eight male elite sprinters ( age , 21.1  1.9 yr ; mass , 74.7  4.1 kg ; height , 181.5  3.9 cm ) ( all mean  sd ) participated in this study .
the sprinters best performance records for 100 m ranged from 10.27 to 10.80 s. subjects were free of musculoskeletal injuries in the lower extremity at least 6 months before the study .
this study was approved by the local ethical committee of shanghai university of sport , and all participants gave an informed written consent before testing .
, zurich , switzerland ) was used to measure subjects maximal isometric knee joint flexion and extension torque before the sprinting trials . during the sprinting trails ,
57 reflective markers were placed on the subjects anatomic landmarks on the basis of the marker setup used in our earlier study ( 8) .
three - dimensional kinematic data were collected at a sampling rate of 300 hz via eight high - resolution cameras ( vicon mx , oxford , united kingdom ) .
the calibration volume for kinematics collection was 10.0 m long , 2.5 m high , and 2.0 m wide and located 40 m away from the starting line .
ground reaction forces ( grf ) were collected with a recessed force platform ( kistler 9287b , 0.6 m  0.9 m ; kistler instruments corp . , winterthur , switzerland ) .
the force signals were amplified and recorded in the vicon system at a sampling rate of 1200 hz .
after sufficient warming up , the subjects wearing spiked shoes performed maximum - effort sprinting on the synthetic track .
one gait cycle was defined from the beginning of the stance phase ( initial foot - to - ground contact determined by the vertical grf ) to the end of the subsequent swing phase ( immediately before the next foot - to - ground contact determined by the vertical velocity of the markers on the forefoot ) .
preprocessed kinematics and kinetic data ( c3d format ) were imported to visual 3d ( 3.390.23 ; c - motion , inc . )
kinematic and force data were filtered through a fourth - order butterworth digital filter at cutoff frequencies of 17 and 55 hz ( 32,34 ) , respectively .
anatomical landmarks and segments were defined according to the visual 3d framework model and the anthropometric data .
the whole - body center of mass was determined using a 14-segment model ( 6 ) .
the average horizontal velocity of the body center of mass during the whole stride cycle was used to represent the running speed . from the collected three - dimensional data ,
stance phase was defined from the right foot touchdown to toe off as measured by the force platform , whereas swing phase was defined as from toe off to touchdown of the same foot .
the intersegmental dynamics analysis was conducted with a customized program using the data from visual 3d .
the lower limb was modeled as a linked - segment system ( thigh , shank , foot ) with frictionless joints at the hip , knee , and ankle ( 8,15 ) .
the origin of the local coordinate system ( x0 , y0 ) for the system was fixed at the hip joint , and therefore , the motion of the lower limb could be described by x0 , y0 and segment angles f , s , and t ( fig .
the definition of the angular motion of a segment was positive when the direction of segmental rotation was counterclockwise .
on the basis of free body diagrams of the segments of the lower extremity , the dynamic equations of motion was derived using the newton  euler formula applied to each body segment .
the anthropometric inertial parameters for chinese adults published by zheng ( 37 ) were used to determine the location of the center of mass and the moment of inertia of each body segment . according to earlier research ( 9,22,36 ) , at each of the joints of the linked segments ,
the torque was separated into five categories : net joint torque ( net ) , gravitational torque ( gtt ) , motion - dependent torque ( mdt ) , contact torque ( ext ) , and generalized muscle torque ( mst ) .
f , s , and t , segment angles for the foot , shank , and thigh measured at the distal joint . x0 and y0 ,
the x and y coordinates of the hip ; xcop and ycop , the x and y coordinates of the center of pressure .
thus , net is the sum of all the positive and negative torque components acting on a joint .
mdt arises from mechanical interactions occurring between limb segments and is the sum of all torques produced by segment movements ( e.g. , segment angular velocity and angular acceleration ) .
mst at each joint is calculated as follows : the equations for each component are as follows : ankle torque components : knee torque components : hip torque components : mf , ms , and mt mass of the foot , shank , and thigh if , is , and it moment of inertia about the center of mass of the foot , shank , and thigh f , s , and t segment angles for the foot , shank , and thigh measured at the distal joint ( orientation angle ) f , s , and t angular velocities of the foot , shank , and thigh f , s , and t angular accelerations of the foot , shank , and thigh rf , rs , and rt distances from the proximal joint to the center of mass of the foot , shank , and thigh ls and lt lengths of the shank and thigh segments fx and fy x and y components of the grf ax and ay x and y components of the linear acceleration of the hip joint ( x0 , y0 ) dx and dy x and y distances from the center of pressure to the center of mass of the foot ( i.e. , xcmfxcop and ycmfycop , respectively , where xcmf and ycmf are the x and y coordinates of the center of mass of the foot , respectively , and xcop and ycop are the x and y coordinates of the center of pressure ) g gravitational constant .
eight male elite sprinters ( age , 21.1  1.9 yr ; mass , 74.7  4.1 kg ; height , 181.5  3.9 cm ) ( all mean  sd ) participated in this study .
the sprinters best performance records for 100 m ranged from 10.27 to 10.80 s. subjects were free of musculoskeletal injuries in the lower extremity at least 6 months before the study .
this study was approved by the local ethical committee of shanghai university of sport , and all participants gave an informed written consent before testing .
, zurich , switzerland ) was used to measure subjects maximal isometric knee joint flexion and extension torque before the sprinting trials . during the sprinting trails ,
57 reflective markers were placed on the subjects anatomic landmarks on the basis of the marker setup used in our earlier study ( 8) .
three - dimensional kinematic data were collected at a sampling rate of 300 hz via eight high - resolution cameras ( vicon mx , oxford , united kingdom ) .
the calibration volume for kinematics collection was 10.0 m long , 2.5 m high , and 2.0 m wide and located 40 m away from the starting line .
ground reaction forces ( grf ) were collected with a recessed force platform ( kistler 9287b , 0.6 m  0.9 m ; kistler instruments corp . , winterthur , switzerland ) .
the force signals were amplified and recorded in the vicon system at a sampling rate of 1200 hz .
after sufficient warming up , the subjects wearing spiked shoes performed maximum - effort sprinting on the synthetic track .
one gait cycle was defined from the beginning of the stance phase ( initial foot - to - ground contact determined by the vertical grf ) to the end of the subsequent swing phase ( immediately before the next foot - to - ground contact determined by the vertical velocity of the markers on the forefoot ) .
preprocessed kinematics and kinetic data ( c3d format ) were imported to visual 3d ( 3.390.23 ; c - motion , inc . )
kinematic and force data were filtered through a fourth - order butterworth digital filter at cutoff frequencies of 17 and 55 hz ( 32,34 ) , respectively .
anatomical landmarks and segments were defined according to the visual 3d framework model and the anthropometric data .
the whole - body center of mass was determined using a 14-segment model ( 6 ) .
the average horizontal velocity of the body center of mass during the whole stride cycle was used to represent the running speed . from the collected three - dimensional data ,
stance phase was defined from the right foot touchdown to toe off as measured by the force platform , whereas swing phase was defined as from toe off to touchdown of the same foot .
the intersegmental dynamics analysis was conducted with a customized program using the data from visual 3d .
the lower limb was modeled as a linked - segment system ( thigh , shank , foot ) with frictionless joints at the hip , knee , and ankle ( 8,15 ) .
the origin of the local coordinate system ( x0 , y0 ) for the system was fixed at the hip joint , and therefore , the motion of the lower limb could be described by x0 , y0 and segment angles f , s , and t ( fig .
the definition of the angular motion of a segment was positive when the direction of segmental rotation was counterclockwise .
on the basis of free body diagrams of the segments of the lower extremity , the dynamic equations of motion was derived using the newton  euler formula applied to each body segment .
the anthropometric inertial parameters for chinese adults published by zheng ( 37 ) were used to determine the location of the center of mass and the moment of inertia of each body segment . according to earlier research ( 9,22,36 ) , at each of the joints of the linked segments ,
the torque was separated into five categories : net joint torque ( net ) , gravitational torque ( gtt ) , motion - dependent torque ( mdt ) , contact torque ( ext ) , and generalized muscle torque ( mst ) .
f , s , and t , segment angles for the foot , shank , and thigh measured at the distal joint . x0 and y0 ,
the x and y coordinates of the hip ; xcop and ycop , the x and y coordinates of the center of pressure .
thus , net is the sum of all the positive and negative torque components acting on a joint .
mdt arises from mechanical interactions occurring between limb segments and is the sum of all torques produced by segment movements ( e.g. , segment angular velocity and angular acceleration ) .
mst at each joint is calculated as follows : the equations for each component are as follows : ankle torque components : knee torque components : hip torque components : mf , ms , and mt mass of the foot , shank , and thigh if , is , and it moment of inertia about the center of mass of the foot , shank , and thigh f , s , and t segment angles for the foot , shank , and thigh measured at the distal joint ( orientation angle ) f , s , and t angular velocities of the foot , shank , and thigh f , s , and t angular accelerations of the foot , shank , and thigh rf , rs , and rt distances from the proximal joint to the center of mass of the foot , shank , and thigh ls and lt lengths of the shank and thigh segments fx and fy x and y components of the grf ax and ay x and y components of the linear acceleration of the hip joint ( x0 , y0 ) dx and dy x and y distances from the center of pressure to the center of mass of the foot ( i.e. , xcmfxcop and ycmfycop , respectively , where xcmf and ycmf are the x and y coordinates of the center of mass of the foot , respectively , and xcop and ycop are the x and y coordinates of the center of pressure ) g gravitational constant .
eight male elite sprinters ( age , 21.1  1.9 yr ; mass , 74.7  4.1 kg ; height , 181.5  3.9 cm ) ( all mean  sd ) participated in this study .
the sprinters best performance records for 100 m ranged from 10.27 to 10.80 s. subjects were free of musculoskeletal injuries in the lower extremity at least 6 months before the study .
this study was approved by the local ethical committee of shanghai university of sport , and all participants gave an informed written consent before testing .
an isokinetic dynamometer ( con - trex pm1/mj ; cmv ag corp . , zurich , switzerland ) was used to measure subjects maximal isometric knee joint flexion and extension torque before the sprinting trials . during the sprinting trails ,
57 reflective markers were placed on the subjects anatomic landmarks on the basis of the marker setup used in our earlier study ( 8) .
three - dimensional kinematic data were collected at a sampling rate of 300 hz via eight high - resolution cameras ( vicon mx , oxford , united kingdom ) .
the calibration volume for kinematics collection was 10.0 m long , 2.5 m high , and 2.0 m wide and located 40 m away from the starting line .
ground reaction forces ( grf ) were collected with a recessed force platform ( kistler 9287b , 0.6 m  0.9 m ; kistler instruments corp . ,
the force signals were amplified and recorded in the vicon system at a sampling rate of 1200 hz .
after sufficient warming up , the subjects wearing spiked shoes performed maximum - effort sprinting on the synthetic track .
one gait cycle was defined from the beginning of the stance phase ( initial foot - to - ground contact determined by the vertical grf ) to the end of the subsequent swing phase ( immediately before the next foot - to - ground contact determined by the vertical velocity of the markers on the forefoot ) .
preprocessed kinematics and kinetic data ( c3d format ) were imported to visual 3d ( 3.390.23 ; c - motion , inc . ) .
kinematic and force data were filtered through a fourth - order butterworth digital filter at cutoff frequencies of 17 and 55 hz ( 32,34 ) , respectively .
anatomical landmarks and segments were defined according to the visual 3d framework model and the anthropometric data .
the whole - body center of mass was determined using a 14-segment model ( 6 ) .
the average horizontal velocity of the body center of mass during the whole stride cycle was used to represent the running speed . from the collected three - dimensional data ,
stance phase was defined from the right foot touchdown to toe off as measured by the force platform , whereas swing phase was defined as from toe off to touchdown of the same foot .
the intersegmental dynamics analysis was conducted with a customized program using the data from visual 3d .
the lower limb was modeled as a linked - segment system ( thigh , shank , foot ) with frictionless joints at the hip , knee , and ankle ( 8,15 ) .
the origin of the local coordinate system ( x0 , y0 ) for the system was fixed at the hip joint , and therefore , the motion of the lower limb could be described by x0 , y0 and segment angles f , s , and t ( fig .
the definition of the angular motion of a segment was positive when the direction of segmental rotation was counterclockwise .
on the basis of free body diagrams of the segments of the lower extremity , the dynamic equations of motion was derived using the newton  euler formula applied to each body segment .
the anthropometric inertial parameters for chinese adults published by zheng ( 37 ) were used to determine the location of the center of mass and the moment of inertia of each body segment . according to earlier research ( 9,22,36 ) , at each of the joints of the linked segments ,
the torque was separated into five categories : net joint torque ( net ) , gravitational torque ( gtt ) , motion - dependent torque ( mdt ) , contact torque ( ext ) , and generalized muscle torque ( mst ) .
f , s , and t , segment angles for the foot , shank , and thigh measured at the distal joint . x0 and y0 ,
the x and y coordinates of the hip ; xcop and ycop , the x and y coordinates of the center of pressure .
thus , net is the sum of all the positive and negative torque components acting on a joint .
mdt arises from mechanical interactions occurring between limb segments and is the sum of all torques produced by segment movements ( e.g. , segment angular velocity and angular acceleration ) .
mst at each joint is calculated as follows : the equations for each component are as follows : ankle torque components : knee torque components : hip torque components : mf , ms , and mt mass of the foot , shank , and thigh if , is , and it moment of inertia about the center of mass of the foot , shank , and thigh f , s , and t segment angles for the foot , shank , and thigh measured at the distal joint ( orientation angle ) f , s , and t angular velocities of the foot , shank , and thigh f , s , and t angular accelerations of the foot , shank , and thigh rf , rs , and rt distances from the proximal joint to the center of mass of the foot , shank , and thigh ls and lt lengths of the shank and thigh segments fx and fy x and y components of the grf ax and ay x and y components of the linear acceleration of the hip joint ( x0 , y0 ) dx and dy x and y distances from the center of pressure to the center of mass of the foot ( i.e. , xcmfxcop and ycmfycop , respectively , where xcmf and ycmf are the x and y coordinates of the center of mass of the foot , respectively , and xcop and ycop are the x and y coordinates of the center of pressure ) g gravitational constant .
the subjects average maximal isometric contraction torque of knee flexors was 164.8  29.6 nm , as measured via the isokinetic dynamometer .
figure 2a shows the ensemble curves for knee and hip joint torque during stance phase .
mst and ext were the two main torques counterbalancing each other during stance phase while the other torques ( gtt , mdt , and net ) were much smaller .
a. averaged time - normalized graphs for joint torques at the knee and hip joints during the stance phase .
+ , extension ;  , flexion . note that the knee flexion mst and the hip extension mst both reached peak values during the initial stance phase ( about 5% of stance phase ) ( fig .
these peak values could be easily removed in the normalization and data smoothing process . to show the real situation , the mean  sd peak values among subjects
figure 2b shows the skeleton diagram of the subjects sprinting during the initial stance phase .
note that the grf passed anteriorly to the knee and hip at this moment , which would generate an extension torque at the knee and a flexion torque at the hip joint .
although hip extension mst has larger values later , the knee mst tended to be positive ( extension ) .
maximum mst , ext at the knee and hip joints , and maximum grf during the initial stance phase .
as shown in figure 3a , both mst and mdt were much greater than the others during the swing phase .
they were counterbalancing and reached the maximum at both knee and hip joints at a time point approximately 80% of the way through swing phase .
the skeleton diagram during late swing phase is shown in figure 3b and the mean peak values at this moment are shown in table 2 .
maximum mst and mdt at the knee and hip joints during the late swing phase .
a. averaged time - normalized graphs for joint torques at the knee and hip joints during swing phase .
b. diagram of sprinting during the late swing phase ; the inertial loads produced by segment motion work at the knee and hip joints .
figure 4 shows the ensemble curves of components of mdt at the hip joint and the knee joint during swing phase .
mdt at the hip joint was mainly composed of the torque due to shank angular acceleration ( saat ) , thigh angular acceleration , and hip linear acceleration .
mdt at the knee joint was mainly constituted of the saat during the entire swing phase .
ensemble curves of subcomponents of mdt at the hip ( a ) and knee ( b ) joints during the swing phase .
+ , extension torque ;  , flexion torque ; faat , torque due to foot angular acceleration ; favt , torque due to foot angular velocity ; hlat , torque due to hip linear acceleration ; saat , torque due to shank angular acceleration ; savt , torque due to shank angular velocity ; taat , torque due to thigh angular acceleration ; tavt , torque due to thigh angular velocity .
during initial stance phase , the grf passed in front of the knee and hip joints , which resulted in a large extension torque at the knee and a flexion torque at the hip ( ext ) ( fig .
these ext acted at both knee and hip joints , applying stress to the hamstring muscles . to counteract this effect of grf ,
the knee flexors and the hip extensors , hamstring muscles served both roles , were required to produce a large flexion torque at the knee and an extension torque at the hip .
this observation is congruent with previous studies ( 3,1618 ) , which showed a large knee flexion mst during initial stance phase but contradicts some kinetic findings of no knee flexion torque at this moment ( 25 ) .
because these large peak values appeared within a very short period , they could easily be removed as a noise spike by using an inappropriate filtering method , which may explain the inconsistent findings in hamstring mechanics during early stance in maximum speed sprinting . in the study of schache
et al . ( 25 ) , peak stance musculotendon force for the biarticular hamstrings would seem to have been underestimated in the early stance phase and the authors ascribed this underestimation to the computational approach used to calculate muscle forces , that is , the limitations of inverse dynamics - based static optimization combined with a minimum stress performance criterion .
however , in our opinion , the cause of this underestimation could be that erroneously low ( or zero ) knee flexion torque and hip extension torque were taken to calculate individual muscle forces . compared with their previous results , which also demonstrated a knee flexion mst during initial stance phase ( 24 )
the average peak mst at knee and hip joints were 203.4  93.6 nm and 455.2  198.7 nm , respectively , during the initial stance phase ( table 1 ) . on the basis of the magnetic resonance imaging and videofluoroscopy results ( 2,10,26 ) , the two - dimensional moment arm of the hamstrings at the knee joint in the sagittal plane was approximately 0.020.04 m. we could reasonably estimate the peak hamstring force across the knee joint on the basis of the mst values at the knee , and it ranged from 5777 to 11,554 n , which is at least 8 times the subjects average body weight .
furthermore , because the subjects maximal isometric contraction force of the knee flexors ranged from 4120 to 8241 n ( estimated from the results measured via the isokinetic dynamometer , 164.8  29.6 nm ) , the knee flexor force during the initial stance phase was 40% larger than that produced by the maximal isometric knee flexion .
clearly , a huge load acts on the hamstrings during sprinting . in addition , the mst is a net effect of both agonist and antagonist activities .
thus , the hamstrings encounter the knee extensors ( quadriceps femoris ) to generate this flexor torque , which means that the actual knee extension torques that need to be generated by the hamstrings might be even greater than those in the present results . in this case
, there would be a high strain injury risk during the initial stance phase because of the sprinter s hamstring strength deficits . during the late swing phase ,
the thigh started to extend backward but the shank still rotated forward because of mdt . to pull the shank backward and downward before ground contact ,
the hamstring muscles are intensely contracted , creating an ( clockwise ) acceleration where there is a rapid change from eccentric to concentric function ( fig .
our data revealed that the largest mst occurred at the end of the swing phase ( fig .
3a ) , where the largest hip extension and knee flexion mst happened at almost the same time and the mst was used mainly to counterbalance the mdt during swing phase .
the mean  sd peak values of mst at the knee and hip joints were 249.3  38.8 nm and 650.8  101.1 nm ( table 2 ) , respectively . using the force arm of the hamstring muscles based on magnetic resonance imaging studies
, we could also estimate the force produced by the knee flexors at this moment .
it was from 6225 to 12,450 n , which is approximately 10 times the subjects average body weight and 50% larger than that generated during the maximal isometric knee flexion .
as with the loading conditions during the initial stance phase , it was necessary to take the antagonist activities into consideration .
thus , the actual torques produced by the hamstring muscles at the knee and hip might be greater than those we estimated .
this was consistent with most of the previous studies ( 23,24,28,30,35 ) , which reported that the peak hamstring stretch and force occur during the late swing phase of sprinting before foot contact .
in addition , our results highlighted that this high load on the hamstrings was caused by the mdt because the mst functioned to counterbalance the mdt to control the rapid limb rotation during the swing phase .
we further found that the major component of mdt at both the knee and hip was the mdt due to the acceleration of shank ( fig .
4 ) . these findings may answer the question of why the hamstrings were stretched to their maximum length and the muscle force reached its maximal value during the late swing phase according to the observations of other researchers . in summary , our analysis of mst via intersegment dynamics indicated that the hamstring muscles experience tremendous loads in both the initial stance phase and late swing phase .
this is consistent with previous emg studies ( 5,35 ) reporting that peak activities of the medial and lateral hamstrings occurred during the initial stance and late swing phases .
although force load on its own is not a strong predictor of injury , the results suggest that there would be greater strain risk during these two phases .
furthermore , our analyses revealed the reasons behind those high loading conditions , that is , ext ( by grf ) in the initial stance phase and mdt ( mainly by shank angular acceleration ) in the late swing phase , respectively .
the values of flexion torque at the knee and extension torque at the hip in those two phases were considerable , indicating that the knee flexors and hip extensors play a very important role in sprint running , especially during the initial stance phase and late swing phase .
these findings may help inform coaches and athletes in designing appropriate training protocols and injury prevention strategies that focus on emphasizing knee flexors and hip extensors on the basis of the characteristics of mst .
our previous work ( 13 ) showed that all of the major muscles that cross the hip and knee joint were activated above minimum level during running , including monoarticular ( gluteus maximus , vastus lateralis , biceps femoris short head ) and biarticular ( rectus femoris , hamstrings , and gastrocnemius ) muscles .
however , hamstrings are the only biarticular muscles that flex the knee and extend the hip , in addition to the fact that hamstrings are the most injured muscles during sprint ( 14,33 ) .
future studies need to consider the role of other active and passive structures that cross the hip and knee joints .
their contributions to hip joint extension and knee joint flexion torque and their influence on the dynamics of the hamstrings need to be further studied .
moreover , some recent research indicates that during inverse dynamics analysis of locomotion , mismatched cutoff frequencies applied to the kinematic and kinetic data will likely affect the calculated joint torques ( 1,11 ) .
this might be a potential limitation of this study and should be treated with caution in further research . during the initial stance phase and late swing phase , the passive torques ( ext and mdt produced by grf and the inertial movement of the segments of the lower extremity ) applied stress to the hamstring muscles in opposite directions at both the knee and hip joints . to counter these large passive effects ,
the hamstring muscles endure high mechanical loads , which may lead to strains . by understanding the loading condition on hamstring muscles , especially the load production mechanism , injury prevention programs and rehabilitation approaches
can be developed to mitigate the high risk of hamstring strain injuries during high - speed running .
 abstractpurposethe potential mechanisms of hamstring strain injuries in athletes are not well understood . 
 the study , therefore , was aimed at understanding hamstring mechanics by studying loading conditions during maximum - effort overground sprinting.methodsthree-dimensional kinematics and ground reaction force data were collected from eight elite male sprinters sprinting at their maximum effort . 
 maximal isometric torques of the hip and knee were also collected . 
 data from the sprinting gait cycle were analyzed via an intersegmental dynamics approach , and the different joint torque components were calculated.resultsduring the initial stance phase , the ground reaction force passed anteriorly to the knee and hip , producing an extension torque at the knee and a flexion torque at the hip joint . 
 thus , the active muscle torque functioned to produce flexion torque at the knee and extension torque at the hip . 
 the maximal muscle torque at the knee joint was 1.4 times the maximal isometric knee flexion torque . during the late swing phase 
 , the muscle torque counterbalanced the motion - dependent torque and acted to flex the knee joint and extend the hip joint . 
 the loading conditions on the hamstring muscles were similar to those of the initial stance phase.conclusionsduring both the initial stance and late swing phases , the large passive torques at both the knee and hip joints acted to lengthen the hamstring muscles . 
 the active muscle torques generated mainly by the hamstrings functioned to counteract those passive effects . 
 as a result , during sprinting or high - speed locomotion , the hamstring muscles may be more susceptible to high risk of strain injury during these two phases . 
METHODS
None
Subjects
Data collection
Data reduction
Intersegmental dynamics analysis
RESULTS
DISCUSSION