Sarcomere length measurement permits high resolution normalization of muscle fiber length in architectural studies
Departments of Orthopaedic Surgery and Bioengineering, University of California and Department of Veterans Affairs Medical Centers, San Diego, CA 92161, USA
* Author for correspondence at Department of Orthopaedic Surgery, UC San Diego School of Medicine and VA Medical Center, La Jolla, CA 92093-9151, USA (e-mail: rlieber{at}ucsd.edu)
Accepted 27 June 2005
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Summary |
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Key words: sarcomere compliance, muscle architecture, modeling, surgery, fiber length, physiological cross-sectional area
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Introduction |
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Physiological cross-sectional area is typically calculated from muscle
specimens (see, for example, Lieber et
al., 1992), using the equation:
![]() | (1) |
![]() | (2) |
|
![]() | (3) |
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Materials and methods |
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Fiber bundle dissection
Tibialis anterior (TA), extensor digitorum longus (EDL), and soleus muscles
were removed from the limbs, digested in 15% H2SO4 for
30 min to facilitate fiber bundle isolation and stored in 1x PBS at room
temperature until fiber bundle dissection. Small fiber bundles (550
fibers) were dissected from the whole muscle in 1x PBS under a
dissecting microscope using 820x magnification
(Sacks and Roy, 1982). Special
care was taken to remove the entire bundle, from tendon to tendon. At least
three bundles were isolated from different regions of each soleus and TA
muscle while four bundles were isolated from the EDL, one from each muscle
belly (Chleboun et al., 1997
).
Fiber bundle length was measured under the microscope with a digital caliper
to the nearest 0.01 mm. Only fibers that remained straight after fixation were
measured. This criterion excluded soleus muscle bundles fixed at ankle joint
angles of 150° since, at this angle, fibers had a distinctly wavy
appearance and length could not be reliably measured with calipers. Sarcomere
length was measured at three different points along each mounted bundle using
laser diffraction as previously described
(Lieber et al., 1990
). Fibers
were used only if at least two useable sarcomere lengths were obtained. Such a
criterion was necessary to preclude the possibility of normalizing sarcomere
length in damaged muscles, where severe nonhomogeneities can exist
(Talbot and Morgan, 1996
).
This criterion excluded 17 fibers from soleus muscles. In general, diffraction
pattern quality from the soleus was poor compared to TA or EDL, as has been
previously observed (Burkholder et al.,
1994
).
Raw fiber lengths were normalized to a standard sarcomere length of 2.5
µm (assumed to be mouse muscle optimal sarcomere length; see
Walker and Schrodt, 1973)
using Eq. 3. Two separate statistical approaches were used to determine the
quantitative effect of sarcomere length normalization. First, raw fiber length
was regressed against ankle and knee angle using simple and multiple linear
regression to determine whether fiber length varied with either ankle or knee
joint angle. Then, the same procedure was performed on normalized fiber length
to determine whether this variation was eliminated by the sarcomere length
normalization procedure. Next, to quantify the resolution of the normalization
procedure, raw and normalized fiber lengths were compared across groups by
one-way analysis of variance (ANOVA). Attempted and actual joint angles were
compared by one-sampled t-test. Resolution of the method was defined
based on the statistical power (1-ß) achieved using standard statistical
power equations (Sokal and Braumann,
1980
). This is because the normalization procedure must still have
adequate resolution in experimental studies, even after sarcomere length is
accounted for. For all tests, critical P-value (
) was set to
0.05 and values are reported in the text as mean ±
S.E.M. unless otherwise noted.
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Results and discussion |
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Variation between intended and actual joint angles was significant for six of the 14 groups of muscles within each intended joint angle (P<0.05). The average joint angle variability around the intended angle was 7.9±1.4° for the knee joint and 4.4±0.8° for the ankle joint. The fact that the variability for the knee was greater probably reflected the greater volume of proximal muscle mass on the femur (Fig. 1A).
Multiple regression analysis revealed that, for the EDL only, raw fiber length was significantly correlated with knee joint angle (P<0.05). This is reasonable based on the fact that the EDL is the only one of the three muscles studied that crosses the knee joint. In spite of this significant correlation, inclusion of knee joint angle in the regression relationship only increased the coefficient of determination marginally (from 0.26 to 0.31). One-way ANOVA results supported regression results in that raw fiber length was significantly different across ankle joint angles for all three muscles (P<0.02).
Sarcomere length normalization effectively eliminated the joint-angle dependent variation in fiber length, evidenced by both linear regression and one-way ANOVA analysis. Linear regression of normalized fiber length on ankle joint angle yielded no significant relationship between the two variables for any of the three muscles (Fig. 2D-F; P>0.2, r2 range 0.0010.028), while one-way ANOVA revealed no significant differences in normalized fiber length across all angles for any of the three muscles (P>0.1). This result validates statistically, the use of sarcomere length for fiber length normalization.
A concern in this analysis was that systematic size differences between animals could affect the experimental results. For example, some of the raw fiber length differences between groups could simply reflect animal size. Thus, to determine whether animal size varied significantly among groups, both animal mass and tibial length were compared across groups. Neither animal mass nor tibial length varied significantly among groups, as revealed by one-way ANOVA (P>0.5) and neither were significantly correlated with ankle angle as determined by linear regression (animal mass: r2=0.008, P>0.7; tibial length: r2=0.008, P>0.7). Thus, animal size did not affect the fiber length analysis presented above.
Having determined that sarcomere length effectively normalizes fiber
length, a practical consideration becomes defining the resolution of the
normalization method. It could be that, due to the large degree of natural
variability that occurs in fiber length within muscles fixed at the same joint
angle, the lack of significant differences among angles after normalization
renders the method imprecise. Note that, in
Fig. 2, a great deal of natural
fiber length variation occurs within angles that is not eliminated, even after
sarcomere length normalization (average within-group coefficient of variation
for all muscles at all angles was 11.1±0.9%). This large natural
variability is a real phenomenon that has been observed in animal muscles and
reported for comparatively large human muscles (Fridén et al.,
2001,
2004
). Since architectural
studies often attempt to define fiber length differences among muscles (see,
for example, Lieber et al.,
1992
) or fiber length changes after surgical intervention (see,
for example, Burkholder and Lieber,
1998
), it is of interest to determine the ability of such
architectural analysis to resolve various relative fiber length differences.
This relationship is shown for the EDL, soleus and TA muscles in
Fig. 3. The abscissa represents
the percentage change in fiber length that could be resolved for a given
experiment. As expected, because experimental variability was lowest for the
TA muscle, statistical power was highest for this muscle. Both soleus and EDL
demonstrate a slight decrease in power at the same relative fiber length
difference due to slightly higher intramuscular fiber length variability.
Overall, it can be seen that, for all muscles studied, there is >90% chance
of detecting a 15% fiber length difference among muscles and >60% chance of
detecting fiber length differences as small as 10%. We thus conclude that the
use of sarcomere length normalization in architectural studies permits
resolution of fiber length variations of 15% and may even be effective at
resolving 10% fiber length variations. Of course, this conclusion assumes that
fiber length variability in the experimental system chosen is similar to that
reported here for the mouse hindlimb. If the variability is much greater than
that reported here, it may be necessary to restrict fiber sampling to
analogous anatomical regions of muscles or to increase sample size to obtain
the same resolving power as presented here.
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It should be noted that, while the method of measuring sarcomere length in the current study was laser diffraction, any sarcomere-length measuring approach can be used. This could include phase microscopy of fixed fibers or even paraffin embedding of muscle with longitudinal sectioning of stained tissue. The main point is that sarcomere length must be measured in some way that avoids unnecessary intermuscular variation. The data from Fig. 2 demonstrate that, in the mouse hindlimb system, there is no joint angle at which fiber lengths become `less variable' such that normalization would become unnecessary. This is supported by the fact that, for all muscles, one-way ANOVA reveals no significant difference among joint angles for coefficient of variation (P>0.6). Alternatively, one might simply try to fix joints at the angle that corresponds to the reference sarcomere length. However, as can be appreciated from Fig. 2, there is no single angle that fulfills this criterion for all muscles, which emphasizes the need for direct sarcomere length normalization.
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Acknowledgments |
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