نوع مقاله : مقاله کامل پژوهشی

نویسندگان

1 دانشجوی کارشناسی ارشد، گروه مکانیک، دانشکده مهندسی، دانشگاه فردوسی فردوسی مشهد

2 دانشیار، گروه مکانیک، دانشکده مهندسی، دانشگاه فردوسی مشهد

3 استادیار، دانشکده مهندسی پزشکی، دانشگاه صنعتی امیرکبیر، تهران گروه مهندسی مکانیک، دانشگاه اتاوا

10.22041/ijbme.2011.13139

چکیده

پیچ‌های اورتوپدی ابزار رایجی برای تثبیت استخوان شکسته محسوب می‌شوند. شل شدن پیچ‌ها در اثر نبودن تنش کافی در استخوان مجاور پیچ و جذب استخوان ناشی از آن، یکی از عوامل موفق نبودن ترمیم شکستگی‌ها است. در این مطالعه، پیچ اورتوپدی هدفمند از ماده تیتانیوم و هیدروکسی اپتایت، Ti-Hap، همراه استخوان‌های اسفنجی و متراکم در نرم‌افزار اجزای محدود، مدلسازی شده است. پارامتر انتقال تنش، STPو پارامتر انتقال چگالی انرژی کرنشی، SEDTPتعریف می‌شود که به ترتیب نسبت تنش و نسبت چگالی انرژی کرنشی را در دندانه‌های پیچ به نقاط مجاور در استخوان بیان می‌کنند. مقادیر کم این پارامترها انتقال ضعیف تنش و چگالی انرژی کرنشی را به استخوان مجاور نشان می‌دهد که نشانه‌ای از پدیده مضر سپر تنش است. نتایج این تحقیق نشان داد که مقدار پارامترهای STPو SEDTP، برای پیچ هدفمند در مقایسه با پیچ فلزی، بیشتر است. بعلاوه با کاهش مدول الاستیسیته جزء فلزی و با افزایش جزء حجمی سرامیک، آثار منفی سپر تنش کاهش می‌یابد. برای پیچی که دارای یک قسمت همگن و یک قسمت هدفمند است؛ هر چه طول قسمت هدفمند بیشتر باشد، پارامترها مقدار بزرگتری را نشان می‌دهند. بنابراین اثر سپر تنشی و مقدار شل‌شدگی پیچ کاهش می‌یابد. همچنین هر چه قسمت هدفمند در موقعیتی نزدیک‌تر به دندانه‌های ابتدایی قرار گیرد، مقدار پارامترهای STPو SEDTP، افزایش می‌یابد. به علاوه نتایج نشان داد با کاهش توان ترکیب توزیعی که نشان‌دهندة نحوه تغییر ترکیب هدفمند از فلز به سرامیک است، مقدار پارامترها افزایش می‌یابد. نتایج این تحقیق با مطالعات بالینی و آزمایشگاهی در دسترس، تطابق خوبی دارد.

کلیدواژه‌ها

موضوعات

عنوان مقاله [English]

Analysis of Bone Remodeling around Functionally Graded Orthopedic Screws and Comparison with Metal Screws Using Finite Element Method

نویسندگان [English]

  • Behnoud Haghighi 1
  • Masoud Tahani 2
  • Gholam Reza Rouhi 3

1 M.Sc, Mechanics Group, Faculty of Engineering, Ferdowsi University

2 Associate Professor, Mechanics Group, Faculty of Engineering, Ferdowsi University

3 Assistant Professor , School of Biomedical Engineering , Amirkabir University of Technology Uottawa University, Tehran & Uottawa, Iran & Canada,

چکیده [English]

Orthopedic screws are widely used devices for fixation of bone fractures. Progressive loosening of bone fixation screws, induced by stress shielding and subsequent adaptive bone remodeling, results in bone loss around the screw. A set of two-dimensional finite element models including cortical and cancellous bone with a functionally graded Ti-Hap screw was developed. A dimensionless set of stress-transfer parameters (STP) and strain energy density-transfer parameter (SEDTP) were developed to quantify the screw–bone load sharing. Lower STP and SEDTP values indicate weak stress and strain energy density transfer to bone which is a sign of stress shielding. The results indicated that STP and SEDTP values for FGM screw are higher than those of a fully metal screw. Moreover, reducing elastic modulus of metal fraction and increasing the volume fraction of ceramic decrease the stress shielding. For a partially graded screw (with both homogenous and FGM parts), the longer FGM part is, the greater are STP and SEDTP values. Furthermore, the results showed that decreasing compositional distribution exponent which shows composition change of FGM content from metal fraction toward ceramic fraction, increases the parameters. Results from this study are in admissible agreement with available clinical and experimental study.

کلیدواژه‌ها [English]

  • bone remodeling
  • Compositional distribution exponent
  • finite element method
  • Functionally graded material
  • Orthopedic screw
  • Strain energy density
  • Stress shielding
  • Ti-Hap
[1] Andakhshideh A., Tahani M., Maleki S., Aghdam M.M., Linear and Non-linear Analysis of Functionally Graded Plates Using Generalized Differential Quadrature Method; 2nd ECCOMAS Thematic Conference on the Mechanical Response of Composites. 2009; Imperial College London, UK.
[2] Maleki S., Static Analysis of Functionally Gradede Cylindrical Panel with the GDQ Method; PhD Thesis, 2006;Amir Kabir University of Technology. Tehran, Iran.
[3] Tahani M., Anbarsouz M., "Effect of Functionally Graded Materials on Maximum Stress at the Bone-Implant Interface in Dental Implants; 15th Iranian        Conference of Biomedical Engineering (ICBME2008), 2009.
[4] Watari F., Yokoyama A., Omori M., Hirai T., Kondo H., Uo M., Kawasaki T., Biocompatibility of Materials and Development to Functionally Graded Implant for Bio-Medical Application; Composites Science and Technology, 2004; 64: 893–908.
[5] Lin D., Li Q, Li W., Zhou S., Swain M.V., Design Optimization of Functionally Graded Dental Implant for Bone Remodeling; Composites, 2009; 40: 668-675.
[6] PourAkbar S., Jamilpour N., Rouhi G., Carbon nanotubes in bone tissue engineering; Biomedical Engineering (edited by: Carlos Alexandre Barros de Mello), ISBN: 978-953-307-013-1, INTECH, 2009.
[7] Hedia H.S., "Design of Functionally Graded Dental Implant in the Presence of Cancellous Bone; Wiley InterScience (www.interscience.wiley.com), 2004; DOI: 10.1002/jbm.b.30275.
[8] Pompe W., Gelinsky M., Hofinger I., Knepper-Nicolai B., Functionally Graded Collagen-Hydroxyapatite Aterials for Bone Replacement; Ceramic Transactions, 2001; 114: 65-72.
[9] Gonzalez C.D., Propabilistic Finite Element of Analysis of the Uncemented Total Hip Replacement; PhD Thesis, University of Southampton, Southampton, 2009; England.
[10] Coco S.K., A Mechanical and Histological Study of Functionally Graded Hydroxyapatite Implant Coatings; Master Thesis, University of Tennessee. USA, 2008.
[11] Chu C., Xue X., Zhu J., Yin Z., In Vivo Study on Biocompatibility and Bonding Strength of Ti/Ti–20 vol.% HA/Ti–40 vol.% HA Functionally Graded Biomaterial with Bone Tissues in the Rabbit; Materials Science and Engineering A, 2006; 429: 18–24.
[12] Ye H., Liu X.Y., Hong H., Characterization of Sintered Titanium/Hydroxyapatite Biocomposite using FTIR Spectroscopy; Journal of Materials Science. Materials in Medicine., 2009; 20: 843–850.
[13] Saulo M., Development of Musculoskeletal Models for the Design and the Pre-Clinical Validation of Hip Resurfacing Prosthesis; MS Thesis, University of Bologna, Bologna, 2008; Italy.
[14] Gefen A., Computational Simulations of Stress Shielding and Bone Resorption Around Existing and Computer-Designed Orthopaedic Screws; Medical & Biological Engineering& Computing., 2002; 40: 311–322.
[15] Murin J., Kutiis V., An Effective Solution of the Composite (FGM's) Beam Structures; EngineeringMechanics, 2008; 15(2): 115–132.
[16] Lee J.C., Park J.H., Ryu S.H., Hong H.J., Hyung Riu D., Ahn S.H., Lee C.S., Reduction of Functionally Graded Material Layers for Si3N4-Al2O3 System Using Three-Dimensional Finite Element Modeling; 2008; 49: 829-834.
[17] Gao D.Y., Ogden R.W., Advances in Mechanics and Mathematics; Spirnger, 2003; 2.
[18] Nemat-Alla M., Reduction of thermal stresses by composition optimization of two - dimensional functionally graded materials; Acta Mechanica, 2009; 207:147-161.
[19] Kingery W.D., Bowen H., Uhlmann D.R., Introduction of ceramics; New York: John Wiley & Sons, 1976.
[20] Kerner E.H., The elastic and thermo-elastic properties of composite media;  Proc Phys Soc Lond B, 1956.
[21] Gefen A., Optimizing the Biomechanical Compatibility of Orthopedic Screws for Bone Fracture Fixation; Medical Engineering & Physics, 2002; 24: 337–347.
[22] Haase K., Finite Element Analysis of Orthopaedic Plates and Screws to Reduce the Effects of Stress Shielding; MS Thesis, University of Ottawa, Ottawa, 2010; Canada.
[23] Kido H., Schulz E., Kumar A., Lozada J., Saha S., Implant diameter and bone density: effect on initial stability and pull-out resistance; J Oral Implantol, 1997; 23:163-169.
[24] Wu X., Deng F., Wang Z., Zhihe Z., Wang J., Biomechanical and histomorphometric analyses of the osseointegration of microscrews with different surgical techniques in beagle dogs;  Oral Surg Oral Med Oral Pathol Oral Radiol Endod, 2008;106: 644-650
[25] Skoglund B., Holmertz J., Aspenberg P., Systemic and local ibandronate enhance screw fixation; Journal of Orthopaedic Research, 1996; 22: 1108–1113
[26] Shelton J.C., Loukota R.A., Pull-out strength of screw from cortical bone in maxilla-facial region;  Journal of material science: material medicine, 1996; 7: 231-235.
[27] Kwok A.W.L., Finkelstein J.A., Woodside T., Hearn T.C., Hu R.W., Insertional torque and pull-out strengths of conical and cylindrical pedicle screws in cadaveric bone; Spine, 1996; 21: 2429– 2434.
[28] Chao J., Pena C., Failure analysis of zinc-plated self-drilling screws used to assemble metallic grille panels on a building façade; Engineering Failure Analysis, 2008; 15: 958- 969.
[29] Zhang Q.H., Tan S.H., Chou S.M., Investigation Of Fixation Screw Pull-Out Strength On Human Spine; Journal Of Biomechanics, 2004; 37: 479-485.
[30] Shuib S., Ridzwan M.I.Z., Mohamad Ibrahim M.N.,  Tan C.J., Analysis of Orthopedic Screws for Bone Fracture Fixations with Finite Element Method; Journal of Applied Science, 2007; 7(13):1748-1754.
[31] Chazistergos P., Ferentinos G., Magnissalis E.A., Kourkoulis S.K., Investigation of the Behaviour of the Pedicle Screw – Vertebral Bone Complex, When Subjected to Pure Pull - Out Loads; Internal ANSYS conference, 2006; USA.
[32] Zanetti E.M., Salaorno M., Grasso G., Audenino A.L., Parametric Analysis of Orthopedic Screws in Relation to Bone Density; The Open Medical Informatics Journal, 2009; 3:19-26.
[33] Haase K., Rouhi G., FE analysis of Mechanical Stimuli Transfer Between Orthopaedic Screws and Surrounding Bone: a Possible Method for Predicting Stress Shielding in Relation to Implant Geometry and Material Properties; 16th Biennial Conference for the Canadian Societyof Biomechanics, 2010; Kingston.
[34] Lin C.L., Lin Y.H., Chen A.C.Y., Buttressing angle of the double-plating fixation of a distal radius fracture: a finite element study; Med Bio Eng Comput, 2006; 44: 665–673.
[35] Lin C.L., Lin Y.H., Chang S.H., Multi-Factorial Analysis of Variables Influencing the Bone Loss of an Implant Placed in the Maxilla: Prediction Using FEA and SED Bone Remodeling Algorithm; Journal of Biomechanics, 2010; 43: 644-651.
[36] Huiskes R., Weinans H., Van Rietbergen B., The Relationship Between Stress Shielding and Bone Resorption Around Total Hip Stems and the Effects of Flexible Materials; Clinical Orthopaedics and Related Research, 1992; 274: 124-134.
[37] Huiskes R., Ruinerman R., van Lenthe G.H., Janssen J.D., Effects of Mechanical Forces on Maintenance and Adaptation of Form in Tabecular Bone; Nature, 2000; 405: 704-706.
[38] Vahdati A., Rouhi G., Ghalichi F., Tahani M., Mechanically Induced Trabecular Bone Remodeling Including Cellular Accommodation Effect: a Computer Simulation; Canadian Society for Mechanical Engineering Transactions, 2008; 32 (3-4): 371- 382.
[39] Weinans H., Huiskes R., Grootenboer H.J., The Behavior of Adaptive Bone- Remodeling Simulation-Models; Journal of Biomechanics, 1992; 25 (12): 1425– 1441.
[40] Lin D., Li W., Li Q., Swain M.V., Dental Implant Induced Bone Remodelling and Associated Algorithms; Journal Of The Mechanical Behavior Of Biomedical Materials, 2008; 2: 410–432.
[41] Lin D., Li W., Li Q., Duckmanton N., Swain M., Mandibular Bone Remodeling Induced By Dental Implant; Journal of Biomechanics, 2010; 43(2): 287-293.
[42] Wirtz D.C., Schiffers N., Pandorf T., Radermacher K., Weichert D., Forst R., Critical Evaluation of Known Bone Material Properties to Realize Anisotropic Fe-Simulation of the Proximal Femur; Journal of Biomechanics, 2000; 33: 1325-1330.
[43] Troy K.L., Grabiner M.D., Off-Axis Loads Cause Failure Of The Distal Radius At Lower Magnitudes Than Axial Loads: A Finite Element Analysis; Journal of Biomechanics, 2007; 40(8): 1670-1675.
[44] Miller Z., Fuchs M.B., Arcan M., Trabecular Bone Adaptation With an Orthotropic Material Model; Journal of Biomechanics, 2002; 35: 247–256
[45] Malmqvist J.P., Sennerby L., Clinical Report on the Success of 47 Consecutively Placed Core-Vent Implants Followed from 3 Months to 4 Years; The International Journal of Oral & Maxillofacial Implants,  1990; 5: 53-60.
[46] He G., Xinghua Z., The Numerical Simulation Of Osteophyte Formation On The Edge Of The Vertebral Body Using Quantitative Bone Remodeling Theory; Joint Bone Spine, 2006; 73: 95–101.
[47] Li J., Li H., Shi L., Fok A.S., Ucer C., Devlin H., Horner K., Silikas N., A Mathematical Model For Simulating The Bone Remodeling Process Under Mechanical Stimulus; Dental Materials, 2007; 2:1073–1078.
[48] Van Staden R.C., Guan H., Loo Y.C., Application of Finite Element Method in Dental Implant Research; Comput Methods Biomech Biomed Engin., 2006; 9(4): 257-270.
[49] Collings E.W., The Physical Metallurgy of Titanium Alloys; ASM Series in Metal Processing. Gegel HL, editor, 1984; American Society for Metals, Cleveland, Metals Park, OH, USA.
[50] Kevin L., Ong, Day J.S., Kurtz S.M., Field R.E., Manley M.T., Role of Surgical Position on Interface Stress and Initial Bone Remodeling Stimulus around Hip Resurfacing Arthroplasty; The Journal of Arthroplasty, 2009; 24 (7): 1137-1341.
[51] Duncan R.M., Hanson B.H., The Selection and Use of Titanium; British Standards Institution, Council of Engineering Institutions, Design Council. Oxford University Press for the Design Council, 1980; the British Standards Institution and the Council of Engineering Institutions, 42 pages.
[52] Katoozian H., Davy D.T., Arshi A., Saadati U., Material Optimization of Femoral Component of Total Hip Prosthesis Using Fiber Reinforced Polymeric Composites; Medical Engineering & Physics, 2001; 23(7): 505-511.
[53] Lakes R., Composite Biomaterials; The Biomedical Engineering Handbook: Second Edition. Ed. Joseph D. Bronzino Boca Raton: 2000; CRC Press LLC.
[54] Chenglin C., Jingchuan Z., Zhongda Y., Shidong W., Hydroxyapatite–Ti Functionally Graded Biomaterial Fabricated by Powder Metallurgy; Materials Science and Engineering, 1999; A271: 95–100
[55] Eraslan O., Inanand O., The Effect of Thread Design on Stress Distribution in a Solid Screw Implant: A 3D Finite Element Analysis; Clinical Oral Investigation, 2010; 14: 411–416.
[56] Misch C.E., Dietsh-Misch F., Hoar J., Beck D.G., Hazen R., Misch C.M., A Bone Quality-Based Implant System: First Year Of Prosthetic Loading; Journal of Oral Implantology, 1999; 15(3): 185-197.
[57] Shelton J.C., Loukota R.A., Pull-out strength of screw from cortical bone in maxilla-facial region; Journal of material science: material medicine, 1996; 7: 231-235.
[58] Chu C., Zhu J., Yin Z., Lin P., Structure Optimization and Properties of Hydroxyapatite-Ti Symmetrical Functionally Graded Biomaterial; Materials Science and Engineering, 2001; A316: 205–210.