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Lower extremity control and dynamics during backward angular impulse generation in forward translating tasks
ARTICLE IN PRESS
Journal of Biomechanics 39 (2006) 990–1000 www.elsevier.com/locate/jbiomech www.JBiomech.com
Lower extremity control and dynamics during backward angular impulse generation in forward translating tasks W. Mathiyakoma,e, J.L. McNitt-Graya,b,c,, R. Wilcoxd a
Department of Kinesiology, 3560 Watt Way, PED 107, University of Southern California, Los Angeles, CA 90089-0652, USA b Biomedical Engineering, University of Southern California, Los Angeles, CA 90089-0652, USA c Biological Sciences, University of Southern California, Los Angeles, CA 90089-0652, USA d Psychology, University of Southern California, Los Angeles, CA 90089-0652, USA e Andrus Gerontology Center, University of Southern California, Los Angeles, CA 90089-0652, USA Accepted 26 February 2005
Abstract Observation of complex whole body movements suggests that the nervous system coordinates multiple operational subsystems using some type of hierarchical control. When comparing two forward translating tasks performed with and without backward angular impulse, we have learned that both trunk-leg coordination and reaction force-time characteristics are significantly different between tasks. This led us to hypothesize that differences in trunk-leg coordination and reaction force generation would induce between-task differences in the control of the lower extremity joints during impulse generation phase of the tasks. Eight highly skilled performers executed a series of forward jumps with and without backward rotation (reverse somersault and reverse timer, respectively). Sagittal plane kinematics, reaction forces, and electromyograms of lower extremity muscles were acquired during the take-off phase of both tasks. Lower extremity joint kinetics were calculated using inverse dynamics. The results demonstrated between-task differences in the relative angles between the lower extremity segments and the net joint forces/reaction force and the joint angular velocity profiles. Significantly less knee extensor net joint moments and net joint moment work and greater hip extensor net joint moments and net joint moment work were observed during the push interval of the reverse somersault as compared to the reverse timer. Between-task differences in lower extremity joint kinetics were regulated by selectively activating the bi-articular muscles crossing the knee and hip. These results indicate that between-task differences in the control of the center of mass relative to the reaction force alters control and dynamics of the multijoint lower extremity subsystem. r 2005 Elsevier Ltd. All rights reserved. Keywords: Total body center of mass; Reaction force; Angular impulse; Joint kinetics; Muscle activation pattern
1. Introduction Task-specific modification of total body momentum requires that the performer generates net linear and angular impulse during contact with the environment. Observation of complex whole body movements, such as Corresponding author. Biomechanics Research Lab, Department of Kinesiology, 3560 Watt Way, PED 107, University of Southern California, Los Angeles, CA 90089-0652, USA. Tel.: +1 213 740 7902; fax: +1 213 740 7909. E-mail address: [email protected] (J.L. McNitt-Gray).
0021-9290/$ - see front matter r 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.jbiomech.2005.02.022
jumping, suggests the nervous system organizes the human body into a number of operational subsystems that are coordinated by using some type of hierarchical control (Arabyan and Tsai, 1998; Flashner et al., 1988; Requejo et al., 2002). For example, during the impulse generation phase, the motion of multiple body segments is coordinated so that the position of the center of mass (CoM) relative to the reaction force (RF) satisfies both the linear and angular impulse requirements of the task. During the impulse generation phase of a standing forward jump, the segments are configured such that the CoM is aligned with the forward-directed
ARTICLE IN PRESS W. Mathiyakom et al. / Journal of Biomechanics 39 (2006) 990–1000
RF (Ridderikhoff et al., 1999). In contrast, during the take-off phase of a forward jump with backward rotation (reverse somersault), the segments are configured such that the CoM is positioned posterior to the line of action of forward directed RF. As a result, both upward and forward linear impulse and backward angular impulse requirements of the task are satisfied (Mathiyakom et al., accepted). By determining how coordination between subsystems change between tasks performed under various conditions (Bernstein, 1967), we can advance our understanding of the control structure. Regulation of CoM position relative to the RF involves coordination between the trunk and leg subsystems during weight bearing tasks. The magnitude of the RF is regulated by the rate of lower extremity joint extension (Bobbert and van Ingen Schenau, 1988; Ridderikhoff et al., 1999), whereas the position of the CoM relative to the feet is most sensitive to trunk motion (Horak and Nashner, 1986; Shenckman et al., 1996; McNitt-Gray et al., 2001). Although modifications in trunk-leg coordination provide a mechanism for regulating the position of the CoM relative to the RF during impulse generation, between-task differences in
991
lower extremity segment orientation relative to the RF is expected to influence how the lower extremities contribute to the linear and angular impulse required to perform the task (McNitt-Gray et al., 2001). Comparison of two related, well-practiced tasks with common linear impulse and different angular impulse requirements performed by the same highly skilled performers provides us with a unique opportunity to determine how control and coordination of local subsystems are modified to achieve specific task objectives at the total body level (Miller et al., 1990). Previous study of reverse somersaults and reverse timers (common linear impulse requirement (forward, upward) with and without angular impulse) indicates that trunkleg subsystem coordination, lower extremity joint coordination, and reaction force-time characteristics were significantly different between these two tasks (Mathiyakom et al., accepted). These results led us to hypothesize that lower extremity control, as indicated by (a) net joint moment (NJM), net joint moment power (NJMP), work done by the NJM, and (b) muscle activation patterns would be different between these two tasks (McNitt-Gray et al., 2001; McNitt-Gray, 1993; McFadyen and Winter, 1988; Elftman, 1939). The
Fig. 1. Body configuration, estimated total body center of mass position (), and forward horizontal (-) and upward (m) vertical reaction force during the take-off phase of the reverse somersault (top) and reverse timer (bottom) of an exemplar subject. During the take-off phase of both tasks, the performers need to generate forward and upward linear impulse. In addition, the performers need to generate backward angular impulse during the take-off phase of the reverse somersault.
ARTICLE IN PRESS W. Mathiyakom et al. / Journal of Biomechanics 39 (2006) 990–1000
magnitude of the lower extremity NJMs were expected to increase as the relative angle between the lower extremity segments and the RF increased and the magnitude of the adjacent NJMs decreased. The work done by NJM was also expected to increase as the NJMs and the joint angular velocities increased. Activation of the lower extremity muscles were expected to scale to accommodate for between-task differences in mechanical demand imposed on the lower extremity joints (NJM, NJMP, and work done by NJM). Differences in the lower extremity joint kinetics and its associated muscle activation patterns provides insight as to how the nervous system controls the lower extremity subsystem in order to achieve task objectives at the total body level (e.g. CoM trajectory relative to the RF).
Pasadena, CA, USA) were simultaneously collected during the performance of each experimental task. These three sets of data were synchronized at the time of plate departure. Thirteen body landmarks (vertex, C7, shoulder, elbow, wrist, finger, iliac crest, greater trochanter, knee, lateral malleolus, heel, 5th metatarsal, and toe) of the
4 Vertical Reaction Force (BW)
992
3 2 1
2. Methods
0 -0.6
-0.5
-0.4
-0.3
-0.2
-0.1
0
0.1
2.1. Subjects
2.2. Tasks Each participant performed a series of reverse timer and reserve somersault take-offs from a force plate into a landing mat (Fig. 1). The participant initiated each task by facing away from the take-off surface as performed from the 10-m platform during competition. During the reverse timer take-offs, the participant jumped from the platform as if performing a reverse somersault without the intent of rotating about the somersault axis during flight and landed feet first on the landing mat. During the reverse somersault take-off, the participant jumped from the platform (upward and forwards) and performed one complete backward somersault during the flight phase and landed feet first on the landing mat. Each task was blocked and randomized for each participant. Three successful trials of each task were analyzed. 2.3. Data collection Prior to data collection, participants warmed up and practiced the experimental tasks until they were familiar with the experimental set up. Sagittal plane kinematics (200 fps, C2S NAC Visual Systems, Burbank, CA USA), reaction forces (0.6 0.9 m2, 1200 Hz, Kistler, Amhurst, MA, USA), and activation patterns of the lower extremity muscles (1 1 cm2, 1200 Hz, Konigsberg,
Event
IP 1st BW 1st PFv
Interval
Load
LMFv Tip
2nd BW PD Push
Time Prior to Plate Departure (s) Fig. 2. Multiple events and intervals within the take-off phase of the experimental tasks were defined using the vertical reaction force. The load interval was defined as the interval from initial rise of the vertical reaction force (initial position (IP)) to the time of first peak vertical reaction force (1stPFv). An absence of the vertical reaction force prior to the IP indicated that the performer was not in contact with the ground. The Tip interval was identified as the time from the peak to the local minimum vertical reaction force (LMFv). The Push interval started at the LMFv to plate departure (PD). The time of 1st BW and 2nd BW corresponded to the time when the vertical reaction force equaled to the body weight. These two events occurred prior to the 1st PFv and PD, respectively.
Normalized NJM Impulse (Nms/kg)
Eight (3 females and 5 males) skilled performers (national level divers) between the ages of 20–25 years participated in this study. The mean (SD) height was 1.70 (0.06) m and the mean (SD) mass was 61.48 (5.88) kg. All subjects provided informed consent in accordance with the Institutional Review Board.
0.8 0.6
Hip Knee Ankle
0.4 0.2 0 RT Load
RS
RT
RS Tip
RT
RS
Push
Fig. 3. Mean (SD) of ankle, knee, and hip normalized NJM impulse during the load, tip and push intervals of the reverse timer (RT) and reverse somersault (RS). Significant between task differences in normalized NJM impulse were observed at the knee () and hip (’) during the push interval ðPp0:05Þ.
ARTICLE IN PRESS W. Mathiyakom et al. / Journal of Biomechanics 39 (2006) 990–1000
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Mechanical Demand Imposed on the Lower Extremity Joints An Exemplar Subject Reverse Timer
Reverse Somersault
Thigh PM Thigh DM Hip NJM
Thigh PM Thigh DM Hip NJM
600
600
300
300
0
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0
0.1
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0
0.1
0
0.1
0
0.1
0 -0.1 -500 0
0.1
-300
Net Joint Moment (Nm)
-300 Shank PM Shank DM Knee NJM
Shank PM Shank DM Knee NJM
600
600
300
300
0
0 -0.5
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-0.1
0
0.1
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-300 600
Foot PM Foot DM Ankle NJM
600
Foot PM Foot DM Ankle NJM
300
300
0
0 -0.5
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0
0.1
-0.5
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-300
-300
Reaction Force (N)
-0.1
Horizontal Force
2500
Horizontal Force
2500
Vertical Force
2000
Vertical Force
2000
1500
1500
1000
1000
500
500
0 -0.5
-0.4
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-0.2
-0.1 -500 0
Time Prior to Plate Departure (s)
0.1
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-0.3
-0.2
Time Prior to Plate Departure (s)
Fig. 4. Reaction force and NJM imposed on the lower limb during the take-off phase of a reverse somersault (left) and reverse timer (right) of an exemplar subject. Ankle plantar flexor, knee and hip extensor NJMs were presented in positive values. All subjects demonstrated similar patterns of the NJMs. The free body diagrams depicted orientation of the segment, reaction force or net joint force, and adjacent NJMs. The PM and DM indicated the proximal and distal moments created by the reaction force or net joint forces about the segment center of mass.
side of the body closer to the camera were manually digitized (Peak Performance, Inc., Englewood, CO, USA). Digitized x and y coordinates of body landmarks were individually filtered with a fourth order Butterworth filter (zero phase lag) with cut-off frequencies (5–20 Hz) based on a method described by Jackson (1979). Body segment parameters of an athletic population (de Leva, 1996; Zatsiorsky and Seluyanov, 1983, 1987) were used to calculate the total body and segment center of mass. Three functional intervals within the take-off phase of the experimental tasks were defined to describe the RF-time characteristics (Fig. 2). The magnitude and orientation of the RF and the angular orientation of the body segments around the time of each event (7 10 ms) were calculated. Positive values of the RF corresponded
to upward vertical and forward horizontal RFs. The orientation of the resultant RF was defined as an angle of the RF relative to the forward horizontal passing through the center of pressure. Likewise, the angular orientation of each body segment was defined as an angle of the segment relative to the forward horizontal passing through the distal end of the segment. Synchronized RF and kinematic data were used to calculate net joint force (NJF) and NJM at the ankle, knee and hip using Newtonian equations and inverse dynamics approach (Elftman, 1939). Ankle plantar flexor, knee and hip extensor NJMs were presented in positive values. The ankle, knee, and hip NJMP were calculated as a product of the NJM and their corresponding joint angular velocity. The magnitude of the NJM impulse and the work done by the NJM was determined by
55.99* (8.12)
118.26 (10.67)
67.95* (7.12)
156.95 (4.99)
Thigh
Shank
Foot
159.58 (5.17)
70.80* (7.64)
121.76 (9.47)
162.56* (6.52)
59.97* (5.90)
130.75 (9.63)
51.90* (8.75)
165.29* (5.83)
64.17* (6.70)
133.05 (8.21)
47.06* (6.75)
86.44 (4.88)
1.05 (0.03)
1.04 (0.03)
0.07 (0.09)
RS
164.40* (6.41)
51.47* (6.21)
141.61* (8.90)
42.98* (9.67)
84.15 (2.25)
2.87 (0.49)
2.85 (0.49)
0.29 (0.13)
RT
168.27* (4.83)
55.84* (5.43)
145.54* (6.73)
38.48* (8.18)
85.27 (3.44)
3.18 (0.41)
3.17 (0.39)
0.27 (0.23)
RS
1st peak vertical reaction force
161.82* (7.99)
50.03* (6.37)
138.44* (8.11)
48.97 (10.21)
81.04 (3.79)
2.37 (0.39)
2.37 (0.41)
0.03 (0.10)
RT
165.14* (5.51)
54.53* (4.73)
141.70* (6.31)
48.84 (7.34)
81.04 (1.96)
2.37 (0.24)
2.37 (0.24)
0.03 (0.06)
RS
Local minimum vertical reaction force
159.68* (6.72)
51.34* (5.04)
128.38* (7.36)
57.46 (7.98)
83.94* (2.15)
2.69* (0.20)
2.68* (0.20)
0.28* (0.10)
RT
162.79* (4.80)
54.64* (3.71)
134.89* (6.43)
57.97 (6.66)
81.04* (4.44)
2.37* (0.12)
2.37* (0.11)
0.03* (0.09)
RS
2nd peak vertical reaction force
Significant differences in reaction force and orientation of lower extremity segments (*, Pp0.05) were observed between tasks.
61.15* (8.78)
Trunk
86.27 (5.43)
1.04 (0.12)
Resultant
Orientation (1) Resultant reaction force
1.03 (0.12)
0.06 (0.09)
RT
Vertical
Reaction force (BW) Horizontal
RT
Task
1st body weight
140.27 (7.08)
67.45* (4.86)
98.21* (3.85)
66.98* (7.34)
82.84* (4.33)
1.04* (0.04)
1.03 (0.04)
0.12* (0.07)
RT
139.63 (6.63)
57.81* (4.25)
109.01* (3.72)
79.94* (7.45)
66.06* (4.81)
1.09* (0.04)
1.00 (0.04)
0.42* (0.09)
RS
2nd body weight
132.44* (6.27)
73.98* (4.16)
89.87* (3.76)
63.39* (6.92)
RT
124.28* (7.02)
60.55* (4.03)
101.22* (3.96)
88.88* (7.71)
RS
Plate departure
994
RS
Initial contact
Events
Table 1 Mean (SD) of the magnitude of the reaction force and the orientation (degrees) of the reaction force and body segments around the time (710 ms) of each event of the reverse timer (RT) and reverse somersault (RS)
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W. Mathiyakom et al. / Journal of Biomechanics 39 (2006) 990–1000
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interval of the reverse somersault as compared to the reverse timer. These between-task differences in NJMs (Fig. 4) were associated with between-task differences in the orientation of lower extremity segments relative to either the RF or NJFs (Tables 1 and 2). During the load and tip intervals, the relative angles between the NJFs and the shank and thigh segments were not significantly different between tasks (Table 2) despite between-tasks differences in shank and thigh segment angles (Table 1). As a result, no significant between-task differences in knee and hip extensor NJMs were observed during these two intervals (Fig. 3). Ankle plantar NJMs were observed during the takeoff phase of both tasks. Although between-task differences in relative angle between the foot segment and RF were observed during the push interval, these differences were not large enough to induce significant between-task differences in ankle plantar flexor NJM during the push interval.
integrating the NJM and the NJMP during each time interval and then normalized to the subjects’ body mass. Activation (EMG) of lower extremity muscles (glutues maximus, semitendinosus, rectus femoris, vastus lateralis, tibialis anterior, gastrocnemius, and soleus) acquired using surface electromyography were filtered using a fourth order recursive Butterworth filter (zero phase lag, 10–350 Hz bandwidth). The magnitude of muscle activation was quantified using root-meansquared (RMS) values (20 ms binned, De Luca, 1997). The RMS values were normalized to maximum RMS values obtained during isometric manual muscle tests (Kendall et al., 1993) and averaged for each interval. 2.4. Statistical analysis Between-task differences in kinematic, kinetic, and muscle activation variables were compared using a within-subject design. Statistical analyses were performed using software written in S-PLUS (Insightful Corporation) and described in special functions written for the software (Wilcox, 2003). Robust statistical methods were used to accommodate the small sample size and the inability to assume normality (e.g. asymmetrical distribution, heavy tails) associated with standard method of paired t-test. Within-subject comparisons using bootstrap-t method were used to test the null hypothesis of equal trimmed means between tasks. The null hypothesis was rejected at Pp0:05.
Normalized Work (J/kg)
8
3. Results
6
Hip Knee
4
Ankle
2 0 -2 -4
3.1. Lower extremity NJMs
RT
RS
RT
Load
During the push interval, the observed between-task differences in lower extremity NJMs were attributed to between-task differences in trunk-leg coordination (Figs. 3 and 4). Significantly less knee extensor and greater hip extensor NJMs were observed during push
RS
RT
Tip
RS
Push
Fig. 5. Mean (SD) of the normalized negative or positive work done by the ankle, knee, and hip extensor NJMs during the take-off phase of the reverse timer (RT) and reverse somersault (RS). Between-task differences in work done at the hip (’) and knee () were noted ðPo0:05Þ.
Table 2 Mean (SD) of the relative angles (degrees) between the orientation of the lower extremity segment (ySegment) and the reaction force (yRF) or net joint force (yNJF) around the time (710 ms) of each event of the reverse timer (RT) and reverse somersault (RS) Event
1st body weight
1st peak vertical reaction force
Local minimum vertical 2nd peak vertical reaction force reaction force
2nd body weight
Task
RT
RS
RT
RS
RT
RS
RT
RS
RT
RS
yThighyNJF
44.47 (10.26) 26.31 (9.05) 76.28 (8.78)
46.61 (10.42) 22.27 (10.79) 78.85 (7.20)
57.46 (9.40) 32.68 (6.65) 80.26 (7.14)
60.28 (7.32) 29.43 (7.46) 83.00 (6.17)
56.50 (9.26) 31.90 (9.94) 79.88 (9.81)
58.15 (6.10) 29.02 (6.48) 81.60 (5.81)
44.44* (8.61) 32.61* (4.47) 75.74* (4.96)
56.09* (8.77) 24.15* (5.11) 83.99* (5.16)
15.37* (7.68) 15.39* (3.12) 57.44* (10.66)
42.94* (6.71) 8.25* (7.03) 73.57* (8.94)
yShankyNJF yFootyRF
Significant differences in the relative angle were observed between tasks (*, Pp0.05), contributed to between-task differences in net joint moments.
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3.2. Lower extremity NJMPs and work done
and hip NJMs. For example, synergistic activation of the medial hamstrings, gluteus maximus, and vastus lateralis corresponded with a relatively large hip extensor NJM, and a relatively small knee extensor NJM observed during the push interval of the reverse somersault (Fig. 7). Likewise, synergistic activation of the rectus femoris, gluteus maximus, and vastus lateralis resulted in a more equal distribution between the knee and hip NJMs during push interval of the reverse timer as compared to the reverse somersault. Ankle plantar flexors were activated throughout the take-off phase and contributed to the ankle plantar flexor NJMs. As with the NJMs and NJMP, no significant between task differences in ankle plantar flexor activation level were observed. Co-activation of ankle dorsiflexor muscles were observed during the load and tip intervals suggesting co-activation may serve as a mechanism for stabilizing the ankle joint.
During the push interval, between-task differences in NJMP and work done by the knee and hip extensor NJMs were observed (Fig. 5). Significantly greater work done by hip extensor NJM and less work done by knee extensor NJM were observed during the push interval of the reverse somersault as compared to the reverse timer (Fig. 6). During the load and tip interval, work done by the hip extensor NJM was also significantly greater during the reverse somersault than the reverse timer. Between-task differences in work done by the knee and hip NJMs were attributed to between-task differences in both the NJMs and joint angular velocities (Table 3). No significant differences in ankle NJMPs and work done were observed between tasks. 3.3. Lower extremity muscle activation Examination of muscle activation patterns indicated lower extremity muscle activation was scaled to accommodate for between-task differences in NJMs (Fig. 7). Selective activation of the bi-articular muscles crossing the knee and hip corresponded with the adjacent knee
4. Discussion Goal-directed movements reflect the ongoing interaction between the nervous system and the musculoske-
Between-Task Differences in Net Joint Moment, Joint Angular Velocity, and Net Joint Moment Power An Exemplar Subject NJM (Nm) Hip
JAV (rad/s)
NJMP (W)
800
30
4000
600
20
3000 2000
400
10 1000
200 0 0 -0.5
-0.4
-0.3
-0.2
-0.1
Knee
-200
-0.5 0
-0.4
-0.3
-0.2
-0.1
0.1
0
0
0.1 -0.5
-10
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600
30
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400
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0
0
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0
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3000 2000 1000
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Ankle
0
0.1
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0
0.1
0 -0.5
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-200
-10
-400
-20
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600
30
4000
400
20
3000
200
10
0
0
-1000
2000 1000 -0.5
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0
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-200 -400
Load
Tip
Push
Time Prior to Plate Departure (s)
0 -10
0
0.1 -0.5
-0.4
-0.3
-0.2
-0.1 -1000
-20
Load
Tip
Push
Time Prior to Plate Departure (s)
-2000
Load
Tip
Push
Time Prior to Plate Departure (s)
Fig. 6. Lower extremity NJM, joint angular velocity (JAV), and NJMP during the take-off phase of the reverse somersault (thick line) and the reverse timer (thin line) of an exemplar subject. Between-task differences in the knee and hip NJMs, JAVs, NJMPs were observed primarily during the push interval. All subjects demonstrated similar patterns of all three variables.
ARTICLE IN PRESS
Positive and negative values indicated joint extension and flexion velocity, respectively. Significant between-task differences in joint angular velocity were observed (*, Po0:05).
750.01 (90.33) 687.98 (116.9) 660.53* (90.01) 795.77* (106.3) 76.86* (32.14) 119.54* (76.72) 46.25* (44.28) 28.13* (37.96) 48.08 (47.48) 33.14 (38.87) 201.52 (46.03) 191.52 (55.91) 220.36 (92.11) Ankle
219.06 (115.9)
332.80* (109.1) 753.42* (123.1) 462.91* (79.53) 818.73* (109.8) 139.94* (48.05) 236.27* (89.65) 81.91 (59.01) 86.22 (61.41) 95.65 (54.66) 88.11 (54.02) 306.59 (35.77) 306.95 (38.27) 336.63 (47.21) Knee
336.35 (34.93)
625.16* (83.44) 559.97* (118.9) 692.42* (68.23) 595.70* (91.25) 284.80 (75.93) 278.17 (57.01) 203.08 (63.05) 182.43 (52.00) 48.01 (69.43) 56.62 (78.35) 347.41 (30.94) 317.09 (30.94) 354.91 (75.32) Hip
381.16 (58.45)
RS RT RS RT RS RT RS RT RS RT RS RT RT Task
RS
1st peak vertical reaction Local minimum vertical 2nd peak vertical force reaction force reaction force 1st body weight Initial contact Event
Table 3 Mean (SD) of the joint angular velocity (deg/s) around the time of each event (710 ms) of the reverse timer (RT) and reverse somersault (RS)
2nd body weight
Plate departure
W. Mathiyakom et al. / Journal of Biomechanics 39 (2006) 990–1000
997
letal system. During the impulse generation phase of whole body movements, the nervous system organizes the human body into a number of operational subsystems that are coordinated by using some type of hierarchical control (Arabyan and Tsai, 1998; Flashner et al., 1988; Requejo et al., 2002). In this study, lower extremity joint kinetics and muscle activation patterns were compared between two related tasks with similar linear impulse specifications yet different angular impulse requirements. Between task modifications in control of the CoM trajectory relative to the RF redistributed the mechanical demand (NJM, NJMP, work done by NJM) imposed on the muscles controlling knee and hip during the push interval of the take-off phase. Impulse during the push interval of the reverse somersault was generated using a set of lower extremity NJMs dominated by a relatively large hip extensor NJM (hip biased strategy). In contrast, impulse generated during the push interval of the reverse timer was generated using a set of lower extremity NJMs with a more equal distribution between the knee and hip NJMs (knee–hip strategy). Both the hip biased and knee–hip impulse generation strategies were implemented by selective activation of the bi-articular muscles crossing the knee and hip. These results indicate that the distribution of the mechanical demand imposed on the lower extremity is affected by between-task differences in trunk–leg coordination. Synergistic activation of biarticular muscles crossing the knee and hip provides the nervous system with a mechanism for accommodating for between-task differences in CoM trajectory relative to the RF. Lower extremity muscles work synergistically to accomplish task objectives at the local lower extremity level as well as at the total body level. Activation patterns of both uni- and bi-articular muscles observed during the take-off phase of our experimental tasks are inline with the rules of muscle coordination proposed by Prilutsky (2000) and van Ingen Schenau (1990) observed during tasks without angular impulse generation. For example, activation of the uni-articular gluteus maximus and vastus lateralis muscles contribute to the NJMs and work done to the joints they crossed (van Ingen Schenau et al., 1987, 1995). Whereas, the bi-articular hamstrings and rectus femoris muscles are selectively activated to coordinate the adjacent knee–hip NJMs and control the direction of the reaction force (van Ingen Schenau et al., 1987; van Ingen Schenau, 1990). Activation of the bi-articular muscles also contributes to the control of CoM trajectory relative to the RF by modulating trunk and hip angular motion. For example, activation of the rectus femoris observed during rapid hip extension during the push interval of the reverse timer limited backward trunk rotation about the hip thereby satisfying the task requirements at the total body level. Likewise, activation of the hamstrings during
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Muscle Activation Patterns During the Take-off Phase of the Reverse Somersault and Reverse Timer An Exemplar Subject Reverse Somersault
Normalized Muscle Activation Pattern (%Maximum Voluntary Contraction)
150 GMax
Reverse Timer 150
*
100
100
50
50
0
0
150 ST
150
100
*
*
50
100 50
0
150
*
*
100 50
*
0
VL
150 100
50
50 0
0
TA
150
100
100
50
50 0
0 150 GAS
150
100
100
50
50
0
0
SOL
150
100
100
50
50
0
0
60
60
40
*
100
100
150
*
50
0
150
*
0
150 RFem
150
*
Horizontal Impulse Vertical Impulse
40
20
20
0
0
-20
-20
Load
Tip
Push
Load
Tip
Push
Fig. 7. Mean (SD) of normalized muscle activation (RMS, 20-ms binned) of the gluteus Maximus (Gmax), semitendinosus (ST), rectus femoris (RFem), vastus lateralis (VL), tibialis anterior (TA), gastrocnemius (GAS), and soleus (SOL) of an exemplar subject. Similar activation patterns were observed within-tasks, between-subjects. Within-subject comparison (mean of 3 trials) of RMS during each interval demonstrates between-task differences in activation of the rectus femoris, hamstrings, and gluteus maximus during the tip and push intervals (*, Po0:05). The between-task differences in muscle activation corresponded with between-task differences in NJMs.
the push phase of the reverse somersault assisted backward trunk rotation about the hip to promote a more backward position of the CoM relative to the RF. Between-task differences in activation of the bi-articular muscles associated with task-specific control of the CoM relative to the RF suggest scaling activation of bi-articular muscles serves as a relatively simple
mechanism for regulating angular impulse during complex whole body movements. Task-specific control of CoM relative to the RF redistributes lower extremity NJMs by altering the relative angles between the lower extremity segments and the RF and/or NJF, as well as the magnitude of the adjacent NJM. During the contact phase, the observed
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segment motion reflects the net effect of the moments imposed by the NJFs about the segment CoM and the NJMs at the adjacent joints. As the relative angle between the segment and the RF increases, the magnitude of the moments created by the RF imposed on the segment increases, thereby requiring greater NJMs. If the NJM controlling the motion of the distal joint is relatively small, then a relatively large NJM acting at the proximal end of the segment is needed to counteract the moments imposed by the NJFs. In contrast, if the NJM acting to control the motion of the distal joint is relatively large, then a relatively small NJM acting at the proximal joint is required to control the observed motion. For example, during the push interval of the reverse somersault, the relative angles between the thigh and the NJF were significantly larger and the knee extensor NJMs than during the reverse timer. As a result, significantly greater hip extensor NJMs were required to control the thigh motion during push interval of the reverse somersault as compared to the revere timer. The redistribution of lower extremity NJMs associated with task specific differences in segment orientation relative to the reaction force and adjacent joint NJMs has been observed in other multijoint, goal directed, weight bearing tasks without the need to generate angular impulse such as sit-to-stand (Mathiyakom et al., 2005), walking (Elftman, 1939), running (Bobbert et al., 1992), jumping (Ridderikhoff et al., 1999), and landing (McNitt-Gray et al., 2001). Modification in knee–hip coordination in order to achieve task-specific CoM trajectory relative to the RF alters distribution of work done by lower extremity NJMs during the push interval by altering the joint angular velocity profiles. During the push interval of the reverse somersault, the backward position of the CoM relative to the RF was facilitated by backward rotation of the trunk about the hip joint. Likewise, restricted backward trunk rotation observed during the push interval of the reverse timer aligned the CoM relative to the RF. These between-task differences in CoM control, as manifested in task-specific knee–hip coordination and task-specific NJMs, significantly altered the distribution of work done across the lower extremity joints. These results demonstrate how coordination between subsystems change between tasks performed under various impulse generation conditions and support the need for task-specific training programs to guide rehabilitation and improve overall performance of goal directed multijoint tasks.
Acknowledgements The authors would like to thank US divers and their coaches for their participation in this project, Doris Miller, for providing significant work in biomechanics
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of diving, Janet Gabrile, Ron O’Brien, Barry Munkasy, James Eagle, Kathleen E. Costa, and Laurie Held for their assistance with data collection, and Melissa McDonough and USC undergraduate students their assistance in data reduction. This project was supported in part by US diving, USOC, Intel, and NIA Training Grant 5 T32 AG00093.
References Arabyan, A., Tsai, D., 1998. A distributed control model for the airrighting reflex of a cat. Biological Cybernetics 79, 393–401. Bernstein, N., 1967. The Co-ordination and Regulations of Movements. Pergamon Press, Oxford. Bobbert, M.F., van Ingen Schenau, G.J., 1988. Coordination in vertical jumping. Journal of Biomechanics 21, 249–262. Bobbert, M.F., Yeadon, M.R., Nigg, B.M., 1992. Mechanical analysis of the landing phase in heel-toe running. Journal of Biomechanics 25, 223–234. de Leva, P., 1996. Adjustments to Zatsiorsky–Seluyanov’s segment inertia parameters. Journal of Biomechanics 29, 1223–1230. De Luca, C., 1997. The use of surface electromyography in biomechanics. Journal of Applied Biomechanics 13, 135–163. Elftman, H., 1939. Forces and energy changes in the leg during walking. American Journal of Physiology 125, 339–356. Flashner, H., Beuter, A., Arabyan, A., 1988. Fitting mathematical functions to joint kinematics during stepping: implications for motor control. Biological Cybernetics 58, 91–99. Horak, F., Nashner, L., 1986. Central programming of postural movements: adaptation to altered support-surface configurations. Journal of Neurophysiology 55, 1369–1391. Jackson, K.M., 1979. Fitting of mathematical functions to biomechanical data. IEEE Transaction on Bio-medical Engineering 26, 122–124. Kendall, F., McCreary, E., Provance, P., 1993. Muscle Testing and Function. Williams & Wilkins, Baltimore. Mathiyakom, W., McNitt-Gray, J.L., Requejo, P., Costa, K., 2005. Modifying center of mass trajectory during sit-to-stand tasks redistributes the mechanical demand across the lower extremity joints. Clinical Biomechanics (Bristol, Avon) 20, 105–111. Mathiyakom, W., McNitt-Gray, J. Wilcox, R. Regulation of backward angular impulse during forward translating tasks. Journal of Applied Biomechanics, accepted for publication. McFadyen, B.J., Winter, D.A., 1988. An integrated biomechanical analysis of normal stair ascent and descent. Journal of Biomechanics 21, 733–744. McNitt-Gray, J.L., 1993. Kinetics of the lower extremities during drop landings from three heights. Journal of Biomechanics 26, 1037–1046. McNitt-Gray, J.L., Hester, D.M., Mathiyakom, W., Munkasy, B.A., 2001. Mechanical demand and multijoint control during landing depend on orientation of the body segments relative to the reaction force. Journal of Biomechanics 34, 1471–1482. Miller, D., Jones, I., Pizzimenti, M., Hennig, E., Nelson, R., 1990. Kinetic and kinematic characteristics of 10-m platform performances of elite dives: II-Reverse takeoffs. International Journal of Sport Biomechanics 6, 283–308. Prilutsky, B.I., 2000. Muscle coordination: the discussion continues. Motor Control 4, 97–116. Requejo, P., McNitt-Gray, J., Flashner, H., 2002. An approach for developing an experimentally based model for simulating flightphase dynamics. Biological Cybernetics 87, 289–300.
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Ridderikhoff, A., Batelaan, J.H., Bobbert, M.F., 1999. Jumping for distance: control of the external force in squat jumps. Medicine and Science in Sports and Exercise 31, 1196–1204. Schenkman, M., Riley, P.O., Pieper, C., 1996. Sit to stand from progressively lower seat heights—alterations in angular velocity. Clinical Biomechanics (Bristol, Avon) 11, 153–158. van Ingen Schenau, G., 1990. On the action of bi-artibular muscles. A review. Netherlands Journal of Zoology 40, 521–540. van Ingen Schenau, G.J., Bobbert, M.F., Rozendal, R.H., 1987. The unique action of bi-articular muscles in complex movements. Journal of Anatomy 155, 1–5. van Ingen Schenau, G.J., Dorssers, W.M., Welter, T.G., Beelen, A., de Groot, G., Jacobs, R., 1995. The control of mono-articular muscles
in multijoint leg extensions in man. Journal of Physiology (London) 484, 247–254. Wilcox, R.R., 2003. Applying Contemporary Statistical Techniques. Academic Press, San Diego, CA. Zatsiorsky, V.M., Seluyanov, V., 1983. The mass and inertia characteristics of the main segments of the human body. In: Matsui, B., Kobayashi, K. (Eds.), Biomechanics VIII. Human Kinetics, Champaign, pp. 1152–1159. Zatsiorsky, V.M., Seluyanov, V., 1987. Estimation of the mass and inertia characteristics of human body by means of the best predictive regression equations. In: Winter, D., Norman, R., Wells, R., Hayes, K., Patla, A. (Eds.), Biomechanics IX-B. Human Kinetics, Champaign, pp. 233–239.
Journal of Biomechanics 39 (2006) 990–1000 www.elsevier.com/locate/jbiomech www.JBiomech.com
Lower extremity control and dynamics during backward angular impulse generation in forward translating tasks W. Mathiyakoma,e, J.L. McNitt-Graya,b,c,, R. Wilcoxd a
Department of Kinesiology, 3560 Watt Way, PED 107, University of Southern California, Los Angeles, CA 90089-0652, USA b Biomedical Engineering, University of Southern California, Los Angeles, CA 90089-0652, USA c Biological Sciences, University of Southern California, Los Angeles, CA 90089-0652, USA d Psychology, University of Southern California, Los Angeles, CA 90089-0652, USA e Andrus Gerontology Center, University of Southern California, Los Angeles, CA 90089-0652, USA Accepted 26 February 2005
Abstract Observation of complex whole body movements suggests that the nervous system coordinates multiple operational subsystems using some type of hierarchical control. When comparing two forward translating tasks performed with and without backward angular impulse, we have learned that both trunk-leg coordination and reaction force-time characteristics are significantly different between tasks. This led us to hypothesize that differences in trunk-leg coordination and reaction force generation would induce between-task differences in the control of the lower extremity joints during impulse generation phase of the tasks. Eight highly skilled performers executed a series of forward jumps with and without backward rotation (reverse somersault and reverse timer, respectively). Sagittal plane kinematics, reaction forces, and electromyograms of lower extremity muscles were acquired during the take-off phase of both tasks. Lower extremity joint kinetics were calculated using inverse dynamics. The results demonstrated between-task differences in the relative angles between the lower extremity segments and the net joint forces/reaction force and the joint angular velocity profiles. Significantly less knee extensor net joint moments and net joint moment work and greater hip extensor net joint moments and net joint moment work were observed during the push interval of the reverse somersault as compared to the reverse timer. Between-task differences in lower extremity joint kinetics were regulated by selectively activating the bi-articular muscles crossing the knee and hip. These results indicate that between-task differences in the control of the center of mass relative to the reaction force alters control and dynamics of the multijoint lower extremity subsystem. r 2005 Elsevier Ltd. All rights reserved. Keywords: Total body center of mass; Reaction force; Angular impulse; Joint kinetics; Muscle activation pattern
1. Introduction Task-specific modification of total body momentum requires that the performer generates net linear and angular impulse during contact with the environment. Observation of complex whole body movements, such as Corresponding author. Biomechanics Research Lab, Department of Kinesiology, 3560 Watt Way, PED 107, University of Southern California, Los Angeles, CA 90089-0652, USA. Tel.: +1 213 740 7902; fax: +1 213 740 7909. E-mail address: [email protected] (J.L. McNitt-Gray).
0021-9290/$ - see front matter r 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.jbiomech.2005.02.022
jumping, suggests the nervous system organizes the human body into a number of operational subsystems that are coordinated by using some type of hierarchical control (Arabyan and Tsai, 1998; Flashner et al., 1988; Requejo et al., 2002). For example, during the impulse generation phase, the motion of multiple body segments is coordinated so that the position of the center of mass (CoM) relative to the reaction force (RF) satisfies both the linear and angular impulse requirements of the task. During the impulse generation phase of a standing forward jump, the segments are configured such that the CoM is aligned with the forward-directed
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RF (Ridderikhoff et al., 1999). In contrast, during the take-off phase of a forward jump with backward rotation (reverse somersault), the segments are configured such that the CoM is positioned posterior to the line of action of forward directed RF. As a result, both upward and forward linear impulse and backward angular impulse requirements of the task are satisfied (Mathiyakom et al., accepted). By determining how coordination between subsystems change between tasks performed under various conditions (Bernstein, 1967), we can advance our understanding of the control structure. Regulation of CoM position relative to the RF involves coordination between the trunk and leg subsystems during weight bearing tasks. The magnitude of the RF is regulated by the rate of lower extremity joint extension (Bobbert and van Ingen Schenau, 1988; Ridderikhoff et al., 1999), whereas the position of the CoM relative to the feet is most sensitive to trunk motion (Horak and Nashner, 1986; Shenckman et al., 1996; McNitt-Gray et al., 2001). Although modifications in trunk-leg coordination provide a mechanism for regulating the position of the CoM relative to the RF during impulse generation, between-task differences in
991
lower extremity segment orientation relative to the RF is expected to influence how the lower extremities contribute to the linear and angular impulse required to perform the task (McNitt-Gray et al., 2001). Comparison of two related, well-practiced tasks with common linear impulse and different angular impulse requirements performed by the same highly skilled performers provides us with a unique opportunity to determine how control and coordination of local subsystems are modified to achieve specific task objectives at the total body level (Miller et al., 1990). Previous study of reverse somersaults and reverse timers (common linear impulse requirement (forward, upward) with and without angular impulse) indicates that trunkleg subsystem coordination, lower extremity joint coordination, and reaction force-time characteristics were significantly different between these two tasks (Mathiyakom et al., accepted). These results led us to hypothesize that lower extremity control, as indicated by (a) net joint moment (NJM), net joint moment power (NJMP), work done by the NJM, and (b) muscle activation patterns would be different between these two tasks (McNitt-Gray et al., 2001; McNitt-Gray, 1993; McFadyen and Winter, 1988; Elftman, 1939). The
Fig. 1. Body configuration, estimated total body center of mass position (), and forward horizontal (-) and upward (m) vertical reaction force during the take-off phase of the reverse somersault (top) and reverse timer (bottom) of an exemplar subject. During the take-off phase of both tasks, the performers need to generate forward and upward linear impulse. In addition, the performers need to generate backward angular impulse during the take-off phase of the reverse somersault.
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magnitude of the lower extremity NJMs were expected to increase as the relative angle between the lower extremity segments and the RF increased and the magnitude of the adjacent NJMs decreased. The work done by NJM was also expected to increase as the NJMs and the joint angular velocities increased. Activation of the lower extremity muscles were expected to scale to accommodate for between-task differences in mechanical demand imposed on the lower extremity joints (NJM, NJMP, and work done by NJM). Differences in the lower extremity joint kinetics and its associated muscle activation patterns provides insight as to how the nervous system controls the lower extremity subsystem in order to achieve task objectives at the total body level (e.g. CoM trajectory relative to the RF).
Pasadena, CA, USA) were simultaneously collected during the performance of each experimental task. These three sets of data were synchronized at the time of plate departure. Thirteen body landmarks (vertex, C7, shoulder, elbow, wrist, finger, iliac crest, greater trochanter, knee, lateral malleolus, heel, 5th metatarsal, and toe) of the
4 Vertical Reaction Force (BW)
992
3 2 1
2. Methods
0 -0.6
-0.5
-0.4
-0.3
-0.2
-0.1
0
0.1
2.1. Subjects
2.2. Tasks Each participant performed a series of reverse timer and reserve somersault take-offs from a force plate into a landing mat (Fig. 1). The participant initiated each task by facing away from the take-off surface as performed from the 10-m platform during competition. During the reverse timer take-offs, the participant jumped from the platform as if performing a reverse somersault without the intent of rotating about the somersault axis during flight and landed feet first on the landing mat. During the reverse somersault take-off, the participant jumped from the platform (upward and forwards) and performed one complete backward somersault during the flight phase and landed feet first on the landing mat. Each task was blocked and randomized for each participant. Three successful trials of each task were analyzed. 2.3. Data collection Prior to data collection, participants warmed up and practiced the experimental tasks until they were familiar with the experimental set up. Sagittal plane kinematics (200 fps, C2S NAC Visual Systems, Burbank, CA USA), reaction forces (0.6 0.9 m2, 1200 Hz, Kistler, Amhurst, MA, USA), and activation patterns of the lower extremity muscles (1 1 cm2, 1200 Hz, Konigsberg,
Event
IP 1st BW 1st PFv
Interval
Load
LMFv Tip
2nd BW PD Push
Time Prior to Plate Departure (s) Fig. 2. Multiple events and intervals within the take-off phase of the experimental tasks were defined using the vertical reaction force. The load interval was defined as the interval from initial rise of the vertical reaction force (initial position (IP)) to the time of first peak vertical reaction force (1stPFv). An absence of the vertical reaction force prior to the IP indicated that the performer was not in contact with the ground. The Tip interval was identified as the time from the peak to the local minimum vertical reaction force (LMFv). The Push interval started at the LMFv to plate departure (PD). The time of 1st BW and 2nd BW corresponded to the time when the vertical reaction force equaled to the body weight. These two events occurred prior to the 1st PFv and PD, respectively.
Normalized NJM Impulse (Nms/kg)
Eight (3 females and 5 males) skilled performers (national level divers) between the ages of 20–25 years participated in this study. The mean (SD) height was 1.70 (0.06) m and the mean (SD) mass was 61.48 (5.88) kg. All subjects provided informed consent in accordance with the Institutional Review Board.
0.8 0.6
Hip Knee Ankle
0.4 0.2 0 RT Load
RS
RT
RS Tip
RT
RS
Push
Fig. 3. Mean (SD) of ankle, knee, and hip normalized NJM impulse during the load, tip and push intervals of the reverse timer (RT) and reverse somersault (RS). Significant between task differences in normalized NJM impulse were observed at the knee () and hip (’) during the push interval ðPp0:05Þ.
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Mechanical Demand Imposed on the Lower Extremity Joints An Exemplar Subject Reverse Timer
Reverse Somersault
Thigh PM Thigh DM Hip NJM
Thigh PM Thigh DM Hip NJM
600
600
300
300
0
0 -0.5
-0.4
-0.3
-0.2
-0.1
0
0.1
-0.5
-0.4
-0.3
-0.2
-0.1
0
0.1
0
0.1
0
0.1
0 -0.1 -500 0
0.1
-300
Net Joint Moment (Nm)
-300 Shank PM Shank DM Knee NJM
Shank PM Shank DM Knee NJM
600
600
300
300
0
0 -0.5
-0.4
-0.3
-0.2
-0.1
0
0.1
-0.5
-0.4
-0.3
-0.2
-0.1 -300
-300 600
Foot PM Foot DM Ankle NJM
600
Foot PM Foot DM Ankle NJM
300
300
0
0 -0.5
-0.4
-0.3
-0.2
-0.1
0
0.1
-0.5
-0.4
-0.3
-0.2
-300
-300
Reaction Force (N)
-0.1
Horizontal Force
2500
Horizontal Force
2500
Vertical Force
2000
Vertical Force
2000
1500
1500
1000
1000
500
500
0 -0.5
-0.4
-0.3
-0.2
-0.1 -500 0
Time Prior to Plate Departure (s)
0.1
-0.5
-0.4
-0.3
-0.2
Time Prior to Plate Departure (s)
Fig. 4. Reaction force and NJM imposed on the lower limb during the take-off phase of a reverse somersault (left) and reverse timer (right) of an exemplar subject. Ankle plantar flexor, knee and hip extensor NJMs were presented in positive values. All subjects demonstrated similar patterns of the NJMs. The free body diagrams depicted orientation of the segment, reaction force or net joint force, and adjacent NJMs. The PM and DM indicated the proximal and distal moments created by the reaction force or net joint forces about the segment center of mass.
side of the body closer to the camera were manually digitized (Peak Performance, Inc., Englewood, CO, USA). Digitized x and y coordinates of body landmarks were individually filtered with a fourth order Butterworth filter (zero phase lag) with cut-off frequencies (5–20 Hz) based on a method described by Jackson (1979). Body segment parameters of an athletic population (de Leva, 1996; Zatsiorsky and Seluyanov, 1983, 1987) were used to calculate the total body and segment center of mass. Three functional intervals within the take-off phase of the experimental tasks were defined to describe the RF-time characteristics (Fig. 2). The magnitude and orientation of the RF and the angular orientation of the body segments around the time of each event (7 10 ms) were calculated. Positive values of the RF corresponded
to upward vertical and forward horizontal RFs. The orientation of the resultant RF was defined as an angle of the RF relative to the forward horizontal passing through the center of pressure. Likewise, the angular orientation of each body segment was defined as an angle of the segment relative to the forward horizontal passing through the distal end of the segment. Synchronized RF and kinematic data were used to calculate net joint force (NJF) and NJM at the ankle, knee and hip using Newtonian equations and inverse dynamics approach (Elftman, 1939). Ankle plantar flexor, knee and hip extensor NJMs were presented in positive values. The ankle, knee, and hip NJMP were calculated as a product of the NJM and their corresponding joint angular velocity. The magnitude of the NJM impulse and the work done by the NJM was determined by
55.99* (8.12)
118.26 (10.67)
67.95* (7.12)
156.95 (4.99)
Thigh
Shank
Foot
159.58 (5.17)
70.80* (7.64)
121.76 (9.47)
162.56* (6.52)
59.97* (5.90)
130.75 (9.63)
51.90* (8.75)
165.29* (5.83)
64.17* (6.70)
133.05 (8.21)
47.06* (6.75)
86.44 (4.88)
1.05 (0.03)
1.04 (0.03)
0.07 (0.09)
RS
164.40* (6.41)
51.47* (6.21)
141.61* (8.90)
42.98* (9.67)
84.15 (2.25)
2.87 (0.49)
2.85 (0.49)
0.29 (0.13)
RT
168.27* (4.83)
55.84* (5.43)
145.54* (6.73)
38.48* (8.18)
85.27 (3.44)
3.18 (0.41)
3.17 (0.39)
0.27 (0.23)
RS
1st peak vertical reaction force
161.82* (7.99)
50.03* (6.37)
138.44* (8.11)
48.97 (10.21)
81.04 (3.79)
2.37 (0.39)
2.37 (0.41)
0.03 (0.10)
RT
165.14* (5.51)
54.53* (4.73)
141.70* (6.31)
48.84 (7.34)
81.04 (1.96)
2.37 (0.24)
2.37 (0.24)
0.03 (0.06)
RS
Local minimum vertical reaction force
159.68* (6.72)
51.34* (5.04)
128.38* (7.36)
57.46 (7.98)
83.94* (2.15)
2.69* (0.20)
2.68* (0.20)
0.28* (0.10)
RT
162.79* (4.80)
54.64* (3.71)
134.89* (6.43)
57.97 (6.66)
81.04* (4.44)
2.37* (0.12)
2.37* (0.11)
0.03* (0.09)
RS
2nd peak vertical reaction force
Significant differences in reaction force and orientation of lower extremity segments (*, Pp0.05) were observed between tasks.
61.15* (8.78)
Trunk
86.27 (5.43)
1.04 (0.12)
Resultant
Orientation (1) Resultant reaction force
1.03 (0.12)
0.06 (0.09)
RT
Vertical
Reaction force (BW) Horizontal
RT
Task
1st body weight
140.27 (7.08)
67.45* (4.86)
98.21* (3.85)
66.98* (7.34)
82.84* (4.33)
1.04* (0.04)
1.03 (0.04)
0.12* (0.07)
RT
139.63 (6.63)
57.81* (4.25)
109.01* (3.72)
79.94* (7.45)
66.06* (4.81)
1.09* (0.04)
1.00 (0.04)
0.42* (0.09)
RS
2nd body weight
132.44* (6.27)
73.98* (4.16)
89.87* (3.76)
63.39* (6.92)
RT
124.28* (7.02)
60.55* (4.03)
101.22* (3.96)
88.88* (7.71)
RS
Plate departure
994
RS
Initial contact
Events
Table 1 Mean (SD) of the magnitude of the reaction force and the orientation (degrees) of the reaction force and body segments around the time (710 ms) of each event of the reverse timer (RT) and reverse somersault (RS)
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interval of the reverse somersault as compared to the reverse timer. These between-task differences in NJMs (Fig. 4) were associated with between-task differences in the orientation of lower extremity segments relative to either the RF or NJFs (Tables 1 and 2). During the load and tip intervals, the relative angles between the NJFs and the shank and thigh segments were not significantly different between tasks (Table 2) despite between-tasks differences in shank and thigh segment angles (Table 1). As a result, no significant between-task differences in knee and hip extensor NJMs were observed during these two intervals (Fig. 3). Ankle plantar NJMs were observed during the takeoff phase of both tasks. Although between-task differences in relative angle between the foot segment and RF were observed during the push interval, these differences were not large enough to induce significant between-task differences in ankle plantar flexor NJM during the push interval.
integrating the NJM and the NJMP during each time interval and then normalized to the subjects’ body mass. Activation (EMG) of lower extremity muscles (glutues maximus, semitendinosus, rectus femoris, vastus lateralis, tibialis anterior, gastrocnemius, and soleus) acquired using surface electromyography were filtered using a fourth order recursive Butterworth filter (zero phase lag, 10–350 Hz bandwidth). The magnitude of muscle activation was quantified using root-meansquared (RMS) values (20 ms binned, De Luca, 1997). The RMS values were normalized to maximum RMS values obtained during isometric manual muscle tests (Kendall et al., 1993) and averaged for each interval. 2.4. Statistical analysis Between-task differences in kinematic, kinetic, and muscle activation variables were compared using a within-subject design. Statistical analyses were performed using software written in S-PLUS (Insightful Corporation) and described in special functions written for the software (Wilcox, 2003). Robust statistical methods were used to accommodate the small sample size and the inability to assume normality (e.g. asymmetrical distribution, heavy tails) associated with standard method of paired t-test. Within-subject comparisons using bootstrap-t method were used to test the null hypothesis of equal trimmed means between tasks. The null hypothesis was rejected at Pp0:05.
Normalized Work (J/kg)
8
3. Results
6
Hip Knee
4
Ankle
2 0 -2 -4
3.1. Lower extremity NJMs
RT
RS
RT
Load
During the push interval, the observed between-task differences in lower extremity NJMs were attributed to between-task differences in trunk-leg coordination (Figs. 3 and 4). Significantly less knee extensor and greater hip extensor NJMs were observed during push
RS
RT
Tip
RS
Push
Fig. 5. Mean (SD) of the normalized negative or positive work done by the ankle, knee, and hip extensor NJMs during the take-off phase of the reverse timer (RT) and reverse somersault (RS). Between-task differences in work done at the hip (’) and knee () were noted ðPo0:05Þ.
Table 2 Mean (SD) of the relative angles (degrees) between the orientation of the lower extremity segment (ySegment) and the reaction force (yRF) or net joint force (yNJF) around the time (710 ms) of each event of the reverse timer (RT) and reverse somersault (RS) Event
1st body weight
1st peak vertical reaction force
Local minimum vertical 2nd peak vertical reaction force reaction force
2nd body weight
Task
RT
RS
RT
RS
RT
RS
RT
RS
RT
RS
yThighyNJF
44.47 (10.26) 26.31 (9.05) 76.28 (8.78)
46.61 (10.42) 22.27 (10.79) 78.85 (7.20)
57.46 (9.40) 32.68 (6.65) 80.26 (7.14)
60.28 (7.32) 29.43 (7.46) 83.00 (6.17)
56.50 (9.26) 31.90 (9.94) 79.88 (9.81)
58.15 (6.10) 29.02 (6.48) 81.60 (5.81)
44.44* (8.61) 32.61* (4.47) 75.74* (4.96)
56.09* (8.77) 24.15* (5.11) 83.99* (5.16)
15.37* (7.68) 15.39* (3.12) 57.44* (10.66)
42.94* (6.71) 8.25* (7.03) 73.57* (8.94)
yShankyNJF yFootyRF
Significant differences in the relative angle were observed between tasks (*, Pp0.05), contributed to between-task differences in net joint moments.
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3.2. Lower extremity NJMPs and work done
and hip NJMs. For example, synergistic activation of the medial hamstrings, gluteus maximus, and vastus lateralis corresponded with a relatively large hip extensor NJM, and a relatively small knee extensor NJM observed during the push interval of the reverse somersault (Fig. 7). Likewise, synergistic activation of the rectus femoris, gluteus maximus, and vastus lateralis resulted in a more equal distribution between the knee and hip NJMs during push interval of the reverse timer as compared to the reverse somersault. Ankle plantar flexors were activated throughout the take-off phase and contributed to the ankle plantar flexor NJMs. As with the NJMs and NJMP, no significant between task differences in ankle plantar flexor activation level were observed. Co-activation of ankle dorsiflexor muscles were observed during the load and tip intervals suggesting co-activation may serve as a mechanism for stabilizing the ankle joint.
During the push interval, between-task differences in NJMP and work done by the knee and hip extensor NJMs were observed (Fig. 5). Significantly greater work done by hip extensor NJM and less work done by knee extensor NJM were observed during the push interval of the reverse somersault as compared to the reverse timer (Fig. 6). During the load and tip interval, work done by the hip extensor NJM was also significantly greater during the reverse somersault than the reverse timer. Between-task differences in work done by the knee and hip NJMs were attributed to between-task differences in both the NJMs and joint angular velocities (Table 3). No significant differences in ankle NJMPs and work done were observed between tasks. 3.3. Lower extremity muscle activation Examination of muscle activation patterns indicated lower extremity muscle activation was scaled to accommodate for between-task differences in NJMs (Fig. 7). Selective activation of the bi-articular muscles crossing the knee and hip corresponded with the adjacent knee
4. Discussion Goal-directed movements reflect the ongoing interaction between the nervous system and the musculoske-
Between-Task Differences in Net Joint Moment, Joint Angular Velocity, and Net Joint Moment Power An Exemplar Subject NJM (Nm) Hip
JAV (rad/s)
NJMP (W)
800
30
4000
600
20
3000 2000
400
10 1000
200 0 0 -0.5
-0.4
-0.3
-0.2
-0.1
Knee
-200
-0.5 0
-0.4
-0.3
-0.2
-0.1
0.1
0
0
0.1 -0.5
-10
-0.4
-0.3
-0.2
-0.1
-1000
-400
-20
-2000
600
30
4000
400
20
200
10
0
0
0
0.1
0
0.1
0
0.1
3000 2000 1000
-0.5
-0.4
-0.3
-0.2
-0.1
Ankle
0
0.1
-0.5
-0.4
-0.3
-0.2
-0.1
0
0.1
0 -0.5
-0.4
-0.3
-0.2
-0.1
-200
-10
-400
-20
-2000
600
30
4000
400
20
3000
200
10
0
0
-1000
2000 1000 -0.5
-0.4
-0.3
-0.2
-0.1
0
0.1
-0.5
-0.4
-0.3
-0.2
-0.1
-200 -400
Load
Tip
Push
Time Prior to Plate Departure (s)
0 -10
0
0.1 -0.5
-0.4
-0.3
-0.2
-0.1 -1000
-20
Load
Tip
Push
Time Prior to Plate Departure (s)
-2000
Load
Tip
Push
Time Prior to Plate Departure (s)
Fig. 6. Lower extremity NJM, joint angular velocity (JAV), and NJMP during the take-off phase of the reverse somersault (thick line) and the reverse timer (thin line) of an exemplar subject. Between-task differences in the knee and hip NJMs, JAVs, NJMPs were observed primarily during the push interval. All subjects demonstrated similar patterns of all three variables.
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Positive and negative values indicated joint extension and flexion velocity, respectively. Significant between-task differences in joint angular velocity were observed (*, Po0:05).
750.01 (90.33) 687.98 (116.9) 660.53* (90.01) 795.77* (106.3) 76.86* (32.14) 119.54* (76.72) 46.25* (44.28) 28.13* (37.96) 48.08 (47.48) 33.14 (38.87) 201.52 (46.03) 191.52 (55.91) 220.36 (92.11) Ankle
219.06 (115.9)
332.80* (109.1) 753.42* (123.1) 462.91* (79.53) 818.73* (109.8) 139.94* (48.05) 236.27* (89.65) 81.91 (59.01) 86.22 (61.41) 95.65 (54.66) 88.11 (54.02) 306.59 (35.77) 306.95 (38.27) 336.63 (47.21) Knee
336.35 (34.93)
625.16* (83.44) 559.97* (118.9) 692.42* (68.23) 595.70* (91.25) 284.80 (75.93) 278.17 (57.01) 203.08 (63.05) 182.43 (52.00) 48.01 (69.43) 56.62 (78.35) 347.41 (30.94) 317.09 (30.94) 354.91 (75.32) Hip
381.16 (58.45)
RS RT RS RT RS RT RS RT RS RT RS RT RT Task
RS
1st peak vertical reaction Local minimum vertical 2nd peak vertical force reaction force reaction force 1st body weight Initial contact Event
Table 3 Mean (SD) of the joint angular velocity (deg/s) around the time of each event (710 ms) of the reverse timer (RT) and reverse somersault (RS)
2nd body weight
Plate departure
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letal system. During the impulse generation phase of whole body movements, the nervous system organizes the human body into a number of operational subsystems that are coordinated by using some type of hierarchical control (Arabyan and Tsai, 1998; Flashner et al., 1988; Requejo et al., 2002). In this study, lower extremity joint kinetics and muscle activation patterns were compared between two related tasks with similar linear impulse specifications yet different angular impulse requirements. Between task modifications in control of the CoM trajectory relative to the RF redistributed the mechanical demand (NJM, NJMP, work done by NJM) imposed on the muscles controlling knee and hip during the push interval of the take-off phase. Impulse during the push interval of the reverse somersault was generated using a set of lower extremity NJMs dominated by a relatively large hip extensor NJM (hip biased strategy). In contrast, impulse generated during the push interval of the reverse timer was generated using a set of lower extremity NJMs with a more equal distribution between the knee and hip NJMs (knee–hip strategy). Both the hip biased and knee–hip impulse generation strategies were implemented by selective activation of the bi-articular muscles crossing the knee and hip. These results indicate that the distribution of the mechanical demand imposed on the lower extremity is affected by between-task differences in trunk–leg coordination. Synergistic activation of biarticular muscles crossing the knee and hip provides the nervous system with a mechanism for accommodating for between-task differences in CoM trajectory relative to the RF. Lower extremity muscles work synergistically to accomplish task objectives at the local lower extremity level as well as at the total body level. Activation patterns of both uni- and bi-articular muscles observed during the take-off phase of our experimental tasks are inline with the rules of muscle coordination proposed by Prilutsky (2000) and van Ingen Schenau (1990) observed during tasks without angular impulse generation. For example, activation of the uni-articular gluteus maximus and vastus lateralis muscles contribute to the NJMs and work done to the joints they crossed (van Ingen Schenau et al., 1987, 1995). Whereas, the bi-articular hamstrings and rectus femoris muscles are selectively activated to coordinate the adjacent knee–hip NJMs and control the direction of the reaction force (van Ingen Schenau et al., 1987; van Ingen Schenau, 1990). Activation of the bi-articular muscles also contributes to the control of CoM trajectory relative to the RF by modulating trunk and hip angular motion. For example, activation of the rectus femoris observed during rapid hip extension during the push interval of the reverse timer limited backward trunk rotation about the hip thereby satisfying the task requirements at the total body level. Likewise, activation of the hamstrings during
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Muscle Activation Patterns During the Take-off Phase of the Reverse Somersault and Reverse Timer An Exemplar Subject Reverse Somersault
Normalized Muscle Activation Pattern (%Maximum Voluntary Contraction)
150 GMax
Reverse Timer 150
*
100
100
50
50
0
0
150 ST
150
100
*
*
50
100 50
0
150
*
*
100 50
*
0
VL
150 100
50
50 0
0
TA
150
100
100
50
50 0
0 150 GAS
150
100
100
50
50
0
0
SOL
150
100
100
50
50
0
0
60
60
40
*
100
100
150
*
50
0
150
*
0
150 RFem
150
*
Horizontal Impulse Vertical Impulse
40
20
20
0
0
-20
-20
Load
Tip
Push
Load
Tip
Push
Fig. 7. Mean (SD) of normalized muscle activation (RMS, 20-ms binned) of the gluteus Maximus (Gmax), semitendinosus (ST), rectus femoris (RFem), vastus lateralis (VL), tibialis anterior (TA), gastrocnemius (GAS), and soleus (SOL) of an exemplar subject. Similar activation patterns were observed within-tasks, between-subjects. Within-subject comparison (mean of 3 trials) of RMS during each interval demonstrates between-task differences in activation of the rectus femoris, hamstrings, and gluteus maximus during the tip and push intervals (*, Po0:05). The between-task differences in muscle activation corresponded with between-task differences in NJMs.
the push phase of the reverse somersault assisted backward trunk rotation about the hip to promote a more backward position of the CoM relative to the RF. Between-task differences in activation of the bi-articular muscles associated with task-specific control of the CoM relative to the RF suggest scaling activation of bi-articular muscles serves as a relatively simple
mechanism for regulating angular impulse during complex whole body movements. Task-specific control of CoM relative to the RF redistributes lower extremity NJMs by altering the relative angles between the lower extremity segments and the RF and/or NJF, as well as the magnitude of the adjacent NJM. During the contact phase, the observed
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segment motion reflects the net effect of the moments imposed by the NJFs about the segment CoM and the NJMs at the adjacent joints. As the relative angle between the segment and the RF increases, the magnitude of the moments created by the RF imposed on the segment increases, thereby requiring greater NJMs. If the NJM controlling the motion of the distal joint is relatively small, then a relatively large NJM acting at the proximal end of the segment is needed to counteract the moments imposed by the NJFs. In contrast, if the NJM acting to control the motion of the distal joint is relatively large, then a relatively small NJM acting at the proximal joint is required to control the observed motion. For example, during the push interval of the reverse somersault, the relative angles between the thigh and the NJF were significantly larger and the knee extensor NJMs than during the reverse timer. As a result, significantly greater hip extensor NJMs were required to control the thigh motion during push interval of the reverse somersault as compared to the revere timer. The redistribution of lower extremity NJMs associated with task specific differences in segment orientation relative to the reaction force and adjacent joint NJMs has been observed in other multijoint, goal directed, weight bearing tasks without the need to generate angular impulse such as sit-to-stand (Mathiyakom et al., 2005), walking (Elftman, 1939), running (Bobbert et al., 1992), jumping (Ridderikhoff et al., 1999), and landing (McNitt-Gray et al., 2001). Modification in knee–hip coordination in order to achieve task-specific CoM trajectory relative to the RF alters distribution of work done by lower extremity NJMs during the push interval by altering the joint angular velocity profiles. During the push interval of the reverse somersault, the backward position of the CoM relative to the RF was facilitated by backward rotation of the trunk about the hip joint. Likewise, restricted backward trunk rotation observed during the push interval of the reverse timer aligned the CoM relative to the RF. These between-task differences in CoM control, as manifested in task-specific knee–hip coordination and task-specific NJMs, significantly altered the distribution of work done across the lower extremity joints. These results demonstrate how coordination between subsystems change between tasks performed under various impulse generation conditions and support the need for task-specific training programs to guide rehabilitation and improve overall performance of goal directed multijoint tasks.
Acknowledgements The authors would like to thank US divers and their coaches for their participation in this project, Doris Miller, for providing significant work in biomechanics
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of diving, Janet Gabrile, Ron O’Brien, Barry Munkasy, James Eagle, Kathleen E. Costa, and Laurie Held for their assistance with data collection, and Melissa McDonough and USC undergraduate students their assistance in data reduction. This project was supported in part by US diving, USOC, Intel, and NIA Training Grant 5 T32 AG00093.
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