Finite element modelling tibia bone vibration – the influence of shape, twist, and end scale

The percussion response of long bone has the potential to be used as a measure of bone strength for Osteoporosis detection. Modelling the vibration response requires describing the shape of the long bone which can have several features. An overly simplistic model of the shape does not give enough insight into their influence on the vibration response. This paper identifies the key features of the shape of a tibia and femur bone (cross-sectional shape, twist, and scale of the ends) and investigates their individual effects on the eigenfrequencies using finite element modelling. A femur and tibia model are dissected at the thicker ends and length adjusted to isolate the influence of the proximal and distal ends on the eigenfrequencies. Selected cross-sectional shapes are investigated to simplify the modelling and compared to real bone cross-sections and results. The twist is added across the longitudinal axis of the model producing an inline twist to the cross-section and resulting in a 1.5–2.5% decrease in frequencies per 20° of twist. The scale of the cross-sections at the ends of the model are increased along a set length of the bone to emulate the larger proximal and distal end of the long bones. The results show that any model for the vibro-acoustic response of long bones needs to include asymmetry in the cross-section as well as the scaling of the ends.