thus, if the area of a plane within a deformed muscle remains constant, as assumed by traditional models of muscle architecture (5, 13, 18, 20), the dimension perpendicular to that plane must remain constant, if the volume remains constant. Similar geometry shows that, if the area of the plane changes, the dimension perpendicular to the plane must change in reciprocal proportion, if the volume remains constant. In our results, the measured area varied over different angles of the ankle joint movement (Fig. 2A). This contradicts the more traditional view, which reasons that a constant aponeurosis separation, often coupled with an assumption of minimal aponeurosis strain, results in negligible changes of the in-plane muscle area. The reason for this difference may, in part, be due to differences in methods of measurement of the separation and length of the aponeurosis. Most previous studies have typically measured the aponeurosis behavior by pressing an ultrasound probe in the direction of the muscle transverse axis in a small ultrasound window (FOV). This makes it difficult to monitor accurately the behavior of the overall aponeurosis length change and aponeurosis separation as the fascicle length changes. MRI allows one to overcome these difficulties and derive more accurate indexes with visualization of a much larger FOV.

Constant-volume considerations of the whole muscle require, based on geometry, that, as fascicle length increases, their cross-sectional area must decrease in proportion to the length change. Thus the 29% increase of fascicle length measured in these experiments should be accommodated by 29% overall shrinking in one or more orthogonal directions of the cross section. If the change in cross section was radially symmetric, i.e., through-plane and in-plane dimensions of the fascicle changed equally, this would result in an approximate reduction of diameter by ∼12%, resulting in a 12% increase in the in-plane area measurement (29% fascicle length increase and 12% diameter decrease) and a 12% reduction in through-plane thickness. The asymmetry in fascicle cross-section deformation for both passive and active muscle fibers is established in this study with a ∼22% in-plane and ∼6% through-plane fascicle thickness change for a passive length changes and ∼23% in-plane and ∼3% through-plane fascicle thickness change for an eccentric contraction (Fig. 2B). The trend apparent from Fig. 2B appears to be similar in both passive and active muscle, with a decrease in the through-plane fascicle dimension as the area of the muscle plane increases, although this appears to be significant only in the passive movement. Thus fascicles lengthening either passively or actively appear to behave in similar ways, which suggest a mechanism within muscle that constrains the dimensional changes of fascicles. Theory indicates that, since there is no provision for lateral adjustments between fibers that remain in lateral contact with each other, the fibers of a tightly packed fascicle in a pinnate muscle will deform asymmetrically (5). This is illustrated in Fig. 4, where an initially circular cross section deforms into an ovate cross section, thinning in anterior-posterior direction (Fig. 5B).

Fig. 5.

Diagram representing the observed fascicle (and deduced muscle fiber) deformation patterns. The gray and red colors indicate the ankle plantar flexed position and most dorsiflexed position, respectively. A: a constant-volume rule dictates that changes in the dimension perpendicular to the plane (−6.0% for passive condition, −3.3% for active eccentric contraction) equate to the reciprocal of the changes in area (6.8% for passive, 3.7% for active eccentric contraction) for both exercise paradigms. B: the asymmetry in fiber cross-section deformation can be confirmed by ∼22% in-plane thickness change and ∼6% through-plane thickness change.

The asymmetric fiber-shape change observed in our measurements suggests an intramuscular or intrafiber mechanical organization, which influences the way in which a fiber deforms, reducing the change in through-plane fiber cross section and increasing the in-plane dimension relative to changes that would be expected from a simple isotropic material. It is unclear from our present understanding of intramuscular mechanics whether this is a consequence of a systematic difference in stress vectors over the muscle fiber cross section, or due to a specific organization of materials that influence strain in specific directions throughout the muscle. An example of the former may be the orientation of the curvature of fibers in the three-dimensional muscle structure (11, 12). Tension in curved material exerts a stress vector toward the center of curvature, suggested to be a mechanism for producing gradients of intramuscular pressure during a contraction (13, 17). Appropriately oriented fiber curvature may also oppose muscle expansion in the through-plane direction. The fiber curvature may have a further physiological role, generating higher aponeurosis longitudinal strain due to an increase in contact surface between the distal end of fibers and aponeurosis, thereby influencing the aponeurosis movement vector to a greater degree than when the fibers insert into the aponeurosis as a straight line. An alternative means of restricting through-plane changes may be the incorporation of tensile materials (such as costameres) oriented along the through-plane axis of the fiber to limit expansion in that direction. Both of these potential mechanisms may be expressed in computational models of muscle with outputs that can be compared with data from experimental observations on contracting muscle, such as those presented here. Thus a precise definition of muscle behavior is both an input and a test variable for the development and refinement of theoretical models that our laboratory is now in the process of developing (4).

What is surprising in these results is not that the area increased as fascicle length increases, but that it is variable in contraction mode. The area increased with fascicle length change for both the contraction modes, but did not reach statistical significance for active eccentric contraction. The area change of the muscle segment was determined accurately by the vertical length and separation of the aponeurosis with a high spatial resolution. The aponeurosis separation remained constant or slightly narrowed for both contraction modes. The aponeuroses lengthened significantly for both, but strain was greater in the passive condition than the active eccentric contraction. This difference in area response between passive condition and active eccentric contraction appears to arise from the changes in the curvature of the aponeuroses. The eccentric contraction might be accompanied by significantly greater aponeurosis curvature than the passive condition in the ankle dorsiflexed position. We speculate that the aponeurosis curvature observed in this study is ultimately mediated by connective-tissue elements and muscle shape changes or intramuscular pressure. Although fascicle length change exhibited a tendency to be greater in passive condition than in active eccentric contraction (Fig. 3), the difference failed to reach statistical significance. Similar findings of lower pennation angle and fascicle length changes were observed during the eccentric mode relative to the passive condition, as shown in our laboratory's previous study (14). It would be useful to be able to estimate the magnitude of fascicle length change associated with a given contraction so that an accurate estimate of active force can be obtained. This would allow us to account for the fascicle lengthening/shortening that occurs during the contraction when series elastic elements are present.

The most obvious drawback of the present study is that VE-PC MRI technique requires 64 contractions to form a set of cine MR images. The active repetitive contractions might not produce consistently constant volume changes of a muscle, particularly in view of accompanying muscle swelling due to the accumulation of metabolites. However, this factor is probably minimal, given the lack of substantial changes in peak force and lower limb volume between pre- and post-64-repetitive submaximal eccentric contractions. Our results, therefore, suggest an interpretation that takes into account that the eccentric contraction used in the present study does not induce significant changes in muscle volume.

We conclude that the cross-sectional shape of fibers in a tightly packed pinnate muscle deforms asymmetrically during passive condition and active eccentric muscle contraction. We demonstrate how the fiber deforms as fiber length changes to maintain a constant volume throughout the contraction. These fiber deformations have functional relevance, not only because they affect the force production of the muscle itself, but also because they affect the characteristics of adjacent muscles by deflecting their line of pull.

GRANTS

This study was supported, in part, by National Institute of Arthritis and Musculoskeletal and Skin Diseases Grant 2R01-AR-53343-05A1.

DISCLOSURES

No conflicts of interest, financial or otherwise, are declared by the author(s).

AUTHOR CONTRIBUTIONS

Author contributions: R.K., J.A.H., and S.S. conception and design of research; R.K. and S.S. performed experiments; R.K. analyzed data; R.K., J.A.H., V.R.E., and S.S. interpreted results of experiments; R.K. prepared figures; R.K. drafted manuscript; R.K., J.A.H., V.R.E., and S.S. edited and revised manuscript; R.K., J.A.H., V.R.E., and S.S. approved final version of manuscript.