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: email@example.com (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 placed. This fact can be used to modify the stiffness of Alonso, J., Geissler, W., and Hughes, J. 1989. External Fixation of the fixator as needed. During the initial stages of Femoral Fractures: Indications and Limitations, 241, 83-88 healing, the nonossified callus is cartilaginous with an elastic modulus of 6.0 MPa (Blenman et al 1989, Carter Behrens, Fred and Searl, Kate. 1986. External fixation of the tibia. et al. 1988). A high stiffness is required in the fixator to Basic concepts and prospective evaluation. Journal of Bone and support the bone properly. As the fracture heals the Joint Surgery, 68-B, 246-254 modulus of elasticity increases until it reaches 20 GPa, Blenman, P., Carter, D. R., Beaupre, G.S. 1989. Role of cortical bone. The varying strains needed throughout Mechanical Loading in the Progressive Ossification of a Fracture the healing process can be achieved by changing the Callus. Journal of Orthopaedic Research 7, 398-407. distance from the bone to the frame. This means that larger pins than the 30.75 mm pins have to be used to Briggss, Brian T and Chao, Edmund 1982. The mechanical allow adjustment once the elastic modulus at the performance of the standard Hoffman-Vidal external fixation fracture site is larger than 1 GPa. While this means that apparatus. Journal of Bone and Joint Surgery 64-A, 566-573. the overall weight of the fixator will be greater, it also Carter, D.R., Blenman, Beaupre, G.S. 1988. Correlations between means that the patient will not need a microvoment Mechanical Stress History and Tissue Differentiation in Initial device (Kershaw et al. 1993) in the early stages of the Fracture Healing. Journal of Orthopaedic Reserch 6, 738-748. healing process. A micromovement device will still be necessary to obtain the 2% strain at the fracture site in Chandrashekar, N. 2009. Lecture notes: Mechanics of Bone and the late stages of healing when weight bearing is not its Replacements. Chap 2 & 5-2. enough to produce the desired strain. Chao, E. Y.S, Aro, H.T., Lewellen, D.G. and Kelly, P.J. 1989. As mentioned in the previous section, the diameter The effect of rigidity on fracture healing in external fixation. of the pin and the frame had a significant effect on the Clinical Orthopeadics and Related Research, 241, 24-35 stiffness of the fixator due to the relation of the stiffness to the fourth power of the diameter. The objective in Claes, L.E., Heigele, C.A., 1999. Magnitudes of local stress and the optimization of these two values was to minimize strain along bony surfaces predict the course and type of fracture the diameter as much as possible to reduce weight while healing. Journal of Biomechanics 32, 255-266. still maintaining an acceptable axial stiffness. The pin Court-Brown, C. M., 1984. MD Thesis, University of Edinburgh. diameter was chosen to be 9.0 mm and the frame diameter 13.1 mm. It should be noted that if the Court-Brown, C M. and Hughes,S P F. 1985. 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And Prendergast, P.J. 2002. A mechano-regulation model for tissue differentiation during fracture healing: analysis of gap size and loading. Journal of Biomechanics, 35, 1163-1171. McCoy, Micheal T., Chao, Edmund Y, Kasman, Roberta, 1983. Comparison of Mechanical Performance in Four Types of External Fixators. Clinical Orthopeadics and Related Research 180, 23-33 Reilly, Donald T. and Burstein, Albert H. 1974. The Mechanical Properties of Cortical Bone. Journal of Bone and Joint Surgery, 56, 1001-1022 Sanders, R., Swiontkowski, M., Nunley, J., Spiegel, P. 1993. The management of fractures with soft tissue disruptions. Journal of Bone Joint Surgery, 75A, 778-789 Sisk, David. 1983. External Fixation: Historic Review, Advantages, Disadvantages, Complications, and Indications. Clinical Orthopaedics and Related Research 180, 15-22 Shtarker, H., David, R. Stolero, J., Grimberg, B. , Soudry, M. 1997. Treatment of Open Tibial Fractures With Primary Suture and Ilizarov Fixation. 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