3D KinematicsMethods and Instrumentation

Santiago De Grau and Jess Valic

October 28, 2014

Overview

• Introduction to Kinematics

• Kinematic Data Collection

• Coordinate Systems

• Marker Placement

• Kinematic Data

• Application to Neurotrauma Impact Science Laboratory

Introduction to Kinematics

• Describes the motion of points or bodies without consideration of the causes of motion

• What is measured? Not measured?

• Linear and angular– Body landmarks and segments– Joint angles

• Can be either 2D (planar) or 3D (spatial)

Evolution of 3D Kinematics

Applications in Biomechanics• Athlete performance

– Analysis of golf/tennis swing

• Injury rehabilitation (pre vs post)– Joint range of motion differences

• Injured/non-injured – Flexion/extension during stair climb

• Head Impact Reconstructions– Acceleration

Kinematic Data Collection

1) Magnetic

2) Mechanical

3) Optical – Passive (reflective markers – VICON)– Active (IRED – Optotrak)– Sample rates; Capture space– Marker ID; Positional data only

Additional Data Collection Tools

• Accelerometer– Measures acceleration directly velocity,

displacement

• Electrogoniometer– Measures joint angles immediately; cheaper than imaging systems– Encumbers movement; best for hinge joints; ONLY measures joint angles

Motion Capture Data Collection

• Record motion of markers affixed to a moving subject

• Digitize the data marker coordinates

• Process coordinates kinematic variables – Segmental/joint movements

• Multi-camera system– Minimum 2; consider occlusion and rotation

Data Collection

• Calibration necessary– Ensures correct image scaling

• Static Calibration– Control points affixed to a structure in field of view– Orients 3D workspace (GCS)– Establishes origin forceplate often used

• Dynamic Calibration– Relative positions and orientations of cameras

Data Collection

• Cameras capture coordinates in 2D– Need to use a transformation process to convert to

spatial (3D) coordinates

• Direct Linear Transformation (DLT)– A set of equations computed to scale digitized coordinates into metric units– Also corrects errors associated with camera tilting

• Distance distortions

Coordinate Systems

• Cartesian coordinate system– Position vector defines point in space (X,Y,Z)– Stationary orthogonal axes– Origin (0,0,0)– Commonly right handed (counterclockwise +ve)

• Two coordinate systems for 3D analysis– Global Coordinates System (GCS)– Local Coordinate System (LCS)

Global Coordinate System

• Internal reference system – Fixed system

• Determined when object space is defined– Origin from static calibration

• Point of interest (marker) described by position (X,Y,Z)

• Right handed orthogonal

Local Coordinate System

• Fixed within and moves with body or segment– Describes position of body or segment

• Right handed and orthogonal; origin at COM or proximal joint center

• Origin and axes attached to and moves within the body

• Segment volume and shape finite– Orientation described wrt GCS

Local Coordinate System

• Orientation changes as body moves through 3D space– Calculate orientation of LCS to GCS

• Static calibration to align LCS with GCS is useful

• Used to determine joint angles– LCS of two segments– Rotational matrix– Cardan Euler, JCS, Helical Axis

Neurotrauma Impact Science Laboratory

Markers

• Need minimum of 3 non-collinear markers per segment

• Four general configurations1) Markers mounted on bone bins 2) Skin mounted markers 3) Arrays of markers on rigid surface4) Combination of (2) & (3)

• Each have own pros and cons

Marker Placement Guidelines1. Sufficient measurements of each marker should be available. The light reflected from the markers should be visible to sufficient cameras for identification

2. The number of markers associated with each bone must be more than or equal to three

3. The relative movement between markers and the underlying bone should be minimal

4. Mounting the markers on the subject should be quick and easy

Cappello et al. (1997)

• Femoral and Tibial wands as a

reference for other markers• Markers secured at anatomical

landmarks that determine embedded axes for segments

• Use of anthropometric measurements

• ‘Improved Helen Hayes Model’ – medial anatomical markers included, static trial performed, and markers are not placed on wands

Vaughan et al. 1999

Helen Hayes Marker Placement

Pros:• Markers are easy to track in three-dimensional space with

video based kinematic systems• Easy to apply to a subject• Subjects movements are minimally impaired

Cons: • Jerky movement causes wands to vibrate which is picked up by

the cameras• Skin movement relative to the underlying bone• Both create error of marker coordinate reconstruction. Modeling

procedures often do not accommodate these artefacts and assume the marker is rigid with the bone

Vaughan et al. 1999

• Femoral and Tibial clusters• Used to reduce skin

movement artifact for more accurate measurement

• ‘A local reference frame can be defined starting with the co-ordinates of three non-collinear markers’

• Define joint centers • Clusters used as a technical

system along with the anatomical marker placement

• Static trial must be performed

Cappello et al. 1997

Cluster Marker Placement

Pros:• Markers are easy to track in three-dimensional space with

video based kinematic systems• Relative skin movement error is reduced through marker

clustering• Easy to apply to a subject

Cons: • Movement of subject might be impaired or unnatural due to

clusters being placed on large muscles• MARKER PLACEMENT

Cappello et al. 1997

Kinematic Measurements

Consists of two parts: 3D Translation & 3D Rotation (6 degrees of freedom)

Inverse Kinematics: Take motion of markers to determine angles and position of segments in relation to another

Linear Kinematics

Angular Kinematics

Application - NISL

Maximum Linear Magnitudes

Axis Block Acceleration, g Velocity, m/s

X C 165.8 10.8

  S 180.9 -

  T 273.1 -

Y C -15.6 -0.9

  F -32.9 -

  T -31.2 -

Z C -31.6 -2.7

  F -67.0 -

  S -31.9 -

Resultant 167.7 10.9

Maximum Angluar Magnitudes

Axis Acceleration, rad/s2 Velocty, rad/s

X 2299.2 1.3

Y 13856.5 8.5

Z -3260.6 -3.3

R 14258.8 8.9

Lesion type Threshold Measurement method Reference

mTBI 82 g for 50% chance Laboratory reconstruction Zhang et al. (2004)

mTBI 81 g Instrumented helmets Duma et al. (2005)

mTBI 103 g Instrumented helmets Brolinson et al. (2006)

mTBI 82–146 g Instrumented helmets Schnebel et al. (2007)

mTBI 103 g Dynamic modeling Frechede and McIntosh (2009)

mTBI 90 g Primate impacts Gurdjian et al. (1966)

Subdural hematoma 130 g Laboratory reconstruction Willinger and Baumgartner (2003a)

Lesion type Threshold Measurement method Reference

mTBI 5900 rad/s2for50% chance

Laboratory reconstruction Zhang et al. (2004)

mTBI 3000–4000 rad/s2 Laboratory reconstruction Willinger and Baumgartner (2003a)

mTBI 8020 rad/s2 Dynamic modeling Frechede and McIntosh (2009)

Subdural hematoma 4500 rad/s2 Cadaver impacts Lowenhielm (1974a)

mTBI 1800 rad/s2 Primate impacts Ommaya et al. (1967)

DAI 16,000 rad/s2 Primate, physical and numerical model impacts

Ommaya et al. (1967)

Thresholds of Injury

Brain Mapping

Thank you

Questions?