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Analysis of the Impact of Configuration of the Stabilisation System for Femoral Diaphyseal Fractures on the State of Stresses and Displacements

Analysis of the Impact of Configuration of the Stabilisation System for Femoral Diaphyseal... Hindawi Applied Bionics and Biomechanics Volume 2018, Article ID 8150568, 10 pages https://doi.org/10.1155/2018/8150568 Research Article Analysis of the Impact of Configuration of the Stabilisation System for Femoral Diaphyseal Fractures on the State of Stresses and Displacements 1 2 Jakub J. Słowiński and Konrad Kudłacik Department of Mechanics, Materials Science and Engineering, Faculty of Mechanical Engineering, Wroclaw University of Science and Technology, Wrocław, Poland Orthopaedic and Trauma Department, Dr A. Sokołowski Specialist Hospital, Wałbrzych, Poland Correspondence should be addressed to Jakub J. Słowiński; jakub.slowinski@pwr.edu.pl Received 10 September 2017; Revised 21 November 2017; Accepted 29 November 2017; Published 8 January 2018 Academic Editor: Craig P. McGowan Copyright © 2018 Jakub J. Słowiński and Konrad Kudłacik. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Introduction. The treatment of femoral diaphyseal fractures by intramedullary nailing has become a common procedure in orthopaedic surgery. The purpose of this numerical simulation was to present how the changes in configuration of the stabilisation system can affect the stress and displacement state in the bone tissue and implanted device. Material and Methods. The numerical comparison of the stabilisation variants for the type 32-A2 femoral diaphyseal fracture (according to the AO classification) performed by using the Charfix2 (ChM®) anatomical nail locked in a number of chosen ways. The displacement and the stress distributions both in the bone and implant were obtained and analysed by computational simulation. Results.In all models, there was the same characteristic distribution, which shows there were minimal rotational movements of the bone around the anatomical axis. In all cases, stress concentrations were generated in the nail material in the area of the fracture gap. Conclusions. The obtained results indicate that there is a visible advantage to one-plane distal stabilisation in the reduction of stresses regardless of the type of proximal stabilisation. The results of calculations indicate that the use of proximal stabilisation with a neck screw reduces the possibility of damage to the implant. 1. Introduction characterized by a high percentage of possible complications [1–5]. According to some new studies, stabilisation by means of locked plates provides a simpler, less invasive solution with Contemporary surgical treatment of fractures, termed stable osteosynthesis, consists of anatomical bone reduction and fewer complications, which may be important for older oste- fixation of bone fragments, which prevents reciprocal dis- oporotic patients, whose bones show osteoporotic features placement of bone fragments. The fixation is maintained [6]. Standardization of fracture typology introduced by, until the bone union is achieved. Current designs enabled fix- among others, the AO Foundation, enables easier verification ations thanks to which loads are transferred mostly by bone of the case and selection of the optimal method of obtaining rather than fixation elements [1]. The choice of treatment bone union [7–10]. Literature cases of verification of com- for fractures depends on the age and general condition of monly used classification systems suggest that those systems the patient, the type of fracture, the competence of the doc- are not yet fully mature and, for very complex cases, the exist- tor, and technical treatment options. ing procedures are not completely effective [11, 12]. Stabilisation of femoral diaphyseal fractures in adults by The correct placement of the implant together with its intramedullary nailing is now the gold standard of treatment shape reflecting the curvatures of the femoral diaphysis and a major advancement when compared with nonsurgical allows for a more even transfer of loads and, therefore, methods still used at the end of the 20th century, which were diminishes the risk of occurrence of stress-shielding [13]. 2 Applied Bionics and Biomechanics bone tissues and the fracture gap. The size of the element Appropriate insertion of the nail, followed by its securing with locking screws, provides stable fixation of bone frag- was determined to be 1.5 mm globally and 0.25 mm in the ments which, under dynamic loading conditions, enables gap (Figure 2). The size and type of elements were selected regeneration of the bone tissue in the fracture gap. based on a preliminary convergence analyses which have Those methods still have a significant failure rate due to been performed on the bone model with unified material lack of bone union, which can be as high as 21% [14–17]. properties in order to check accuracy and numerical costs. The relatively high percentage of failures in the form of non- This size represents a good trade-off between computational union of the bone contributes to numerical analyses because cost and numerical accuracy. The analysis covered five possible locking methods using of the ability to compare several variants of stabilisation that are usually possible with the implant design. The capabilities both static and dynamic holes on one and two planes of the numerical methods supported by clinical observations (Figure 3). The first way of locking used a static method with are now a powerful tool in predicting the effectiveness of two locking screws in the frontal plane. One screw was treatment [1, 18]. inserted under the lesser trochanter, while the other screw was inserted in the last oval hole of the nail in the distal part, The aim of the work was a numerical comparison of the stabilisation variants for the type 32-A2 femoral diaphyseal located above the level of the patellar surface and condyles. fracture (according to the AO classification) performed by In the second case, a compressive stabilisation method using the Charfix2 (ChM) anatomical nail locked in a num- was used, that is, four locking screws were inserted in the ber of chosen ways. The obtained distributions of displace- frontal plane. In the proximal part, a screw was inserted in the oblong hole above the lower trochanter and a second ments and stresses in the bone-implant system were compared to each other and made it possible to determine screw was inserted in the oval hole below the lower trochan- which of the analysed types of stabilisation gave the most sta- ter. In the distal part, one screw was placed in the oblong hole ble conditions for bone union. and another one was placed below it in the last oval hole of the nail. The third case involved the introduction of three lock- 2. Material and Methods ing screws in the frontal plane and—unusually for the femur—placement of one screw in the sagittal plane. In The geometric model of the femur was developed on the basis of computerized tomography of the bone of a healthy 45- the proximal part, the screws were introduced in the same year-old male and then imported into Ansys Workbench manner as in the second case. In the distal part, one screw was placed in the last oval hole of the nail in the frontal 17.2 software. Next, a 2 mm wide fracture gap was generated in the bone model (Figure 1). The size and the shape of the plane, while the second screw was placed above it in the gap were determined by experimental and mathematical sagittal plane. models [19, 20]. According to the classification maintained The fourth way of locking used a reconstruction method. by the AO Foundation, the model reflected type 32-A2 frac- However, instead of the contemporary technique involving insertion of two screws, only one reconstruction screw was ture located in the middle of the femur length. The nail model was developed based on the data from CT placed at an angle in the head of the femur. In the distal part, scans of a CHARFIX2 antegrade femoral intramedullary nail one screw was inserted in the oblong hole and another one made by ChM. The anatomical nail, with a variable diameter was placed below it in the last oval hole of the nail. and a length of 400 mm, was shaped in several planes to In the fifth case, as in the fourth case, one reconstruction screw was used. In the distal part, one screw was placed in the match the femoral diaphyseal anatomy. The main diameter of the nail was 11 mm, progressing in the upper part to the last oval hole of the nail in the frontal plane, while the second diameter of 14 mm. This size of the nail is typical for screw was placed above it in the sagittal plane. unreamed insertion. Static and dynamic holes were drilled 2.1. Loading Model. The developed numerical model was in both the proximal and distal epiphysis. In the proximal loaded in accordance with the loading model developed by part, the holes were located in the frontal plane, while in Będziński at the Division of Biomedical Engineering and the distal part they were located in a number of planes, which Experimental Mechanics of the Wrocław University of Sci- gives a lot of freedom when choosing the nail locking ence and Technology (Figure 4(a)) [21, 22]. In that model method. The geometric design of the nail does not include of hip joint, based on the ideas of Pauwels and Maquet, the any curves to simplify discretization of the model. effect of the internal rotators (R ), causing the rotation of Matching screws for the selected model of the anatomical the femur, was additionally taken into account. The following nail were also modelled in SolidWorks 2014. The length of the reconstruction screw was chosen based on the size of forces (Figure 4(b)) were found to be acting on the proximal femoral epiphysis during one-leg stance: the femoral head, while the length of the locking screws was chosen depending on the femur diameter of the particular (i) Load from the trunk mass acting on the femoral section. Screw models did not include thread outlines. head (R) Discretization of the model was performed using higher- order 20-node elements for the model of the bone and frac- (ii) Force of abductor muscles (M )(gluteus minimus) ture gap and 10-node elements for the model of the implant and (M )(gluteus medius) with bone screws. High-order elements were used because of the large differences between the material properties of the (iii) Force of the iliotibial band (T)(tractus iliotibialis) Applied Bionics and Biomechanics 3 Figure 1: The geometric model of the femur and a fracture gap. (iv) Force of thigh rotator muscles R (iliopsoas) The following data were recorded as a part of the conducted static analysis for the five cases of stabilisation of It was assumed that the force values will correspond to femoral fractures: 50% of the full load for one-leg stance, reflecting saving of the limb by the patient (one-leg stance with support) (Table 1). (i) Nodal displacements in the bone model (for each The fixation of the model was achieved by removing all axis of the reference system), with particular empha- degrees of freedom from surface knots within condyles, inter- sis on the place of application of the force condylar fossa, and the patellar surface (Figure 4(c)). (ii) Stress in the bone model at the point of contact with The material properties were given in accordance with the implant the data from Table 2 assuming that all objects are isotropic and linear. In order to more accurately reflect the bone- (iii) Stress in the intramedullary nail model implant system, a distinction was made in the bone model between the compact and spongy bone tissues as well as 3. Results the material in the fracture gap. In each case, a system of a physiologically normal, fractured, and stabilised bone Results for all cases were presented in Figure 5. was modelled. Thickness of the compact tissue was deter- mined on the basis of medical records and CT images. CT Case 1. Displacements in the x-axis of the system with the scans were processed with 3DSlicer—an open source soft- maximum value of 2.52 mm indicated bone bending in the ware for visualization and medical image computing. Then, frontal plane and tilting of the proximal part of the bone to for the given bone fragment, an appropriate number of the side of the body. In the y-axis, there was a noticeable for- layers of elements were selected to give them specific mate- ward tilting of the proximal epiphysis with the maximum rial properties. The implant used for the analysis had the value of almost 13.6 mm. Displacements in the z-axis parameters of a titanium alloy with an addition of niobium observed in the greater trochanter and bonehead corre- (Ti6Al7Nb), one of the typical materials used in the produc- sponded to the direction of the axis, while the anterior part tion of implants. of the bone was displaced slightly in the opposite direction. The next step was to define the type of contact between Uneven distribution of isolines indicated slight rotational the given volumes. Although there are some minimal nail movements of the bone around the anatomical axis. displacements inside the bone in the biomechanical system, Reduced stresses observed in the bone peaked in the area no frictional contact was used for the point of contact of the fracture gap at the point of contact between the bone between the bone and the implant; instead, bonded contact and the implant. The recorded maximum value was close to was used between all volumes. This allowed us to focus only 135.85 MPa and was located at the medial edge of the hole on the issue of stabilisation of bone fragments. below the fracture gap. Above the fracture gap, the recorded 2 mm 4 Applied Bionics and Biomechanics Figure 2: The finite element meshes of parts comprising the model: bone structure, implants (proximal parts), and fracture gap. maximum stress was 107.3 MPa and was located at the poste- Case 3. Case 3 is the first one where locking screws were rior part of the medullary canal. The stresses in the implant inserted in the sagittal plane. The largest displacements in material were located in the area of the fracture gap and the x-axis occurred in the proximal part of the femur with amounted to 291.33 MPa. the maximum value of 2.29 mm; there was a visible bending of the bone in the frontal plane and tilting of the proximal Case 2. Displacements in all axes were characterized by distri- part of the bone to the side of the body. The largest displace- ments in the bone were shown by movements along the y- bution analogous to case 1. In the x-axis, the maximum value of displacements was slightly greater at 2.34 mm. In the y-axis, axis. Within the proximal part of the bone, the observed maximum absolute value was as high as 13.30 mm. The the value was 12.91 mm and the displacements were charac- above displacements result in bending in the sagittal plane, terised by distribution analogous to case 1. A similar increase in the value of displacements with the preservation of their and the proximal part of the bone becomes strongly tilted forward. The maximum value of displacements in the z-axis character was observed in the z-axis, where the maximum recorded value was 1.73 mm. The stresses observed in the area was 1.82 mm. The anterior part of the bone is displaced of contact of the implant with the bone tissue were charac- downwards, while within the lower trochanter as well as the posterior part of the greater trochanter and the head, there terised by a similar distribution—maximum stresses were located at the fracture edge on the wall of the medullary canal is a noticeable displacement upwards. The stresses recorded in the bone and on the walls of the medullary canal near containing the nail; in particular, above the fracture gap, the value of stress in the bone tissue was 171.99 MPa, while below the fracture gap amounted to 164.85 MPa and 96.64 MPa, the fracture gap the value already decreased to nearly respectively, above and below the damage site. The maxi- mum stress recorded in the implant material was located, as 102.35 MPa. The stressed recorded in the nail material reached a maximum of 277.8 MPa and were located in the in earlier cases, at the level of fracture gap and reached 332.55 MPa. area of the fracture gap. Applied Bionics and Biomechanics 5 Figure 3: Analysed variants of intramedullary fixation. 6 Applied Bionics and Biomechanics u z x y (a) (b) (c) Figure 4: The boundary conditions: scheme of the Bedzinski’s model (a), loading forces (b), and fixed support (c). influence of positive displacements. However, distribution Table 1: Loading forces at the proximal femoral epiphysis during of displacements in this axis is not represented by evenly one-leg stance. spaced bands, which indicates minimal rotational move- F [N] F [N] F [N] x y z ments of the femur around the anatomical axis. Stress in the bone material reached the maximum value R 245 −35 −651 at the edge below the fracture gap at the point of contact M −44 −11.5 33 with the implant and amounted to almost 131 MPa. Above M −151.5 −101 109 the fracture gap, a similar maximum already achieved a T −20.5 −7.5 0 value nearly twice as low, amounting to 75.44 MPa. The R −21 −178.5 165 maximum stress in the nail material was recorded at the point of contact with the fracture gap at the anterior site and amounted to 266.58 MPa. Table 2: Material properties of the model [1, 23, 24]. Case 5. The maximum displacement in the x-axis was Material properties Material 2.46 mm. This illustrated bending of the bone in the frontal E [MPa] ν [−] plane and tilting of the proximal part to the side of the Compact bone 16.700 0.3 body. The maximum displacement in the y-axis was as high Cancellous bone 155 0.3 as 13.66 mm. There was strong tilting of the proximal part Fracture gap tissue 2 0.4 of the bone and even bending, to a large extent, of the Ti6Al7Nb 105.000 0.36 diaphysis towards the front of the femur. The smallest dis- placements were observed for the z-axis, where the maxi- mum value was 1.85 mm. Distribution of isolines indicated Case 4. The largest displacements in the x-axis occurred in minimal rotational movements of the femur around the the proximal part of the femur—on the femoral head, within anatomical axis. the upper area of the neck, and in the area of insertion of The stresses in the bone tissue in the area of the fracture the intramedullary nail—and their maximum value was gap exceeded 130 MPa both above and below the fracture 1.59 mm. The distribution map of displacements in the x-axis gap. In the case of implant, similarly as before, the maximum shows bone bending in the frontal plane and tilting of the stress fluctuating around 254 MPa was observed at the height proximal femoral epiphysis to the side of the body. Analysis of the fracture gap. of displacements in the y-axis, which is responsible for movement in the sagittal plane, showed the greatest values 3.1. Comparative Analysis of Displacements. Comparative of displacements out of all three axes. Displacements were analysis of displacements (see Figure 6) in the x-axis showed that the differences in displacements in this axis are negligible largest in the area of the head and at the place of nail insertion, with the maximum absolute value of 14.65 mm. except for Case 4. The highest maximum displacement of The resulting displacements are caused by bending of the 2.52 mm occurred in Case 1, and the smallest one, at bone in the sagittal plane and show forward tilting of 1.59 mm, occurred in Case 4. The area of largest displace- the proximal epiphysis and, to a large extent, of the diaph- ments was found on the femoral head, within the upper area of the neck, and around the area of insertion of the intrame- ysis. The smallest displacement values were observed for the z-axis, where the maximum value was 2.11 mm. The area dullary nail into the bone. The distribution map showed bone of greatest displacements in this axis was related to the small bending in the frontal plane and tilting of the proximal part trochanter, the posterior part of the femoral head, and the to the side of the body. Somewhat greater differences in dis- posterior part of the greater trochanter. By far, most of the placements were found in the comparative analysis of the proximal femoral epiphysis moved upwards under the y-axis, in which the highest maximum of 14.65 mm occurred Applied Bionics and Biomechanics 7 von Mises (MPa) Displacement—Ux, Uy, and Uz (mm) 107,3 135,85 291,33 Max 2,5234 0,03 1,9934 95,376 120,75 258,96 2,2404 −1,4857 1,711 83,455 105,66 226,56 1,9575 −3,0013 1,4286 71,535 90,565 194,22 1,6745 −4,517 1,1462 56,615 75,471 161,85 1,3915 −6,0327 0,86379 47,694 60,378 129,48 1,1085 −7,5483 0,58139 35,744 45,284 97,11 0,82557 −9,064 0.29899 23,854 30,191 64,741 0,5426 −10,58 0.016584 11,933 15,097 32,371 0,25963 −12,095 −0,26582 0,012852 0,0039518 0,0017251 Min −0,02334 −13,611 −0,54822 171,99 102,35 227,8 1,8669 0,050866 1,8691 152,88 90,979 246,93 1,6571 −1,4558 1,596 133,78 79,607 216,06 1,4437 −2,9626 1,3229 114,67 68,235 185,2 1,2374 −4,4693 1,0499 95,559 56,863 154,33 1,0276 −5,976 0,77682 76,45 45,491 123,47 0,8178 −7,4827 0,50376 57,341 34,199 92,6 0,60797 −8,9894 0,2307 38,233 22,747 61,734 0,39815 −10,496 −0,042357 19,124 11,375 30,867 0,18833 −12,003 −0,31542 0,015386 0,0032147 0,0014221 −0,021493 −13,51 −0,58847 164,87 96,615 332,55 2,2967 0,047875 1,8216 146,55 85,88 295,6 2,0391 −1,4388 1,551 128,24 75,145 258,65 1,7815 −2,9256 1,2803 109,92 64,411 221,7 1,5238 −4,4123 1,0096 91,6 53,676 184,75 1,2662 −5,899 0,73896 73,282 42,941 147,8 1,0086 −7,3857 0,4683 54,964 32,207 110,85 0,75097 −8,8724 0,19763 36,646 21,472 73,899 0,49334 −10,359 −0,073039 18,328 10,737 36,95 0,23572 −11,846 −0,34371 0,010348 0,0023611 0,00047003 −0.021899 −13,333 −0,61437 130,19 75,441 266,59 1,5877 0,052731 2,1115 115,72 67,06 236,97 1,4087 −1,5813 1,8067 101,26 58,678 207,35 1,2296 −3,2153 1,502 86,791 50,297 177,73 1,0506 −4,8494 1,1973 72,327 41,915 148,11 0,87157 −6,4834 0,89259 57,862 33,534 118,49 0,69255 −8,1174 0,58787 43,398 25,152 88,868 0,51352 −9,7515 0,28315 28,933 16,771 59,247 0,33449 −11,386 −0,021561 14,469 8,3892 29,626 0,15546 −13,02 −0,32628 0.0039518 0.0077446 0.0054492 −0.023565 −14,654 −0,63099 131.61 137,84 253,77 2,4641 −0,049109 1,8479 116,99 122,53 225,58 2,188 −1,4742 1,5739 102,37 107,21 197,38 1,9119 −2,9976 1,2999 87,744 91,897 169,18 1,6359 −4,5209 1,0259 73,122 76,582 140,98 1,3598 −6,0443 0,75193 58,499 61,267 112,79 1,0837 −7,5676 0,47794 43,876 45,953 84,591 0,80766 −9,0909 0,20394 29,254 30,638 56,395 0,53159 −10,614 −0,070054 14,631 15,323 28,198 0,25553 −12,138 −0,34405 0.0085661 0.0077446 0.0012645 −0,020539 −13,661 −0,61805 Figure 5: Results for analysed configurations of the stabilisation system for femoral diaphyseal fractures—state of stresses and displacements. in Case 4, while the smallest one, at 12.91 mm, occurred in part of the femoral head, and the posterior part of the Case 2. Displacements of the order of 13 mm were also greater trochanter. observed in Cases 1, 3, and 5. In this axis, too, the trends in 3.2. Stress Analysis. A comparison was made (see Figure 7) of displacement distribution were the same in all models; the observed bending in the sagittal plane resulted in strong tilt- the maximum stresses recorded at the points of concentra- ing of the proximal femoral epiphysis and, to a large extent, tion in the bone above the fracture gap at the point of contact bending of the diaphysis towards the front of the bone. with the callus and the nail. In all cases, such concentration The trend from the analysis of the y-axis was also visible occurred at the posterior part of the bone. This results from in the z-axis—the highest maximum displacements in this stretching of the bone while bending the proximal epiphysis axis were seen in Case 4, while the smallest ones were seen in the sagittal plane towards the front of the bone. The differ- in Case 2. The differences in displacements for individual ences in stress values are significant, with the highest values cases were negligible (in the order of millimetres). In all obtained in the case that reflected the compressive compres- models, there was the same characteristic distribution of sion method (171.99 MPa), followed by smaller values in the vertical bands arranged at a slight angle, which shows there case that used distal stabilisation in two planes (164.85 MPa), were minimal rotational movements of the bone around the and somewhat smaller values (131.61 MPa) in the case that anatomical axis. In addition, the largest displacements were used a reconstruction screw and locking of the bottom part observed in the area of the small trochanter, the posterior of the nail in the sagittal and frontal planes. The smallest Case 5 Case 4 Case 3 Case 2 Case 1 8 Applied Bionics and Biomechanics 16 the result of stretching of the bone due to bending in the sag- ittal plane. On the other hand, the concentration on the medial part of the bone is the result of minimal rotation of the bone around the anatomical axis. In all cases, stress concentrations were generated in the nail material in the area of the fracture gap. Slight concentra- tions also occurred near the holes through which the screws had been passed as well as in the areas of unused holes. Apart from Case 3, the maximum values for all cases ranged 2 between 253.8 and 291.33 MPa. In Case 3, stress reached the maximum of 332.55 MPa. In each case, those values are Ux Uy Uz well below the critical parameters of the titanium alloy used. I IV II V 4. Discussion III A fracture of the type presented in this study is most often Figure 6: The maximum displacements obtained for every case for caused by a high-energy trauma and, therefore, primarily each axis of the reference system. affects young people [25]. Despite the apparent lack of com- plexity, its treatment is not always successful [26]. The loca- tion of the femur in the kinematic chain and the resulting loads may, in combination with an improperly stabilised fracture, result in the formation of a pseudoarthrosis. In this study, it was assumed that the treated person was healthy with normal a bone tissue structure. It was also assumed that the applied load (half of the nominal value) was associated with protective lifestyle. However, it should be remembered that some of the key factors determining the possibility of using a particular solution include the condition of the bone tissue of the patient, which is especially important in the case of patients, mostly elderly, suffering from osteoporosis [27, 28] and the loads, which can exceed the safe values Bone—above Bone—below Implant—fracture indicated by the medical staff. The stresses observed in the fracture gap fracture gap gap bone tissue in Cases 2 and 3 obtain values which, in the I IV adopted loading model, should be considered potentially II V dangerous and could possibly lead to degradation of the III bone material, which, in turn, could lead to a loss of stability of bone fragment fixation. Destabilisation of the system Figure 7: The maximum stresses obtained for every case at the points of concentration. requires surgical treatment, which in turn raises the risk of treatment failure [16, 29]. Apart from the classic Case 1, the cases developed for the purposes of the analysis were paired in such way as to deter- maximum stress (75.44 MPa) in this area was recorded for the model that used a reconstruction screw and two screws mine if the use of a neck reconstruction screw gives a signif- in the distal part. This value is almost twice as low as the max- icant advantage over static proximal stabilisation with two imum cumulative stress in the bone above the fracture gap in locking screws in the frontal plane. Case 2 was paired with Case 3. The classic case—107.03 MPa had stress values that Case 4 while Case 3 was paired with Case 5. Differences within each pair occurred only in the area of proximal stabi- put it between the obtained maximum values. The comparison of cumulative stresses in the bone below lisation. Cases 2 and 4 represented distal stabilisation realized the fracture gap at the point of contact with the callus, and with two screws in the frontal plane, with one screw placed in the nail showed that the high values of stress on one side of the oblong hole and another one placed below it in the last the gap reduced concentration on the other side, with this oval hole of the nail. Cases 3 and 5 represented distal stabili- trend being disturbed in Case 5. The classic case with the sation realized with two screws, with one screw placed in the maximum value of 135.85 MPa did not differ significantly oval hole in the frontal plane and another one placed in the from Cases 4 and 5 with the values of, respectively, sagittal plane, also in the oval hole. 130.8 MPa and 131.84 MPa. For Cases 2 and 3, the obtained Cases 4 and 5, stabilised proximally with a reconstruction values were 102.35 MPa and 96.64 MPa, respectively. In the screw, give greater displacements along the y-axis and higher cases where reconstruction screws were used in addition to stresses in the bone below the fracture gap, but in relation to locking screws, the concentration covered a larger area—on Case 3, those values can be considered less dangerous. In the medial and posterior sides. The observed concentration those cases, relatively high stresses below the fracture gap at the posterior part of the bone below the fracture gap is result in relatively small stresses on the other side of the von Mises stresses (MPa) Displacements (mm) Applied Bionics and Biomechanics 9 contact phenomena which limited accuracy of the calcula- fracture. In this comparison, Case 4 must be regarded as saf- est due to the lowest obtained stresses. tions. The isotropic and linear mechanical properties of the At the fracture level, stresses in the implant fall within the modelled bone-implant system were also adopted. The range of 230–288 MPa, which is well below the critical model also ignores the presence of the surrounding soft tis- parameters of the material from which the implant was sues, which have a natural tendency to limit the mobility of made. Therefore, it should be assumed that in the modelled bone fragments. The last implemented simplification was in system and for the selected maximum load, the mechanically the fracture gap where any processes of remodeling were weak link will be the tissue of the patient. not taken into account. Presented simulation relates to the With regard to the obtained results, it can be concluded early days after fracture stabilization. This design decision that the use of a greater number of support points and the was dictated by clinical experience, which allows the authors distribution of the load over a greater volume of the femoral to assume that taking into account the presence of such tis- head by means of a reconstruction screw helps to advanta- sues could reduce the intensity of nodal displacements in geously reduce stress concentrations in the implant and the model. diminishes the risk of its damage and the resultant destabili- sation of bone fragments. Compared to the classic case, the Abbreviations use of a reconstruction screw and more comprehensive distal stabilisation allowed to reduce the stresses in the implant AO Foundation: The AO Foundation is a medically guided, itself by 24 MPa in Case 4 and by 37 MPa in Case 5. The not-for-profit organization led by an inter- use of a distal two-plane stabilisation worsened the stress national group of surgeons specialized in conditions in the fracture gap, but they still fall within the the treatment of trauma and disorders of boundaries set by the classic case. the musculoskeletal system (according to The choice of the appropriate type of stabilisation is one aofoundation.org) of the critical factors that largely determine the success of CT: Computed tomography. the treatment [30, 31]. The ever increasing computing capa- bilities in conjunction with the increasingly accurate imaging methods provide tremendous opportunities in the numerical Conflicts of Interest representation of the implant-bone system. Clinical practice combined with numerical calculations is a powerful predic- The authors wish to confirm that there are no known con- flicts of interest associated with this publication and there tion tool that makes it possible to indicate the most advanta- geous stabilisation variant in a given case [32], identify has been no financial support for this work that could have rehabilitation opportunities [33], and so forth. influenced its outcome. 5. Conclusions Acknowledgments Combining practical clinical experience with theoretical The calculations were made using the resources of the numerical models not only allows clinicians to enhance the Wrocław Centre for Networking and Supercomputing diagnosis of the case and take the right steps but also (http://www.wcss.pl), calculation Grant no. 397. Funding increases the ability to generate models more tailored to the for this work was provided by Grant no. 0402/0164/16. actual parameters of the patient. The limitations that arise at modelling and defining boundary conditions mean that the resultant model has a certain margin of error; neverthe- References less, they allow to indicate general trends that may be very helpful in clinical work. Ultimately, the obtained results indi- [1] S. Samiezadeh, P. Tavakkoli Avval, Z. Fawaz, and H. 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Analysis of the Impact of Configuration of the Stabilisation System for Femoral Diaphyseal Fractures on the State of Stresses and Displacements

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Copyright © 2018 Jakub J. Słowiński and Konrad Kudłacik. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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Hindawi Applied Bionics and Biomechanics Volume 2018, Article ID 8150568, 10 pages https://doi.org/10.1155/2018/8150568 Research Article Analysis of the Impact of Configuration of the Stabilisation System for Femoral Diaphyseal Fractures on the State of Stresses and Displacements 1 2 Jakub J. Słowiński and Konrad Kudłacik Department of Mechanics, Materials Science and Engineering, Faculty of Mechanical Engineering, Wroclaw University of Science and Technology, Wrocław, Poland Orthopaedic and Trauma Department, Dr A. Sokołowski Specialist Hospital, Wałbrzych, Poland Correspondence should be addressed to Jakub J. Słowiński; jakub.slowinski@pwr.edu.pl Received 10 September 2017; Revised 21 November 2017; Accepted 29 November 2017; Published 8 January 2018 Academic Editor: Craig P. McGowan Copyright © 2018 Jakub J. Słowiński and Konrad Kudłacik. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Introduction. The treatment of femoral diaphyseal fractures by intramedullary nailing has become a common procedure in orthopaedic surgery. The purpose of this numerical simulation was to present how the changes in configuration of the stabilisation system can affect the stress and displacement state in the bone tissue and implanted device. Material and Methods. The numerical comparison of the stabilisation variants for the type 32-A2 femoral diaphyseal fracture (according to the AO classification) performed by using the Charfix2 (ChM®) anatomical nail locked in a number of chosen ways. The displacement and the stress distributions both in the bone and implant were obtained and analysed by computational simulation. Results.In all models, there was the same characteristic distribution, which shows there were minimal rotational movements of the bone around the anatomical axis. In all cases, stress concentrations were generated in the nail material in the area of the fracture gap. Conclusions. The obtained results indicate that there is a visible advantage to one-plane distal stabilisation in the reduction of stresses regardless of the type of proximal stabilisation. The results of calculations indicate that the use of proximal stabilisation with a neck screw reduces the possibility of damage to the implant. 1. Introduction characterized by a high percentage of possible complications [1–5]. According to some new studies, stabilisation by means of locked plates provides a simpler, less invasive solution with Contemporary surgical treatment of fractures, termed stable osteosynthesis, consists of anatomical bone reduction and fewer complications, which may be important for older oste- fixation of bone fragments, which prevents reciprocal dis- oporotic patients, whose bones show osteoporotic features placement of bone fragments. The fixation is maintained [6]. Standardization of fracture typology introduced by, until the bone union is achieved. Current designs enabled fix- among others, the AO Foundation, enables easier verification ations thanks to which loads are transferred mostly by bone of the case and selection of the optimal method of obtaining rather than fixation elements [1]. The choice of treatment bone union [7–10]. Literature cases of verification of com- for fractures depends on the age and general condition of monly used classification systems suggest that those systems the patient, the type of fracture, the competence of the doc- are not yet fully mature and, for very complex cases, the exist- tor, and technical treatment options. ing procedures are not completely effective [11, 12]. Stabilisation of femoral diaphyseal fractures in adults by The correct placement of the implant together with its intramedullary nailing is now the gold standard of treatment shape reflecting the curvatures of the femoral diaphysis and a major advancement when compared with nonsurgical allows for a more even transfer of loads and, therefore, methods still used at the end of the 20th century, which were diminishes the risk of occurrence of stress-shielding [13]. 2 Applied Bionics and Biomechanics bone tissues and the fracture gap. The size of the element Appropriate insertion of the nail, followed by its securing with locking screws, provides stable fixation of bone frag- was determined to be 1.5 mm globally and 0.25 mm in the ments which, under dynamic loading conditions, enables gap (Figure 2). The size and type of elements were selected regeneration of the bone tissue in the fracture gap. based on a preliminary convergence analyses which have Those methods still have a significant failure rate due to been performed on the bone model with unified material lack of bone union, which can be as high as 21% [14–17]. properties in order to check accuracy and numerical costs. The relatively high percentage of failures in the form of non- This size represents a good trade-off between computational union of the bone contributes to numerical analyses because cost and numerical accuracy. The analysis covered five possible locking methods using of the ability to compare several variants of stabilisation that are usually possible with the implant design. The capabilities both static and dynamic holes on one and two planes of the numerical methods supported by clinical observations (Figure 3). The first way of locking used a static method with are now a powerful tool in predicting the effectiveness of two locking screws in the frontal plane. One screw was treatment [1, 18]. inserted under the lesser trochanter, while the other screw was inserted in the last oval hole of the nail in the distal part, The aim of the work was a numerical comparison of the stabilisation variants for the type 32-A2 femoral diaphyseal located above the level of the patellar surface and condyles. fracture (according to the AO classification) performed by In the second case, a compressive stabilisation method using the Charfix2 (ChM) anatomical nail locked in a num- was used, that is, four locking screws were inserted in the ber of chosen ways. The obtained distributions of displace- frontal plane. In the proximal part, a screw was inserted in the oblong hole above the lower trochanter and a second ments and stresses in the bone-implant system were compared to each other and made it possible to determine screw was inserted in the oval hole below the lower trochan- which of the analysed types of stabilisation gave the most sta- ter. In the distal part, one screw was placed in the oblong hole ble conditions for bone union. and another one was placed below it in the last oval hole of the nail. The third case involved the introduction of three lock- 2. Material and Methods ing screws in the frontal plane and—unusually for the femur—placement of one screw in the sagittal plane. In The geometric model of the femur was developed on the basis of computerized tomography of the bone of a healthy 45- the proximal part, the screws were introduced in the same year-old male and then imported into Ansys Workbench manner as in the second case. In the distal part, one screw was placed in the last oval hole of the nail in the frontal 17.2 software. Next, a 2 mm wide fracture gap was generated in the bone model (Figure 1). The size and the shape of the plane, while the second screw was placed above it in the gap were determined by experimental and mathematical sagittal plane. models [19, 20]. According to the classification maintained The fourth way of locking used a reconstruction method. by the AO Foundation, the model reflected type 32-A2 frac- However, instead of the contemporary technique involving insertion of two screws, only one reconstruction screw was ture located in the middle of the femur length. The nail model was developed based on the data from CT placed at an angle in the head of the femur. In the distal part, scans of a CHARFIX2 antegrade femoral intramedullary nail one screw was inserted in the oblong hole and another one made by ChM. The anatomical nail, with a variable diameter was placed below it in the last oval hole of the nail. and a length of 400 mm, was shaped in several planes to In the fifth case, as in the fourth case, one reconstruction screw was used. In the distal part, one screw was placed in the match the femoral diaphyseal anatomy. The main diameter of the nail was 11 mm, progressing in the upper part to the last oval hole of the nail in the frontal plane, while the second diameter of 14 mm. This size of the nail is typical for screw was placed above it in the sagittal plane. unreamed insertion. Static and dynamic holes were drilled 2.1. Loading Model. The developed numerical model was in both the proximal and distal epiphysis. In the proximal loaded in accordance with the loading model developed by part, the holes were located in the frontal plane, while in Będziński at the Division of Biomedical Engineering and the distal part they were located in a number of planes, which Experimental Mechanics of the Wrocław University of Sci- gives a lot of freedom when choosing the nail locking ence and Technology (Figure 4(a)) [21, 22]. In that model method. The geometric design of the nail does not include of hip joint, based on the ideas of Pauwels and Maquet, the any curves to simplify discretization of the model. effect of the internal rotators (R ), causing the rotation of Matching screws for the selected model of the anatomical the femur, was additionally taken into account. The following nail were also modelled in SolidWorks 2014. The length of the reconstruction screw was chosen based on the size of forces (Figure 4(b)) were found to be acting on the proximal femoral epiphysis during one-leg stance: the femoral head, while the length of the locking screws was chosen depending on the femur diameter of the particular (i) Load from the trunk mass acting on the femoral section. Screw models did not include thread outlines. head (R) Discretization of the model was performed using higher- order 20-node elements for the model of the bone and frac- (ii) Force of abductor muscles (M )(gluteus minimus) ture gap and 10-node elements for the model of the implant and (M )(gluteus medius) with bone screws. High-order elements were used because of the large differences between the material properties of the (iii) Force of the iliotibial band (T)(tractus iliotibialis) Applied Bionics and Biomechanics 3 Figure 1: The geometric model of the femur and a fracture gap. (iv) Force of thigh rotator muscles R (iliopsoas) The following data were recorded as a part of the conducted static analysis for the five cases of stabilisation of It was assumed that the force values will correspond to femoral fractures: 50% of the full load for one-leg stance, reflecting saving of the limb by the patient (one-leg stance with support) (Table 1). (i) Nodal displacements in the bone model (for each The fixation of the model was achieved by removing all axis of the reference system), with particular empha- degrees of freedom from surface knots within condyles, inter- sis on the place of application of the force condylar fossa, and the patellar surface (Figure 4(c)). (ii) Stress in the bone model at the point of contact with The material properties were given in accordance with the implant the data from Table 2 assuming that all objects are isotropic and linear. In order to more accurately reflect the bone- (iii) Stress in the intramedullary nail model implant system, a distinction was made in the bone model between the compact and spongy bone tissues as well as 3. Results the material in the fracture gap. In each case, a system of a physiologically normal, fractured, and stabilised bone Results for all cases were presented in Figure 5. was modelled. Thickness of the compact tissue was deter- mined on the basis of medical records and CT images. CT Case 1. Displacements in the x-axis of the system with the scans were processed with 3DSlicer—an open source soft- maximum value of 2.52 mm indicated bone bending in the ware for visualization and medical image computing. Then, frontal plane and tilting of the proximal part of the bone to for the given bone fragment, an appropriate number of the side of the body. In the y-axis, there was a noticeable for- layers of elements were selected to give them specific mate- ward tilting of the proximal epiphysis with the maximum rial properties. The implant used for the analysis had the value of almost 13.6 mm. Displacements in the z-axis parameters of a titanium alloy with an addition of niobium observed in the greater trochanter and bonehead corre- (Ti6Al7Nb), one of the typical materials used in the produc- sponded to the direction of the axis, while the anterior part tion of implants. of the bone was displaced slightly in the opposite direction. The next step was to define the type of contact between Uneven distribution of isolines indicated slight rotational the given volumes. Although there are some minimal nail movements of the bone around the anatomical axis. displacements inside the bone in the biomechanical system, Reduced stresses observed in the bone peaked in the area no frictional contact was used for the point of contact of the fracture gap at the point of contact between the bone between the bone and the implant; instead, bonded contact and the implant. The recorded maximum value was close to was used between all volumes. This allowed us to focus only 135.85 MPa and was located at the medial edge of the hole on the issue of stabilisation of bone fragments. below the fracture gap. Above the fracture gap, the recorded 2 mm 4 Applied Bionics and Biomechanics Figure 2: The finite element meshes of parts comprising the model: bone structure, implants (proximal parts), and fracture gap. maximum stress was 107.3 MPa and was located at the poste- Case 3. Case 3 is the first one where locking screws were rior part of the medullary canal. The stresses in the implant inserted in the sagittal plane. The largest displacements in material were located in the area of the fracture gap and the x-axis occurred in the proximal part of the femur with amounted to 291.33 MPa. the maximum value of 2.29 mm; there was a visible bending of the bone in the frontal plane and tilting of the proximal Case 2. Displacements in all axes were characterized by distri- part of the bone to the side of the body. The largest displace- ments in the bone were shown by movements along the y- bution analogous to case 1. In the x-axis, the maximum value of displacements was slightly greater at 2.34 mm. In the y-axis, axis. Within the proximal part of the bone, the observed maximum absolute value was as high as 13.30 mm. The the value was 12.91 mm and the displacements were charac- above displacements result in bending in the sagittal plane, terised by distribution analogous to case 1. A similar increase in the value of displacements with the preservation of their and the proximal part of the bone becomes strongly tilted forward. The maximum value of displacements in the z-axis character was observed in the z-axis, where the maximum recorded value was 1.73 mm. The stresses observed in the area was 1.82 mm. The anterior part of the bone is displaced of contact of the implant with the bone tissue were charac- downwards, while within the lower trochanter as well as the posterior part of the greater trochanter and the head, there terised by a similar distribution—maximum stresses were located at the fracture edge on the wall of the medullary canal is a noticeable displacement upwards. The stresses recorded in the bone and on the walls of the medullary canal near containing the nail; in particular, above the fracture gap, the value of stress in the bone tissue was 171.99 MPa, while below the fracture gap amounted to 164.85 MPa and 96.64 MPa, the fracture gap the value already decreased to nearly respectively, above and below the damage site. The maxi- mum stress recorded in the implant material was located, as 102.35 MPa. The stressed recorded in the nail material reached a maximum of 277.8 MPa and were located in the in earlier cases, at the level of fracture gap and reached 332.55 MPa. area of the fracture gap. Applied Bionics and Biomechanics 5 Figure 3: Analysed variants of intramedullary fixation. 6 Applied Bionics and Biomechanics u z x y (a) (b) (c) Figure 4: The boundary conditions: scheme of the Bedzinski’s model (a), loading forces (b), and fixed support (c). influence of positive displacements. However, distribution Table 1: Loading forces at the proximal femoral epiphysis during of displacements in this axis is not represented by evenly one-leg stance. spaced bands, which indicates minimal rotational move- F [N] F [N] F [N] x y z ments of the femur around the anatomical axis. Stress in the bone material reached the maximum value R 245 −35 −651 at the edge below the fracture gap at the point of contact M −44 −11.5 33 with the implant and amounted to almost 131 MPa. Above M −151.5 −101 109 the fracture gap, a similar maximum already achieved a T −20.5 −7.5 0 value nearly twice as low, amounting to 75.44 MPa. The R −21 −178.5 165 maximum stress in the nail material was recorded at the point of contact with the fracture gap at the anterior site and amounted to 266.58 MPa. Table 2: Material properties of the model [1, 23, 24]. Case 5. The maximum displacement in the x-axis was Material properties Material 2.46 mm. This illustrated bending of the bone in the frontal E [MPa] ν [−] plane and tilting of the proximal part to the side of the Compact bone 16.700 0.3 body. The maximum displacement in the y-axis was as high Cancellous bone 155 0.3 as 13.66 mm. There was strong tilting of the proximal part Fracture gap tissue 2 0.4 of the bone and even bending, to a large extent, of the Ti6Al7Nb 105.000 0.36 diaphysis towards the front of the femur. The smallest dis- placements were observed for the z-axis, where the maxi- mum value was 1.85 mm. Distribution of isolines indicated Case 4. The largest displacements in the x-axis occurred in minimal rotational movements of the femur around the the proximal part of the femur—on the femoral head, within anatomical axis. the upper area of the neck, and in the area of insertion of The stresses in the bone tissue in the area of the fracture the intramedullary nail—and their maximum value was gap exceeded 130 MPa both above and below the fracture 1.59 mm. The distribution map of displacements in the x-axis gap. In the case of implant, similarly as before, the maximum shows bone bending in the frontal plane and tilting of the stress fluctuating around 254 MPa was observed at the height proximal femoral epiphysis to the side of the body. Analysis of the fracture gap. of displacements in the y-axis, which is responsible for movement in the sagittal plane, showed the greatest values 3.1. Comparative Analysis of Displacements. Comparative of displacements out of all three axes. Displacements were analysis of displacements (see Figure 6) in the x-axis showed that the differences in displacements in this axis are negligible largest in the area of the head and at the place of nail insertion, with the maximum absolute value of 14.65 mm. except for Case 4. The highest maximum displacement of The resulting displacements are caused by bending of the 2.52 mm occurred in Case 1, and the smallest one, at bone in the sagittal plane and show forward tilting of 1.59 mm, occurred in Case 4. The area of largest displace- the proximal epiphysis and, to a large extent, of the diaph- ments was found on the femoral head, within the upper area of the neck, and around the area of insertion of the intrame- ysis. The smallest displacement values were observed for the z-axis, where the maximum value was 2.11 mm. The area dullary nail into the bone. The distribution map showed bone of greatest displacements in this axis was related to the small bending in the frontal plane and tilting of the proximal part trochanter, the posterior part of the femoral head, and the to the side of the body. Somewhat greater differences in dis- posterior part of the greater trochanter. By far, most of the placements were found in the comparative analysis of the proximal femoral epiphysis moved upwards under the y-axis, in which the highest maximum of 14.65 mm occurred Applied Bionics and Biomechanics 7 von Mises (MPa) Displacement—Ux, Uy, and Uz (mm) 107,3 135,85 291,33 Max 2,5234 0,03 1,9934 95,376 120,75 258,96 2,2404 −1,4857 1,711 83,455 105,66 226,56 1,9575 −3,0013 1,4286 71,535 90,565 194,22 1,6745 −4,517 1,1462 56,615 75,471 161,85 1,3915 −6,0327 0,86379 47,694 60,378 129,48 1,1085 −7,5483 0,58139 35,744 45,284 97,11 0,82557 −9,064 0.29899 23,854 30,191 64,741 0,5426 −10,58 0.016584 11,933 15,097 32,371 0,25963 −12,095 −0,26582 0,012852 0,0039518 0,0017251 Min −0,02334 −13,611 −0,54822 171,99 102,35 227,8 1,8669 0,050866 1,8691 152,88 90,979 246,93 1,6571 −1,4558 1,596 133,78 79,607 216,06 1,4437 −2,9626 1,3229 114,67 68,235 185,2 1,2374 −4,4693 1,0499 95,559 56,863 154,33 1,0276 −5,976 0,77682 76,45 45,491 123,47 0,8178 −7,4827 0,50376 57,341 34,199 92,6 0,60797 −8,9894 0,2307 38,233 22,747 61,734 0,39815 −10,496 −0,042357 19,124 11,375 30,867 0,18833 −12,003 −0,31542 0,015386 0,0032147 0,0014221 −0,021493 −13,51 −0,58847 164,87 96,615 332,55 2,2967 0,047875 1,8216 146,55 85,88 295,6 2,0391 −1,4388 1,551 128,24 75,145 258,65 1,7815 −2,9256 1,2803 109,92 64,411 221,7 1,5238 −4,4123 1,0096 91,6 53,676 184,75 1,2662 −5,899 0,73896 73,282 42,941 147,8 1,0086 −7,3857 0,4683 54,964 32,207 110,85 0,75097 −8,8724 0,19763 36,646 21,472 73,899 0,49334 −10,359 −0,073039 18,328 10,737 36,95 0,23572 −11,846 −0,34371 0,010348 0,0023611 0,00047003 −0.021899 −13,333 −0,61437 130,19 75,441 266,59 1,5877 0,052731 2,1115 115,72 67,06 236,97 1,4087 −1,5813 1,8067 101,26 58,678 207,35 1,2296 −3,2153 1,502 86,791 50,297 177,73 1,0506 −4,8494 1,1973 72,327 41,915 148,11 0,87157 −6,4834 0,89259 57,862 33,534 118,49 0,69255 −8,1174 0,58787 43,398 25,152 88,868 0,51352 −9,7515 0,28315 28,933 16,771 59,247 0,33449 −11,386 −0,021561 14,469 8,3892 29,626 0,15546 −13,02 −0,32628 0.0039518 0.0077446 0.0054492 −0.023565 −14,654 −0,63099 131.61 137,84 253,77 2,4641 −0,049109 1,8479 116,99 122,53 225,58 2,188 −1,4742 1,5739 102,37 107,21 197,38 1,9119 −2,9976 1,2999 87,744 91,897 169,18 1,6359 −4,5209 1,0259 73,122 76,582 140,98 1,3598 −6,0443 0,75193 58,499 61,267 112,79 1,0837 −7,5676 0,47794 43,876 45,953 84,591 0,80766 −9,0909 0,20394 29,254 30,638 56,395 0,53159 −10,614 −0,070054 14,631 15,323 28,198 0,25553 −12,138 −0,34405 0.0085661 0.0077446 0.0012645 −0,020539 −13,661 −0,61805 Figure 5: Results for analysed configurations of the stabilisation system for femoral diaphyseal fractures—state of stresses and displacements. in Case 4, while the smallest one, at 12.91 mm, occurred in part of the femoral head, and the posterior part of the Case 2. Displacements of the order of 13 mm were also greater trochanter. observed in Cases 1, 3, and 5. In this axis, too, the trends in 3.2. Stress Analysis. A comparison was made (see Figure 7) of displacement distribution were the same in all models; the observed bending in the sagittal plane resulted in strong tilt- the maximum stresses recorded at the points of concentra- ing of the proximal femoral epiphysis and, to a large extent, tion in the bone above the fracture gap at the point of contact bending of the diaphysis towards the front of the bone. with the callus and the nail. In all cases, such concentration The trend from the analysis of the y-axis was also visible occurred at the posterior part of the bone. This results from in the z-axis—the highest maximum displacements in this stretching of the bone while bending the proximal epiphysis axis were seen in Case 4, while the smallest ones were seen in the sagittal plane towards the front of the bone. The differ- in Case 2. The differences in displacements for individual ences in stress values are significant, with the highest values cases were negligible (in the order of millimetres). In all obtained in the case that reflected the compressive compres- models, there was the same characteristic distribution of sion method (171.99 MPa), followed by smaller values in the vertical bands arranged at a slight angle, which shows there case that used distal stabilisation in two planes (164.85 MPa), were minimal rotational movements of the bone around the and somewhat smaller values (131.61 MPa) in the case that anatomical axis. In addition, the largest displacements were used a reconstruction screw and locking of the bottom part observed in the area of the small trochanter, the posterior of the nail in the sagittal and frontal planes. The smallest Case 5 Case 4 Case 3 Case 2 Case 1 8 Applied Bionics and Biomechanics 16 the result of stretching of the bone due to bending in the sag- ittal plane. On the other hand, the concentration on the medial part of the bone is the result of minimal rotation of the bone around the anatomical axis. In all cases, stress concentrations were generated in the nail material in the area of the fracture gap. Slight concentra- tions also occurred near the holes through which the screws had been passed as well as in the areas of unused holes. Apart from Case 3, the maximum values for all cases ranged 2 between 253.8 and 291.33 MPa. In Case 3, stress reached the maximum of 332.55 MPa. In each case, those values are Ux Uy Uz well below the critical parameters of the titanium alloy used. I IV II V 4. Discussion III A fracture of the type presented in this study is most often Figure 6: The maximum displacements obtained for every case for caused by a high-energy trauma and, therefore, primarily each axis of the reference system. affects young people [25]. Despite the apparent lack of com- plexity, its treatment is not always successful [26]. The loca- tion of the femur in the kinematic chain and the resulting loads may, in combination with an improperly stabilised fracture, result in the formation of a pseudoarthrosis. In this study, it was assumed that the treated person was healthy with normal a bone tissue structure. It was also assumed that the applied load (half of the nominal value) was associated with protective lifestyle. However, it should be remembered that some of the key factors determining the possibility of using a particular solution include the condition of the bone tissue of the patient, which is especially important in the case of patients, mostly elderly, suffering from osteoporosis [27, 28] and the loads, which can exceed the safe values Bone—above Bone—below Implant—fracture indicated by the medical staff. The stresses observed in the fracture gap fracture gap gap bone tissue in Cases 2 and 3 obtain values which, in the I IV adopted loading model, should be considered potentially II V dangerous and could possibly lead to degradation of the III bone material, which, in turn, could lead to a loss of stability of bone fragment fixation. Destabilisation of the system Figure 7: The maximum stresses obtained for every case at the points of concentration. requires surgical treatment, which in turn raises the risk of treatment failure [16, 29]. Apart from the classic Case 1, the cases developed for the purposes of the analysis were paired in such way as to deter- maximum stress (75.44 MPa) in this area was recorded for the model that used a reconstruction screw and two screws mine if the use of a neck reconstruction screw gives a signif- in the distal part. This value is almost twice as low as the max- icant advantage over static proximal stabilisation with two imum cumulative stress in the bone above the fracture gap in locking screws in the frontal plane. Case 2 was paired with Case 3. The classic case—107.03 MPa had stress values that Case 4 while Case 3 was paired with Case 5. Differences within each pair occurred only in the area of proximal stabi- put it between the obtained maximum values. The comparison of cumulative stresses in the bone below lisation. Cases 2 and 4 represented distal stabilisation realized the fracture gap at the point of contact with the callus, and with two screws in the frontal plane, with one screw placed in the nail showed that the high values of stress on one side of the oblong hole and another one placed below it in the last the gap reduced concentration on the other side, with this oval hole of the nail. Cases 3 and 5 represented distal stabili- trend being disturbed in Case 5. The classic case with the sation realized with two screws, with one screw placed in the maximum value of 135.85 MPa did not differ significantly oval hole in the frontal plane and another one placed in the from Cases 4 and 5 with the values of, respectively, sagittal plane, also in the oval hole. 130.8 MPa and 131.84 MPa. For Cases 2 and 3, the obtained Cases 4 and 5, stabilised proximally with a reconstruction values were 102.35 MPa and 96.64 MPa, respectively. In the screw, give greater displacements along the y-axis and higher cases where reconstruction screws were used in addition to stresses in the bone below the fracture gap, but in relation to locking screws, the concentration covered a larger area—on Case 3, those values can be considered less dangerous. In the medial and posterior sides. The observed concentration those cases, relatively high stresses below the fracture gap at the posterior part of the bone below the fracture gap is result in relatively small stresses on the other side of the von Mises stresses (MPa) Displacements (mm) Applied Bionics and Biomechanics 9 contact phenomena which limited accuracy of the calcula- fracture. In this comparison, Case 4 must be regarded as saf- est due to the lowest obtained stresses. tions. The isotropic and linear mechanical properties of the At the fracture level, stresses in the implant fall within the modelled bone-implant system were also adopted. The range of 230–288 MPa, which is well below the critical model also ignores the presence of the surrounding soft tis- parameters of the material from which the implant was sues, which have a natural tendency to limit the mobility of made. Therefore, it should be assumed that in the modelled bone fragments. The last implemented simplification was in system and for the selected maximum load, the mechanically the fracture gap where any processes of remodeling were weak link will be the tissue of the patient. not taken into account. Presented simulation relates to the With regard to the obtained results, it can be concluded early days after fracture stabilization. This design decision that the use of a greater number of support points and the was dictated by clinical experience, which allows the authors distribution of the load over a greater volume of the femoral to assume that taking into account the presence of such tis- head by means of a reconstruction screw helps to advanta- sues could reduce the intensity of nodal displacements in geously reduce stress concentrations in the implant and the model. diminishes the risk of its damage and the resultant destabili- sation of bone fragments. Compared to the classic case, the Abbreviations use of a reconstruction screw and more comprehensive distal stabilisation allowed to reduce the stresses in the implant AO Foundation: The AO Foundation is a medically guided, itself by 24 MPa in Case 4 and by 37 MPa in Case 5. The not-for-profit organization led by an inter- use of a distal two-plane stabilisation worsened the stress national group of surgeons specialized in conditions in the fracture gap, but they still fall within the the treatment of trauma and disorders of boundaries set by the classic case. the musculoskeletal system (according to The choice of the appropriate type of stabilisation is one aofoundation.org) of the critical factors that largely determine the success of CT: Computed tomography. the treatment [30, 31]. The ever increasing computing capa- bilities in conjunction with the increasingly accurate imaging methods provide tremendous opportunities in the numerical Conflicts of Interest representation of the implant-bone system. Clinical practice combined with numerical calculations is a powerful predic- The authors wish to confirm that there are no known con- flicts of interest associated with this publication and there tion tool that makes it possible to indicate the most advanta- geous stabilisation variant in a given case [32], identify has been no financial support for this work that could have rehabilitation opportunities [33], and so forth. influenced its outcome. 5. Conclusions Acknowledgments Combining practical clinical experience with theoretical The calculations were made using the resources of the numerical models not only allows clinicians to enhance the Wrocław Centre for Networking and Supercomputing diagnosis of the case and take the right steps but also (http://www.wcss.pl), calculation Grant no. 397. Funding increases the ability to generate models more tailored to the for this work was provided by Grant no. 0402/0164/16. actual parameters of the patient. The limitations that arise at modelling and defining boundary conditions mean that the resultant model has a certain margin of error; neverthe- References less, they allow to indicate general trends that may be very helpful in clinical work. Ultimately, the obtained results indi- [1] S. Samiezadeh, P. Tavakkoli Avval, Z. Fawaz, and H. 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