Mechanical properties of rat soleus aponeurosis and tendon during variable recruitment in situ
1 Department of Physiological Science, University of California Los Angeles,
Los Angeles, CA 90095-1761, USA
2 Brain Research Institute, University of California Los Angeles, Los
Angeles, CA 90095-1761, USA
* Author for correspondence (e-mail: rrr{at}ucla.edu)
Accepted 20 June 2003
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Summary |
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Key words: aponeurosis, tendon, muscle-tendon unit, tissue strain, tissue stiffness, soleus muscle, rat, Rattus norvegicus
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Introduction |
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These Young's moduli, however, are tangent moduli measured from free
tendons in vitro. Under conditions that either limit the applied load
to maximal isometric tension (Po) or stimulate the muscle
itself to load the tendon, a different picture emerges. The tendons of the cat
soleus (Proske and Morgan,
1984; Scott and Loeb,
1995
) and frog semitendinosus
(Lieber et al., 1991
) remain
within the early, non-linear region of their stress-strain curves when
subjected to a range of forces up to Po. Therefore, the
use of a Young's modulus derived from the linear portion of an in
vitro stress-strain curve may result in an underestimate of tendon
extension during a movement, particularly at low levels of recruitment.
The relationship between strain and muscle-tendon unit (MTU) force or
length is less clear. In general, two approaches have been used to study this
relationship. Some studies have examined the properties of aponeurosis in
response to passive loading (lengthening) of the specimens
(Lieber et al., 1991;
Trestik and Lieber, 1993
;
van Bavel et al., 1996
).
Generally, this involves stretching the MTU until the passive force is equal
to a maximum tetanic contraction at optimum length (Po).
Alternatively, some investigators have applied varying forces to the
aponeurosis by modulating the contractile force of the muscle being studied
(Ettema and Huijing, 1989
;
Maganaris and Paul,
2000a
,b
;
Rack and Westbury, 1984
;
Zuurbier et al., 1994
).
Experiments using either of these methods represent a combination of
variations in length and applied load and cannot separate the independent
effects of force and MTU length on the mechanical properties of the connective
tissues.
There is no clear consensus on the mechanical properties of the aponeurosis
or on the relationship between tendon and aponeurosis mechanical properties in
the literature. Rack and Westbury
(1984) noted that the total
stiffness of the connective tissue of the cat soleus was 3-5 times less during
isometric contractions than that of the free tendon measured in isolation,
indicating that the tendon was much stiffer than other connective tissue
elements (i.e. the aponeurosis). Other reports in a variety of species have
also indicated differences in the mechanical properties of the tendon and
aponeurosis. Tendon strain is approximately three times the aponeurosis strain
during maximum voluntary contraction in the human tibialis anterior muscle
(Maganaris and Paul, 2000b
) and
is approximately four times higher at a passive load equal to
Po in the frog semitendinosus
(Lieber et al., 1991
). By
contrast, some reports have indicated that the tendon and aponeurosis within a
muscle have similar mechanical properties. Trestik and Lieber
(1993
) reported a 2% strain in
both the tendon and aponeurosis of the frog gastrocnemius passively loaded to
Po. The aponeurosis and tendon of the cat soleus have also
been reported to have similar stiffness during tetanic contractions
(Scott and Loeb, 1995
). It
should be noted that the studies reporting similar or different mechanical
properties for the tendon and aponeurosis include both passive and active
loading, and thus the results cannot be attributed to differences in the
methods used to load the tissue.
In some muscles, the stiffness of the aponeurosis is also nonuniform along
its length. Strain in the portion of the aponeurosis furthest from the tendon
has been reported to be five times greater than the portion closest to the
tendon in the rat medial gastrocnemius during single loading events
(Zuurbier et al., 1994). The
percent strain at the muscular end of the aponeurosis is also three times
greater than at the tendinous end in the frog semitendinosus
(Trestik and Lieber, 1993
) and
human tibialis anterior (Maganaris and
Paul, 2000b
). Thus, not only do the properties of the tendon and
aponeurosis vary relative to one another within individual muscles, but the
mechanical properties of the aponeurosis may also vary along its length.
Given the wide range of techniques and animal models used in these studies,
it is unclear what the independent effects of MTU length and muscle force
production are on the properties of the tendon and aponeurosis. The overall
purpose of the present study was to begin to resolve these issues. To achieve
graded, repeatable contractions without altering the MTU length, we stimulated
the muscle through isolated ventral root filaments. By stimulating these
filaments independently or in combination, we achieved a series of
`recruitment' levels by altering the number of active muscle fibers. Thus, the
same relative recruitment level could be achieved regardless of changes in
muscle length, allowing independent measurement of the force and length
dependence of the mechanical properties of the free tendon and aponeurosis.
Tissue strains were tracked using X-ray videography of metal markers implanted
directly into the tissue of interest. These markers were therefore integrated
within the tissues, avoiding the complicating effects encountered by other
investigators when attaching markers to the surface of the aponeurosis and
tendon (Scott and Loeb, 1995;
van Bavel et al., 1996
).
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Materials and methods |
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Intramuscular marker implantation
All implant surgeries were performed under aseptic conditions at the
University of California Los Angeles. A skin incision was made at the midline
of the posterior surface of the right leg. The fascia covering the lateral
gastrocnemius muscle was incised and the soleus muscle was exposed carefully,
taking care not to disturb its innervation or blood supply.
To allow the strain of the connective tissue to be visualized, small (<100 µm) tungsten particles were implanted into the muscle immediately beneath the aponeurosis and into the tendon. The individual particles were placed into the tip of a 30-gauge hypodermic needle using fine forceps. A 1 mldisposable syringe was used as a holder for the needle. A slot about 2 cm long cut into the side of the syringe allowed a fine wire `plunger' to be manipulated to push the particle out of the tip of the needle. The plunger consisted of a 127 µm-diameter stainless steel wire soldered to a second wire of 300 µm diameter. With the fine wire trimmed to the proper length, the change in wire diameter created a stop that prevented the tip of the wire from pushing further into the tissue than the bevel of the needle. A 90° bend in the larger wire allowed it to be manipulated through the slot in the syringe. When the needle was inserted into the tissue, the plunger was used to push the particle out of the barrel. The needle was then withdrawn, leaving the marker embedded in the tissue.
Approximately 15-20 particles were implanted in each muscle. The particles
were arranged in a series of rows oriented in a medial-lateral plane and
spaced at 2-3 mm. A single particle was placed at the midline of the
soleus tendon, as far distally as it could be distinguished from the tendons
of the gastrocnemii. One additional particle was placed in the tibia for use
as a reference point during analysis of the video images.
Fig. 1 is a captured video
image showing the arrangement of the particles in one representative soleus
muscle.
|
Following surgery, the rats were placed in an incubator maintained at 37°C and returned to their cages when fully recovered. Buprenorphine (0.03 mg kg-1 body mass; i.p.) was given every 8-12 h for the first 48 h post-operatively. During the first three days following surgery, the rats were given ampicillin (100 mg kg-1 body mass; per os). The animals were given at least 5 days to recover before the in situ testing (see below) to allow the insertion sites within the muscle to heal completely.
Preparation for in situ testing
All in situ testing and X-ray videography procedures were
performed at the NASA Jet Propulsion Laboratory (Pasadena, CA, USA) under the
administration of the California Institute of Technology. All animals were
anesthetized with sodium pentobarbital (50 mg kg-1; i.p.). Reflex
checks were performed regularly during the preparation and testing, and
supplements (20% of the initial dose) were given as needed to maintain a deep
level of anesthesia. The animal was warmed by a circulating water heating pad
during all preparatory procedures.
The muscles of the tail, hip, thigh and leg were denervated with the exception of the soleus. A dorsal midline incision was made from approximately T10 to S2. The deep fascia was then opened and the spinal musculature removed, providing access to the vertebral column. A laminectomy was performed from T12 to L6 to allow full access to the spinal cord and spinal roots. The dura mater was left intact on the surface of the spinal cord at this stage. The area was then irrigated thoroughly with physiological saline, covered with saline-soaked cotton gauze, and the skin closed temporarily with clamps during the remaining preparatory surgery.
The tendon of the plantaris muscle was cut and the tendons of the gastrocnemii were separated from the soleus tendon as distally as possible and cut. All three muscles were moved proximally to provide access to the soleus muscle. A small piece of the calcaneus, with the soleus tendon attached, was cut free. A hole was made through the bone fragment to allow insertion of a 300 µm stainless steel wire that was used to attach the muscle to a lever system (Model 305B-LR; Aurora Instruments, Toronto, Ontario, Canada).
The animal was placed on an acrylic sheet heated by a circulating water
pump, which was on risers attached to an acrylic base. The leg was clamped in
place by a pair of screw-driven pins at both the proximal and distal ends of
the tibia. With the leg clamped rigidly in place, a pool was formed from the
skin of the leg and filled with heated mineral oil to maintain the muscle
temperature and to prevent drying. A small piece of cotton soaked in oil was
placed over the distal portion of the tendon as it exited the bath to keep it
moist. The bath temperature was maintained at 34°C by a radiant heat
source. Clamps were then placed on the spinous process of one sacral vertebra
and around the body of an upper thoracic vertebra to fix the spinal
column.
Once the animal was secured on the testing platform, the dura was opened
carefully along the length of the laminectomy. Using fine forceps, the dura
was lifted to allow better visualization of the exit sites of the spinal
roots. Ventral roots L4 to L6 were isolated and cut close to the spinal cord.
Each root was stimulated to determine its contribution to soleus
force-generating capability. With the roots contributing force to the soleus
isolated, the skin of the back was used to form a pool for heated mineral oil.
The innervation of the soleus muscle was derived from two roots in all
animals, typically L5 and L6. The root contributing the greatest amount to the
soleus (usually 75%) was split, providing three ventral root bundles that
could be stimulated separately or in combination to achieve seven different
force levels. After confirming that the sum of the isolated roots agreed with
whole muscle tension, direct stimulation of the tibial nerve rather than
stimulation of all three ventral rootlets was used to elicit all whole-muscle
contractions. Once a satisfactory preparation had been established, the
apparatus holding the animal was transferred into the microscope.
In situ testing procedures
During the in situ testing procedures, the movement of the
implanted particles was tracked using an X-ray microscope (FeinFocus USA,
Inc., Simi Valley, CA, USA; Model FXS-160.30). This microscope provides an
S-VHS output of the phosphor screen image, allowing the movement of the
particles to be recorded on VHS tape at 60 fields s-1. All data
were acquired using a laptop computer (Solo 9100; Gateway, Inc.) running
custom software written in the LabView programming language (National
Instruments, Austin, TX, USA). The computer controlled both the lever system
and the stimulator/stimulus isolator (Model S8800; Grass Instruments, Quincy,
MA, USA) and recorded force and length data from the lever system. The video
and digital data were synchronized using a digital timecode generator.
The optimum length for a whole muscle twitch contraction was determined and used as the start length for the testing procedure. All subsequent in situ testing was repeated for each of the seven possible combinations of ventral root bundles. Testing began with a series of whole-muscle isometric tetani performed in 1 mm increments to determine the optimum length for maximum tetanic tension (Lo). This length was defined as Lo for all subsequent testing, regardless of the recruitment level being used. A length-tension relationship from 2 mm below Lo to 2 mm above Lo was determined for each of the seven recruitment levels. At the conclusion of the testing, a metal square of known dimensions was placed on the surface of the muscle and filmed as a distance calibration. The muscle length and temperature were measured and the animal was removed from the testing apparatus. The muscle was quick frozen in isopentane cooled with liquid nitrogen and stored at -70°C for histological analysis.
Data analysis
To assess the precise location of the implanted markers relative to the
tissue of interest, cross-sections of frozen muscles were cut at 15 µm
intervals. Sections containing fragments of a marker were stained with
hematoxylin and eosin and examined under a light microscope
(Fig. 2). Typically, particles
were within 150 µm of the surface of the muscle. In all cases, the
particles were encapsulated by a thin layer of connective tissue, indicating
that the area of the implant had healed during the recovery period. No signs
of residual trauma from the implantation procedures were observed. The
encapsulating connective tissue was continuous with the endomysium and
aponeurosis. The presence of consistent encapsulation of the implants is
important because it assured a stable position of the particles, thus making
them accurate markers of the movement in the surrounding tissue.
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All digital image analysis was performed with programs written using IMAQ
Vision software (National Instruments). For each contraction, the
corresponding sequence of video frames was acquired digitally and stored on
disks. The boundaries of each implanted particle were determined
programmatically. All pixels darker than the median for their row and column
within a user-defined region surrounding the marker were defined as being part
of the marker. The outline surrounding the pixels satisfying this criterion
was defined as the boundary of the marker. From this boundary, the centroid of
the marker was determined and used to compute all distances. Preliminary
analyses indicated that this method yielded less frame-to-frame variability in
the determination of particle position. However, some noise still exists in
particle location due to signal degradation by the video capture system and
fluctuations in phosphor intensity with time. These factors may cause subtle
changes in the apparent outline of the particles, leading to small
frame-to-frame differences in the calculation of the centroid. Measurement of
video sequences showing particles at rest indicated that this noise is
approximately one pixel width (20 µm) at its peak (data not
shown).
The longitudinal axis of the muscle was defined by measuring the mean path traced by each of the particles. This axis represents the path of shortening of the MTU as a whole. The movement of the markers was split into longitudinal and lateral components parallel or perpendicular to this axis. Longitudinal and lateral strains were computed based on the relative motion of any two particles along these respective axes. However, lateral strains were less than the pixel resolution of the video and are not reported. The initial spacing of the particles for strain computations was taken from the positions of the particles with the muscle at rest and 2 mm below Lo. Thus, zero strain was the same for any two contractions of an individual muscle. In general, the five rows of markers within the muscle allowed four segments to be identified by using the distance between alternate rows: proximal aponeurosis (PA), middle aponeurosis (MA), distal aponeurosis (DA) and proximal tendon/distal aponeurosis (PTDA). Additionally, the distance from the calcaneus to the marker in the proximal portion of the tendon provided strain measurements for the tendon (TEND).
Determination of tissue stiffness
Strain measurements based on the video images were made during the plateau
of the tetanic contractions. Strain measurements from three consecutive frames
(100 ms) were averaged, as was the muscle force recorded over the same time
period (Fig. 3). These values
were used to create plots of tissue strain as a function of muscle force
(Fig. 4). Strains were used
rather than changes in the absolute distances between markers because marker
spacing could not be kept constant among animals. One force-strain plot was
created for each region of the muscle at each MTU length. The force-strain
plots were best fit by an exponential curve of the form
y=aebx. From the equation of the best
fit line for each plot, the slopes of tangent lines could be computed at
uniform force levels across all muscles, regardless of whether that precise
force level was achievable by stimulation of the particular combination of
ventral roots available in an animal (i.e. stiffness was computed at 25% or
75% of Po for any animal for ease of comparison). These
slopes represent the stiffness of the tissue at the chosen level of
recruitment. Because strain was used rather than absolute displacements, and
because stress cannot be computed between each particle pair, stiffness values
in the study are reported as N/% strain using whole muscle force.
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Statistical analysis
Effects of anatomical region and MTU length on strain and stiffness at
Po were assessed by two-way analysis of variance (ANOVA)
with an alpha level of 0.05. When a significant group effect (region, length)
was detected, data for regions or lengths were subjected to multiple paired
comparisons using the Bonferroni adjustment at a group significance level of
P<0.05. To test for effects of recruitment level, stiffness values
within a single region at Lo were compared using a paired
t-test (significance level P<0.05).
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Results |
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Length dependence of tissue properties
Peak strain (strain at Po) in all segments of the
aponeurosis increased with lengthening of the MTU
(Fig. 5), but this increase was
significant only at 2 mm above Lo (P<0.05).
Tendon strain at Po was similar at all MTU lengths and was
approximately half that observed in the aponeurosis (P<0.05).
Total strain in all elements at Po ranged from 9% to 12%
and reached a plateau at lengths above Lo
(Fig. 5). Stiffness generally
increased with increasing MTU length in all tissue segments
(Fig. 6) but, again, was
significant only at 2 mm above Lo (P<0.05).
The patterns for the various portions of the aponeurosis were very similar,
with stiffness increasing slowly up to Lo and then more
rapidly at lengths above Lo. For the tendon, stiffness
appeared to plateau as MTU length increased. Paired t-tests with a
Bonferroni adjustment for multiple comparisons indicate that the TEND is
significantly stiffer than the DA, MA or PA (P<0.05) but not than
the PTDA overlap region at all lengths.
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|
Force dependence of tissue properties
Fig. 7 shows a comparison of
the stiffness at Lo for each of the regions studied for
two different levels of force production. As seen in
Fig. 6, the tendon is stiffer
than the aponeurosis and, after the first few mm (PTDA), the aponeurosis
stiffness is uniform. Stiffness of the PTDA region is not significantly
different from either the tendon or the remainder of the aponeurosis.
Fig. 7 also illustrates the
variation in tissue stiffness as a function of recruitment level. At a low
recruitment level (25% of Po), the pattern of stiffness
variation remains (TEND is still significantly stiffer), but each region is
significantly more compliant at 25% of Po than at
Po (P<0.05). The values for strain and
stiffness at three recruitment levels are summarized in
Table 1 for each region
studied.
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Discussion |
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Tendon strains at peak muscle loads (Po or maximum
voluntary contraction) have been reported to be in the range of 2-5%
(Lieber et al., 1991; Maganaris
and Paul,
2000a
,b
;
Muramatsu et al., 2001
). In
the present study, we observed strains in the rat soleus tendon of 5-6%, in
agreement with these previous results. In addition, tendon strain was not
sensitive to changes in MTU length near and above Lo. Peak
aponeurosis strains reported in the literature have a wider range, from as low
as
1% (van Donkelaar et al.,
1999
) to as high as
50%
(Zuurbier et al., 1994
), with
most investigators reporting strains in the 3-10% range
(Ettema and Huijing, 1989
;
Lieber et al., 1991
; Maganaris
and Paul,
2000a
,b
;
Muramatsu et al., 2001
;
Zuurbier et al., 1994
). The
aponeurosis strains we observed were at the high end of this range, generally
falling between 10% and 12%.
Because force was varied independent of muscle length by stimulating more
or fewer ventral root bundles, the dependence of stiffness on the level of
muscle recruitment was measured in the present study. The results
(Fig. 7) showed that the
aponeurosis and tendon are very compliant at low recruitment levels (0.3-0.5
N/% strain at 25% of Po) and that stiffness increases
rapidly with enhanced recruitment. Above 50% of Po,
the force-strain relationship became nearly linear
(Fig. 4), with a constant
tissue stiffness above this level of recruitment. In addition, it was only at
forces near the lowest measured in this study (near or below 25% of
Po) that stiffness declined significantly. Thus, the
non-linear toe region frequently reported for low force levels was not
apparent at forces greater than 25% of Po in the rat
soleus. These data contrast with reports for some muscles indicating that the
tendon and aponeurosis act exclusively in the non-linear region of their
force-strain relationship at loads typically encountered in vivo
(Lieber et al., 1991
;
Scott and Loeb, 1995
).
However, there is some previous evidence for a transition in connective tissue
behavior within the range of forces observed in vivo. By an extension
of the
-plot technique (Morgan,
1977
), Proske and Morgan
(1987
) showed that at muscle
forces below 20% of Po the stiffness of the connective
tissue in the cat soleus decreased rapidly. Direct measurement of cat soleus
tendon and aponeurosis strain using surface-mounted sonomicrometry crystals
showed a similar reduction in stiffness during contractions below 20% of
Po (Scott and Loeb,
1995
). The shape of the toe region below 15% of
Po cannot be directly addressed in the present study
because the lowest recruitment level achieved was at approximately that
threshold value.
The possibility that the length of the MTU might have an influence on the
connective tissue properties should be considered. The geometry of the
collagen in the endomysium has been examined carefully. Described as a mesh of
randomly oriented collagen fibrils when originally examined by electron
microscopy (Borg and Caulfield,
1980; Rowe, 1981
),
more recent analysis has demonstrated that it is to some degree an ordered
array of fibrils (Purslow and Trotter,
1994
). At short MTU lengths, the arrangement of the collagen is
biased toward circumferential, and as muscle length increases the fibrils
become increasingly oriented with the long axis of the muscle
(Purslow and Trotter, 1994
;
Tidball, 1986
). The collagen
network in the aponeurosis may behave similarly. Additionally, collagen
fibrils at short lengths appear wavy, or crimped. As they are lengthened and
straightened out, they will theoretically become stiffer. This behavior has
been implicated as a possible reason for the observed non-linear increase in
strain with increasing force early during the extension of tendons in
vitro (Diamant et al.,
1972
).
To our knowledge, this is the first study that has independently tested the
effects of muscle force and MTU length on the mechanical properties of tendon
and aponeurosis. When maximally stimulated at MTU lengths from 2 mm below to 2
mm above Lo, the strain observed in the aponeurosis, but
not in the tendon, increased steadily (Fig.
5). Because a common particle spacing at rest was used for all
strain measurements for each pair of markers, this trend cannot be due to an
increase in the passive strain of the tissue and must be an inherent property
of the tissue. In addition, the strain continued to increase at lengths above
Lo, where the maximal force began to decline slightly as
the muscle fibers moved onto the descending limb of their length-tension
relationships. A similar result was obtained for the stiffness of all five
regions studied, with stiffness values for all regions increasing by 50%
over the range of MTU lengths (Fig.
6). In rat extensor digitorum longus, a similar right-shift of the
force-strain relationship with increased strains at a given level of force as
the MTU was lengthened has been observed
(Ettema and Huijing, 1989
), but
no variations in aponeurosis stiffness were observed. However, these authors
used single tetanic contractions at multiple lengths to vary the force applied
to the aponeurosis. Because most of their measurements were made below
Lo, the increase in strain associated with an increase in
length would be accompanied by an increase in muscle force, keeping the total
ratio (F/
L) nearly constant.
One consideration in interpreting the results of the present study is that
the reported relationships are force-strain and not stress-strain. The
ambiguity in defining the cross-sectional area of the aponeurosis, combined
with a contractile force generated by a variable population of muscle fibers,
prevents the calculation of connective tissue stress. Therefore, the stiffness
values reported are the apparent stiffness of the whole tissue or segment
described, not a dimensionless stiffness as derived from in vitro
testing. This apparent stiffness is an accurate representation of the in
vivo behavior but may not reflect the absolute material properties of the
tissues. When interpreting these results, it is necessary to consider the
unique aspects of this preparation. First, because force was varied by
maximally stimulating groups of muscle fibers, the stress exerted by the
muscle belly was constant. This is true because each of the rootlets contained
an approximately equal proportion of fast and slow motor units, so every
increase in force was accompanied by a proportional increase in the total
cross-sectional area of active fibers. This contrasts with protocols varying
the activity of the whole muscle, where muscle stress would increase with
muscle force. Second, the stress applied by the active muscle fibers may not
be borne by the entire cross-section of the aponeurosis or tendon at
submaximal recruitment levels, meaning that connective tissue stress may not
be a simple function of muscle force. Because of this unique in
vivo-like relationship between muscle stress and connective tissue
stress, the observed force-strain relationship could be affected by the
mechanics of the interaction between motor units, or groups of motor units,
and the connective tissues through which they exert their force
(Monti et al., 2001). For the
cat soleus muscle, a model assuming that all muscle fibers act on a common
elasticity can account for most, but not all, of the non-linearity observed in
the addition of forces from two populations of muscle fibers
(Sandercock, 2000
). Similarly,
the relationship between the fraction of the muscle that is active and the
fraction of the connective tissue that is loaded could affect the shape of the
observed force-strain relationship.
Fig. 8 illustrates three
hypothetical relationships between recruitment, the fraction of the connective
tissue that is loaded by active muscle fibers and the resulting stress in the
loaded connective tissues. As in the experiments performed in this study, the
model only considers load imposed on the connective tissue by muscle fibers.
External loads imposed on the muscle are ignored, and therefore parallel
elastic elements are excluded from consideration. In
Fig. 8A, the assumption is that
with each additional muscle fiber recruited, an additional portion of the
connective tissue is loaded. In essence, the connective tissue is `recruited'
along with (or in proportion to) the muscle fibers. Under this assumption, the
connective tissue stress is constant. Thus, the transition from a highly
compliant and variable behavior (the toe region) to a stiff and nearly
constant behavior would require a transition between the properties of the
connective tissues loaded at low and high recruitment levels.
Fig. 8B illustrates the inverse
of this relationship, a situation similar to that proposed by Sandercock
(2000). Here, every muscle
fiber is functionally in series with all of the connective tissues, and the
connective tissue stress therefore rises as a linear function of muscle fiber
recruitment. Under this assumption, the intrinsic stress-strain properties of
the connective tissues would be the same as the observed force-strain
relationship. The third model (Fig.
8C) is a combination of the first two. The assumptions are that
initially there is some portion of the connective tissue that is loaded by any
active muscle fibers (model 1) but that additional connective tissue is loaded
as more fibers are recruited (model 2). In this third model, the sharp
transition in the force-strain properties observed in this study, with a
nearly constant stiffness at higher recruitment levels, can result from a much
shallower stress-strain relationship with a constantly varying stiffness.
Thus, the properties of the connective tissues as loaded in vivo may
be more uniform than would be predicted from the stress-strain
relationships.
|
The results of this study suggest that the mechanical properties of tendon and aponeurosis measured ex vivo, or in situ during isolated contractile events, may not represent the properties of these tissues during normal loading in vivo. Instead, we have observed a nearly constant stiffness as load increased due to muscle recruitment. The difference between our data and published descriptions of the in vitro properties of tendon may be accounted for by some very simple assumptions about the interface between the contractile elements of the muscle and the connective tissues. If the true stiffness of the tissues increases with recruitment, then the apparent, and functional, stiffness remains constant. By providing a series elasticity of nearly constant stiffness, the control of the muscle would be greatly simplified because the nervous system would not have to adjust to a constantly changing interface with the environment.
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Acknowledgments |
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References |
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