Applied Biomedical Engineering

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Applied Biomedical Engineering AMME4981 Lecture
2 Musculoskeletal Biomechanics (Statics and
Dynamics of Muscle and Joint Loads)
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Objectives

• It is important to determine the
  internal/external undergone in the body before we
  carry out biomechanical analysis. Hence, we need
  to discuss the biomechanics issues related to
  body first.
• Calculate the joint reaction force for a defined
  situation
• Estimate muscle forces for a defined situation
• Discuss the relationship between muscle
  performance and anatomic and physiologic
  constraints

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Mechanics Concepts

• Forces and moments
• Degrees of freedom
• Displacement, velocity, and acceleration
• Inertia
• Static/dynamic equilibrium
• Newtons laws
• Free body diagrams/Kinetic diagram
• Vectors and algebraic analysis of vectors
• Linear and angular momentum
• Work and energy

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Anatomical Position

• Movements of the body are taken from the neutral
  anatomical position
• Legs straight with feet pointed forward
• Arms at side with palms facing forward

Transverse Plane
Sagittal Plane
Coronal Plane
Neutral anatomical position
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The Musculoskeletal System
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Musculoskeletal Biomechanics
How do we perform movement and/or apply forces?
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Forces in the Musculoskeletal Systems

• System experiences both internal and external
  loads
• Internal
• Active muscle forces
• Reaction forces of joints and ligaments
• External
• Inertial force due to acceleration of a segment
• Loads directly applied to a body segment
• Muscles transmit a load to the distally attached
  body segment

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Musculoskeletal Dynamics

• Kinematics motion relationship
• Linear and angular displacement
• Linear and angular velocity
• Linear and angular acceleration
• Kinetics motion-load relationship
• Newtons second law
• Work-energy principle
• Impluse-momentum principle
• Anatomical concepts (rigid body)
• Body segments
• Thigh - leg - foot
• Arm - forearm - hand

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Forces in the Musculoskeletal Systems Contd

• Most static and dynamic systems
• Forces (internal/external) generally are given
• Solve for deformation or rigid body motion
• For musculoskeletal system
• Internal forces are not generally known
  (Transducers can be inserted within tendons, but
  only in laboratory animals)
• Motion is relatively easy to measure
• Solve an inverse problem to determine muscle and
  joint forces from motion (displacement, velcotiy,
  acceleration)

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Muscle Force Constraints

• Each individual muscle must have a force such
  that
• Maximum muscle force is dependent on
• The physiological cross-sectional area (PCSA)
• Muscle stress limit (?)
• Active force correction for length-tension and
  force-velocity relationships (?a)
• Passive force correction (?p)

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Inverse and Direct Dynamic Problems

• Direct dynamic problem

F
r
Known forces
Equations of motion
Double integration
Displacement

• Inverse dynamic problem

r
F
Known forces
Double differentiation
Equations of motion
Displacement
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Solving the Inverse Problems

• To calculate internal forces, need
• Full description of movement
• Accurate anthropomorphic measurements
• Knowledge of external forces
• Moment balance done at the center of rotation of
  a joint eliminates the effect of the unknown
  joint reaction force

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Body Segments and Model

• Body segments can be modeled as rigid bodies,
• e.g. foot, leg, forearm, thigh,
• Free body diagrams can be drawn for each segment
• Intersegmental forces and moments acting at
  joint centers
• Gravitational forces acting at the centers of
  mass
• Accurate measurements are needed of
• Segment masses (m)
• Centers of mass
• Joint centers
• Mass moment of inertia (I)

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Model Assumptions

• Rigid body motion - deformation is small
  relative to overall motion
• Body segments interconnected at joints and
  length of each segment is constant
• Each segment has a fixed mass located at its
  center of gravity
• The location of a segments center of mass is
  fixed during any movement
• Joints are considered to be hinge (2D motion) or
  ball and socket (3D motion)
• Moment of inertia of each segment about any
  point is constant during any movement

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Forces

• Gravitational forces
• Act downward through center of mass of each
  segment
• Equal mass ? acceleration due to gravity (mg)
• Ground reaction force
• Distributed over an area of the foot
• To represent as a vector, assume it acts at a
  point, the center of pressure
• Calculated from force plate data
• Externally applied forces
• Any restraining or accelerating force that acts
  outside of the body
• Obstacle being tripped over
• Mass being lifted
• Muscle Forces
• Net effect of agonists and antagonists on body
  segments
• True muscle forces are slightly underestimated
  due to frictional losses in joint
• Ligament forces
• Influence muscle and joint loads at extremes of
  motion

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Analyse Trajectories of Motion
Determine displacement, velocity and acceleration
as a function of time t
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Analyse Angular Motion
Determine angular displacement, velocities and
angular accelerations
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Document Kinematics
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Document the Motion (Kinematics) Contd
Data Presentation
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Measurement of Sagittal motion
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Kinematic Studies

• Segment angles
• Calculated based on the position of two segment
  markers placed along long axis of segment in
  plane of angle
• Segment linear velocities and accelerations
• Use two data intervals to minimize error
• Segment angular velocities and accelerations

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Anthropometry
Use Anthropometry (physical parameters of the
human body) to model human body
Data are per single limb Relative distance
of C.M. (measured from the lower numbered joint)
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Anthropometry Diagram
0.130H
0.186H
0.146H
0.108H
0.129H
0.520H
H
0.259H
0.174H
0.936H
0.191H
0.870H
0.720H
0.530H
0.818H
0.485H
HHeight of standing subject
0.285H
0.377H
0.630H
0.039H
Foot Breadth
Foot Length
0.152H
0.055H
Modified from Drillis and Contini, 1966
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Type of Motions and Equation of Motions

• Translation When all the particles of the body
  move in parallel trajectories

• Rotational (Angular motion)

• General Motion When the body performs
  simultaneous translation and rotation

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Example 1.1 Muscle/Tendon Force
Flexed arm holding a ball of W20N with a
distance of 30cm to the elbow center. What is the
biceps force required (B) if the forearm weighs
15N and the center of mass for forearm is 15cm
from the elbow center of rotation? The biceps
tendon is inserted 3cm from elbow center.
B
Ry
Rx0
mg
W
3
15cm
30cm
Anatomical schematic
Statics model
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Example 1.1 Contd
Step 1 If the arm is in static equilibrium
Step 2 Scalar equation in x and y directions
Step 3 Solve for the equations ( - means
opposite direction to positive sense)
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Example 1.2 Joint Reaction Load
A person stands statically on one foot. Ground
reaction force acts 4cm anterior to ankle center
of rotation. The body mass is 60kg and foot mass
0.9kg. Center of mass of foot is 6cm from the
center of rotation. Determine the forces and
moment in the ankle.
Rotation center
Mass center
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Example 1.2 Contd
More general equation of motion (Newtons 2nd law)

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Example 1.3
A person exercises his left shoulder rotators.
Show how would you go about calculating the
forces and moments exerted on his shoulder.
Consider a quasi-equilibrium
Motion of equation
a
Fjy-F
b
F200 N, a25 cm, b30 cm.
FBD
Answer
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Tutorial 1
A weight lifter raises a barbell to his chest.
Determine the torque developed by the back and
the hip extensor muscles (Mj) when the barbell is
about the knee height (as shown in the
illustration). Weight of barbell Wb1003 N,
Weight of upper body Fw,u525 N a38
cm, b32 cm, d64 cm IG7.43 kg-m2, ?8.7
rad/s2, aGx0.2 m/s2, aGy - 0.1 m/s2.
O
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Solution to Tutorial Problem
Step 0 Newtons 2nd law
Step 1 Mass moment of inertia about O
Step 2 Dynamic equilibrium of forces
Step 3 Dynamic equilibrium of moments
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Other example
A man walks in the platform with test markers in
his right limb as shown. Determine the forces and
moments (1) at the ankle and (2) at the knee,
based upon the following measurements. Determine
force/moment in the ankle and knee.
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Summary

• Measurement of motion
• Kinematic analysis to determine linear/angular
  displacement, velocity and acceleration
• Kinetic analysis to determine the force and
  moment in muscle and joints

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