1Rehabilitation Research and Development
Center,
Raasch, Christine C. and
Felix E. Zajac.
Locomotor Strategy for Pedaling: Muscle Groups and Biomechanical
Functions.
J. Neurophysiol. 82: 515-525, 1999.
A group of coexcited muscles alternating with
another group is a common element of motor control, including locomotor
pattern generation. This study used computer simulation to investigate human pedaling with each muscle assigned at times to a group. Simulations were generated by applying patterns of muscle excitations to a musculoskeletal model that includes the dynamic properties of the
muscles, the limb segments, and the crank load. Raasch et al. showed
that electromyograms, pedal reaction forces, and limb and crank
kinematics recorded during maximum-speed start-up pedaling could be
replicated with two signals controlling the excitation of four muscle
groups (1 group alternating with another to form a pair). Here a
four-muscle-group control also is shown to replicate steady pedaling.
However, simulations show that three signals controlling six muscle
groups (i.e., 3 pairs) is much more biomechanically robust, such that a
wide variety of forward and backward pedaling tasks can be executed
well. We found the biomechanical functions necessary for pedaling, and
how these functions can be executed by the muscle groups. Specifically, the phasing of two pairs with respect to limb extension and flexion and
the transitions between extension and flexion do not change with
pedaling direction. One pair of groups (uniarticular hip and knee
extensors alternating with their anatomic antagonists) generates the
energy required for limb and crank propulsion during limb extension and
flexion, respectively. In the second pair, the ankle plantarflexors
transfer the energy from the limb inertia to the crank during the
latter part of limb extension and the subsequent limb
extension-to-flexion transition. The dorsiflexors alternate with the
plantarflexors. The phasing of the third pair (the biarticular thigh
muscles) reverses with pedaling direction. In forward pedaling, the
hamstring is excited during the extension-to-flexion transition and in
backward pedaling during the opposite transition. In both cases
hamstrings propel the crank posteriorly through the transition. Rectus
femoris alternates with hamstrings and propels the crank anteriorly
through the transitions. With three control signals, one for each pair
of groups, different cadences (or power outputs) can be achieved by
adjusting the overall excitatory drive to the pattern generating
elements, and different pedaling goals (e.g., smooth, or
energy-efficient pedaling; 1- or 2-legged pedaling) by adjusting the
relative excitation levels among the muscle groups. These six muscle
groups are suggested to be elements of a general strategy for pedaling
control, which may be generally applicable to other human locomotor tasks.
A common idea in motor control is the use of
primitives to control complex tasks. Bernstein
(1967) Functional muscle groups have been identified in intact animals during
walking and postural balance (Engberg and Lundberg 1969 Alternating muscle groups are a basic tenet in the concept of pattern
generation of rhythmic locomotor movements (Grillner 1975 In humans, elucidation of locomotor muscle groups from studies of
walking is difficult because of the complexity of the task. Nevertheless studies of supported treadmill stepping in
spinal-cord-injured patients have suggested the existence of pattern
generators in the human spinal cord (Barbeau and Rossignol
1994 Pedaling is a bipedal locomotor task well suited to the identification
of functional muscle groups and propulsion strategies in humans. Both
pedaling and walking are cyclical at about the same frequency (~1 Hz)
(Coast and Welch 1985 We have used a computer model of the musculoskeletal system, in
conjunction with experimental work, to begin to characterize the
essential neural-control elements required for pedaling propulsion based on the biomechanical requirements of the task. In an experimental and theoretical study of maximum-speed start-up forward pedaling, Raasch et al. (1997) In this simple control scheme of pedaling, one pair of alternating
muscle groups produces the energy needed to propel the crank through
limb extension (the uniarticular hip and knee extensor muscles, EXT)
and flexion (the uniarticular hip and knee flexor muscles, FLEX), with
some energy to accelerate the limb segments first. The other pair
facilitates the transfer of energy to the crank produced by the other
muscles and also produces energy to propel the crank directly, near the
end of extension and during the limb transition from extension to
flexion (the hamstring and ankle plantarflexor muscles, HAM/TS) and
near the end of flexion and during the flexion-to-extension transition
(the rectus femoris and ankle dorsiflexor muscles, RF/TA). A muscle
transfers energy by essentially acting as a rigid link to constrain the
acceleration of limb segments (though it also may be simultaneously
absorbing or generating energy, and so may not be strictly isometric).
For example, plantarflexors can constrain ankle motion in downstroke so
that acceleration of the shank by nonankle muscles now also will
accelerate the foot and, by intersegmental coupling (Zajac and
Gordon 1989 The biomechanical functions performed by the four muscle groups
(Raasch et al. 1997 The objective of this study was to use computer simulations to
ascertain how adaptable the four muscle groups or, equivalently, the
biomechanical functions are to pedaling under a variety of conditions.
Pedaling at different cadences, with different workloads, and in
different directions (forward and backward) was studied because these
conditions, when imposed on locomoting animals, have led to the
development of principles of locomotion in animals (Buford and
Smith 1990 This work is based on a PhD dissertation by C. C. Raasch (1996) Musculoskeletal model and the four muscle groups
The dynamic musculoskeletal model was identical to the one used
to study coordination of muscles for maximum acceleration of the crank
from rest (Raasch et al. 1997
ABSTRACT
TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES
INTRODUCTION
TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES
posited that because of the large number of
degrees of freedom involved in multijoint movement (including muscle
states as well as kinematic states), control must be hierarchical.
Understanding how a muscle-coordination pattern required to execute one
task changes to execute another may give insight into the way existing
motor patterns serve as "initial guesses" in the learning of new
tasks (Greene 1982
) and into the features common among
the patterns (the "primitives") (Giszter et al.
1993
; Mussa-Ivaldi et al. 1994
). Coexcitation of
muscles (i.e., partitioning of muscles into a group, called a
"functional muscle group") (Jacobs and MacPherson
1996
; Raasch et al. 1997
) is one possible
primitive and is a common concept in motor control (McCollum
1993
; Zajac and Gordon 1989
).
;
Macpherson et al. 1986
; Rasmussen et al.
1978
). Two groups alternating in excitation with one another
(called a pair of alternating muscle groups) (Raasch et al.
1997
) are often anatomic antagonists (Bradley and Smith
1988
; McCollum 1993
) though not necessarily (Jacobs and MacPherson 1996
).
,
1981
; Shik and Orlovsky 1976
). Electromyographic
(EMG) recordings from animal locomotor preparations have been shown to
be compatible with the idea of grouped-muscle control (Rossignol
1996
). In "fictive" locomotion, the basic alternation of
neural output to the muscle groups even can be generated in the absence
of movement (Grillner 1988
; Grillner and Zangger
1979
). To respond to disturbances and changing task demands,
however, movement and other feedback are believed to be critical to
locomotor pattern modulation (i.e., gain and phase modulation of muscle
groups) (Pearson 1993
; Rossignol et al.
1988
). For example, the cat "locomotor pattern generator" could produce a faster walking speed or a higher limb power output at
the same speed (e.g., to walk upslope) by increasing the neural excitation to the muscle groups without changing their phasing. This
can be achieved by increasing the overall tonic drive to the spinal
cord through supraspinal descending or unspecific afferent signals
(Grillner 1975
, 1981
, 1988
; Shik and Orlovsky
1976
). Changing the gain of one or more groups may be a
sufficient control strategy for responding to disturbances
(Forssberg 1979
). At other times, changing muscle
phasing is required as well, such as to switch to a different gait
(Grillner 1981
; Shik and Orlovsky 1976
).
; Calancie et al. 1994
; Dietz et al.
1995
; Rossignol and Barbeau 1995
;
Rossignol et al. 1996
). The mutability of human
locomotor patterns has been examined in split-treadmill walking, where
different belt speeds cause ankle flexors to be excited longer because
a longer swing phase of the leg on the slower belt is needed
(Dietz et al. 1994
). Also in backward walking,
uniarticular knee extensors remain excited in the support phase (as in
forward walking) (Winter et al. 1989
), while
bifunctional thigh muscles switch in phase relative to the two
transitions between stance and swing (heel-strike and toe-off in
forward walking; toe-strike and heel-off in backward walking) (Thorstensson 1986
). Thus it appears that some parts of
the locomotor pattern can be modified with some muscles more dependent
on task directionality than others.
; Winter 1983
). Both tasks require the legs to alternate in flexion and extension with most
of the propulsive energy generated in extension. Both demonstrate the
same phase-dependent modulation of reflexes (Brooke et al. 1992
; Brown and Kukulka 1993
; Yang and
Stein 1990
). Ergometer pedaling is, however, different from
walking in other ways, some of which are advantageous to the study of
legged propulsion and muscle coordination. Balance is not a factor in
seated pedaling, so muscle-coordination patterns applicable to
propulsion per se should dominate. In fact, experiments to elucidate
the pattern-generating properties of locomotion in animals
(Forssberg et al. 1980
; Grillner 1981
;
Grillner and Zangger 1979
) and infants (Forssberg
1985
) also have emphasized propulsion coordination (cf. balance
coordination). Because pedaling is a kinematically constrained task
with fewer degrees of freedom than walking, it is easier to simulate
with a computer model and more amenable to experimentation. Still, pedaling is sufficiently complex that muscle coordination is not trivial. For example, because of dynamic interactions among the segments (Zajac and Gordon 1989
) and the constraints of
the closed linkage in pedaling (which also occurs in the double-support
phase of walking), the actions of individual muscles on the system are not obvious; e.g., the biarticular hamstrings, anatomically classified as a hip extensor and a knee flexor, act to accelerate the knee oppositely, into extension, in the crank downstroke (Raasch et al. 1997
). Therefore it is important to account for the complex mechanics of muscle and segments when hypothesizing neural control strategies or attempting to deduce underlying strategies from experimental data.
have shown that a controller
constrained by lower limb muscles organized into four groups performs
as well (within 4% of maximum speed during start-up) as an
unconstrained controller where each muscle is excited independently
from the others (Raasch et al. 1997
). Nearly equal
performance is achieved because the biomechanics of the task,
specifically, the individual muscle contributions to crank and limb
propulsion, is nearly replicated with control of the four muscle
groups. In fact, the control strategy can be simplified further because
it was found that each group alternates in phasing with one other
group. Thus the four groups can be arranged into two pairs, with only
one signal controlling each pair because the two groups in each pair
alternate due to their nearly opposing biomechanical functions.
), the crank.
) (see preceding text) have been the
basis for analysis of EMG patterns generated by neurologically healthy and impaired individuals during pedaling. Kautz and Brown
(1998)
found that the degradation of pedaling performance
measured in older adults with poststroke hemiparesis was related to
abnormalities in the execution of specific biomechanical functions, as
evidenced by changes in EMG timing. In a study of forward pedaling at
different cadences by young healthy adults, Neptune et al.
(1997)
concluded that the phasing of the functions remain
unaltered, although a few muscles under specific pedaling conditions
may contribute to more than one biomechanical function. These studies
suggest, therefore, that while the phasing of a biomechanical function (e.g., leg extension) remains constant for a given pedaling task, a
muscle's contributions to it may depend on the specific pedaling condition. Nevertheless each muscle group, as defined and studied here,
can be associated with one primary biomechanical function. Thus
coordination of biomechanical functions, which may serve as control
primitives for pedaling (Ting et al. 1999
), can be revealed by studying functional muscle-group control of pedaling.
; Grillner 1981
). Pedaling at a
constant crank angular velocity and at a steady cadence (i.e.,
"smoothly") and with high metabolic energy efficiency, also was
studied to obtain insight into the role of the muscle groups and to
assess the ability of a simple controller to provide sufficient
richness for a range of pedaling goals. Finally, to assess how the
basic pattern could be adapted to a significantly altered loading
condition, pedaling with one leg was studied because this task is
similar kinematically but different biomechanically from a two-legged pedaling task (i.e., the contralateral nonpedaling leg no longer provides crank propulsion when the pedaling leg is undergoing limb flexion).
.
METHODS
TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES
). Briefly, it consists of
two legs rigidly connected by cranks to an inertial and frictional load
emulating a Monarch ergometer flywheel with a changeable frictional
load. The model includes a state-dependent load so that, like a normal
ergometer, the crank can freewheel (decouple from the flywheel) when
the total cranking torque drops to approximately zero. When
freewheeling occurs, the inertia of the load is reduced ~500-fold
(i.e., to that of the crank and chain drive system only) and the
frictional load to virtually zero. During freewheeling, pedaling may
continue although crank rotation lags flywheel rotation. If enough
propulsive force again is created, the crank accelerates and impacts
the inertia of the flywheel, causing a sudden jerk during recoupling.
Each leg of the model is constrained to a parasagittal plane with hip
center fixed, and feet attached to the pedal to emulate fixation with
cleats or clipless pedals. The dynamic equations of motion of the crank
and load, the limb segments, and the muscles are of the general form
(1)
where q is a vector of generalized coordinates (i.e.,
crank angle, qcrank; right and left
pedal angles);
(2)
,
are the angular velocity and
acceleration vectors with, for example,
crank (an element of
) being the crank angular velocity;
M(q) and RM are the
system mass and moment arm matrices, respectively;
lM and aM are
vectors of muscle fiber length and activation, respectively; FM(q,
,
lM, aM) is a vector of
muscle forces and includes the active and passive force-length and
velocity properties of muscle and accounts for compliance in tendon and
aponeurosis [note:
M is a
vector of muscle fiber velocities and is imbedded in
FM(···) since
M = f(lM, q,
)];
G(q), V(q,
), and
D(q,
) are vectors of gravity, motion-dependent, and frictional terms, respectively. Nine
"muscles" (Fig. 1) provide the
forces required to move each leg. Excitation-contraction dynamics
(Eq. 2), which describe the relation between neuromuscular excitation u(t) and muscle activation
a(t), include terms
c1 and c2, which are related to muscle
activation/deactivation time constants, with
c1 =
act
1
deact
1 and
c2 =
deact
1. Activation and deactivation time
constants were 50 and 66 ms, respectively (Winters and Stark
1987
).
View larger version (26K):
[in a new window]
Fig. 1.
Nine "muscles" in the model (Raasch et al. 1997 ).
Thirty-two muscles from SIMM (MusculoGraphics , Evanston, IL) that
contribute significantly to sagittal-plane motion were represented by
15 "equivalent" muscles, with each modeled by Hill-type active
and passive elements. These 15 muscles were combined further into 9 muscle sets, with muscles in each set receiving the same excitation
signal. The 9 muscle sets (shown in figure) and the 15 muscles are:
gluteus maximus and adductor magnus (GMAX); medial hamstrings and
biceps femoris long head (HAM); rectus femoris (RF); three-part vastus
(VAS); gastrocnemius (GAS); soleus and a muscle representing other
uniarticular plantarflexors (SOL); tibialis anterior (TA); biceps
femoris short head (BFsh); iliacus and psoas (IL). The 9 muscle sets
are the 9 "muscles" referred to in the text.
Inset: configuration of legs relative to pedal, crank,
and seat post.
The nine muscles (Fig. 1) of each leg were partitioned into four muscle
groups (Fig.
2A, black
bars). The nominal ON/OFF phasing of the groups were
derived by averaging the ON (OFF) times of the
homologous muscle groups in the right and left legs of the simulated
first-cycle of maximum-speed start-up forward pedaling (Raasch
et al. 1997). For submaximum speed pedaling, this corresponds to a simple strategy of exciting muscles when they can contribute to
crank propulsion. Such a strategy should be sufficient to achieve forward pedaling but not necessarily optimal in any sense. The first
cycle was used because it was the closest to 60 rpm (the nominal
pedaling cadence). The four groups of each leg were assumed to
alternate 180° out of phase with their contralateral counterparts. All muscles in a group were excited at the same intensity level.
|
A study of the capability of such a four-group control was our primary goal. Nevertheless unconstrained optimizations also were run, with all nine muscles excited independently, as a check to see if the groupings were producing unrealistic constraints on excitation timing and excitation levels. Detailed performance figures for these studies are not included; however, key similarities and differences are noted in the following text.
Different cadences and workloads
Simulations of pedaling at different cadences (60 and 90 rpm)
and power outputs (120 and 180 W) in the forward direction were attempted by exciting the four groups with the nominal phasing pattern
(Fig. 2A). For any given cadence and power output, muscle groups were excited at the same intensity level because such excitation of groups is the strategy required in maximum-speed start-up pedaling (i.e., excitation of a muscle is maximum during its burst)
(Raasch et al. 1997). Thus it was assumed that a
reduction in excitation intensity of the groups, each by the same
amount, would achieve less-than-maximum crank power output [crank
power output = cadence (cycles/s) × workload (energy output
per cycle)].
Different pedaling goals
A parameter optimization algorithm (Pandy et al.
1992) was used to determine how the four-group control would
need to be modified to pedal more smoothly or efficiently. The
algorithm found the phasing and the level of excitation of each of the
four groups that minimizes either the amount of nonsmoothness or
metabolic muscular energy consumed. No constraint of alternation of one group with another was imposed (however, see RESULTS).
Muscle metabolic energy consumption EM was
calculated from mechanical work and heat production as follows (Schutte et al. 1993
):
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(3) |
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(4) |
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(5) |
The effectiveness of the four muscle groups to achieve forward pedaling with one leg was explored. The four groups were phased with the nominal pattern (Fig. 2A) and excited at the same intensity level. Improvement in performance was explored by changing the relative levels of excitation among the four groups without altering their phasing. In all simulations of one-legged pedaling, the model was modified. One leg and a pedal were removed, and the frictional load was halved from the nominal. Thus the mechanical work performed by the leg over the crank cycle in one-legged pedaling was identical to the work performed by the leg in two-legged pedaling.
Backward pedaling
The feasibility of using the nominal forward-pedaling muscle-excitation pattern (Fig. 2A) to pedal backward was explored. That is, the four muscle groups were phased (Fig. 6A) with respect to limb extension and flexion and the transitions between extension and flexion according to the nominal pattern (cf. Fig. 6A, left: phasing diagram, with Fig. 2A). Muscle groups were excited at the same intensity at a level compatible with the achievement of forward pedaling (see RESULTS). Other attempts to pedal backward used excitation patterns where either the levels of excitation differed among the groups or the phasing of the groups or muscles within a group differed from the nominal pattern.
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RESULTS |
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Nominal cadence and workload
The simulation was able to pedal forward at a steady 60-rpm, 120-W
power level with the excitation level of the four-group control set at
0.27 of maximum. The nonsmoothness cost was 0.685 rpm and the metabolic
cost 611 W. The oxygen consumption rate for the nominal 60-rpm
simulation, computed by assuming an aerobic metabolism of 20.1 kJ/L
O2 (Astrand and Rodahl
1977) and a baseline/resting
O2 of 0.3 L
O2/min (no-load pedaling) (Croisant and
Boileau 1984
), was within 5% of measured oxygen uptake rate
(Croisant and Boileau 1984
; Swain et al.
1987
). The pedaling simulation was very realistic, as judged by
graphic display of the motion of the body segments and crank relative
to one another. The crank angular velocity was maintained to within 1.2 rpm (1.8%) of the desired crank angular velocity, so that cadence was
constant to within ± 0.1%.
The crank and pedal kinematics were similar to those recorded from
subjects (Fig. 2C, gray regions) (Fregly et al.
1996). The phasing pattern of the four groups corresponded
generally well to the EMG pattern recorded during pedaling
(Neptune et al. 1997
) (Fig. 2B, gray bars).
However, subtle differences between simulation and experimental data
exist (see DISCUSSION). Nevertheless if muscles are allowed
to be excited independently instead of being constrained into four
groups, our musculoskeletal model can replicate the experimental data
even better (Neptune and Hull 1998
).
Different cadences and workloads
Continuous pedaling in the forward direction at the higher cadence (90 rpm) and power output (180 W) was achieved with the nominal phasing pattern (Fig. 2A). Pedaling at the faster cadence or higher power output required, however, a higher excitation intensity (0.349 and 0.365 of maximum, respectively) and cost more metabolic energy J2 (913 and 823 W). The nonsmoothness cost increased for higher power (1.157 rpm) but decreased for higher cadence (0.538 rpm). Pedaling at other cadence/workload combinations, though not thoroughly studied, also were achieved with the nominal pattern.
Different pedaling goals
To maximize smoothness, the intensity of excitation of the four
muscle groups had to be changed much more than the phasing of the
excitations (Fig. 3A). The
excitation levels of the RF/TA and HAM/TS groups had to be increased
substantially (50 and 44%, respectively) and the excitation of the EXT
group decreased (25%). During limb flexion, the excitation level of
the FLEX group had to be increased (36%). Nonsmoothness cost was
reduced from 0.685 to only 0.247 rpm. These changes decreased the crank
deceleration at the limb transitions and reduced the peak-to-peak crank
velocity variations (from 2 to 1 rpm; Fig. 3B, compare
with · · ·), but metabolic energy consumption increased (from
611 to 648 W, +5%). Unconstrained optimization with all nine muscles
excited independently produced very similar results. Excitation of some
muscles in the RF/TA, HAM/TS, and FLEX groups had to be increased
(i.e., RF, TA, HAM, IL, BFsh) and excitation of muscles in the EXT
group decreased [i.e., VAS, GMAX]. Only very small changes in phasing occurred.
|
To maximize energetic efficiency, excitation of the four muscle
groups also had to be changed much more than their phasing (Fig.
4A). Propulsion was provided
almost exclusively by the EXT group through an increase in its
excitation level (+85%), although its burst duration was shorter. The
FLEX group was not excited anywhere in the cycle, and the excitation
levels of the RF/TA and HAM/TS groups decreased substantially (85 and
37%, respectively). The metabolic energy cost decreased from 611 to
518 W. Consistent with the decreased use of the RF/TA and HAM/TS
groups, peak-to-peak crank velocity variations increased (to 5 rpm)
although freewheeling did not occur. With muscles excited
independently, a similar emphasis on the use of extensors was seen,
with VAS recruited first and then GMAX at higher workloads. Some
excitation of SOL and TA still was required. However, HAM and RF were
not excited at all and freewheeling occurred.
|
Smooth one-legged pedaling in the forward direction was found to be
possible with the four groups, though the excitation levels among the
groups had to be quite different (Fig.
5A). The EXT group was not
excited, even during limb extension, but the FLEX and RF/TA groups had
to be excited with more intensity. The FLEX group, which produces three
times less energy than the EXT group in two-legged pedaling
(Raasch et al. 1997), was required in one-legged pedaling to generate more power in the upstroke than the EXT group does
in downstroke because the weight of the leg decelerates the crank in
upstroke and accelerates the crank in downstroke. Because the weight of
the limb opposes the initial part of the flexion-to-extension transition (Fig. 5A, diagram), the RF/TA group also must
contribute more energy than the HAM/TS group in one-legged pedaling.
With all four groups excited at the same (high) intensity, pedaling with one leg was feasible but it was very nonsmooth (nonsmoothness cost
of 22 vs. 0.8 rpm for unequal excitation) and freewheeling occurred
(Fig. 5B). With a lower intensity of excitation of the groups, pedaling through limb flexion was impossible (not shown).
|
Backward pedaling
Continuous backward pedaling was found to be impossible with the
four groups excited at the same intensity and phasing as in forward
pedaling, where phasing is relative to limb extension, flexion, and the
extension/flexion transitions (Fig.
6A). The resulting
freewheeling and reversals in crank direction at the limb transitions
were due to the high deceleration of the crank caused by ipsilateral
HAM and contralateral RF forces near 180°, and ipsilateral RF and
contralateral HAM forces near 360°. This retardation became evident
by analyzing the contributions of the HAM/TS group and the RF/TA group
to the two propulsive components essential to cranking the limb through
its transitions (i.e., through 180 and 360°), which are to accelerate
the crank and to transfer energy from the limb inertia to the crank
(Raasch et al. 1997). Continuous backward pedaling was,
nevertheless, possible as long as HAM and RF muscles were not excited
anywhere in the crank cycle and the other muscles were excited as in
forward pedaling, although freewheeling occurred at transitions (Fig.
6B). In this case, TS and TA muscles were able to transfer
to the crank the energy delivered previously to the limb inertia by the
EXT and FLEX groups, respectively, as in forward pedaling
(Raasch et al. 1997
).
|
Very smooth backward pedaling was achievable with the groups excited at the same intensity, however, if the RF/TA-HAM/TS pair was subdivided into two pairs (RF-HAM pair and TA-TS pair; Fig. 6C). Importantly, the phasing of the HAMS and RF groups had to be reversed from that required in forward pedaling, relative to the limb transitions, so they could propel the crank through the limb transitions (cf. Fig. 6C with Fig. 2A near 180 and 360°). Decoupled from HAM and RF, the TS and TA groups were able to transfer energy from limb inertia to crank as in forward pedaling. With the RF and HAM groups now able to provide crank propulsion at the limb transitions rather than retardation, excitation of all six groups could be at the same intensity.
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DISCUSSION |
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Continuous, smooth, efficient pedaling in the forward direction at different cadences and workloads was found to be possible with just four muscle groups of coexcited muscles. The successful pattern is simpler than four independent controls because each group alternates with another (i.e., 2 pairs, with each pair consisting of 1 muscle group alternating with another). In fact, a control strategy that is constrained further to excite all muscles at the same intensity also suffices well. However, the excitation levels of the groups must be different to accomplish different pedaling goals, such as to pedal smoothly with one or two legs or to pedal with the highest energetic efficiency.
Robust pedaling strategy: six muscle groups arranged into three pairs
We believe that a strategy employing fewer than six muscle groups is not biomechanically adaptable to be considered a general pedaling strategy because pedaling forward and backward imposes different biomechanical requirements. Nevertheless, it is possible, at times, to turn the crank forward and backward by controlling less than six groups (e.g., 4 groups, Figs. 2A and 6B). In this case, smooth crank progression when pedaling in reverse is impossible because no four-group excitation pattern that smoothly pedals, say, forward can accelerate the crank backward at the limb transitions adequately (e.g., cf. Fig. 6B with Fig. 2). In fact, if the frictional load is sufficiently high, continuous progression in reverse is not possible at all, and the demand for six muscle groups to be controlled becomes even more evident.
Of course, pedaling with fewer than four groups is even less adaptable,
not only with respect to pedaling direction but even in a given
direction. For example, continuation of forward cranking is impossible
when the biarticular thigh and the ankle muscles are combined with
either the FLEX or the EXT group (Fig.
7A, left). The leg
oscillates forward/backward at the limb extension/flexion transitions
(Fig. 7A, right). Changing the phasing of the groups of the
one pair, or the grouping of muscles, does not improve performance
because the EXT and FLEX muscles then decelerate the crank during their
relaxation. Also the improperly phased biarticular thigh muscles and
ankle muscles are then unable to provide propulsion at the limb
transitions. Shortening the burst durations of the two groups of the
one pair alleviates the otherwise high deceleration during limb
extension and flexion, but freewheeling still occurs at the limb
transitions (Fig. 7B). For smooth pedaling, the biarticular thigh and ankle muscles must be excited during the limb transitions (Raasch et al. 1997). Of course, any strategy that
delivers sufficient energy to overcome the load and propel the limb
will suffice to turn the crank, although not necessarily smoothly
(e.g., the metabolically efficient use of EXT, SOL, and TA in the
unconstrained optimization). If the inertia of the ergometer is very
high (e.g., to emulate bicycle riding) (Fregly et al.
1996
), such a strategy might even produce acceptable
smoothness. Hard-coupling of the crank and flywheel would simplify
further control of smooth pedaling because the inertia of the flywheel
would assist the limb in coasting through transitions.
|
The ability to control six muscle groups to execute six biomechanical
functions is required, therefore, to be able to fulfill a variety of
pedaling goals, including forward and backward pedaling. Four groups
are insufficient because the phasing of the HAM and RF groups are
directionally sensitive and the phasing of the TS and TA groups are
not. Thus HAM control must be separated from TS control and RF from TA
control. Nevertheless HAM and RF still can be paired because they still
alternate with one another, and TS still can be paired with TA. Similar
uncoupling of muscles is seen in posture, where the "ankle
strategy" (HAM/TS alternating with RF/TA) is in some situations
replaced with a mixed strategy(Horak and Nashner 1986).
The "coupling" of HAM/TS and RF/TA in the four-group control may
be more accurately described as "coincidence" because the groups
actually serve different biomechanical functions in pedaling.
The ankle muscles (TS-TA pair, particularly TS) must position the feet
properly at the limb transitions to transfer energy from the limb to
the crank. This transfer redirects energy that would otherwise go
toward accelerating the limb segments, prevents extreme ankle
dorsiflexion and knee hyperextension at the end of limb extension, and
avoids excessive ankle plantarflexion at the end of limb flexion
(Raasch 1996; Raasch et al. 1997
).
Indeed, other backward-pedaling simulations by us with TS-TA switched in phase do indeed hyperextend the knee. Thus the phasing of TS should
be near the end of limb extension (i.e., following/overlapping activation of the EXT group), and TA near the end of flexion, irrespective of pedaling direction (Figs. 2A and
6C). The TS-TA pair therefore is associated closely with the
EXT-FLEX pair with a phase delay between the pairs to properly
configure the limb segments for energy transfer (cf. alternative
strategies, see following text).
In contrast, HAM and RF act primarily to accelerate the crank when the leg is moving posteriorly (HAM) or anteriorly (RF), also regardless of pedaling direction. Their phasing, however, reverses with pedaling direction (Figs. 2A and 6C). Other simulations by us also support the decoupling of HAM-RF from TS-TA and the different biomechanical functions executed by these two pairs. For example, with the two pairs separated, maximum smoothness is obtained by exciting HAM-RF more than TS-TA because more crank power is desired at the transitions and HAM and RF can produce such power. On the other hand, maximum metabolic efficiency is obtained by exciting TS more because the ankle must be stabilized to ensure more complete transfer of the EXT-produced energy to the crank.
A strict association between each of the six functional muscle groups
and a specific biomechanical function, as emphasized earlier for
clarity, however, should be viewed cautiously because recent studies
suggest that a muscle can contribute to more than one biomechanical
function in pedaling (Neptune et al. 1997; Ting et al. 1999
). For example, a backward-pedaling experimental
study showed that the transition muscles HAM and RF change their
phasing, as compared with forward pedaling (Ting et al.
1999
). However, the change in RF phasing was much less
than 180°, probably because RF contributes to limb extension as well
as to the flexion-to-extension transition function. Nevertheless all
these studies agree that six biomechanical functions must be performed
to pedal smoothly. The association of a functional muscle group with a
biomechanical function, initially proposed by Raasch et al.
(1997)
, thus provides a foundation for interpreting pedaling
EMG patterns.
Alternative ankle-control strategies
Analysis of the differences between simulated pedaling with the
four muscle groups and the kinematics and EMGs recorded from pedaling
subjects (Fig. 2B) suggests that a variety of ankle
strategies are possible. EMG amplitudes are unequal from one another,
probably due to their dependence on the specific pedaling task (e.g.,
pedaling both smoothly and efficiently; cf. Figs. 3 and 4). The earlier onset of TA and SOL in pedaling subjects is probably due to subjects employing a different ankle strategy than assumed in the simulation. Simulations show that some latitude is possible in controlling the
ankle (i.e., TA and SOL) as long as the essential biomechanical requirement of transfer of energy from the hip and knee extensors to
the crank is accomplished. SOL and TA may be excited earlier because of
their participation in the execution of the EXT and FLEX biomechanical
functions (i.e., extension/flexion of the limb). In this case, SOL and
TA still stiffen the ankle to facilitate energy transfer from the limb
to the crank, but the stiffening is earlier. Consequently less kinetic
energy is stored temporarily in the limb segments. Pedal kinematics
then more closely match the subjects' (e.g., peaks in pedal angles are
reduced) and ankle motion is reduced. This explanation is compatible
with the suggested secondary contribution of TA to flex the limb in
pedaling (Ting et al. 1999) and the suggested
contribution of SOL to extend the limb as well as plantarflex the foot
(Neptune et al. 1997
). Another feasible ankle strategy
is to maintain the foot near-horizontal throughout the cycle (a
strategy more "comfortable" for many subjects). In this case, SOL
and TA must be excited slightly through much of down- or up-stroke,
even though this does not contribute significantly to crank
acceleration (and hence is not selected by an optimization that does
not consider comfort). Still other strategies are possible; for
example, "locking" the ankle in a plantarflexed position for much
of the cycle with prolonged TS excitation (Raasch 1996
). Such a strategy effectively removes the ankle degree of freedom and
prevents knee hyperextension. However, this ankle strategy requires
more metabolic energy than the default strategy, and the resulting
kinematics may be undesirable for subjects.
Phase control of motor output
Timing of the excitation of the muscle groups within the pedaling
cycle could be regulated by afferent feedback from the limbs as in
locomoting animals (Pearson 1993; Rossignol et
al. 1988
). An estimate of the position of the feet relative to
the hips through neural processing of afferent information could be the
trigger signal for limb extension and flexion, as in animal locomotion (Andersson and Grillner 1983
; Grillner and
Rossignol 1978
). Phasing of the TS-TA pair could be time
delayed from EXT-FLEX phasing to assure appropriate transfer of energy
from the limb inertia to the crank. Although a continuous estimate of
feet location also could be used to precisely time (i.e.,
phase-control) the excitation of all six groups within the cycle,
motion-dependent cues (e.g., anterior/posterior motion of the ankles)
also may participate. For example, if RF was to be excited when the
ankle is moving anteriorly, and HAM when moving posteriorly, then the HAM-RF pair would be phased properly in both forward and backward pedaling. If the phasing of the biarticular thigh muscles is set primarily by motion-dependent feedback, similar to the "mutable synergies" postulated by Smith (1987)
in the
restructuring of the cat locomotor pattern, simple rule-based logic
networks acting on sensory information might be sufficient to implement
the required phase control (Cruse et al. 1995a
,b
). Such
control of locomotion is being employed in the development of
Functional Electrical Stimulation controllers to restore gait
in paraplegics (Popovic 1991
, 1993
).
Gain control of motor output
Pedaling at a faster cadence or a higher workload can be achieved
by increasing the excitation of the muscle groups equally. This
regulation of cadence and power output could be accomplished by a
common gain control of the excitations of the muscle groups. Common
gain control could be effected by neural control and neuromodulator concepts derived from animal locomotion studies (Grillner 1981, 1988
; Pearson 1993
; Rossignol et al.
1988
). For example, a descending tonic drive from supraspinal
structures onto pattern generator elements could set the common scaling
factor for excitation of the muscle groups compatible with the desired
limb power output (equivalent to a certain cadence with a specific
energy output from the limb per cycle), similar to the setting achieved
by descending pathways from brain stem locomotor regions
(Grillner 1988
; Shik et al. 1966
).
Regulation of the intensity of motor output could be accomplished by
afferent feedback. Neural processing of load-sensing feedback from the
limb in pedaling (Raasch 1996) or walking
(Duysens and Loeb 1980
; Duysens and Pearson 1976
,
1980
; Pearson et al. 1992
), should be especially
effective (Raasch et al. 1997
).
Relative excitation levels of the muscle groups
Some pedaling tasks require the excitation levels of the muscle
groups to be different, such as to pedal with one leg or to pedal with
ultrasmoothness or the highest energetic efficiency. Processing of
afferent feedback to ensure that the specific goals of the pedaling
task are fulfilled could be attained through high-level control of
parameters utilized by a lower-level controller (Loeb et al.
1990; Prochazka 1989
). In this scheme, a
specific pedaling task would be accommodated by the setting of
parameters, or "schedules" (Prochazka 1989
), which
may be part of the initialization of the pedaling motor program. This
could allow for a more complex "recruitment scheme" for muscles
within a group, as conditions require, as seen in the selective
activation of individual extensor muscles with increased load when
muscles were allowed to be excited independently (Raasch
1996
). After initial parameter selection by the high-level controller, pedaling could proceed by activating the low-level controller. Feedback would be used by the high-level controller only to
check periodically (e.g., once per half-cycle) the appropriateness of
the parameter set (e.g., the phasing and excitation-level parameters of
each muscle group). In conjunction with the parameter set, feedback
would be employed by the low-level controller to assure continuous task
execution in the presence of "reasonable" environmental (and
internal) uncertainties; e.g., muscle and joint receptors could be used
to modulate TS-TA to prevent excessive ankle motion and fine-tune the
control of the pedal trajectory.
Locomotor strategies in animals and humans may be similar
The locomotor features outlined in the preceding text based on
pedaling, with muscles organized into alternating functional groups and
phase- and amplitude-controlled (perhaps through high- and low-level
neural controllers), have features common to animal locomotion. First,
spinal neuronal elements exciting motor pools alternately through
(perhaps) other interneurons have long been the basis of locomotor
concepts (Grillner 1975), and now their cellular,
molecular, and pharmacological properties are being elucidated in even
vertebrates (Grillner 1988
; Rossignol and Dubuc 1994
). Second, phase-control of these elements through neural processing of peripheral proprioceptive information is critical to
pattern generator execution of locomotion (Pearson 1993
;
Rossignol et al. 1988
). For example, load-bearing
feedback in animal locomotion is important to flexor initiation and
excitation of the extensors (Pearson and Duysens 1976
),
and to the relative excitation of flexors to extensors (Smith
and Carlson-Kuhta 1995
). In pedaling, because cranking force
(and the reaction force felt on the foot) is primarily a function of
the contributing muscle forces (Kautz and Hull 1993
),
force feedback could be used to balance the excitation between the EXT
and FLEX groups (e.g., as required to achieve 1-legged pedaling, Fig.
5). Also, the position of the limb relative to the hip is critical to
phase selection in cat locomotion (Andersson and Grillner
1983
; Grillner and Rossignol 1978
) and could be
in human pedaling as well (see preceding text).
The features used by humans to provide propulsion to walk and pedal
also may be similar (see INTRODUCTION). For example, the switch in phasing of the thigh bifunctional muscles (e.g., HAM and RF)
with walking direction (Thorstensson 1986) and to
anterior/posterior postural balance disturbances (Nashner and
McCollum 1985
) is similar to the switch occurring in HAM and RF
in pedaling. We believe, therefore, that humans pedal by using some of
the sensorimotor control mechanisms employed to walk (and stand).
Conclusion
When muscles are assigned into groups, our simulations show that
six groups are the minimal set to pedal in different directions under a
variety of conditions. Phasing of four groups (uniarticular hip and
knee extensors in alternation with hip and knee flexors; ankle
plantarflexors in alternation with dorsiflexors) do not change with
direction. The biarticular thigh muscles (anterior alternating with
posterior muscles) do change with direction (e.g., rectus femoris is
excited during the transition from flexion to extension in forward
pedaling and during the opposite transition from extension to flexion
in backward pedaling). Different cadences and limb power output can be
achieved by controlling the overall excitatory drive to the pattern
generating elements, and different pedaling goals (e.g., 1- versus
2-legged pedaling) can be achieved by controlling the relative
excitation levels among the muscle groups. We suggest that these six
muscle groups form a basic strategy for pedaling propulsion and also
may be a subset of the elements of a general strategy for human
locomotor propulsion. We believe that pedaling affords a rich milieu
for performing not only detailed theoretical studies, such as those
here, but also for conducting controlled locomotor experiments in
healthy and neurologically impaired subjects (Brooke et al.
1987, 1992
; Brown and Kautz 1998
; Brown
and Kukulka 1993
; Brown et al. 1996
, 1997
;
Kautz and Brown 1998
; Kautz and Hull
1993
; Pierson-Carey et al. 1997
; Ting et al. 1998
, 1999
), which together may reveal motor control
mechanisms of human locomotion.
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ACKNOWLEDGMENTS |
---|
We thank D. Brown and L. Ting for very helpful comments on an
earlier version of the manuscript, S. Kautz for insightful suggestions for improving the different drafts of the manuscript, and D. Denney for
assistance with figure preparation. Special thanks to R. Neptune for
providing us with experimental pedaling data (Neptune et al. 1997).
The work was supported by National Institute of Neurological Disorders and Stroke Grant NS-17662 and the Rehabilitation R&D Service of the Department of Veterans Affairs (VA).
Present address of C. C. Raasch: 1108 W. Oraibi Dr., Phoenix, AZ 85027-4651.
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FOOTNOTES |
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Address for reprint requests: F. E. Zajac, Rehab R&D Center (153) (Bldg. 51), VA Palo Alto Health Care System, 3801 Miranda Ave., Palo Alto, CA, 94304-1200.
The costs of publication of this article were defrayed in part by the payment of page charges. The article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.
Received 26 May 1998; accepted in final form 22 March 1999.
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REFERENCES |
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