مدل‌سازی اجزای محدود-بدون ‌مش مبتنی بر موجک در حل مساله پیشرو مقطع‌نگاری القای مغناطیسی

یوسفی نجف‌آبادی, محمدرضا; جعفری, رضا; ابریشمی مقدم, حمید

doi:10.22041/ijbme.2014.13557

نوع مقاله : مقاله کامل پژوهشی

نویسندگان

¹ ﺩﺍﻧﺸﺠﻮی ﺩﻛﺘﺮی، ﮔﺮﻭﻩ ﻣﻬﻨﺪﺳﻰ ﭘﺰﺷﻜﻰ، ﺩﺍﻧﺸﻜﺪﮤ ﻣﻬﻨﺪﺳﻰ ﺑﺮﻕ، ﺩﺍﻧﺸﮕﺎﻩ ﺻﻨﻌﺘﻰ ﺧﻮﺍﺟﻪ ﻧﺼﻴﺮﺍﻟﺪﻳﻦ ﻃﻮﺳﻰ

² ﺍﺳﺘﺎﺩﻳﺎﺭ، ﮔﺮﻭﻩ ﻣﻬﻨﺪﺳﻰ ﭘﺰﺷﻜﻰ، ﺩﺍﻧﺸﻜﺪﮤ ﻣﻬﻨﺪﺳﻰ ﺑﺮﻕ، ﺩﺍﻧﺸﮕﺎﻩ ﺻﻨﻌﺘﻰ ﺧﻮﺍﺟﻪ ﻧﺼﻴﺮﺍﻟﺪﻳﻦ ﻃﻮﺳﻰ

³ ﺍﺳﺘﺎﺩ، ﮔﺮﻭﻩ ﻣﻬﻨﺪﺳﻰ ﭘﺰﺷﻜﻰ، ﺩﺍﻧﺸﻜﺪﮤ ﻣﻬﻨﺪﺳﻰ ﺑﺮﻕ، ﺩﺍﻧﺸﮕﺎﻩ ﺻﻨﻌﺘﻰ ﺧﻮﺍﺟﻪ ﻧﺼﻴﺮﺍﻟﺪﻳﻦ ﻃﻮﺳﻰ

10.22041/ijbme.2014.13557

چکیده

ﺩﺭ ﺍﻳﻦ ﻣﻘﺎﻟﻪ ﺭﻭﺵ ﺍﺟﺰﺍی ﻣﺤﺪﻭﺩ - ﺑﺪﻭﻥ ﻣﺶ ﻣﺒﺘﻨﻰ ﺑﺮ ﻣﻮﺟﮏ ﺑﻪ ﻣﻨﻈﻮﺭ ﺣﻞ ﻣﺴﺄﻟﻪ ﭘﻴﺸﺮﻭ ﻣﻘﻄﻊﻧﮕﺎﺭی ﺍﻟﻘﺎی ﻣﻐﻨﺎﻃﻴﺴﻰ ﺍﺭﺍﺋﻪ ﺷﺪﻩ ﺍﺳﺖ. ﻃﺒﻴﻌﺖ ﺑﺪﻭﻥ ﺗﻤﺎﺱ ﻭ ﺍﻳﻤﻦ ﺍﻳﻦ ﻓﻦ ﺗﺼﻮﻳﺮﺑﺮﺩﺍﺭی، ﺁﻥ ﺭﺍ ﺑﻪ ﺭﻭﺷﻰ ﻣﻨﺎﺳﺐ ﺑﺮﺍی ﺗﺼﻮﻳﺮﺑﺮﺩﺍﺭی ﭘﺰﺷﻜﻰ ﻭ ﺻﻨﻌﺘﻰ ﻏﻴﺮﺗﻬﺎﺟﻤﻰ ﺗﺒﺪﻳﻞ ﻛﺮﺩﻩ ﺍﺳﺖ. ﺩﺭ ﺍﻳﻦ ﺭﻭﺵ ﺍﺑﺘﺪﺍ ﺑﺎ ﻋﺒﻮﺭ ﺟﺮﻳﺎﻧﻰ ﻣﺘﻨﺎﻭﺏ ﺍﺯ ﻳﮏ ﻳﺎ ﭼﻨﺪ ﺳﻴﻢﭘﻴﭻ ﺗﺤﺮﻳﮏ، ﻣﻴﺪﺍﻥ ﻣﻐﻨﺎﻃﻴﺴﻰ ﺗﺤﺮﻳﮏ ﺩﺭﻭﻥ ﺟﺴﻢ ﻣﻮﺭﺩ ﻧﻈﺮ ﺍﻳﺠﺎﺩ ﺷﺪﻩ؛ ﺳﭙﺲ ﻭﻟﺘﺎﮋﻫﺎی ﺍﻟﻘﺎﻳﻰ ﺩﺭ ﺳﻴﻢﭘﻴﭻﻫﺎی ﮔﻴﺮﻧﺪﻩ ﺍﻧﺪﺍﺯﻩﮔﻴﺮی ﻣﻰﺷﻮﻧﺪ. ﺗﺼﻮﻳﺮ ﺑﺎ ﺗﺨﻤﻴﻦ ﺿﺮﺍﻳﺐ ﻫﺪﺍﻳﺖ ﺍﻟﻜﺘﺮﻳﻜﻰ ﺟﺴﻢ ﺑﺎ ﺍﺳﺘﻔﺎﺩﻩ ﺍﺯ ﻧﺘﺎﻳﺞ ﺣﺎﺻﻞ ﺍﺯ ﺍﻧﺪﺍﺯﻩﮔﻴﺮی، ﻧﺘﺎﻳﺞ ﺣﻞ ﻣﺴﺄﻟﻪ ﭘﻴﺸﺮﻭ ﻭ ﺣﻞ ﻣﺴﺄﻟﻪ ﻣﻌﻜﻮﺱ ﺑﺎﺯﺳﺎﺯی ﻣﻰﺷﻮﺩ. ﺷﺒﻴﻪﺳﺎﺯی ﻣﺴﺄﻟﻪ ﭘﻴﺸﺮﻭ ﺑﻪ ﻃﻮﺭ ﻣﻌﻤﻮﻝ ﺑﺎ ﺭﻭﺵ ﺍﺟﺰﺍی ﻣﺤﺪﻭﺩ ﺍﻧﺠﺎﻡ ﻣﻰﺷﻮﺩ؛ ﺍﻣﺎ ﻭﺍﺑﺴﺘﮕﻰ ﺟﻮﺍﺏ ﺣﺎﺻﻞ ﺑﻪ ﻣﺶ ﻣﻮﺭﺩ ﺍﺳﺘﻔﺎﺩﻩ، ﺑﻮﻳﮋﻩ ﻭﻗﺘﻰ ﻛﻪ ﻧﺎﺣﻴﻪ ﻫﺪﻑ ﺷﺎﻣﻞ ﺍﺟﺴﺎﻡ ﻣﺘﺤﺮک ﺑﺎﺷﺪ، ﻣﺤﺪﻭﺩﻳﺘﻰ ﺑﺮﺍی ﺭﻭﺵ ﺍﺟﺰﺍی ﻣﺤﺪﻭﺩ ﻣﺤﺴﻮﺏ ﻣﻰﺷﻮﺩ. ﺩﺭ ﺍﻳﻦ ﺗﺤﻘﻴﻖ، ﺑﻪ ﻣﻨﻈﻮﺭ ﺭﻓﻊ ﻣﺸﻜﻞ ﻭﺍﺑﺴﺘﮕﻰ ﺑﻪ ﻣﺶﺑﻨﺪی ﺩﺭ ﺭﻭﺵ ﺍﺟﺰﺍی ﻣﺤﺪﻭﺩ ﻭ ﺍﻋﻤﺎﻝ ﺩﻗﻴﻖﺗﺮ ﻭ ﺳﺮﻳﻊﺗﺮ ﺷﺮﺍﻳﻂ ﻣﺮﺯی ﺩﺭ ﺭﻭﺵ ﺑﺪﻭﻥ ﻣﺶ، ﺭﻭﺵ ﺗﺮﻛﻴﺒﻰ ﺍﺟﺰﺍی ﻣﺤﺪﻭﺩ - ﺑﺪﻭﻥ ﻣﺶ ﻣﺒﺘﻨﻰ ﺑﺮ ﻣﻮﺟﮏ ﺑﺮﺍی ﺣﻞ ﻣﺴﺄﻟﻪ ﭘﻴﺸﺮﻭ ﻣﻘﻄﻊﻧﮕﺎﺭی ﺍﻟﻘﺎی ﻣﻐﻨﺎﻃﻴﺴﻰ ﭘﻴﺸﻨﻬﺎﺩ ﻣﻰﺷﻮﺩ. ﻫﻤﭽﻨﻴﻦ ﺑﺮﺍی ﺍﻋﻤﺎﻝ ﺷﺮﺍﻳﻂ ﭘﻴﻮﺳﺘﮕﻰ ﺣﺪ ﻓﺎﺻﻞ ﺑﻴﻦ ﺩﻭ ﻧﺎﺣﻴﻪ ﺍﺟﺰﺍی ﻣﺤﺪﻭﺩ ﻭ ﺑﺪﻭﻥ ﻣﺶ، ﺗﻮﺍﺑﻊ ﭘﺮﺵ ﺷﻴﺐ ﺑﻪ ﻛﺎﺭ ﮔﺮﻓﺘﻪ ﺷﺪﻩﺍﻧﺪ. ﺑﺮﺍی ﺍﺭﺯﻳﺎﺑﻰ ﻛﺎﺭﺍﻳﻰ ﺭﻭﺵ ﭘﻴﺸﻨﻬﺎﺩی، ﻧﺘﺎﻳﺞ ﺷﺒﻴﻪﺳﺎﺯی ﺑﺎ ﻧﺘﺎﻳﺞ ﺑﺪﺳﺖ ﺁﻣﺪﻩ ﺍﺯ ﺭﻭﺵ ﺍﺟﺰﺍی ﻣﺤﺪﻭﺩ ﻣﻌﻤﻮﻝ ﺍﺯ ﻟﺤﺎﻅ ﺩﻗﺖ ﻭ ﺯﻣﺎﻥ ﻣﺤﺎﺳﺒﺎﺕ ﻣﻘﺎﻳﺴﻪ ﺷﺪﻩﺍﻧﺪ.

کلیدواژه‌ها

موضوعات

عنوان مقاله [English]

A Combined Wavelet Based Mesh Free-Finite Element Method for Solving the Forward Problem in Magnetic Induction Tomography

نویسندگان [English]

Mohammad Reza Yousefi ¹
Reza Jafari ²
Hamid Abrishami Moghaddam ³

¹ Ph.D. Student, Faculty of Electrical Engineering, K. N. Toosi University of Technology

² Assistant Professor, Faculty of Electrical Engineering, K. N. Toosi University of Technology

³ Professor, Faculty of Electrical Engineering, K. N. Toosi University of Technology

چکیده [English]

In this paper, a combined wavelet based mesh free method has been presented to solve the forward problem in magnetic induction tomography (MIT). Being a non-contact safe imaging technique, MIT has been an appropriate method for noninvasive industrial and medical imaging. In this imaging method, a primary magnetic field is applied by one or more excitation coils to induce eddy currents in the material to be studied, and then the secondary magnetic field from these eddy currents is detected in sensing coils. Image reconstruction is obtained from estimated electric conductivity coefficients by using measurement data and solutions of forward and inverse problems. In general, the forward problem is solved using finite element method (FEM) with acceptable accuracy but in problems involving moving objects or objects with changing geometrical appearance, mesh distortion is inevitable and susceptible to producing error in numerical results. Since the solution of the FEM depends on the mesh shape and boundary condition constraints are difficult to be applied to the mesh free method, in this paper, the combined wavelet based mesh free approach is suggested to resolve the disadvantages of both methods in the MIT forward problem. In order to apply interface conditions between the two finite element and mesh free sub-domains, slope jump functions are entered to the set of basis functions. The simulation results obtained by the proposed method are compared with the FEM in terms of accuracy and computational cost.

کلیدواژه‌ها [English]

Magnetic induction tomography
combined wavelet based mesh free-finite element method
wavelet-Galerkin method
forward problem
wavelet method

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نشریه‌ی علمی مهندسی پزشکی زیستی

مدل‌سازی اجزای محدود-بدون ‌مش مبتنی بر موجک در حل مساله پیشرو مقطع‌نگاری القای مغناطیسی

مراجع

مراجع

دوره 8، شماره 1 - شماره پیاپی 1
فروردین 1393
صفحه 69-86

مدل‌سازی اجزای محدود-بدون ‌مش مبتنی بر موجک در حل مساله پیشرو مقطع‌نگاری القای مغناطیسی

مراجع

مراجع

دوره 8، شماره 1 - شماره پیاپی 1فروردین 1393صفحه 69-86

دوره 8، شماره 1 - شماره پیاپی 1
فروردین 1393
صفحه 69-86