Download Decreasing stimulation frequency-dependent length-force

Decreasing stimulation
frequency-dependent
characteristics
of rat muscle
BORIS ROSZEK,
GUUS C. BAAN,
AND PETER
A. HUIJING
Vakgroep Functionele Anatomie, Faculteit der Bewegingswetenschappen,
Amsterdam,
The Netherlands
Roszek, Boris, Guus C. Baan, and Peter A. Huijing.
Decreasing
stimulation
frequency-dependent
length-force
characteristics
of rat muscle. J. Appl. Physiol. 77(5): 21162124,
1994.-Effects
of decreasing stimulation
frequency on lengthforce characteristics
were determined for rat medial gastrocnemius muscle. The peripheral
nerve was stimulated supramaximally with a succession of twitch and frequencies of 100,50,40,
30, and 15 Hz. Active peak tetanic and twitch forces and active
muscle geometry were analyzed. Optimal muscle length and
active slack length shifted significantly
(P < 0.05) to higher
muscle length by a maximum of 2.8 and 3.2 mm, respectively.
Further significant
effects were found for distal fiber length
and mean sarcomere length of distal fiber (increases) and for
fiber angle and aponeurosis length (decreases). Neither muscle
length range between active slack and optimal length nor aponeurosis angle was altered significantly.
We concluded that decreasing stimulation
frequency-dependent
length-force
characteristics are affected by a complex interaction
of length-dependent calcium sensitivity,
potentiation
of the contractile
system, distribution
of sarcomere length, and interactions
between force exerted and aponeurosis length. Length-dependent
calcium sensitivity seems to be a major factor determining
the
magnitude of the shift of optimal muscle length.
skeletal muscle; medial gastrocnemius
try; isometric contraction;
electrical
nerve; calcium sensitivity; distribution;
tentiation
muscle; muscle geomestimulation;
peripheral
sarcomere length; po-
MUSCLE LENGTH is a mechanical factor modifying muscle force. The interaction between muscle length and
force is expressed in length-force characteristics. Investigations dealing with muscle function often study
length-force characteristics of maximally activated muscle. In those conditions development of force is achieved
by recruitment of all motor units. Another important
neurophysiological factor affecting muscle force is stimulation frequency. In 1930 Cooper and Eccles (10) already
showed the mechanical response of several cat muscles
to stimulation frequencies. Rack and Westbury (26) demonstrated the effects of interaction between muscle
length and stimulation frequency on length-force data of
fully excited cat soleus muscle, known as stimulation frequency-dependent length-force characteristics. In these
studies, discrete constant stimulation frequencies were
applied to the nerve. However, variable motoneuron firing frequencies are encountered during muscle activity.
For example, during maximal voluntary contractions the
initial firing frequency of motor units is high and declines
as the contraction sustains (13).
To adjust muscle force in a way more comparable to
daily activity, Solomonov et al. (28) reintroduced an electrical stimulation technique that provided submaximal
contractions levels by using simultaneous classic lOO-Hz
0161-7567/94
$3.00 Copyright
length-force
Vrije Universiteit,
1081 BT
stimulation at the proximal end of the motor nerve and a
high-frequency block (600 Hz) at the distal end of the
nerve. This stimulation method supplies selective activation of motor units by the size principle: according to
their size, small motor units are recruited first and derecruite last and large motor units are recruited last and
derecruited first (3). Recently, Huijing and Baan (22)
used this stimulation with high-frequency block to study
stimulation level-dependent length-force characteristics
of rat medial gastrocnemius muscle (GM). Their results
showed a shift in optimal muscle length to higher muscle
length during blocking, which could be a consequence of
different properties of derecruited motor units: it was
hypothesized that this shift may be attributed to distribution of sarcomere length with respect to muscle length.
However, part of the shift in optimal muscle length could
be attributed to stimulation frequency-dependent effects
on the length-force characteristics if a lowering of stimulation frequency were caused by the nerve block. Therefore we decided to use a stimulation pulse train with successively decreasing stimulation frequencies during an
isometric contraction. Because such a sequence of decreasing firing frequencies also occurs during in vivo
muscle activity (13, I9), a description of complex effects
will also be relevant for understanding muscle performance during in vivo movement.
The major purpose of the present study was to examine length-force characteristics of rat GM at various decreasing stimulation frequencies during supramaximal
stimulation of the peripheral nerve to determine the
maximal effect of decreasing stimulation frequency on
optimal muscle length. Furthermore, muscle geometry
was analyzed to determine whether the interaction effect
of decreased force and aponeurosis length contributes to
alterations of length-force characteristics. A simple muscle model is presented incorporating distribution of
mean sarcomere length of fibers. The purpose of this
model is to show that in principle a shift in optimal muscle length during lowering of stimulation frequency can
be related in part to the distribution of sarcomere length.
An attendent phenomenon evoked by decreasing stimulation frequency is a temporal enhancement of muscle
force at low frequencies. Well-known enhancement phenomena are posttetanic potentiation (9) and the catchlike property of skeletal muscle (7). Posttetanic potentiation refers to an augmentation of twitch force and unfused tetanic force during low-stimulation frequency
after brief repetitive stimulation. The catchlike property
is force enhancement evoked by brief initial high frequency (usually 2 spikes) preceding submaximal stimulation frequencies. Initial firing doublets have also been
reported in human muscle (4). In our experimental de-
0 1994 the American
Physiological
Society
2115
2116
LENGTH-FORCE
:-Ima
:
CHARACTERISTICS
b:
Schematic presentation of rat gastrocnemius muscle (GM).
were inserted at proximal end of proximal aponeurosis
(marker
I), distal end of proximal aponeurosis (marker Z), and distal
end of most distal fiber (marker 3). Muscle geometry is represented as
triangle with distance between markers I and 2 as estimate for active
aponeurosis length (I,,), between markers 2 and 3 for active fiber length
(If,), and between markers 1 and 3 for active muscle length (Ima). Fiber
angle (cu)and aponeurosis angle (p) were calculated according to law of
cosines.
FIG.
1.
Markers
creasing stimulation frequency protocol, any force enhancement is manifested mainly in the later part of the
contraction and is referred to as potentiation. An additional experiment was performed with both decreasing
and constant stimulation frequency protocols to illustrate some unraveling of the complex interaction between stimulation frequency and potentiation.
MATERIALS
AND
METHODS
Surgical procedure. Six male Wistar rats [mean body mass
301 t, 4 (SE) g] were anesthetized
with pentobarbital
sodium
(initial dose 0.08 g/kg body mass) injected intraperitoneally.
Supplementary
doses were given intraperitoneally
if anesthesia became less deep. The skin of the hindlimb and the surronding tissue was removed, exposing the medial head of the GM
with the blood supply intact. The ischiadic nerve was dissected
free and was cut as proximally
as possible.
The calcaneus was cut, and the GM was separated from its
lateral head and the soleus muscle. The Achilles tendon, attached to a piece of calcaneal bone, was wrapped around a
metal hook and was secured with a ligature. In addition, the
connection was glued with histoacryl (Braun Melsungen).
Subsequently, the hook was connected to a force transducer
(Hottinger Baldwin,
maximal
output error <O.l%, compliance
0.0048 mm/N). The femur was clamped and positioned
in a
rigid frame such that the muscle was aligned with the force
transducer, avoiding torsion of the muscle.
Under observation with an operation microscope (magnification X10-16; Carl Zeiss) and with help of a small needle,
copper wire markers (diam 0.1 mm) were inserted in the muscle
at three locations: the proximal end of the proximal aponeurosis (marker I), the most distal end of the proximal aponeurosis
(marker Z), and the distal end of the most distal fiber bundle
(marker 3) (Fig. 1).
The muscle was covered with a layer of paraffin oil to prevent it from drying. A thermosensor
positioned under the muscle measured muscle temperature,
and with a feedback control
system using radient heat the ambient temperature
was kept
constant at 27 t 1°C.
Experimental
procedure. The ischiadic nerve was stimulated
supramaximally
using a bipolar
silver electrode
(constant
current 3 mA, width square pulse 100 ps). The distance between the electrodes was 3 mm. A stimulation
frequency protocol with variable pulse train was used to achieve gradation in
OF
RAT
MUSCLE
muscle force. The peripheral nerve was stimulated at the following frequencies: twitch and 100,50,40,30,
and 15 Hz. A typical
force trace resulting from the decreasing stimulation
frequency
protocol is shown in Fig. 2.
Isometric contractions
were performed
at different muscle
lengths starting near active slack length (a low muscle length at
which active muscle force approached
0). The muscle-tendon
complex was lengthened with LO-mm
increments.
In the range
just below and over optimal length, O.&mm increments were
used. After lengthening
of the muscle to the desired length, the
measurements
started with recording of passive muscle force
during 100 ms in which time the muscle-tendon
complex adjusted to the new length (Fig. 2). Subsequently,
a twitch contraction was induced; 250 ms after the onset of the twitch contraction, the nerve was stimulated
with a succession of five
frequencies
in decreasing
order. For each stimulation
frequency, a pulse train of 200 ms was used. After the stimulation
sequence, the muscle was brought near slack length. The muscle was allowed to recover for 3 min, and the stimulation
protocol was repeated at a different muscle length.
An additional
experiment
was carried out using the varying
stimulation
frequency protocol as well as four constant stimulation frequencies (15,30,40, and 50 Hz). First, isometric contractions were performed with the decreasing stimulation
sequence
described
above. Subsequently,
length-force
data were obtained from tetani evoked by a constant stimulation
frequency
of 15 Hz in a muscle length sequence from low length to a
higher length. This procedure was repeated for 30-, 40-, and
50-Hz stimulation
in all cases. The duration of the constant
stimulation
frequency pulse train was equal to that of the decreasing stimulation
frequency pulse train. The magnitude of
the force was determined
at instants identical to those of the
decreasing stimulation
frequency protocol (Fig. 2). Recovery
time between the isometric contractions
was 3 min for the decreasing stimulation
frequency sequence and 2 min for the constant stimulation
frequencies experiments.
Images of the muscle were recorded with cinematography
at
24 frames/s using a 16-mm camera (Arriflex 16SR) with a zoom
lens (aperture lo-150 mm). A special-purpose
microcomputer
controlled timing of events related to generation of the stimulation pattern as well as analog-to-digital
conversion and cinematography.
Data collection and treatment. Muscle force and cinematographic synchronization
signals were acquired using a 12-bit
9
II
89
;lOOHz:
I
50Hz
I
I
I
] 40Hz
j 30Hz
j
1
0.8
1.0
1.2
15Hz:
E
IA
d
0.0
0.2
0.4
0.6
time
1.4
1.6
(s)
2. Example of time-force data of isometric contraction of rat
GM. Stimulation protocol used for each measurement is indicated.
Muscle force (F,) and geometry were analyzed at instants marked with
asterisk. Note that contractions became less fused at stimulation frequency of 150 Hz.
FIG.
LENGTH-FORCE
CHARACTERISTICS
OF
RAT
MUSCLE
2117
analog-to-digital converter with a l,OOO-Hz sampling frequency
(resolution of force <0.05 N). Signals were stored using a second microcomputer.
Images obtained by cinematography were projected onto a
translucent screen (magnification x4-5). On the screen, appropriate distances between the markers were measured using a
motion analyzer (accuracy 0.05 mm; Dynamic Frame) and were
taken as estimates for the proximal aponeurosis length (distance between markers 1 and 2), distal fiber length (distance
betweenmarkers 2 and 3), and musclelength (distancebetween
markers 1 and 3) (Fig. 1). Note that any effect of curvature of
fiber and aponeurosisis neglected by this method. The fiber
angle (ar) and aponeurosisangle (p) with respect to the line of
pull of the musclewere calculated according to the law of cosines.
Active muscle force was estimated by subtracting passive
force from total force exerted by the muscle. Data for muscle
active force (i.e., peak force) and musclelength data were fitted
with a polynomial
sarcomeresin a fiber was calculated by dividing the treated
distal fiber length by the mean sarcomerelength of that fiber.
Optimal sarcomere length was defined as that sarcomere
length at which force production is expected to be maximal on
the basisof optimal overlap between thick and thin filaments.
Optimal sarcomerelength wasobtained from filament parameters electromicroscopically for rat GM (17). Optimal fiber
length was estimated by the product of number of sarcomeres
and optimal sarcomerelength.
Statistics. One-way analysis of variance (ANOVA) (25) was
usedto selectthe lowest order of the polynomials for the fitting
of the relationships between musclelength, muscleforce, and
fiber and aponeurosislengths and angles.One-way ANOVA for
repeated measurementswas performed to test for the effect of
decreasingstimulation frequency on optimal muscleforce, optimal musclelength, and active slack length and musclelength
range between optimal and slack length and to test for a possible difference between fiber length at optimal sarcomerelength
and fiber length at optimal muscle length. Two-way (muscle
length and stimulation frequency) ANOVA for repeated measurementswasusedto test the effect of decreasingstimulation
frequency on muscle force, fiber and aponeurosislengths and
where y represents active muscle force, x respresentsactive angles,and sarcomerelength in the musclerange between27.3
musclelength, and co,. . . , c, are fitting constants. Polynomial and 34.9 mm. Post hoc tests among factor level meanswere
curve fitting accordingto Eq. 1 wasalsousedfor data concern- performed using the Bonferroni procedure for multiple pairing the relationshipsbetweenmusclelength, fiber length, and cy wise comparisonsto locate differences amongstimulation freas well as betweenaponeurosislength, ,8, and mean sarcomere quency with respect to lOO-Hz stimulation. A difference at P <
length. In this casey represents one of the before-mentioned 0.05was consideredsignificant. Data and fitted curves are preparametersand z representsactive musclelength. Polynomials sented as meanst SE.
that most adequately describedthe experimental data were selected (seeStatistics). Optimal musclelength wasdefined asthe
active muscle length at which the fitted curve for each fre- RESULTS
quency showedoptimal active muscle force within the muscle
Muscle length-force characteristics. Length-force charlength range usedin the experiment. Muscle slack length was acteristics of rat GM are shown in Fig. 3. Decreasing
defined as the least active muscle length at which the fitted
frequency was attended by a decline in active
curve for each frequency approachedzero active muscle force. stimulation
muscle
force
together with a shift in optimal muscle
Maximal optimal muscle force was defined as optimal active
muscleforce for lOO-Hz stimulation. Fitted curves were usedto length to a higher muscle length (Fig. 3A). Note that the
calculate meanvalues of active muscleforce, fiber and aponeu- progressive shift in optimal muscle length with decreasfrequency was accompanied by a similar
rosislengths and angles,and mean sarcomerelength of distal ing stimulation
fibers for a given musclelength.
shift in active slack length.
Force-frequency relationships were obtained by fitting data
The optimal muscle force ranged from 10.10 N for 100
for normalized muscle force and stimulation frequency with Hz to 2.57 N for twitch (Table 1). One-way ANOVA for
use of a nonlinear least-squaresfitting procedure. The equa- repeated measurements
showed a significant effect of
tion fitted to the data was
decreasing stimulation
frequency on optimal muscle
y
=
co
y/y,,
+
qx
+
=
$X2
ebO+blx/(l
+
c3x3
+
+
ebO+blr)
l
l
.
c,xn
(1)
(2)
where y represents active muscle force and ymaxrepresents
maximal active muscleforce, both at a given musclelength; x
representsstimulation frequency; and b, and b, are constants
selectedin the fitting procedure.
Number of sarcomeres. After the length-force measurements,
the GM was removed carefully and was fixed (4% formaldehyde, 15%absolutealcohol, and 1.5 mg/l of thymol) for several
days. The musclewaskept near optimal length (100 Hz). Subsequently, the muscleswere exposedfor 4 h to a 26%nitric acid
solution to soften the connective tissue, after which they were
stored in a 50% glycerol solution for 2-6 days (20). Under observation through a dissectionmicroscope,the most distal fiber
bundle was taken from the muscle.From this bundle, four intact fibers were isolated and prepared on a microscopeslide.
The number of sarcomereswas determined according to Huijing (20): the number of sarcomereswas counted in 80-pm samples every 800 pm along the length of the fiber. This method
provided estimates of mean treated sarcomerelength of the
distal fiber. Subsequently, the length of the treated fiber was
measuredusing a curvimeter on a projection of the slides(magnification -X24; overhead projector). The mean number of
force [F&25) = 204.41. Post hoc tests showed that optimal muscle force for stimulation
frequency of 550 Hz
was significantly decreased with respect to IOO-Hz stimulation. Optimal
muscle lengths were observed in the
muscle range of 32.11 mm for 100 Hz to 34.89 mm for
15-Hz stimulation,
which is an increase of 9% relative to
optimal muscle length at 100 Hz (Table 1). Estimates of
active slack length were observed in the muscle range of
21.88 mm for 100 Hz to 25.05 mm for twitch stimulation,
which is an increase of 14% relative to slack length at 100
Hz (Table 1). One-way ANOVA for repeated measurements showed a significant effect of decreasing stimulation frequency on optimal muscle length and muscle
slack length [F(5,25) = 91.4 and 33.0, respectively]. Post
hoc testing showed that optimal and slack length for
r40-Hz stimulation
were significantly
higher with respect to lOO-Hz stimulation.
Two-way ANOVA for repeated measurements
revealed a significant effect of decreasing stimulation
frequency on muscle force [F(5,265) = 533.21. No significant
interaction was found between muscle length and stimu-
LENGTH-FORCE
2118
CHARACTERISTICS
OF RAT MUSCLE
progressively by equal amounts to higher muscle length
in such a way that no change in muscle length range
between optimal and slack lengths is proved.
* 100 Hz
To evaluate the effects of potentiation
on the length10
force characteristics,
we compared effects of constant
+5o
Hz
stimulation
frequencies with the decreasing stimulation
Hz
8 - *40
frequency protocol in an additional experiment. Poten030
Hz
tiation highly enhanced muscle force at muscle lengths
6 - -15Hz
below optimal muscle length (Fig. 4A). For low-stimulation frequencies (15, 30, and 40 Hz), muscle force was
- twitch
enhanced up to 850%. At a muscle length in the range of
optimal muscle lengths, potentiation
was drastically reduced. Although potentiation
was less in this optimal
muscle length range, it was still maintained,
ranging
from 42 to 3% for 15- and 50-Hz stimulation
frequency,
respectively. A striking difference was shown between
30
35
20
25
40 decreasing and constant stimulation
frequencies in optimal muscle length (Fig. 4B). For l5- and 30-Hz decreasIma (mm)
B
ing stimulation
frequencies, optimal muscle length was
12
lower than that obtained during constant stimulation
frequency. However, for 40-Hz stimulation
optimal muscle
length
was
very
similar
for
the
two
protocols,
and
10
50-Hz constant stimulation
frequency yielded a lower
optimal muscle length.
8
We concluded that, because of the decreasing stimulation frequency protocol, muscle force is potentiated, espea 6
cially at a muscle length below optimal muscle length,
E
whereas
at higher muscle length potentiation
is present
IA
but considerably smaller. Moreover, potentation affects
4
optimal muscle length.
Fiber and aponeurosis lengths and angles. The relation2
ships between the muscle length and the fiber and aponeurosis lengths and angles are shown in Fig. 5. Although
two-way ANOVA for repeated measurements showed a
-8 -6
0
2
4
6
8 significant effect of decreasing stimulation
frequency on
fiber length [F(5,265) = 10.21, differences in fiber length
Alma (mm)
from that of lOO-Hz stimulation
could be located only by
FIG. 3. Effect of stimulation frequency on length-force characterispost hoc testing for 15-Hz and twitch stimulation
(Fig.
tics of rat GM. A: active F, (F,,) as function of I,,. B: F,, as function of
5A).
Within
the
range
of
optimal
muscle
length,
the
indeviation in optimal I, (A!,,). Fitted curves of F,, are represented as
means t SE (n = 6) for 6 frequency conditions. Vertical dashed lines,
crease in fiber length at l5-Hz stimulation was limited to
optimal Z,, (Imao)range (A) or Zmao(B).
-0.12-0.19
mm with respect to lOO-Hz stimulation.
We
concluded that decreasing stimulation
frequency caused
lation frequency [F(40,265) = 1.11. This means that the significant lengthening of the fiber.
combination of muscle length and stimulation
frequency
The effect of stimulation
frequency on the aponeurosis
does not lead to substantial additional change in muscle
force. Post hoc testing showed that muscle force for r50TABLE
1. Effect of decreasing stimulation frequency on
Hz stimulation
was significantly decreased with respect
F ??uw)
1?nuc,1,-, and muscle length range of rat GM
to 100 Hz in the length range of 27.3-34.9 mm.
To visualize possible changes in muscle length range
Range
1ma0 9
1 ma8 9
F ma0 9
(I,aa
- I,ao),
between slack and optimal lengths, active muscle force
Frequency
N
mm
mm
mm
was expressed as a function of length deviation of optimal muscle length from its corresponding stimulation
100 Hz
lO.lOt0.58
32.11t0.52
21.88t0.38
- 10.23t0.38
frequency (Fig. 3B). Muscle length ranges were observed
50 Hz
9.03tO.57*
32.41t0.55
22.41t0.50
-10.01+0.32
40 Hz
7.51&0.62*
32.78*0.58*
23.27+0.53*
-9.51t0.20
in the range of -10.23 mm to -9.25 mm (Table 1). One30 Hz
6.02t0.64*
33.73t0.54*
23.51t0.47*
- 10.22t0.35
way ANOVA for repeated measurements showed that no
15 Hz
2.82t0.29*
34.89t0.48*
24.98t0.35”
-9.91t0.36
significant effect of decreasing stimulation
frequency on
-9.25t0.34
Twitch
2.57t0.37*
34.30t0.44”
25.05t0.59”
muscle length range could be demonstrated
[F&25) =
Values are means t SE; n = 6. F,,,, optimal active muscle force;
2.4; NS].
mao,optimal active muscle length; Zmas,active muscle slack length; GM,
We concluded that length-force characteristics of the 1gastrocnemius
muscle. * Significant difference (l-way analysis of varirat GM depend on decreasing stimulation
frequency. Op- ance for repeated measurements using Bonferroni post hoc test, P <
timal muscle length and muscle slack length are shifted
0.05) with respect to loo-Hz stimulation frequency.
A
c
L
LENGTH-FORCE
CHARACTERISTICS
* Ima=
+ lma=32
-Q- lma=37
10
30
20
40
50
60
B
40
39
* DSF
38
E
g 37 .
is
-E 36
-o- CSF
35
34
0
I
I
I
I
20
40
60
80
stimulation
frequency
I
100
I
120
(Hz)
FIG. 4. Effects of potentiation
illustrated on basis of results of additional experiment. A: difference in force exerted during decreasing and
constant stimulation frequency protocols normalized for maximal
force exerted at particular Z,, during constant frequency protocol. Data
are shown as function of stimulation frequency for 2 Zmavalues below
I,,, (Z,, = 30 and 32 mm) and for 1 I,, value within Z,, range (I,, = 37
mm). B: Z,,, as function of decreasing and constant stimulation frequencies (DSF and CSF, respectively). Note that decreasing stimulation frequency protocol causes less pronounced shift in I,, to higher
lengths.
length was compatible (Fig. 5B). Two-way ANOVA for
repeated measurements demonstrated
a significant effect of decreasing stimulation
frequency on aponeurosis
= 12.01: decreasing stimulation
frelength [F&265)
quency was accompanied by shortening of the aponeurosis. Post hoc tests showed that the aponeurosis length for
15Hz and twitch stimulation
was significantly
shortened with respect to lOO-Hz stimulation.
The extent of
aponeurosis length difference within in the range of optimal muscle lengths was ~0.15 mm at optimal muscle
length of lOO-Hz stimulation
and 0.20 mm at optimal
muscle length of 15-Hz stimulation.
The effect of stimulation
frequency on CYand 0 is presented in Fig. 5, C and D, respectively. Two-way ANOVA
revealed a significant effect of decreasing stimulation
frequency on cx [F(5,265) = 2.71. Post hoc tests showed
that a was significantly decreased only for twitch stimula-
OF
RAT
MUSCLE
2119
tion. Two-way ANOVA could not detect significant effects of stimulation
frequency on p [F(5,265) = 1.7; NS].
The net sum of these small alterations in muscle geometry is that distal fiber length increases during force decline by lowering stimulation
frequency. As a consequence, optimal muscle length should be reached at
lower muscle length. However, the experimental lengthforce data show a leftward shift in optimal muscle length.
We concluded that fiber and aponeurosis characteristics
cannot account for the observed shift in optimal muscle
length in rat GM.
The relationship
between mean sarcomere length of
the distal fiber and muscle length is shown in Fig. 6A.
Sarcomere length was estimated by dividing fiber length
by the mean number of sarcomeres (5,877 t 72; n = 24).
Two-way ANOVA showed that stimulation
frequency
had a significant effect on sarcomere length [F(5,265) =
9.81. Post hoc testing showed that sarcomere length at
15-Hz and twitch stimulation
was significantly increased
with respect to lOO-Hz stimulation.
Within the range of
optimal muscle lengths, a range of sarcomere lengths was
observed from 2.40 to 2.87 pm. It can be seen from Fig.
6B, a detailed section of sarcomere characteristics, that
muscle length at optimal sarcomere length in the distal
fiber (2.3 pm) was shifted to the left by ~0.11 and 0.17
mm for 15-Hz and twitch stimulation,
respectively.
Estimated optimal fiber length (i.e., product of optimal
sarcomere length and number of sarcomeres) was 13.52
3- 0.17 mm (n = 6) and was significantly
smaller than
fiber length at optimal muscle length at lOO-Hz stimulation [14.12 t 0.22 mm; n = 6; F( 1,5) = 8.21. This fiber
length difference is an indication of distribution
of mean
sarcomere length of the fibers with respect to muscle
length.
Force-frequency relationship. The effect of muscle
length on the force-frequency curve is illustrated in Fig.
7. Normalized muscle force (i.e., muscle force relative to
the maximal muscle force at a particular muscle length)
decreases for submaximal stimulation
frequencies as the
muscle shortens. It should be noted that the magnitude
of this decrease is determined by two factors: 1) the decrease in force due to the transfer to a length-force curve
of a lower stimulation
frequency and 2) the magnitude of
the shift in optimal muscle length of that curve to higher
lengths (Fig. 3A). The latter factor particularly creates
the interaction
with muscle length: at higher muscle
lengths the decrease in force may be less than expected,
and at lower muscle lengths the decrease in force will be
higher than expected. It should be noted particularly that
the shift in optimal muscle length is the result of a complex interaction of several factors, which is analyzed in
DISCUSSION.
The fitting constants for the sigmoid muscle forcestimulation
frequency curves describing the experimental data are shown in Table 2, as this information may be
quite useful for muscle modeling.
DISCUSSION
In this study we showed that length-force characteristics of fully recruited rat GM muscle are affected by a
protocol of decreasing stimulation frequency. An impor-
2120
LENGTH-FORCE
CHARACTERISTICS
OF RAT MUSCLE
B
A
1
-1
E
g1
a
=
loo
Hz
18
50 Hz
1
40
Hz
30
Hz
t
15 Hz
-
P-
I
35
520
twitch
J
40
16'
20
I
25
1
30
I
35
1
40
9
20
25
30
35
40
C
45
15
5
20
I
I
25
30
Ima
I
35
I
40
(mm)
Ima
(mm)
5. Effect of stimulation frequency on architectural characteristics of rat GM. Shown are relationships of I,,
and If, (A), proximal l,, (B), distal CY(C), and proximal ,8 (D). Fitted curves of muscle geometry are shown as means + SE
(n = 6) for 6 frequency conditions.
FIG.
tant feature of the decreasing stimulation
frequency-dependent length-force characteristics is the reciprocal relationship between stimulation
frequency and optimal
muscle length (Fig. 4B).
In natural movements, decreasing firing frequencies
are very common. For example, Hoffer et al. (19) showed
recordings of in vivo motor unit firing frequencies in
walking cats and demonstrated
that decreasing firing
frequencies generally occur. Therefore, it is essential to
have two types of experimental evidence: 1) evidence of
the net effects of decreasing stimulation
frequency, as
provided in the present study, involving possible interaction between stimulation
frequency effects and potentiation and 2) detailed studies on the isolated effects of
these phenomena to quantify the importance of individual effects and possible interactions for the net effect.
Below we focus the discussion on such effects. However, other phenomena, such as effects of changes in
muscle geometry and effects of possible sarcomere
length distribution
with respect to muscle length, must
be considered as well for a more detailed analysis of muscle functional capabilities during submaximal activation.
General effects of decreased force: interaction between
fiber and aponeurosis lengths and angles. Decreasing stim-
ulation frequency causes muscle force to decrease. Considering the fact that aponeurosis and fiber are connected in series and given the elastic properties of the
aponeurosis, any decrease in force will cause a shortening of the aponeurosis. For any given muscle length a
shortening aponeurosis will cause an increased fiber
length. Furthermore,
in pennate muscle angular effects
can reduce fiber lengthening by changing the fiber angle.
Hence, the effect of decreasing force on fiber length is
determined by a complex interaction
between muscle
force, elastic properties of intramuscular
aponeurosis,
and angular effects (37). In the present study, we found
small increases in fiber length as the stimulation
frequency was lowered and the force dropped. As a consequence, optimal sarcomere length should be reached at
shorter muscle length (leftward shift of ~0.11-0.17 mm).
This is expected to happen to all fibers and leads to a
shift in optimal muscle length to lower muscle length as
muscle force declines with decreasing stimulation
frequencies. However, the experimentally
determined
length-force characteristics show a net shift to increased
muscle length, i.e., in the opposite direction. Therefore,
LENGTH-FORCE
CHARACTERISTICS
2121
OF RAT MUSCLE
13r
x
; 0.8
cv
E
L 0.6
?a
E
IL 0.4
30
l
z 2.5
2
t co
2 20.
-O- Ima=
-i+ Ima=
*
Ima=
O- Ima=
15.
0.2
lmao
15 Hz
~
20
25
*loo
35
30
Hz *50
Hz
*40
4
Ima=
40
Hz
stimulation
frequency
(Hz)
7. Force-frequency relationship. Effect of 5 Zma
values on stimulation force-frequency relationship is presented. F,, normalized for
maximal force at particular L, value (F,,/F,, max)is shown as function
of decreasing stimulation frequency. Twitch stimulation is not included in nonlinear fitting procedure. Data are means + SE; n = 6. I,, is
given in mm.
FIG.
*30
B
Hz
-0-15 Hz
-twitch
25.
leading to decreased inactivation
of the contractile elements. However, an important
factor that should be regarded is the functional consequence of changes in calcium concentration
within the fibers. Calcium is the intracellular messenger linking membrane depolarization
of the T tubules to activation of the contractile elements,
i.e., actin and myosin filaments. Decreasing stimulation
frequency leads to fewer action potentials conducted by
the peripheral
nerve. This reduces the frequency of
membrane
depolarization
of the T tubules. ConseI :
I
I I
71
quently, the release of calcium from the sarcoplasmic
-50.5
31 .o
31.5
32.0
32.5
reticulum into the sarcoplasm decreases and influences
force development (5,24). In addition, length-dependent
Ima (mm)
calcium effects are well known in skeletal and cardiac
FIG. 6. A: actual sarcomere length (I,,) as function of Zma.Optimal ISa
muscle
(e.g., see Refs. 11,31,32). These sarcomere length
us,,; 2.3 Pa Li, of lOO-Hz stimulation (32.11 mm), and Z,, of E-Hz
effects have important
consequences. Stephenson and
stimulation frequency (34.89 mm) are indicated by horizontal dashed
line and 2 vertical dashed lines, respectively. Box indicates section en- Wendt (30) showed in rat extensor digitorum
longus
larged in B. B: detail of I,,-I,, relationship. Note that I,,, is reached at muscle skinned fibers that sarcomere optimal
length
muscle length lower than I,,,. Fitted curves of I,, for 6 frequency condishifts
~0.5
pm
to
higher
sarcomere
lengths
at
the
20%
tions are represented as means t SE (n = 6).
level of full calcium activation. Several other experimental observations support such a shift in optimal sarcothese fiber length changes cannot explain the stimulamere length. In frog muscle, Close (8) showed that optition frequency-dependent
length-force
characteristics
mal sarcomere length for twitch stimulation
is shifted to
found experimentally
in this study.
higher sarcomere length with respect to tetanic stimulaEffects of stimulation frequency per se. A dependence of tion. Furthermore,
decreasing calcium concentration
optimal muscle length on stimulation
frequency was al- and thus activation levels achieved by administration
of
ready reported for cat soleus muscle by Rack and Westbury (26): a higher optimal muscle length was found for TABLE 2. Fitting constants of force-frequency
lower stimulation frequencies. Constant stimulation
fre- relationships of rat GM for five muscle lengths
quency of 5 and 35 Hz shifted optimal muscle length
Muscle Length, mm
bl
bcl
-5.0 mm. Our additional
experiment showed qualitatively similar effects for rat GM (Fig. 4B). Optimal mus0.11
26
-4.42
cle length shifted to a maximal of ~4.0 mm (i.e., optimal
-3.47
0.10
28
0.10
muscle length difference between 15- and 50-Hz constant
30
-2.99
0.09
32
-2.47
stimulation
frequency). Rack and Westbury hypothe-2.11
0.09
34
sized that such effects could be related to alterations of
the structure of the T tubules at short muscle lentih.
b,, and b, , values of fitting constants of Eq. 2.
8
a
1
8
2122
LENGTH-FORCE
CHARACTERISTICS
OF
RAT
MUSCLE
C
1.2r
I
120
stimulation
frequency
-0
2
4
6
8
Aim
(Hz)
D
9
10
12
14
16
14
16
18
(mm)
r+l
shift
8
10
lmao
8
a
g6
F
E
IA
0
2
4
6
8
Alm
10
12
14
16
18
(mm)
0
2
4
6
12
18
A lm (mm)
relationships
for slow- and
8. Modeled
effect of distribution
of I,, with respect to I,, on I,,. A: force-frequency
fast-type
motor units (MU)
[according
to Einsiedel
and Luff (1291. B: high stimulation
frequency
activates
all fiber
populations
maximally.
C: low stimulation
frequency
reduces force of fiber populations
with short optimal
If, (i.e., short
I,,). D: muscle force-length
curve estimated
by linear summation
of fiber force (F,) for high stimulation
frequency
(high
SF) and low stimulation
frequency
(low SF). Muscle length (Alm) is function
of deviation
from active slack length.
Note that with decreasing
stimulation
frequency
F, is reduced and Z,,, is shifted to higher muscle length.
FIG.
dantrolene led to higher optimal muscle lengths in mouse
extensor digitorum longus muscle (33). Dantrolene is a
drug that interferes with the release of calcium from the
sarcoplasmic reticulum. For skinned rabbit gracilis muscle fibers, optimal sarcomere length is shifted -0.4 pm
when the fibers are exposed to a low-calcium medium
(11). Thus, optimal sarcomere length of skinned fibers as
well as intact fibers depend on calcium activation level.
In addition, sarcomere length at which the ascending
limb of the sarcomere length-force relationship reaches
zero force is increased for a lower calcium concentration
in rabbit skinned muscle fibers (1). If we assume that the
shift in optimal sarcomere length (0.5 pm; Ref. 30) found
for the 20% calcium level is comparable to our low-stimulation frequencies (15 Hz and twitch), we can estimate
the magnitude in optimal muscle length shift that can be
ascribed to this phenomenon. If we substitute that value
in Fig. 6A, we see that for an increase in sarcomere length
from 2.3 to 2.8 ,urn the muscle length would be increased
by ~3.0 m m. Note that the magnitude of the calcium
effect is on the sam .e order as the total net effect found
experimentally.
Therefore, we can conclude that the calcium effect is a major contributor to the shift in optimal
muscle length.
Effects of distribution of mean sacomere length with respect to muscle length. A striking observation in this study
is that optimal sarcomere length is reached in distal
fibers at muscle length lower than optimal length for
lOO-Hz stimulation
(-0.6 mm below optimal muscle
length for lOO-Hz stimulation;
Fig. 6B). In contrast,
other investigations in our laboratory showed that optima1 sarcomere length was reached at muscle lengths
higher than optimal muscle length (18,38). Because large
individual
variation was reported for the same muscle
from different animals (34), these contrasting findings
could well be related to individual variation. For maximally active muscle, any deviation in sarcomere length at
optimal muscle length from optimal sarcomere length is
taken as an indication of a distribution
of mean sarcomere lengths of the fibers of a muscle with respect to
muscle length (18, 21, 34, 38).
For rat GM, the existence of a distribution
of sarcomere length is supported by experimental data obtained
from twitch and tetanic contractions of motor units (16).
Such evidence is also available for cat muscles (2,23,29).
In several muscles the muscle length at which motor u.nit
OPtimal length occurs is related to motor unit type (z 9
14). Larger and faster units seem to exert their optimal
LENGTH-FORCE
CHARACTERISTICS
force at lower muscle lengths than do smaller and slower
units. Faster motor units are more susceptible to a decrease in force because of lowering stimulation
frequency
than are slower motor units (12,16), as illustrated in Fig.
8A. Interaction
between this phenomenon
and the sizerelated distribution
of sarcomere length should lead to
effects on the muscle length at which optimal muscle
force is exerted. To illustrate this effect, we modeled a
parallel fibered muscle. The constructed
parallel fibered
muscle consisted of several groups of fibers with distributed sarcomere length with respect to muscle length (Fig.
8B). We assigned fiber populations
with low optimal
fiber length (i.e., low sarcomere length) to fast-twitch
motor units and populations
with high optimal fiber
length (i.e., high sarcomere length) to slow-twitch
motor
units. Because the whole fiber population is recruited at a
high stimulation frequency, fiber force is maximal for all
fibers (Fig. 8B). At low stimulation
frequency, all fibers
are also recruited;
however,
fiber force of fast-twitch
units is reduced (Fig. 8C). Muscle force is obtained by
linear summation of fiber forces. For high and low stimulation frequency, this is illustrated
in Fig. 80. Note that
low stimulation
frequency
shifts the optimal muscle
length to higher muscle length. Note also that the active
slack length is not shifted, resulting in an increased muscle range between optimal and slack lengths.
Effects ofpotentiatiort.
Because of the short successive
sequence of decreasing stimulation
frequencies,
muscle
force is potentiated during low frequencies in our experiment. In several preparations
of cat and rat muscles,
force enhancement
was demonstrated
for whole muscle
(6, 9) and motor units (7, 27). Muscle force potentiation
can be ascribed to posttetanic
potentiation,
the catchlike
property of the skeletal muscle, or both. Posttetanic
potentiation decays exponentially
(time course in minutes)
in rat fast-twitch
muscle (9). Burke et al. (7) showed that
the catchlike
property
is rather diverse in cat motor
units. The response to the initial high frequency followed
by submaximal frequencies ranged from 500 ms to 5 s for
fast-twitch
and slow-twitch
GM motor units, respectively. Considering
the difference in time constants
of
these potentiation
effects [minutes vs. (milli)seconds],
it
is likely that two separate mechanisms
may be active. It
is conceivable that both mechanisms affected our results
to some extent. To our knowledge, no data are available
on the potentiation
effects on length-force
characteristics of rat GM. Our additional experiment indicates that
effects of potentiation,
as apparent from differences between the results of the decreasing stimulation
and constant stimulation
frequency protocols, may be substantial. For example, a difference in the magnitude of the
maximal shift in optimal muscle length to higher muscle
length was encountered
(Fig. 4B). Therefore,
potentiation per se is likely to cause a shift in optimal length to
lower muscle lengths. Further experimental
work is indicated to illuminate the effects of potentiation
on muscle
length-force characteristics.
Functional consequences for in vivo movement. In this
study it is shown that in situ length-force
characteristics
are related to the frequency of stimulation.
The functional significance of this finding for in vivo daily activity
needs to be addressed. The combination of the results of
OF
RAT
2123
MUSCLE
Woittiez et al. (35) relating muscle length change to joint
angle changes and of Gruner et al. (15) describing hindlimb joint angles during in vivo locomotion indicates that
the muscle length range studied in the present study
agrees with the length range encountered
during rat locomotion. During the stance phase, the muscle length
range is relatively small and is below or near the optimal
muscle length range as determined in this study. In contrast, the greatest length change is encountered during
the swing phase with muscle lengths ranging from below
to well above optimal muscle length (i.e., optimal muscle
length range). Therefore,
our results have some significance for in vivo movements. In general, our results indicate that if muscle shortening were accompanied by decreasing firing frequencies
it would mean that, for the
length range below optimal muscle length range, the resulting drop of force would be larger than expected without these frequency effects. It should be noted that these
firing frequency effects are not usually included in modeling of human movement (36). The additional decrease in
force would allow a greater release of energy stored in
elastic tendons and aponeuroses.
During in vivo movements, stretch is often accompanied by increasing activation (due to both increased recruitment
and firing frequency). Electromyographic
records of the rat step cycle
show that electrical activity is very high during stretch at
the beginning of the stance phase (i.e., E2 phase with
eccentric muscle action) (15). The subsequent shortening phase (E3 phase with concentric
muscle action)
showed
moderate
to low electromyographic
activity.
Thus, our findings could indicate that more elastic energy would be released.
The authors
gratefully
acknowledge
the technical
assistance
of Kenneth Meijer
and Peter Bosch with the determination
of number
of
sarcomeres.
Address
for reprint
requests:
P. A. Huijing,
Vakgroep
Functionele
Anatomie,
Faculteit
der Bewegingswetenschappen,
Vrije Universiteit,
van der Boechorststraat
9, 1081 BT Amsterdam,
The Netherlands.
Received
6 January
1994; accepted
in final
form
16 June
1994.
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