End Flexibility Incorporated Into a Model of a Vibrating Human Tibia for Non-Invasive Test of Bone Properties

An appropriate mathematical model of the physical system must be the basis for dynamic testing. A biological vibration response technique, Mechanical Response Tissue Analysis, has shown promise in tests of human ulnas and monkey tibias, for which firm support at the ends of the bones is easily achieved. For the human tibia, however, a greater amount of soft tissue surrounding the proximal and distal bone prominences makes firm support difficult or impossible to achieve in many subjects. An earlier mathematical model (assuming simply-supported boundary conditions) was expanded to incorporate concentrated mass, stiffness, and damping elements at one or both ends of the tibia. A curve-fitting parameter optimization algorithm was developed to fit the complex frequency response curves by varying the model parameters.