Patterson, C.W. (2010)
ASSESSMENT OF DYNAMIC KNEE MOMENTS AND POWERS
A Case Study Comparison of Two Collegiate Soccer Players
The contraction of the quadriceps femoris muscle group produces a moment that results in the extension of the knee joint with the muscular contraction caused by the K4 power burst. The first phase of the methodology in the current study was the development of a formula for calculating muscular contraction moments and motion power from anthropometric and kinematic measures. The second phase was the application of the formula to assess the muscular contraction moment and resulting kicking power production of two collegiate soccer players, one of whom was recovering from a grade 2 anterior cruciate ligament (ACL) strain. Despite the formula predicting that, from anthropometric data, the rehabilitating player would produce higher moments and powers, the opposite occurred with the lower moments and powers attributed to the ACL injury.
The dynamic extension of the knee is a vital part of many sports techniques such as shooting in soccer with the production of a powerful extension being a determining factor in technical performance. The extension is produced by the K4 power burst which initiates the contraction of the quadriceps femoris muscle group which pulls the lower leg up, rotating it around the knee joint’s axis of rotation (Winter, 1987; Lelas et al., 2003; Strike, 2009). The extension of the knee joint is controlled by the anterior cruciate ligament (ACL) as the ligament prevents the joint from hyperextending thus offering protection to the musculature around the joint from excessive stresses (Grood et al., 1984; Liu-Ambrose, 2003; Behnke, 2006). Grood et al. (1984) and Bobert & Harlaar (1992) state that the knee extension moment rises, during the initial stages of the extension movement before decreasing or plateauing, respectively. Grood et al. (1984) attributes the initial rise in quadriceps muscle group contraction forces to the short moment arm formed by a flexed knee, a moment arm which increases as the knee extends resulting in lesser muscular contraction forces to be required for motion. In their analysis of separate muscles in the knee extension, Bobbert & Harlaar (1992) show that the reported plateauing occurs in the biceps femoris and the vastus lateralis but not in the rectus femoris and vastus medialis muscles despite their high levels of electromyographical activity.
A multitude of reasons have been suggested as sources for ACL injuries, including an imbalance between the strength of the quadriceps femoris and the strength of the hamstring muscle group (Behnke, 2006). The effects of the muscular imbalance are acutely demonstrated by Renström et al. (1986) who identified that isolated hamstring activity can decrease the strain on the ACL while the isolated quadriceps activity induces significant increases in ACL strains. When combined, as seen during knee extension and flexion exercise protocols on an isokinetic dynamometer, the strains on the ACL were further enhanced leading to the suggestions that the hamstrings are unable to mask the harmful quadriceps influences (Renström et al., 1986). The findings from Renström et al. (1986) would question the suggested use of the knee extension should be avoided until the ACL tissue has fully healed. With the knee extension motion a common component of ACL rehabilitation programmes, the ability to monitor the strength capacities of the quadriceps, in the absence of external resistance mechanisms, is vital for ensuring that strains placed on the recuperating tissue are not excessively high. One such method would be through the monitoring of the muscular contraction moments that produced the desired movement and the powers that the resulting motion utilises.
Multiple devices, including the isokinetic dynamometer, can provide a direct measure of the moments responsible for joint motions, and the powers behind the resultant motion. In the absence of direct measurements, Baltzopoulos (2007) suggests using angular kinetics in a specifically formulated equation which allows the muscular contraction moment, that is ultimately responsible for the motion, to be calculated. Through inverse engineering, it is possible to produce a simple formula which only requires the insertion of specific kinematic and anthropometric parameters, a process that the current study aims to utilise in producing a simple formula for the knee extension movement. The aim of the investigation was to develop and test a formula for calculating dynamic knee extension moments and powers from kinetic angular data. The secondary aim of the case study was to compare two collegiate soccer player’s production of such moments and powers, given that one of the players has recently recovered from an ACL injury.
Phase 1: Formula Development
The knee extension moments (ƩM) is the resulting product of the moment of inertia (I) and the angular acceleration of the extension movement (α) [Equation 1], however this is the sum of knee extension moments. To compare the participant’s moment and power production, the moment created through the contraction of the quadriceps femoris muscle group (Mc) must be isolated from the gravitational moment (Mg) [Equation 2]. The isolation of the two moments contributing to the extension moment can be substituted into the original formula in place of the knee extension moment components [Equation 3]. For the knee joint to extend, the muscular contraction moment must exceed the gravitational moment created by gravity’s actions through the shank’s centre of mass (CoM; Figure 1), with the magnitude of the difference between the two moments resulting in the velocity of the knee’s extension.
Figure 1. Free body diagram of the knee extension movement
The gravitational moment can be calculated using a three-stage equation [Equation 4]. The first stage is the product of the shank’s mass (Sm), which is the equivalent of 0.061 of the participant’s whole-body mass (m) [Equation 5]. The second stage is the identification of the shank’s CoM location, located by multiplying the shank’s measured length (l) by 0.606 [Equation 4]. The final stage is the sine wave multiplication of the knee’s extension angle (θ), with the product of these three stages signifying the gravitational moment for the knee joint at that extension angle [Equation 4]. The full formula for gravitational moment can be substituted into one side of the original formula [Equation 7]. The mass of the shank (Sm) features in the calculation of the moment of inertia for the knee extensions motion. The moment of inertia is calculated through the multiplication of the shank’s mass by the squared product of the radius of gyration (p) and the shank’s length (l) [Equation 8]. Winter (2005) states that the shank’s mass is 0.061 of the participant’s whole-body mass and the radius of gyration is 0.735, while the shank’s length is measured between the knee’s lateral epicondyle and the ankle’s lateral malleolus [Equation 9]. The identified interial equations can therefore be substituted into the moment formula [Equation 10].
The final component required by the calculation of the knee’s extension moments, and more importantly the moment producing capability of the limb’s bodily tissues is the angular acceleration of the motion (α) [Equation 11]. Angular acceleration is the result of dividing the change in angular velocity (Δω) by the time taken (Δt) to complete the motion [Equation 11] with angular velocity representing the change of knee angle (Δθ) over the time taken (Δt) to complete the change in angle [Equation 12]. Therefore, angular acceleration can be expressed as the change in knee angle over time divided by time [Equation 13] which can be substituted into the extended formula for calculating knee extension moments [Equation 14]. The equation can then be rearranged to solve for the muscular contraction moment (Mc) [Equation 15] with the resultant figure multiplied by the action’s angular velocity (ω) to calculate the knee extension power [Equation 16 and Equation 17].
Phase 2: Formula Application
Two male University of Roehampton soccer players (both aged 22 years old; 1.80 ±0.08m in height, 74 ± 5.66kg in mass), one of whom had recently recuperated from a grade 2 ACL strain while the other reported in full health, volunteered for this study (Table 1). The participants were matched for age, playing level and experience, and their relative power to weight ratios for knee extensions and squat exercises, prior to participant 1’s ACL injury. The required anthropometric data of body mass and shank length were recorded using a SECA weighting scales (SECA GmbH; Hamburg, Germany) and a standard measuring tape denoting centimetre increments, respectively. In accordance with the criteria for the formula development, shank length was measured from the knee’s lateral epicondyle to the ankle’s lateral malleolus. Angular data was gathered using a specifically designed electric goniometer (Biometrics SG105B electrogoniometer; Biometrics Ltd.; Cwmfelinfach, Gwent, UK), with a sampling rate of 50Hz, attached to a Biometrics 8-channel surface electromyography (sEMG) device (Biometrics DataLog P2XB surface electromyography device; Biometrics Ltd.; Cwmfelinfach, Gwent, UK). The goniometer was securely attached to the lateral aspect of the participant’s preferred limb when the knee was flexed at a 90° angle in a manner that the knee could be fully extended to 180° without excessive strain being placed on the cable connecting the two goniometer sensors.
Table 1. Participant's anthropometric data
Following a self-directed individualised warm-up, the participants were securely seated in a Cybex isokinetic dynamometer (Cybex Isokinetic Norm Testing and Rehabilitation System; Cybex International Inc.; New York, USA) with a Velcro strap tightly fastened across the thigh of the participant’s preferred limb to prevent it from being lifted off the seat (Figure 2). After 10 unrecorded submaximal knee extensions for familiarisation with the isokinetic dynamometer and the motion requested, 5 maximal effort knee extension moments were performed with the goniometer recording both the time and knee angle throughout the knee’s extension and flexion phases.
The goniometer data was exported from the Biometrics DataLog software package (Analysis Software for DataLog, Version 8.5; Biometrics Ltd.; Cwmfelinfach, Gwent, UK) into the MatLab Analysis and Calculation software package (MatLab Analysis and Calculation Software, Version 8.5; MathWorks; Natick, MA, USA) for processing. The data was processed using a multiple stage protocol converting the electrogoniometer analogue counts into angular values and the frame spacing into time values. The second stage of the processing protocol was to use a Butterworth filter with a 5Hz cut-off frequency to filter the raw angular data, before calculating the knee extension moments and powers, including the individual calculations of angular acceleration and velocities. The final step of the protocol was to identify the single highest maximal power and moment values for the participants during each of their five maximal effort knee extension trials.
Figure 2. Participant set-up on the isokinetic dynamometer (sEMG goniometer attachment not shown)
Participant 1, the one whom was nearing the end of the ACL rehabilitation program, had a lower maximal muscular contraction moment for the knee extension motion than the healthy participant (Table 2). The increase in moment production was replicated in the maximal power values for the knee extensions (Table 2), although nearly half of the relative increase of the moment (5.52% compared to 9.80%). The five extension trials were completed in, approximately, the same duration of time (~10 seconds) for both participants (Figure 3 and Figure 4).
Table 2. The maximal muscular contraction moments and maximal knee extension power production of each participant's five maximal effort trials
Figure 3. Traces from the quadriceps muscle contraction moments for the five trials for Participant 1 (Left) and Participant 2 (Right)
Figure 4. Traces of the knee extension power production for the five trials for Participant 1 (Left) and Participant 2 (Right)
The primary aim of the current study was to outline and test a method for using anthropometric and kinematic data to calculate knee extension moments and powers generated by the muscular contraction of the quadriceps femoris muscle group. The study had a secondary aim which was to investigate the impact of an ACL injury on the production of the moments and powers during a knee extension movement. The results of the findings indicate that the participant currently recuperating, though nearing completion of a rehabilitation program, from a Grade 2 ACL strain produced lower contraction moments and power calculated through the formulated equations.
The formulae developed for calculating both muscular contraction moment and the knee extension power rely on certain anthropometrical information, primarily shank length and mass but also indirectly with whole body height and mass. The length of the shank is used to calculate both the location of the segment’s CoM and the resulting gravitational moment that needs to be overcome by the muscular contraction for the knee joint to extend [Equation 7] as well as the moment of inertia for the extending joint [Equation 8]. The whole-body mass is used to calculate the mass of the shank [Equation 5] which is then a component in the formulas for both the gravitational moment [Equation 4] and the moment of inertia [Equation 9]. The resulting combination states that participants with longer legs or higher body mass will have to overcome greater gravitational moments and moments of inertia to get the knee to extend, thus requiring greater muscular contraction moments to initiate motion. The final kinematic component for consideration is the angular acceleration of the movement which is a resulting action from the muscular contraction moments and powers in conjunction with the knee joint’s flexibility. Following the logical assumptions proposed through the formula development, Participant 1 should record higher muscular contraction moments and power dur to their greater shank mass and length.
However, the results of the current study contradict those assumptions indicating that there is an external factor influencing the production of the knee extension moments and powers. It is postulated by the author that, from the information known, this external factor is the participant’s current recuperation from the ACL strain. In a study regarding dynamic knee extension motions, Aagard et al. (1984) indicates that the observed improvements in the moments and powers produced can be generally attributed to the angular velocities used during athletic strength training sessions. With the durations of the five knee extensions relatively similar for both participants, the only component responsible for the differing velocities is the range of motion (RoM) available for the knee to extend through. Due to the immobilisation of the knee joint early in the rehabilitation program, the tissues in and around the knee joint become stiffer thus limiting the total RoM in the knee (Akeson et al., 1987; Trudel et al., 1999). The relationship between joint flexibility and movement power production has been investigated through a series of projects assessing the relationship during knee extension exercises (Yamaguchi & Ishii, 2005; Yamaguchi et al., 2006; Yamaguchi et al., 2007). Generally, the peak power production values increased following short periods of dynamic stretching routines that mimic the extension movements, regardless of the load being applied (Yamaguchi & Ishii, 2005; Yamaguchi et al., 2006; Yamaguchi et al., 2007).
Aagard et al. (1994) states that a period of strength training, regardless of whether it is high resistance, low resistance or loaded repetitions of the kicking movement, provides significant improvements in peak moments and power during dynamic knee extensions. While immobilisation has known to cause rapid reduction in muscular strength (Booth, 1987; Woo et al., 1987; Newton et al., 1995). Woo et al. (2006) indicates that tissue properties, including power production capability, can diminish when the stresses applied to the tissues are reduced. The author hypothesises that the lessened muscular contraction moments are an automatic response by the central nervous system to control the amount of stress and strain applied through the rehabilitating tissue. Whether it is a result of the period of slight immobilisation and limited stress application through a lack of training, or a protective measure by the body to aid in the rehabilitation of the ACL, the lessened capacity of the quadriceps femoris muscle to produce a powerful contraction could be a determining factor in the difference of moments and power between the two soccer players in this study.
The paper outlined a potential procedure for calculating the kinetics of the knee extension motion from anthropometric and kinematic components. The first stage of the methodology was to outline the generated formula used to calculate the knee extension moments and powers using shank length, shank mass, and the angular velocity of the extension motion. The second stage was to assess the effectiveness of these formulae by using them to assess the knee extension muscular contraction moments and power production of a pair of collegiate soccer players. Furthermore, the results of the analysis of the participants indicate how an injury to a component of the knee joint can influence the moment and power production of an individual. In this case the injury was a grade 2 ACL strain and resulted in a participant who should have produced greater muscular contraction moments and kicking power produced weaker moments and powers when tested.
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The author would like to thank the two participants for volunteering their time to participate in the study. Additionally, the author would like to express their gratitude to Dr Jin Luo and Alison Carlisle, of the University of Roehampton for their advice and assistance throughout the study and access to the university’s facilities and equipment.