In Vivo Determination of the Direction of Rotation and ...

L. Zhang [email protected] Sensory Motor Performance Program, Rehabilitation Institute of Chicago; Departments of Orthopaedic Surgery, Physical Medicine and Rehabilitation, and Biomedical Engineering.

J. Butler Department of Orthopaedic Surgery.

T. Nishida

In Vivo Determination of the Direction of Rotation and Moment-Angle. Relationship of Individual Elbow Muscles

Department of Neurology.

G. Nuber Department of Orthopaedic Surgery.

H. Huang Biomedical Engineering.

W. Z. Rymer Sensory Motor Performance Program, Rehabilitation Institute of Chicago; Department of Physical Medicine and Rehabilitation.

The direction of rotation (DOR) of individual elbow muscles, defined as the direction in which a muscle rotates the forearm relative to the upper arm in three-dimensional space, was studied in vivo as a function of elbow flexion and forearm rotation. Electrical stimulation was used to activate an individual muscle selectively, and the resultant flexion-extension, supination-pronation, and varus-valgus moments were used to determine the DOR. Furthermore, multi-axis moment-angle relationships of individual muscles were determined by stimulating the muscle at a constant submaximal level across different joint positions, which was assumed to result in a constant level of muscle activation. The muscles generate significant moments about axes other than flexion-extension, which is potentially important for actively controlling joint movement and maintaining stability about all axes. Both the muscle DOR and the multi axis moments vary with the joint position systematically. Variations of the DOR and moment-angle relationship across muscle twitches of different amplitudes in a subject were small, while there were considerable variations between subjects.

Northwestern University, Chicago, IL 60611

Introduction Although the major function of a limb muscle as a joint flexor or extensor seems obvious, the exact direction in which the muscle rotates one limb segment relative to another in threedimensional space at different joint positions is not clear. For example, the relative amplitudes of flexion, supination, and valgus moments produced by the biceps muscle are not clear. Whether the biceps still flexes the elbow when the forearm is pronated is also uncertain (Basmajian and Latif, 1957; Morrey, 1993). To develop an in vivo method of quantifying individual muscles' actions at a joint in general and to quantify the action of an elbow muscle as it rotates the forearm relative to the upper arm in particular, the DOR and moment-angle relationship of individual elbow muscles are determined in this study through in vivo experiments on human subjects. Muscle DOR directly characterizes the muscle's mechanical action at the joint and is closely related to the line of action (LOA) and multi-axis moment arms (MAs), which are generally determined from cadaveric or radiographic measurements (Amis et al., 1979; An et al., 1984; Brand et al, 1982; Koolstra et al., 1989; Pierrynowski, 1995). An et al. (1981) measured the centroid, MAs, volume and fiber lengths of cadaveric elbow muscles using serial cross-sectional anatomy analysis, and estimated the moment potentials of each muscle at the elbow joint. Koolstra et al. (1989) used an iterative procedure to estimate muscle LOA in vivo using computed tomography or magnetic resonance imaging. Since there exist substantial moiphological Contributed by the Bioengineering Division for publication in the JOURNAL OF BIOMECHANICAL ENGINEERING. Manuscript received by the Bioengineering Division January 28, 1997; revised manuscript received April 23, 1998. Associate Technical Editor: K.-N. An.

Journal of Biomechanical Engineering

variations in the human musculoskeletal system and various musculoskeletal injuries change muscle LOA and MAs, scaling of cadaver measurements to individual subjects is difficult. It is also difficult to determine the different fiber lengths and orientations through radiographic measurement, especially for muscles with large areas of origin or insertion. Furthermore, the muscle LOA and MAs may be changed significantly by muscle contraction and by anatomical structures near the joint and insertion sites where muscle-tendon units may be bound by fascial attachments to capsule, muscles, and bone (Nathan, 1992), which are difficult to quantify reliably through radiographic and cadaveric measurements. Muscle DOR gives information on the relative MA: relative amplitudes of the three MAs about the elbow flexion-extension, supination-pronation, and varus-valgus axes. Since the in vivo measured moments used to quantify the DOR already reflect the possible deflection of the muscle-tendon at the current physical, anatomical, and pathological conditions, the aforementioned difficulties associated with the LOA and MA measurement using cadaveric and radiographic methods may be minimized. Several in vivo studies have been done recently to characterize the DOR or similar properties of individual muscles by measuring the multi-axis forces/moments generated by a muscle. Nathan (1992) strapped two rows of electrodes around the forearm and used a cathode selected from the first row of 18 surface electrodes and an anode from the second row of 27 electrodes to stimulate each of 13 forearm muscles. The isometric force generated at the fingertips in a plane perpendicular to the forearm long axis and the supination-pronation moment were measured by a triaxial dynamometer. Lawrence et al. (1993) studied the contributions of several cat hind limb muscles to ankle torques. Individual muscles were activated through muscle

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nerve stimulation, selective denervations and tenotomies, and the dorsiflexion/plantarflexion, inversion/eversion, and toe-in/ toe-out moments were measured with a six-axis force sensor. It was found that substantial torques outside the sagittal plane were generated. Young et al. (1993) measured the multi-axis MAs at the cat ankle joint using the tendon excursion method. They found that the ankle joint permits substantial motion in all three axes, and many muscles have their largest MA about axes other than flexion-extension. Closely related to the DOR-angle relationship is the momentangle relationship of individual muscles, which is important in movement control, in understanding muscle coordination and load sharing, and in biomechanical modeling (Gonzalez et al., 1996; Out et al., 1996). Although many studies have been done on maximum voluntary isometric torque as a function of joint angle, the individual muscle's torque-angle relationship is not clear (Kulig et al, 1984; Winters and Kleweno, 1993). van Zuylen et al. (1988) measured the tiny twitch torque of a motor unit using a spike-triggered averaging technique, and determined the flexion twitch torque-angle relationship for the biceps and brachialis muscles. Marsh et al. (1981) studied the ankle dorsiflexion torque-angle relationship by stimulating the peroneal nerve constantly at different joint angles to activate the dorsiflexors (tibialis anterior in particular). Hasan and Enoka (1985) measured the voluntary isometric elbow flexion torqueangle relationship under constant brachioradialis EMG activity. The objectives of this study were to quantify in vivo the DOR and moment-angle relationship of individual elbow muscles of human subjects. Electrical stimulation was used to activate an individual muscle selectively. The flexion-extension, supination-pronation, and varus-valgus moments generated by the muscle were used to quantify the DOR as a function of elbow flexion and forearm supination. Furthermore, moment-angle relationships of individual muscles were determined by stimulating the muscle at a constant level across different joint positions, which was assumed to result in a constant level of muscle activation. In vivo quantification of the DOR and moment-angle relationship of individual muscles is useful in many applications, including biomechanical modeling, functional electrical stimulation of paralyzed muscles, understanding joint stability and movement control, evaluating surgical procedures such as joint replacement, and developing rehabilitation treatments. Methods The right elbow joints of nine right-handed subjects without prior history of injury or neurological disorder were studied. All the subjects gave informed consent before the experiments. Preliminary results of the study were reported previously (Zhang etal., 1995b). Apparatus. The subject was seated, placed in a shortarm fiberglass cast, and coupled to an aluminum ring (Fig. 1(a)). The ring consisted of two half-rings, and arched hard plastic pieces were fit between the ring and cast. Several bolts were screwed into the rings and pressed onto notches on the plastic pieces radially so that a tight coupling between the cast and ring was obtained. The aluminum ring was mounted on the distal end of a beam located in parallel and beneath the forearm. The proximal end of the beam was mounted on a six-axis force sensor (JR3 Inc., Woodland, CA), which was in turn mounted on a motor shaft. The elbow flexion axis and the Z axis of the force sensor were aligned with each other using the pointer shown in the inset of Fig. 1(a). The beam and arm were in horizontal planes. The position of the forearm and cast relative to the beam could be adjusted in the proximal-distal, mediolateral, upward-downward, and pronation-supination directions to align the anatomical axes of the elbow with the axes of the force sensor and to avoid excessive loading of the joint. The motor was locked at one of the several selected elbow flexion angles and thus the elbow joint was restricted isometrically. 626 / Vol. 120, OCTOBER 1998

pointer

- ulna

radius-

- humerus motor and supporting frame

torque sensor

(a)

(b)

Fig. 1 (a) Experimental setup: A shortarm cast is made and fixed to a beam through an aluminum ring. The beam is mounted on the motor shaft through a force sensor measuring six-axis moments and forces at the elbow joint. The relative position between the coupling ring and the beam can be adjusted along the X , V, and Z axes (right-hand rule). The forearm supination angle is adjusted by rotating the forearm and cast within the ring and tightening the bolts. The elbow flexion angle is changed by rotating the motor shaft. The motor is not turned on and is locked at a selected angular position, keeping the elbow at an isometric condition. The force/moment, position, EMG signals are amplified and filtered before sampled by the computer. The computer also controls the stimulator and displays the data in real time. As shown in the inset, the arch fits the outer round surface of the force sensor and the pointer coincides with the elbow flexion axis and points to the center of the arc. Therefore, the elbow flexion axis is aligned with the force sensor Z -axis, (b) The anatomical coordinate system of the right elbow joint, the total moment vector M, and the Euler angles 6„, 0y, and 8Z. ,

Anatomical Axes of the Elbow Joint Moments. Although the elbow joint is regarded as having only two degrees of freedom: flexion-extension and supination-pronation (An and Morrey, 1993), muscles crossing the elbow joint may produce significant moments about all three axes. The axis of elbow flexionextension was defined as passing through the centers of the arc formed by the trochlear sulcus and capitellum (An et al., 1981; London and Pedro, 1981). From anatomical measurement of a typical skeleton, the flexion-extension axis was assumed to be the vertical axis passing through the point 10 mm distal and 9 mm anterior to the tip of the lateral epicondyle. The axis of supination-pronation was assumed to be the line between the axis of elbow flexion and the ring finger in the horizontal plane. The axis of varus-valgus moment was assumed to be at the level of the groove between the ulna and radius in the horizontal plane. The axes of elbow supination-pronation, varus-valgus, and flexion-extension were assigned as the X, Y, and Z axes, respectively, following the right-hand rule (Fig. 1(b)). Locating the Motor Point. To activate a targeted muscle without significant stimulation current overflow to others, it is critical to locate the muscle motor points accurately. Both monopolar and bipolar stimulation were tested to locate the motor points. It was found that bipolar stimulation was more appropriate for this study because of its more localized current flow. Furthermore, the methods of locating the motor point and actually stimulating the muscle should be the same, because the optimal motor point located with one method was generally not optimal for the other. A pair of surface electrodes with 9 mm diameter conducting area and a 3 cm spacing were moved around on the muscle belly to search for the motor point. The stimulation pulse width was 0.3 ms and repeated at 1 Hz continuously. The current amplitude was adjusted for different muscles and subjects. The location where a moderate stimulation elicited the strongest contraction of the target muscle as compared to the surrounding locations (checked by visual inspection, palpation of the corresponding tendon, subject's sensation, and the measured torque) was used as the motor point in subsequent stimulation. The Transactions of the ASME


slow stimulation rate of 1 Hz was helpful for the comparison. The motor points may need to be adjusted slightly for different elbow flexion angles. Intramuscular wire electrodes were also used to stimulate the brachialis muscle. The motor point was determined through surface electrodes. Simultaneous palpation of both the brachialis and biceps muscle tendons was used to make sure only the former contracted. Wire electrodes were then inserted at the motor point.

at which the passive constraints are most likely to contribute to the measured varus-valgus moment. A downward force / ( f ) (measured by a single-axis force sensor) was applied at a known distance (d) from the elbow varus-valgus axis with the elbow under different passive varus-valgus loads (by putting pads of different thickness underneath the wrist). Iff(t)*dmatches the varus-valgus moment measured by the six-axis force sensor, it will indicate that the varus-valgus moment is measured reliably and the passive constraints do not contribute significantly.

Stimulation. A Grass Instruments S8800B stimulator with CCU1-A constant current units was used to apply the stimulation. The monophasic square wave pulse train had a pulse width of 0.3 ms repeated at 50 Hz. The pulse train duration was about 300 ms. The current amplitude was adjusted for each muscle so that moderate contraction of the target muscle was elicited without significant current overflow to the surrounding muscles. The current polarity that elicited stronger contraction (by comparing the torque generated, by the subject's sensation and experimenter's palpation) was used. For the muscle DOR study, several amplitudes of the stimulation current were used to activate the targeted muscle at different levels to get more reliable results. It was expected that if there was no significant current overflow and thus only the targeted muscle was activated, the DOR would remain in the same directions, irrespective of the muscle contraction level. For the moment-angle relationship, an appropriate stimulation intensity needs to be chosen so that moments can be measured accurately at different joint angles without significant current overflow. Starting from weak stimulation, if the stimulation current was too weak for some joint angles, the current amplitude would be increased until a stimulation intensity that elicited significant muscle twitches across the flexion range was found. The same level of stimulation was then used across the different joint angles to activate the muscle at a constant level. The electrode location was adjusted slightly at different angles to keep the electrodes at the muscle motor point.

Experimental Protocol. The subject was seated with the shoulder abducted and flexed at 90 deg and 15 deg, respectively. The elbow flexion angle was changed in the range of 0 to 120 deg. The forearm rotation was varied from —60 deg (pronation) to 90 deg (supination) with 0 deg being the neutral position (palm facing downward). The long and short heads of the biceps, brachioradialis, brachialis, lateral head of the triceps, and anconeus muscles were stimulated individually, and the torques/forces generated at the elbow joint were measured by the six-axis force sensor. The subject was asked to relax his elbow muscles during the trials. Because of the time needed for each experimental condition and the possible pain involved if high amplitude of stimulation current was used, not every muscle was studied at every joint position for each subject. A train of stimulation pulses was applied to the targeted muscle every 3 s during a 20-s-long trial. Each stimulation train generated a muscle twitch and about seven twitches were recorded during each trial. A rest period of 30 s was used between two consecutive trials to minimize muscle fatigue. The procedure was repeated for different muscles and different joint positions. The force-moment signals were low-pass filtered with eighth-order Butterworth filters with 40 Hz cutoff frequency, and were sampled at 125 Hz. When M-wave signals were also recorded, a sampling rate of 2 kHz and 600 Hz low-pass cutoff frequency were used.

M-Wave Recording. The selective activation of an individual muscle was checked using the compound muscle action potential (CMAP or M-wave) signal. For selected cases, besides the pair of stimulation electrodes for each muscle, a pair of surface electrodes was also mounted on each muscle to detect the M-wave. A computer-controlled circuit was developed to control the stimulation, remove the stimulation artifact, and record the M-wave signal (Zhang et al., 1995a). The M-wave signals of multiple elbow muscles were recorded simultaneously to monitor the contraction of the targeted muscle and stimulation current overflow to the surrounding muscles. If the M-wave was detected only at the targeted muscle but not the others, it indicated that only the targeted muscle was contracting and the joint moments/forces measured were generated solely by this muscle. Contribution of Passive Structures. The passive structures of the elbow (bones, ligaments, and joint capsule), as well as the contracting muscle, may contribute to the moments measured by the six-axis force sensor, especially in the relatively tight varus-valgus direction. Several procedures were followed to minimize the passive contributions to the measured moments: First, the experiment was conducted under an isometric condition with the six-axis force sensor coupled to the bony wrist tightly through the aluminum beam and shortarm cast. Second, the elbow was put in a "neutral" position during the experiment so that the passive structures were not loaded significantly in the three rotational directions. Third, the moment generated by a contracting individual muscle was not too strong to cause significant involvement of the passive constraints. An experiment was done on selected subjects to evaluate the passive contributions to the measured varus-valgus moment. Using the setup shown in Fig. 1, the elbow was put at the full extension Journal of Biomechanical Engineering

Data Analysis. The measured force/moment signals were low-pass filtered, decoupled between the different components, scaled to the appropriate physical units, and transformed into the elbow joint coordinate system. All six force and moment components were used in the decoupling and transformation. Only the three moment components (Mx: supination-pronation, My: varus-valgus, Mz: flexion-extension) were studied in subsequent analysis. The three force components might be affected by the joint bone-on-bone contact force and were not analyzed in the study. The measured signals were inspected and edited interactively to discard low-quality signals. First, if the stimulation electrodes were not at the motor point or if the stimulation was too weak, the muscle contraction would not be strong enough and the signal-to-noise ratio of the measured twitch moments would be too low. In such a case, the corresponding trial would not be used in further analysis. Second, if the subject voluntarily contracted his/her muscles during a trial, as indicated by the baseline shift of the measured moments, the corresponding twitch moments would be discarded. Sometimes, the first twitch moment was a little different from the others (Fig. 2), possibly because the subject reacted to the unexpected shock. The first twitch was then discarded. Third, the analysis procedure calculated and displayed the statistical information on the directional cosines DCX, DCy, and DCZ (defined in Eq. (1)) over the multiple muscle twitches in a trial. A muscle twitch would be discarded if the directional cosines DCX, DCy, or DCZ of the twitch was an outlier, defined as a value more than 1.5 times the interquartile range away from the 25th or 75th percentile (Jones, 1993). The inter-quartile range is the distance between the 25th and 75th percentiles. Fourth, if more than one head of muscles were activated, as revealed by the M-wave signals, the corresponding trial would also be discarded. For each muscle, the strongest twitch moment among Mx, My, and Mz was used to determine the duration of the twitch OCTOBER 1998, Vol. 120 / 627


stim iat. trie ep s

) supination-pronation 2 B

stim anconeus

0

*-2

0

0

-2

-2

50

0.5

0.5

)

50 2

2

I.

:

°\ ...v. 50

5.-2

f

2

Fig. 2 The M x , M y , and M z twitch moments generated by the lateral head of the triceps muscle activated electrically during a trial. The positive directions of M„, M y , and M z are supination, varus, and flexion, respectively. The shoulder abduction, shoulder flexion, and elbow flexion were 90, 15, and 30 deg, respectively. The forearm was supinated at 90 deg (palm facing medially). The peak M x , M y , and Mz twitch moments as compared to their pretwitch baseline values were used to calculate the DCX, DCy, and DCZ

moments. After low-pass filtering, the selected moment component was differentiated twice and the peaks of the second-order derivative were used to determine the beginning and end of the twitch moment time window. The mean values of the Mx, My, and Mz moments during the 600 ms interval prior to the windows were taken as their pretwitch baseline values. Peak values of the Mx, My, and Mz moments in the windows were used to quantify the amplitude of each of the torque components. The following three directional cosines about the X, Y, Z axes were used to quantify the DOR: DCX

Mx

JMI + Ml + Mi DC7

DCV

My

4 Ml + M], + Ml

M7

-J Ml + Ml + M\

(1)

where the X, Y, Z axes are the axes of supination-pronation, varus-valgus, and flexion-extension, respectively (Fig. 1(b)). For example, DCZ = 1, DCX = 0, and DCy = 0 means the muscle functions as a pure elbow flexor. Since the DOR might not be determined at exactly the same elbow flexion angles for different subjects, individual subject's DOR as a function of elbow flexion was fitted by the thirdorder polynomial and interpolation was used to determine the directional cosines at joint angles common to all subjects.

)

50

(

50

-2 50

C

0

0.2 0.1 0

-2

0 time (ms)

time (sec)

50

0

2

E

)

0

~

-2 50

C

0.5

0.5

)

0

«,

50

. /U

0 -0.5

(c) flexion-extension

stim. short bice 3S

2

time (ms)

Fig. 3 The M-waves and elbow extension torque recorded during stimulation of an individual muscle. The elbow flexion angle is 90 deg. From left to right, the three columns correspond to stimulation of the lateral head of the triceps, the anconeus, and the short head of the biceps muscles. The first three rows give the M-wave recorded from the abovementioned three muscles during stimulation. A train of current pulses are used to activate the muscle and each pulse elicits an M-wave. To show the M-wave more clearly, only the first M-wave (elicited by the first stimulation current pulse) is given. The artifact preceding some of the M-waves is the remaining stimulation artifact not completely taken out by the recording device. It may also be the artifact caused by the recording device itself. Significant M-wave is only seen at the muscle stimulated. The last row shows the elbow extension torque generated by a single contracting muscle activated by the stimulation pulse train. Different time scales are used for the M-wave (corresponding to one stimulation pulse of 0.3 ms wide) and torque signals (corresponding to the whole trial of 640 ms long).

of one of them (Fig. 3). When a muscle was stimulated, Mwave was observed on the activated muscle due to the synchronized contraction of muscle fibers. Stimulation artifact was sometimes seen on the muscles at the time when the stimulation pulse was delivered. Generally, there was no significant Mwave induced by the stimulation pulse on muscles other than the targeted one under the moderate stimulation used in the study. When the lateral head of the triceps was stimulated at a relatively high level, there was a little activity at the anconeus muscle, which could be due to stimulation current overflow or cross-talk (volume conduction). However, compared to the Miwave when the anconeus itself was stimulated (the second col-

Results Generally, selective activation of an individual elbow muscle produces significant moments about all three orthogonal axes. For example, contraction of the lateral head of the triceps muscle generates significant pronation and valgus moments as well as extension moment. Quantitatively, the directional cosines and their standard deviations for Fig. 2 are DCX = -0.2471 ± -0.4132 ± 0.0110, and DC7 0.0105, DCV -0.8763 0.0061. The corresponding three angles (between the rotational axis of the total moment M and the X, Y, and Z axes in Fig. 1(b)) are dx = 104.3 ± 0.6 deg, 6y = 114.4 ± 0.7 deg, and 9Z = 151.2 ± 0.7 deg, respectively. Notice that the first muscle twitch was discarded in the editing process due to its different shape from that of the other twitches. The selectiveness of muscle activation is shown by the Mwave signals recorded from multiple muscles during stimulation 628 / Vol. 120, OCTOBER 1998

Time (sec) Fig. 4 The applied (solid line) and measured (dashed line) varus moment at the elbow joint. The elbow was at full extension. The applied torque was calculated with a known force applied at a known distance (208 mm) from the elbow varus-valgus axis ( f ( f ) * d ) ; while the measured torque was determined using the six-axis force sensor (M(t)).

Transactions of the ASME


(a) long head of biceps

. 50

0

2p

(c) brachioradialis ! !

'

0

—> 100

•

50 100 elbow flexion angle

1

'

-0.2 ^ 0

1p

-0.5

u

' 20

• 40

-80

(d) brachialis !

•

0

• 60

(b) short head of biceps

(c) brachioradialis

(d) brachialis

elbow flexion angle

elbow flexion angle

•—

50 100 elbow flexion angle

Fig. 5 The moments Mx{o), My( + ) , and M z (*) generated by the long and short heads of the biceps, brachioradialis, and brachialis muscles, shown as a function of the elbow flexion angle. For each muscle, constant stimulation was used across different flexion angles. About ten to sixteen muscle twitches (single subject data) were used to calculate each point in the plots. The standard deviations represented by the vertical lines are rather small and can only be seen at several places. The positive directions of Mx{o), My(+), and Mz(*) are supination, varus, and flexion, respectively. The third-order polynomial was used to fit the torque-angle curves for the biceps and brachioradialis muscles and the sixth-order polynomial was used for the brachialis muscle. The forearm was in the neutral position.

Fig. 6 The DOR of individual elbow flexor muscles described as the directional cosines DCX (o), DCy ( + ) , and DCZ{*), The X, Y, and Z axes correspond to the supination-pronation, varus-valgus, and flexion-extension axes, respectively. The positive directions of the moments M„, My, and M z are supination, varus, and flexion, respectively. The vertical lines represent the standard deviations across multiple twitches and multiple trials (single subject data). Twenty-two muscle twitches were used to calculate the DOR at each elbow flexion angle for the two heads of biceps brachii, and 15 and 17 muscle twitches were used for the brachioradialis and brachialis, respectively. The third-order polynomial was used to fit the D C , DCy, and DCZ across different elbow flexion angles. The forearm was at the neutral position.

umn of Fig. 3), the effects of the current overflow or crosstalk was rather small. The insignificance of the passive contributions in the varusvalgus moment is shown by the matched f(t)*d and the measured varus-valgus moment M(t). At the "neutral" position, f(t)*d virtually overlapped with M(t) (Fig. 4 ( a ) ) . Next, the thick plastic pad (22 mm thick) under the wrist was replaced by a thin pad (8 mm thick) and the downward force/(f) was applied to the wrist again. The elbow was loaded modestly about the varus-valgus axis during the trial, and M(t) and f(t)*d still matched each other closely (Fig. 4(b)). Finally, the thin pad was also taken away a n d / ( 0 was applied again. A strong varus load was applied to the elbow, and significant difference were shown between M(t) and f(t)*d (Fig. 4 ( c ) ) .

(Fig. 6). The DOR of the elbow flexor muscles quantified by the DCX, DCy, and DCZ were dependent on the elbow flexion angle. Each data point (mean ± a) in the figure was obtained from about 20 muscle twitches across different amplitudes of stimulation current. The three angles between the rotational axis of the total moment and the X, Y, and Z axes (and their standard deviations) are given in Table 1 as 9X, 0y, and 9Z, respectively. The long head of the biceps acted mainly as an elbow flexor. Its secondary role was an elbow supinator and abductor (Fig. 6 ( a ) ) . As the elbow joint moved from the middle range of flexion to full extension, it contributed less to flexion and supi-

Moment-Angle Relationship of Individual Muscles. The moment-angle relationship of individual muscles under submaximal and constant activation were determined by stimulating the muscle at a constant level across different elbow flexion angles (Fig. 5). Variations over multiple muscle twitches of an individual subject were rather small. The several flexor muscles reached peak flexion torque in the middle range of elbow flexion, between 60 deg and 105 deg. The peak flexion torque of the brachialis occurred at the more flexed angle. The supination moment of the biceps muscle was more significant than that of the brachialis and brachioradialis muscles and generally increased with elbow flexion. The valgus moment generated by the long head of the biceps was larger near the two extremes of joint flexion. The valgus moment produced by the brachioradialis and brachialis muscles increased as the elbow was extended. Notice that intramuscular stimulation was used to activate the brachialis muscle and thus relatively low stimulation intensity and low level of joint torques were involved (Fig. 5(d)). DOR at Different Muscle Contraction Levels and Elbow Flexion Angles. The DOR determined over multiple trials with different stimulation intensities gave repeatable results Journal of Biomechanical Engineering

Table 1 Euler angles of elbow flexor muscles over multiple muscle twitches

MUSCLE Long Head of Biceps

Short Head of Biceps

Brachioradialis

Brachialis

Elbow Flexion 0° 30° 60° 90° 120° 0° 30° 60° 90° 120° 0° 30° 60° 90° 105° 0° 30° 60° 90° 120°

0*±erO 84.9+1.3 86.1+1.1 83.9+0.8 79.7+0.8 77.8±1.2 89.3±1.2 82.5+1.5 77.7+1.1 75.9±0.8 74.1±1.5 95.2+0.8 93.1+0.7 89.4+0.3 84.1±0.6 79.5+1.5 90.5+1.9 91.2+2.6 90.8+0.9 90.5+0.3 89.2+0.8

e^crO 128.8±2.0 106.4±1.5 100.5±1.1 101.6+2.3 121.2+1.4 98.1+4.3 76.9+3.4 76.5±2.0 86.2+1.3 106.3+3.1 112.3±3.0 89.0+1.7 87.1±1.9 84.510.5 86.4+1.2 125.7+7.7 101.514.2 92.812.5 90.7+0.6 98.711.6

G+aC) 34.212.0 17.011.4 12.211.0 15.811.4 34.0+1.4 8.413.9 15.213.5 18.512.0 14.710.9 23.3+2.3 23.0+3.1 3.610.8 3.111.6 8.110.5 11.211.4 35.817.7 12.013.7 3.3+2.0 1.010.5 8.711.5

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brachioradialis

long head of biceps, n=9

iateral head of triceps, n=9

short head of biceps, n=8

3 0.5

WHE. 0

brachioradialis, n*=8

50

0

100

50

100

anconeus, n=8

brachialis, n=7 1 0.5 0 0.5

supination " 5 0

Fig. 7 The DOR of the brachioradialis, long head of the biceps, and lateral head of the triceps muscles, shown as a function of the elbow flexion and forearm supination angles. The three rows correspond to the directional cosines D C , DCy, and DCZ, and the positive directions of them are supination, varus, and flexion, respectively. About 15 muscle twitches (single subject data) are used to calculate each set of the D C , DCy, and D C values. Although not shown in this three-dimensional figure, the amplitudes of the standard deviations are rather small and similar to those in Fig. 6. For each supination position, a third-order polynomial is used to fit the D C , DCy, and DCZ across different elbow flexion angles.

nation, but more to elbow abduction. The supination moment generated by the biceps muscle increased with elbow flexion, which could be felt by palpating the biceps during supination activities at different elbow flexion angles. Similar results were observed for the short head of the biceps muscle (Fig. 6(b)). Comparing their DCy, the long head of the biceps abducted the elbow, while the short head tended to rotate the forearm more in the adduction direction (Fig. 6 (a, b)). Besides its major function as an elbow flexor, the brachioradialis could produce either varus or valgus moment and it could either supinate or pronate the forearm (Fig. 6(c)). With the forearm at the neutral position and the elbow flexed, the brachioradialis supinated and adducted the forearm moderately. The two moments changed gradually into pronation and abduction when the forearm was extended. The brachialis was predominantly an elbow flexor. Its contribution to forearm axial rotation was minimal. However, it may produce significant valgus moment when the elbow is near full extension or full flexion (Fig. 6(d)). Dependence of Muscle DOR on Forearm Rotation and Elbow Flexion. The DOR of elbow muscles depended not only on elbow flexion but also on forearm rotation. When the forearm was pronated and the elbow was flexed, the brachioradialis muscle generated significant supination and varus moments (Fig. 7). When the forearm was supinated and the elbow was extended, the supination and varus moments gradually reduced and changed into pronation and valgus moments, respectively (Figs. 8 and 7 ( c ) ) . At full extension and 90 deg of supination, the valgus moment produced by the brachioradialis was even larger than the flexion moment. The biceps muscle always generated flexion and supination moments across the tested ranges of elbow flexion and forearm supination (Fig. 7 ) . The long head of the biceps always produced valgus moment, especially near full extension and full flexion. Although not shown in Fig. 7, the short head of the biceps rotated the forearm similarly but was more likely to generate varus moment, especially in the middle range of elbow flexion (see also Fig. 6(b)). 630 / Vol. 120, OCTOBER 1998

U

0 elbow flexion (deg)

50 100 elbow flexion (deg)

50 100 elbow flexion (deg)

Fig. 8 The DOR of the individual elbow muscles obtained from multiple subjects, n is the number of subjects involved. D C , DCy and D C are represented by the " o " , " + " , and " * " symbols, respectively. The X, Y, and Z axes correspond to the supination-pronation, varus-valgus, and flexion-extension axes, respectively. The positive directions of the moments Mx, My, and Mz are supination, varus, and flexion, respectively. The vertical lines give the standard deviations across subjects, which are shown only in one direction to minimize overlap between different curves. The third-order polynomial was used to fit the D C , DCy, and D C across different elbow flexion angles. The forearm was at the neutral position.

The lateral head of the triceps is primarily an elbow extensor. However, this role became less significant as the elbow was extended. At full extension, its extension capability was reduced

Table 2

Euler angles of individual elbow muscles over multiple subjects

MUSCLE Long Head of Biceps

Short Head of Biceps

Brachioradialis

Brachialis

Lateral Head of Triceps

Anconeus

Elbow Flexion

e^vO

0) across the range of elbow flexion (Mest with/? < 0.0013). The relative strength of supination (among flexion, valgus, and supination) increased with elbow flexion. For example, for the long head of biceps, paired Mest showed that the DCX at 75 deg elbow flexion was significantly larger than the DCX at 15 deg (p = 0.032), and the DCX at 120 (was significantly larger than that at 60 deg (p = 0.0084). For the short head, paired Mest showed that the DCX at 60 deg was significantly larger than that at 0 deg (p = 0.014), and the DCX at 120 deg was larger than that at 60 deg with p = 0.0037. Comparing their DOR, the long head of the biceps rotated the forearm more into the valgus direction than the short head, and paired Mest showed that the DCy of the long head was smaller (more negative) than that of the short head (p = 0.03 in the range of 15 deg to 90 deg elbow flexion). The relative amplitude of the valgus moment (among the flexion, valgus, and supination moments) of both heads of the biceps was higher (less negative) at the midflexion than that at near full extension and near full flexion. Paired Mest showed that the DCy of the biceps at 60 deg elbow flexion was higher than that at 0 deg and also higher than that at 120 deg (p = 0.0025 in all cases). For both brachioradialis and brachialis, their valgus torque component (among the flexion, valgus, and supination components) increased near full extension, accompanied by a decrease in the flexion component. For both brachioradialis and brachialis, paired Mest corroborated that the DCy and DCZ at the 60 deg elbow flexion was greater than their counterparts at 0 deg (p < 0.0042 for all cases). Neither the brachioradialis nor the brachialis generated significant supination moment at the neutral forearm position (Mest at the significance level of a = 0.05). As expected, the lateral head of the triceps extended the elbow across the range of flexion. However, its extensor role decreased as the elbow was extended. Near full extension, it could generate more of a valgus moments than extension moment. However, paired Mest showed that the DCy was not significantly different from the DCZ at the 0 deg elbow flexion (a = 0.05). At the full extension, the anconeus lost its role as an elbow extensor and turned into an elbow abductor, and paired Mest showed that the DCy was more negative than the DCZ at the significance level of a = 0.001. Both the anconeus and the lateral head of the triceps pronated the forearm moderately. Student Mest showed that the DCX was significantly lower than zero in the range of 15 to 120 deg elbow flexion (a = 0.001).

long head of biceps, n=9

u

0

• 30

• 60

• 90

J

120

short head of biceps, n=8

-0.5 L 0

brachioradialis, n=7

L, 0

. . . J 30 60 90 120 elbow flexion (deg)

• 30

60

• 90

J

120

lateral head of triceps, n=9

-110

brachialis, n=7

_1 U 0

. , , J 30 60 90 120 elbow flexion (deg)

• 30

• 60

• 90

J

120

anconeus, n=8

_, b 0

, , , J 30 60 90 120 elbow flexion (deg)

Fig. 9 The moment-angle relationships of individual elbow muscles: the long and short heads of the biceps, brachioradialis, brachialis, lateral head of the triceps, and anconeus, n is the number of subjects involved. The moments Mx[o), M y (V), and Mz{*) are normalized to the peak Mz moment for each subject and their positive directions are supination, varus, and flexion, respectively. For each muscle, the moments were produced under a constant level of stimulation at different elbow flexion angles, which was assumed to result in a constant level of muscle activation. The third-order polynomial was used to fit the torque-angle curve for each of the subjects and for their average. Notice that the vertical lines give the standard error of mean across multiple subjects. The forearm was in the neutral position.

neutral forearm rotation. The flexor muscles tended to produce more valgus moment near full extension. The long head of the biceps generally produced valgus moment across the range of elbow flexion. The lateral head of the triceps and anconeus muscles reached the peak extension moment at the more flexed position than the flexion peak of the flexor muscles (Fig. 9). From about 120 to 45 deg, the extension torque generated by the lateral head of the triceps did not change significantly (ANOVA test at the significance level a = 0.05), which might be related to the relative constant MA of the muscle (Amis et al., 1979). However, as the elbow was further extended (the muscle length was shortened), the extension torque decreased considerably, accompanied by an increasing valgus moment. The anconeus showed a similar trend. For both the lateral head of the triceps and the anconeus, paired Mest showed that the normalized My and Mz at the 60 deg elbow flexion was greater and smaller than their counterparts at 0 deg, respectively ( a = 0.05 for My and a = 0.001 for Mz).

Discussion

This study presented an in vivo method to determine the DOR and torque-angle relationship of individual muscles through exVariations of Moment-Angle Relationship Across Multi- periments on human subjects. The mechanical measurement ple Subjects. Joint moments generated by the elbow muscles gives the end-effect of muscle contraction, and interactions bevaried with the elbow flexion angle systematically (Fig. 9). tween the studied muscle-tendon unit and other musculoskeletal Similar to the DOR, variations of the moment-angle relationship structures, effect of muscle contraction on its LOA, and variaacross multiple subjects were considerably larger than the variation in fiber orientation and length are accounted for. tion across multiple levels of muscle twitches of an individual It is important to minimize the contributions of the passive subject. The several flexor muscles all had a flexion torque peak constraints in order to get accurate measurement of the elbow in the middle range of flexion and the flexion moment decreased ' varus-valgus and pronation-supination moments (An et al., gradually at both sides. Across the range of elbow flexion, the 1984). Experimentally, thejoint was put in a "neutral" position flexor muscles generated significant flexion moment. The biceps at which the passive constraints were not loaded significantly muscle generated significant supination moment, which in- in the rotational directions. To evaluate the varus-valgus laxity creased with elbow flexion and reached its peak around 90 deg and its effect on our varus-valgus moment measurement, anteelbow flexion. In contrast, the brachioradialis and brachialis rior-view images of the elbow joint were taken using a fluoromuscles generated little supination-pronation moment at the scope (Siemens, Inc.) while the forearm was abducted and adJournal of Biomechanical Engineering

OCTOBER 1998, Vol. 120 / 631


ducted passively and moderately with the elbow at full extension. The dynamic fluoroscopic imaging shows that there was moderate degree of freedom in both the varus and valgus directions. This is consistent with the varus-valgus laxity of several degrees (dependent on joint position) reported in a previous study using 17 cadaver upper extremities (King et al., 1994). The moderate varus-valgus laxity and the tight coupling between the bony wrist and the attachment allow us to measure the varus-valgus moment reliably. Significant moments are generated by the elbow muscles about axes other than flexion-extension (Figs. 8 and 9). The supination and valgus moments generated by the long head of the biceps at 60 deg elbow flexion, for example, are about 20 percent of the flexion moment. Sometimes the moments about axes other than flexion-extension even become the dominant component. At full extension, the valgus moment generated by the lateral head of the triceps and anconeus muscles is considerably higher than the corresponding extension moment (Figs. 9 and 8). The valgus moment at full extension is significant even compared to the maximum extension moment across the range of elbow flexion (Fig. 9). The strong valgus moment may help the elbow sustain an external varus load such as gravity and unload the lateral ligaments. Most daily activities load multiple axes of the elbow joint and thus require corresponding muscle actions about all the axes. In cadaveric elbows, Morrey et al. (1991) showed that simulated biceps, brachialis and triceps loads of only 5 percent of the maximum potential muscle force reduced valgus joint laxity significantly and restored nearly normal abduction-adduction patterns of medial collateral ligament excised elbow joints. The ligaments and congruous articular surfaces of the elbow joint provide only passive constraints, while the significant muscular moments about multiple axes as shown in this study may play an important role in actively increasing joint stiffness, promoting joint stability, controlling joint movement, and reducing load on the passive structures. This study addresses the following question: ' 'In the pronated position, the biceps is a strong supinator, but in this position, it is probably unable to play a simultaneous major role as an elbow flexor" (Basmajian and Latif, 1957; Morrey, 1993). Figure 7 shows that at the pronated position, the biceps can produce strong supination, especially when the elbow is flexed, but its major action is still elbow flexion. The study also addresses the disagreement as to whether the brachioradialis normally participates at all in either pronation or supination (Hollinshead, 1982; Morrey, 1993). The question was answered partially in a recent cadaveric and computer simulation study conducted at 85 deg elbow flexion (Murray et al., 1995). Figures 8 and 9 show that the brachioradialis did not generate significant supination-pronation moment at the neutral forearm rotation. However, the brachioradialis produced significant supination when the forearm was pronated, and it pronated the forearm significantly when it was supinated, and the supinationpronation moment was dependent on elbow flexion (see DCX in Fig. 7). The moment-angle relationship was obtained under a constant level of stimulation across different elbow flexion angles, which was assumed to result in constant muscle activation. The relationship reflected the dependence of MA, muscle length, and force on the joint angle and gave their combined end-effects at the joint. Compared to a previous study on single motor unit twitch flexion moment-angle relationship (van Zuylen et al., 1988), the moments measured in this study were much larger in amplitude and all three orthogonal moment-angle relationships were determined. The flexion torque-angle relationship obtained under different levels of contraction in the two studies are comparable (the biceps and brachioradialis muscles show their maximum flexion torque in the midflexion, the brachialis reaches its flexion peak at a more flexed angle. Besides, all the flexor muscles generate significant flexion torque across the range of 632 / Vol. 120, OCTOBER 1998

elbow flexion, which is consistent with the study of van Zuylen et al. (1988) but in contradiction with that of Ismail and Ranatunga (1978). Compared to studies on muscle strength curves (Kulig et al, 1984; Winters and Kleweno, 1993), the current study gives the individual muscle's torque-angle relationship under submaximal activation instead of under maximal activation of a group of muscles, which may provide insights into load sharing among the muscles. Between the flexor and extensor muscles, the reduction of extension moment of the triceps and anconeus muscles at the full extension is more significant than the flexion moment reduction of the flexor muscles at the full extension, which seems to be related to the functional differences between the two groups of muscles. It may reflect a selfprotection mechanism that prevents the extensor muscles from hyperextending the joint. On one hand, these results show rather small variation of the muscle DOR over different sized muscle twitches of a subject. On the other hand, consistent with previous human and animal studies (Nathan, 1992; Young et al., 1993), the current study shows that there exist significant variations in muscle DOR and torque-angle relationship across individuals. The variations reflect significant morphological differences across subjects and indicate the importance of individualized measurement. Other potential sources of the variations include low signal-to-noise ratio at some joint positions, malalignment between the anatomical and force sensor coordinate systems, contribution from other muscles, activation of different portions of a muscle for different subjects, and change in motor point location at different joint angles. Strong efforts were made to minimize these errors using the various measures discussed above. Compared to previous work on cadavers (Amis et al, 1979; An et al., 1981; Murray et a l , 1995), the muscle DOR characterized in this study only gives the relative instead of absolute values of multi-axis MAs. The addition of this study lies in that the measurement is done in vivo about three orthogonal axes on individual human subjects with the internal interaction between the muscle-tendon unit and other tissues occurring at physiological states. Furthermore, multi-axis moment-angle relationships of individual muscles were also determined, which provides us a tool to quantify their biomechanical function and study the coordination and load sharing among muscles (Gregor, 1993; Maton et al., 1987; Zhang et al, 1995a). Acknowledgments The authors gratefully acknowledge the support of the Whitaker Foundation, the Northwestern Memorial Foundation, and the Falk Medical Research Trust. References Amis, A. A., Dowson, D., and Wright, V„ 1979, "Muscle Strengths and Musculoskeletal Geometry of the Upper Limb," Eng. in Med., Vol. 8, 41-48. An, K.-N., and Morrey, B., 1993, "Biomechanics of the Elbow," in: The Elbow Joint and Its Disorders, 2nd ed., B. Morrey, ed., Saunders, Philadelphia. An, K. N., Hui, F. C , Money, B. F„ Linscheid, R. L., and Chao, E. Y„ 1981, "Muscles Across the Elbow Joint: A Biomechanical Analysis," J. Biomech., Vol. 14, 659-669. An, K. N., Takahashi, K., Harrigan, T. P., and Chao, E. Y., 1984, "Determination of Muscle Orientations and Moment Arms," ASME JOURNAL OF BIOMECHANICAL ENGINEERING, Vol. 106, 280-282.

Basmajian, J. V., and Latif, A., 1957, "Integrated actions and functions of the two flexors of the elbow: a detailed myographic analysis," J. Bone Joint Surg., Vol. 39A, 1106. Brand, R. A., Crowninshield, R. D., Wittstock, C. E„ Pederson, D. R., Clarke, C. R., and van Krieken, F. M., 1982, " A Model of Lower Extremity Muscular Anatomy," ASME JOURNAL OF BIOMECHANICAL ENGINEERING, Vol. 104, 3 0 4 -

310. Gonzalez, R. V„ Hutchins, E. L., Barr, R. E., and Abraham, L. D„ 1996, "Development and Evaluation of a Musculoskeletal Model of the Elbow Joint Complex," ASME JOURNAL OF BIOMECHANICAL ENGINEERING, Vol. 118, 32-40. Gregor, R. J., 1993, "Skeletal Muscle Mechanics and Movement," in: Current Issues in Biomechanics, M. D. Grabiner, ed., Human Kinetics, Champaign. Hollinshead, W. H., 1982, Anatomy for Surgeons: The Back and Limbs, 3rd ed., Harper & Row, Philadelphia.

Transactions of the ASME


Ismail, H. M., and Ranatunga, U. W., 1978, "Isometric Tension Development in a Human Skeletal Muscle in Relation to Its Working Range of Movement: the Length-Tension Relation of Biceps Brachii Muscle," Exp. Neurol., Vol. 62, 5 9 5 604. Jones, B., 1993, Statistics Toolbox: for Use With MATIAB, 2nd ed., The MathWorks, Inc., Natick. King, G. J. W„ Itoi, E„ Niebur, G. L., Morrey, B. F., and An, K. N„ 1994, "Motion and laxity of the capitellocondylar total elbow prosthesis," J. Bone Joint Surg., Vol. 76-A, 1000-1008. Koolstra, J. H., van Eijden, T. M. G. J„ and Weijs, W. A., 1989, "An Iterative Procedure to Estimate Muscle Lines of Action In Vivo," J. Biomech., Vol. 22, 911-920. Kulig, K., Andrews, J. G., and Hay, J. G., 1984, "Human Strength Curves," Exerc. Sport Sci. Rev., Vol. 12, 417-466. London, J. T., and Pedro, S., 1981, "Kinematics of the Elbow," /. Bone Joint Surg., Vol. 63-A, 529-535. Marsh, E., Sale, E., McComas, A. J., and Quinlan, J., 1981, "Influence of Joint Position on Ankle Dorsiflexion in Humans," J. Appl. Physiol.: Respirat. Environ. Exercise Physiol., Vol. 51, 160-167. Maton, B., Peres, G., and Landjerit, B., 1987, "Relationships Between Individual Isometric Muscle Forces, EMG Activity and Joint Torque in Monkeys," Eur. J. Appl. Physiol., Vol. 56, 487-494. Money, B., 1993, "Anatomy of the Elbow Joint," in: The Elbow Joint and Its Disorders, 2nd ed., B. Morrey, ed., Saunders, Philadelphia. Murray, W. M., Delp, S. L., and Buchanan, T. S., 1995, "Variation of Muscle Moment Arms With Elbow and Forearm Position," J. Biomech., Vol. 28, 5 1 3 525.

Nathan, R. H., 1992, "The Isometric Action of the Forearm Muscles," ASME JOURNAL OF BIOMECHANICAL ENGINEERING, Vol. 114, 162-169.

Out, L., Vrijkotte, T. G. M., van Soest, A. J., and Bobbert, M. F., 1996, "Influence of the Parameters of a Human Triceps Surae Muscle Model on the Isometric Torque-Angle Relationship," ASME JOURNAL OF BIOMECHANICAL ENGINEERING, Vol. 118, 17-25. Pierrynowski, M. R., 1995, "Analytic Representation of Muscle Line of Action and Geometry," in: Three-Dimensional Analysis of Human Movement, P. Allard, I. A. F. Stokes, and J.-P. Blanchi, eds., Human Kinetics, Champaign. van Zuylen, E. J., van Velzen, A., and Denier van der Gon, J. J., 1988, " A Biomechanical Model for Flexion Torques of Human Arm Muscles as a Function of Elbow Angle," /. Biomech., Vol. 21, 183-190. Winters, J. M., and Kleweno, D. G„ 1993, ' 'Effect of Initial Upper-Limb Alignment on Muscle Contributions to Isometric Strength Curves," /. Biomech., Vol. 26, 143-153. Young, R. P., Scott, S. H„ and Loeb, G. E., 1993, "The Distal Hindlimb Musculature of the Cat: Multi-axis Moment Arms at the Ankle Joint," Exp. Brain Res Vol. 96, 141-151. Zhang, L., Rymer, W. Z., and Nuber, G., 1995a, "Load Sharing Among Muscles and Dynamic Relationship Between Multi-Muscle EMG's and Isometric Joint Moment," Proc. 17th Ann. Int. Conf. IEEE EMBS, Montreal, CDROM, 2 pages. Zhang, L.-Q., Nishida, T., Butler, J., Nuber, G., and Rymer, W. Z„ 1995b, '' In Vivo Measurement of the Muscle Direction of Rotation Across the Range of Elbow Flexion," Proc. 13th Conf. Am Soc. Biomech., Stanford, CA, 2 7 3 274.

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Journal of Biomechanical Engineering

OCTOBER 1998, Vol. 120 / 633
