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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

matteo2.zago@polimi.it