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INTRODUCTION TO SPORTS BIOMECHANICS Matteo Zago
Università degli Studi di CagliariSeptember 26th, 2019
HUMAN MOVEMENT ANALYSIS AIMS AT
GATHERING QUANTITATIVE
INFORMATION ON THE MECHANICS OF
THE MUSCOLO-SKELETAL SYSTEM
SPORTS BIOMECHANICS AIMS AT
GATHERING QUANTITATIVE INFORMATION
ABOUT MOVEMENT PATTERNS
EXPERIMENTAL PHILOSOPHYCommon techniques, different approach
Determinants allowing an athlete
to perform at the highest possible
level
Diagnose which weaknesses to
tackle and how
Whether a motion is physiological
or if it differs and how much from
normal values
Diagnose symptoms and prepare
to treat the conditions
CLINICAL BIOMECHANICS SPORTS BIOMECHANICS
IMPROVE PERFORMANCE
REDUCE INJURY RISK
WINDOW ON MOTOR LEARNING AND MOTOR CONTROL
AIMS
TECHNOLOGY
1
TECHNOLOGYOverview
OPTICAL SYSTEMS FORCE PLATFORMS INERTIAL SYSTEMS
TECHNOLOGYOverview
OPTICAL SYSTEMS FORCE PLATFORMS INERTIAL SYSTEMS
OPTICAL MOCAP SYSTEMSDetectors
A CCD (charge coupled device) or CMOS
(complementary metal oxide semiconductor) sensor
converts light into electronic signals
OPTICAL MOCAP SYSTEMSCamera parameters
SHUTTER SPEED1/500 – 1/1000 s
EXPOSURE
PULSED IR LIGHT
SAMPLING FREQ
50 – 500 Hz
OPTICAL MOCAP SYSTEMSAlignment between image point and object point
Object space
Image plane
OPTICAL MOCAP SYSTEMSAlignment between image point and object point
Object space
Image plane
Collinearity equations
b1… b11: cameras internal parameters
OPTICAL MOCAP SYSTEMSCamera view: ideal scenario
OPTICAL MOCAP SYSTEMSCamera view: real scenario
Misrecognised markers
Missing markers
Blinking markers
OPTICAL MOCAP SYSTEMSCamera view: real scenario
Misrecognised markers
Blinking markers
Missing markers
Interpolation
Manual tracking
Prediction algorithms
PRELIMINARY DATA PROCESSING
2
PREDICTION AND TRACKINGTrajectory tracing algorithms
INTERPOLATIONFilling the gaps
INTERPOLATIONFilling the gaps
INTERPOLATIONFilling the gaps
ynew = interp1(x, y, xnew, ‘spline’)
FILTERINGThe derivation problem
first derivative increases the amplitude
proportional to frequency
second derivative increases the amplitude
proportional to frequency squared
FILTERINGChoosing the cut frequency
FILTERINGOutcome
3D JOINT KINEMATICS
3
2D ANGLESThe simplest approach
AN OBJECT IN SPACEPosition and heading
AN OBJECT IN SPACEPosition and heading
AN OBJECT IN SPACEPosition and heading
AN OBJECT IN SPACEPosition and heading
AN OBJECT IN SPACEPosition and heading
AN OBJECT IN SPACEPosition and heading
AN OBJECT IN SPACEPosition and heading
position vector (in the global RS)
AN OBJECT IN SPACEPosition and heading
position of the local RS
AN OBJECT IN SPACEPosition and heading
orientation matrix of the local RS
director cosines
AN OBJECT IN SPACEHeading
How to compute a local reference frame
REFERENCE FRAMESSigns conventions
y: vertical (positive upwards)
z: mediolateral (positive to the right)
x: anteroposterior (positive forward)
BIOMECHANICAL MODELAssumptions
§ collection of rigid segments
§ 3 non-collinear
markers fixed on a
single segment
§ some segments
may represent
several bones
(foot, torso)
REFERENCE FRAMESExamples
>
3D ANATOMICAL ANGLESFrom reference frames
Relative orientation of 2 local coordinate systems
independently of their origin
3D ANATOMICAL ANGLES3 angles fully specify the 9 components of a 3x3 rotation matrix
3D ANATOMICAL ANGLESWarning!
Rotation angles depend on the
order they are applied
EXAMPLESGlobal reference system
EXAMPLESLocal reference systems
EXAMPLESAnatomical angles
knee flexion/extension
CENTER OF MASSKINEMATICS
4
CENTER OF MASSSynthetic measure of human movement
CENTER OF MASSDefinition
Body Center of MassSpecifies the overall motion of a sports performer
[15]) is small enough to be ignored. CoM of the segment ‘‘head &neck’’ was computed as the midpoint of the two markers at thetragi [11,14]. Anthropometric data, including the mass distributionwithin the segments and the location of their CoM, were takenfrom [15].
Inertial parameters of each segment allow the computation ofthe body center of mass through the weighted average of the CoMof each segment. Therefore, CoM position is given by:
rCoM ¼ xCoM yCoM zCoM½ # ¼XN
i¼1
miri
M(1)
where ri ¼ xi yi zi½ # are the CoM coordinates of the ith bodysegment, mi its mass, M the whole body mass and N = 10 thenumber of considered body segments. The following signconvention was adopted: x: anteroposterior direction (positiveforward); y: craniocaudal direction (positive upwards); z: med-iolateral direction (positive to the right). Knowing the position ofeach marker, CoM coordinates are given by:
rCoMi¼ r pi
þ p rdi% r pi
! "
where p is the percentage distance of CoM between theproximal (r pi
) and the distal marker (rdi) of each segment. The CoM
of torso was estimated as the midpoint of the segment joining theinter-acromia and inter-trochanters landmarks’ midpoints.
Two sets of experiments were conducted. The first investigatedthe agreement between measurements of CoM displacementxCoM; yCoM; zCoMð Þ using SKC and GRF methods. Three healthy adult
men (24.0 ( 2.2 years; height 1.80 ( 0.09 m; body mass 73 ( 13 kg;BMI 22.4 ( 2.0 kg/m2) were asked to perform four simple gestureseach (squat, fast squat, lower limb lifting, upper limb lifting) on apiezoelectric force platform (Kistler, Winterthur, Switzerland),synchronized with the motion capture system. In the aggregate, 19acquisitions were recorded, with a minimum of five acquisitions foreach subject. Results were also compared with sacrum andreconstructed pelvis methods. Data for all four methods werecollected simultaneously (a similar approach was adopted in [16]).
A second experiment was designed to assess the agreementbetween sacrum, reconstructed pelvis and SKC in various move-ments comprising an aerial phase. Other four men (23.6 ( 1.9years; height 1.81 ( 0.08 m; body mass 75 ( 12 kg; BMI 22.8 ( 1.9kg/m2) were asked to perform horizontal jumps with a time of flightas long as possible. Each subject did at least five jumps, 26acquisitions were recorded on the whole. Proper informed consentwas obtained from the subjects. This study complied with the ethicalprinciples of the Declaration of Helsinki.
While in flight, considering the aerodynamic forces negligible atlow speed, human body can not apply any force to the
environment, hence the CoM is only subjected to the gravityforce, and its spatial displacement follows a ballistic (parabolic)trajectory.
SKC, sacrum and reconstructed pelvis methods were comparedon the basis of three kinematic indices evaluated in the arial phaseof each trial. Firstly, the acceleration of gravity was estimated asthe second derivative of yCoM tð Þ. Furthermore, we assessed thedifferences between the temporal path of yCoM tð Þ and its idealparabolic regression, since it should be: yCoM tð Þ ¼ y0 þ vy0t%ð1=2Þgt2. Finally, we evaluated the variability of CoM speed alongthe directions parallel to the ground.
2.2. Statistical calculations
In the first experiment, for each subject’s trial, the root meansquare error (RMSE) between each CoM spatial coordinate,measured with each of the three methods, and the correspondingoutput of the force platform was calculated. In the secondexperiment, for each subject’s trial, the coefficient of determina-tion (R2) related to the fitting of the temporal path of yCoM with theideal parabola, the mean of the estimated accelerations of gravityand the standard deviation (SD) of fore-aft and lateral CoM velocitywere computed for each method. For all these variables, inter-methods agreement was assessed with one-way ANOVA forrepeated measures, deepened with two-tailed paired t-tests (withBonferroni’s correction) when significant. A significance level of 5%(p < 0.05) was set.
3. Results
3.1. Comparison with GRF method
CoM three dimensional displacements were computed for eachmovement, subject and trial. As an example, Fig. 2 depicts CoMdisplacement along the three axes during a squat measured withSKC and GRF. Results about CoM displacement and statisticalanalysis are reported in Table 1.
Anteroposterior CoM displacement. RMSEx relative to thereference (GRF) measured with the segmental method wassignificantly lower than RMSEx obtained with the other twomethods (p < 0.001 both for ANOVA and t-tests). On the otherhand, reconstructed pelvis and sacrum methods were notsignificantly different one to each other.
Craniocaudal CoM displacement. Movements along the y axiswere wider than those in the other two directions. As observedbefore, SKC results appear to be closer to GRF than results yieldedby sacrum and reconstructed pelvis methods. RMSEy wassignificantly different in every test.
0 2 4 6−20
0
20
40
60
80
100
time [s]
CoM
dis
plac
emen
t [m
m]
Anteroposterior direction
SKCGRF
0 2 4 6−500
−400
−300
−200
−100
0
100
time [s]
CoM
dis
plac
emen
t [m
m]
Craniocaudal direction
SKCGRF
0 2 4 6−10
−5
0
5
10
15
20
25
30
time [s]
CoM
dis
plac
emen
t [m
m]
Mediolateral direction
SKCGRF
Fig. 2. Experiment 1: example of CoM displacements for a single participant during a single trial (a squat), computed with SKC (solid line) and GRF (dashed line) methods.
A. Mapelli et al. / Gait & Posture 39 (2014) 460–465462
Gait and Posture, 2013
CENTER OF MASSComputation basics
CENTER OF MASSComputation basics
CENTER OF MASSDuring a jump
CENTER OF MASSComputing mechanical energy
kinetic energy
potential energy
external energy
SYMMETRY ANDREPEATIBILITY
5
CYCLOGRAMSAngle-angle plot
SIMMETRYBilateral cyclograms (angle-angle plot)
Goswami et al., 2009
SIMMETRY MEASURESTrend symmetry, linear fit
Iosa et al., 2009 Crenshaw and Richards, 2006
Pre Post
α 41° 42°R2 0.9 1A
(deg2)204 85
KARATE
BALANCE MASTERY
AND CONTROLYU
RI
SH
IRA
I
WO
RL
D C
HA
MP
ION
AL
ES
SIO
CA
ST
EL
LA
NO
ITA
LIA
N C
HA
MP
ION
DYNAMIC BALANCE IN KARATEA Center-of-Mass perspective
? Differences in CoM kinematics between
proficiency levels
6 elite vs. 4 amateur karateka / 11 kata steps
Step
% o
f bod
y he
ight
CoM Height
DYNAMIC BALANCE IN KARATEElite athletes postural strategies
CoM displacement, speed and momentum
Support base: different hip/knee kinematics
Journal of Electromyography and Kinesiology, 2015
INITIAL FREEZING OF JOINT MOTIONS
TECHNIQUE DEPENDS ON HOW THE MOTOR SYSTEM HANDLES DOFs
BERNSTEIN, MOTOR LEARNING
AND DEGREES OF FREEDOM
RELEASE OF DOFs AS THE SKILL LEVEL IMPROVES
LEARNING TO KICKDominance-driven insights
? Understand sport-specific motor learning
12 under-14 soccer players
by Zago M. et al. 55
© Editorial Committee of Journal of Human Kinetics
preferred leg (p<0.01), with an effect size of 1.7. No significant differences at impact were found regarding the support knee angle, whereas while kicking with the preferred leg the knee was significantly more extended (p<0.001) as compared to kicking with the non‐preferred leg. Time curves, reported in Figure 3, show a similar trend in both cases.
Upper body kinematics Distance between the support‐side forearm and
total‐body CoM was wider with the preferred leg
during all the ground‐support phases (Figure 2), and significantly different (p<0.01) at impact. The forearm velocity was significantly lower in preferred leg kicks on both the support side (p<0.05) and the kicking side (p<0.01), with a large effect size. The support‐side elbow flexion/extension angle (Figure 3), did not differ at impact with respect to kicking laterality (small effect size). The shoulders inclination towards the target (i.e. upper trunk orientation) was lower when kicking with the preferred leg (p<0.01, large effect size), while shoulders obliquity relative to the ground was higher (p<0.01, d=1.3).
Figure 1 Laboratory setting: positioning of the subject, of the target and of the nine infra‐red cameras
15 right and left pass kicks
Speed vs. accuracy trade off
LEARNING TO KICKPreferred-leg kicking…
CoM and foot/shank speed
arms more abducted & different trunk rotation
Journal of Human Kinetics, 2014
LEARNING TO DRIBBLESpeed, accuracy and degrees of freedom
? Understand sport-specific motor learning
10 sub-elite under-12 soccer players
* Mann-Whitney, p<0.05
Journal of Sports Sciences, 2016 Scienza & Sport, 2014
LEARNING TO DRIBBLESpeed, accuracy and degrees of freedom
Pathway of organizing joints motion towards a low dimensional coordination mode
INJURY PREVENTION
6
ACL injury
• 3/10.000 hours
• 43% non contact
• only 55% return to
competitive level
• $1 billion/year
spent for ACL
reconstruction
ACL injury mechanism
CHANGES OFDIRECTION
Power actions with
short recovery periods
High mechanical and
metabolic impact
Changes of Direction mechanics
Return to play tests
• Balance & proprioceptive knee function
(stabilometry)
CoP
GRF
Davies et al., 2017; Grindem et al., 2016
Return to play tests
• Balance & proprioceptive knee function
(stabilometry)
• Closed-chain isokinetic testing (no more
than 10% difference between sides)
Davies et al., 2017; Grindem et al., 2016
Return to play tests
• Balance & proprioceptive knee function
(stabilometry)
• Closed-chain isokinetic testing (no more
than 10% difference between sides)
• Functional jump tests (squat jump, drop
jump)
Davies et al., 2017; Grindem et al., 2016
Return to play tests
• Balance & proprioceptive knee function
(stabilometry)
• Closed-chain isokinetic testing (no more
than 10% difference between sides)
• Functional jump tests
Hewett et al., 2005
External knee adduction moment
landing with (dynamic)
valgus knee moments
increases the risk of ACL
rupture by 250%
Return to play tests
• Balance & proprioceptive knee function
(stabilometry)
• Closed-chain isokinetic testing (no more
than 10% difference between sides)
• Functional jump tests
• Functional hop tests (within 10%
difference between sides)
Davies et al., 2017; Grindem et al., 2016
Background and aim
FATIGUE
deterioratesneuromuscularcontrol and postural stability
Barber-Westin and Nayes, 2017; McLean et al, 2007
Background and aim
FATIGUE
deterioratesneuromuscularcontrol and postural stability
45°-90° CoD
fatigue alterssagittal and frontal planemechanicsincreasingACL injury risk
Cortes et al, 2013; Nyland et al, 1997
Background and aim
FATIGUE
deterioratesneuromuscularcontrol and postural stability
45°-90° CoD
fatigue alterssagittal and frontal planemechanicsincreasingACL injury risk
180° TURNS
key technicalmodificationsdue to fatigue.Are they harmfulfor the knee?
?
CoDs mechanics and fatigue
Methods
PARTICIPANTS
20 young men18-23 yearsBMI: 21-24 kgm-2
PROTOCOL
5 minutes5-m shuttle runSpeed: 75% MAS
KINEMATICS
optical mocapstance-phaseCoM and joints
PHYSIOLOGY
oxygen uptakeheart-rate, lactateRPE
10
deg
40
0 10050
hip flexion
% stance phase
-30
30
deg
0 10050
hip rotation internal (-) / external (+)
20
deg
0 1005% stance phase
knee flexion60
0 1050
% stance phase
0.0
ms-1
2.0
0 10050
CoM speed
Data analysis
20
deg
60peaks
early turnslate turns
% stance phase
0 10050
30
RoM
(deg
)
60
turn number1 5010 60
RoM
turns 6-10
last 5 turnsWithin-subjects statistics: mean, ICC
Between-subjects statistics:mean, sd, 2w-ANOVA, !2, CI
% HRmax Resultsexercise physiology
At a shuttle speed of 3.1±0.3 ms-1,
the protocol intensity matched the
common demands of many team sports.
The test involved mixed aerobic and
anaerobic exercise, with substantial
muscular load.
Ciprandi et al, 2017; Zago et al, 2018
94±4%
% V’O2,max
88±11%
RPE 6-20
17.5±1.3
Blood lactate
10.3±2.7 mM l-1
4 m
Ml-1
Discussion
HIP FLEXION
KNEE FLEXION
SAGITTAL PLANEFatigued muscles absorb less energy: ligaments load may increase.CoM speed dropped at toe-off: reduced storage-release of elastic energy?
Alentorn-Geli et al, 2009; David et al, 2017; Nyland et al, 1997; Rafeuddin et al, 2016
HIP ADDUCTION
INT. ROTATION
CORONAL AND TRANSVERSE PLANEAttempt to readily redirect the pelvis. Higher hip internal rotation might decrease the load absorbed on the frontal plane. Possible higher knee adduction moment.
Jones et al, 2016
WHAT TO DO NEXT?EMG, 3D knee kinematics and kinetics.Unplanned turns? Women? Elite athletes?
91
INTRODUCTION TO SPORTS BIOMECHANICS Matteo Zago
Università degli Studi di CagliariSeptember 26th, 2019
MATTEO ZAGO