“Oh
my aching back!”
Vertebral Discs and
The Effects of Aging
Molly M. Miller
EN 175 – Professor Blume
December 6, 2001
Introduction:
Back pain is one of the
major causes of missed days of work and limited activity, especially as we
age. The components of the spine
degenerate with age and become less accepting of what used to be normal
movement. A functional spinal unit, or
FSU, consists of a vertebra, a disc, and another vertebra connected by the
appropriate muscles, ligaments and other soft tissue. Such a unit will be the basis for the investigation in this report.
The lumbar spine feels from
three times to as many as six times the weight of the trunk, making it a large
part of the weight bearing capacity of the spine. For this reason, I will analyze a simplified FSU from the lumbar
region and examine what effect aging has on the compressive stress capacity of
the spine.
Background:
The spine consists of seven
cervical, twelve thoracic, and five lumbar vertebrae in addition to five fused
vertebrae forming the sacral regions and an additional four fused vertebrae,
which form the coccyx. Between each vertebra
is a vertebral disc, connected to the superior and inferior vertebrae, forming
a functional spinal unit. There are a
total of twenty-three intervertebral discs.
Some other important anatomical parts of the vertebrae are the facets
and spinal processes. There are also
eleven spinal ligaments which assist in the articulation of the joint. The muscles attached to each vertebrae allow
movement in flexion and extension as well as lateral movement and coupled
movements involving both types.[1]
In
the lumbar section of the spine the lordosis, or curvature of the spine, is
slight enough that the lumbar functional spinal unit can be approximated as
coaxial objects. This means that the
end plates are perpendicular to the discs themselves. The facets in this section of the spine are oriented
perpendicularly to each other and therefore absorb no force in
compression. It is for this reason that
many simplifications can be made in the geometry and force application in the
lumbar spine.
The disc is the major
compressive carrier of the spine and many tests have been done measuring the
carrying capacity of the disc. It
consists of two separate parts, the inner nucleus pulposus and the outer
annulus fibrosus. The length of the
spine is 20-33% disc height while the remainder is mainly vertebral body
height.[2]
The inner material is
composed of a loose network of fibers that exist in a mucoprotein gel. The water content of the nucleus is
approximately 70% but decreases with age. This decrease causes a gradual hardening
of the nucleus, which causes the disc to be less able to adapt to
compression. In the lumbar section of
the spine, which is the section being examined in this experiment, the nucleus
fills around 30% of the cross sectional area of the disc.[3]
The
annulus fibrosus is a much denser and stronger material than the nucleus
pulposus. Fibrous tissue arranged in
concentric bands constitutes this portion of the nucleus. The tissue itself is oriented in a helicoids
manner with all fibers in the same direction within the band, but oriented
approximately 30º to the fibers in the adjacent band.
The
annulus and nucleus fit together like two concentric cylinders, held at each
end by cartilaginous end-plates. These
endplates are significantly stiffer and harder than the annulus and
nucleus.
Goals:
Compression
testing is one of the most common tests performed on spinal segments. This is because when we stand, the spine can
feel compression forces up to three times the weight of our trunk. What is being tested in most cases is the
compression of the spine on a daily basis.
As we lie down, the deformation from gravitational forces is released
and the spine elongates. This is why we
are taller in the morning than we are at night!
The
goal of this experiment is to show that deformation decreases as the spine ages
due to an increased Young’s modulus in the nucleus. This corresponds to decreased water content of the nucleus,
causing it to become stiffer. The
stresses felt in the nucleus will increase during this same aging. Also important in aging is the idea that the
collagen content is changing in the discs.
Type I and type II collagen have been identified as present in the
annulus and nucleus; the ratio of these two type of collagen is representative of
the age of the disc. More type I will
be found in the annulus and more type II in the nucleus when the disc is young
and healthy. As the disc ages, this
ratio begins to reverse itself. This is
most likely due to the lordosis of the spine; areas in tension tend to have
more type I while those in compression would have type II [4]. As the spine ages, the forces change and
therefore the collagen contents shift.
The cartilaginous end plates evenly distribute the overall compression
force to the annulus and nucleus. The
main focus in this analysis will be the increasing Young’s modulus due to the
decreased presence of water in the nucleus.
Realistic
loads were used in this experiment, such that failure did not occur. Spinal failure never occurs because of a
disc failure. Most likely, failure will
appear first in the endplates. The disc
will then creep into the vertebrae, causing disc herniation, but only because
end-plate failure occurs. The focus of
this paper is the disc and therefore failure is not a direct
consideration. It can also be assumed
that uniform stress occurs in the disc under compressive loading, unless point
loads are applied.
Method:
The lordosis can loosely be
called an S-shape. This curvature in
the lumbar to sacral region is slight in healthy adults such that the following
is a good approximation of the geometry involved.
This picture on the left has the annulus removed to
show the nucleus better. The one on the
right is the full geometric model of the spinal segment. Load application occurs in an overall
pressure and then as a point force on the posterior edge of the end plate. This is because the lumbar vertebrae feel a
force of approximately three times the weight of the trunk simply while
standing. Take an average person who
weighs 150 pounds, take the trunk weight as approximately 60%, change that into
a force and find that the lumbar segments of the spine feel around 400N of
force. Then add a force that accounts
for a person holding weights or lifting an object; this force is applied to the
posterior region.[5]
The geometry of the spine is
shown here, all dimensions are given in centimeters and the drawing is to be
rotated about the left hand side to sweep into a cylinder.
The following forces were
tested.
The first case is not realistic in terms of loading,
but it proves that the force is distributed axisymmetrically. 
[1]
The finite element mesh on the right essentially
replicates the intervertebral discs and end plates shown in the picture on the
right.
We
must also model aging in the disc. The
following material properties are used 
These are realistic numbers according to several
sources.[6]
Please
see the appendix for the full pictorial results of the analysis. When loads of 400N and 600N are applied to the
posterior part of the end plate, the displacements seen in the end plate and
nucleus decrease with age. But, when a
posterior load of 1100N is applied, the nucleus continues to deform with age. This could be the first sign of possible
failure in the end plate and eventual disc herniation. It could also be one of the ways that the
nucleus distributes the pressure that is incurred from the applied load. The nucleus tries to expand into the annulus
and the end plates. So the end plates
will feel even more stress than just from the applied load. The following charts summarize the
displacement due to applied posterior loads.
Essentially, it can be assumed that we are seeing failure begin at
1100N.
For the stresses felt, they increase with an
increased load, as we see in the pictures in the appendix depicting the finite
element analysis of the model. This is
particularly noticeable in the model of the 600N posterior load. You can see the stress increase, especially
the stress at the application of the point load at the posterior edge of the
disc. This is expected due to the
Young’s modulus increasing and the nucleus essentially becoming stiffer.[7] The stress and displacement from the applied
load is absorbed fully by the disc and endplates such that the displacement at
the bottom endplate is zero. This is
not physiologically true because the endplate would move towards the next
vertebral section in a human spine, but it is accurate enough for our analysis
to say that it doesn’t move. This in
effect says that whatever displacement would be left over is absorbed by the
next vertebral body. It is a simplification
made for our purposes.
These
effects make sense when thinking about the formula 
, where E is Young’s modulus and e is correlated to
displacement. Therefore, as we increase
E by aging, we would increase the stress.
Even if the displacement or strain is not as large, E increases enough
to make the stress increase with age.
The following chart outlines the Mises stresses,
which are incurred by the samples for the various loading situations.
This compounds the ideas presented previously. The stress increases as the nucleus ages and
becomes stiffer. But in the 1100N case,
the stress slightly decreases in the older nucleus indicating the beginning of
non-linear deformation and probably failure in some form. This is like the load falling off when
failure occurs in testing. When this
happens, nothing can be assumed about the stress or displacement of such a
material. Again, it seems that failure
begins to occur at 1100N in the “older” nucleus.
Suggestions
for further analysis:
A
more complex geometry would give a more physiologically accurate result by
including the varying shapes of each vertebrae and accounting for
non-cylindrical shape of the disc.
Also, the disc does not age evenly across its cross sectional area. So accounting for this would also be
helpful. Testing with a larger segment
of the lumbar spine would give a result that is more applicable to medicine. A doctor could take those results and tell
him patients not to lift large weights due to what that does to a large segment
of their spine. It would also be
interesting to see what effect posture has on the cervical spine and finite
element analysis of that. The lumbar
spine does not play a large role in a person’s posture; it is mainly the
thoracic and cervical vertebrae which contribute to hunched shoulders and
slouching. Testing of those segments
with “good” and “bad” posture could be interesting.
Conclusions:
In
summary, the experiment was a success in the fact that deformation can be
followed with respect to age.
Displacement is larger when the nucleus is younger. This is partially due to the fact that there
is a lot of water in the nucleus at that time and it allows the nucleus to
compress. As the water content decreases
with age so does the ability of the nucleus to compress. This is true until failure begins, when any
linear relationships previously valid now become invalid.
Stress
follow the pattern of increasing linearly for 400N and 600N loads, but become non
linear for the 1100N load as can be seen in the following graph of Stress
versus Age. 
With the 1100N load, all bets are off. It seems to be linear at first, but then
become non linear when the nucleus is “Older.”
Sources
1. Dai L.. “The relationship
between vertebral body deformity and disc degeneration in lumbar spine of the
senile.” European Spine Journal. Vol
7, pp. 40-44.
2. Kumaresan S, Yoganandan N,
Pintar FA. ”Finite element analysis of the cervical spine: a material property
sensitivity study.” Clinical Biomechanics.
Vol 14(1999), pp 41-53.
3. Norkin CC, Levangre K.. Joint
Structure and Function: A Comprehensive Analysis. 2nd Edition.
Philadelphia: Davis, 1992.
4. Spilker RL, Jakobs DM,
Schultz AB. “Material Constants for a Finite Element Model of the
Intervertebral Disk With a Fiber Composite Annulus.” Journal of Biomechanical Engineering, Vol 108, pp. 1-11.
5. The Spine Page. http://www.thespinepage.com/anat.htm
6. White, A.W., Panjabi, M.M.. Clinical
Biomechanics of the Spine. Philadelphia: J.B. Lippincott Company, 1978.
7. Yoganandan N, Kumaresan S.,
Pintar FA.. “Biomechanics of the cervical spine Part 2. Cervical spine soft tissue
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Biomechanics. Vol 16(2001), pp1-27.
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