Propulsive fractions of joint work during maximal sprint running

Sprint running is the fastest kind of human locomotion. Special kinematic characteristics of sprint running are (1) touch down on the forefoot, (2) a highly flexed knee joint during the swing phase, and (3) the foot descend with a horizontal velocity close to zero. The latter was described already in 1930 by Fenn [1, 2]. Regarding the kinetics, different investigators have addressed the problem of individual joint contribution to forward acceleration and horizontal running velocity. Net joint moments measured by inverse dynamics have been described in detail by Mann and Sprague [3], by Bezodis et al. [4], and by Hunter et al. [5]. Although the latter study analyzed one step after app. 25 m acceleration, the net joint moments resembled the previously reported moments to a very high degree. An important objective has been to identify which joint contributes mostly to horizontal speed during maximal sprint running. It has consistently been suggested that hip joint extension during late swing and during the first part of the stance phase is the most important action for driving the whole body forward. It is thought that the hip extensor muscles, especially the hamstrings and the gluteus maximus, are responsible for the generation of a large ground reaction force (GRF) in the sagittal plane [3, 6‐9]. Furthermore, a ratio between the resulting and the horizontal GRF has been shown to be related to sprint running performance, both for physical education students as well as for sprinters of national and international level. This ratio, called RF, should ideally be maximized with respect to horizontal force for a given vertical force [10, 11]. It is, however, not trivial to maximize the horizontal GRF while keeping other mechanical aspects of running constant. During normal running and especially during powerful sprint running, the athlete has to deal with balance. As stated by Fenn [2] and Cavagna et al. [12], the mechanical work during running can be divided into (1) work against gravity and (2) work due to velocity changes. However, also a third mechanism has some serious consequences for the entire movement pattern, namely the generation of angular momentum and thereby balance of the whole body. During the contact phase with the ground, the athlete generates angular momentum by the direction of the resulting GRF vector. This vector may pass behind or in front of or directly through the body center of mass (BCM). When it passes in front of the BCM, positive angular momentum is generated and vice versa when the force vector passes behind the BCM. When the vector passes directly through the BCM, no angular momentum is generated. This is the mechanism by which the human body can be kept in dynamic balance during, e.g., running. The actual amount of angular momentum is being summed up during the ground contact and it is a fact that the athlete should enter the flight phase with an angular momentum close to zero, otherwise it will lead to rotation during flight and loss of balance. Accordingly, it is certain that a significant proportion of the forces and muscle work produced about the anatomical joints will have to generate angular momentum and can, therefore, not be used exclusively to drive the BCM in forward direction. Also, an unknown proportion of muscle work is used to stabilize the joints and the segments. Therefore, the purpose of the present study was to quantify the proportion of power and work about the hip, knee, and ankle joint, which actually ‘drives’ the BCM in forward direction using a method originally presented by Dumas and Cheze [13]. It was hypothesized that the hip joint would turn out to be the most important joint and further that a relatively large proportion of the muscle work at the hip joint would be of propulsive nature.

Seven athletes of national class served as subjects, four males and three females (Table 1).

All participants gave their informed consent to the conditions of the experiments, which were approved by the local ethics committee, journal number 504-0007/17-5000.

The athletes were running on an indoor synthetic track with their spiked shoes normally used for competition. After 40 m approach from starting blocks, they were recorded by four cameras (iPhone 6 Apple Inc.) operating at 240 frames per second. The four cameras were placed in a square around a recessed force platform (AMTI OR6) with the same synthetic track material mounted separately on top of the platform. The signals from the force platform were sampled to a PC at 1200 Hz and synchronized to the video signals by LED’s placed in the field of view. The LED’s remained turned on when the vertical force exceeded 15 N corresponding to the contact phase. The linearity of the iPhone cameras was measured by recording a known scale in various places of the field of view. This was found to highly accurate as was the frame rate of 240 frames/s.

A total of 37 reflective spherical markers were placed on the subjects at certain anatomical landmarks and digitized by the APAS system (Ariel Performance Analysis System, California, USA). A calibration cube (2 x 1.5 x 1.5 m) was filmed by the four cameras and used to calculate the third dimension by direct linear transformation. Four markers were placed at the corners of the force platform to align the center of pressure (COP) measurement on the platform with the coordinate data of the video recordings. The APAS system has previously been evaluated and found highly accurate in comparison with similar systems providing 3D movement data [14].

The coordinates of each marker were digitized semi-automatically. After direct linear transformation, the coordinates of each marker were digitally low-pass filtered (fourth order, zero lag) with a cutoff frequency of 15 Hz. The force platform signals were digitally low-pass filtered also at 15 Hz (fourth order, zero lag) and reduced to 240 Hz to match the video signals. The cutoff frequency of 15 Hz was chosen based on the study of Bezodis et al. [15]. The center of pressure (COP) was calculated corresponding to each video frame and aligned to the coordinate system of the video recordings. All data were stored in the c3d file format (c3d.org) by use of a custom written Matlab script (Mathworks).

Musculoskeletal models were created based on a modified version of the MocapModel from the AnyBody Managed Model Repository (AMMR) version 1.6.2, using the AnyBody Modeling System (AMS version 7.1, AnyBody Technology A/S, Aalborg, Denmark). AMS is a multibody dynamics system, which discretizes the body into links representing the bones as rigid segments articulating at the anatomical joints. In the MocapModel template, the lower extremity model is based on the cadaver dataset of Klein Horsman et al. [16], the lumbar spine model based on the work of de Zee et al. [17], and the shoulder and arm models based on the work of the Delft Shoulder Group [18‐20] capturing 2 × 2 DOF at the wrist joints, 2 × 5 DOF at the glenohumeral joints, 2 × 2 DOF at the elbow joints, 3 DOF between pelvis and thorax, 6 DOF at the pelvis, 2 × 3 DOF at the hip joints, 2 × 1 DOF at the knee joints and 2 × 2 DOF at the ankle joints. Joint moments of the hip, ankle, and knee joint and the corresponding joint angular velocities were output in 3D by the AnyBody system.

To scale the musculoskeletal model to each subject, a length-mass scaling law was applied [21]. In terms of geometric scaling of each segment, a diagonal scaling matrix was applied to each point on the segment. For the longitudinal direction, the entry of the scaling matrix was computed as the ratio between the unscaled and scaled segment lengths. In the two other orthogonal directions, the scaling was computed as the square root of the mass ratios divided by the length ratios between the scaled and unscaled models. To distribute the total body mass to the individual segments, the regression equations of Winter were applied [22]. Finally, the inertial parameters were estimated by assuming that the segments were cylindrical with a uniform density. As part of the scaling procedure, the optimization method of Andersen et al. was applied to one trial and utilized to scale the segment lengths and the marker coordinates of markers not placed on bony landmarks [23]. These parameters were then saved and used for the remaining trials for each subject. Subsequently, kinematic analysis was performed by minimizing the least-square difference between model and experimental markers using the method of Andersen et al. during all tasks [23]. Finally, inverse dynamics analysis was performed by utilizing a third-order polynomial muscle recruitment criterion [24]. Although the model estimates all muscle and joint reaction forces, only the joint moments and joint angular velocity vectors were extracted from the model for further analysis. Net moments in 2D were additionally calculated as described by Mann and Spraque for comparative purposes [3].

As stated above, the joint moments in 3D were calculated by inverse dynamics and joint power was obtained by the formula:where P is joint power, M is net joint moment, and \(\omega\) is joint angular velocity. Positive power indicates concentric muscle contraction and negative power indicates eccentric muscle contraction. Power (P₀) was then normalized to dimensionless values by:where m is the body mass, g is the acceleration of gravity, and L is the lower limb length from ground to hip joint center [25]. The joint moments were transformed into the segment coordinate system of the proximal segment and expressed as x, y, z coordinates.

As described by Dumas and Cheze [13], the 3D angle α_Mω between the joint moment and joint angular velocity is directly related to the 3D power:However, the 3D angle α_Mω was computed numerically asand defined positive in the range 0°–180°.

As suggested by Dumas and Cheze [13], α_Mω was considered propulsive (driven) in the range of 0°–60°, stabilizing in the range 60°–120° and repulsive in the range 120°–180°.

In addition, the ratio RF between the resulting and the horizontal GRF was calculated as described by Morin et al. [11, 26].

Interpretations of moment, power, and work were limited to the contact phase during the running cycle.

Pearsons product was used for correlation analysis between various biomechanical parameters and maximal running velocity. Level of significance was set to 5%.

The peak ankle joint moment was on average − 284 Nm (− 209 to − 423) and normalized to − 0.52 (− 0.34 to − 0.72) (Table 2). The peak knee joint extensor moment was on average 201 Nm (50–327) and normalized to 0.35 (0.12–0.57) (Table 2). The peak hip joint extensor moment varied to a large extent between the athletes from 0 to − 677 Nm and normalized from 0 to − 0.91 (Table 2).

The ankle joint moment was in all athletes plantar flexor dominated during the contact phase—first, by negative joint work during an eccentric contraction and then followed by a concentric contraction generating positive joint work (Figs. 1 and 2). Peak positive ankle power averaged 2629 W (1804–4399) and normalized 4.56 (2.63–7.50) (Table 2). Peak knee joint power was on average 1827 W (197–4693) and normalized to 3.40 (1.41–7.99) (Table 2). Peak power at the hip joint varied from 0 to 12430 W and normalized from 0 to 16.66 (Table 2). Not all athletes showed an extensor dominated hip joint moment just after touchdown. However, all athletes showed flexor dominance about the hip joint during the second half of the contact phase and this moment was in all cases of eccentric origin. This can clearly be seen in Fig. 3 in which joint moments and power were normalized to body mass and leg length, time normalized to 100% running cycle and averaged across all subjects (Fig. 3). It can further be seen that the largest forces were developed about the ankle joint, that the knee flexor muscles exerted a large eccentric moment about the knee joint in the late swing phase and that the hip extensors performed pure concentric muscle work during late swing and in the first halt of the contact phase (Fig. 3).

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When the three joint moments were added to form a support moment representing the whole leg with extensor moment defined as positive values [27], it was revealed that peak support moment and maximal sprint running velocity correlated significantly for absolute values (r = 0.77; p = 0.045) and for normalized values (r = 0.81; p = 0.026).

Calculation of propulsive power and the corresponding work showed significant differences among the athletes. Figure. 4 shows an athlete with a high contribution in form of propulsive normalized work from the knee joint while Fig. 5 shows an athlete with a high contribution from the hip joint. In both figures, the area under the curve showing propulsive power is equal to propulsive work for the interval in which the 3D angle is below 60°.

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Figure. 6 shows a comparison between normalized total positive work about the ankle, knee, and hip joint and the corresponding propulsive work. Total positive work (normalized) was 37, 56, and 45 averaged across all subjects for ankle, knee, and hip joint, respectively. Figure. 7 shows the propulsive work as a percentage of the positive work about the actual joint and the percentage joint contribution to the total propulsive work of the whole leg. In normalized values, propulsive work of the ankle, knee, and hip joint averaged across subjects was 25, 24, and 24, which corresponded to 64%, 71%, and 29% of total positive work, respectively (Table 2). It is seen that in four athletes, the hip joint did not contribute at all to propulsion, while athlete S and H showed high work contributions of 118 and 57 (normalized work), and 96% and 97% of this work was propulsive (Figs. 6 and 7) (Table 2). Propulsive work for the whole leg as percentage of the total positive work was on average 70% (40–87) (Table 2). Total normalized propulsive work of the whole leg was significantly correlated with maximal running velocity (r = 0.84; p = 0.02). Neither RF_max nor RF_mean (ratios between resulting ground reaction and horizontal ground reaction vector) correlated significantly with running velocity (Table 2).

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The net joint moments of the present study are somewhat difficult to compare with earlier studies of sprint running primarily due to a low cutoff frequency (15 Hz) of the low-pass filter applied to the ground reaction forces. Earlier studies have shown high frequency oscillations of the ground reaction forces, which apparently caused oscillations in the net joint moments [3, 4, 28]. It has been argued that these oscillations are due to impact forces, which are ‘non physiological’ and accordingly should be removed by filtering both movement data and ground reaction forces at the same cutoff frequency [15, 29, 30]. The net joint moments of the present study were besides 3D also calculated in 2D while low-pass filtering the ground reaction forces at a cutoff frequency of 100 Hz. This yielded moments highly comparable to those of the previous 2D studies. One direct change caused by the present approach with cutoff frequencies of 15 Hz was that four of the present athletes did not show any hip joint extensor moment immediately after touchdown. It must, however, be kept in mind that a zero moment could mean a balanced moment due to co-contraction of agonists and antagonists. At the time instant of touchdown, co-contraction exists between the quadriceps and the hamstring muscles [31].

As the filtering process used in the present study appears to have become the ‘golden standard’ [15, 29, 30], the moments of the present study remain to be compared to those of future studies of maximal sprint running.

It was a remarkable finding that only 70% (40–87%) of the positive work of the whole leg was propulsive and could theoretically contribute to forward velocity. However, total propulsive work was significantly correlated with maximal running velocity while the ground reaction ratios RF_max and RF_mean were not. The latter was contradictory to earlier reports [10, 26].

One important limitation of the method adopted from Dumas and Cheze [13] is that only an interval of the 3D angle between the two vectors can indicate when the joint is ‘driven’. Thus, it cannot be deducted to which degree the muscle work about the joint actually contributes to forward acceleration of the whole body during this interval. However, more information is provided by this method than just moment, power, and angular velocity.

As mentioned in Introduction, it has often been suggested that extension of the hip joint by the gluteus maximus and the hamstring muscles should be the most important contributor to forward propulsion of the BCM. It has been shown that these bi-articular muscles seem to shorten during the entire stance phase as opposed to the soleus and the quadriceps muscles, which are limited to shorten only during the second half of the stance phase [6, 8, 32]. Positive and negative joint power may indicate concentric and eccentric muscle contractions, but the free body segment method only applies to one-joint muscles and within the muscle-tendon unit the muscle fibers and the tendons may not follow the same pattern of shortening and lengthening. Furthermore, the net joint moment about the hip joint only shows extensor dominance in the first half and flexor dominance in the rest of the stance phase. This moment pattern is consistently reported in the literature both during walking, running, and sprint running [3, 5, 33]. It has been suggested by Mann and Sprague that the purpose of this flexor moment should be to prevent backward rotation of the upper body during the power-full take off [3]. However, Simonsen et al. failed to relate this flexor moment to movements of the upper body during normal and tilted walking [33] and suggested that the flexor moment was generated by strong ligaments about the hip joint and that balance of the upper body is likely to be maintained by controlling the ground reaction vector at the foot as this vector produces angular momentum, which is directly responsible for balance [34]. It follows that the muscle work, which generates angular momentum, cannot contribute to propulsion of the BCM. At the same time, it is obvious that it is necessary to produce an optimal horizontal ground reaction force to accelerate the BCM in horizontal direction to obtain a maximum horizontal velocity at takeoff. In the present study, the ratio between the resulting and the horizontal ground reaction force (RF) was not significantly correlated to running velocity. However, the support moment of the whole leg was significantly correlated to running velocity, which indicated that very complex mechanisms lie behind the forces driving the BCM in forward direction.

The methodology introduced by Dumas and Cheze [13] made it possible to subdivide the produced joint power into propulsive (driving), stabilizing and repulsive components. To interpret the results, it is necessary to look both at the total work and the work distribution over the joints. Looking at individual data, subject S was by far the fastest sprint runner, which was also reflected by the largest total work of the leg and the fact that the largest work contribution came from the hip joint (Figs. 6 and 7) of which as much as 96% was propulsive (Table 2). However, the same was seen for subject H, who was female and a much slower runner (Table 2). Subject B was also a sub 11 s. 100 m runner, but he did not use the hip joint for propulsion and the total positive work of the leg was much lower than in subject S (Figs. 6 and 7). However, as much as 87% of his joint work was propulsive (Table 2). Based on the present results, it can be stated that the hip joint is very important for some athletes but obviously not for all athletes.

It should be noted that the present group of subjects represented trained sprint runners over a wide range, also because both sexes were represented. However, this does not exclude comparisons with previous studies as many of these also used athletes of very different levels [3, 4, 11, 28]. Bezodis et al. found very little positive muscle power about the knee joint in elite sprinters during maximal velocity [4], which is partly contradictory to the present results as, e.g., subject A, G, and K of the present study showed normalized propulsive work of 73, 35, and 29 corresponding to 98%, 100%, and 100% of the total positive work about the knee joint (Table 2).

On average across all athletes, propulsive work about the knee joint constituted 33% of the total propulsive work of the whole leg.

The notion made by Mann that the plantar flexor’s main function is to work against gravity [35] or the statement made by Brown and Vescovi that ankle activity does not cause horizontal propulsion in sprinting [36] did not concur with the present study as the ankle joint contributed with 34% of the total propulsive work.

The ankle, knee, and hip joint showed on average propulsive normalized work of 25, 24, and 26, respectively, so the present data clearly showed that work contributing to accelerate the BCM in forward direction may come from any of the three joints of the supporting leg. The working hypothesis of the study that the hip joint would be the most important contributor to forward velocity could only be partly confirmed and it was clear that the whole leg must be considered as one functional unit during maximal sprint running. This has the practical implications, that, e.g., the ankle joint cannot be considered as less important than the hip joint and the same goes for the knee joint. The extensor muscles about the hip and knee joint as well as the plantar flexor muscles must be trained equally in strength training regimes for sprint running.

During maximal sprint running, only a fraction (on average 70%) of the generated positive joint work can be used for forward propulsion of the body. During maximal sprint running, the whole leg should be considered as one functional unit in which one or more of the joints may dominate generation of propulsive joint work.