بررسی تاثیر ناهمگنی استخوان تیبیا بر فرکانس طبیعی به کمک تست مودال و مدل‌سازی اجزا‌‌‌‌ی محدود

نوع مقاله : مقاله پژوهشی

نویسندگان

1 دانشکده مهندسی مکانیک، دانشگاه تهران، تهران، ایران

2 دانشکده مهندسی مکانیک، دانشگاه تهران، تهران، ایران عضو مرکز مطالعات ارتوپدی پیشرفته، دانشکده پزشکی هاروارد، بوستون، ماساچوست،

چکیده

فرکانس‌های طبیعی و شکل مودهای استخوان به طور گسترده در تشخیص بهبود شکستگی استخوان، بازسازی مجدد استخوان، تشخیص پوکی استخوان و برهم‌ کنش ایمپلنت و استخوان مورد استفاده قرار می‌گیرد. این مشخصه‌ها را می‌توان با استفاده از تحلیل‌های عددی و مدل‌سازی اجزای محدود تخمین زده و با تست مودال نمونه‌های آزمایشگاهی اندازه‌گیری و صحه‌گذاری نمود. ناهمگنی استخوان در مدل‌های اجزای محدود بر فرکانس‌ طبیعی آن تاثیر می‌گذارد. در این تحقیق تاثیر ناهمگنی استخوان و روابط چگالی-الاستیسیته بر فرکانس‌ طبیعی استخوان و دقت تخمین آنها بررسی شده است. یک استخوان تیبیا گاوی تهیه و مورد تست مودال قرار گرفت. نتایج تجربی تست مودال با نتایج مدل اجزای محدود سه بعدی ایجاد شده از روی تصاویر سی تی اسکن استخوان، مقایسه گردید. ناهمگنی بر مبنای روابط چگالی-الاستیسیته پیشنهادی به صورت المان به المان (پیوسته) و به صورت ناحیه‌ای بر مبنای یک تلرانس (گسسته) در مدل اعمال شد. مقایسه نتایج مدل‌های ناهمگن با نتایج تجربی نشان می‌دهد که تفاوت بسیار کمی بین فرکانس‌های طبیعی مدل‌های ناهمگن گسسته و پیوسته وجود دارد. بطوریکه برای پنج فرکانس اول، یک مدل ناهمگن گسسته با 20 ناحیه، می‌تواند فرکانس‌های طبیعی را با خطای کمتر از 2درصد و صرف هزینه و زمان کمتر پیش بینی نماید.

کلیدواژه‌ها

موضوعات

عنوان مقاله [English]

Investigating the Effect of Tibia Bone Heterogeneity on Natural Frequency Using Modal Test and Finite Element Modeling

نویسندگان [English]

  • Hamid Dehghan Tarzjani 1
  • Mohammad Ali Nazari 1
  • Mohammad Mahjoob 2
1 Faculty of Mechanical Engineering, University of Tehran, Tehran, Iran
2 professor, Faculty of Mechanical Engineering, University of Tehran,, Tehran,, Iran Member, of Center for Advanced Orthopedic Studies, Harvard Medical School, Boston,, Massachusetts,, USA
چکیده [English]

The natural frequencies and mode shapes of bone are widely used in the diagnosis of bone fracture healing, bone remodeling, osteoporosis diagnosis, and implant-bone interaction. These characteristics can be estimated using numerical analysis and finite element modeling and measured and validated by modal testing of laboratory samples. Bone heterogeneity in finite element models affects its natural frequency. In this research, the effect of bone heterogeneity and density-elasticity relationships on the natural frequency of bone and the accuracy of their estimation have been investigated. A cow tibia bone was prepared and subjected to modal test. The experimental results of the modal test were compared with the results of the 3D finite element model created from the bone CT scan images. Inhomogeneity based on the proposed density-elasticity relationships was applied element by element (continuous) and regionally based on a tolerance (discrete) in the model. Comparing the results of heterogeneous models with experimental results shows that there is very little difference between the natural frequencies of discrete and continuous heterogeneous models. So, for the first five frequencies, a discrete heterogeneous model with 20 regions can predict the natural frequencies with an error of less than 2% with less cost and shorter time.

کلیدواژه‌ها [English]

  • Natural Frequency
  • Mode Shapes
  • Tibia Bone
  • Bone Heterogeneity
  • Modal Test
  • Finite Elements

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