mecanica alergarii

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    Titolo

    BIOMECHANICS

    OF HUMAN MOVEMENT

    Rita Stagni, Silvia Fantozzi, Angelo Cappello

    Biomedical Engineering Unit, DEIS,

    University of Bologna

    Aurelio CappozzoDepartment of Human Movement and Sport Sciences

    IUSM, Rome

    SUMMER SCHOOL 2006 Monte S.Pietro, Bologna

    ADVANCED TECHNOLOGIES FOR NEURO-MOTOR ASSESSMENT AND REHABILITATION

    Biomechanics, kinematics, kinetics

    Biomechanics is the science concerned with the internaland external forces acting on the human body and theeffects produced by these forces.

    Kinematics is the branch of biomechanics concernedwith the study of movement from a geometrical point ofview.

    Kinetics is the branch of biomechanics concerned withwhat causes a body to move the way it does.

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    Anthropometric parameters

    Segmental kinematics (stereophotogrammetry, wearable sensors, etc)

    External forces and moments (dynamometry, baropodometry, etc)

    Muscular electrical activity (electromyography)

    Metabolic energy (indirect calorimetry)

    Some variables and parameters can be measured

    DiSMUSDiSMUSDiSMUSDiSMUS

    BTS

    BTS

    BTSBTS

    BTSBTSBTSBTS

    BTSBTSBTSBTS

    BTS

    BTS

    BTS

    BTS

    BTSBTSBTSBTS

    BTSBTSBTSBTS

    Gait Analysis Laboratory

    BTS

    ELITEplus

    STEREOPHOTOGRAMMETRIC

    SYSTEM

    KISTLER

    PLATFORM

    AMPLIFIER

    TELEMG

    DYNAMIC

    ELECTROMYOGRAPHY

    SYSTEM

    BTS

    DIGIVEC

    VHS

    VHS AND DIGITAL

    RECORDING

    SYSTEM

    Cameras & Infra-red Strobes

    Videocamera

    DynamometricPlatforms

    LTM

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    Instantaneous bone pose(virtual representation of the skeletal system in motion)

    Relative movement between adjacent bones(joint kinematics)

    Forces transmitted by muscles-tendons-ligaments-bones(joint kinetics)

    Muscular mechanical work/powersystem energy variation

    (joint energetics)

    1

    The estimable quantities

    4

    3

    2

    DiSMUSDiSMUSDiSMUSDiSMUS

    In order to describe the pose of the bone as a rigid body

    we assume a local reference frame such that the local coordinates

    of the bone points are time invariant

    Yg

    XgZg

    yl

    xl

    zlDiSMUSDiSMUSDiSMUSDiSMUS

    INSTANTANEOUS 3D BONE POSE

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    Yg

    XgZg

    The problem is now the mathematical description of the position and orientationof the local reference frame with respect to the global one

    The description of the pose

    yl

    xl

    zl

    DiSMUSDiSMUSDiSMUSDiSMUS

    Numerical description of the pose vs time (3-D case)

    orientation vector

    [ ] kjlzj

    g

    lyj

    g

    lxj

    g

    lj

    g ,...,1; ==

    [ ] kjtttlzj

    g

    lyj

    g

    lxj

    g

    lj

    g ,...,1; ==t

    position vector

    Six scalar quantitiesin each sampled instant of time

    yl

    xl

    zl

    Yg

    XgZg

    Oll

    gtl

    g

    orientation matrix

    kjlj

    g ,...,1 =RDiSMUSDiSMUSDiSMUSDiSMUS

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    The orientation matrix of the local frame with respect tothe global one is defined by:

    1st column xl axis versor components

    2nd column yl axis versor components

    3rd column zl axis versor components

    These components are the cosines of the angles betweeneach versor and the XYZ global axes.

    JOINT KINEMATICS

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    y

    x

    z

    Sagittal plane

    Frontal (coronal)

    plane

    Transverse plane

    Anatomical planes and axes

    AP axis

    ML axis

    V axis

    DiSMUSDiSMUSDiSMUSDiSMUS

    Hip flexion-extension

    Flexion (+) Extension (-)

    a a

    DiSMUSDiSMUSDiSMUSDiSMUS

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    Knee flexion-extension

    Flexion (-) Extension (+)

    a g

    DiSMUSDiSMUSDiSMUSDiSMUS

    Ankle dorsal and plantar flexion

    Dorsal flexion (+)

    Plantar flexion (-)

    c

    c

    Neutral position

    DiSMUSDiSMUSDiSMUSDiSMUS

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    h

    a

    k

    H

    K

    A

    M

    A lower limb model

    Joint centres:

    H Hip

    K Knee

    A Ankle

    M Metatarsus-phalanx V toe

    Hypotheses: Planar motion (sagittal plane) Joints are modelled using

    cylindrical hinges (1 dof)

    DiSMUSDiSMUSDiSMUSDiSMUS

    Yg

    Xg

    H

    K

    A

    M

    Experimental protocol

    Joint centres:

    H greater trochanter

    K lateral femoral epicondyle

    A lateral malleolus

    M metatarsus-phalanx V toeDiSMUSDiSMUSDiSMUSDiSMUS

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    Yg

    Xg

    Flexion-extension angles of the lower limb joints during walking

    k

    a

    hip

    knee

    ankle

    0 50 100

    [% cycle]

    40

    -20

    90

    30

    0

    -60

    [deg]

    h

    H

    K

    A

    MDiSMUSDiSMUSDiSMUSDiSMUS

    Motor task classification

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    1) starts from the knowledge, in each sampled instant of time, of the

    pose of the bony segments involved in the laboratory frame

    2) entails the estimation of the instantaneous pose (position andorientation) of one bony segment relative to the other.

    The description of 3-D joint kinematics

    yg

    zg xg DiSMUSDiSMUSDiSMUSDiSMUS

    Motion capture provides these data

    yg

    xg

    zg

    orientation vector

    [ ] kjczj

    g

    cyj

    g

    cxj

    g

    cj

    g ,...,1; ==

    kjtttczj

    g

    cyj

    g

    cxj

    g

    cj

    g,...,1; ==t

    position vector

    [ ] kjcippp zijg

    yijg

    xijg

    ijg ,...,;,...,; 11 ===p

    position vectors

    xczc

    yc

    xczc

    yc

    xc

    zc

    yc

    mathematicaloperator

    DiSMUSDiSMUSDiSMUSDiSMUS

    kjcj

    g,...,1; =R

    orientation matrix

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    Relative pose

    global orientation matrix

    cpgR

    Femur

    global position vectorycp

    xcp

    zcp

    ycd

    xcd

    zcd

    global orientation matrix

    cdgR

    Tibia

    global position vector

    relative position vector&

    relative orientation matrix

    In any given instant of time:

    proximal frame

    distal frame

    [ ]PzgPygPxgPg ttt=t [ ]DzgDygDxgDg ttt=t

    P

    D

    DiSMUSDiSMUSDiSMUSDiSMUS

    Relative position

    Femur

    global position vector

    Tibia

    global position vector

    relative position vector in the proximal frame

    In any given instant of time:

    cp

    gR

    +

    ( ) ( ) Pg

    cp

    g

    D

    g

    cp

    g

    PD

    cp

    Pg

    gcp

    Dg

    gcp

    PDcp

    Pg

    Dg

    PDg

    tRtRt

    tRtRt

    ttt

    TT=

    =

    =

    [ ]PzgPygPxgPg ttt=t [ ]DzgDygDxgDg ttt=tycp

    xcp

    zcp

    ycd

    xcd

    zcd

    PDgt

    P

    D

    DiSMUSDiSMUSDiSMUSDiSMUS

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    Relative orientation

    Femur

    global position matrix

    Tibia

    global position matrix

    ( ) cdgT

    cpg

    cdcp RRR =

    relative orientation vector in the proximal frame

    In any given instant of time:

    cp

    gRcd

    gRycp

    xcp

    zcp

    ycd

    xcd

    zcd

    DiSMUSDiSMUSDiSMUSDiSMUS

    The two systems of reference are assumed to be aligned,

    In summary

    then the distal system of reference moves in its new position,

    yd

    xd

    zd

    and then it rotates in its new orientation

    yp

    xpzp

    yd

    xd

    zdDiSMUSDiSMUSDiSMUSDiSMUS

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    At the time t1

    In summary

    at the time t2

    yd

    xd

    zd

    yp

    xpzp

    yd

    xd

    zd

    and so forth

    yd

    xd

    zd

    yd

    xd

    zd

    yd

    xd

    zd

    t2t1

    DiSMUSDiSMUSDiSMUSDiSMUS

    Motion is described as the ensemble of

    the positions and orientations of the distal

    bone with respect to the proximal bone

    determined in sampled instants of time

    during the observation interval

    This matrix, and the three independent scalar quantities embedded in it,completely describe the orientation of the

    distal relative to the proximal bone.

    orientation matrix of the distal relative to the proximal cluster frame

    Orientation

    =

    pdpdpd

    pdpdpd

    pdpdpd

    zzzyzx

    yzyyyx

    xzxyxx

    cdcp

    coscoscos

    coscoscos

    coscoscos

    R

    yd

    xd

    zd

    yp

    xpzp

    cdcpR

    However, the relevant scalar components have no physical meaning and, assuch, do not convey readable information about joint rotation. DiSMUSDiSMUSDiSMUSDiSMUS

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    Orientation

    [ ]cdzcp

    cdy

    cp

    cdx

    cp

    cd

    cp

    cd

    cp

    cd

    cp == n

    orientation vector of the distal relative to the proximal cluster frame

    This vector, and the three independent scalar quantities embedded in it,completely describe the orientation of thedistal relative to the proximal bone.

    However, the relevant scalar components have no physical meaning as such.

    yd

    xd

    zd

    yp

    xpzp

    cdcp

    DiSMUSDiSMUSDiSMUSDiSMUS

    n

    rotationvirtuala

    representsand

    rotation,ofaxisvirtuala

    representsvectorThecd

    cp

    cd

    cp

    n

    Problem

    Relative position and orientation descriptions illustrated so far carry

    all the necessary information relative to joint kinematics,

    but

    have no direct use in movement analysis

    DiSMUSDiSMUSDiSMUSDiSMUS

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    Orientation

    The orientation of the distal relative to the proximal cluster frame

    may be described using

    a sequence of three rotations about selected axes (Euler Angles).

    These rotations have a physical meaning,

    Nevertheless, still represent an abstraction !

    DiSMUSDiSMUSDiSMUSDiSMUS

    yp

    xpzp

    yd

    zd

    xd

    Example: hip joint

    pelvis frame

    femur frame

    DiSMUSDiSMUSDiSMUSDiSMUS

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    yp

    xp

    yd

    zdzpx

    d

    zp

    yp

    xp

    yd

    zd

    xd

    Starting orientation Orientation at time t

    Example: hip joint

    DiSMUSDiSMUSDiSMUSDiSMUS

    yp

    xp

    yd1

    zd1 zpxd1

    Rotation about the axis zd1: femur or pelvis medio-lateral axis

    First rotation: flexion-extension

    DiSMUSDiSMUSDiSMUSDiSMUS

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    yp

    xp

    yd1

    zd1

    zp

    zd2

    yd2

    xd2 xd1

    Rotation about the axis xd2: femur antero-posterior axis

    Second rotation: abduction-adduction

    DiSMUSDiSMUSDiSMUSDiSMUS

    yd3 yd2

    xd3xd2

    yp

    xp

    zd2zp

    zd3

    Rotation about the axis yd2: femur longitudinal axis

    Second rotation: internal-external rotation

    DiSMUSDiSMUSDiSMUSDiSMUS

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    The three angles of the rotation sequence

    depend on both

    In summary

    ,,

    the axes about which the rotations are made to occur

    the relevant sequence

    A generic orientation of a distal relative to a proximal frame

    may be obtained as a result of three successive and ordered rotations

    about two or three different axes (belonging to either frames).

    DiSMUSDiSMUSDiSMUSDiSMUS

    The Cardan convention

    The rotation sequence illustrated previously provides angles that are often

    referred to as Cardan Angles*

    Grood ES, Suntay WJ. A joint co-ordinate system for the clinical description of three-dimensional motions:application to the knee. Transactions of ASME Biomechanical Engineering1983

    DiSMUSDiSMUSDiSMUSDiSMUS

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    ADDUCTION (-)

    ABDUCTION (+)

    INT. ROTATION (+)EXT. ROTATION (-)

    EXTENSION (-)

    FLEXION (+)

    JOINT ANGLES

    (Grood and Suntay, ASME J.Bionech. 1983)

    A question

    What happens if the rotation sequence is changed?

    Given an orientation of the distal relative to the proximal frame,

    60.060.560.460.958.560.5

    5.010.011.24.921.711.2

    10.01.30.610.019.40.6

    zxyyzxxyzzyxxyzyxz[deg]

    zp

    yp

    xp

    ydzd

    xddepending on the sequence selected the following descriptions are obtained:

    DiSMUSDiSMUSDiSMUSDiSMUS

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    The orientation vector convention

    [ ]cdz?cdy?cdx?cdcpcdcpcdcp == n

    orientation vector of the distal relative to the proximal frame

    yd

    xd

    zd

    yp

    xpzp

    cdcp

    The problem is: in what system of reference should this vector be represented?

    The options are:

    either the proximal or the distal frame

    the joint axes as defined by the Cardan convention

    Do not forget: it is a totally abstract representation !

    Woltring HJ. 3-D attitude representation of human joints: A standardization proposal. Journal of Biomechanics1994

    DiSMUSDiSMUSDiSMUSDiSMUS

    Sensitivity of the knee joint kinematics to the angular convention

    1 - Cardan convention

    2 - Orientation vectorprojection on theproximal axes

    3 - Orientation vector

    projection on theCardan (joint) axes

    DiSMUSDiSMUSDiSMUSDiSMUS

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    position vectoryd

    xd

    zd

    yp

    xpzp

    Position

    PDt?

    [ ]???? PDzPDyPDxPD ttt=t

    The position vector is represented relative to two points (rigid with theproximal and distal bone, respectively, and

    a set of axes of choice

    P

    DThe selected points may bethe origins of the framesinvolved

    DiSMUSDiSMUSDiSMUSDiSMUS

    The position vector is represented relative to two points (rigid with theproximal and distal bone, respectively) and

    a set of axes of choice

    yd

    xd

    zd

    yp

    xpzp

    Position

    thus the three scalar quantities that represent positiondepend on the choice of the two reference points and the set of axes.

    PDt?

    P

    D

    position vector

    [ ]???? PDzPDyPDxPD ttt=t

    The selected points may bethe origins of the framesinvolvedor two points arbitrarilyidentified

    DiSMUSDiSMUSDiSMUSDiSMUS

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    c displacement along the distal z axis (coinciding with the proximal z axis)

    a displacement along the distal x axis (after the first rotation)

    b displacement along the distal y axis (after the second)

    The axes with respect to which we represent

    the position vector

    yd

    xdzd

    yp

    xpzp

    PDt?

    P

    D

    yd2

    xd1

    zdzp a

    b

    c

    An option is represented by the joint axes:

    DiSMUSDiSMUSDiSMUSDiSMUS

    The points with respect to which we represent

    the position vector

    Example with reference to the knee joint:

    P

    D

    A point (P) in the

    proximal set of axes

    A point (D) in the

    distal set of axes

    P and D coincide while the subject assumes an orthostatic posture

    DiSMUSDiSMUSDiSMUSDiSMUS

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    The six degrees of freedom of a joint according to the Cardan convention

    about the distal z axis (coinciding with the proximal z axis)

    about the distal x axis (after the first rotation) about the distal y axis (after the second rotation)c displacement along the distal z axis (coinciding with the proximal z axis)

    a displacement along the distal x axis (after the first rotation)

    b displacement along the distal y axis (after the second)

    yd2

    xd1

    zdzp

    cb

    a

    In summaryDiSMUSDiSMUSDiSMUSDiSMUS

    A set of orthogonal axes rigid with the proximal bone (p)

    A set of orthogonal axes rigid with the distal bone (d)

    A point (P) in the proximal set of axes

    A point (D) in the distal set of axes

    The three axes with respect to which the position vector of the distal

    bone relative to the proximal bone is represented

    The axis about which the first rotation is performed

    The axis about which the second rotation is performed

    The axis about which the third rotation is performed

    In summary

    In order to determine the six quantities that describe the position and

    orientation of the distal bone relative to the proximal bone the following

    entities must be defined:

    DiSMUSDiSMUSDiSMUSDiSMUS

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    Knee joint kinematics vs orientation of the proximal axes

    proximal frame rotatedabout the y axis of 5

    proximal frame rotatedabout the x axis of 5

    nominal referencesystems

    DiSMUSDiSMUSDiSMUSDiSMUS

    The representation of jointkinematics, whateverconvention is chosen, isvery sensitive to thedefinition of the set of axesinvolved

    The two requirements are met by using anatomical frames

    These sets of axes are repeatable

    because they rely on identifiable anatomical landmarks

    They are anatomical axes and define anatomical planes: thus,

    the joint six degrees of freedom may be named in a manner

    consistent with functional anatomy

    DiSMUSDiSMUSDiSMUSDiSMUS

    The definition of anatomical frames is not unique

    Possible definitions are

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    Conventional Gait Model (Plug-in-Gait di VICON) 1

    Calibrated Anatomical System Technique (CAST)2

    ISB recommendation3

    Pelvis

    1 Davis III RB, Ounpuu S, Tyburski D, Gage JR. A gait analysis data collection and reduction technique.Human

    Movement Sciences, 19912Cappozzo A, Catani F, Croce UD, Leardini A. Position and orientation in space of bones during movement:

    Anatomical frame dedinition and determination.Clinical Biomechanics 19953Wu G, Cavanagh PR. ISB recommendations for standardization in the reporting of kinematic data.Journal of

    Biomechanics1995

    DiSMUSDiSMUSDiSMUSDiSMUS

    Centre of head of the femur

    Femur

    TF

    Conventional Gait ModelCAST

    ISB recommendation

    DiSMUSDiSMUSDiSMUSDiSMUS

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    Femur

    Mid-point between the femur epicondyles

    ELEM

    Conventional Gait Model

    CASTISB recommendation

    DiSMUSDiSMUSDiSMUSDiSMUS

    Femur

    Conventional Gait ModelCAST

    ISB recommendation

    DiSMUSDiSMUSDiSMUSDiSMUS

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    JOINT KINETICS

    Example: internal loads

    acting at the knee

    DiSMUSDiSMUSDiSMUSDiSMUS

    The problem: musculo-skeletal loading

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    Loads transmitted by relevant tissues

    http://www.rad.upenn.edu/rundle/Knee/kneeMRICONT.htmlDiSMUSDiSMUSDiSMUSDiSMUS

    Semimembranosus Muscle

    Gastrocnemius, Medial Head

    Biceps Femoris

    Gastrocnemius, Lateral Head

    Sartorius Muscle

    Plantaris

    Medial Collateral Ligament

    Posterior Cruciate Ligament

    Patellar tendon

    http://www.rad.upenn.edu/rundle/Knee/kneeMRICONT.html

    Loads transmitted by relevant tissues

    DiSMUSDiSMUSDiSMUSDiSMUS

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    Loads transmitted by relevant tissues

    http://www.rad.upenn.edu/rundle/Knee/kneeMRICONT.htmlDiSMUSDiSMUSDiSMUSDiSMUS

    Gastrocnemius, Medial HeadGastrocnemius, Lateral Head

    Patellar tendon

    Loads transmitted by relevant tissues

    http://www.rad.upenn.edu/rundle/Knee/kneeMRICONT.htmlDiSMUSDiSMUSDiSMUSDiSMUS

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    Gastrocnemius, Medial Head

    Gastrocnemius, Lateral Head

    Semimembranosus Muscle

    Patellar tendon

    Loads transmitted by relevant tissues

    http://www.rad.upenn.edu/rundle/Knee/kneeMRICONT.htmlDiSMUSDiSMUSDiSMUSDiSMUS

    Gastrocnemius, Medial HeadGastrocnemius, Lateral Head

    Semimembranosus Muscle

    Bone-to-bone

    Patellar tendon

    Loads transmitted by relevant tissues

    http://www.rad.upenn.edu/rundle/Knee/kneeMRICONT.htmlDiSMUSDiSMUSDiSMUSDiSMUS

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    Forces transmitted by muscles

    http://www.rad.upenn.edu/rundle/Knee/kneeMRICONT.htmlDiSMUSDiSMUSDiSMUSDiSMUS

    QFh

    Fg

    Fp

    Q centroid of the cross sectional area

    Forces transmitted by muscles

    distributed forces are assumed to be parallel and uniform

    http://www.rad.upenn.edu/rundle/Knee/kneeMRICONT.htmlDiSMUSDiSMUSDiSMUSDiSMUS

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    Forces transmitted by muscles

    Gastrocnemius, Medial Head

    Gastrocnemius, Lateral Head

    Patellar tendon

    Semimembranosus MuscleBone-to-bone Fh

    FgFp

    http://www.rad.upenn.edu/rundle/Knee/kneeMRICONT.htmlDiSMUSDiSMUSDiSMUSDiSMUS

    Forces exchanged between bones

    http://www.rad.upenn.edu/rundle/Knee/kneeMRICONT.html

    Gastrocnemius, Medial Head

    Gastrocnemius, Lateral Head

    Patellar tendon

    Semimembranosus MuscleBone-to-bone Fh

    FgFp

    http://www.rad.upenn.edu/rundle/Knee/kneeMRICONT.htmlDiSMUSDiSMUSDiSMUSDiSMUS

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    Forces exchanged between bones: resultant force and couple

    http://www.rad.upenn.edu/rundle/Knee/kneeMRICONT.html

    Gastrocnemius, Medial Head

    Gastrocnemius, Lateral Head

    Patellar tendon

    Semimembranosus MuscleBone-to-bone Fh

    FgFp

    Q

    Fb

    http://www.rad.upenn.edu/rundle/Knee/kneeMRICONT.htmlDiSMUSDiSMUSDiSMUSDiSMUS

    Forces exchanged between bones: resultant force and couple

    http://www.rad.upenn.edu/rundle/Knee/kneeMRICONT.html

    Gastrocnemius, Medial Head

    Gastrocnemius, Lateral Head

    Patellar tendon

    Semimembranosus MuscleBone-to-bone Fh

    FgFp

    Q

    Fb

    X

    assumption

    http://www.rad.upenn.edu/rundle/Knee/kneeMRICONT.htmlDiSMUSDiSMUSDiSMUSDiSMUS

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    Q

    Forces exchanged between bones: resultant force

    ?

    http://www.rad.upenn.edu/rundle/Knee/kneeMRICONT.html

    DiSMUSDiSMUSDiSMUSDiSMUS

    http://www.rad.upenn.edu/rundle/Knee/kneeMRICONT.html

    K

    Q

    LE

    ME

    Forces exchanged between bones: resultant force

    http://www.rad.upenn.edu/rundle/Knee/kneeMRICONT.html

    DiSMUSDiSMUSDiSMUSDiSMUS

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    Forces exchanged between bones: resultant force and couple

    Gastrocnemius, Medial Head

    Gastrocnemius, Lateral Head

    Patellar tendon

    Semimembranosus MuscleBone-to-bone Fh

    FgFp

    K

    Fb

    Cb

    Q

    http://www.rad.upenn.edu/rundle/Knee/kneeMRICONT.htmlDiSMUSDiSMUSDiSMUSDiSMUS

    Internal load modelling

    Gastrocnemius, Medial Head

    Gastrocnemius, Lateral Head

    Patellar tendon

    Semimembranosus MuscleBone-to-bone

    Fh

    FgFp

    K

    Fb

    Cb

    http://www.rad.upenn.edu/rundle/Knee/kneeMRICONT.htmlDiSMUSDiSMUSDiSMUSDiSMUS

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    Muscles, tendons and ligaments are treated as if they were ropes!

    no 3-D modelling

    no interaction with surrounding muscles and bony structuresis taken into consideration

    Continuum mechanics (FEM) and a 3-D approach should be used

    Internal load modellingDiSMUSDiSMUSDiSMUSDiSMUS

    Construction of the free-body diagram

    of the shank and foot system

    DiSMUSDiSMUSDiSMUSDiSMUS

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    =+++++++=+++++

    ICCMMMMMMamFFFFWR

    KRb

    K

    F

    K

    F

    K

    F

    K

    F

    K

    W

    K

    R

    CMbpgh

    bpgh

    Fh

    Fp

    FgFb

    Cb

    W

    CR

    R

    The equations of motion (limited to plane motion)

    K

    DiSMUSDiSMUSDiSMUSDiSMUS

    Intersegmental force and couple: definition

    W

    CR

    R

    Fis

    Cis

    K

    b

    K

    F

    K

    F

    K

    F

    K

    Fis

    bpghis

    CMMMMC

    FFFFF

    bpgh++++=

    +++=

    for the time being the point K is chosen arbitrarily

    Fh

    Fp

    FgFb

    Cb

    W

    CR

    R

    DiSMUSDiSMUSDiSMUSDiSMUS

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    inertia parameters

    Intersegmental force and couple: estimation (limited to plane motion)

    kinematic quantities

    reaction forcesW

    CR

    R

    Fis

    Cis

    K

    =++++

    =++

    ICCMMM

    amFWR

    KRisKF

    KW

    KR

    CMis

    is

    DiSMUSDiSMUSDiSMUSDiSMUS

    Kinematic quantities

    position vector and orientation matrix ,relative to the

    laboratory (g) frame, of the anatomical frame (a), in

    each sampled instant of time

    local position vector of the intersegmental loads

    reduction point K

    For each body segment of interest, the following quantities are estimated:

    Kap

    ag

    ag , Rt

    DiSMUSDiSMUSDiSMUSDiSMUS

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    Kinematic quantities & inertia parameters

    position vector and orientation matrix ,relative to the

    laboratory (g) frame, of the anatomical frame (a), in

    each sampled instant of time

    local position vector of the intersegmental loads

    reduction point K

    mass

    local position vector of the CM

    principal axes of inertia (i) orientation matrix relative

    to the anatomical frame (a)

    moments of inertia

    m

    ia

    zyx ,I,II

    CM

    ap

    For each body segment of interest, the following quantities are estimated:

    ag

    ag , Rt

    Kap

    DiSMUSDiSMUSDiSMUSDiSMUS

    W

    CR

    R

    Fis

    Cis

    K

    Intersegmental force and couple: estimate

    =++++

    =++

    ICCMMM

    amFWR

    KRis

    K

    F

    K

    W

    K

    R

    CMis

    is

    DiSMUSDiSMUSDiSMUSDiSMUS

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    CR

    R

    Forces exchanged between foot and floor

    (ground reactions)

    DiSMUSDiSMUSDiSMUSDiSMUS

    Forces exchanged between foot and floor

    (ground reactions)

    DiSMUSDiSMUSDiSMUSDiSMUS

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    Foot-ground contact area during level walking

    BIOM-Essen/HennigDiSMUSDiSMUSDiSMUSDiSMUS

    Forces acting on the force plate

    distributed forces force-couple system

    in a given instant of time

    C

    F

    Y

    X

    ZO

    DiSMUSDiSMUSDiSMUSDiSMUS

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    The force plate supplies six scalar quantities

    O

    Y

    X

    Z

    O

    Fx Fy Fz Cx Cy Cz

    F

    C

    DiSMUSDiSMUSDiSMUSDiSMUS

    Reaction force and couple

    For each body segment interacting with the environment, the followingquantities are estimated:

    three force components three couple components.

    These quantities are given with respect to the dynamometer frame. Since,normally, the kinematic quantities are given with respect to another set of

    axes (referred to as the laboratory axes), the transformation matrix betweenthe former and the latter set is to be provided.

    Y

    ZX

    DiSMUSDiSMUSDiSMUSDiSMUS

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    Intersegmental force and couple: estimate

    W

    CR

    R

    Fis

    Cis

    K

    ?inverse dynamics

    How accurately do we estimate the intersegmental force and couple?

    Do intersegmental loads carry functional information?

    is

    is

    C

    F

    =++++

    =++

    ICCMMM

    amFWR

    KRisKF

    KW

    KR

    CMis

    is

    DiSMUSDiSMUSDiSMUSDiSMUS

    Intersegmental force and couple: accuracy factors

    The physical model (degrees of freedom)

    Inertia parameter estimate

    Time differentiation

    External forces

    Position and orientation reconstruction of the model links

    External and internal anatomical landmarks identification

    DiSMUSDiSMUSDiSMUSDiSMUS

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    R

    CR

    R

    CR

    estimated measured

    open kinematic chain 2-D model 3 dof

    Intersegmental force and couple: accuracy

    Model (includes input data errors) fidelity assessment

    Herbert Hatze, Journal of Biomechanics, 2002

    DiSMUSDiSMUSDiSMUSDiSMUS

    Intersegmental force and couple: accuracy

    estimated using photogrammetric data (inverse dynamics)measured

    average rms difference = 17% of peak-to-peak valueaverage correlation coefficient = 0.87

    M-L COUPLE (Nm)A-P FORCE (N) VERTICAL FORCE (N)

    850

    -200

    -150

    -100

    -50

    050

    100

    0 100

    % of task duration-50

    0

    50

    0 100

    % of task duration650

    700

    750

    800

    0 100

    % of task duration

    DiSMUSDiSMUSDiSMUSDiSMUS

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    RCR

    O

    DiSMUSDiSMUSDiSMUSDiSMUS

    Redundancy may be exploited for finetuning the parameters and variablesinvolved.

    In the bottom-up approach a possiblecriterium is to minimize the trunkresidual moment and force.

    Intersegmental force and couple: accuracy

    Position and orientation reconstruction of the model links

    photogrammetric errors soft tissue artefacts anatomical landmark identification

    DiSMUSDiSMUSDiSMUSDiSMUS

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    Shank soft tissue artefacts: effect on knee intersegmental couple

    Manal et al., Gait and Posture, 2002

    % of stance

    Flexion/extension Adduction/abduction Internal/external rot.

    Intersegmental couple [Nm]

    DiSMUSDiSMUSDiSMUSDiSMUS

    minimization of skin movement artefacts and/or theirassessment and compensation

    minimization of misidentification of both internal andexternal anatomical landmarks

    identification of the bone-to-bone resultant forceapplication line

    standardization of procedures

    muscle, tendon, and ligament modelling

    Problems still seeking for an optimal solution

    DiSMUSDiSMUSDiSMUSDiSMUS

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    Do intersegmental loads carry functional information?

    W

    CR

    R

    Fis

    Cis

    K

    all vectors are represented in the global (inertial frame)

    =++++

    =++

    ICCMMM

    amFWR

    KRisKF

    KW

    KR

    CMis

    is

    DiSMUSDiSMUSDiSMUSDiSMUS

    The intersegmental couple

    point K was chosen arbitrarily !

    bKF

    KF

    KF

    KFis CMMMMC bpgh ++++=

    Fh

    Fp

    FgFb

    Cb

    W

    CR

    RK

    W

    CR

    R

    Fis

    Cis

    K

    DiSMUSDiSMUSDiSMUSDiSMUS

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    Forces exchanged between bones: resultant force and couple

    http://www.rad.upenn.edu/rundle/Knee/kneeMRICONT.html

    Gastrocnemius, Medial Head

    Gastrocnemius, Lateral Head

    Patellar tendon

    Semimembranosus MuscleBone-to-bone Fh

    FgFp

    Q

    Fb

    X

    assumption

    http://www.rad.upenn.edu/rundle/Knee/kneeMRICONT.htmlDiSMUSDiSMUSDiSMUSDiSMUS

    The muscular moment

    there exists a point Q for which 0CM bQ

    Fb=+

    thus:

    In this case we may refer to the intersegmental couple as muscular moment

    W

    CR

    R

    Fis

    Cis

    K

    Fh

    Fp

    FgFb

    Cb

    W

    CR

    RK

    QF

    QF

    QFis pgh

    MMMC ++=

    bKF

    KF

    KF

    KFis CMMMMC bpgh ++++=

    DiSMUSDiSMUSDiSMUSDiSMUS

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    The challenge

    is to find the point Q for which it is true that

    and thus:

    NIH

    Q

    Q

    F

    Q

    F

    Q

    Fis pghMMMC ++=

    0CM bQFb

    =+

    DiSMUSDiSMUSDiSMUSDiSMUS

    If the knee joint is modelled using a spherical hinge

    0C b = 0MQFb=

    Fh

    Fp

    FgFb

    Cb

    W

    CR

    R

    Fh

    Fp

    FgFb

    Cb

    W

    CR

    R Q

    by definition

    and, thus, the intersegmental couple is the muscular momentDiSMUSDiSMUSDiSMUSDiSMUS

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    The muscular forces

    W

    CR

    R

    Fis

    Cis

    K

    This relationship cannot be solved with respect to a single muscular force*unless it is known or assumed that only one muscular force is present

    Fh

    Fp

    FgFb

    Cb

    W

    CR

    RK

    QF

    QF

    QFis pgh

    MMMC ++=

    DiSMUSDiSMUSDiSMUSDiSMUS

    Gait Analysis

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    Gait Phases

    INVERSE PENDULUMThe body center of mass rotates

    around the support and increases itspotential energy during the initialstance phase: This energy isconverted in kinetic form during thesecond stance phase (Cavagna et al.1977). Il center of mass isaccelerated forward.

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    Ground Reaction Forces in Normal Gait

    0

    0.6

    1.2

    0 50 100

    0.3

    0

    -0.3

    0.1

    -0.2

    0

    % stanceScaled by body weight

    Medial/Lateral

    Anterior/Posterior

    Vertical

    Courtesy of National Institutes of Health - USA

    DiSMUSDiSMUSDiSMUSDiSMUS

    Center of Pressure during Normal Gait

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    Joint Moments during Normal Gait

    HipFlexor (+)

    KneeExtensor (+)

    AnkleDorsiflexor (+)

    0.5

    -0.75

    -2.00

    1.0

    0

    -1.01.0

    0

    -1.0

    0 25 50 75 100% stance

    Nm/kg

    Courtesy of National Institutes of Health - USA

    DiSMUSDiSMUSDiSMUSDiSMUS

    Joint Moment Interpretation

    Limitations

    Cannot distribute moment among each agonist of a musclegroup

    Moment does not account for co-contraction (moment =agonist + antagonist effects)

    Moment reflects contributions from active (muscular) andpassive (ligament, joint contact) sources

    Areas of caution

    End range of motion

    External devices orthoses, prostheses

    DiSMUSDiSMUSDiSMUSDiSMUS

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    Electromyography

    Electromyography

    Electromyography (EMG) Study of muscle

    function through the examination of the

    muscles electric signals

    Why EMG?

    Estimate in vivo muscle forces for various

    activities

    Help solving the inverse dynamic problem

    Detect muscle fatigue

    Quantify pathological muscle behaviour

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    History Luigi Galvani 1791

    Observed the relationship between muscle and electricity

    by depolarizing frog legs with metal rods

    Father of neurophysiology

    De Viribus Electricitatis work was introduced

    Carlo Matteucci 1838

    Proved that electric currents originated in muscles

    Du Bois-Reymond 1849 Designed a Galvanometer to record electrical current

    Reduced skin impedance by rubbing blisters on his arms

    and opening them

    Galvani

    De Luca 1985

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    EMG types

    Surface EMG (SEMG) Electrodes areapplied to the surface of the skin.

    Used to measure muscle signals in largemuscles that lie close to the surface of the skin

    Indwelling EMG Electrodes are insertedinto the muscle (usually via a needle)

    Used to measure muscle signals in small ordeep muscles, which cannot be adequatelymonitored using SEMG.

    EMG Characteristics

    Ranges from 0-10mV (peak to peak)

    Usable frequency range: 0-500Hz

    Dominant frequencies 50-150Hz

    Random in nature

    Mixture of signals from different motor units

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    Action Potentials

    De Luca 1982

    Surface or Indwelling EMG

    Electrodes

    Single electrode with reference

    Measure action potential at one electrode

    Subtract common as measured from reference

    Two electrodes with reference

    Measure action potentials at both electrodes

    Use differential amplifier

    Subtract common signal at source

    Amplify differences

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    Noise

    EMG signals are very small

    External noise

    Electronics noise

    Recording/measuring equipment

    Ambient noise

    TV, radio, overhead lights Motion artifact

    Movement of electrodes or wires

    Electrode Placement

    Place electrodes In line with muscle fibers

    At the midline of the muscle

    Not over or near tendon insertion sites or innervation zone(motor point) Electrical stimulation at this point results in muscle contraction

    Action potentials move oddly and EMG detection is affected

    Reference electrode is far away and over electrically neutralarea

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    Electrode Placement

    De Luca

    De Luca

    Effects of

    Muscle Fatigueon EMG Signal

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    Experimental Example

    Agonist and Antagonist Muscle

    Activity

    De Luca 1985

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    Data Acquisition and Analysis Sampling

    1024 Hz, 12 bit resolution

    Bandpass 1st order filter: 10-500Hz

    Filter Data

    Full wave rectified

    4th order Butterworth filter: Fc = 3Hz (smooth)

    Further analysis options

    Integrated over specific time periods for iEMG

    EMG Limitations

    Difficult to compare between subjects

    SEMG is not appropriate for all muscles

    Electrode positioning must be consistent

    MVC can vary between days and time of day Cant ensure that all motor units are firing for MVC

    Difficult to hold isometric contractions for some muscles

    Force is not proportional to EMG amplitude for many muscles

    MUST CALIBRATE AT START OF SESSION

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    SUMMER SCHOOL 2006 Monte S.Pietro, Bologna

    ADVANCED TECHNOLOGIES FOR NEURO-MOTOR ASSESSMENT AND REHABILITATION