Influence of leg stiffness and its effect on myodynamic jumping performance

Influence of leg stiffness and its effect on myodynamic jumping performance

Journal of Electromyography and Kinesiology 11 (2001) 355–364 www.elsevier.com/locate/jelekin Influence of leg stiffness and its effect on myodynamic...

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Journal of Electromyography and Kinesiology 11 (2001) 355–364 www.elsevier.com/locate/jelekin

Influence of leg stiffness and its effect on myodynamic jumping performance Adamantios Arampatzis *, Falk Schade , Mark Walsh , Gert-Peter Bru¨ggemann German Sport University of Cologne, Institute for Biomechanics, Carl-Diem-Weg 6, 50933 Cologne, Germany Accepted 25 January 2001

Abstract The purposes of this study are: a) to examine the possibility of influencing the leg stiffness through instructions given to the subjects and b) to determine the effect of the leg stiffness on the mechanical power and take-off velocity during the drop jumps. A total of 15 athletes performed a series of drop jumps from heights of 20, 40 and 60 cm. The instructions given to the subjects were a) “jump as high as you can” and b) “jump high a little faster than your previous jump”. The jumps were performed at each height until the athlete could not achieve a shorter ground contact time. The ground reaction forces were measured using a “Kistler” force plate (1000 Hz). The athletes body positions were recorded using a high speed (250 Hz) video camera. EMG was used to measure muscle activity in five leg muscles. The data was divided into 5 groups where group 1 was made up of the longest ground contact times of each athlete and group 5 the shortest. The leg and ankle stiffness values were higher when the contact times were shorter. This means that by influencing contact time through verbal instructions it is possible to control leg stiffness. Maximum center of mass take-off velocity the can be achieved with different levels of leg stiffness. The mechanical power acting on the human body during the positive phase of the drop jumps had the highest values in group 3. This means that there is an optimum stiffness value for the lower extremities to maximize mechanical power.  2001 Elsevier Science Ltd. All rights reserved. Keywords: Joint stiffness; Mechanical power; Drop jumps; Inverse dynamic

1. Introduction During human activities there is an energy exchange between muscles, tendons and ligaments. This energy exchange is important for efficient movement [30,21,5] and can be influenced by muscle stiffness [30,15]. In the literature the stiffness of the lower extremities for both humans and animals is often approximated using a spring constant (the “leg spring stiffness”) from a springmass model [3,20,9–11,5,21,29]. In several studies [28,5,21] a correlation was found between the leg spring stiffness and oxygen intake during running. Farley et al. [9], Ferris and Farley [14] and Farley and Morgenroth [13] reported that the frequency of human hopping influences leg stiffness. This increase in leg stiffness is caused mainly by the increase in ankle stiffness [13]. Voigt et al. [37] demonstrated that during short contact

* Corresponding author. Fax: +49-221-497-3454. E-mail address: [email protected] (A. Arampatzis).

time hopping, the mechanical power and level of activation of the soleus muscle were increased with respect to preferred contact time hopping. Stefanyshyn and Nigg [34] reported a difference in ankle stiffness between running and sprinting. They proposed that it is possible to produce better performance through greater stiffness at the ankle joint. It has also been suggested [18,2] that the muscle must have a high degree of stiffness to effectively utilize elastic energy. In other studies [24,25] it has been reported that stretch-shorten-cycle fatigue causes changes in knee stiffness and take-off velocity during drop jumps. We can conclude from this that the stiffness of the lower extremities influences athletic performance in various sport activities. The relationship between leg stiffness and performance during explosive movements has not yet been reported in the literature although in terms of performance enhancement, it is significant when one considers how such information could be used to optimize muscular output after an active stretch [38]. Stefanyshyn and Nigg [34] reported that ankle stiffness

1050-6411/01/$ - see front matter  2001 Elsevier Science Ltd. All rights reserved. PII: S 1 0 5 0 - 6 4 1 1 ( 0 1 ) 0 0 0 0 9 - 8

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is not a specialized characteristic of each individual but is rather a specialized characteristic of the activity or demand placed upon the ankle. In general the passive joint stiffness, the intrinsic muscle stiffness and stretch reflexes each contribute significantly to the net joint stiffness [23,33,4]. Co-contraction of two antagonist muscles can also influence the joint stiffness [31] and leg stiffness [26]. The value of joint stiffness may depend on the activation level of muscles acting at other joints [4]. This means that the leg- and joint stiffness are dependent on several different parameters and it is difficult to control the stiffness during complex activities. However leg stiffness can be influenced by stride frequency while running [11] or hopping frequency when bouncing in place [9,13,14]. These findings support the idea that it is possible to control leg stiffness by means of the ground contact time. During drop jumps the parameters which characterize the myodynamic jumping performance are the jumping height or take-off velocity of center of mass, the mechanical work and the mechanical power during the positive (propulsion) phase [19]. The purposes of this study are: 1. to examine the possibility of influencing the leg stiffness through instructions given to the subjects 2. to determine the effect of the leg stiffness on the mechanical power and take-off velocity during the drop jumps.

2. Methods A total of 15 athletes (decathletes, height: 1.83±0.06 m, weight: 78.94±5.86 kg) participated in this study. The subjects performed drop jumps (DJ) from three different heights (20, 40 and 60 cm). For control purposes the subjects were instructed to keep their hands on their hips during the drop jumps. The instructions given to the subjects were a) “jump as high as you can” and b) “jump high a little faster (with relation to ground contact time) than your previous jump”. The ground contact time was measured and checked after every jump using a “Kistler” force plate. The jumps were performed at each height until the athlete could not achieve a shorter ground contact time. The first jump from each subject tended to have a contact time of over 200 ms. In the case that it was less than 200 ms the subject was instructed to perform another jump but with a longer contact time. Each athlete performed a total of 6–9 jumps at each height. The jumps were grouped in the following way: One group was made up of the shortest contact times, another was made up of the longest contact times. The other groups were formed using jumps with contact times of less than 200 ms with a difference of 10 to 20 ms between jumps. The contact time difference of 10 to 20

ms was examined in a pilot study, and clear differences in leg stiffness could be measured. Using this criteria five jumps per athlete per height were analyzed and from this 5 groups were formed. The human body was represented using a 15 segment two-dimensional human body model [1]. The masses and moments of inertia of the various segments were calculated using the data provided by Zatsiorsky and Selujanov [41]. The ground reaction force was measured using a “Kistler” force plate (1000 Hz). The movement of the athlete was captured using a high speed (250 Hz) digital camera (“redlake motionscope 250 C”). The optical axis of the camera was approximately perpendicular to the plane of motion. To improve the quality of the video analysis six reflective markers (radius 10 mm) were used to mark joint positions. The markers were fixed on the following body landmarks: the tip of the foot at the height of the metatarsals, lateral maleolus, lateral epicondylus, trochanter major and C7-Vertebrae. These markers defined the position of the feet, lower legs, upper legs and the torso. The position of the head and arms in relation to the body remains constant in this model (Fig. 1). The video was digitized using the “Peak– Motus” automatic tracking systems. The two-dimensional coordinates were smoothed using a fourth-order lowpass Butterworth filter with a cut-off frequency of 15 Hz [27]. The vertical center of mass velocity during the support phase was calculated through integration of the vertical ground reaction force. The center of mass velocities at touch down were estimated from the video data. The mechanical power was calculated by multiplying the vertical ground reaction force with the vertical velocity of the center of mass. The Inverse dynamics method [22] was used to calculate resultant joint moments. The mechanical power at the joints was estimated by multiplying the joint moment with the joint angular velocity. The leg stiffness was approximated using a linear spring and the stiffness of the ankle and knee joints through rotational springs. A Linear regressions equation was used to calculate the stiffness [34]. The equations presented the relationship between the vertical ground reaction force and the vertical downward displacement of the center of mass for the leg stiffness and between the moment and change in angle for the stiffness of the knee and ankle joints. The regression equation was used during the negative phase. The linearity between vertical force and downward displacement of the center of mass and between joint moment and angular displacement for ankle and knee joints was checked using the coefficient of determination (r2). Surface electromyography (EMG) was used to measure muscle activity (sample frequency 1000 Hz) in five muscles (gastrocnemius lateralis, gastrocnemius medialis, tibialis anterior, vastus lateralis and hamstring) of the left leg. Pre-amplified (bandwidth 10–500 Hz),

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Fig. 1.

Modeled representation of the human body during drop jumps.

bipolar electrodes with a 2 cm inter-electrode distance were placed on the muscle belly. The EMG-data were rectified and smoothed a using a second-order Butterworth filter with a cut-off frequency of 10 Hz [7]. The filtered EMG data were normalized as follows: EMGNk⫽

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EMGFk ·100 Maxk

EMGNk: normalized EMG-Data from k-Muscle; EMGFk: filtered EMG-Data from k-Muscle; Maxk: Maximum filtered EMG-Data from k-Muscle of every athlete from the trial in which the athlete demonstrated the highest leg stiffness. The pre-activation time (from onset of the muscle activity until touch-down) and the integral of the preactivation signal (IEMGPA) were calculated from the normalized EMG data. The onset for the pre-activation time of every muscle was considered to be at the point when the normalized EMG value exceeded the mean value plus 2 standard deviations of the normalized EMG signal when the given muscle was relaxed. The observation window for the relaxed muscle signal was 200 ms. The synchronization of the kinematic, dynamic and EMG data was achieved by starting the three measurement systems at the same time. All analyzed jumps were divided into 5 groups. Group 1 contained the jump from each subject with the longest contact time. Group 5 contained the jumps with the shortest contact times. Groups 2, 3 and 4 contained the three remaining jumps from each subject which were assigned to the given groups based on contact time. The differences among groups were checked using a non parametrical test for several dependent samples (Friedman-test). At those parameters where differences were found a non parametrical test for two dependent samples (Wilcoxon-test) was applied to

assess the differences between the groups. The level of significance was set at P⬍0.05. Pearson’s correlation coefficients were calculated to examine the relationships between the different parameters.

3. Results All groups showed significantly different contact times (Tables 1–3). The center of mass velocities at touch down showed no significant differences within the 5 groups. The ground contact time influenced the leg stiffness and the stiffness at the ankle joint (Tables 1– 3). The leg stiffness and the ankle stiffness increased with shorter ground contact times (DJ 20 cm: rKLeg=⫺0.85, P⬍0.01, rKAnkle=⫺0.62, P⬍0.01; DJ 40 cm: rKLeg=⫺0.86, P⬍0.01, rKAnkle=⫺0.63, P⬍0.01; DJ 60 cm: rKLeg=⫺0.88, P⬍0.01, rKAnkle=⫺0.57, P⬍0.01). The vertical ground reaction force and the vertical path of the center of mass showed a high coefficient of determination for all jump heights (r2KLeg=0.75±0.19 to r2KLeg=0.97±0.03, Tables 1–3). A similar coefficient of determination can be seen between the moment and the change in the ankle angle (r2KAnkle=0.78±0.11 to r2KAnkle=0.98±0.01). At the knee joint the coefficient of determination is not as pronounced (r2KKnee=0.42±0.27 to r2KKnee=0.86±0.08). The maximum ground reaction force in all cases was lowest in group 1 and was consistently higher in each group with the highest values being found in group 5 (Fig. 2). In contrast the vertical sinking of the center of mass during the support phase was always the highest in group 1 and the lowest in group 5 (Fig. 2). The center of mass take-off velocity did not show any statistically significant differences among the first 3 groups (Fig. 3).

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Table 1 Support time (tsupport), leg stiffness (KLeg), ankle stiffness (KAnkle), knee stiffness (KKnee) and coefficient of determination (r2) during drop jumps from 20 cm [Mean (SD), n=15] Parameter (DJ 20 cm) Group 1

Group 2

Group 3

Group 4

Group 5

tsupport [ms] KLeg [kN/m] r2 KLeg KAnkle [Nm/°] r2 KAnkle KKnee [Nm/°] r2 KKnee

182 (12)a 48.80 (14.89)a 0.94 (0.07)a 39.43 (23.99)a 0.93 (0.05)a 41.40 (16.89)a 0.86 (0.08)

163 (11)a,b 62.74 (13.76)a,b 0.97 (0.02)a 57.54 (29.26)a,b 0.97 (0.02)a,b 58.97 (16.91)a,b 0.80 (0.13)

152 (10)a,b,c 70.06 (15.02)a,b,c 0.97 (0.02)a 63.56 (37.10)a,b 0.97 (0.03)a,b 72.10 (50.30)a 0.82 (0.07)

136 (9)a,b,c,d 78.71 (15.31)a,b,c,d 0.97 (0.02)a 80.66 (31.84)a,b,c,d 0.97 (0.03)a,b 69.59 (42.71)a 0.65 (0.18)a,b,c,d

a b c d

Statistically Statistically Statistically Statistically

210 (13) 32.41 (7.69) 0.83 (0.23) 25.08 (12.11) 0.87 (0.10) 28.83 (7.23) 0.88 (0.07) significant significant significant significant

(P⬍0.05) (P⬍0.05) (P⬍0.05) (P⬍0.05)

difference difference difference difference

between between between between

group group group group

1 2 3 4

and and and and

groups 2,3,4 and 5. groups 3,4 and 5. groups 4 and 5. group 5.

Table 2 Support time (tsupport), leg stiffness (KLeg), ankle stiffness (KAnkle), knee stiffness (KKnee) and coefficient of determination (r2) during drop jumps from 40 cm [Mean (SD), n=15] Parameter (DJ 40 cm) Group 1

Group 2

Group 3

Group 4

Group 5

tsupport [ms] KLeg [kN/m] r2 KLeg KAnkle [Nm/°] r2 KAnkle KKnee [Nm/°] r2 KKnee

179 (11)a 46.11 (12.69)a 0.90 (0.09)a 35.18 (19.79)a 0.91 (0.06)a 36.25 (11.40)a 0.74 (0.18)a

161 (10)a,b 55.10 (13.60)a,b 0.97 (0.02)a,b 39.42 (14.36)a 0.94 (0.05)a,b 46.05 (14.72)a,b 0.67 (0.22)

150 (8)a,b,c 61.38 (15.67)a,b,c 0.97 (0.02)a,b 47.79 (14.67)a,b 0.93 (0.06)a 47.56 (18.29)a,b 0.59 (0.22)a,b

139 (10)a,b,c,d 66.35 (15.46)a,b,c,d 0.97 (0.02)a,b 53.87 (27.78)a,b 0.98 (0.01)a,b 38.42 (19.08)a 0.52 (0.23)a,b,c

a b c d

Statistically Statistically Statistically Statistically

218 (18) 27.55 (7.92) 0.78 (0.17) 16.64 (5.87) 0.78 (0.14) 23.11 (6.75) 0.80 (0.12) significant significant significant significant

(P⬍0.05) (P⬍0.05) (P⬍0.05) (P⬍0.05)

difference difference difference difference

between between between between

group group group group

1 2 3 4

and and and and

groups 2,3,4 and 5. groups 3,4 and 5. groups 4, and 5. group 5.

Table 3 Support time (tsupport), leg stiffness (KLeg), ankle stiffness (KAnkle), knee stiffness (KKnee) and coefficient of determination (r2) during drop jumps from 60 cm [Mean (SD), n=15] Parameter (DJ 60 cm) Group 1

Group 2

Group 3

Group 4

Group 5

tsupport [ms] KLeg [kN/m] r2 KLeg KAnkle [Nm/°] r2 KAnkle KKnee [Nm/°] r2 KKnee

184 (10)a 38.01 (7.74)a 0.81 (0.13) 21.01 (9.26) 0.82 (0.15)a 30.73 (7.84)a 0.66 (0.17)

166 (11)a,b 48.38 (10.98)a,b 0.90 (0.06)a,b 32.76 (22.81)a,b 0.86 (0.10)a 37.83 (12.27)a,b 0.66 (0.19)

153 (9)a,b,c 54.81 (11.48)a,b,c 0.93 (0.03)a,b 33.94 (18.34)a,b 0.88 (0.11)a 39.81 (10.17)a,b 0.51 (0.25)a,b,c

145 (9)a,b,c,d 58.99 (14.16)a,b,c,d 0.94 (0.03)a,b 40.43 (25.44)a,b 0.86 (0.10)a 37.14 (13.52)a 0.42 (0.27)a,b,c,d

a b c d

Statistically Statistically Statistically Statistically

222 (15) 22.00 (4.97) 0.75 (0.19) 15.51 (6.06) 0.78 (0.11) 18.95 (7.14) 0.66 (0.13) significant significant significant significant

(P⬍0.05) (P⬍0.05) (P⬍0.05) (P⬍0.05)

difference difference difference difference

between between between between

group group group group

1 2 3 4

and and and and

In groups 4 and 5 it was less. The maximum and average mechanical power during the positive phase show the highest values in group 3 (Fig. 3). This was seen for all three jump heights. The ground contact time influences the joint moment as well as the mechanical power at both the ankle and knee joints (Figs. 4–6). Groups 1 and

groups 2,3,4 and 5. groups 3,4 and 5. groups 4, and 5. group 5.

2 showed the lowest maximum moment values at the ankle joint and groups 1 and 5 the lowest moment maximums at the knee joints (Figs. 4–6). The lowest mechanical power at the knee joint was found to be in groups 4 and 5 and at the ankle joint in group 1. The amplitude of the change in ankle and knee angles was

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Fig. 2. Leg stiffness (KLeg), maximum vertical ground reaction force (FZmax), vertical sinking of the center of mass (⌬SZ) (n=15, mean±SD). 1 Statistically significant (P⬍0.05) difference between group 1 and groups 2,3,4 and 5; 2Statistically significant (P⬍0.05) difference between group 2 and groups 3,4 and 5; 3Statistically significant (P⬍0.05) difference between group 3 and groups 4, and 5; 4Statistically significant (P⬍0.05) difference between group 4 and group 5.

found to be less in accordance with shorter ground contact times (Figs. 4–6). The pre-activation times were not influenced by the different jumping conditions (Fig. 7). During the preactivation phase some differences were seen in the IEMG (Fig. 7). In general higher values were seen in groups 3, 4 and 5 than in group 1. In the drop jumps from a starting height of 20 cm a significant correlation

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Fig. 3. Vertical take off velocity (VZEnd), mean and maximum mechanical power (Pmean, Pmax) during the positive phase of the drop Jumps (n=15, mean±SD). 1Statistically significant (P⬍0.05) difference between group 1 and groups 2,3,4 and 5; 2Statistically significant (P⬍0.05) difference between group 2 and groups 3,4 and 5; 3Statistically significant (P⬍0.05) difference between group 3 and groups 4, and 5; 4Statistically significant (P⬍0.05) difference between group 4 and group 5.

was found between leg stiffness and IEMGPA for the m. gastrocnemius lateralis (r20 cm=0.48, P⬍0.01), m. gastrocnemius medialis (r20 cm=0.54, P⬍0.01) the m. vastus lateralis (r20 cm=0.49, P⬍0.01) and the hamstrings (r20 cm=0.60, P⬍0.01). In the drop jumps from 40 and 60 cm significant correlations were found between leg stiffness and IEMGPA for the m. vastus lateralis (r40 cm=0.48,

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Fig. 4. Maximum moment at the ankle and knee joints (MAnkle max, MKnee max), maximum mechanical power at the ankle and knee joints (PAnkle max, PKnee max) and change in ankle and knee angles (⌬⌰Ankle, ⌬⌰Knee) during drop jumps from 20 cm height (n=15, mean±SD). 1Statistically significant (P⬍0.05) difference between group 1 and groups 2,3,4 and 5; 2Statistically significant (P⬍0.05) difference between group 2 and groups 3,4 and 5; 3Statistically significant (P⬍0.05) difference between group 3 and groups 4, and 5; 4Statistically significant (P⬍0.05) difference between group 4 and group 5.

Fig. 5. Maximum moment at the ankle and knee joints (MAnkle max, MKnee max), maximum mechanical power at the ankle and knee joints (PAnkle max, PKnee max) and change in ankle and knee angles (⌬⌰Ankle, ⌬⌰Knee) during drop jumps from 40 cm height (n=15, mean±SD). 1Statistically significant (P⬍0.05) difference between group 1 and groups 2,3,4 and 5; 2Statistically significant (P⬍0.05) difference between group 2 and groups 3,4 and 5; 3Statistically significant (P⬍0.05) difference between group 3 and groups 4, and 5; 4Statistically significant (P⬍0.05) difference between group 4 and group 5.

P⬍0.01; r60 cm=0.46, P⬍0.01) and the hamstrings (r40 cm=0.59, P⬍0.01; r60 cm=0.49, P⬍0.01).

leg stiffness values and b) there is an optimal leg stiffness value to maximize the mechanical power during the positive phase of the drop jumps (Figs. 2 and 3). These results are important because performance in many sports is determined by the mechanical power output [16,17,6]. Furthermore the stiffness of the lower extremities during drop jumps can be regulated by changing the contact time. Through the use of different

4. Discussion The main findings of this study are: a) it is possible to maximize vertical take off velocity through various

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Fig. 6. Maximum moment at the ankle and knee joints (MAnkle max, MKnee max), maximum mechanical power at the ankle and knee joints (PAnkle max, PKnee max) and change in ankle and knee angles (⌬⌰Ankle, ⌬⌰Knee) during drop jumps from 60 cm height (n=15, mean±SD). 1Statistically significant (P⬍0.05) difference between group 1 and groups 2,3,4 and 5; 2Statistically significant (P⬍0.05) difference between group 2 and groups 3,4 and 5; 3Statistically significant (P⬍0.05) difference between group 3 and groups 4, and 5; 4Statistically significant (P⬍0.05) difference between group 4 and group 5.

instructions jumping leg stiffness values between 32 and 78 kN/m and ankle stiffness between 25 und 80 Nm/° were attained (Table 1). That indicates that an observed change in stiffness of the lower extremities is not necessarily caused by morphological changes in the muscle tendon complex [25]. Anyway it seems necessary to examine the entire range of achievable leg stiffness values before making such conclusions.

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Also, changes in the level of muscle activation during the pre-activation phase were observed. Based on these findings it can be argued that the athletes developed a higher muscle activation in response to the given instruction. This higher muscle activation caused changes in the stiffness of the lower extremities and this way also higher maximal ground reaction forces and lower vertical downward displacement of the center of masses during ground contact, as well as shorter contact times. These results are in accordance with those reported by Nigg and Liu [32]. Nigg and Liu [32] studied the effect of muscle stiffness on impact forces during running by means of a simplified model of the human body. They found that increasing stiffness also increases impact forces and lowers the maximal vertical displacement of the upper body. The pre-activation times of the studied muscles did not change in relation to the changes in leg stiffness (Fig. 7). The IEMG of the pre-activation phase showed differences which may indicate that the activation level causes the change in leg stiffness. Nielsen et al. [31] also reported that the ankle stiffness was dependent on the amount of muscle activity during plantar flexion. Although it is possible to change leg stiffness by altering the body geometry at touch-down [12]. Farley et al. [12] found that the leg stiffness is adjusted for different surfaces by compensation changes in ankle stiffness and knee angle. They reported that not only no increase in EMG activity but rather a decrease in EMG activity in the gastrocnemius, soleus and tibialis anterior muscles occurred concurrent with an increase in ankle stiffness. In our study we found no statistically significant (P⬍0.05) difference in ankle, knee- and hip angle at touchdown among the 5 groups so the possibility of the leg stiffness being affected by body geometry can be excluded. Through increased pre-activation and increased cocontraction the reflex activity of the muscles and the joint stiffness can be influenced [4,31]. In our experiment it is not possible to calculate the exact influence of passive stiffness, of the intrinsic muscle stiffness or of the stretch reflexes on the leg and joint stiffness. It can assumed, that the increase in leg and joint stiffness is not due to the passive stiffness (inactive muscle and soft tissues crossing the joint) because the range of joint angles attained decreased with shorter contact times (Figs. 4–6). The passive stiffness is generally low at the middle of the range of joint angles [40]. Whether or not the leg stiffness is influenced by a stretch reflex can not be definitely answered here. However an increased muscle activation of the lower extremities during the contact phase of the shorter contact times could not be determined although a change in joint moments and in the mechanical power occurred. The Maximum EMGActivity of the examined muscles during the contact phase showed no significant differences among the 5 groups. Similar results have been reported by Walshe et

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Fig. 7. Pre-activation time (from onset of muscle activity until touch-down [1]), integrated EMG during the pre-activation phase (IEMGPA [2]) and normalized EMG-activation during drop jumps (n=15, the x-axis is normalized as follows: ⫺100 until 0% represents the flight phase, 0 until 100% represents the support phase). 1Statistically significant (P⬍0.05) difference between group 1 and groups 2,3,4 and 5; 2Statistically significant (P⬍0.05) difference between group 2 and groups 3,4 and 5; 3Statistically significant (P⬍0.05) difference between group 3 and groups 4, and 5; 4 Statistically significant (P⬍0.05) difference between group 4 and group 5.

al. [38] and Takarada et al. [35,36]. Takarada et al. [35] found no significant differences in the integrated EMG activity of the biceps brachii or triceps brachii in both the negative as well as in the positive phase of movement with varied stretching speeds. In spite of the EMG values the torque and the mechanical work values during the positive phase showed clear differences. In another study Takarada et al. [36] found that during counter movement jumps there was no increase in time averaged integrated EMG in the vastus lateralis although the power output in the knee joint increased. Walshe et al. [38] also found no differences in the IEMG values between concentric squat preceded by an isometric preload and counter movement although clear differences existed in the mechanical power during the positive phase. The results bring into question the assumption of Gollhofer et al. [18] that during drop jumps an optimum use of energy present in the system can be achieved through a maximum activation of the triceps surae muscles before touch down. For example group 5 produced the highest EMG activation of the gastrocnemius muscle during the pre-activation phase. The gastro-

cnemius muscle influences the stiffness at both the knee and ankle [39,8,31]. Similarly the vastus lateralis muscle produced the highest activation during the pre-activation phase in group 5. The average mechanical power, the maximum mechanical power and the vertical take off velocity for group 5 are less then those of group 3. It appears that there is not a maximum activation but rather that there is an optimum activation of the lower extremity muscles during the pre-activation phase to maximize the mechanical power. The increase in the mechanical power of the entire system from group 1 to group 3 was achieved mainly through an increase in mechanical power at the ankle joint (Figs. 4–6). In contrast the decrease in groups 4 and 5 was achieved through a decrease in mechanical power at the knee joint. It is clear from this that the mechanical power of the entire system is dependent on the mechanical power from both the knee and ankle joints. From this observation a question arises about the hypothesis from Stefanyshyn and Nigg [34]. They proposed that it was possible to produce better performance in sprinting through higher stiffness at the ankle joint. The performance in sprinting is dependant on the mech-

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anical power output [17]. No linear relationship between ankle stiffness and mechanical power was observed in this study. The ankle stiffness influences the mechanical power during the positive phase of the drop jumps, but a higher ankle stiffness doesn’t necessarily mean a higher mechanical power of the entire system. It has also been found that during drop jumps the leg stiffness as well as the ankle stiffness can be approximated using two spring constants (one linear spring and one rotational spring). This illustrates the linear relationship between force and change in position of the center of mass for the leg stiffness and between moment and change in angle for the ankle stiffness (Tables 1–3). Stefanyshyn and Nigg [34] observed a similar linear relationship between moment and change in angle of the ankle during sprinting. The knee stiffness during drop jumps can not be approximated using a rotational spring. The relationship between knee joint moment and knee joint angle is weak and with higher starting heights and shorter contact times becomes weaker (Tables 1–3). From this we can conclude that the leg stiffness influences the vertical take off velocity the maximum and mean mechanical power during the positive phase of the drop jumps. It is possible to maximize vertical take off velocity through various leg stiffness values. The maximization of mechanical power is attained through optimum leg stiffness and ankle stiffness values as well as the optimum amount of activation in the muscles of the lower extremities during the pre-activation phase. Furthermore the leg stiffness during drop jumps can be controlled through the contact time. References [1] Arampatzis A, Bru¨ ggemann G-P. A mathematical high barhuman body model for analyzing and interpreting mechanical– energetic processes on the high bar. J Biomech 1998;31:1083–92. [2] Avela J, Komi PV. Reduced stretch reflex sensitivity and muscle stiffness after long-lasting stretch-shortening cycle exercise in humans. Eur J Appl Physiol 1998;78:403–10. [3] Blickhan R. The spring-mass model for running and hopping. J Biomech 1989;22:1217–27. [4] Carter RR, Crago PE, Gorman PH. Nonlinear stretch reflex interaction during cocontraction. J Neurophysiol 1993;69:943–52. [5] Dalleau G, Belli A, Bourdin M, Lacour J-R. The spring-mass model and the energy cost of treadmill running. Eur J Appl Physiol 1998;77:257–63. [6] de Konig JJ, de Groot G, van Ingen Schenau GJ. A power equation for the sprint in speed skating. J Biomech 1992;25:573–80. [7] DeVita P. The selection of a standard convention for analyzing gait data based on the analysis of relevant biomechanical factors. J Biomech 1994;27:501–8. [8] Dyhre-Poulsen P, Simonsen EB, Voigt M. Dynamic control of muscle stiffness and H reflex modulation during hopping and jumping in man. J Physiol (Lond) 1991;437:287–304. [9] Farley CT, Blickhan R, Saito J, Taylor CR. Hopping frequency in humans: a test of how springs set stride frequency in bouncing gaits. J Appl Physiol 1991;71:2127–32. [10] Farley CT, Glasheen J, McMahon TA. Running springs: speed and animal size. J Exp Biol 1993;185:71–86.

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Adamantios Arampatzis received his physical education degree from the University of Thessaloniki in 1984. He studied mathematics at the University of Cologne and received his PhD at the German Sport University of Cologne in 1995. His major research interest is the energy production storage and utilization between biological and mechanical systems.

Peter Bru¨ggemann completed his studies in sport and mathematics in 1976 at the University of Munster. He completed his Doctorate work in biomechanics at the Johann–Wolfgang–Goethe University in Frankfurt, Germany in 1980. In 1983 he was named head of the Department of Track and Field and Gymnastics Department and in 2000 he became Chair of the Biomechanics Department at the German Sport University of Cologne. His main research interests are biomechanics of elite and normal sports, occupational biomechanics and biomechanics of the spine. Mark Walsh received his MSc degree in biomechanics from California State University, Northridge in 1993. Since then he has had a research position at the German Sport University in Cologne. He is also working towards his PhD in biomechanics. His main areas of focus are fatigue and the stretch shorten cycle.

Falk Schade graduated from the German Sport University, Cologne in 1995. Currently he is working towards a PhD in the Institute for Biomechanics of the German Sport University. His research involves mechanical energy considerations with a special focus on the energy exchange between the athlete and elastic implements. Additionally he works in the Olympic Training Centre, Cologne; he is responsible for the biomechnaical support of several members of the German Olympic Team.