Bovine bone natural frequencies evaluation by using transfer matrix method based upon DICOM images

This study presents the use of the transfer matrix method to calculate the natural frequencies for bovine bone. The bovine bone was considered as continues system. This continues system was transferred to discrete system by discretizing it using the Digital Imaging and Communications in Medicine (DICOM) images obtained from CT-Scan test. Those images were used to evaluate the geometrical properties of the bone segments. Geometrical properties variation along the bone length were evaluated by using image-processing technique (Binary Image). Each slice was considered as beam and the total number of beam segments is equal to the number of DICOM images. The bone was divided into 226 segments (1.25 mm slice thickness). Euler Bernoulli equation of motion was used to formulate the transfer matrix. Finite elements method based on ANSYS mechanical APDL version 14.5 was used to calculate the natural frequency. This method was used to check the discrepancy of the results obtained from the transfer matrix method. This method was done by building the three dimensional modal based upon the DICOME images and solving the modal analysis by using ANSYS software. The deviation in the results obtained from the two methods was less than 15%. The simplicity and efficiency of transfer matrix method recommends further improvement by using the gray images instead of binary images to evaluate bone geometrical, physical, and mechanical properties based upon the grayscale value of each pixel for both cortical and compact bone.