Stability assessment of a tibia fracture xation in the case of thermal stresses

Transcription

1 Stability assessment of a tibia fracture xation in the case of thermal stresses Stability assessment of a tibia fracture xation in the case of thermal stresses Elena Y. Belova eyshukeylo@gmail.com Abstract Fractures of a tibial diaphysis constitute the largest percentage among all cases of fractures of long bones, namely 32-37%. Internal osteosynthesis is one of the modern operational treatment methods of these fracture types. Problems of determining thermal stresses and their further consideration when choosing a treatment method of a patient are resolved with regard to such the medicine section as the traumatology. However, temperature drop at a bone surface in an installation place of a plate and screws during surgery and temperature change of xators after sealing of a wound are not taken in conducting similar studies for biotechnological systems (BTS) "boneplate screws". The aim of this study is determination of maximum values of thermal stresses in components of a BTS "tibia boneplate TRKhscrews". 3D computer models of a tibia bone and a segmental fracture of this bone are created in the CAD SolidWorks. Fragment is localized to a middle third of a diaphysis, its size 50 mm. Height of a diastase is 0.5 mm. Modelling of an internal osteosynthesis of the segmental tibia fracture are performed by a plate TRKh (named after the plate authors Dr. S.Tkachenko, Dr. V.Rutsky and Dr. V.Khomutov) and 9 screws. An area, which is a contour projection of the plate TRKh, is built on the tibia bone surface. 3D computer nite element model of the BTS "tibia boneplate TRKh screws" is created in SolidWorks Simulation module. Diaphysis consists of cortical bone tissue, epiphyses and metaphyses cancellous tissue, xators titanium alloy VT6. Temperature of the tibia bone is 37 C, temperature of the area 34.5 C. Air temperature in an operating room is 21 C. Maximum values of thermal stresses occurring in components of the BTS "tibiaplate TRKhscrews", do not exceed values of dangerous stresses for materials of these components according to the results of this study. Stability xation of the segmental fracture is not violated. Heating the area on the tibia surface and xators to 37 C occurs for 25 minutes. 1 Introduction Fractures of a tibial diaphysis constitute the largest percentage among all cases of fractures of long bones, namely 32-37% [1]. The situation is compounded by the 83

2 Proceedings of XLV International Summer School Conference APM 2017 fact that this type of fracture is most common in individuals of working age with the age category up to 40 years [2]. Internal osteosynthesis, which is based on a principle of connection of bone fragments by surgical way using various xators inside a patient's body, is one of the modern operational treatment methods of the diaphyseal fracture. Thermal stresses occur in living tissue due to uneven temperature distribution. Problems of determining thermal stresses and their further consideration when choosing a treatment method of a patient are resolved with regard to such the medicine section as the traumatology. Studies (in most cases) are performed for the purpose of rationale for an optimal choice of the xator in a transverse fracture of femur, humerus, tibia bones [3, 4, 5, 6, 7, 8]. The authors suppose that bone temperature before installation of the metal construction is constant and equal to 37 C. At that the change of temperature distribution that occurs in cortical and trabecular bone tissues in the process of operation, is not taken into account. In cases when a plate and screws are used to stabilization of the fragments, a surgeon makes an incision of soft tissues and exposes a part of the bone surface an area. Temperature values of the area and air owing around it are dierent, so convective heat transfer occurs and a cooling front starts to spread into the deep of the bone. Gradual heating of the bone tissue and metal construction occurs after installation of the xators and wound closure. Therefore, change of temperature distribution in the BTS "boneplatescrews" in the process of operation should be considered in determining of maximum values of the thermal stress. Aim of this work is determining of maximum values of the thermal stress when occur in components of the BPS "tibia bonetrkh platescrews" after wound closure. Main tasks of this study are listed below. 1. Create 3D computer model of the BTS "tibia bonetrkh platescrews" with the area, which is a projection of a contour line of the TRKh plate to a surface of the tibia bone. 2. Create 3D computer nite element model of this BTS. 3. Perform a biomechanical study of BTS "tibia bonetrkh platescrews" subject to the uneven temperature distribution in the bone tissues and xators. Temperature studies of the segmental tibia fracture model with the area and the BTS "tibia bonetrkh platescrews" are conducted by the author earlier. 2 Materials and methods 2.1 Modeling of the BPS "tibia bonetrkh platescrews" 3D computer model of the tibia bone is built in the SolidWorks CAD system. 50 cross-sectional (tomographic) images are used to create it: 9 for proximal, 11 for distal and 30 for diaphyseal aspects. The patient, whose cross-sectional images of the bone are used in this study, is considered average. This patient hasnâ t accompanying pathologies. His body mass is 70 kg, age 40 years. Building of the 3D computer model of segmental bone fracture is made using the created tibia bone model. Fragment is localized in the middle third of the diaphysis 84

3 Stability assessment of a tibia fracture xation in the case of thermal stresses and its size is 50 mm. Gap diastasis is formed at the moment of the fracture between fragments. Its height is taken equal to 0.5 mm [9]. Modeling internal osteosynthesis of segmental tibia fracture is made by TRKh plate, its length is 224 mm, and 9 screws. Four screws, their length are 40 mm and a diameter is 4.5 mm, are installed in order, starting with the top plate holes. Other ve screws, their length are 35 mm and a diameter is 4.5 mm, are used to fastening of the lower plate part. Area, which is a projection of a contour line of the TRKh plate to a surface of the tibia bone, is created after the installation of the TRKh plate and screws in a predetermined position. 3D computer nite element model BTS "tibia bonetrkh platescrews" is built in the SolidWorks Simulation module. High quality mesh of parabolic tetrahedral solid elements is used in its creation. Average global element size is 6.10 mm, tolerance 0.30 mm. Number of nodes is 49497, number of elements Built 3D computer model of the BTS "tibia bonetrkh platescrews" and its nite element model are presented in gure 1, a,b, respectively. a b Figure 1. BTS "tibia bonetrkh platescrews": a 3D computer model, b 3D computer nite element model 2.2 Physicomechanical characteristics of the tibia bone materials Epiphyses and metaphysi in the nite element model of the BTS "tibia bonetrkh platescrews" are modeled entirely from nite elements that have physical characteristics of trabecular bone tissue. Diaphysis is formed from cortical bone tissue excluding a bone marrow that lls an internal space [10]. Fixators TRKh plate and screws are made from VT6 titanium alloy. Elastic modulus of cortical bone 85

4 Proceedings of XLV International Summer School Conference APM 2017 tissue, trabecular bone tissue, VT6 titanium alloy is 35,3 [11, 12], 0,40 [12], 115,00 GPa [13, 14], respectively. Poisson's ratio of these materials is 0.30 [15], 0.20 [15], 0.32 [14] respectively. Density 1850 [16, 17], 300 [16, 17], 4430 [13] kg/m 3, dangerous stress 129 [11, 12], 6 [18], 900 [13, 14] MPa. Linear temperature expansion coecients of cortical bone tissue, trabecular bone tissue, VT6 titanium alloy is 32 [19], 10 [20], 8.4 [13] C 1, respectively. 2.3 External loads Results of the temperature study of the considered BPS after installation of the xators and wound closure obtained by the author earlier is used as the external load. Temperature distribution in the model in this study had determined at 10 dierent time stages from 150 to 1500 seconds with a step of 150 seconds, which allowed to trace a process of heating of the BPS components to a temperature of 37 C. In addition, convective heat transfer, which occurs due to the dierence of temperatures of the exposed area and air owing around it, was taken into account. 3 Results Biomechanical study of the BTS "tibia bonetrkh platescrews" subject to change of temperature distribution in a heating process of the BPS components after wound closure to a temperature of 37 C is carried out in the SolidWorks Simulation module. a b c d Figure 2. Stressstrain state: a BTS on the rst stage, b BTS on the tenth stage, c tibia bone diaphysis on the rst stage, d tibia bone diaphysis on the tenth stage Maximum values of equivalent stress (von Mises stress) in the diaphysis, epiphyses and xators are dened for each of 10 considered stages. Criterion according to which maximum values of equivalent stress in the system components must not exceed corresponding values for dangerous stress in materials of these components which is numerically equal to yield stress, is used for evaluation of xation stability 86

5 Stability assessment of a tibia fracture xation in the case of thermal stresses of the BTS. Stressstrain state of the BPS on the rst (150 seconds) and tenth (1500 seconds) stages is shown in a gure 2, a, b respectively as an example. Note that contains of minimum value of equivalent stress in the model is shown on the gure. Stressstrain state of the tibia bone diaphysis on the rst and tenth stages is shown in a gure 2, c, d. Dependency graph of maximum values of equivalent stress in the considered BTS from time is presented in a gure 3. Figure 3. Dependency graph of maximum values of equivalent stress from time 4 Discussion Conducted study is shown that occurrence of thermal stress in the BTS "tibia bone TRKh platescrews" after wound closure does not lead to violation of xation stability of the considered BTS. Maximum value of equivalent stress on the rst and tenth stages, which are shown in gures 2 a,b, dier by 5.19 MPa, which is insignificant. Maximum values of equivalent stress in the BPS grow with increasing time, as can be seen from the graph which presented in a gure 3. However, these values change slightly after the fth stage. Maximum value of equivalent stress in the xators occurs in the fourth screw at the bottom and it doesnâ t exceed of dangerous stress for titanium alloy VT6, which is equal to 900 MPa. Maximum value of this stress in epiphyses on the same stage is 0.57 MPa, that is 10 times less of the value of dangerous stress for trabecular bone tissue. TRKh plate and screws are installed on the tibia diaphysis, therefore dierence between maximum value of equivalent stress in this aspect and value of dangerous stress for cortical bone tissue isnâ t as great as in the previous cases. Values dier by 2.5 times. 5 Conclusion Maximum values of equivalent stresses in the 3D computer nite element model of the BPS "tibia bonetrkh platescrews", subject to change of temperature 87

6 REFERENCES distribution after wound closure in 10 dierent stages are found in this study. Source data and described methodology of work realization is appropriate to use in carrying of biomechanical studies 3D computer nite element models of bone fracture, in which other types of plates are xators. References [1] Shchukin V.M. Compression plate-dynamic osteosynthesis of diaphyseal fractures of shin bones in peacetime and in emergency situations: abs. dis... cand. med. sciences. Moscow: I.M. Sechenov First Moscow State Medical University, p. [2] Selitskii A.V., Kezlia O.P., Diatel S.V. Choice of optimal tactics of treatment of severe high-energy injury to the shin // Modern medical technologies in the context of regional health: collection of articles of the Republican scientic practical conference. Pinsk, 5th October Pinsk: PolesSU, P [3] Nyashin Y.I., Kiryukhin, V.Y. Biological stresses in living tissues. Issues of modeling and management // Russian journal of biomechanics V. 6. N o 3. P [4] Kiryukhin, V.Y., Nyashin Y.I. Management task of stress in actual problems of biomechanics // Russian journal of biomechanics V. 9. N o 4. P [5] BayramoÄŸlu E. et al. Analysis of plate-screw xation by nite element method in transverse fractures of the tibia diaphysis // Analysis V. 55. N o 3. P [6] Tarnita D. et al. Modular adaptive bone plate for humerus bone osteosynthesis // Romanian Journal of Morphology and Embryology V. 50. N o 3. P [7] Shukeilo Y.A. Inuence of temperature deformations of the implant with shape memory on the stress state of bone tissue // Biomechanics2006: 8th Russian conference on biomechanics, N. Novgorod, 2226 may 2006: thesis of reports. N. Novgorod, P [8] Shukeilo Y.A., Khomutov V.P., Samsonov S.Y. Inuence of temperature eects on the system of plate osteosynthesis during rehabilitation of the patient // International conference on soft computing and measurements. SPb. : Publishing house ETU "LETI", V. 2. P [9] Lavrishcheva G.I., Onoprienko G.A. Morphological and clinical aspects reparative regeneration of supporting organs and tissues. M.: Medicine, p. 88

7 REFERENCES [10] Maslov L.B. Resonance properties of the tibia in intact condition and with devices of external xation // Russian journal of biomechanics V. 7. N o 2. P [11] Nahum A.M., Melvin J.W. Accidental injury: biomechanics and prevention. Springer Science and Business Media, [12] Burstein A.H., Reilly D.T., Martens M. Aging of bone tissue: mechanical properties // The Journal of Bone and Joint Surgery Ð. 58. N o 1. Ð [13] Structural materials: reference book / B.N. Arzamasov [et al.].; ed. by B. N. Arzamesov. M.: Mashinostroenie, p. [14] Physical quantities: reference book / A.P. Babichev [et al.].; ed. by I.S. Grigoriev, I.S. Meilikhov. M.: Energoatomizdat, p. [15] Wirtz D.C. et al. Critical evaluation of known bone material properties to realize anisotropic FE-simulation of the proximal femur // Journal of biomechanics V. 33. N o 10. P [16] Marieb E.N., Hoehn K. Human anatomy and physiology. Pearson Education, [17] Gong J.K., Arnold J.S., Cohn S.H. Composition of trabecular and cortical bone // The Anatomical Record V N o 3. P [18] Morgan E.F., Keaveny T.M. Dependence of yield strain of human trabecular bone on anatomic site // Journal of biomechanics V. 34. N o 5. P [19] Pal S., Saha S. Coecient of thermal expansion of bone // Biomechanics P. 52. [20] Magne P., Versluis A., Douglas W.H. Eect of luting composite shrinkage and thermal loads on the stress distribution in porcelain laminate veneers // The Journal of prosthetic dentistry V. 81. N o 3. P Elena Y. Belova, Saint Petersburg, Russian Federation 89