1. Table of Contents
Abstract iv
1 Introduction 1
2 Literature Review 2
2.1 Anatomy of the human pelvis 2
2.2 Details on the structure of bone 3
2.3 Different non-invasive methods used to monitor bone healing 3
2.3.1 X-Ray and DEXA scans 3
2.3.2 Quantitative Computed Tomography (QCT) 4
2.3.3 Strain gauge measurements 4
2.3.4 Ultrasound 4
2.3.5 Vibration analysis 5
2.4 Synthetic materials used as models for bone 6
2.5 Mobility and Impedance 7
3Project Aims 9
4Use of Vibration Theory to Determine the Healing of Fractured Pelvis 10
4.1 Pelvis model 10
4.2 Modal Analysis 11
4.3 Drive-point impedance using fixation pin 11
4.4 Preliminary results and discussion from FEA 12
5Outline of Proposed Experimental Work 19
5.1 Impact hammer testing 19
5.2 Monitoring the cure of epoxy using ultrasound 20
5.3 Drive-point mobility technique via fixation pin using PZTs 20
6Conclusions 21
7Timeline 21
ii
3. Abstract
Pelvic fractures in the sacrum involving a complete disruption of the pelvic ring causes rotational and
vertical instability. Internal fixation by surgery allows the fracture edges sufficient contact for bone
healing to occur. Monitoring the healing of bone by vibration analysis hopes to be able to determine
the exact point at which the pelvis is stable enough to support the weight and movement of a
patient to shorten hospitalisation time as well as ensuring the uniform healing of bone. The theory
of vibration analysis relies on the shift in resonant frequency of the bone structure as stiffness
recovers from bone recovery.
An FE model of a fixated pelvis is modelled with varying material properties to represent healing
bone at the fracture gap. Utilising the fixation pin as a device for delivering broadband vibration
signals to the pelvis, frequency response collected shows a trend which can be easily identified with
healing of the bone. Resonance frequency of the pelvis mode shapes are shown to increase with
stiffer material properties in the fracture. This result is also observed in the FE model with
sacrotuberous and sacrospinous ligaments and muscles. Actuating and receiving vibration signals
from one pin location could mean the implementation of drive-point mechanical impedance and
mobility techniques in further research.
This project proposes the use of a fixated synthetic Sawbone pelvis to replicate the analysis
conducted on FEA. This will include cutting the sacrum to represent the fracture and then using a
slow curing epoxy to fill the cut to replicate the healing of bone. This will be monitored by
accelerometers around the pelvis to see if change in stiffness of the epoxy can be detected. With the
success of the experiment, a clinical trial can hopefully be conducted to test the vibration analysis
technique.
iv
4. 1 Introduction
Pelvic fractures are becoming increasingly common with the greatest fatality caused by high-impact
trauma from motor vehicle crash or fall from a significant height. In the elder generation, even a fall
from standing position can cause a fracture as the bone becomes weaker due to the onset of
osteoporosis. The spine and pelvis represent the central support of the body, with the pelvis’
stability derived from its shape which is in the form of a ring (Gross, et.al., 2003). Most pelvic
fractures caused by low-energy injuries are stable but sacral fractures involving a complete
disruption of the pelvic ring would cause the bony structure to lose its stability.
Sacral fractures can be classified using the Dennis zone of injury. In a Dennis zone I injury, the sacral
alar region is involved, Dennis II involves the sacral foramina and Dennis III involves the central sacral
canal (eMedicine, 2011). One way of treating sacral fractures is by internal fixation through surgery
as seen in Figure 1 below. This fixation clamps the fractured pelvis together to allow necessary bone
contact for healing to occur. This essentially means movement of the lower body of the patient
becomes limited as walking or unnecessary stress on the pelvic bone may cause the bone to not heal
properly and also generates pain. Depending on the severity of the injury, this could take about 6 -
12 weeks of immobility (Russ, 2010). Such long periods could mean bedridden patients would
eventually require physiotherapy treatments from muscle degradation. To reduce this period of
immobility, it becomes really important to have a reliable method to identify the point at which the
bone has regained enough stability in the pelvis to allow movement. Thus reducing muscle wastage
and limiting the amount of time required for post-operative rehabilitation. This is also true for the
opposite case, where bone union is unsuccessful or premature. A close observation would prevent
re-fractures of bone if a patient is allowed to move before the pelvis becomes stable.
A lot of study on the healing process of human
bones has been done only on long bones. This
also includes studies of non-invasive methods
used to monitor bone healing such as
radiology, ultrasound, quantitative computed
tomography (QCT) and vibration analysis. The
pelvis however, has a very complicated bone
structure and differs to long bone in terms of
bone material properties and mechanical
characteristics with limited to no literature on
its fracture healing stages.
Figure 1 – Posterior view of synthetic pelvis with
fixation, connecting bar removable, for sacral fractures
After extensive review of current available literature, vibration analysis seems to be the most
convenient method for this project. It has been reported that the introduction of a broadband pulse
in the low frequency range can theoretically excite the pelvis without much influence from
surrounding tissue and ligaments (Conza, 2006). For the type of pelvis fracture of interest in this
project, this methodology may lead to information that can be analysed to reveal the current state
of the fracture’s recovery.
1
5. 2 Literature Review
The review includes an anatomic overview of the pelvis and its bone structure. It also briefly
describes the different monitoring techniques that have been reported in the open literature. A
review of the different composite materials used to replicate the different bone properties during
the healing stages shall also be conducted. These results shall be used for the experiments to
simulate and to determine an acceptable method for monitoring of healing. A review of vibration
theory including impedance and mobility that is potentially applicable to the monitoring of healing
of bones will also be reported.
2.1 Anatomy of the human pelvis
Anatomically, the pelvis is divided into the greater pelvis and the lesser pelvis. The greater pelvis,
also known as the pelvis major or false pelvis, is situated above the pelvic brim shown in Figure 2.
The lesser pelvis i.e., pelvis minor or true pelvis is situated below the pelvic brim (Sauerland, 1999).
The pelvic outlet, also called the inferior pelvic aperture on the other hand is enclosed by the lower
circumference of the lesser pelvis where the abdominopelvic organs are held up by muscles forming
the floor of the pelvis. The lumbosacral junction connects the pelvis to the spine and the head of the
femurs fit into the socket at the acetabulum.
Figure 2 – The bony pelvis obtained from <http://home.comcast.net/~wnor/pelvis.htm>
According to eMedicine (2011), disruption of the pelvic ring due to large forces often involves severe
injury to organs and haemorrhaging within the bony pelvis. The Dennis II fracture of the sacrum is
characterised by the complete disruption of the ring involving the sacral foramina, often with
progressive rupture of the supporting ligaments and joints, making it rotationally and vertically
unstable.
2
lumbosacral
junction
6. 2.2 Details on the structure of bone
The pelvic bone consists of cancellous bone surrounded by a thin layer of cortical bone and
subchondral bone at the acetabulum. According to Dalstra (1993), most research done on the pelvis
assumes the bone to be isotropic for purposes of finite element studies. Because of its sandwich
construction, the overall mechanical behaviour of the pelvic bone is insensitive to variations of the
mechanical properties of its cancellous bone to a certain extent.
The outer cortical shell is solid with spaces only for osteocytes, canaliculi, capillaries and erosion
sites. Cancellous bone on the other hand, has really large spaces (Currey, 1984). The material making
up cancellous bone of adults is usually primary lamellar bone or fragments of Haversian bone and in
young mammals may be made of woven or parallel-fibered bone.
Bone above the molecular level has three distinct structures: the woven bone, lamellar bone and
parallel-fibered bone (Currey, 1984). The woven bone is usually laid down quickly, found in the callus
produced during fracture repair and also in the foetus whereas lamellar bone is more precisely
arranged and laid down more slowly than woven bone (Boyde, 1980). As for parallel-fibered bone, it
is structurally intermediate between woven bone and lamellar bone and is highly calcified.
2.3 Different non-invasive methods used to monitor bone healing
Several known methods have been used to monitor fracture repair mostly in long bones. This section
describes some of these methods in use including their advantages and disadvantages.
2.3.1 X-Ray and DEXA scans
X-ray examinations is the most conventional method used to gauge bone union in a fracture but it
can only show evidence of bone healing when calcification at the callus site starts to take place
(Tiedeman, 1990). Callus formation as seen from the X-ray often correlates poorly with an accurate
estimate of bone union (Webb, 1996) and it also does not give any information about bone density
or any of its mechanical properties which can help determine the healing status of the bone as well
as its structural integrity. X-rays are still used clinically but it depends a lot on the surgeon’s
experience to determine whether or not the bone has fully healed. With the recent adaptation and
spread of digital radiography, a quantitative method of using radiography to assess bone healing is
possible (Babatunde, 2009). This would mean a relatively cheap and readily available technology to
patients while exposing them to lower radiation. However, this method converts a 3-dimensional
object into a 2-dimensional image and then to a 1-dimensional number. This may mean overlooking
small cortical gaps which could develop into new fractures.
DEXA scans are used to determine bone mineral density (BMD) and bone mineral content (BMC) and
used mainly to diagnose osteopenia and osteoporosis but bone density is also a good indicator for
bone healing. However, DEXA, like radiographs, also converts a 3-dimensional object into a 1-
dimensional number and therefore suffers similar disadvantages of X-rays (Babatunde, 2009).
2.3.2 Quantitative Computed Tomography (QCT)
3
7. QCT is based on the differential absorption of ionising radiation by calcified tissue or bone which is
also a non-invasive method to measure bone healing. According to Babatunde (2009), it can provide
high-resolution imaging of the healing bone while providing quantitative analysis of this area to help
the clinician make an objective assessment of whether the bone has healed enough. However, it is
limited in availability, high cost and relatively higher radiation exposure to patients compared to
DEXA, ultrasound and X-rays. It is also hard to get a clear image of the pelvic bone which is
surrounded by vast amounts of muscles, ligaments with the presence of internal organs in the pelvis.
Signs of bone healing will be hard to identify in such a crowded environment.
2.3.3 Strain gauge measurements
For strain measurements on the bone surface, strain gauges are often used as they are sensitive and
can measure strains directly as well as allowing continuous monitoring of a dynamic loading
situation (Szivek and Gharpuray, 2000). They can be attached to the lateral, medial, anterior and
posterior bone surfaces. However, these gauges measure strain at discrete points only and must be
used in conjunction with material properties derived from separate tests like the CT or DEXA scans,
to determine the stress state of the bone. The use of strain gauges has been mentioned for ex vivo
experiments but does not prove to be practical for monitoring the healing state of the bone.
However, this method could be useful for validation of experimental results in conjunction with
stress results obtained from FE models.
2.3.4 Ultrasound
Ultrasound is another non-invasive method researchers have investigated. It is inexpensive,
accessible and does not expose patients to any radiation. It has also been shown to reveal new bone
formation up to 3 weeks earlier when compared with standard radiography or DEXA scan. However,
studies by Eyres (1993) and Bail (2002) showed that it cannot differentiate changes in bone stiffness
and strength after a certain point during healing. It is also found to be unreliable due to the many
variables that cannot be controlled from one measurement to another such as changes in the site of
measurement over the healing period. In addition, ultrasound is transmitted through soft tissue and
can cause the fluctuations in measurements from varying amounts of soft tissue surrounding the
bone (Babatunde, 2009).
This lead to the development of quantitative ultrasound which has been used a lot in recent
research on monitoring the healing of long bones. This theory uses the marked changes in bone
mineral composition around the fracture site and the change in interface between the fracture
segments in the case of healing, leading to a change in the ultrasonic velocity across the site (Njeh,
1998). This can be related to elasticity of the bone and can therefore be related to strength. The
velocity of the ultrasound waves propagating along the bone can be determined by the ratio of
transducers’ in-between distance to time-of-flight (TOF) of the first-arrival-signal (FAS). Research by
Cunningham (1990) and Saulgozis (1996) has shown that velocity across fractured long bones
increases during healing. Problems occur due to the presence of surrounding soft tissue and body
sites containing unknown variations in bone shape and size as well as significant amounts of
damping, which give rise to measurement errors. Inaccurate measurements are also caused by the
ultrasound probe separation (the way the ultrasound is transmitted and received). Its application on
non-long bones is also unsuitable as this resonant frequency technique is limited to only the ulnae
4
8. and tibia, both of which are long bones. The quantitative ultrasound method must be used in
conjunction with bone mineral density (BMD) measurements obtained from quantitative computed
tomography (QCT) or DEXA scans as with the other monitoring techniques mentioned above.
2.3.5 Vibration analysis
The vibration methods used are based upon the determination of change in frequency response to
lateral vibration due to local softening in the fracture area. Research done by Nikiforidis (1990)
looked at the development and validation of an objective method for monitoring fracture healing
based on vibration response. The paper included both analytical and experimental work which
investigated the fracture site of a human tibia in both the axial and lateral direction.
The experimental model by Nikiforidis (1990) involved constraining fresh human tibiae obtained
from amputations to preserve their in vivo characteristics using a well recognised method
(Villanueva, 1980). The vibration spectra for axial and lateral vibration were firstly obtained from an
intact tibia which was later osteotomised with the gap filled with silicone rubber. Silicone rubber was
used as it has mechanical properties which were similar to those of the soft callus of a healing
fracture. To replicate the formation of new bone, epoxy resin was used. The materials chosen were
based off studies of mechanical characteristics of the callus during healing by Ham and Harris (1972),
Perren (1979), Davy and Connoly (1982), Yamada (1970), and Yamagishi and Yoshimura (1955) to
simulate the fracture callus in different stages of healing.
The vibration analysis was carried out by attaching the distal end of the tibia and subjecting it to a
sweeping excitation of harmonic motion (20 – 1500Hz) in both the axial as well as lateral directions
to excite its global modes. An accelerometer of 65g was attached to the proximal end to detect the
vibration of the tibia. Results obtained showed a shift in natural frequency of the osteotomised bone
towards the natural frequency of the intact bone as the model ‘healed’ as expected.
The paper also included a clinical case in which the vibration analysis method was used to monitor
the healing process of a patient with a fractured tibia. Results obtained from the patient
demonstrated a coupling between axial and lateral response which according to their model,
signified non-uniform healing. A radiological examination was later performed which proved the
results to be correct.
Nakatsuchi et.al., (1996) conducted a similar experiment on the human tibia using the impulse
response method but included the effect of fixations. A cut is introduced to the tibia and the fracture
gap is injected with an adhesive consisting of Araldite AW2104 and hardener HW2934. The natural
frequency was found to increase steadily with the initial phase of consolidation of the adhesive, up
to about 40% of its hardness. In their experiment involving external fixators, the resonant frequency
was found to be the highest. This was likely due to the tibia and the fixator vibrating as one body and
increasing its apparent bending rigidity. Results also showed that each construct provided a
distinctive feature in its impulse response. No responses were detected for the plate or Elder’s pins
construct while responses were detected immediately after the injection of the adhesive for the
external fixator. This was because the vibrations were transmitted across the fracture site via the
fixation materials.
5
9. Problems involved with this method which are caused by damping due surrounding soft tissue giving
rise to low signal to noise ratio. Also, stiffness recovery of bone during healing is not linear as the
development of the callus goes beyond the original bone so the natural frequency becomes higher
than that of intact bone until the callus disappears. There has been little research done with this
method on bones other than long bones and the effect of more severe deviations of crack geometry
on the response spectrum. More research is also needed on the applicability of this method to the
assessment of other bone conditions such as osteoporosis. Following this, the vibration analysis
technique is the only paper which has successfully done a clinical trial. This suggests the use of
technique which can overcome some damping by surrounding muscle tissue and ligaments if
improved.
2.4 Synthetic materials used as models for bone
For this research, it is important to carry out preliminary work to validate the method used for
assessing the healing of bones. Most monitoring methods are invasive and would require a lot of
testing before being used on human test subjects. Also, obtaining disease-free cadaver bones to be
used during mechanical testing is becoming more difficult and extremely expensive. In order to
replicate the ex vivo healing of bones, synthetic materials can be used as substitutes for cadaver
bones and as well as soft bone during the healing process. This would allow for tests to be run
repetitively on ‘identical’ specimens without having to perform them on huge populations. Other
advantages include its easy availability, absence of the need for preservation and maintaining
moisture levels of natural specimens during experiments as well as having to comply with ethical
issues.
Accurately simulating the stiffness of bone is most important when “stress shielding” near artificial
joints or fracture fixation devices are being evaluated while accurately simulating the strength of
bone is most important when screws or other orthopaedic attachment devices are being evaluated.
Therefore synthetic materials have to be chosen wisely to reflect the overall loading and support
conditions of the bone in question.
Research done by Szivek J.A. (2000) has found that glass fibre-reinforced epoxy has similar
properties to the cortical component of the bone and that polyurethane foam can be used for
substituting cancellous bone. Saw bone models have also been used for strength tests and were
found to closely resemble the properties of real bones.
Further research has lead to the development of synthetic specimens. In recent years, Sawbones
Europe AB, Sweden has manufactured bone specimens which not only replicate the shape of the
human bone but also its mechanical properties (Zanetti and Bignardi, 2009). These synthetic bones
have gone through substantial improvement since the introduction of the first generation and are in
its fourth generation at the time of writing. The synthetic pelvis was added to the third generation
sawbones using short, randomly oriented glass fibres immersed in epoxy resin to mimic the cortical
shell and uses polyurethane foam for the spongy cancellous bone.
The geometry and mechanical properties of Sawbones have been shown to lie within the acceptable
range of variation (Zanetti and Bignardi, 2009). This included mechanical tests such as displacement
under certain loading conditions as well as stress/strain distributions on the bone surface.
For this research, 3rd generation composite pelvic bones will be used to run experiments.
6
10. Most information found was on fracture repair of long bones only. But review of all papers has
focused on modelling the healing of bone by varying the stiffness of new bone in the fracture gap.
Isaksson et.al., (2009), listed cortical bone to have a Young’s modulus of 15.7GPa and marrow
(cancellous bone) of 2MPa. Immature bone was assigned a modulus of 1GPa and mature bone 6GPa.
Newly formed bone has a much lower modulus than mature bone which is inferior to the stiffness of
the cortical bone.
Research by Nakatsuchi et.al., (1996), studied the fracture healing of the tibia by simulating the
healing bone using an epoxy adhesive (Araldite, Ciba-Geigy Company Limited, Swiss) which was
injected into the fracture gap and was allowed to cure over 60 minutes using hardness of the epoxy
as a measure of healing. Another method used silicone rubber to simulate the soft callus of a healing
fracture and then replaces it with an epoxy resin to mimic properties of new bone which is 20 – 40
greater than the modulus of soft callus (Nikiforidis et.al., 1990).
Njeh et.al., (1998) uses ultrasound velocity of materials to choose suitable substitutes to bone in
experiments. Cortical bone was modelled with Perspex while natural rubber was used to replace
Tissue Equivalent Material. Healing of the fracture was mimicked by moving 2 blocks of Perspex with
rubber lining closer together. Fundamentally, this method still relies on ultrasound velocity being
related to the elasticity of the materials.
2.5 Mobility and Impedance
Mechanical impedance is defined as the ratio of a force-like quantity to a velocity-like quantity when
the arguments of the real (or imaginary) parts of the quantities increase linearly with time (Harris,
2002). Examples of force-like quantities are: force, sound pressure, voltage, temperature. Examples
of velocity-like quantities are: velocity, current, heat flow. Impedance is the reciprocal of mobility
(Harris’ Shock and Vibration Handbook).
According to Gardonio and Brennan (2001), mechanical impedance and mobility are mostly used for
passive/active vibration control, structural acoustics problems, and rotor dynamics problems. Early
analysis of vibratory systems in terms of mechanical impedances was probably linked to studies of
electrical communication. Electrical impedance was explained by Heaviside (1884) as a substitution
for apparent resistance and is “the ratio of the amplitude of the impressed force to that of the
current when their variations are simply harmonic”. In other words, it represents the ratio of e.m.f.
across an electrical element to the current flowing through it (Gardonio, 2001). The concept of
mechanical impedance was first discovered by Professor Arthur G. Webster. He was able to define
the impedance for a mass, spring and dash-pot for a mechanical oscillator system:
)exp()()( tjFtf ωω= where f(t) is the periodic force applied on the mass
)exp()()( tjVtv ωω= where v(t) is the periodic displacement of the mass
Therefore, )(/)()( ωωω VFZm = is the mechanical impedance, which he has defined to be the
ratio of the cause of motion (force) to its effect (displacement).
Driving point impedance is defined as the impedance involving the ratio of force to velocity when
both the force and velocity are measured at the same point and in the same direction (Harris, 2002).
The transfer impedance between two points is the impedance involving the ratio of force to velocity
7
11. when force is measured at one point and velocity at the other point. The term transfer impedance is
also used to denote the ratio of force to velocity measured at the same point but in different
directions.
Mechanical impedance has been widely used for damage detection and structural health
monitoring. Bamnios et.al. (2001) researched the use of mechanical impedance for crack
identification in beam structures. Their hypothesis lay on the local flexibility of a crack in a structure
affecting its dynamic behaviour resulting in reduction of natural frequencies and changes in mode
shapes of vibration. The research team found that driving-point impedance changes substantially in
the case of flexural vibrations of a plexiglass beam due to the presence of the crack. It was found
that natural frequencies of the cracked beam are much lower than that of the uncracked beam.
Crack location and size was also found to influence the mechanical impedance of the beam
depending on crack’s depth.
Results obtained by Prabhakar et.al. (2001) found that impedance decreases as the crack depth
increases at significant frequencies for transverse cracks on a rotor-bearing system which is
consistent with findings shown above.
This technique has been further developed for the use of structural health monitoring using electro-
mechanical impedance signatures of attached piezoelectric sensors (Zagrai & Giurgiutiu, 2002 & Park
et.al., 2008). Zagrai’s observations show that presence of damage significantly changes the electro-
mechanical impedance spectrum which features frequency shifts, peaks splitting and appearance of
new harmonics. These changes in the spectrum were found to increase with severity of damage.
Park et.al. (2008) has also found damage detection using electro-mechanical impedance to be
successful for real-time damage diagnosis for critical engineering structures.
8
12. 3 Project Aims
This research involves developing a reliable method for monitoring the healing progress of a Dennis
Zone II fracture of the fixated pelvis without invasive surgery. This leads the project to have the
following aims:
1) To investigate the use of vibration analysis in monitoring healing of bone disruptions and
implement it for the fixated pelvis
2) Validate the use of vibration analysis by using an FE model to obtain the frequency response
of a fixated pelvis model
3) To develop an experimental pelvis model using composite materials to replicate the healing
of a fracture in the sacrum
4) To determine the behaviour of a fixated pelvis across the fracture when actuated with a low
frequency pulse throughout the different healing stages
These hypotheses were developed and tested to help achieve the aims:
1) Healing process of bone simulated as increase in stiffness of bone material can be detected
by modal response of a fixated pelvis
2) Drive-point impedance can be used to monitor changes in stiffness of bone as fracture heals
The project requires the use of numerical as well as experimental methods to achieve its aims.
Results collected from numerical analysis serve as a validation method as well as preliminary findings
to help understand the dynamic response on the pelvis structure. These results will be used as a
guide for future experimental results.
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13. 4 Use of Vibration Theory to Determine the Healing of Fractured Pelvis
4.1 Pelvis model
An FE model of a pelvis was used to validate the use of vibration analysis to monitor the healing of a
fixated pelvis (Ilahee, 2010). Frequency response analysis was conducted for a fractured pelvis with
and without fixation where the Dennis II fracture is modelled as a 2mm wide gap. The analysis was
conducted for different healing conditions:
0.1%, 1%, 10%, 20%, 40% and 100%
The percentages represent the material properties of new bone which fills the gap such as elastic
modulus and density. This mimics the ‘healing’ of bone where 0.1% healing relates to recovery of
0.1% of the properties of fully healed bone and 100% represents complete bone union.
Assumptions for the modelling of the pelvis are listed as shown:
o Recovery of bone properties is linear as healing progresses
o The cortical and subchondral outer shell are considered to have a uniform thickness of 2mm
o The cortical, subchondral and cancellous bones are assumed to be isotropic
The outer shell of the bone consisting of the cortical and subchondral bone are modelled as a 2D
triangle mesh with an element size of 2mm whereas the cancellous bone is modelled as a 3D
tetrahedral mesh also of element size 2mm.
The pelvis model is constrained at the acetabulum surface to simulate a simplified version of a stable
support from the femurs and a few nodes on the top surface of the lumbosacral junction which
connects the pelvis to the spine. The whole top surface of the lumbosacral junction is constrained
such that the surface can only slide horizontally and rotates without any vertical translation.
The model used is shown in Figure 3 and bone properties used for FEA are shown in Table 1.
Figure 3 – Constraints applied on the Pelvis model in NX
10
Vertical constraint
Fixed constraint
ZC
XC YC
Sacral fracture
14. Table 1 – Bone material properties used for the FE model
Cortical Subchondral Cancellous
Young’s Modulus (E/GPa) 17 2 0.07
Poisson’s ratio (ν) 0.3 0.3 0.2
Density (ρ/kgm-3
) 3000 171.4 43.9
Thickness (t/mm) 2 2 n/a
4.2 Modal analysis
Modal analysis was conducted on both the fixated and non-fixated models to observe the resonant
frequencies and mode shapes of each model. The hypothesis is that the mode shapes of the pelvis
are sensitive to fracture healing and will change for the different healing conditions. This was done
by analysing the first 10 modes of each model. All 10 modes for different healing percentages were
found to be within the frequency range of 200 to 2000 Hz.
4.3 Drive-point impedance using fixation pin
The second hypothesis involves testing the implementation of drive-point impedance for monitoring
the healing of bone. For non-invasive monitoring the healing of the fracture, the fixation pin is
thought to be the most accessible area for signal input.
For this project, a random power spectral density force has been applied to the pelvis model using
the pin of the fixation as a guide for quantitative monitoring of fracture healing. The force input is
applied in the same direction of the pin and displacement and velocity data is collected from the
same location as well as from the other pin. This signal was actuated on a surface node of the pelvis
from 200Hz to 2200Hz to excite the first 10 known modes of the pelvis as shown in Figure 4(b). A
constant maximum force of 10N/Hz was applied across 200Hz to 2000Hz and then reduced linearly
to zero from 2000Hz to 2200Hz. The bandwidth was chosen based on the findings from the modal
analysis (refer to results in Section 4.4).
(a) (b)
Figure 4(a) – Location of nodes for collection of data and signal excitation; Figure 5(b) – Random PSD signal
to excite the first 10 modes of the pelvis model
Response of the cortical shell is collected from nodes at the pin locations of the model as highlighted
in Figure 4(a) and then exported to Excel to be analysed. Both the fixated and non-fixated pelvis
models were used to determine the effect the fixation has on the frequency response.
11
Pin #1 Pin #2
15. Response is also collected from the fracture
vicinity to observe the convergence, if any, of
displacements of the fracture edges to show
that increase in percentage properties does
represent healing and bone union. Results were
collected from two nodes shown in Figure 5 for
the non-fixated model.
Figure 5 – (Right) Displacement of fracture edges
collected to observe convergence with respect to
healing
Modal and vibration analysis was repeated on a
pelvis model with sacrospinous and
sacrotuberous ligaments included to see if it
affects the dynamic characteristics of the
response. The ligaments are modelled as
springs with stiffness 1500N/mm connecting
the sacrum to the ischial spine and to the ischial
tuberosity as seen on Figure 6.
Figure 6 – (Right) Pelvis model on NX with
ligaments
4.4 Preliminary results and discussion from FEA
The first 10 mode shapes were collected for both the fixated and non-fixated pelvis models for each
healing condition. Results in Figure 7 show the first mode shape for each healing percentage for the
fixated pelvis model.
At 0.1% healing, a large displacement is observed for the left ilium but only a slight displacement can
be seen on the right side. But with 1% healing in the fracture, displacement of the right ilium is more
evident and this displacement increases at 10% healing. This proves the first hypothesis which
proposes that varying stiffness in the fracture gap can influence mode shape changes.
The frequency at which the first modes occur is also found to increase with increase in healing
percentage. This is consistent with vibration analysis research done by Nikiforidis et.al. (1990) and
Nakatsuchi et.al. (1996) whose results show a shift in natural frequency as healing of bone
progresses.
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16. Figure 7 – 1st mode shape for fixated pelvis at healing stages 0.1%, 1%, 10%, 20%, 40% and 100%
Results from modal analysis also show that at higher frequency ranges, the modes become crowded
as individual modes become harder to identify. Higher frequency vibrations are also more
susceptible to damping from surrounding tissue and ligaments (Njeh, 1998). From these findings, the
signal input for driving point impedance used a frequency range which did not exceed 2000Hz.
The frequency response was collected in real data format and was collected for directions X, Y and Z.
Two main sets of data were collected for each model on the pin locations, displacement and
velocity. Figure 9 shows displacement results collected from pin 1 in the X, Y and Z directions for
both fixated and non-fixated models.
Looking at the X-direction results from the earliest stage of healing at 0.1%, the modes with the
largest displacements occur at 510Hz and 722Hz for the fixated pelvis and at 510Hz and 685Hz for
the non-fixated model. By healing at 1%, the two highest peaks are observed at 900Hz and 1200Hz
for the fixated model and for the non-fixated, 950Hz and 1300Hz. Displacements become very
13
0.1%
510Hz
1%
568Hz
10%
583Hz
20%
584Hz
40%
585Hz
100%
586Hz
17. similar for healing at 10% and above where the highest peak occurs at a frequency of 1330 Hz and
1350Hz for the fixated and non-fixated models respectively. The graphs show the resonant
frequency peaks shift to the right as the simulated bone heals and the magnitude of displacement
becomes less and less pronounced. This is consistent with results from modal analysis as well as
studies by Nikiforidis et.al. (1990). Shift in the resonant frequency relates to the recovery of the
material properties in the simulated fracture, namely the stiffness, which is a good indicator for
bone healing and bone union. This shift in peak frequencies is also evident in the Y and Z direction
displacements.
The displacement trends for both the fixated and non-fixated pelvis at 10% and greater start to
converge suggesting that this method is sensitive to change in stiffness of up to 10% only. This is also
supported by results in the Y and Z directions (Figure 9) which show little or no separation between
graphs of 10%, 20%, 40% and 100% healing.
Comparing results from the fixated to the non-fixated model shows more than just a change in
amplitude in the response. Differences are more noticeable at lower healing percentage. The shape
of the slope changes when the pelvis is fixated. This suggests the mode shape is affected by the
presence of the fixation which is consistent with findings by Nakatsuchi (1996). The fixation may
have contributed to the increase in stiffness of the pelvis structure and vibrated as one body.
The frequency shift trend which is evident in all X, Y and Z directions for pin 1 demonstrate only a
slight shift when looking at results collected from pin 2. Decrease in amplitude of displacements with
respect to bone healing percentage was also not as pronounced. Results collected from pin 2 in the
Z-direction are shown in Figure 8. Even though results from Nakatsuchi (1996) showed that some
vibrations can be transmitted across the fracture site via the fixators, results shown here indicate
that pin 2 may be too far from the fracture site to receive information about the healing progress.
This potentially means collection of results from pin 2 is not necessary to gauge the status of healing.
Figure 8 – Displacement PSD of node at pin #2 in the Z-direction with and without fixation against frequency
14
18. Figure 9 – Displacement PSD of pin #1 node in the X, Y, Z-direction of models against frequency
As mentioned earlier, another set of results was collected from the frequency response analysis.
Velocity of the node on the cortical shell at pin 1, see Figure 10, also shows trends similar to the ones
observed in displacements. This proves to be promising as these observations can lead to the use of
mobility techniques, which are easier to measure (Bamnios, 2002) for assessing the status of healing
in a fractured pelvis.
Looking at both displacement and velocity, the significant frequency shift and displacement trends
are more obvious in the X and Y directions compared to the Z direction. This is true for both fixated
and non-fixated models. This probably means the fractured pelvis is more rigid in the Z-direction as
the dynamic response does not differ much with increasing percentage recovery.
15
19. Figure 10 – Velocity PSD in the X, Y, Z-direction of the cortical shell at pin #1 with and without fixation
16
20. Figure 11 – Velocity PSD in the X, Y Z-direction of the cortical shell at pin #1 of fixated model with ligaments
Figure 11 shows the velocity results for the fixated pelvis model with ligaments. Again, the frequency
shift is clearly demonstrated in all the directions as the bone heals. There are slight differences in
peak frequencies especially the 3rd detectable mode in the X and Y directions when comparing this
to the results in Figure 10 (results from model without ligaments). These results are significant in
which the presence of the ligaments does not severely affect the trends which are important for
identifying healing in the bone. This is supported by research done by Conza et.al. (2006), conducting
virbation tests on fresh-frozen human pelvis to investigate the role of pelvic ligaments. It was found
that the sacrospinous, sacrotuberous and the iliolumbar ligaments do not contribute to the dynamic
response of the human pelvis in the low frequency range.
Results so far have shown that frequency response can detect changes in stiffness from 0.1% to 10%
but starts to converge at 10% and higher healing conditions. Displacement at 2 nodes separated by
the 2mm gap, one from each edge of the sacral fracture, were collected for the non-fixated model to
test the sensitivity of the vibration analysis technique. The series of graphs below show the
displacements for the 2 nodes in X, Y and Z directions. Displacement PSD results were collected in
real data format of unit mm2
/Hz.
Figure 12 shows convergence starting to occur when the bone has recovered 10% of its material
properties. This is consistent with FE model studies by Ilahee (2010), where stress distributions of
the pelvis during conditions of the one-legged-stance also start to converge at 10% healing.
Conclusions drawn from these results and the observations obtained in Figure 9 and Figure 10 point
17
21. to the fact the conditions of the pelvis at 10% healing seem to resemble that of a fully healed pelvis.
This could mean that the pelvis is structurally stable enough to function when 10% of the mechanical
properties have recovered.
In conclusion, the vibration analysis technique needs to be able to correctly identify the point at
which the new bone of a fractured pelvis has recovered up to 10% of its material properties.
Figure 12 – Convergence of displacement PSD of 2 nodes on either side of the fracture as healing progresses
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22. 5 Outline of Proposed Experimental Work
This research aims to develop a technique for monitoring the healing of a fixated pelvis. This allows
the determining of a proper time to remove the fixation when the structure of the pelvis is stable
and the patient can walk without its support. With satisfying results validated on FEA, the project
looks to progress towards experimental validation of bone healing monitoring technique.
As mentioned previously, the experiments will be conducted on synthetic Sawbone 3rd generation
pelvis specimens. The synthetic bones and fixations are provided by the Alfred hospital, Victoria
courtesy of orthopaedic surgeon, Dr Russ. The synthetic bones provided have already been fixated,
which will then need to be properly mounted to replicate the constraints used in FEA. One
experimental set-up suggestion is shown in Figure 13, which was used by Simonian et.al., in their
research. The pelvis is clamped at the lumbosacral junction and supported by femur stands at the
acetabulum. However, their set-up allows rotation and movement of the hip. To modify the set-up
to suit this project, rigid femur stands will be used. There are 3 sets of experiments planned so far.
Figure 13 – Proposed experimental set-up showing loading method and constraints imposed used by
Simonian et.al. to be modified to suit this project
5.1 Impact hammer testing
Firstly, vibration analysis using impact-hammer testing will be done by tapping the pin closest to the
fracture vicinity shown in Figure 14, fixated on the pre-disrupted pelvis model. This will induce a shot
burst of low frequency vibrations into the pelvis. Accelerometers mounted around the model will be
used to collect information for regenerating the mode shapes of the pelvis on the computer.
Position of these accelerometers will be determined by results collected from FEA. A ‘fracture’ is
then introduced to the sacrum cutting vertically through the sacral foramina. With the fixation still in
place, the impact hammer test and result collection is repeated. After obtaining the mode shapes of
the disruption pelvic ring, a slow curing epoxy is applied to bridge the gap. Accelerometers around
the synthetic pelvis will continue to collect results at different curing times to observe the different
mode shapes of the pelvis as the gap regains material stiffness.
19
23. Figure 14 – Schematic diagram of proposed signal actuation and result collection
5.2 Monitoring cure of epoxy using ultrasound
Results from the first set of experiments are not complete as stiffness of the curing epoxy is not
known. This brings the second set of experiment to be done using actuators and sensors in the form
of small PZTs mounted on either side of the fracture to record the rate of stiffness recovery with
respect to time. The PZTs transmit ultrasonic waves across the fracture site with the epoxy injected
into the fracture gap and the time taken for the FAS (first-arrival-signal) can measure the stiffness
across the gap (Njeh, 1998). These results allow the different mode shapes of the pelvis during
‘healing’ to be plotted as a function of stiffness of the epoxy in the gap. The purpose of the first 2
stages of the experiment is to determine the difference the dynamic characteristics of the pelvis as
the stiffness of the epoxy increases and compare them to existing FEA results.
5.3 Drive-point mobility technique via fixation pin using PZTs
Finally, a third set of experiments need to be run. Realistically, it is not possible to conduct vibration
analysis on the internally fixated pelvis in an actual patient with an impact hammer. Tests need to be
done to see if PZTs can generate the same power of vibrations from the pins which can also be
detected by a sensor PZT on the pins. This stage is to test the mobility of the pelvis at different
healing stages in a way which will not be uncomfortable for the patient. If successful, hopefully a
trial can be done on a real patient using a prototype smart fixation.
The experiments outlined above will be conducted for both the fixated and non-fixated synthetic
model. The embedded pins will not be removed as they will serve as the drive point for signal
actuation but the horizontal bar can be removed and re-installed when required as long as it is
properly torqued at 10Nm. These models assume the healing of bone to have a steady increase in
stiffness until full recovery but Nikiforidis et.al., (1990) states that development of callus during bone
healing goes beyond the original bone until the callus disappears and the original dimension of bone
is restored.
20
pins
Slow curing
epoxy over
fracture gap
Actuation point
Monitoring PZTs
Accelerometers
24. 6 Conclusions
Preliminary results via FEA have validated the use of vibration analysis for monitoring the healing of
bone in a fixated pelvis. A frequency signal of 200Hz to 2000Hz range was introduced to one of the
fixation pins and the natural frequencies of the pelvis were observed for all healing conditions.
Natural frequencies were found to increase as the bone recovers, increasing in stiffness. This
technique was sensitive to changes in bone stiffness of 0.1% original property to 10% property
whereby frequency response did not yield significant changes for higher healing conditions.
Driving-point impedance method was also tested and was found to give satisfying results which
correlated well with existing research. Results collected from the signal input location showed a shift
in resonant frequency with improving healing conditions which suggest this technique is viable for
monitoring the healing of bone.
Running the proposed experiments hope to validate the use of vibration analysis using
impedance/mobility techniques for the implementation of smart fixations to assess the condition of
the fracture in the fixated pelvis. Successfully identifying the time at which the pelvis has healed
enough to be structurally stable will allow patients to shorten the immobility period and reduce
post-surgery rehabilitation from muscle degradation.
7 Timeline
Table 2 – Proposed schedule for duration of study
8 Communication of results
Published works with the listed topics are planned to be produced this year:
o Monitoring techniques used for assessing the healing progress of bones
o FEA using vibration analysis to monitor the healing of sacral fractures for a fixated pelvis
Papers are intended to be submitted to the Journal of Biomechanics and Structural Health
Monitoring – An International Journal and presented at the 7th Australasian Congress on Applied
Mechanics and the 8th International Workshop on Structural Health Monitoring to be held in
September 2011 at California, US.
9 Acknowledgements
Dr Matthias Russ (Alfred Hospital, VIC)
Dr Susan Liew (Alfred Hospital, VIC)
Mr Nabil Ilahee (Monash University)
21
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