MEASURING AND QUANTIFYING THE
GRAVITATIONAL FORCES ACTING ON
THE VERTEBRAL COLUMN DUE TO
THE EFFECTS OF GRAVITY
Usama Abdul Matin
170113869
ME3046 Final Year Project
Dr Xianghong Ma
Aston University
1
Abstract
The purpose of this paper is to address how gravity affects the spine. There are normal gravitational
conditions and microgravitational conditions as exists in space: normal gravity is the one that is
experienced on Earth while microgravity is the one that is known as the absence of gravity in space. A lot
of methods have been tried to examine how these two types of loading affect the spine. A SolidWorks
model of the spine was created, transferred to Ansys and then ran with a FEA to establish exactly how
different loads affected the vertebral column.
In order to support the finite element analysis results, it was backed up by research and theoretical
calculations. The literature review exhibited how the spine acted under different loading conditions and
provided a foundation to base the finite element analysis off.
It is said spending a prolonged amount of time in space has an adverse effect on the recovery of astronauts
once they make it back to Earth. Thus, when considering a design for a medical device that alleviates the
pain of astronauts, it must be made with an artificial gravity so that the spine can be loaded as it would be
on Earth and imitate normal gravity conditions. The same goes for any exercise equipment that is
designed for the astronauts. It is hoped that by applying these principles, the gravity that is experienced on
Earth can be imitated and the astronauts can be saved from the pains and troubles that comes with space
travel.
2
Acknowledgements
My deepest gratitude goes out to my supervisor who oversaw my journey for the entirety of my final year
project and helped me during any roadblocks I was met with. Thanks to her guidance and support,
whether that be for research or any teething Ansys problems, her help ensured I was able to complete my
final year project to a satisfactory standard.
For constantly being in my corner, appreciation must go out to my wife who kept me going on my darkest
days and allowed me to have the required motivation to complete this dissertation to the best of my
abilities.
3
Table of Contents
1 Introduction
1.1 Background
1.2 Aim
1.3 Objectives
5
5
5
6
2 Literature Review
2.1 Gravitational loads and biology concerning the vertebral column
2.2 Microgravity and biology concerning the vertebral column
2.3 The biomechanics of the vertebral column
2.4 Biomechanics and modelling of the vertebral column
2.5 Results
6
6
8
12
16
19
3 Methodology
3.1 Obtaining a model of the vertebral column and importing into Workbench
3.2 Applying a mesh and boundary conditions to the thoracic and lumbar vertebrae
22
22
25
4 Results
4.1 Results for the lumbar vertebrae
27
27
5 Theoretical calculations
5.1 Lower back compressive forces
28
28
6 Discussion and Analysis
6.1 Research finding concerning gravitational loads acting on the vertebral column
6.2 Research findings concerning micro gravitational loads acting on the vertebral column
6.3 Research finding concerning biomechanics of the vertebral column
6.4 Finite element analysis and results
6.5 Theoretical calculations
29
29
30
32
32
33
7 Conclusion
34
8 Beneficiaries and recommendations for future work
34
References
36
4
1
Introduction
1.1
Background
On a daily basis, the human body is affected by gravity - in particular, the spine. Every object that exists
on this planet is anchored by this force of gravity. The force of gravity varies at different points of the
planet as well as differing on different planets hence why the gravity experienced on Earth is very unique.
The body is constantly pushed down by gravity during walking, sitting, lying down and even while being
idle. Since gravity is a downward acting force, it starts acting at the highest part of the body i.e. from the
head and neck. However, when lying down, this force of gravity is spread out equally over the entire body
since the body is on one level horizontally[1].
Due to gravity acting on the body at all times, the spine (around 2-4cm) and the organs are compressed
each day, causing the water retention of the spinal discs to decrease daily. In turn, this does not allow
water and blood to flow uphill in the body which then leads to swollen legs, dry skin and deterioration of
the body in general [2].
Opposingly, in space, the spine is stretched out in the weightless environment of space and is instead
increased by around 2cm. A way to explain this phenomenon would be to think of the spine as a spring.
When a spring is pushed down, the coils are tightly coiled. As soon as this force is removed, the spring
stretches back out. This is what happens to the spine in space and causes an elongation of about 3% (7.6
inches) due to there being less gravity acting on the vertebrae.
Two theories have come forth as to why the spine acts like this in space. In the first theory it is stated that
the only part of the body that elongates is the spine and not the legs or arms etc. This is due to the fact that
the bones cannot be compressed whereas the spinal discs can. The usual configuration of the spine comes
with a slight curve; in space however the absence of gravity relaxes the spine and the curve subsequently
straightens as a result ultimately leading to spinal elongation.
The second theory states that on Earth the discs between each vertebrae are pressed together due to the
gravity pulling the spine down. In space however there is no gravity, leaving more spaces between the
spinal discs for more fluid retention in between and subsequently increasing the size of the spine [3].
1.2
Aim
The aim of this project is to measure and quantify the forces that act on the spine due to gravity. Whether
that may be on the Earth where gravity is ever present and the various muscles of the vertebrae are
compressed or in outer space, where the absence of gravity elongates the spine. By conducting finite
element analyses on the spine in both environment on Earth and outer space, the relationships between
5
these parameters allow the determination of the exact forces on the vertebrae in both gravity and zero
gravity.
1.3
Objectives
In order to make sure the aims of the project are met, a few steps need to be carried out chronologically to
ensure success. SolidWorks and Ansys Workbench are the two softwares predominantly used. At first,
SolidWorks is used to generate a model of the vertebral column and then converted into a step.205 file to
be compatible with Ansys Workbench. Once the file is imported onto Workbench to conduct the finite
element analyses. One finite element analysis is done using microgravitational loading and another one is
done using gravitational loading on the Earth. By reading the results from the finite element analyses, the
forces acting on the vertebrae is determined and can then be compared with manually derived results for
the forces. This allows to see if the results are correct and whether conducting finite element analyses
only is feasible in finding out the impact gravity has on the spine, any improvements that can be made and
how to develop the research further.
2
Literature Review
2.1
Gravitational loads and biology concerning the vertebral column
In all vertebrates, the central axis of the skeleton is the vertebral column. The vertebrae serve several
purposes like providing attachment to muscles, supporting the trunk, protecting the spinal cord and nerve
roots and serving as a site for hematopoiesis. A typical mammalian vertebrae usually consists of five
different groups: the cervical, thoracic, lumbar, sacral and coccygeal (caudal). While usually the vertebral
column consists of 33 vertebrae, there are cases where the number has varied from 32 to 35, with the
vertebrae placed in series and connected by ligaments and intervertebral discs. The 33 vertebrae
arrangement consists of 7 cervical, 12 thoracic, 5 lumbar, 5 sacral and 4 caudal (coccygeal) vertebrae. The
average length of the human male spine is 71cm while the female average comes in at 61cm.
6
Figure 1: The human vertebral column
In order to carry out the normal kinesiology of the body, the vertebral column is built in a very specific
way. The fact that it is semi-rigid allows it to provide a stable axis for the entire trunk, head, neck and
even the upper extremities. The vertebrae is also the main source of protection for the spinal cord and the
exiting spinal nerves, from the atlas to the lower sacrum due to how delicate they are. At the cranial end
of the vertebrae the joints and vertebrae also need to be highly specialised. In order for there to be
optimum space orientation of the special senses, the atlanto-occipital, atlanto-axial and intracervical joints
interact to provide extensive three-dimensional placement of the head and the neck. In any given part of
the body it is this craniocervical region that moves more than any other area of the vertebrae. It is these
controlling muscles that control the precise and miniscule movements in the craniocervical region; these
muscles are also in constant danger of causing pain and inflammation due to improper posture, cervical
arthritis and the compressed exiting spinal nerves.
The thoracolumbar region has three major requirements. First and foremost, the thoracic region is
responsible for protecting some of the most important organs in the body such as the heart and the lungs.
Secondly, the joints and the muscles that are present in the thoracolumbar region must be sufficiently
mobile and coordinated in order to perform the required function of serving as a mechanical chamber for
breathing, which includes coughing and forced exhalation. Furthermore core stability must be provided by
the abdominal muscles, posterior trunk muscles, iliopsoas and the quadratus. By controlling these a firm
base of support is made for the extremities as well as providing mechanical support for the vulnerable and
naturally highly stressed lumbar and lumbosacral regions.
Even the supposedly inferior part of the spine, the caudal end, is highly specialised for it to be able to
carry out its functions. Firstly, since the body is sometimes responsible for transferring large amounts of
forces through the pelvis and to the lower extremities, these must be done by the lumbosacral junction and
sacroiliac (SI) joints. Due to there being a possibility of these large forces exceeding the physical
tolerance this region can handle, the body may be susceptible to impairments like anterior
spondylolisthesis and partial dislocation of the SI joints. Secondly, this seemingly insignificant part of the
spine is also responsible for allowing the maximum movement of the trunk by interacting mechanically
7
with the hip joint (pelvis or femur). For example, a classic case is how complex the ability to touch the
floor while standing is; an ample forward bend is required in the lumbar region, as well as the pelvis,
relative to the femurs. However should there be any limitation in any part of the region, naturally the
range of motion demands would increase in other parts potentially causing hip arthritis, disc herniation
and inflamed facet joints in the lumbar spine [5].
Sometimes the spine may also be described as a modified segmented rod that is stabilised by both
intrinsic (static) and extrinsic (dynamic) factors. Examples of the intrinsic stabilisers come in the form of
the intervertberal discs, the capsule of the facet joints and various other ligaments particularly the anterior
longitudinal and supraspinous ligaments and the ligamentum flavum. Examples of the extrinsic stabilisers
include the paraspinal muscles (erector spinae, trunk and abdominal muscles). By contracting the trunk
and the abdominal muscles a rigid-walled cylinder is made in front of the spine. This is then transmitted
to the forces generated by the pelvis to load the spine and also acts as a lever in order to reduce the load
on the spine. In turn this either causes the centre of gravity line to fall through the L4 vertebra or 1cm
anterior to it. Thus the balanced spinal curves, intervertebral discs, paravertebral and trunk muscles
attenuate shock absorption and vertical loads on the spine [6].
2.2
Microgravity and biology concerning the vertebral column
There is a phenomenon in science where objects seem like they carry no weight i.e. they are weightless.
This is called microgravity. Since the word “micro” is defined as “very small” it refers to gravity being
very small too. Astronauts often experience microgravity when they are in outer space and as a result float
inside their spaceships [7]. Since human beings are frequenting visits to space even more nowadays, it is
imperative to understand the physiological effects that long-term spaceflight has on the body. When the
body is exposed to microgravity for a prolonged period of time, it can have a detrimental effect on the
muscles and bones of the body; more specifically it can cause a reduction in bone density, muscle volume
and changes in the muscle fibre properties [8]. These weaknesses in the musculoskeletal system has other
repercussions as well; compromising astronauts’ ability to carry out their space missions effectively and
hindering from performing their day to day tasks upon re-entering into the earth’s gravitational field.
Research has shown that although various measures and exercises have been tested to prevent
musculoskeletal changes to astronauts, as of now, not one suitable method has been found to combat this.
Targeting one part of this system is impossible too and therefore creating one exercise that will protect
astronauts from the effects of microgravity is not feasible due to the fact that skeletal muscles, tendons,
ligaments and bones are functionally and anatomically interconnected.
Substantial variance has been found on which part of the body is affected by microgravity space flight
however it has been narrowed down to showing increased effects in the inferior direction e.g. the lower
spine and the legs. For example when the effects of spaceflight lasting 4-6 months was examined on the
neck musculature of astronauts it was found that the muscle cross-sectional area and the fatty infiltration
was changed. The most profound changes in the muscle cross-sectional area were found in the following
regions: 23.1% in the rhomboid minor between T1 and T2, 9% in the sternocleidomastoid between C4
and C5, 25.1% in the trapezius between C6 and C7 and 11.5% in the semispinalis capitis between C4 and
8
C5. These changes have been presumed to be because of exercise countermeasures [9]. Evidence has
shown that there is strength reduction in the arms too as a result of spaceflight lasting up to six months.
Specifically it was isometric hand grip and precision pinch force that decreased during this time. In
essence a conclusion can be drawn that long term spaceflight may have heavy repercussions on astronaut
health and efficacy for tasks requiring full arm strength and functionality [10].
Other than that, the integrity of the spinal musculature is also important for the body to function properly.
When the spinal muscle volume was measured for astronauts before and after prolonged flights, it was
found that the volume and density of the back muscles slightly decreased. Therefore, researchers posed a
suggestion that perhaps the countermeasures designed were having some effect in preventing changes to
the spinal musculature however as can be seen negative changes were not completely negated [11]. A
study was also conducted considering changes in both the spinal muscles and the intervertebral discs.
After the flight was completed, the results came out to show a decrease in the lumbar paraspinal
functional cross-sectional area (FCSA) by 19%; the lumbar lean muscle FCSA percentage decreased from
86%± 5% to 72%±7%. Even though the subjects were put through the usual pre-flight, in-flight and
post-flight exercise programs, lumbar paraspinal muscle atrophy was found, which was theorised to be
because of the lack of exercise countermeasures targeting the lumbar paraspinal muscles [12].
Another study was conducted to see how the lumbar spine changed in six months. The subsequent results
showed a 11% decrease in lumbar lordosis. In two subjects it was found that the total lumbar wedging
decreased by 13% and 23%. The active flexion-extension range of motion decreased by 22.1%, 17.3%
and 30.3% for L2-L3, L3-L4 and L4-L5, respectively. In five subjects, a 20% decrease in the FCSA on
average and 8-9% decrease in CSA for both multifidus (MF) and erector spinae (ES). Overall the
conclusion was drawn that lumbar flattening and increased stiffness was caused by MF atrophy [13].
When the study was increased to include lumbopelvic musculature and observed over a period of
four-seven months it was found that CSA of the ES, MF and quadratus lumborum (QL) decreased from
4.6% to 8.4% however after a period of a year they were found to be fully recovered. With regards to the
paraspinal muscle attenuation (density), it was negatively affected by -5.9% to -8.8% and even after two
to four years the values did not return to their original values [14]. In another study, the lumbopelvic
muscles (PS, QL, ES and MF) were looked at after being exposed to prolonged spaceflight. Out of the 16
astronauts examined, 14 of them found that their lumbopelvic muscles decreased by 2.4% - 10.5% in
volume - the average value across the board being a decrease of 5.1%. In the ES and MF, individual
muscle volume and attenuation changes were found to have increased by 5.3% and by 9.5% in the QL.
However, in the PS, no significant muscle volume and attenuation changes were noted [15].
Although during day to day activities, the lumbopelvic muscles are involved in a significant amount of
weight-bearing, it is the lower limbs that are equally, if not more loaded. Hence the legs can be examined
and studied in a way that perhaps the pelvic and spinal muscles cannot. An astronaut was studied for a
period of 31 days in a microgravity environment to determine how the maximum explosive power (MEP)
of the lower limbs were affected. Once the astronaut returned to Earth, it was found that the mean force,
maximal velocity, maximal power (Wpeak and Wmean), maximal acceleration and overall mechanical
work decreased between 60% - 80% from the pre flight values [16]. Thus, the conclusion was drawn that
spaceflight affects the functional capacity of the lower limbs and the MEP declines post space flight
9
happen at about the same rate as the EMG activity of the quad muscles. However when the previous study
was compared again after 21 days, the Wpeak and Wmean were found to have declined even further. It
was thus suggested that individual characteristics as well as the in-flight exercises may be responsible for
these changes [17]. A further four astronauts, labelled S1, S2, S3 and S4, were studied from a time period
of a month to six months to see how their MEP was affected. Two days after returning to Earth, it was
found that for S1, the MEP dropped to 68% of its original value having spent a month in space. The three
astronauts that spent six months - S2, S3 and S4 - all found a decrease of 50% of the original value. As
well as that, the maximal force value (Fpeak) decreased by 11.7%, 26.2%, 31.5% and 27.0% for S1, S2,
S3 and S4, respectively. With regards to the peak velocities (Vpeak), S1 decreased by 24.2% and from
27.8% to 35.8% for subjects S2, S3 and S4. Lastly, for every subject, the lower limbs’ muscle mass
decreased from 9% to 13%. This then shows that the fall in muscle mass was much smaller than the fall in
MEP. Researchers have suggested that the cause for this was complex mechanisms that can not be
completely identified yet [18].
Variance has been found in the lower limb muscles since they have different functions. This was found
when the knee extensor and flexor muscle size were studied post spaceflight to see how the astronauts’
functionality was affected. The maximum voluntary contraction (MVC) decreased by 10%, the concentric
force reduced by 9% and the eccentric force reduced by 11%. Since the knee flexors are not very involved
in anti gravity functions, they did not reduce much in size however the CSA of the gluteal and quadriceps
decreased by a significant amount of 8%. On average, it was estimated that the knee extensors decreased
by 3-4% a week while in outer space [19]. Another study was used to investigate the changes to the knee
flexors caused by travel in outer space. Three astronauts (A, B and C) flew nine, fifteen and sixteen days
in space; the biggest decrease in the knee extensor volume was found in subjects A and C - coming in at
15.4% and 11.6% respectively. This case was the same for the knee flexor volume too - decreasing by
14.1% and 8.6% for A and C after four days on Earth and 11.6% for B after a day on Earth. With regards
to the Plantaris (PL) volume, there was a change of -12% for subject A, -8% for subject B and -15% for
subject C. In conclusion, the muscle atrophy ranged from 0.62% to 1.04% per day, suggesting that
individuals and muscle groups affect muscle atrophy [20]. A microscopic study on the knee extensors
were also conducted to examine them at a more micro level to see how the fibre size and enzymatic
properties of the VL muscle are affected in eight astronauts; three of whom partook in two five day flights
and five of whom partook in an eleven day flight. The 11 day flight astronauts found that their quantity of
type 1 fibres decreased by 6% to 8% and the CSA decreased by 16%. For fibre types IIA and IIB, the
CSA decreased by 23% and 36%. The mean number of capillaries per fibre for fibre type I decreased by
19%, for type IIA, CSA decreased by 25% and 26% for fibre type IIB. The average ratio of alpha
glycerophosphate dehydrogenase (GPD) to SDH activity increased by 85% for type I fibres. For the
ATPase, it increased by 9% and the ratio of ATPase to SDH increased by 38% for type II fibres. Thus, it
was concluded that during muscle fibres as well as their thickness, metabolism and blood supply can still
be affected, no matter how short the duration of the flight. [21].
The lower leg is equally as complex as the other parts of the body. When studied over a period of 17 days
on Earth and in other space, it was found that the maximal isometric calf strength, muscle force-velocity
properties, fibre composition or size of the calf muscles did not change significantly. The reason behind
this is thought to be the extensive in-flight testing of the ankle plantar flexor function in preserving the
muscle [22]. However, in other studies, significant changes in the lower leg were found. A study was
10
conducted on the density and length of thin filaments of the SOL muscle fibres during and after 17 days
of spaceflight. The CSA of the SOL muscle fibres reduced by 15% after returning to Earth, myofibrils
became slimmer and Z bands became shorter in length. Since no myofilaments were lost, the sarcomeres
remained the same. As the sarcomere length varied, the density of the myofilaments also varied. The time
in space did not affect the thickness of the filament density or the spacing between the filaments either.
However, the density of the thin filaments did decrease by 17% when close to the Z band. Similarly, the
mid-I band value reduced by 21% and the density of the A band decreased by 26%. At the overlap of the
A band region, a 22% decrease was found compared to the overlap of the Z band region. Therefore it was
suggested that sarcomeres are damaged by atrophied muscle fibres after landing [23] .
There was also a study done on a cellular level to see how the structure and function of the skeletal
muscle is affected. When the pre-flight values, fibre mass, force and power were studied, it was found that
in SOL type I, SOL type II, gastrocnemius (GAS) type I and GAS type II there was a decrease in all of
them respectively. In SOL type I, the fibre CSA decreased considerably by a percentage of 20%. Even
with regards to the peak force in SOL type I, it decreased by 35%. A correlation was found between the
mean fibre diameter and the number of fast type II fibres, with the crewmates with the highest percentage
decline in the mean fibre diameter exhibiting the greatest increase in the number of fast type II fibres.
Thus, it was concluded that a significant difference was found in both the degree of fibre atrophy and the
loss of peak force [24].
In yet another study, the lower and upper extremities of four astronauts were examined. It was found that
the SOL experienced the biggest decrease in muscle volume (19±7%) then in the GAS (10±5%) and
finally in the ankle dorsiflexor muscles (10±3%). Even in the thigh muscles, some losses were noted: in
the knee extensors by 6±3%, in the knee flexors by 7±4% and in the adductors by 4±3%. In the arm
muscles, little to no volume decreases were detected. Other changes were also found in the thigh muscles,
the isokinetic strength in the knee flexors decreased by 24±8% and 10±11% in the knee extensors. The
anke PL strength also decreased by 22±6% and the dorsiflexor strength decreased by 8±16%. On top of
that, isometric strength was reduced by 20±16% in PL, 4±22% in the dorsiflexors, 15±13% in the knee
extensors and 20±17% in the knee flexors. The hip extensor isometric strength also decreased by 15±26%
and the hip flexor isometric strength decreased by 28±9% [25].
Another study was conducted with an additional functional layer to the calf muscle findings. The
contractile and elastic features were examined in 14 astronauts over a period of three to six months. It was
found that the maximal isometric torque decreased by 17% while the maximal shortening velocity
(Vmax) increased by 31%. Other findings showed the maximal muscle activation decreased by 39% while
the musculotendinous stiffness increased by 25%. Although under active conditions following spaceflight
the whole joint stiffness was retained, under passive conditions there was a significant decrease of 21%.
The study was completed under the conditions of the astronauts having access to a cycle ergometer,
treadmill and other resistance training devices, it cannot be confirmed whether they were used [26].
This study was again further enhanced by checking the calf muscle functioning in eight astronauts over
213±30.5 days. The architectural and contractile properties of the triceps surae (TS) muscles were
measured before and after the mission was completed. The variables that were measured were the MVC,
tetanic tension (Po), voluntary and electrically evoked contraction times and force deficiency (Pd), fibre
11
length (Lf) and muscle thickness (Hm). For the exercise regimen, a four day cycle was used and it was
found that the maximum voluntary isometric contraction (MVIC) decreased by 41.7%, Po decreased by
25.6% while Pd increased by 49.7%. The time from the moment of simulation to peak switch (TPT)
increased by 4% while the time from contraction to half-relaxation (½ RT) decreased by 17.6%. The
electromechanical delay (EMD) increased by 34%. Lf decreased by 22.5% in the gastrocnemius medialis
(GM), in the gastrocnemius lateralis by 35.2% and in the SOL by 28.1%. With regards to the Hm, in the
GM, it decreased by 18.9%, in the LG, it decreased by 19.8% and in the SOL, it decreased by 18.8%. It
was thus suggested by the research that in order to counteract the changes induced by microgravity, the
specific functions of the individual calf muscles must be taken into account [27].
2.3
The biomechanics of the vertebral column
The essence of the biomechanics of the vertebral column is defined by forces and moments. A force is
when an object interacts with another object in either a pushing or a pulling manner. Any interaction
between two objects can essentially be defined as a force. Likewise, when there is no interaction, there is
no force [28]. A moment stems from a force and is regarded as the ability of a body to rotate about a
specific point or axis. The key factor in defining a moment is that the body must twist due to the force
acting upon it. In order to fulfil this condition, the force must not pass through the centroid of a body; in
short, making sure the force does not have an equal and opposite force directly along its line of action
[29].
At its simplest, the spine is a complex multi articular system that is controlled by the muscles. Its main
function is to support the head and trunk for posture and during movements and to enclose within it and
protect the spinal cord, nerve roots and even the vertebral arteries at a cervical level. Apart from
protecting the nervous structures, spinal stability is also required for many functions such as transfer of
power forces between the upper and lower limbs, the active generation of forces in the trunk, to prevent
early biomechanical deterioration of the spine components and to reduce the amount of energy used
during muscle action [30][31].
It is when the stability is lost that problems arise in the spine such as back pain at a lumbar level. This
clinical stability has been defined as the ability of the spine to limit displacement patterns in order to
ensure the spinal cord is not damaged or irritated as well as making sure changes to the structure of the
spine do not cause deformity or pain under physiologic loads [32]. Likewise, instability has been defined
as the opposite of stability in the way that it does not allow the spine to maintain its patterns of
displacement and may cause initial or additional neurologic deficit, deformities and/or pain [33] as well as
that instability is said to lessen stiffness of the spine and lead to abnormalities and cause increased
movement in the motion segments [34]. The abnormalities are usually caused due to the location of the
dominant lesion in the MS while the dysfunctional motions that are caused in more than one direction is
caused by tissue derangement since spinal movement is 3-d with coupled movements.
In space, a vertebra is able to rotate and rotate around each of the x, y and z cartesian axes as well as
various combinations of coupled movements, with the latter taking place simultaneously along or around
12
an axis different from that of the principal motion [35]. When the spine undergoes flexion and extension,
the vertebra moves around a transverse rotation axis however it is not in the subjacent disc but rather in
the vertebral body below [36]. Two circumference arcs are performed by both the endplates and the facet
joints around the same rotation centre however the location can change according to the level; they are
placed in the superior cervical spine two vertebral bodies below and in the inferior cervical which is the
subjacent vertebral body as well as in the dorsal and the lumbar spine. Since the rotation centres are found
very low, there is coupled movement in the antelisthesis and this movement can be anywhere from a
maximum of 2-3mm at C2-C3 to a minimum of 0.5-1.5mm from D1 to L5.
Figure 2: Lateral conventional radiograph of the cervical spine in flexion
Due to the oblique orientation of both the facet joints and the muscles, this causes the axial rotation and
lateral bending to always be coupled movements. This coupling is most evident at a cervical level.
Although the location of the centroid for lateral bending is located between the facets, the location of the
centroid for axial rotation depends according to the level: for the dorsal spine it lies in the central body
and for the lumbar segment it lies in the spinous processes. Due to a lot of effort being required for
movement changes in various phases to have proper spinal function, there must be a high nonlinear
load/displacement ratio of the FSU [37].
During day to day activities, the spine must be able to support loads of up to 500-1000N, which is about
twice the average human body weight, however during lifting, the spine can increase this amount to
5000N, which is nearly 50% of the final failure load [38]. The passive stabilisation and intrinsic structural
role depends on several factors including the vertebral architecture and bone mineral density,
disc-intervertebral joints, facet joints, ligaments and physiological curves.
Exactly how much load the vertebrae can take depends on three key factors: the size and the shape of the
vertebrae, the integrity of the trabecular system and the bone system. Mainly, the vertebral body is made
up of spongy bone and it is of course three dimensional in nature, shaped like a honeycomb much akin to
the wings of an aeroplane and this shape allows the vertebrae to have the best strength/weight ratio. In
13
order to increase the load the spine is able to take, there must be a progressive increase in the the body
size downward in the spine and would allow for 2000N in the cervical segment increasing up to 8000N in
the lumbar spine [40].
A cancellous bone exists in the vertebral body which has four main trabecular systems with a constant
orientation:
- A vertical system that extends between the endplates and is capable of accepting and transmitting
vertical loads.
- A horizontal system that travels in the posterior arch and joins the transverse processes.
- Two curved oblique systems, one that is inferior and one that is superior; it starts from the
endplates, crosses in the peduncles and then ends in the spinous and joint processes. The main
function of these two oblique systems is to make sure the neural arch of the body is able to exist
by withstanding the horizontal shear stresses that they will be subject to.
The trabecular struts initially accept the axial loads; the bowing of which is restrained by tension present
in the horizontal lamellae and thereby allows horizontal dispersion of the vertical loads, ultimately
making the cancellous bone more resilient.
Figure 3a: The vertical compressive loads that are accepted by vertical trabecular columns in order to transmit
forces between the endplates. However the vertical struts present may be susceptible to bowing. Figure 3b: It is
restricted due to the presence of the horizontal lamellae as not only do they join the vertical struts, the tension tends
to favour radial dispersion of forces which allows the vertebral body to be more resilient.
While the spongy bone of the body cortical shell is highly resistant, it has very low elasticity. The
resistance of this is highly dependent on the mineral density (BMD). However, any bone loss taking place
during osteoporosis causes this resistance to decrease at a disproportionate exponential amount e.g. when
there is 25% bone loss, there is a 50% loss in resistance. When this is described mechanically, the
relationship can be explained by the resistance of the columns decreasing by the square of increasing
length and by the square of decreasing cross section.
In osteoporosis, there is a progressive relative elongation of the vertebral columns during the early stages
due to resorption of the horizontal lamellae. During the later stages, these columns become thinner and
there is a culmination of both of these symptoms coming together.
14
Figure 4: How much load the vertebrae is able to take is heavily dependent on the vertical trabecular struts joining
the endplates. (a) The relationship between the length and the cross section is that as the length increases, the
resistance of the column decreases by the square of the decreasing cross section. During osteoporosis, both of these
processes are undertaken as a result of progressive elongation of the columns provoked by the resorption of the
horizontal lamellae. (b) Thinning of the columns. (c) The bone resistance and load bearing capacity of the vertebrae
decreases at a disproportionate exponential amount.
Where the conception may be that a single load would cause the vertebrae to fatigue however multiple
small loading forces may be enough to cause fatigue. In order for the vertebrae to be damaged like this,
focal osseous microdamage first takes place which develops until final fatigue takes place. The anterior
half of the vertebral bodies are usually involved during osteoporosis and this is usually not a homogenous
process.
With regards to elderly people combating degenerative disc collapse, on the endplates, there are no longer
evenly distributed forces; instead the loads are much more focused on the posterior facets during erect
standing posture. By relatively stress-shielding the anterior bodies like this, the local bone loss and bone
weakening is reduced since the bones adapt their mass and architecture to combat all the forces that are
regularly applied to them [41].
The “mechanostat” theory states that after peaks strain and fall below a certain threshold, the bones may
be susceptible to weakening [42]. An example of this can be seen when the standing posture is off-loaded
and then spinal flexion occurs subsequently leading to the stresses placed on the anterior bodies to
increase by upto 300%. It is due to this high difference in loading that the anterior bodies may fail with
wedging and ultimately lead to osteoporotic fracture as well as explaining why this injury is re-aggravated
by any form of forward bending.
When these fractures take place, naturally the mechanical properties of the injured vertebra change as
well as the surrounding vertebra and disc. When the endplates end up being deflected, the adjacent disc
nucleus ends up being depressurised; the compressive stress afterwards being placed on the annulus,
mainly posterior to the nucleus and the neural arch.
Percutaneous vertebroplasty which is used to augment the vertebrae by reversing the effects and an
injured vertebral body becomes more stiff and stronger. Pressure in the adjacent disc returns to normal
and the load that is shared between the vertebral body and the arch returns to normal [43]. The greatest
15
stabilisation and pain relief are caused due to the macroscopic intervertebral instability (vacuum cleft
phenomenon and its changes during flexion-extension) [44].
How stress is distributed inside the fractured vertebra and between the affected vertebra, adjacent vertebra
and disc in cadaveric motion segments is affected by the volume of cement injected [45]. Simple
abnormalities such as abnormal end plate deflection and normalising intradiscal pressure under load can
be easily fixed using little amounts of cement - 13% of volumetric filling, to be precise. However, in order
to stabilise injured trabecular bone and equalise stress distribution between the vertebral body and the
neural arch, larger quantities of cement must be injected - 25% upwards on average. Even so, when the
biomechanics of load transfer to the adjacent vertebrae are altered, the new adjacent fractures are created
increase in risk through a “stress-riser” effect.
In a study examining 147 patients with vertebroplasty or kyphoplasty to find out what factors may
indicate these diseases, it was found that the factors that could be used to predict for adjacent refracture
such as age, gender, BMD, location of treated vertebra, the amount of cement that is injected into the
bone, collapse degree, the pattern in which the cement is distributed, treatment modality, the cement that
leaks into the disc space were cement leakage into the intervertebral disc space - which would cause the
load stresses to become more highly concentrated - and evolving osteoporosis [46].
2.4
Biomechanics and modelling of the vertebral column
One of the most common incidents that takes place in orthopaedics are thoracolumbar vertebral
compression fractures including any osteoporotic fractures that may happen to old people or any fractures
caused by falls or car accidents. If these fractures are not treated at the earliest sign of them developing,
they may transform into older fractures including kyphotic deformities; the symptoms of which are low
back pain that is persistent and that may be accompanied by symptoms of spinal cord compression.
Treating these issues cannot simply be done conservatively and surgery is required in most cases [47]. For
the ones that are particularly old, a vertebral column resection surgery (VCR) can be done to take away
the compression of the spinal cord and to restore the balance of the vector sequence. However, these
surgeries traditionally take a long time and cause a lot of surgical trauma, meaning it is difficult for
surgeons to carry out. In order to combat these problems, it has been suggested that posterior unilateral
vertebral resection and reconstruction (PUVCR) should be carried out to fix the kyphotic deformities
using an unilateral approach and partial osteotomy. Finite element analysis was used to simulate the T12
VCR and PUVCR for bone cutting. In order to measure the biomechanical stability after surgery, either a
long segment or a short segment fixation was done.
The subjects that were gathered had their computed tomography (CT) images imported into a computer
modelling software in order to establish and create a model so that various surgical osteotomy modes
could be simulated, the vector balance could be restored and a screw-rod system could be installed. An
FEA was thus run to calculate and compare the biomechanical parameters.
In order to conduct the FEA, 128 row, 256-slice GE spiral CT thin-section scans with a slice thickness of
1mm and resolution of 512 x 512 were obtained so that 2d sagittal tomographic images of the T8-L3
16
vertebral body could be made. These files were subsequently saved in a DICOM format. After that, these
DICOM images were used so that they could be imported into MIMICS 20.0 so that 2d images could be
made into a 3d image, modelling from T10 to L2, eventually being stored as STL format files. Another
software - 3-Matic 12.0 software was used in order to wrap, smooth and remove any excess tringulars.
Thus, in order to solidify the model, it was finally imported into Geomagic Studio 12.0.
Thereafter, to grid and construct the intervertebral disc, bone and ligament structures, Hypermesh was
used. By using Hypermesh, the intervertebral disc can be composed of annulus fibrosus matrix, nucleus
pulposus, annulus fibrosus fibres, upper and lower endplates; with the nucleus pulposus being responsible
for 43% of the total intervertebral disc [48]. Hypermesh was used to process the model and then
Pro/Engineer was used to make the screw-rod system and then Hypermesh used again for assembly. To
define the material properties, assemble the model, load and then finally finite element analyse it, a
software named Abaqus was used. In order to validate the materials that were used in this study,
previously published finite element models and thoracolumbar spines of human cadavers were analysed
[49-51].
17
Different screw combinations were used to fabricate four fixation models. 6mm by 40mm pedicle screws
were inserted into the T11-12 while 6.5mm by 45mm pedicle screws were inserted into the L1 and two
vertebral bodies. The LVCR model represents the removal of the whole T12 vertebral body and T11/12,
T12/L1 intervertebral disc, applying a 18mm diameter cylinder with a 1mm thickness in order to simulate
a titanium cage fixed in the vacant position of the vertebral body, with cancellous bone in the middle. At
T10, T11, L1 and L2 further pedicle screws are fixed. With regards to SVCR, that is the model in which
the pedicle screws are removed from T10 and L2 from the LVCR model. In the LPUVCR model, the T12
right vertebral plate, facet joint and vertebral body as well as the T11/12, T12/L1 right intervertebral discs
are all removed with a 10mm diameter and 1mm thickness cylinder being used for the titanium cage.
Where the vertebral body is vacant, that is where the cage was fixed with the cancellous bone being
placed in the middle of this in order to conduct the tests. The pedicle screws were applied at T10, 11, L1
and L2. Likewise, in the SPUVCR, the pedicle screws are removed from T10 and L2 as well as the ones
from the LPUVCR.
18
Figure 5: The FEA of the fixation constructs: LVCR - long vertebral column resection, SVCR - short vertebral
column resection, LPUVCR - long posterior unilateral vertebral column resection and reconstruction, SPUVCR short posterior unilateral vertebral column resection and reconstruction
In order to figure out the boundary and loading conditions as well as simulate the spinal motion, the
Abaqus software was used. A couple of assumptions were made before running tests including assuming
that the L2 vertebral was fixed and that there is no displacement or rotation within the substructure. The
movement in the spinal sagittal planes, coronal planes and transverse planes were said to have
flexion-extension, lateral bending and rotation, respectively. To simulate this, an axial load of 200N and
an additional torque load of 7.5Nm were applied. The axial load was applied to the superior surface of the
T10 vertebral body while the torque load was applied to the centre of the T10 vertebral body.
To see how they performed, three metrics were used: the ROM of the overall fixation from T10-L2, the
von Mises stress of the instrumentation system and the stress magnitude and distribution of the inferior
endplate of T11 and superior endplate of L1. The reason for choosing these metrics was to assess how the
different vertebral reconstruction methods affect the roles of the overall fixation system. Statistical
analysis is usually conducted at the end however only one subject was studied.
2.5
Results
When compared with other biomechanical experiments and finite element models, the model was
determined to be reasonable and trustworthy enough to proceed with. After using the same loading
conditions, the 7.5N calculated for the ROM was found to be the same as other studies done in the past
[52-54]. Thus, it was concluded that the model generated can be used to further study old fractures of the
thoracolumbar spine.
19
It was found that under load, the ROMs all decreased; the largest decrease coming with the LVCR, with
forward flexion decreasing by 88.8%, extension decreasing by 97.3%, left lateral bending decreasing by
89.6%, right lateral bending decreasing by 90.8%, left lateral rotation decreasing by 88.8% and right
lateral rotation decreasing by 88.9%. The smallest decreased came with the SPUVCR, with forward
flexion decreasing by 51.2%, extension decreasing by 33.8%, the left lateral curve decreasing by 17.6%,
the right lateral curve decreasing by 14.6%, left rotation decreasing by 78.8% and right rotation
decreasing by 79.1%.
Figure 6: Angular ROM of the thoracolumbar junction (T10 - L2)
Regardless of the fixation modes, all the screw-rod system stress concentration points were located at the
junction. In the long-segment fixation, the stress of the screw-rod system is within the bearing range of
internal fixation as opposed to the short-segment fixation; in the LPUVCR model, during the lateral
bending motion, the maximum stress was 213.25 mPa while in the SVCR, the minimum stress was 40.22
mPa. Even in the VCR, the maximum stress was greater than PVCR.
20
Figure 7: von Mises stress on the rods and the pedicle screws
Furthermore, in all four models, the contact area between the titanium mesh and the upper and lower
endplates was where the stress concentration area was present thus placing significant stress upon the
upper and lower endplates. In the SPUVCR model, the maximum stress was 36.25mPa which was
produced in the lateral bending movement of the inferior endplate of T11. On the other hand, the
minimum stress was 3.87 mPa and this was found in the LPVCR model. With regards to the upper
endplate of L1, the minimum stress was produced in the extension movement and returned with a figure
of 1.91mPa while the maximum stress was produced in the lateral bending in the SVCR, returning with a
44.77mPa.
21
Figure 8: Flexion movement stresses from the inferior endplate of T11 to the upper endplate of L1
Figure 9: Extension movement stresses from the inferior endplate of T11 to the upper endplate of L1
3
Methodology
3.1
Obtaining a model of the vertebral column and importing into Workbench
A healthy male was studied and his information was extracted; it was checked to see if there were any
defects in the spine whether that be via pathological or spinal trauma. Having collected all the CT slices
from a software called MIMICS, a solid model of the spine was made.
22
Figure 10: Vertebral column obtained from SolidWorks
Figure 11: Thoracic vertebrae on SolidWorks
Since it was known from previous studies that running a FEA on the entire vertebral column would cause
the mesh to fail and show up the error messages: ‘obsolete mesh’ and ‘failed mesh, it was decided by the
supervisor that it would be best if only the thoracic vertebrae was modelled and analysed from the
beginning. Therefore, when the vertebrae was stripped down to just the thoracic vertebrae, it was saved as
a step.203 file and transported into Ansys Workbench. In the ‘Design Modeller Geometry’, the model was
uploaded, ready for use.
In order to conduct the analysis, the ‘Static Structural’ function was then used. This allows steady and
consistent loading to be placed on the vertebrae and cancels out damping and inertia that arises due to
time-varying loads. After that, the relevant details were filled in to run the FEA. As per the research
23
conducted, a Poisson’s ratio of 0.3 and a Young’s Modulus of 58.7MPa was used for the thoracic
vertebrae. Later on, when the lumbar vertebrae was modelled, a Poisson’s ratio of 0.3 and a Young’s
Modulus of 12000MPa was used.
Table 2: The engineering data for the thoracic vertebrae
Figure 12: The thoracic vertebrae having been imported into Ansys Workbench
24
3.2
Applying a mesh and boundary conditions to the thoracic and lumbar vertebrae
After the model was transferred into Workbench, a mesh needed to be applied as a prerequisite of running
the finite element analysis. A very coarse mesh of 0.01m was used for the thoracic vertebrae and it look a
long time to mesh as well as popping up with the ‘failed and obsolete mesh’ messages.
Figure 13: The thoracic vertebrae meshed and returning with several ‘obsolete and failed’ mesh messages
In an attempt to mesh the thoracic vertebrae, a smaller mesh was used however even after meshing for an
hour, the vertebrae still failed to mesh. Due to not being an efficient use of time, it was decided to
abandon the thoracic vertebrae and look at a different section of the vertebrae.
Since the lumbar vertebrae is the least complex part of the spine, it was assumed that it would be the
easiest to mesh and run for finite element analysis. Like the thoracic vertebrae, the lumbar vertebrae was
imported into Workbench after being converted into a step.203 file. The relevant engineering data was
input as per the research conducted as part of the literature review.
25
Figure 14: The lumbar vertebrae having been exported into Ansys Workbench
Thus, as per procedure, the lumbar vertebrae was meshed. Initially, it was meshed with a mesh of 0.01m
and came back with a ‘failed mesh’ at the L5 vertebrae. Thereafter, it was meshed with a mesh of 0.005m
to see if the ‘failed mesh’ message would be overridden. However, this attempt was not successful. It was
decided the best course of action would be to take out the L5 vertebrae and proceed with vertebrae L1-L4
only. Thus, the L1-L4 vertebrae was meshed using a mesh of 0.005m and fixed with a fixed support at the
bottom of the L4 and a 400N force applied.
Figure 15: The lumbar vertebrae with a 0.005m mesh applied
26
4
Results
4.1
Results for the lumbar vertebrae
Having met all the requirements in order to run the finite element analysis, it was finally run with a bid to
find the total deformation, the equivalent von Mises stress and the maximum principal stress. The total
deformation shows how the force changes the vertebrae. The equivalent von Mises shows if the vertebrae
will fracture or yield under the force applied. The maximum principal stress shows if the vertebrae will
compress or stretch under the load applied. However, as soon as the solver was run, all three came back
with values of 0. This could not be rectified and thus did not give conclusive results for how much load
the lumbar vertebrae could take.
Figure 16: The maximum principal stress run on the lumbar vertebrae
Figure 17: The equivalent von Mises stress run on the lumbar vertebrae
27
Figure 18: The total deformation run on the lumbar vertebrae
5
Theoretical calculations
5.1
Lower back compressive forces
The limit that has been specified for maximum back compression force is 770lbs. During lifting and
bending of the waist as well as extending the upper body, the alignment of the back and the centroid of the
body is the abdomen. As a result, not only does the spine support the load of the weight that is being lifted
or the weight that is being lowered, it must also support the weight of the entire upper body. By
calculating the moment and forces of both of these loads, the forces that go through the lower back can be
calculated. A moment can be defined by the force acting over a distance and is related by the equation:
Moment = Force x Distance (1)
The moment can also be defined by:
Moment = Weight of load x Distance from centre of weight of load to a fulcrum (2)
If a person is assumed to be bending over to pick a load out of a box with a 40 degree bend from the
horizontal and with a load of 40lbs as well as reaching 15 inches in front of the lumbar spine to lift the
load, with the centre of mass (the abdomen) being at 10.4 inch anterior of the lumbar spine. The average
bodyweight of a human is 160lbs therefore the upper body can be assumed to be 80lbs.
From equation 1, it can be determined:
Moment from the weight of the load = 40lbs x 15in = 600in-lbs
Moment from the weight of the upper body = 80lbs x 10.4in = 832in-lbs
28
Total clockwise moment = 1432in-lbs
In order to even attempt to lift this load, the clockwise moment must be countered by an anticlockwise
moment. This anticlockwise moment is given by the contraction of the erector spinae muscles - which are
the muscles that are present 2 inches behind the lumbar spine.
Therefore, from equation 2, the anticlockwise moment can be calculated:
Anticlockwise moment = Force generated by erector spinae muscles x 2in
Should the person be in a stooped nature and be holding the load in a static posture at the start of the lift,
the clockwise moment must be equal to the anticlockwise moment to prevent the person from falling
forward onto their face, thereby ensuring the anticlockwise moment is also equal to 1432in-lbs.
From equation 2, it can be verified:
Force generated by erector spinae muscles x 2in = 1432in-lbs
Force generated by erector spinae muscles = 1432in-lbs/2in
Force generated by erector spinae muscles = 716in-lbs
Since the total compressive force = sum of all moments, the total compressive force is 2148in-lbs [55].
6
Discussion and Analysis
6.1
Research finding concerning gravitational loads acting on the vertebral column
Due to the upright position that humans are in throughout the day, it is said that is the cause of the S shape
of the spine. It is from quadrupled ancestors that the kyphotic curves are said to be inherited from birth
while the lordotic curves develop later, with lumbar lordosis coming later still at a stage where an erect
posture is assumed.
Although it may be obvious to note how an S-shaped column may be inferior to a straight one, the fact
that the spine must carry load means it must be curved meaning a spine with a double curve would be
stronger and more suitable for the job than a single curved C-shaped column [56]. The other pro of the
S-shaped column is its ability to act as a spring and absorb energy meaning any impactful force travelling
from the feet to the head can be dampened. The assumption has been made that a passive equilibrium
exists in the spine with the line of gravity running down the middle sandwiched by the spinal curves on
both sides. This line of gravity is said to go through the atlanto-occipital joint and intersect the spine at
C6, Th9 and S3.
29
Figure 19: How the line of gravity passes through with relation to the spine
It is quoted by Steindler (1955) that “the spine as a whole approaches the line of gravity” and that “each
curve is compensatory to its neighbour with the result that the line of gravity as it passes
upward…intersects with all four curves of the spine at certain levels” [57]. However, the term “line of
gravity” has not been defined yet, all that can be said is gravity can increase the size of any curve of the
spine e.g. the spine may bend backwards in the lumbar portion [58].
Figure 20: The lumbar spine and its spring-like action
Since it can be assumed that gravity increases lumbar lordosis, the forces must act ventrally on the spine
in order to counteract. On top of that, should muscular work not be involved, the long anterior ligaments
have to carry the full load.
6.2
Research findings concerning micro gravitational loads acting on the vertebral column
When in space, the chances of back pain increase due to the vertebral discs being unloaded and taking on
more water. Once the astronauts return to Earth and are subject to normal gravity, this can cause disc
30
herniation. The exact percentage of water intake increase is thought to be 13% however this only affects
some of the intervertebral discs and not all of them.
This phenomenon can be explained by the fact that during conditions of normal gravity, the spine
experiences diurnal changes in both height and hydration. As is obvious during standing, the spine is in a
vertical manner and thus since it is thought to be like a spring, the spine compresses and as a result, water
is secreted out of the discs. Due to this, a couple of changes occur in the spine: the disc height decreases,
the spine curvature changes and the spine becomes more flexible. Sleep acts as a form of resetting the
spine, the gravitational load upon the spine is removed since it is horizontal and the discs are able to
retake water into them and rehydrate into their original form. Any height and stiffness lost in the discs
during the day is recovered during sleep subconsciously showing off the diurnal fluctuation of the spine.
The reason why lower back pain and disc herniation increases in space is because in space, there is no
opportunity for the body to reset and thus the body cannot perform its natural diurnal fluctuations. Instead
of the discs recovering height and stiffness like on Earth, in space, they continue to swell and increase in
height due to the absence of gravity and as the discs’ natural tendency is to attract water it continues to
swell up with water and becomes hyper-inflated. As a result, it leads to a more stiff spine and the spine
becomes flatter due to so much water intake in the discs and thus the spine actually increases about an
inch or two in length [59].
Figure 21: How the lumbar range of motion changes pre and post space flight.
31
6.3
Research finding concerning biomechanics of the vertebral column
Studying forces and how it affects humans is how biomechanics is defined. The spine goes through four
main movements on a regular basis: flexion, extension, rotation and lateral flexion. These movements
take place due to a combination of rotation and translation in 3 particular planes of motion: the sagittal,
coronal and horizontal planes [61]. When these movements occur, naturally, forces then act on the lumbar
spine and sacrum: compressive force, tensile force, shear force, bending moment and torsional moment
[62]. E.g. When the spine undergoes lumbar flexion, there are two forces applied upon it: a compressive
force is applied to the anterior side of the disc and a destructive force is applied to the posterior side of the
disc. With lumbar extension, it is the exact opposite [63].
An effective load-bearing system is created by the lumbar spine complex. When an external load is
applied on the vertebrae, the vertebral body and the elastic discs stiffen due to the stress placed upon them
and the discs are more easily strained [64]. In the nucleus pulposus the pressure is always greater than
zero, acting as being ‘pre-loaded’ ensuring that any force that is applied is met with a greater resistance
[65]. As well as that, an outward pressure is created towards the vertebral endplates by an increase in the
hydrostatic pressure within the intervertebral discs resulting in the annulus fibrosis bulging and tensile
forces being present within the concentric annular fibres. By transferring the forces in this way, the
pressure on the adjacent vertebra decreases and acts as a shock absorber. Thus, essentially, the
intervertebral discs are a form of biomechanical feature and transmits forces between adjacent vertebrae
when the spine is moving, acting as a fibrocartilage “cushion”. Due to these, the lumbar disc is more
susceptible to injury compared to any other disc in the spine for a few reasons: the annular fibres are
arranged in a more parallel manner and on the posterior side are thinner than the anterior side, the nucleus
is also placed in a more posterior position as well as the holes in the cartilaginous endplates.
Conversely, when a load is applied along the spine, there are shear forces acting parallel to the
intervertebral disc due to the nucleus compressing causing a lateral bulge of the annulus. The shear forces
can also take place when one vertebra moves e.g. it can move forwards or backwards with respect to an
adjacent vertebrae with flexion and extension. Torsional stresses, on the other hand, develop from external
forces about the axis of twist and happens in the intervertebral disc during activities like twisting the
spine.
With respect to the shear forces, stability can be provided to the intervertebral joints via zygapophysial or
“facet” joints, ultimately allowing flexion and extension movements.
6.4
Finite element analysis and results
Since it is not possible to verify and study the vertebra through physical tests, the literature review from
the modelling and the finite element analysis allowed invaluable information to be gathered. It allowed to
model and test loads on the vertebral column realistically without having the facilities to do so.
32
A CT scan of a vertebral model used by MIMICS to model the spine served as the cornerstone of the
FEA. The model was obtained from a healthy male and was deemed to not have any deficiencies or flaws
in the anatomical structure of the vertebral column. Despite this, it was known that once the mesh is run in
Workbench, a number of ‘holes’ would be found resulting in the ‘obsolete mesh’ and ‘failed mesh’ error
messages. The reason for the ‘holes’ could have been due to one of two things: the model may have
contained trauma that would have passed unseen through the models or more logically, while transporting
the model from SolidWorks to Ansys Workbench, the file may have been corrupted.
With regards to modelling the entire vertebral column, once meshed, the information was given that about
72 hours would have to be taken in order to conduct the FEA, ultimately restricting in obtaining thorough
results. A sacrifice had to be made and it was decided the best course of action would be to split the
vertebrae into its respective sections: cervical, thoracic, lumbar etc and then to run a FEA on each section.
This meant that the forces would have to be calculated cumulatively and a FEA on the whole vertebrae
could not be possible. Had there been access to a more powerful computer, perhaps this situation may
have been worked around.
As a result, the thoracic vertebrae were modelled individually on SolidWorks. Since they have to be
meshed before the finite element analysis, they were attempted to be meshed however the attempts were
not successful. Thus, it was decided to move onto the lumbar vertebrae, mesh that as well as apply a fixed
support and a forced load in order to conduct the finite element analysis. The FEA was conducted and
then it was found that there were no results produced for the maximum principal stress, von Mises stress
and the total deformation. Thus it was not possible to check and verify how the calculations measured up
to the theoretical values researched and calculated.
6.5
Theoretical calculations
The theoretical calculations were done to serve the purpose of verifying the FEA and supplementing the
corresponding results. It is known that the lower back can only handle a maximum compressive load of
700lbs. As well as supporting the weight of the entire upper body, the spine must also support the weight
of any object being lifted. Thus, if the moments and forces of these two loads are found, the forces present
in the lower back can be calculated. If a 40lbs load is pulled out of a box with 40 degree bend to the
horizontal when reaching 15inches in front of the lumbar spine, the moment from the weight of the load
can be calculated via the product of the load and distance: 40lbs x 15in = 600in-lbs. Likewise, the weight
if the average human body is 160lbs therefore the upper body can be estimated to be 80lbs. If the load
being picked up is 10.4in in front of the centre of mass, the upper body load is given by: 80lbs x 10.4in =
832in-lbs thus generating a total clockwise moment of 1432in-lbs.
The anti-clockwise moment is also 1432in-lbs. The erector spinae muscles are 2in behind the lumbar
spine therefore to calculate the load, 1432in-lbs / 2in = 716in-lbs of load on the erector spinae muscles.
The total compressive force is the sum of all the moments therefore it can be calculated by 1432 + 716
giving a final value of 2148in-lbs.
33
7
Conclusion
The overall aim of this paper was to measure and quantify the forces acting on the spinal vertebrae due to
the effects of gravity. By comparing data from appropriate literature, theoretical calculations and a finite
element analysis, this was hoped to be achieved and was achieved to a successful degree. The
overwhelming evidence proves there is a relationship between all forms of loading, whether that be
extreme or microgravitational, and has an adverse biomechanical effect on the spine.
The objectives for the project were also set out and met. A model of the vertebral column was supposed to
be obtained and then analysed using FEA and this was done from the CT scan model in SolidWorks being
transported to Ansys Workbench before being put through a FEA. The vertebrae modelled were assumed
to be operating under normal gravitational conditions. It can be seen from the results that gravitational
loads clearly have an effect on the vertebral column and this relationship is explored throughout the paper.
The type of people most at risk from different types of gravitational loading were also identified through
this study. Astronauts experiencing microgravitational loading in space were found to be most at risk. It
was found that this can be relieved by putting the body into a horizontal position like in sleep, which
would elongate the spine by 2-4cm.
8
Beneficiaries and recommendations for future work
The most common beneficiaries from this paper ought to be space-related programs such as NASA and
Space X as well as a wider audience. For example, space programs that look into biomechanics, could
greatly benefit from the insight provided on the behaviour of the spine under load, astronauts themselves
could look into the paper to see how which specific muscles are affected in the vertebral column due to
the microgravitational loads they experience during spaceflight. This concern could lead to a
groundbreaking invention of an orthopaedic device to counteract these issues. The device could be used to
lessen the impact that microgravity has on their intervertebral discs and vertebral column as well as
making the transition to and fro gravity and microgravity easier on their bodies, in particular their spine
since it usually takes around 6 months for the spine to adjust after returning from space.
Since there is no gravity in space and thus this causes the spine to elongate, to create a solution for the
problem, there must be a way for the device to generate its own gravity and prevent the spine from
elongating and compress it as it would on Earth so that normal, earthly conditions can be mimicked. Even
the exercise equipment that are used in space should be modified to make sure they can generate artificial
gravity and support the spine by preventing elongation. It is hoped that by applying these principles, the
gravity that is experienced on Earth can be imitated and the astronauts can be saved from the pains and
troubles that comes with space travel.
34
Obtaining a CT scan model of the vertebral column directly from a medical department will aid in the
development of a model, instead of relying on secondary data. Additionally, not enough research exists
concerning the effects on the vertebral column as a whole although research specifically into the lumbar
vertebrae is abundant. Therefore, if a study was to be carried out on the lumbar vertebrae instead of the
entire vertebrae, perhaps a more fruitful and more in-depth study could be carried out.
The vertebral column is also able to manifest itself in several different positions: seated, standing, lying
down etc; by stating exactly which position is being looked into, the study could be narrowed even more
and more thorough results may be able to be obtained.
35
References
[1] MyChiroPractice (2022). How Does Gravity Affect My Posture? | Advanced Spine and Posture.
[online] Advanced Spine & Posture - Advanced Chiropractic Care.
‌[2] www.healthstate.com.au. (n.d.). Gravity and the effect it has on you. [online]
[3] MSFC, B.L. (n.d.). NASA - My How You’ve Grown!
[‌ 4] Watson, C. (2009). The spinal cord : a Christopher and Dana Reeve Foundation text and atlas.
Amsterdam: Elsevier.
[‌ 5] Jackson, P. (2018). Essentials of Kinesiology for the Physical Therapist Assistant (Third Edition).
Mosby.
[‌ 6] Lawry, G.V. and Fam, A.G. (2010). Fam’s Musculoskeletal Examination and Joint Injection
Techniques (Musculoskeletal Examination and Joint Injections Techniques). Mosby.
‌[7] May, S. (2011). What Is Microgravity? [online] NASA.
[‌ 8] Trappe, S., Costill, D., Gallagher, P., Creer, A., Peters, J.R., Evans, H., Riley, D.A. and Fitts, R.H.
(2009). Exercise in space: human skeletal muscle after 6 months aboard the International Space Station.
Journal of Applied Physiology, 106(4), pp.1159–1168. doi:10.1152/japplphysiol.91578.2008.
[‌ 9] McNamara, K.P., Greene, K.A., Moore, A.M., Lenchik, L. and Weaver, A.A. (2019). Lumbopelvic
Muscle Changes Following Long-Duration Spaceflight. Frontiers in Physiology, 10.
doi:10.3389/fphys.2019.00627.
[‌ 10] Puglia, I., Balsamo, M., Vukich, M. and Zolesi, V. (2018). Long-Term Microgravity Effects on
Isometric Handgrip and Precision Pinch Force with Visual and Proprioceptive Feedback. International
Journal of Aerospace Engineering, 2018, pp.1–11. doi:10.1155/2018/1952630.
[‌ 11] Oganov, V.S., Rakhmanov, A.S., Novikov, V.E., Zatsepin, S.T., Rodionova, S.S. and Cann, Ch.
(1991). The state of human bone tissue during space flight. Acta Astronautica, 23, pp.129–133.
doi:10.1016/0094-5765(91)90109-i.
[‌ 12] Chang, D.G., Healey, R.M., Snyder, A.J., Sayson, J.V., Macias, B.R., Coughlin, D.G., Bailey, J.F.,
Parazynski, S.E., Lotz, J.C. and Hargens, A.R. (2016). Lumbar Spine Paraspinal Muscle and
Intervertebral Disc Height Changes in Astronauts After Long-Duration Spaceflight on the International
Space Station. SPINE, 41(24), pp.1917–1924. doi:10.1097/brs.0000000000001873.
[‌ 13] Bailey, J.F., Miller, S.L., Khieu, K., O’Neill, C.W., Healey, R.M., Coughlin, D.G., Sayson, J.V.,
Chang, D.G., Hargens, A.R. and Lotz, J.C. (2018). From the international space station to the clinic: how
36
prolonged unloading may disrupt lumbar spine stability. The Spine Journal, [online] 18(1), pp.7–14.
doi:10.1016/j.spinee.2017.08.261.
[‌ 14] Burkhart, K., Allaire, B. and Bouxsein, M.L. (2019). Negative Effects of Long-duration Spaceflight
on Paraspinal Muscle Morphology. SPINE, 44(12), pp.879–886. doi:10.1097/brs.0000000000002959.
[‌ 15] McNamara, K.P., Greene, K.A., Moore, A.M., Lenchik, L. and Weaver, A.A. (2019). Lumbopelvic
Muscle Changes Following Long-Duration Spaceflight. Frontiers in Physiology, 10.
doi:10.3389/fphys.2019.00627.
[‌ 16] Antonutto, G., Capelli, C., Giradis, M., Zamparo, P. and di Prampero, P.E. (1995). Effects of
microgravity on muscular explosive power of the lower limbs in humans. Acta Astronautica, 36(8-12),
pp.473–478. doi:10.1016/0094-5765(95)00133-6.
[‌ 17] Antonutto, G., Bodem, F., Zamparo, P. and di Prampero, P.E. (1998). Maximal power and EMG of
lower limbs after 21 days spaceflight in one astronaut. Journal of gravitational physiology, [online] 5(1),
pp.P63-6.
[‌ 18] Antonutto, G., Capelli, C., Girardis, M., Zamparo, P. and di Prampero, P.E. (1999). Effects of
microgravity on maximal power of lower limbs during very short efforts in humans. Journal of Applied
Physiology, 86(1), pp.85–92. doi:10.1152/jappl.1999.86.1.85.
[‌ 19] Tesch, P.A., Berg, H.E., Bring, D., Evans, H.J. and LeBlanc, A.D. (2004). Effects of 17-day
spaceflight on knee extensor muscle function and size. European Journal of Applied Physiology, 93(4),
pp.463–468. doi:10.1007/s00421-004-1236-9.
[‌ 20] AKIMA, H., KAWAKAMI, Y., KUBO, K., SEKIGUCHI, C., OHSHIMA, H., MIYAMOTO, A. and
FUKUNAGA, T. (2000). Effect of short-duration spaceflight on thigh and leg muscle volume. Medicine
& Science in Sports & Exercise, 32(10), pp.1743–1747. doi:10.1097/00005768-200010000-00013.
[‌ 21] Edgerton, V.R., Zhou, M.Y., Ohira, Y., Klitgaard, H., Jiang, B., Bell, G., Harris, B., Saltin, B.,
Gollnick, P.D., Roy, R.R. and et (1995). Human fiber size and enzymatic properties after 5 and 11 days of
spaceflight. Journal of Applied Physiology, 78(5), pp.1733–1739. doi:10.1152/jappl.1995.78.5.1733.
[‌ 22] Trappe, S.W., Trappe, T.A., Lee, G.A., Widrick, J.J., Costill, D.L. and Fitts, R.H. (2001). Comparison
of a space shuttle flight (STS-78) and bed rest on human muscle function. Journal of Applied Physiology,
91(1), pp.57–64. doi:10.1152/jappl.2001.91.1.57.
[‌ 23] Riley, D.A., Bain, J.L.W., Thompson, J.L., Fitts, R.H., Widrick, J.J., Trappe, S.W., Trappe, T.A. and
Costill, D.L. (2000). Decreased thin filament density and length in human atrophic soleus muscle fibers
after spaceflight. Journal of Applied Physiology, 88(2), pp.567–572. doi:10.1152/jappl.2000.88.2.567.
[‌ 24] Fitts, R.H., Trappe, S.W., Costill, D.L., Gallagher, P.M., Creer, A.C., Colloton, P.A., Peters, J.R.,
Romatowski, J.G., Bain, J.L. and Riley, D.A. (2010). Prolonged space flight-induced alterations in the
37
structure and function of human skeletal muscle fibres. The Journal of Physiology, 588(18),
pp.3567–3592. doi:10.1113/jphysiol.2010.188508.
[‌ 25] Gopalakrishnan, R., Genc, K.O., Rice, A.J., Lee, S.M.C., Evans, H.J., Maender, C.C., Ilaslan, H. and
Cavanagh, P.R. (2010). Muscle Volume, Strength, Endurance, and Exercise Loads During 6-Month
Missions in Space. Aviation, Space, and Environmental Medicine, 81(2), pp.91–104.
doi:10.3357/asem.2583.2010.
[‌ 26] Lambertz, D., Pérot, C., Kaspranski, R. and Goubel, F. (2001). Effects of long-term spaceflight on
mechanical properties of muscles in humans. Journal of Applied Physiology, 90(1), pp.179–188.
doi:10.1152/jappl.2001.90.1.179.
[‌ 27] Koryak, Y.A. (2019). Architectural and functional specifics of the human triceps surae muscle in
vivo and its adaptation to microgravity. Journal of Applied Physiology, 126(4), pp.880–893.
doi:10.1152/japplphysiol.00634.2018.
‌[28] The physics classroom (2019). The Meaning of Force.
‌[29] web.mit.edu. (n.d.). What is a Moment? ‌
[30] Haher, T.R., O’Brien, M., Kauffman, C. and Liao, K.C. (1993). Biomechanics of the spine in sports.
Clinics in sports medicine, [online] 12(3), pp.449–464.
[31] Guillot, M., Fournier, J., Scheye, T., Escande, G., Chazal, J., Tanguy, A. and Vanneuville, G. (1990).
[Mechanics of the characteristic geometry of the human spine undergoing vertical pressure]. Bulletin de
l’Association des anatomistes, [online] 74(225), pp.7–8. ‌
‌[32] europepmc.org. (n.d.). Europe PMC. [online] ‌
[33] WHITE, A.A. and PANJABI, M.M. (1978). The Basic Kinematics of the Human Spine. Spine, 3(1),
pp.12–20. doi:10.1097/00007632-197803000-00003.
[‌ 34] POPE, M.H. and PANJABI, M. (1985). Biomechanical Definitions of Spinal Instability. Spine, 10(3),
pp.255–256. doi:10.1097/00007632-198504000-00013.
[‌ 35] Panjabi, M.M., Krag, M.H., White, A.A. and Southwick, W.O. (1977). Effects of Preload on Load
Displacement Curves of the Lumbar Spine*. Orthopedic Clinics of North America, [online] 8(1),
pp.181–192. doi:10.1016/S0030-5898(20)30944-5.
‌[36] R. Louis, Chirurgia del rachide, Padova: Piccin ed. (1989), pp. 67-69
[37] M.M. Panjabi, The stabilizing system of the spine. Part II. Neutral zone and instability hypothesis
Journal of Spinal Disorders, 5 (1992), pp. 390-397
38
[38] LWW. (2019). New In Vivo Measurements of Pressures in the Intervertebral ... : Spine. [online] ‌
[39] Bell, G.H., Dunbar, O., Beck, J.S. and Gibb, A. (1967). Variations in strength of vertebrae with age
and their relation to osteoporosis. Calcified Tissue Research, 1(1), pp.75–86. doi:10.1007/bf02008077.
[40] Oda, K., Shibayama, Y., Abe, M. and Onomura, T. (1998). Morphogenesis of Vertebral Deformities
in Involutional Osteoporosis: Age-Related, Three-Dimensional Trabecular Structure. Spine, [online]
23(9), pp.1050–1055. ‌
[41] Pollintine, P., Dolan, P., Tobias, J.H. and Adams, M.A. (2004). Intervertebral Disc Degeneration Can
Lead to ‘Stress-Shielding’ of the Anterior Vertebral Body. Spine, 29(7), pp.774–782.
doi:10.1097/01.brs.0000119401.23006.d2.
[‌ 42] Frost, H.M. (1987). Bone ?mass? and the ?mechanostat?: A proposal. The Anatomical Record,
219(1), pp.1–9. doi:10.1002/ar.1092190104.
[‌ 43] Luo, J., Skrzypiec, D.M., Pollintine, P., Adams, M.A., Annesley-Williams, D.J. and Dolan, P. (2007).
Mechanical efficacy of vertebroplasty: Influence of cement type, BMD, fracture severity, and disc
degeneration. Bone, [online] 40(4), pp.1110–1119. doi:10.1016/j.bone.2006.11.021.
[‌ 44] Kim, D.-Y., Lee, S.-H., Jang, J.S., Chung, S.K. and Lee, H.-Y. (2004). Intravertebral vacuum
phenomenon in osteoporotic compression fracture: report of 67 cases with quantitative evaluation of
intravertebral instability. Journal of Neurosurgery: Spine, 100(1), pp.24–31.
doi:10.3171/spi.2004.100.1.0024.
[‌ 45] Luo, J., Daines, L., Charalambous, A., Adams, M.A., Annesley-Williams, D.J. and Dolan, P. (2009).
Vertebroplasty. Spine, 34(26), pp.2865–2873. doi:10.1097/brs.0b013e3181b4ea1e.
[‌ 46] Rho, Y.-J., Choe, W.J. and Chun, Y.I. (2011). Risk factors predicting the new symptomatic vertebral
compression fractures after percutaneous vertebroplasty or kyphoplasty. European Spine Journal, 21(5),
pp.905–911. doi:10.1007/s00586-011-2099-5.
[‌ 47] Tang, H., Xu, H., Yao, X. and Lin, S. (2015). Single-stage posterior vertebral column resection and
internal fixation for old fracture–dislocations of thoracolumbar spine: a case series and systematic review.
European Spine Journal, 25(8), pp.2497–2513. doi:10.1007/s00586-015-3955-5.
[‌ 48] ​Polikeit, A., Ferguson, S.J., Nolte, L.P. and Orr, T.E. (2003). Factors influencing stresses in the
lumbar spine after the insertion of intervertebral cages: finite element analysis. European Spine Journal,
12(4), pp.413–420. doi:10.1007/s00586-002-0505-8.
[49] Zhong, Z.-C., Wei, S.-H., Wang, J.-P., Feng, C.-K., Chen, C.-S. and Yu, C. (2006). Finite element
analysis of the lumbar spine with a new cage using a topology optimization method. Medical Engineering
& Physics, [online] 28(1), pp.90–98. doi:10.1016/j.medengphy.2005.03.007.
39
[‌ 50] Zhong, Z.-C., Wei, S.-H., Wang, J.-P., Feng, C.-K., Chen, C.-S. and Yu, C. (2006). Finite element
analysis of the lumbar spine with a new cage using a topology optimization method. Medical Engineering
& Physics, [online] 28(1), pp.90–98. doi:10.1016/j.medengphy.2005.03.007.
[‌ 51] Zhang, L., Yang, G., Wu, L. and Yu, B. (2010). The biomechanical effects of osteoporosis vertebral
augmentation with cancellous bone granules or bone cement on treated and adjacent non-treated vertebral
bodies: A finite element evaluation. Clinical Biomechanics, [online] 25(2), pp.166–172.
doi:10.1016/j.clinbiomech.2009.10.006.
[‌ 52] Alizadeh, M., Kadir, M.R.A., Fadhli, M.M., Fallahiarezoodar, A., Azmi, B., Murali, M.R. and
Kamarul, T. (2013). The use of X-shaped cross-link in posterior spinal constructs improves stability in
thoracolumbar burst fracture: A finite element analysis. Journal of Orthopaedic Research, 31(9),
pp.1447–1454. doi:10.1002/jor.22376.
[‌ 53] Panjabi, M.M., Oxland, T.R., Lin, R.M. and McGowen, T.W. (1994). Thoracolumbar burst fracture.
A biomechanical investigation of its multidirectional flexibility. Spine, [online] 19(5), pp.578–585.
Available at: https://europepmc.org/article/med/8184353 [Accessed 6 Aug. 2022].
[‌ 54] Elmasry, S., Asfour, S. and Travascio, F. (2017). Effectiveness of pedicle screw inclusion at the
fracture level in short-segment fixation constructs for the treatment of thoracolumbar burst fractures: a
computational biomechanics analysis. Computer Methods in Biomechanics and Biomedical Engineering,
20(13), pp.1412–1420. doi:10.1080/10255842.2017.1366995.
‌[55] Wong, V. (2021). Forces on the Spine & Load Moments | SwiftMotion. [online] ‌
[56] Straßer, H. (1913). Lehrbuch der Muskel- und Gelenkmechanik. Berlin, Heidelberg: Springer Berlin
Heidelberg. doi:10.1007/978-3-642-47744-7.
[‌ 57] Wetz, H.H. and Jacob, H.A.C. (2001). On the functional anatomy and kinematics of the femorotibial
joint. Der Orthopäde, 30(3), pp.135–144. doi:10.1007/s001320050586.
[‌ 58] Luck, J.V. (1955). Kinesiology of the Human Body under Normal and Pathological Conditions.
Arthur Steindler, M.D., (Hon.) F.R.C.S. Eng., F.A.C.S., F.I.C.S. Springfield, Illinois, Charles C. Thomas,
1955. $19.75. The Journal of Bone & Joint Surgery, 37(6), p.1325.
doi:10.2106/00004623-195537060-00027.
[‌ 59] www.healio.com. (n.d.). Microgravity negatively affects vertebral discs of astronauts during space
flight. [online]
[60] Jensen, G.M. (1980). Biomechanics of the Lumbar Intervertebral Disk: A Review. Physical Therapy,
60(6), pp.765–773. doi:10.1093/ptj/60.6.765.
[‌ 61] Bogduk, N. (2012). Radiological and Clinical Anatomy of the Lumbar Spine (5th ed.). China:
Churchill Livingstone.
40
[62] Adams M., Bogduk N., Burton K. Dolan P.. The Biomechanics of Back Pain. Eds. 2002. P238
[63] McKenzie, R. (1981). The lumbar spine : mechanical diagnosis and therapy. Waikanae, New
Zealand: Spinal Publications.
[64] White A, Panjabi M. Clinical Biomechanics of the Spine. 1978, Philadelphia: JB Lippincott Co.
[65] Hirsch C. The reaction of intervertebral discs to compression forces. J Bone Joint Surg (Am) 1955;
37:1188-1191
41