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Collagen fibers in annulus fibrosus are in 30 degree to disk as shown.
Assume that above intervertebral disk is circular shape, and has diameter of 2 inch
and height of 0.5 inch.
At certain moment, disk deforms 10% in compression, and top bone segment (above
disk) rotate 4 degree clockwise with respect to bottom bone segment.
Under the above loading condition and for the very outside annular layer,
1. Determine the change of the length of fiber.
2. For above loading, combination of compression and torsion, investigate if 30 degree
is the best. If not, what degree would be better?
Assume Poisson’s ratio of annulus fibrosus (annulus fibrosus layer) is 0.5 in
Assume other factors reasonably if needed.
You need to calculate the amount of torsional strain first using the given info.
Cervical Spine
• Supports the head
• Mobility > Stability.
• Wide range of motion
– Rotation
– Flexion
• Peripheral nerves
– Arms
– Shoulder, Chest and
Cervical Spine
• Seven vertebrae
– C 1-7
• The two most cranial vertebrae, C1 and C2, have a unique
structural role in the articulation between the head and the
cervical spine
• Five typical cervical vertebrae, C3 to C7, that are similar in
structure and function
• Most mobile spinal segment
• C1-C2 is responsible for approximately
40% of cervical flexion and 50-60% of
cervical rotation
• C2-C4 has most side bending and great
• C5-C6 has great amount of flexion and
• There is no intervertebral disc between C1
and C2
• The seventh cervical vertebra is slightly
different in that it has a transitional form
Intervertebral Discs
• Highly specialized structures – up to one-third of the height of
the vertebral column
• Increase in size from cervical to lumbar
• The nucleus pulposus is
centrally located within the disc
and consists of almost 90%
• The rest of the nucleus
pulposus consists of
proteoglycan and type II
• The annulus fibrosus is the outer portion of the disc, approximately 78%
• The collagen fibers in these sheets run at approximately 30° to the disc or
120° to each other
• Compressive stresses on the disc translate into tensile stresses in the
annulus fibrosis This makes the disc stiffer which adds stability and support
to the spine
• 60% type II collagen and 40% type
I collagen
• As the disc ages, amount of type I
collagen increases, replacing type
II collagen in the disc
The movement capabilities of the spine are those of a ball and
socket joint, including movement in all three planes and
Annulus fibrous – acts like coiled spring
Nucleus pulposus – acts like ball bearing
Anterior longitudinal
Posterior longitudinal
Ligamentum flavum (elastic)
In general,
1. Cortical bone is stiffer than cancellous bone
2. Cortical bone has higher failure stress
3. Cancellous bone has higher failure strain
4. Bone is stronger in compression
• Vertebral compression strength increases from the upper cervical to the
lower lumbar levels.
• Spine  Beam
• During bending, tension on posterior  Higher risk of failure
• Posterior paraspinal muscle contraction can decrease the tensile stress on
bone by producing a compressive stress  reduces or neutralizes the
posterior cortical tensile stresses
MECHANICAL PROPERTIES – Intervertebral Discs
• Intervertebral discs exhibit viscoelastic properties and hysteresis
• Degenerated discs are less viscoelastic in nature
• Losing 20% of their water during the first hour of the morning
 Very similar to cartilage
Amount and direct of motion
in a segment is determined by:
Vertebral body/disc size.
Facet orientation
• Superior vertebra will anterior tilt and forward gliding will
– Widening the intervertebral foramina 24%.
– Adds compressive forces on the anterior aspect of the
anterior segment moving the nucleus pulposus
• Superior vertebra will tilt and glide posteriorly and the
intervertebral foramina narrowed up to 20%.
• The central canal is also narrowed.
• Nucleus pulposus moves anteriorly
The size of the
intervertebral foramina
increases with flexion and
decreases with extension
The spinous
processes limit
entension motion
Range of motion
The stretch test  1 year treatment
Unilateral facet dislocation
Open reduction – posterior tension band
Cervical artificial disk
Cervical screw-rod system
Biomechanics of Cervical Trauma
Dislocation for chold during low speed crash – airbag is too strong
and fast
Struck from behind  the unsupported head falls backward,
resulting in an extension strain to the neck.
Then the vehicle just struck then strikes another vehicle in
front and, throwing the occupant forward once more. resulting in
an flexion strain to the neck
Thoracic Spine
• Mid-back or dorsal region
• Twelve vertebrae
– T 1 – T12
• Ribs attached to vertebrae
• Relatively immobile
Lumbar Spine
• Lower back
• Five vertebrae
– L 1 – L5
• Carries the weight of the upper body
– Larger, broader
• Peripheral nerves
– Legs
– Pelvis
Sacral and Coccygeal region
• Sacrum
– Triangular structure
– Base of the spine
– Connects spine to pelvis
– Nerves to pelvic organs
• Coccyx
– Few small bones
– Remnant of tail
Compressive Strength and Failure Strength of Spine
• The Motion Segment (Min functional unit of the spine)
– Two adjacent vertebrae and their intervening soft tissues
Types of motion
• The lumbar region are thicker and wider than
those in the thoracic and cervical regions
• The intervertebral disc bears and distributes
loads and restrains excessive motion (main
function of Anterior portion)
• During daily activities, the disc is loaded in a
complex manner and is usually subjected to a
combination of compression, bending, and
• In the lumbar spine, the tensile stress in the
posterior part of the annulus fibrosus has been
estimated to be four to five times the applied
axial compressive load
• Degeneration of a disc reduces
its proteoglycan content and thus
its hydrophilic capacity
• As the disc becomes less
hydrated, its elasticity and its
ability to store energy and
distribute loads gradually
• These changes make the disc(s)
more vulnerable to stresses and
impact on the loading of other
portions of the motion segment
• The posterior portion of the motion segment guides its movement.
• By the orientation of the facets of the intervertebral joints to the
transverse and frontal planes
The facets of the C3 to C7 cervical
intervertebral joints are
oriented at a 45° angle to the
transverse plane and are parallel
to the frontal plane that allows
flexion, extension, lateral flexion,
and rotation
The facets of the thoracic joints are
oriented at a 60° angle to the
transverse plane and at a 20° angle
to the frontal plane; this orientation
allows lateral flexion, rotation, and
some flexion and extension
The lumbar facets are oriented at
right angles to the transverse plane
and at a 45° angle to the frontal plane
This alignment allows flexion,
extension, and lateral flexion,
but almost no rotation
• The range of motion differs at various levels of the spine and depends
on the orientation of the facets of the intervertebral joints
• Motion between two vertebrae is small and does not occur
independently; all spine movements involve the combined action of
several motion segments.
• The skeletal structures that influence motion of the trunk are the rib
cage, which limits thoracic motion, and the pelvis, which augments
trunk movements by tilting.
Range of Motion
Relative Motion
• Motion between the surfaces of two adjacent vertebrae during
flexion-extension or lateral flexion may be analyzed by means of the
instant center method
• With abnormal conditions such as pronounced disc degeneration, the
instantaneous center pathway will be altered and move outside of the
disc, toward the facet joints
• The main flexors are the abdominal muscles (the rectus abdominis
muscles, the internal and external oblique muscles, and the
transverse abdominal muscle) and the psoas muscles
• In general, muscles anterior to the vertebral column act as flexors
• In general, muscles posterior
to the vertebral column act as
Flexion and Extension
• Flexion-extension range of motion, the first 50° to 60° of spine flexion
occurs in the lumbar spine,
• Tilting the pelvis forward allows for further flexion
• The posterior hip muscles are active in controlling the forward tilting
of the pelvis as the spine is flexed
• From full flexion to upright positioning of the trunk, the pelvis tilts
backward and the spine then extends
• The gluteus maximus comes into action early together with the
hamstrings and initiates extension by posterior rotation of the pelvis
Lateral Flexion and Rotation
• During lateral flexion of the trunk, motion may predominate in either
the thoracic or the lumbar spine
• In the thoracic spine, the facet orientation allows for lateral flexion, but
the rib cage restricts it
• Axial rotation occurs at the thoracic and lumbosacral levels but is
limited at other levels of the lumbar spine, being restricted by the
vertical orientation of the facets
• Coupling of rotation and lateral flexion also takes place in the lumbar
Pelvic motion
Lateral Tilt
• tilting of the pelvis from neutral
position to the right or left
• lateral tilt tends to occur naturally
when you support your weight on
your leg
• this allows you raise your
opposite leg enough to swing
through during gait
Pelvic Rotation
• rotation of the pelvis defined by the
direction in which the anterior aspect
of the pelvis moves
• occurs naturally during unilateral leg
movements (walking)
– as the right leg swings forward
during gait the pelvis rotates left
Lower Spine + Pelvic  One System.
Loads on the spine are produced primarily by body weight,
muscle activity, pre-stress exerted by the ligaments, and
externally applied loads
 Simplified F.B.D
 Statics and Dynamics
When a person stands, the postural
muscles are constantly active. This
activity is minimized when the body
segments are well aligned
During standing, the line of gravity of the
trunk usually passes ventral to the center
of the fourth lumbar vertebral body
spine and the motion segments are
subjected to a forward-bending moment
Counterbalanced by ligament forces and
erector spine muscle forces
The pelvis also plays a role in the muscle activity and resulting loads on
the spine during standing
The base of the sacrum is inclined forward and downward. The angle of
inclination, or sacral angle, is approximately 30° to the transverse plane
during relaxed standing
Pelvic movement
• Concomitant movement of the
pelvic girdle and the thigh at the hip
joint are necessary for efficient joint
• Movements of the pelvis are
described by monitoring the,
especifically, the anterior superior
iliac spine.
Anterior Tilt
• forward tilting and
downward movement of
the pelvis
• occurs when the hip
Posterior Tilt
• tilting of the pelvis
• occurs when the hip

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