LOWER EXTREMITY MUSCLE ROLES DURING     TWO-LEGGED PUSH-OFF PHASE

Grega Hočevar, dr. Vojko Strojnik

(Faculty of Sport, University of Ljubljana, Slovenia)

(grafi izpuščeni) 

Abstract 

       The aim of the present study was to reveal the global (agonistic/antagonistic) roles of lower extremity  muscles during the two-legged push off in a horizontal lying position. These muscles were vastus lateralis, vastus medialis (VAS), gluteus maximus (GLU), biceps femoris (BF), rectus femoris (RF), soleus (SOL)  and gastrocnemius (GAS). One male athlete participated in the study. He performed 5 push-offs in 3 different starting positions. The kinematic trajectories were measured. The mathematical model of human body was applied, the six muscular forces being the outer variables determining the action. The roles have been defined according to partial derivative of front surface force with respect to muscles' forces, that followed Lagrange-Euler equations, describing the motion of the model. Comparing the values of how much muscles could affect the movement, it is possible to set the criterium of motor control sensitiveness, which defines the boundary limit of a large range of starting positions, for which the general, close to optimal muscle coordination pattern assures performance with almost neglecting reduction of performance.      

Keywords :  muscle activation, coordination, agonist, push-off, motor control   

Introduction

    The understanding of mechanics of human movements is essential for the improvement of the performance in many sports. Measurements concerning intermuscular coordination are therefore very important. Applying a mechanical model helps in analysis and better understanding of movement dinamics. The model may enable us to define exact muscular roles during a certain action. The model has to be sophisticated yet simplified enough in order to get precise results. When applying the model, the initial presumptions and relevant parameters of the model are of great importance.

       Several studies have been made concerning intermuscular coordination during explosive movements. There is always only one coordination pattern that results in optimal performance for simple, stereotyped actions. Confining to vertical jumps or actions like push-off, the studies clearly show proximal to distal activity succesion of lower extremity muscles (Bobbert and van Ingen Schennau, 1988). But starting positions are never exactly the same. Small deviations in initial position implies motor control system being ultimately capable of generating adequate muscle activation patterns. Sometimes it may lead to unsuccessful and less-controlled movement, which is less effective and consequently demands higher energy cost. However, there exists a certain muscle activation pattern that yields close to optimal behaviour over a certain range of starting positions. That is how the nervous sistem reduces the complexity of the problem of generating optimal coordination pattern (van Soest and van Ingen Schenau, 1998). This is possible only as long as certain muscle roles deviate as much as the reduction of performance is no more acceptable.   

       The aim of the present study was to reveal the global (agonistic/antagonistic) roles of leg muscles during the two-legged push off in a horizontal lying position by applying a mathematical model of human body. Comparing the values of how much muscles could affect the movement, it is possible to set the criterium of defining the boundary limit of a large range of starting positions, for which the general, close to optimal muscle coordination pattern exists.     

Methods

Measurement of the movement

   The push-offs were performed in horizontal direction using leg press device (model M051, Technogym, Gambettola, Italy). The back support was lowered to the horizontal position so that the push-off in a lying position in a backward direction was possible (Figure 1). The force plate (model 9287, Kistler, Winterthur, Swiss) was attached to the front surface. One male (age 26 years, height 176 cm, mass 68 kg) participated in the study. He gave his informed consent prior the experiment, while the study was conducted in accordance with the Helsinki-Tokyo declaration.

    The athlete pushed off with maximal power 5 times at 3 different starting positions. They were chosen so that positions 1 and 2 were more ergonomic (usual) and position 3 was less ergonomic. The angular velocity of knee joint        extension was measured with goniometer (Biometrics, Gwent, UK) fixed on the left knee joint. A potentiometer (custom made), connected to an iron wire that was fixed on the left hip, was used to measure a distance between the hip and the fixed front surface. The horizontal hip velocity was obtained as a time derivative of hip coordinate in time. The kinematic trajectories of the body coordinates were calculated from hip coordinate and knee angle in time. In order to prevent injuries the actions were free only in the first 15 cm of push-offs.

    The activations of 7 muscles were measured with EMG telemetric device (Biotel 88, Glonner, Munich, Germany). The bipolar EMG electrodes (Hellige, Freiburg, Germany) were placed on the skin above the muscles of the left leg and were separated by 22 mm (centre to centre). The skin was prepared in order to reduce interelectrode resistance under 5 kV. The electrodes were placed on muscles vastus lateralis and vastus medialis (VAS), gluteus maximus (GLU), biceps femoris (BF), rectus femoris (RF), soleus (SOL)  and gastrocnemius (GAS) in accordance with SENIAM recommendations (Hermens et al., 2000). The EMG and all other signals were acquired at 1000 Hz. In order to quantify a muscle activation the raw EMG signal was rectified, averaged and smoothed with low-pass filter. The time dependent EMG signal was transformed proportionally to the relative muscle activation (Enoka, 1994), in the following text the relative muscle activations are denoted by a_i . The values of  (dimensionless) a_i  refer to the maximal activation of the i-th muscle, measured at maximal isometric contraction corresponding with a_i = 1. According to the muscle that acts with force within interval (0, maximal muscle force), the respective  a_i  lay within the interval (0,1). The calculation of value a_VAS was based on average of EMG signal values of muscles vastus lateralis and vastus medialis.

    The time dependent coordinates of body joints and muscle activations a_i were calculated as an average of all push-offs for each of three starting positions.

Description of the model

   The 2D mathematical model of human body was applied, the six muscular forces being the outer variables determining the action. The model included 4 rigid, one-dimensional body segments (foot, shank, thigh and trunk) connected with muscles. The model could move only in sagital plane. The model of a single muscle was extremely simplified. It was described as a no mass bond, acting with force between two points of attachement to the bones. The muscle force-velocity and force-lenght dependences were neglected. The coordinates of muscle attachments to the bones and other model parameters were determined according to Bobbert and Huijing (1990).

Lagrange-Euler equations and the relevant derivatives

    In order to reveal the muscle roles during the push-off phase, the Lagrange-Euler equations describing the motion of the model, were applied.

    The body position was precisely determined with two angles j₁ and  j₂ .The first one is the angle between vertical axis and foot segment while j₂ is the angle between vertical axis and shank segment. The kinetics of the body was described with Lagrange - Euler equation with two angles j_a = j₁ , j₂ being the generalized coordinates:

                                     (1)

The quality L denotes the difference between kinetic energy T and potential energy V of the body, F_j forces of six muscles and r_j their respective coordinates of attachement. The equation (1) is followed by two coupled nonlinear second order differential aquations:

                                A₀   + B₀ + C₀ = G₀                     (2)

                                D₀   + E₀  + F₀ = H₀                                (3)

with coeficients  A₀ , ... , H₀  being very complex mathematical functions, derived from equation (1). The coeficients  A₀ , ... , F₀ were functions of two coordinates  j₁ and j₂  and their time derivatives. The coeficients G₀ and H₀ were functions of muscle forces, consequently depending on a_i (because of the direct relation between muscle force and its relative activation a_i). The pushing force F (front surface force) could be expressed with angles j₁ and j₂  and their first and second-order time derivatives and was therefore connected with muscle activations a_i (coeficients G₀ and H₀) according to equations (2) and (3). The angle between vertical axis and thigh segment, denoted by j₃ , was calculeted from values of angles  j₁  and  j₂ .

   The relevant quality, that describes the global muscular roles, was said to be the partial derivative of front surface force F (perpendicular component) with respect to muscle activations a_i ( D_F/a ):

                                                    .                       

The derivative D_F/a(t) depend on model parameters, time dependent generalized coordinates j₁ and j₂  and their time derivatives. With respect to measured body kinetics, the derivative  D_F/a  based on Lagrange - Euler equation enabled us to determine the global muscle roles during the push off phase. It specified a sensitiveness of the front surface force to muscle activations. Greater the derivate D_F/a value, greater change in force will result at the same activation change. Positive or negative derivative values signified the certain muscle as agonist or antagonist, respectively.  

Results

   The starting and final segment angles of three different starting positions are presented in Table 1. The average times, front surface forces durig push-off and average terminal velocities of hips are presented in Table 2 for all starting positions. It is well seen that the average terminal velocities were almost the same at positions 1, 2 and 3 while there were only small differences between times of push-offs and average front surface forces as well. The measured EMG values during push-off phase were transformed to get the relative muscle activations in time a_i (t). The average values of a_i (t) were calculated for all starting positions regarding all push-offs (Table 3). The average muscle activation of VAS, RF and GLU during push-off were more than two thirds of their absolute maximal values (corresponding with a_i=1). In the average the muscles VAS and RF were the most, while BF was the least activated during the push-off phase. The overall average value of muscle activations was 0.57 . For each muscle the time dependent derivative  D_F/a(t)  was calculated (Figures 2-7). During the push-off the values were negative only for musculus BF (neglecting values around 0 for GLU at starting position 2). The differences between time dependent derivative  D_F/a  for starting position 1 and 2 were quite small comparing to starting position 3 for VAS, GLU, BF, RF (Figures 2-5), while there was practically no differences for SOL and GAS (Figures 6,7). The derivative tended to increase at the final part of push-off for muscles VAS, GLU and RF, while it tended to decrease for muscle BF. For example, 1% higher activation of muscle VAS would have caused   2.0 N higher front surface force at the start of the push-off while 1% higher activation of muscle BF would have lowered front surface force at the start of the push-off for 1.8 N at the starting position 3. 

Discussion

   The most important findings of this study were differences in sensitiveness of front surface force among the analysed muscles. Muscles GLU, VAS, RF, SOL and GAS proved to be agonists, while BF role was antagonistic. Among three different starting positions the more ergonomic ones (positions 1 and 2) showed quite similar sensitiveness of all muscles. The muscles' roles at less ergonomic starting position 3 where heel was more distant from front surface, was distinctive. Their sensitivity to activation was much greater than in other two positions. Interestingly, no differences among positions were found in SOL and GAS (Figures 6 and 7). 

   However, the above conclusions are to be discussed in more detailes. The push-off phase is very complex motoric action. The front surface force is not the only quality determining the efficassy of the movement. Each muscle has to be regarded as flexor or extensor in every single joint as well. In another study it has been shown that every muscle is two-fold extensor and one-fold flexor or two-fold flexor and one-fold extensor, according to ankle, knee and hip joint (Hočevar, 1999). Therefore the global role of single muscle is only a sum of flexor/extensor roles in the joints. For example, the differences between the average activations of VAS and BF were more than twofold (Table 3). That is because the muscles have different global roles. According to derivative of  force with respect to the muscle activations D_F/a that follows from equation (1), the global muscle roles could be determined for single muscle. The calculations showed that theoretical enlargement of all muscle activations result in bigger force on the front surface except muscle BF (Figures 2-7). The study showed BF is antagonist and other muscles (GLU, VAS, RF, SOL and GAS) are agonists during push-off phase for all starting positions.

    Because of the existence of a certain muscle activation pattern that yields close to optimal behaviour over a certain range of starting positions, a small perturbations of starting position imply very small deviations of performance. In such cases, a single general coordination pattern is sufficient in order to perform over a wide range of positions without almost any reduction of performance. The counteracting such small state perturbations, assuring the reduction of performance as low as possible, is guaranteed by feedback mechanisms. The first order being so called preflexes, the viscoelastic muscle properties (muscle force-lenght-velocity relation), that counteract segments' position disturbances without any time delay (van Soest and van Ingen Schenau, 1998). If perturbations of starting positions increase significantly, the motor controll is impaired. In Figures 2-7 the muscle influences can be compared for different starting positions, revealing their roles defined with derivative of front surface force with respect to muscles' activation D_F/a. If the starting position 3 is compared to 1 and 2 for muscles VAS, GLU, BF and RF, it is obvious that the values of derivative D_F/a are three times larger in starting position 3. It means that a small change in single muscle force at starting position 3 implies not only much bigger front surface force, but also changes in joint torques. The consecutive increase of the co-contraction in certain joints is folowed by lesser degree of effectiveness and higher degree of consumption of the energy. If it is to be so, the small deviations of single muscle activation from general coordination pattern at starting position 3 lead to bigger deviations in the trajectories of movement as well. The general coordination pattern could also be applied in less ergonomic starting positions (like position 3), but higher peripheral feedback mechanisms have to be assured. The derivative D_F/a could therefore be the measure of the range of starting positions, where the general coordination pattern could be applied and where the motor control is still very high.        

Conclussion

   The present study revealed the six muscles' roles during the push-off phase. The muscle BF showed to be antagonist while other muscles VAS, GLU, RF, SOL and GAS were agonists. According to motor control sensitiveness, it concerned two essential findings. In the first place, the sensitiveness is greater at the final part comparing to the start of the push-off, and secondly, the sensitiveness is greater when starting position is less ergonomic (i.e. unusual). The last two findings imply the conclussion that the motor action is more easily controlled at the start of the movement and within certain interval of starting positions (so called ergonomic starting positions) comparing to its final part and unergonomic positions. From a motor control point of view, this is a favorable situation since there is no need to have a great number of motor programmes that are very specialized for specific tasks and conditions.

References 

1.   Bobbert F., Huijing P.A. (1990). Length and moment arm of human leg muscles as a function of knee and hip joint angles. Journal of Applaied Phisiology, 61:453-460

2.   Bobbert F., van Ingen Schenau G. J. (1988). Coordination in vertical jumping. Journal Biomechanics, 21: 249-262

3.   Enoka R. M. (1994). Neuromuscular Basis of Kinesiology. Cleveland: The Cleveland Clinic Foundation.

4.   Hermens H.J., Merletti R., Rix H., Freriks B., (2000). Seniam Deliverable 8, Roessingh Research and Developement b.v., Enshede.

5.   Hočevar G. (1999). Vloga mišic pri sonožnem odrivu. (Diploma), Ljubljana, Fakulteta za matematiko in fiziko.

6.   Van Soest A. J., van Ingen Schenau G. J. (1998). How are explosive movements controlled. Latash Mark L., Progress in Motor Control. Volume one: Bernstein's Traditions in Movement Studies, Pennsylvania State University, 361-387

Legend 

Table 1: The starting and final body segment angles. 

The angles were measured between vertical axis and the certain segment. The distance between hips and front surface were constant for all starting positions. The vertical distance between foot and frontal plane (the horizontal one) of trunk segment were 37 cm, 20 cm and 12 cm for starting position 1, 2 and 3, respectively. The foot segment was quite approached to the front surface at starting positions 1 and 2 and distant for starting position 3. 

Table 2:  Times, forces and velocities of the body during the push-off.

The velocities were very similar no matter the starting position was the least ergonomic. Longer time of the push-off phase is directly connected with lower front surface force and vice versa.        

Table 3: The average (dimensionless) muscle activations over all push-offs and starting positions with their deviation values.

The muscles VAS and RF were most activated during the push-off while muscle BF was drastically the least activated. The overall average of average muscle activations was 0.57.

Figure 1:  The body model

The body model is composed with four segments, the joints (ankle, knee, hip) marked with small circles. The body position is exactly defined with angles j₁ and j₂. The left rectangular is front surface tension measuring device, the bottom one is the back support was lowered to the horizontal position.

Figures 2-7: The front force derivative according to muscles

The calculations of the derivative gave negative values only for muscle BF, showing its antagonistic role durig push-off phase. Comparing to starting positions 1 and 2 (fat and thin continuous lines, respectivelly) the derivative values for starting position 3 (dotted line) are distinctive for muscles VAS, GLU, BF and RF, while there are practically no differences between derivatives for muscles SOL and GAS.