MECHANICAL AND MUSCULAR FACTORS …e.guigon.free.fr/rsc/article/VoigtEtAl95a.pdf · MECHANICAL AND MUSCULAR FACTORS INFLUENCING ... In 1885 Marey and Demeny observed that the jump-

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J. Btomechanics. Vol. 28. No. 3, 293 307, pp. 19‘45 Copywright Q 1994 Elsevier Science L[d

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MECHANICAL AND MUSCULAR FACTORS INFLUENCING THE PERFORMANCE IN MAXIMAL VERTICAL JUMPING

AFTER DIFFERENT PRESTRETCH LOADS

M. Voigt,* E. B. Simonsen,* P. Dyhre-Poulsent and K. Klausenf * Department of Medical Anatomy, sect C, Panum Institute; t Department of Medical Physiology, Panum Institute, $ Laboratory Human Physiology, August Krogh Institute, Umversity of Copenhagen, Denmark

Abstract--~The objective of the present work was to study the interaction between the tendon elasticity, the muscle activation-loading dynamics, specific actions of the biarticular muscles, preloading and jumping performance during maximal vertical jumping. Six male expert jumpers participated in the study. They performed maximal vertical jumps with five different preloads. The kinematics and dynamics of the jumping movements were analysed from force plate and high speed film recordings. The amount of elastic energy stored in the tendons of the leg extensor muscles was calculated by a generalised tendon model, and the muscle coordination was analysed by surface EMG. The best jumping performances were achieved in the jumps with low preloads (counter movement jumps and drop jumps from 0.3 m). A considerable amount of the energy imposed on the legs by prestretch loading was stored in the tendons (26k 3%), but the increased performance could not be explained by a contribution of elastic energy to the positive work performed during the push off. During the preloading, the involved muscles were activated at the onset of the loading. Slow prestretches at the onset of muscle activation under relatively low average stretch loads, as observed during counter movement jumps and drop jumps from 0.3 m, prevented excessive stretching of the muscle fibres in relation to the tendon length changes. This consequently conserved the potential of the muscle fibres to produce positive work during the following muscle-tendon shortening in concert with the release of the tendon strain energy. A significant increase in the activity of m. rectus femoris between jumps with and without prestretch indicated a pronounced action of m. rectus femoris in a transport of mechanical energy produced by the proximal monoarticular m. gluteus maximus at the hip to the knee and thereby enhanced the transformation of rotational joint work to translational work on the mass centre of the body. The changes in muscle activity were reflected in the net muscle powers. Vertical jumping is like most movements constrained by the Intended direction of the movement. The movements of the body segments during the prestretches induced a forward rotation and during the take off, a backward rotation of the body. A reciprocal shift in the activities of the biarticular m. rectus femoris and m. semitendinosus indicated that these rotations were counteracted by changes in the direction of the resultant ground reaction vector controlled by these muscles. The rotational actions around the mass centre of the body should be minimised in maximal vertical jumping because the muscle work used to controt these actions is lost for the achievement of jumping height

INTRODUCTION

In 1885 Marey and Demeny observed that the jumping height increased if human subjects were allowed to perform a preparatory counter movement (prestretching of the leg extensor muscles) before a vertical take- off compared to a take-off starting from semi-squat; ting position (no prestretch). Ascribing this fact to storage of elastic energy in the leg muscles, Asmussen and Bonde-Petersen (1974) proposed a simple but genius protocol to quantify the possible amount of stored elastic energy that can be released from human leg muscles during explosive jumps. They perceived the human body as one big mass with one big muscle,

the latter always acting under maximal stimulation. The subjects performed vertical jumps with maximal effort and the work on the mass centre of the body (MCB) was calculated from force plate recordings. Negative work i.e. the prestretch load ( WReg) was defined as the work performed during the braking of MCB during the downward movement and the posrt- ive work (W,,) as the work performed during the upward movement of MCB. The maximal positive work potential of the ‘muscle’ without prestretch load

was determined as the (positive) work performed during a push-off starting from semi-squatting position (squat jump, SQJ) not allowing any downward movement of MCB. Then, an increasing amount of negative work was imposed on the ‘muscle’ by allowing the

subjects to perform a preparatory counter movement (counter movement jumps, CMJ) or by asking the subjects to jump down from increasing heights before the push-off (drop jumps, DJ). The positive work output after the different prestretch loads was measured and the amount of stored elastic energy in the

Received in final form 17 March 1994. Address for correspondence: M. Voigt Ph.D. Laborat-

ory for Functional Anatomy and Biomechanics, Dept. of Medical Anatomy, sect. C, Panum Institute, University of Copenhagen, Blegdamsvej 3c. 2200 Copenhagen N, Denmark.

293

‘94 M. Voigt rf al

muscle-tendon complex (E,,,) was calculated as

Em,,% = w*os, i - wpos. SQJ 100 W (1)

neg. i

where i=CMJ and DJs from different heights. The location of the elastic elements in the

muscle-tendon complex has been a matter of discussion (for a review see Zahalak, 1990); however, Alexander and Bennet-Clark (1977) estimated that the energy stored in the active muscle fibres of a human triceps surae muscle-tendon complex during maximal isometric muscle action only amounts to approximately 1% of the elastic energy stored in the tendinous structures. Therefore, the dominant elastic property of the muscle-tendon complex resides in the tendinous structures, and the amount of elastic energy that can be stored in and released from the muscle-tendon complex depends on the mechanical properties of the tendons i.e. the Young’s modulus of the tendon tissue, the shape of the tendon force-deformation function, the tendon dimensions, the loading rate and the hysteresis (Alexander, 1989).

It has been shown very elegantly that when the muscle-tendon complex is activated at the onset of external loading, the maximal force achieved and the length change of the muscle fibres in relation to the tendon length change is determined by the interaction between the rate of force development in the muscle fibres and the rate of external loading (Griffiths, 1991), which again determines the amount of elastic energy stored in the tendons at the end of the preloading and the potential of the muscle fibres to perform positive work immediately after the preloading, depending on the position in the force-length-velocity relationship. Therefore, the interaction between the muscle activation and the rate of external loading might be very important for the performance in maximal vertical jumping following prestretch loading.

Several studies have indicated that a co-activation of mono- and biarticular muscles in the lower extremities during the push off induces a transport of muscle power produced by the monoarticular muscles via the biarticular muscles in proximal-distal direction (Bobbert et al., 1986; Bobbert and Ingen Schenau, 1988; Gregoire et al., 1984; Soest et al., 1993). This mechanism increases the efficiency of how the rotational energy produced by a proximal joint is transferred to translational energy of MCB via the adjacent distal joint.

It has recently been proposed that biarticular muscles are engaged in the control of the direction of the external forces (Ingen Schenau et al., 1992; Jacobs and Ingen Schenau, 1992). This function might be evident in vertical jumping because the constraint of keeping the MCB in a vertical movement path might induce a high demand on the control of the direction of the resultant ground reaction force.

The purpose of the present study was to analyse the relationships between the tendon elasticity, the activa-

tion-loading dynamics, the action of biarticular muscles, the level of prestretch loading, and the jumping performance in maximal vertical jumping.

A protocol identical to the one described by Asmus- sen and Bonde-Petersen (1974) was used. In addition the methodology included a two-dimensional movement analysis of the jumping movements by high speed film, inverse dynamics calculations, a quantifi- cation of the elastic energy stored in the leg extensor tendons by application of a general tendon model and an analysis of the changes in muscle coordination by surface EMG.

Parts of the data have previously been presented in abstract form (Voigt et al., 1992).

MATERIAL AND METHODS

Subjects and experimental procedures

Six skilled male jumpers participated in the study (four elite volleyball players and two professional bal- let dancers). Age 27 + 2 yr, body mass 78 f 11 kg and body height 1,86 + 0.09 m (mean + SD.). All subjects gave their informed consent to participate in the study. After a 15 min warm up each subject performed (a) SQJs, (b) CMJs and (c) DJs from 0.3,0.6 and 0.9 m, respectively (Fig. 1). The different jumps were performed at random. Eleven trials were performed within each jumping task and there was a minimum of 2 min between each trial to avoid fatigue. All jumps were performed barefooted and the subjects were in- structed to keep their hands on the hips and to jump as high as possible.

All jumps were performed on a force plate (AMTI OR6-5-1) and the vertical ground reaction force (F,), the sagittal reaction force (F,) and the reaction moment around the frontal axis of the force plate (M,) were recorded.

Muscle activity (EMG) was recorded with surface electrodes from seven leg muscles, m. tibialis anterior (TA), m. soleus (SO), m. gastrocnemius cap. laterale (GA), m. semitendinosus (ST), m. vastus lateralis (VL), m. rectus femoris (RF) and m. gluteus maximus (GM). Prefilled electrodes (Medicotest Q-10-A) were used. Electrode pairs were placed 3 cm apart on the mid- portion of the muscle bellies with the connecting line between the centres of the electrodes approximately parallel to the muscle fibres. The short leads from the electrode pairs were connected to a light weight volt- age follower (FET). The signals were lead through long cables to the amplifiers allowing the subjects to move freely. Electrodes and FETs were taped to the skin and secured with elastic bandages. This recording procedure effectively reduced movement artefacts.

The analog signals were recorded on a FM- taperecorder (TEAC-XRS 10) and later A/D converted (DT2801-A) into a PC at 1 kHz and digitally pro- cessed.

Markers were placed over the following anatomical landmarks on the right side of the subjects: the fifth

Mechanical and muscular factors 295

a.

b.

c.

Fig. 1. The jumping tasks performed by the subjects in this study. (a) Push-offs starting from semi-squatting position (SQJ), (b) push-offs preceded with a preparatory counter movement (CMJ) and (c) Push-offs preceded with a downward jump from three different heights (DJs from 0.3, 0.6, 0.9 m, 0.3 m in the figure). The stick diagrams represents every 40th picture from the film analysis (500 framess-‘) superimposed on the ground reaction forces on an arbitrary

scale.

metatarsal joint, the lateral malleolus, the lateral epi- condyle of the knee, the tip of the trochanter major and the lateral side of the neck at the level of the fifth cervical vertebra. The markers defined the position of the body segments (feet, lower legs, thighs and upper body) and the angles between them. The 11th trial in each jumping task was filmed from the right side in the sagittal plane with a high speed camera at 500 frames s- ’ (TeleDyne DBM45). The film and the analog signals were synchronized by simultaneously lightening of a red diode in the photograhic field and sending a TTL pulse to a separate channel on the tape recorder during each film recording. The films were frame-by-frame projected on a digitiser (Calcomp Drawingboard) scaled 1: 8 and the coordinates of the markers were manually digitised.

Data treatment and calculations

Force plaie recordings. The vertical ground reaction forces were used for calculation of the mechanical

work on MCB. In the cases of the SQJs and the CMJs the initial conditions were known, i.e. the initial velocity of MCB was zero and the subjects were standing on the force plate before jumping. Therefore, the velocity of the MCB during ground contact (~~cn,*~,) could be calculated by forward integration of F, with respect to time after dividing by the body mass and subtraction of the gravitational acceleration. The mechanical work rate (power) was calculated by mul- tiplying the velocity of MCB with F,. The negative and positive mechanical work were calculated as the time integral of the mechanical power over the negative and positive work periods, respectively. In the case of a DJ, the initial conditions for an integration cannot be directly obtained from F, and must be estimated. This was done by calculating the take off velocity of the MCB after the ground contact (~~cn,,~) from the flight time (tri): first the jumping height (A&s) was calculated as

AhhtcB = 0.125 g t; (2) according to the laws of free falling in the gravitational field, where g is the gravitational acceleration, and then ~~~a,~,, could be calculated as

” MCB.lo = $ g Ah,cB (3) according to the interchange between kinetic and potential energy during the flight. During the following integration of F,, the order of the movements that actually happened was reversed corresponding to a backwards integration with respect to time:

where t,rr is the time when the toes left the ground, ttd the time when the toes touched the ground at the beginning of the ground contract and BM the body mass. In this way, the negative and positive velocity of MCB during ground contact could be separated, and the corresponding power and work obtained.

In the calculation of UM(Cs&, from tfl, it is assumed that MCB is exactly at the same height above the ground at the time of take off and at the time of landing after the flight. This is usually not the case, and an evaluation of the error was made. For the SQJs and the CMJs (22 trials pr. subject) t)Mca& was calculated in two ways, from the flight time and by integration of F, using the latter as reference. The subjects showed reproducible take-off-landing pattern during both the SQJs and the CMJs. Three subjects showed a significant overestimation (p <: 0.05) of U&$ca, ,0 calculated from tr, of 5 + 3, 3 It 3 and 3 + 3 % (mean+S.D.). The remaining three subjects did not show any significant deviations. Although the errors were small, u~c~,,~ calculated from trl after the DJs performed by the three subjects mentioned above were corrected with the average error, before it was included in the backward integration. F, from the best trials, evaluated from the jumping height (A&n) calculated from tfl, were selected for analysis.

296 M. Voigt rt al.

The negative work phase was defined as the time interval between when MCB started to move downward (CMJs) or when the feet touched the ground (DJs) and zero velocity of MCB (tupwm) before the start of the upward movement. The positive work phase was defined as the time interval between tupwm and the time where the feet left the ground at the end of the take-off.

EMG analysis. The raw EMG signals were high- pass filtered at 20 Hz, low-pass filtered at 500 Hz (fourth order digital Butterworth filters) and rectified. Integrated EMG (IEMG) was calculated over negative and positive work periods as the mean of the rectified signal. No corrections for electro-mechanical delays were made. The IEMG from the SQJ (positive work without prestretch) was then used as reference for each subject, and the percentage change in IEMG during the negative and the positive phases was culated as

IEMGpas,i-IEMGpos,sQ~ 100% IEM'&~,sQQ,

in analogy with equation (1). Kinematics and dynamics. In the computer

body was transformed into a four segment link ment model with lumped feet, shanks, thighs

cal-

(54

(W

the seg- and

lumped head, arms and trunk. The coordinates of the digitised markers were low-pass filtered 8 Hz. The cut-off frequency was determined by examining the relationship between the peak vertical velocity of MCB of the link segment model during the take off and the cut-off frequency and by comparing the results to the peak vertical velocity of MCB calculated from F,. The cut-off frequency that reduced the peak velocity with a maximum of 5% was chosen (8 Hz). A residual analysis (Winter, 1990) of the coordinates gave a cut-off frequency of 6 Hz, but at this cut-off frequency the peak vertical take-off velocity was reduced by more than 10%. The kinematic data were calculated from the filtered coordinates. The centre of pressure on the force plate (P,) was calculated as M,/F,. F,, F, and P, were reduced to the film frequency (500 frames s-‘) by averaging every two suc- ceeding data points, and the dynamic data were calculated by the inverse dynamic approach including F,, F,, and P, in the calculation (Winter, 1990). In the present study, net extensor moments and powers were defined as positive.

In order to evaluate differences in kinematic and dynamic data calculated from the film recordings and from the force plate recordings two control analyses were performed: (1) the kinematics of MCB during ground contact were calculated both from the measured F, and the film. A set of data from one subject is presented in Fig. 2. For all subjects, the position and the velocity curves were almost identical; however, the vertical ground reaction force estimated from the film

deviated substantially from the measured I.‘;. The

velocity of MCB at the time of toe-off (I.~~~.,~,! &al- culated from the film was on average (ail jumps included) slightly, but significantly lower (2.41 i 5. ! “,, / than the same velocity calculated from p,, which should be expected as a consequence of the filtering of the coordinates extracted from the films. (2). The pas.. itive work on MCB was calculated from net joinr moments (TBW,,,) as described by Hubley and Wells (1983) and compared to the same paratneter calculated from force plate data ( Wpos). TBW,,, did not differ significantly from W,,,. The variatiutl in TBW,,, was rather large (+ 11%); but tahing the accuracy of the inverse dynamic calculation into con- sideration, the results from the two different calculations were considered to be comparable.

Tendon model. In order to calculate the possible amount of stored elastic strain energy in the tendons. a general tendon model was defined. The load--deformation relationship for tendons typically consists of an initial non-linear part, the ‘toe piece’ at low loads followed by an approximately linear part until the deformation limit is reached (Fli,, Fig. 3), and the curve starts to deviate from linearity due to the beginning of ruptures of the collagen fibres in the tendon. A general loaddeformation relationship (Fig. 3) was approximated by a quadratic function (Ingen Schenau, 1984) and the elastic energy stored in a tendon, equal to the area under the loaddeformation curve was calculated as

(6)

where F, is the tendon force, &, the tendon resting length, E,,, the maximal tolerable strain, cr the length of the initial unlinear part of the load-deformation curve, Y the normahsed tangential modulus (Young’s modulus) of the tendon and A, the cross-sectional area of the tendon [see the appendix for the derivation of equation (6)].

The maximal tolerable strain (cmax) for human tendon tissues reported in the literature lies between 4% and 8% (Abrahams, 1967; Hubbard and Southas- Little, 1984). Therefore, a,,, for the tendon model was chosen as 6%. The length of the initial non-linear part of the load-deformation curve (or) was defined as the intercept between the tangent to the linear part of the load-deformation curve and the abscissa and set at 2% (Fig. 3) (Abrahams, 1967). The tangent modulus (Young’s modulus, Y) for human tendons is reported to he in the interval between 0.6 and 1.8 GPa (Ab- rahams, 1967; Hubbard and Southas-Little, 1984) and

the average, 1.2 GPa, was chosen for the model. The energy dissipation (hysteresis) in large load

bearing (extensor) tendons in the extremities of humans has not been reported, but assuming that the human extensor tendons are comparable to the extensor tendons of large mammals, the hysteresis should be about 7% (Bennett et al., 1986; Ker, 1981). This


- force plate -- film subject TK

2.0 1 DJ 0.9 m [ 4.5

0 400 800

(md

Fig. 2. Comparison between the velocity and the position of the mass centre of the body calculated from the measured vertical ground reaction force (F,) and the same parameters obtained from high speed film recordings at 500 frames s- ’ m five different jumps performed by the same subject. The film coordinates were low-pass filtered at 8 Hz. F, and the vertical ground reaction force was estimated from the film (the vertical acceleration of MCB plus the gravitational acceleration multiplied with the mass of the subject) is included in each panel. The sequence of curves in each panel is given in left uppermost panel. SQJ is the push-off starting from a semi-squatting position, CMJ a push-off after a preparatory counter movement and DJs the push-offs after down downward jumps from 0.3, 0.6 and 0.9 m, respectively. The force plate calculation only gives position changes and not the height of MCB over the ground, therefore, the position

curves were aligned at the minimum height of MCB over the ground calculated from the film.

was considered low and, therefore, neglected in the present calculations.

The muscles acting during the push-off were reduced to three large extensor muscles, one for each joint. At the ankle and the knee joints, the three heads of m. triceps surae and the four heads of m. quadriceps, respectively, were lumped and at the hip m. gluteus maximus was used. Tendon dimensions were obtained from Yamaguchi et al. (1990), and the average of the listed values for each parameter was used. Tendon dimensions are presented in Table 1.

The instantaneous tendon moment arms at t upwm were obtained from the joint angle-moment arm transfer functions as described in Table 2. The estimated tendon forces (FT) were determined by dividing the net joint moments by the lengths of the moment arms, and FT was used to calculate the amount of stored elastic strain energy (E) in the tendons from equation (6). AT was multiplied by 2 before the calculation of E to include both legs. The sum of the stored

elastic strain energy in the ankle. knee and hip extensor tendons (E,) at fupwm was considered to be the total amount of tendon strain energy available to be used during the following take-off.

In order to control the model calculations, the tendon strains at FT were examined. This revealed that the strain exceeded E,,, in several cases, and this was especially evident for the knee extensor tendons. This fact pin points the problems introduced by using data from cadaver studies where the biological age of the subjects generally lies between 60 and 80 yr, the measured dimensions are subjected to age-dependent atrophy and to tissue and fluids losses during the dissections and errors are made when measuring tendon cross-sectional areas (Ellis, 1969). Therefore, the tendon cross-sectional areas were increased until the tendon strain at the knee joints stayed within the strain limit. This resulted in a general increase in the tendon cross-sectional areas of 25%, and the resulting cross-sectional areas at the ankle, knee, and hip joints

298 M. Voigt et al.

load

F Ilm

c max rtraln

Fig. 3. The general force-deformation relationship defining the tendon model. Eli,,, is the maximal tolerated force before failure, E,,, the maximal relative length-change (strain) tolerated before failure, .sT the strain value determining the length of the ‘toe piece’ (see text), K the tangential modulus. The area under the curve at any force level represents the amount

of stored elastic strain energy.

Table 1. Tendon parameters. AT is the tendon cross-sectional area and lo the tendon resting length. The values were calculated as averages of the values presented by Yamaguchi

et al. (1990)

m. triceps m. quadriceps m. gluteus surae femoris maximus

(lumped) (lumped)

A,(IO-‘+m’) 0.49 2.01 0.98 Mm) 0.364 0.231 0.132

became 0.63,2.50 and 1.25 cm2 (one leg!), respectively, which is within the range of cross-sectional areas that can be observed by Magnetic Resonance Imaging in subjects with the same fitness level and in the same age group as used in this study (Voigt, 1994).

Statistics. The Friedman two-way analysis of vari- ance by ranks (k-sample case) was used to test changes

between jumping situations (Siegel and Castellan,

1988). The level of significance was in all cases chosen to be at ~~0.05.

RESULTS

Typical examples of ‘raw’ data from the movement

analysis are shown in Fig. 4. The graphs describe the activation-loading patterns of the two extremes of preloading imposed on the subjects in this study: (1) a slow long lasting loading phase under low average muscle forces represented by the CMJ and (2) a fast short preload under high average muscle forces represented by the DJ 0.9m.

Force plate recordings

The jumping height (A&a) increased significantly after prestretch except for the highest imposed negative loads compared to the situation without preload (Fig. 5(a), upper panel, filled circles). AhMce after CMJs and DJs from 0.3 m were significantly higher than in the other situations, but not significantly different from each other. The results were very similar to the results in the study of Asmussen and Bonde-Petersen (1974) [Fig. 5(a), upper panel, open circles].

The best jump (the maximal Ahh(& performed by each subject in each jumping situation was on average obtained in trial # 7 k 4 (S.D.). Twenty seven percent of the maximal jumps occurred in trial # 11 which was filmed. Although there on average was a tendency towards a decreased performance in trial # 11, the jumping performance in these jumps for all subjects did not differ significantly from the performance at the best trials [Fig. 5(a), upper panel, filled diamonds]. Therefore, the jumping patterns analysed from the films were considered to be comparable to the jumping patterns in the best trials.

E,,, [equation (l)] from the maximal jumps and the jumps from the film recordings are presented in Fig. 5(a) (lower panel). E,,, decreased with increasing preload apart from the highest preload where it increased again. None of the changes were significantly different from each other. This pattern was similar to

Table 2. Least squares polynomial coefficients for transfer functions between enclosed joint angles (0) obtained from film recordings and instantaneous tendon moment arms at the ankle (Achilles tendon) and the knee joint (rectus femoris part of the quadriceps tendon) and the hip (the tendon of m. gluteus maximus) extracted from Spoor et al. (1990), Spoor and Leewen (1992) and Nemeth and Ohlsen (1985) respectively. The least-squares polynomials had the form a+ bO+c@ +d@+e@. A third-order polynomial was used at the ankle joint, a fourth- order polynomial was used at the knee joint and a second-order polynomial at the hip. The resultant moment arms are expressed in percentage of the shank length (ankle) and thigh length

(knee and hip), respectively

Coefficient Ankle Knee Hip

a - 5.03442 x lo- ’ - 8.36305 x 10’ - 1.39085 x 10’ b 1.10511 X 100 3.46853 x 10” 2.94400x 10-l f; - - 4.78432 2.00026 x x lo-’ lo-’ - 4.47360 3.12694 x x 10-2 lo--’ - 6.15768 x 1O-4

e - 7.15577 x lo-’

Mechanical and muscular factors

CMJ DJ (0.9 m)

800 0 ankle 600

l knee 400 - 200 hip

V 0

299

net moments

angular velocities

RF

ST

GA

TA

-800 -600 -400 -200 0 -800 -600 -400 -200 0

(ms>

Fig. 4. Rectified raw EMGs, angular velocities and net joint moments from a typical counter movement jump (left) and a drop jump from 0.9 m (right) (from the same subject). The vertical lines indicates (from left to right) start of the movement or touch down, the time where the body centre of mass is at its lowest point and the time where the toes leaves the ground. TA = m. tibialis anterior, SO = m. soleus, GA = m. gastrocnemius caput laterale, ST = m. semitendinosus, VL = m. vastus lateralis, RF = m. rectus femoris.

GM = m. gluteus maximus.

the pattern found in the original study by Asmussen and Bonde-Petersen (1974) [Fig. 5(a), lower panel, open circles].

The average positive power produced on MCB [Ppos, Fig. 5(b), upper panel] did not increase significantly between SQJs and CMJs, but there was a significant increase in DJs compared to SQJs and CMJs. DJs from 0.3 and 0.6 m were significantly different from the DJ from 0.9 m but not from each other. The average positive power could also be calculated as the average ground reaction force (F,, & during the positive phase multiplied by the corresponding vertical change in position of MCB (s~~~+,~) divided by the duration of the positive phase (t,,,,). The changes in these parameters are shown in Fig. 5(b), lower panel. By comparison of the upper and the lower panel in Fig. 5(b) it can be seen that there are essentially two different ways in which the same maximal jumping height can be achieved (CMJ and DJ from 0.3 m); either by producing low forces over a long time and

distance or by producing a high force over a short time and distance. However, none of the changes in F z.pOos, SMCB. pOS or tpos were significant.

Tendon strain energy

The joint angles and net joint moments, measured and used as input for the calculation of the strain energy stored in the tendons at tupwm are presented in Table 3.

The results from the tendon strain energy caicu- lations are presented in Table 4. Some strain energy (ET) was stored in the leg extensor tendons just to maintain the posture in the SQJs, but also to a lesser extent because most subjects were unable to perform SQJs without any counter movement (Fig. 1, top). The amount of stored tendon strain energy increased from SQJs to DJs from 0.3 m and stayed approximately the same during the DJs. The amount of negative work imposed on the leg extensor muscles that was stored in the tendons was calculated as ET W,,;:%. This

300 M. Voigt et al

a. b.

preload, Wnrg (J)

Fig. 5. Parameters obtained from analysis of the vertical ground reaction force signal during five different vertical jumping tasks expressed as a function of the mean preload (W& (N=6) during each jumping situation. (a) Upper panel: Jumping height calculated from the tlight time (Ah,,&; filled circles = maximal jumps, filled diamonds =jumps recorded on film, open circles = the data from the original study (Asmussen and Bonde-Petersen, 1974). (a) Lower panel: The amount of stored elastic energy in the leg muscles (E,,,) calculated from equation (1) in the text (symbols as above). (b) Upper panel: Positive mechanical power (P,,) performed on MCB during the push-off. (b) Lower panel: Factors determining P,,. Except the data from Asmussen and Bonde-Petersen (1974) each data point represents the mean + SE. (error bars) of the X- and Y-values from the six subjects. spoS reaction force, t,,

is the distance travelled by MCB, F,.,, the average vertical ground the push-off time. The asterisks indicates significant increases compared to the other

jumping tasks (p < 0.05).

Table 3. Joint angles and net joint moments (mean f S.D.) at the time of zero velocity of the mass centre of the body before the push off from six subjects performing five different vertical jumping tasks. Jumps without prestretch of the leg muscles (SQJ) and jumps with prestretch (CMJ and DJs). The joint angles served as input for the calculation of the instantaneous tendon moments and the tendon forces were

calculated from the net joint moments

Joint angles (deg)

Net joint moments (Nm)

Ankle Knee Hip

Ankle Knee Hip

SQJ CMJ DJ (0.3 m) DJ (0.6 m) DJ (0.9 m)

68+9 68&10 67k7 66k8 68+9 105&11 94* 13 loo*11 99+ 14 89+ 16 91+30 89k21 103 * 12 103+11 90+ 12

94*32 148k 131 174+131 94+45 161+ 73 296k 130 506k115 6405186 563+151 6@O+ 188 125+47 304+74 271* 102 210* 122 265 + 62

amount was highest during CMJs and decreased with increasing amount of negative work imposed. Basi- cally, E,,,% calculated from equation (1) is an expression of ET W&i %. The two parameters were, therefore, highly correlated but different in magnitude with ET W”i:% always the highest. The amount of stored elastic enegy in the tendons available for positive work was calculated as ET Wi:%; and it increased

from SQJs to DJs from 0.3 and stayed approximately at the same level during the DJs thereby following the same patterns as ET.

Correlation analysis

The correlation between ET and the work output during the push-off ( W,,) and between ET and jumping performance (A.h,& was positive, but low and


Table 4. The average amount (N=6) of the negative preload work stored as elastic energy in the tendon available for positive work (ET) in five different maximal vertical jumping tasks. Jumps without prestretch (SQJ) and jumps with prestretch (CMJ and DJs). The data were calculated from the model described in the text. ET was calculated as the sum of the tendon strain energy stored at the ankle, knee and hip joints respectively (EAN + EKN + En,). The amount of elastic energy stored during the preload was calculated as E, Ck’,$?‘a. The possible amount of tendon strain energy available for positive work during the take-off was

calculated as E, WP;: %

SQJ CMJ DJ (0.3 m) DJ (0.6) DJ (0.9)

EJ&, I 13 17 20 15 E,,(J) 41 91 103 107 118 En, 6 23 9 24 19

E, 54 127 156 151 152

E-, cv";; (%) 0 54 46 23 17 E, w,;: ("A) 10 21 27 28 26

not significant (r = 0.620 and r = 0.538, respectively). Correlations between ET W”;:% and W,,, and ET W,$% and AhhlCB were positive and rather high (r = 0.746 and r =0.997, respectively) but only the latter (Fig. 6, upper panel) significant. The three lower paneis in Fig. 6 show negative relationships to the average ground reaction force during the negative phase (F,,&, the downward distance travelled by MCB during the negative phase (AIMcrincg) and the average velocity of MCB also during the negative phase (+.KYB,~~~).

Electromyographic analysis

The analysed IEMGs are presented in Fig. 7. The drastic increase in TA IEMG during the negative phase was due to a low activity level in TA during the positive phase. but also an indication of that TA pulls the tibia forward during the period of prestretch. With the exceptions of TA and VL the calculated IEMGs from the muscles during the negative phase in CMJs were low because they were gradually activated over a long prestretch and eventually only fully active at the end of relatively long negative phase (Fig. 4 left). Generally, the activity ievels of the individual extensor muscles were lower during the negative phase than during the positive phase with two exceptions, namely ST and VL where the opposite was the case. The most evident changes in activity during the positive phase were seen in the biarticular muscles (Fig. 7, filled symbols). The general increase in RF and decrease in ST were significant and there was a tendency to a general increase in GA, but only significant during DJ from 0.6m. Due to large variations in the IEMGs, none of the changes in activity of the monoarticular extensor muscles were significant.

DISCUSSION

Methodological considerations

Application of musculo-skeletal parameters from cadaver studies. Body segment parameters, tendon cross-sectional areas, lengths and moment arms used

60

(%I

(N)

0 CMJ

l DJ (0.3 m)

v DJ (0.6 m)

1 . DJ (0 9 m)

0.25

r = -0.844 (p < 0.08)

\ D

A

AI MCB.“y? 0

.

Cm)

2.5

-1 (ms 1

” MCEl.risg

0.32 0.38 (ml

jumping performance

Fig. 6. Correlations to jumping performance. E, JV”;: is the amount of the elastic energy stored in the tendons (ET) in percent of the imposed negative work (WDeg) stored in the tendons. F,, aY. neg the average ground reaction force during the negative work phase. AlhfCB.“=% is the average distance travelled by MCB during the negative work phase. uh(c8.neg is the average downward velocity of MCB during the negative work phase. CMJs are open circles, DJ (0.3 m) are filled circles, DJ (0.6 m) are open triangles and DJ (0.9 m) are filled

triangles. For further explanation see text.

in the present study were obtained from cadaver studies. A considerable inter-individual variation in the size of these parameters should be expected due to biological variation, but to our knowledge any well

302 M. Voigt et a/.

negative phase positive phase

r

--

0 iA

v so l GA . ST

0 VL n RF a GM

preload, Wneg (J) Fig. 7. Integrated EMGs from seven leg muscles during the push-off in five different maximal vertical jumping tasks with increasing preload ( Wnc8). TA = m. tibialis anterior, SO = m. soleus, GA = m. gastrocnemius caput laterale. ST=m. semitendinosus, VL=m. vastus lateralis, RF=m. rectus femoris, GM =m. gluteus maximus. The open symbols represents the monoarticular muscles and the filled symbols the biarticular muscles. Each data point represents a given jumping task. The preload was defined as the negative work performed on the mass centre of the body and is represented by the mean (N = 6) from each jumping situation. The IEMGs are presented as the mean+ 1 SE. The percentage changes were calculated according to equations (5a) and (5b) in the text and each subject was represented with an average of 11 trials

in each jumping task.

defined relationship between each of these parameters and some anthropometric parameter that can be measured non-invasively on subjects in viva (e.g. body height, body area, segment length, condyle width, etc.) has not yet been proven to be valid in order to preserve the information about the inter individual variation in inverse dynamic calculations or model calculations including such data. Therefore, the results presented in Table 4 must be considered to be a measure of an average person and the variation has been omitted because it does not give any relevant information.

Model calculations. The net joint moments around the ankle, knee and hip joints were used to estimate tendon force by dividing the net joint moments with tendon moment arms. Thus, if there was any co- contraction between extensors and flexors, the muscle force estimated from the net joint moment was under- estimated in proportion to the degree of co-contraction. The most important antagonists for the extension of the ankle, knee and hip joint are TA, the hamstrings and m. iliopsoas; however, from inspec- tions of the raw EMG levels in TA and ST at t uDvm expressed in microvolts it was generally seen that the activity was low. EMG in m. ilio-psoas was not measured.

At the hip and the ankle the tendons of several extensor muscles that might be active were ignored in the calculations and this simplification tends to

overestimate the amount of stored strain energy in the tendons.

Our model approach includes major simplifications and in the present study we could not make a satisfactory validation on the calculation of tendon strain energy. However, in a recent study (Voigt et al., 1994) we estimated the influence of tendon work on the mechanical efficiency of the muscle-tendon complex during hopping by application of the same methodology as described here. As a control we calculated the mechanical efficiency of the contractile machinery during concentric muscle action. The efficiency was estimated to be 0.21 which was considered to be a satisfactory estimate in comparison to the measured efficiency of 0.25 (Haan et al., 1989).

Jumping performance

It should be noted that the jumping heights reported in this study (total range=0.222-0.427 m) are low compared to jumping heights of e.g. trained volleyball players in other jumping tests (e.g. sergeants jumps). In order to simplify the calculations and the interpretation of the results the subjects were instruc- ted to hold their hands on the hips during the jumps. Consequently, jumping technique was restricted.

Tendon strain energy and jumping performance

We found that on an average 26 f 3% of the mechanical energy imposed during the preloading was


stored in the tendons of the leg extensor muscles and available in addition to the mechanical work produced by the contractile elements during the positive work phase. We did not attempt to estimate how much of the stored energy was transferred to the environment or lost as eccentric work on the muscle fibres during the push OR however, the correlations between the amount of stored elastic energy in the tendons (E,) and the total positive work (W,,,) and ET and the jumping performance (Ah& were positive but weak and insignificant. Therefore, we conclude that it was not the amount of elastic energy stored in the tendons by the prestretch loads that optimised the jumping performance.

Anderson and Pandy (1993) have presented a very detailed analysis of muscle-tendon action during SQJs and CMJ by comparing experimental data and the computed optimal control solutions to simulated maximal jumping of a four link segment model driven by eight musculo-tendon actuators. The subjects jumped 5% higher in the CMJs than in the SQJs, but the model jumped 2% lower during the CMJs than the SQJs, and the model calculations could not re- solve whether the tendon elasticity was responsible for the difference observed experimentally. Several ques- tionable features of the musculo-skeletal model used (Pandy et al., 1990) could explain the above mentioned inconsistency. (1) The mechanical properties of the series-elastic component (SEE) defined in the model of the musculo-tendon actuator corresponds to the mechanical properties of the active muscle fibres (i.e. the cross-bridges). The active muscle fibres and the tendons seem to have the same mechanical properties because they stored equal amounts of elastic energy [see Anderson and Pandy, 1993, Fig. 8(a)] which is impossible. The elasticity of the contractile machinery itself (Alexander and Bennet-Clark, 1977) and the possible effects of potentiation of the contractile machinery as a consequence of the prestretch (Cavagna et al., 1968) must be considered to be insignificant in comparison to the positive work output from the muscle-tendon complex due to the small energy potential of these mechanisms in comparison to the energy potential of tendon elasticity and regulation of the force-length-velocity relationship of the muscle fibres (Ettema et al., 1990). (2) The instantaneous origin to insertion lengths of the musculo- tendon actuators was defined as the linear distance between the origin and insertions points. This defini- tion ignores the anatomical dimension and the instantaneous changes in the tendon moment arms and the muscle forces calculated to drive the model is very sensitive to the lengths of the instantaneous tendon moment arms (Voigt et al., 1994). (3) The loaddeformation functions used for the tendons in the model are linear, and this will tend to overestimate the contribution of tendon work compared to real tendons with the characteristic non-linear 1oadAeformation relationship.

Activation-loading dynamics

The muscle-tendon dynamics during the prestretches were deduced from the relationships shown in Fig. 6. ET W,,;: % can also be expressed as AlT A&‘, where Al, is an estimate of the average tendon length change and Al,, is an estimate of the average origin- to-insertion length change, because the force acting over the muscle fibres and the tendons is always the same. The average ground reaction force is an estimate of the average muscle force, the distance travelled by MCB during ground contact is an estimate of the average origin-to-insertion length change of the muscle-tendon complexes involved, and the velocity of MCB during ground contact is an estimate of the average velocity of the origin-to-insertion length change. Consequently, the correlations presented in Fig. 6 can be summarised in the following way: optimal jumping performance after a prestretch is obtained when the prestretch is performed slowly and under a relatively low average force, consequently with a short and slow stretch of the muscle fibres in relation to tendon length changes (i.e. when AITAl~,’ is large). Suboptimal jumping performances after prestretches were obtained when the prestretches were performed fast under high forces and with long and fast stretches of the muscle fibres in relation to the tendon length changes.

These observations can be interpreted in the light of the findings of Griffiths (1991) obtained from in situ and in vivo measurements of muscle-fibre-tendon- length changes in the cat medial gastrocnemius muscle. Muscle stretches at different velocities over the same length were initiated at the onset of maximal stimulation. During the slowest stretches, the muscle fibres shortened against the tendon without any lengthening and reached high forces. At faster stretches, there was slippage in the muscle fibres resulting in loss of force (and energy !) probably because the speed of the loading rate imposed by the stretch in this situation exceeded the rate of the force development in the muscle fibres that was determined by the dynamics of the activation<ontraction coupling. The same type of muscle-tendon dynamics was predicted by Hof et al. (1983) in the triceps surae muscle during walking by means of EMG-to-force processing. They concluded that ‘concerted contractions’ or muscle fibre shortening against the tendons during eccentric muscle-tendon action in a stretch-shortening cycle favours the output of mechanical work because it enhances the spring-like behaviour of the muscle-tendon complex and prevents excessive muscle-fibre lengthening and loss of energy. Excessive stretch of the muscle fibres might shift the contractile state in relation to the optimum of the force-length-velocity (and power) relationships (Partridge and Benton, 1981) significantly and, consequently, deteriorate the capacity of the muscle fibres to perform positive work during the following concentric phase.

104 kl. Voigt er ui

It is assumed that the patterns of muscle activation and loading applied by Griffiths (1991) from a muscle-tendon point of view are comparable to the prestretch situations applied in the present study. In order to compare the activation patterns in relation to the loading in CMJs and the DJs, it should be noted that in CMJs, the point where MCB has its fastest downward velocity corresponds to touch down in DJs i.e. the onset of loading. This is (Fig. 4, left) approximately in the middle of the prestretch as indicated by the angular velocities of the joints and the EMGs of the extensor muscles. The subjects performed best during CMJs and DJs (0.3 m) and in these jumping situations the timing of the onset of muscle activation and the loading during the prestretching was probably adjusted so the stretching of the muscle fibres was minimized and a shift to suboptimal regions of the force-length-velocity relationship avoided. Con- sequently, the possibility of the muscle fibres to perform positive work optimally in concert with a simul- taneous effective release of the strain energy stored in the tendons was conserved.

These results are comparable to the results of Avis et al. (1986) where they applied an experimental protocol inspired by Asmussen and Bonde-Petersen (1974). They concluded that during a standardised

maximal stretch-shortening cycle the prestretches increased the amount of energy released from the ten-. dons during a prestretch, but the total power outpui did not increase compared to a push off without prestretch load due to a loss of power generated by the muscle fibres caused by a difference in muscle fbrc length at the time when the push off started.

It can be concluded that a regulation of the position of the muscle fibres in the force-lengtbvelocity reiation by a proper coordination of muscle activation and external loading is necessary to optimise the work output from the muscle-tendon complex in stretch shortening cycles like jumping with prestretch.

Specijic actions of biarticular muscles

Transport of power produced by wlonoarticular muscles. Several studies have shown that the biarticular m. gastrocnemius transports mechanical power generated by the more proximal and monoarticular parts of m. quadriceps in distal direction, when these muscles are co-activated (Bobbert et al., 1986, Bob- bert and Ingen Schenau, 1988; Gregoire et al., 1984; Ingen Schenau et al., 1987; Soest et al.. 1993). The mechanical advantage of these actions is an increased efficiency in the transformation of muscle power via

a. SQJ b. l SQJ

- individual v CMJ . average v DJ (0.3 m)

100

onkle

0 -100 0

(X push off time)

Fig. 8. Time- and amplitude-normalised net joint powers from ankle knee and hip joints during the push-off in vertical jumping. (a) Individual curves (N =6) and average curves (symbols) from jumps starting from semi squatting position. (b) Average curves (N =6) from three different jumping tasks. Jumps starting from semi-squatting position (SQJ), jumps preceded with a preparatory counter movement (CMJ) and jumps preceded with a downward jump from 0.3 m (DJ). The time was normalized to the push-off time and the net joint powers were normalized to peak positive amplitude. The vertical lines indicate the time where

the toes leave the ground.

Mechanical and muscular factors JOT

joint rotations to translation of MCB (Ingen Schenau, 1989).

The increase in the activities of the biarticular muscles in the positive work phase (Fig. 7, right panel) between the SQJs and the jumps with prestretch strongly sugge$ts the action of this mechanism. How- ever, the significant and very prominent increase in the activity in RF indicates a pronounced transport of muscle power via RF from the hip to the knee. The observed change in muscle activity was supported by the observed changes in the net joint powers generated at the hips and the knees. In Fig. 8(a) (see average curves) the fast decrease in the hip net joint power to negative values (eccentric muscle action) and the phase shift to the right of the knee net joint power in relation to the hip net joint power indicates the transport of muscle power from the hips to the knees via RF during the SQJs. The increase in activity in RF between the SQJs and the jumps with prestretch (Fig. 7) was reflected as an increase in the phase shift between the hip and the knee joint powers and as an increase in the amplitude of the negative hip joint power at the end of the take off [Fig. 8(b)]. The transporting action of GA was indicated by the changes in IEMG, but was probably not reflected in the net joint powers at the knee due to a dominating action of the knee extensor muscles.

The transporting action of RF could not be quanti- fied with the present methodology. The power trans- ported by GA during maximal one-legged vertical jumping has been estimated to account for 26% of the work produced by m. triceps surae at the ankle (Bob- bert et al., 1986) and 22% of the ankle work in two-legged SQJs (Soest et al., 1993). The biarticularity of GA accounted for 3% of the jumping performance (calculated as Ah,,,) in SQJs (Soest et al., 1993) and it is assumed that the transporting action of RF observed in the present study adds significantly to this fraction.

Control of direction of movement. It has recently been demonstrated that the biarticular leg muscles are specifically engaged in the control of the direction of the force vector under the foot by distributing the net joint moments over the hip and knee joints by a reciprocal activation pattern between the hamstrings and RF (Ingen Schenau et al., 1992: Jacobs and Ingen Schenau, 1992).

In vertical jumping the movement is constrained in order to keep the MCB in a vertical movement path and prevent rotational actions around MCB. Figure 9 illustrates that in the typical prestretch situation the body has a tendency to rotate forward and this rotation must be counteracted by directing the resultant ground reaction vector ventral to MCB (Fig. 9, left). During the following take-off, the body has a tendency to rotate backwards, and this rotation must then be counteracted by directing the resultant ground reaction force vector dorsal to MCB (Fig. 9, right).

The reciprocal change in the activity of ST and RF between the negative and positive phase in the jumps

down

120ms t upwm + 120 rns

Fig. 9. Typical example of body position, location of the mass centre of the body (MCB) and the direction of the resultant ground reaction vector at tlipwm (middle), 120 rn.\ before (left) and (120 ms) after (right). The curved arrouh indicates the direction of the rotation of MCB introduced b) the movements of the body segments that has to be ctmnter-

acted by reaction forces.

with prestretch (Fig. 7) indicated the control of direction. The low activity in RF and high activity in ST during the prestretch directed the ground reaction vector forward (the action vector backwards) and

a shift to high activity in RF and low activity in ST, as seen during the take-offs, directed the ground reaction vector backwards (the action vector forwards) and. thereby, the rotations around MCB described in Fig. 9 were controlled. When the work produced by the muscles during the take-off is used to counter act a rotation around MCB, it is lost in reiation to the achievement of jumping height, and therefore the rotational actions should be minimised during optimal vertical jumping.

Acknowledgements-This study was granted by The Danish Research Academy, The Danish Elite Sports Association and The Danish Research Council of Sports.

REFERENCES

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Alexander, R. McN. (1989) Elastic Mechanisms in Animcil Mouement. Cambridge University Press, Cambridge.

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Asmussen, E and Bonde-Petersen, F. (1974) Storage of clasric energy in skeletal muscles in man. Acta Physiol. Stand. 91, 385-392.

Avis, F. J., Touissaint, H. M., Huijing, P. A. and In&en Schenau, G. J. van (1986) Positive work as a function of eccentric load in maximal leg extension movements. Ew. J. Appl. Physiol. 55, 562-568.

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Bobbert, M. F., Huijing, P. A., Ingen Schenau and Ci. J. van (1986) An estimation of the power output and work done

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Ingen Schenau G. J. van (1989) From rotation to translation: constraints on multi-joint movements and the unique action of biarticular muscles. Hum. Mop. Sci. 8, 301-337.

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lngen Schenau G. J. van, Boots, P. J. M., Groot, G. de, Snackers. R. J. and Woensel, W. W. L. M. van (1992) The constrained control of force and position in multi joint movements. Neuroscience 46, 197-207.

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APPENDIX

The general tendon model

A general load-deformation relationship (Fig. 3 in the text) was approximated by a quadratic function (Ingen Schenau, 1984) as follows:

(Al)

where Fr is the tendon force, k a constant dependent on tendon cross-sectional area, the Young’s modulus for tendon tissue, the maximal tolerable strain, the length initial non- linear part and the tendon resting length and Al the tendon length change.

The ability to store elastic energy (E) in tendons was calculated by integrating the left-hand side of equation (Al) and after insertion of FT and substitution of AI both obtained from equation (Al) the following equation was found:

E=;(kAl’)Ai=; FT L4.2)

The Young’s modulus (Y) is defined as the stress divided by strain and the coefficient of elasticity for a specific tendon (K) was determined as the slope of the tangent (AF’r AI - ’ ) to the linear part of their load-deformation relationship:

l!z\ y&% / AFT Y&

Al

0

*-=---=K. Al lo

(A3)

r,

where A, is the cross-sectional area of the tendon and I, the tendon resting length.

Then the ultimate load (Fnm) could be expressed in two ways:

where E,,, is the maximal tolerable strain and sr the length of the initial unlinear part of the loadcleformation curve. because Kl, = YA, according to equation (A3)

Mechanical and muscular factors 30:

and in equations (A4) and (A5) were equalled, k isolated and substituted in the rightmost expression in equation (A2) and 2

(A5) a general equation obtained: -

according to equation (Al). Then, the rightmost expressions (A61

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