A biomechanical study of the Hughes external fixator in by NatePotter

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									     A biomechanical study of the Hughes external fixator in
                 treatment of tibial fractures
                                                  Salas Bolaños, Gerardo*
                Department of Mechanical and Mechatronics Engineering, University of Waterloo, Waterloo, Ontario, Canada

                                                                  4 April 2009




Abstract

Fractured tibia must be immobilized properly in order for it to heal correctly. External fixation devices have been found to be the best
method. Two main types of external fixators exist: unilateral and bilateral, each with its own advantages and disadvantages. Extensive
research has been carried out to evaluate the rigidity of external fixators. Many of these studies fail to take into account the
intrafragmentary theory of strain which guarantees optimal fracture healing. In this paper, a finite element analysis of the Hughes
external fixator is used to select the design parameters of the fixator to obtain optimal fracture healing by taking into account the
intrafragmentary strain. Two dimensional beam elements are used to create the model. The load applied is calculated based on the
length of the tibia analyzed. The fatigue life of the fixator elements is analyzed based on the maximum stress experienced. The results
show that the axial stiffness and strain at the fracture site are very dependent on the material of the elements, the pin length, and the
diameter of the pin and frame. The pin angle and location were found to have little effect. The selected configuration is a titanium
alloy frame with a 13.1 mm diameter at 30.75 mm from the bone and stainless steel pins with a 9.0 mm diameter at 15.0 mm from the
fracture site at an angle of 0 degrees. The selection of materials guarantees an acceptable axial stiffness and also provides the lightest
configuration. The pin angle is selected at 0 degrees given that it is the easiest installation angle. The pins are kept as close as possible
(15.0 mm) to the fracture site to increase the distance from the outer pins and increase the bending stiffness. The distance of the frame
from the bone at the given stage of healing provides the appropriate strain. However, this distance should change as the healing
process progresses to maintain the appropriate strain. The pin and frame diameter are kept as small as possible to have a low weight
fixator. The result is a fixator with a mass of 174.01 grams that provides 1.995% strain. The fixator has infinite life with a safety
factor of 17.0.

Keywords: Hughes external fixator; finite element analysis; tibia, fracture; healing




1. Introduction

    Fractured tibia is common in patients with trauma. In                    followed two paths: unilateral and bilateral frames
order for the tibia to heal correctly it must be properly                    (Court-Brown and Hughes, 1985). Unilateral frames are
immobilized. Several methods can be used: cast                               safe and provide easy access to the wound, but are not
immobilization, internal fixation with nails, or by an                       rigid enough to support unstable fractures, deal with
external fixation device (Shtarker et al, 1997). The use                     heavy limbs, or permit early weight-bearing. Bilateral
of an external fixation device has been found to be the                      frames are more complex to increase their versatility.
safest method for stabilizing fractures in the tibial shaft                  These frames limit wound access and often interfere
(Sanders et al, 1993).                                                       with the opposite leg making weight bearing difficult
    External fixation devices have evolved since they                        and in some cases impossible (Behrens and Searls,
were first used in the mid 19th century (Sisk, 1983). In                     1986). It has been found that there is no set of
the last 20 years the evolution of external fixators has                     parameters that can be followed to meet the clinical and
                                                                             mechanical demands of each particular case. The
  *Corresponding author. Tel: +519-721-5224                                  selection of fixation devices is based largely on clinical
  E-mail address: gsalas@engmail.uwaterloo.ca (G. Salas                      experience (McCoy et al., 1983).
  Bolanos)
2                                                    G.Salas Bolaños (2009)


    Extensive research has been carried out to evaluate              This paper will analyze the Hughes external fixator.
the fracture fixation rigidity of many external fixators.        The Hughes external fixator is a unilateral fixator used
McCoy et al. (1983) evaluated the rigidity of the                in the treatment of tibial fractures. The fixator consists
Hoffman-Vidal apparatus, the Kronner ring device, the            of a fixator bar connected to the tibia using four pins.
Roger-Anderson apparatus, and the Hoffman-Vidal                  The fixator’s geometry and materials will be modified to
quadrilateral configuration. Briggs and Chao (1982) also         create a Hughes external fixator device that will allow
evaluated the mechanical performance of the Hoffman-             for optimal healing (strain at fracture site less than or
Vidal apparatus in order to increase its rigidity. Both          equal to 2%). The objective is to create a fixator that is
these studies succeed at optimizing design parameters to         rigid enough to allow weight bearing and at the same
create a rigid fixation device. However, they fail to take       time allow micromovement at the fracture site.
into account that if micromovement is not allowed to
occur at the fracture site the formation of callus is
affected. Burny et al. (1982) believed that non-rigid            2. Methods
fixation devices (“elastic fixation”) could enhance the
                                                                          A two-dimensional finite element model of the
healing process in bone fracture. Goodship and
                                                                 Hughes external fixator and the fractured tibia was
Kenwright (1985) showed that a 1 mm micromovement
                                                                 created. The construction of the model is based on the
in a 3 mm tibial fracture increased the rate of healing
                                                                 diagrammatic representation of the model shown in Fig.
due to the early formation of periosteal callus induced
                                                                 1. The pin angle (A), pin location (B) and pin length (C)
by movement. Kershaw et al. (1993) found that in the
                                                                 are the design parameters along with the pin and frame
treatment of tibial fractures with a cast there is
                                                                 diameter and material.
significant fracture movement during everyday activities
in the first three weeks after injury. This movement
promotes callus formation. In external fixation devices
this movement does not occur if the device is too rigid.
To solve this problem Kershaw et al. attached a                                                    C
micromovement module to a fixation device to induce
movement at the fracture site. The result was that the
group treated with a micromovement module reached a
bending stiffness of 15 Nm/degree five weeks earlier                                           B
than the group that had a rigid fixation device. The use                                               A
                                                                                               B
of a micromovement module was necessary because the
fracture movement due to weight bearing was only 0.5
mm. Chao et al. (1989) found that the fracture
movement is affected by the fixator stiffness and                                                C
geometry. There are limits to the changes that can be
made to modify the stiffness of the fixator and thus the
fracture movement.
    The interfragmentary strain theory states that at a
                                                                 Fig. 1: Diagrammatic representation of the Hughes external
strain of 2% bone formation will occur since compact             fixator. A represents the pin angle, B represents the pin location,
bone can only tolerate 2% strain. Chao et al. adapted            and C represents the pin length.
the interfragmentary strain theory to explain fracture
healing under external fixation. They stated that the                The finite element model was developed using
rigidity of a fixation device should be such that when           ABAQUS 6.5-1. The model of the Hughes fixator was
the fracture gap tissue has a low modulus, the stress            developed as a general model from which each frame
created from load on the bone passes mainly through the          configuration could be analyzed. It was constructed
fixation pin and the side bar, not the fracture gap. As          using two-dimensional beam elements. Each beam
the fracture callus begins to mature more stress should          element was assigned a different profile depending on
pass through the fracture site. This ensures that the            what it represented. The tibial shaft is idealized as a
strain at the fracture is 2%.                                    hollow cylinder with a 15.0 mm outer diameter and a
                                                                 5.0 mm inner diameter. The callus at the fracture site is
3                                                                       G.Salas Bolaños (2009)


assumed to be 1-mm thick with the same inner and outer                                 The fatigue strength of the pin of the pin and the
diameter as the bone. The pins and the frame were                                   frame are calculated using:
modelled as cylinders. A healing of 5% is assumed. The                                                                                   1/ b
                                                                                                                                     a
fracture is modelled at the middle of diaphysis of a                                                                     N                                                (2)
                                                                                                                                     a
250.0 mm long tibial bone. The material properties used
are listed in Table 1.                                                              where,
                                                                                                                         2
                                                                                                                 f Sut                   1     f Sut
Table 1                                                                                                      a                   b         log                            (3)
                                                                                                                   Se                    3      Se
Material properties
                                  Young’s Modulus       Poisson’s                   and N is the number of cycles until failure, Sf is the
                                      (MPa)               ratio                     fatigue strength, Sut is the tensile strength, Se endurance
                                                 a              a
     Cortical Bone                    20000.00            0.3                       limit, and f is the is the fraction of Sut represented by
     Immature Bone                    1000.00
                                                b
                                                          0.3
                                                                a                   ( Sf )103cycles.
     Titanium Alloy                                 c           c
                                     114000.00           0.33
     (6Al-4V)                                                                       3. Results
                                                    c               c
     Stainless Steel                 192000.00           0.285
a
    Lacroix and Prendergast (2002)                                                      The results of the finite element simulation of the
b
    Ganesh et al. (1999                                                             external fixator are shown in the following figures. The
c
    Matweb (2009)                                                                   amount of strain at the fracture site and the axial
                                                                                    stiffness of the Hughes external fixator are shown. The
   The axial load on the bone is assumed to be the                                  axial stiffness is given by dividing the applied load by
maximum load experienced during a gait cycle. The                                   the displacement at the fracture site.
maximum load experienced during a normal cycle                                          Fig. 3 shows the effect of different material
happens at about 48% of the cycle. At this point the                                configurations on the pins and the frame. The plot
load is equal to approximately 2.2 times the body weight                            shows that the stiffest configuration, C, is obtained by
(Zhao et al. 2006). The body mass index of a person can                             using stainless steel for both the pin and the frame.
be used to determine the weight if the height is given.                             Configuration A, which uses titanium alloy for both
Duyar and Pelin (2003) developed a formula to estimate                              elements, allows the most strain and has lowest axial
a person’s height based on the length of the tibia.                                 stiffness. The difference between configuration A and C
                                                                                    reflects the difference between the elastic modulus of
           m
St at ure(m )          678.68 2.738 *t i bi al engt h                    (1)        the titanium alloy and that of stainless steel.
                                                                                    Configurations B and D have very similar results.
    Given a tibia length of 250 mm, the expected height
is 1363.18 mm. Using the body mass index for a normal                                                 2.08                                                        45600
weight person yields a mass of 40.32 kg and a weight of                                               2.06                                                        45200
395.58 N. Therefore, the force applied in the finite                                                                                                              44800
                                                                                                      2.04
element model is 870.276 N.
                                                                                                                                                                          AXIAL STIFFNESS (N/mm)


                                                                                                                                                                  44400
                                                                                                      2.02
    The finite element model of the Hughes external                                                                                                               44000
                                                                                       STRAIN ( % )




                                                                                                        2
fixator and the tibia is shown in Fig. 2. Three-node                                                                                                              43600
quadratic elements were used to mesh the model.                                                       1.98
                                                                                                                                                                  43200
                                                                                                      1.96
                                                                                                                                                                  42800
                                                                                                      1.94
                                                                                                                                                                  42400
                                                                                                                                                Strain
                                                                                                      1.92                                                        42000
                                                                                                                                                Axial Stiffness
                                                                                                       1.9                                                        41600
                                                                                                                 A           B             C             D
                                                                                                                         MATERIAL

                                                                                    Fig. 3: Effect of altering pin and frame material on the strain at the
                                                                                    fracture and the compressive stiffness of the fixator. A = Titanium pin,
                                                                                    Titanium frame, B = Stainless steel pin, Titanium frame, C = Stainless
                                                                                    steel pin, stainless steel frame, and D = Titanium pin, Stainless steel
                                                                                    frame. (Fixator parameters: A = 5 degrees, B = 15 mm, C = 30.75 mm,
                                                                                    Pin diameter = 9 mm, Frame diameter = 13 mm).
Fig. 2: Finite element model of the Hughes external fixator.
4                                                                                                                      G.Salas Bolaños (2009)


          Fig. 4 shows the effect of altering the pin angle                                                                                             The effect of modifying the distance between the
on the strain and the axial stiffness. The amount of strain                                                                                         tibia and the frame is shown in Fig. 6. The shorter the
increases as the angle increases. The axial stiffness of                                                                                            pin length is the lower the strain at the fracture site. The
the fixator decreases with increasing angle. The results                                                                                            stiffness is highest when the frame is closest to the tibia
match previous result studies (Court-Brown, 1984) that                                                                                              given that shorter pins will deflect less under the same
found that the stiffest configuration is found when the                                                                                             load.
angle is zero and then decreases with increasing angle.                                                                                                 The diameter of the pin and frame had a greater
    The plot in Fig. 5 shows that as the distance of the                                                                                            effect on the stiffness of the fixator than the angle of the
pins from the fracture site is increased, the amount of                                                                                             pins and the pin location. Fig. 7 and Fig. 8 show how the
strain and the axial stiffness increase. A similar result                                                                                           stiffness of the fixator increases with increasing frame
was obtained by Briggs and Chao (1982) when                                                                                                         and pin diameter respectively. The sensitivity of the
evaluating the Hoffman-Vidal apparatus. They found                                                                                                  device being greater to the diameter of the elements than
that as the pins were moved away from the fracture site                                                                                             the pin angle and location is expected since the bending
the motion at the fracture site increased.                                                                                                          stiffness of the pin and frame are proportional to their
                                                                                                                                                    moment of inertia, which is in turn related to the fourth
                   2.07                                                                         44400
                                                                                                                                                    power of the diameter (Briggs and Chao).
                                                                                                                                                                             2.5                                                                250000
                   2.05                                                                         44000
                                                                                                                           AXIAL STIFFNESS (N/mm)




                   2.03                                                                         43600                                                                          2                                                                200000
    STRAIN ( % )




                                                                                                                                                                                                                                                         AXIAL STIFFNESS (N/mm)
                   2.01                                                                         43200
                                                                                                                                                                             1.5                                                                150000
                                                                                                                                                             STRAIN ( % )




                   1.99                                                                         42800
                                                                                                                                                                               1                                                                100000

                   1.97                                                                         42400
                                                                     Strain
                                                                                                                                                                             0.5                                                                50000
                                                                     Axial Stiffness
                   1.95                                                                         42000                                                                                                                    Strain
                          0   5        10          15           20             25          30                                                                                                                            Axial Stiffness
                                             ANGLE (DEGREES)                                                                                                                   0                                                                0
                                                                                                                                                                                   0    10   20         30          40        50           60
                                                                                                                                                                                                  PIN LENGTH (mm)
Fig. 4: Effect of altering pin angle on the strain at the fracture and the
compressive stiffness of the fixator. (Fixator parameters: B= 35 mm,                                                                                Fig. 9: Effect of altering pin length on the strain at the fracture and the
C= 32 mm, Pin diameter = 10 mm, Frame diameter = 14 mm, Pin                                                                                         compressive stiffness of the fixator. (Fixator parameters: A= 5 deg, B=
material = Titanium, Frame material = Stainless steel).                                                                                             15 mm, Pin diameter = 10 mm, Frame diameter = 14 mm, Pin material
                                                                                                                                                    = Titanium, Frame material = Stainless steel).

                   2.02                                                                         46500
                                                                                                                                                                            2.05                                                                48000

                      2                                                                         46000                                                                                                                                           47500

                                                                                                                                                                              2                                                                 47000
                   1.98                                                                         45500
                                                                                                                                                                                                                                                46500
                                                                                                        AXIAL STIFFNESS (N/mm)




                                                                                                                                                                                                                                                46000
    STRAIN ( % )




                                                                                                                                                                                                                                                         AXIAL STIFFNESS (N/mm)




                   1.96                                                                         45000                                                                       1.95
                                                                                                                                                       STRAIN ( % )




                                                                                                                                                                                                                                                45500
                   1.94                                                                         44500                                                                                                                                           45000
                                                                                                                                                                             1.9
                                                                                                                                                                                                                                                44500
                   1.92                                                                         44000
                                                                                                                                                                                                                                                44000

                    1.9                                                                         43500                                                                       1.85                                                                43500
                                                                         Strain
                                                                                                                                                                                                                         Strain
                                                                         Axial Stiffness                                                                                                                                                        43000
                   1.88                                                                         43000                                                                                                                    Axial Stiffness
                                                                                                                                                                             1.8                                                                42500
                          0       10         20          30                   40           50
                                                                                                                                                                                   11   12   13         14          15        16           17
                                            PIN LOCATION (mm)
                                                                                                                                                                                             FRAME DIAMETTER (mm)
Fig. 5: Effect of altering pin location on the strain at the fracture and
the compressive stiffness of the fixator. (Fixator parameters: A= 5
                                                                                                                                                    Fig. 10: Effect of altering frame diameter on the strain at the fracture
degree, C= 32 mm, Pin diameter = 10 mm, Frame diameter = 14 mm,
                                                                                                                                                    and the compressive stiffness of the fixator. (Fixator parameters: A= 5
Pin material = Titanium, Frame material = Stainless steel).
                                                                                                                                                    degree, B= 15 mm, C= 32 mm, Frame diameter = 13 mm, Pin material
                                                                                                                                                    = Titanium, Frame material = Stainless steel).
5                                                                                                                     G.Salas Bolaños (2009)


    Table 2 summarizes the parameters that were                                                                                   4. Discussion
selected for the final design of the fixator. As well it
shows the final mass of the fixator and the strain at the                                                                             For this simulation, the bone was idealized as a
fracture site given these parameters.                                                                                             cylindrical bone with only axial load acting on it.
    The maximum stress in a pin was 21.3 MPa and on                                                                               Bending of the bone is not included in this analysis.
the frame 18.50 MPa. From these values the pins were                                                                              Lacroix and Prendergast (2002) made the same
found to have infinite life with a safety factor of 17.0.                                                                         assumption in their study of fracture healing. To validate
The frame was also found to have an infinite life with a                                                                          this assumption they performed both axial loading and
safety factor of 41.0. The results are summarized in                                                                              three dimensional loading on the bone and found that
Table 3.                                                                                                                          the comparison of results is valid. They found that the
                                                                                                                                  axial loading case gives a clearer visualization of the
                    2.15                                                                       46000

                                                                                               45500
                                                                                                                                  process.
                                                                                               45000
                                                                                                                                      The selected material configuration was titanium
                     2.1
                                                                                               44500                              alloy (6Al-4V) for the frame and stainless steel for the
                                                                                               44000                              pins. The advantage of the titanium frame with respect
                                                                                                       AXIAL STIFFNESS (N/mm)


                    2.05
     STRAIN ( % )




                                                                        Strain
                                                                                               43500                              to the stainless steel frame is the weight of the overall
                      2
                                                                        Axial Stiffness
                                                                                               43000
                                                                                                                                  fixator. Using a titanium alloy frame and stainless steel
                                                                                               42500
                                                                                                                                  pins represents a weight saving of 29% with respect to
                                                                                               42000
                    1.95                                                                       41500
                                                                                                                                  using stainless steel frame and titanium alloy pins.
                                                                                               41000
                                                                                                                                  Briggs and Chao (1982) found that using more-rigid
                     1.9                                                                       40500                              pins is the most effective way of increasing the overall
                           7   8           9          10           11            12       13
                                                                                                                                  stiffness of fixation. The higher modulus of elasticity of
                                               PIN DIAMETER (mm)
                                                                                                                                  stainless steel is the best option to have a stiff fixator.
Fig. 11: Effect of altering pin diameter on the strain at the fracture and                                                        Using stainless steel for both the pins and the frame
the compressive stiffness of the fixator. (Fixator parameters: A= 5                                                               does provide the stiffest configuration; however, the
degree, B= 15 mm, C= 32 mm, Pin diameter = 13 mm, Pin material =
Titanium, Frame material = Stainless steel).
                                                                                                                                  fixator would be too heavy and the amount of strain at
                                                                                                                                  the fracture site is very little. The titanium alloy option
                                                                                                                                  for both elements was discarded given that it did not
Table 2                                                                                                                           provide the required stiffness. It was found that if
Design parameters and results                                                                                                     material in the pin or frame were changed, the pin angle
     A – Pin Angle                                         5.0 degrees                                                            and pin location do not have to be modified but the pin
     B – Pin Location                                       15.0 mm                                                               length, pin diameter, and frame diameter do have to be
     C – Pin Length                                        30.75 mm                                                               modified.
                                                                                                                                      The effect of the angle on the stiffness and on the
     Outer pin separation                                   200 mm
                                                                                                                                  strain at the fracture sight was minimal. The difference
     Pin Diameter                                           9.0 mm
                                                                                                                                  between the maximum strain and the minimum strain
     Pin Material                                     Stainless Steel                                                             was only 0.082% and the range in the axial stiffness
     Frame Diameter                                         13.1 mm                                                               values was 1764.78 N/mm. These two values are quite
     Frame Material
                                                      Titanium Alloy                                                              small when compared to the final values of strain
                                                         (6Al-4V)                                                                 (1.995%) and axial stiffness (42699.91 N/mm). This
     Mass                                                   174.01 g                                                              shows that the pin angle has very little influence. Court-
     Strain at fracture                                     1.995%                                                                Brown and Hughes (1985) found that the pin angle had
                                                                                                                                  no significance in the time for union. The minimal
Table 3                                                                                                                           effect of the angle of the pin is advantageous for the
Fatigue strength – Infinite life                                                                                                  orthopaedic surgeon, as additional time will not have to
                                   Safety
                                                   Endurance Limit                    Ultimate Strength                           be wasted ensuring that the angle is exactly right. An
                                   Factor
      Pin                                                                                                                         angle of zero degrees was chosen given that it is easier
                                    17.0                   260 MPaa                       586 MPaa
 Stainless steel                                                                                                                  to attach a pin at this angle.
Frame Titanium
                                    41.0                   620 MPaa                       965 MPaa                                    As the inner pins were moved away from the
     Alloy
a
    Chandrashekar, 2009                                                                                                           fracture site motion at this location increased. When
6                                                       G.Salas Bolaños (2009)


the pins move away from the fracture site they get closer               A person, in average, takes 6500 steps per day
to the outer pins. Reducing the distance between the                (Tudor-Locke and Bassett, 2004) and the maximum
inner and outer pins reduces the bending stiffness of the           time for tibia healing is approximately 45 weeks. This
fixator substantially (Briggs and Chao 1982). Bending               is the equivalent of 2.05x106 steps. Nonetheless, the life
stiffness was not measured in this study since only an              of the fixator is infinite. The lowest safety factor is 17.0
axial load was applied and not an anterior-posterior or             in the stainless steel pins. The titanium alloy frame has
lateral load. Nonetheless, previous studies by Briggs               a safety of factor 41.0.
and Chao, Johnson and Fischer (1983), and McCoy et                      The final mass of the Hughes external fixator is
al. (1983) have shown that reduction in pin separation              174.01 grams. Its axial stiffness provided a strain of
reduces bending stiffness significantly, thus increasing            1.995% at the fracture site. This guarantees optimal
motion at the fracture site. The distance of 15.0 mm                fracture healing.
was chosen given that it is close to the fracture site
while still allowing placement of the pin without                   Acknowledgements
affecting the fracture site.
     The distance between the tibia and the frame was                  Verification of the finite element model was
found to have a significant effect on the stiffness of the          provided by Umakaran Nemellan.
fixator. Out of all the design parameters, this is the only
one that can be modified once the fixator has been                  References
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7                                                               G.Salas Bolaños (2009)

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