STUDY OF THE VIBRATIONAL BEHAVIOR OF A HEALING TIBIA USING FINITE-ELEMENT MODELING

Two finite element models of a fractured tibia with healing callus wer e developed. In the first model, the callus was modelled at the middle of the diaphysis, while in the second one the callus was located at t wo-thirds of the length, distal from the knee. From these two models t he static torsional stiffness as well as the resonant frequencies and mode shapes of the first four vibration modes were calculated for a se ries of increasing values of Young's modulus of the callus. Two situat ions were considered. In the first situation, the geometry of the call us was kept constant, while in the second, the dimensions of the callu s were reduced while its Young's modulus was increased. The resonant f requencies were found to increase with increasing stiffness of the cal lus. The single bending modes were found to be more sensitive when the callus was at the middle of the diaphysis, whereas the double bending modes were more sensitive when the callus was situated distally. Mode shapes were similar to those for the intact tibia when the stiffness of the callus was 5% of the stiffness of the intact bone or higher. A basically linear relation was found between the torsional stiffness an d the resonant frequencies. A theoretical relation between resonant fr equencies and torsional stiffness was evaluated and found to be valid if the Young's modulus of the callus was equal to or greater than 5% o f the Young's modulus of the intact bone. The present results support the quantitative interpretation of vibration analysis measurements for the assessment of tibial fracture healing. Copyright (C) 1996 Elsevie r Science Ltd.