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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
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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
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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
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The force plate supplies six scalar quantities
O
Y
X
Z
O
Fx Fy Fz Cx Cy Cz
F
C
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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 ++++=
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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
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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