An exponential law for stretching–relaxation properties of bone piezovoltages

An exponential law is presented for modeling piezoelectric behavior of bone tissues. The law is established based on experimental observation and existing empirical decay function. The model is then used to investigate the relaxation behavior of pizeovoltages induced by external load. Piezovoltages between the two opposing surfaces of bovine tibia bone samples under three point bending deformation are measured using an ultra high input impedance bioamplifier. The experimental results indicate that the pizeovoltages of bone show different relaxation behaviors during loading and unloading process. It is found that the piezovoltage decay follows a stretched exponential law when the load increases from zero to its maximum value, while it follows a typical relaxation exponential law when the load is kept its maximum value. The stretching-exponential behavior is independent of loading amplitude and rate. One possible reason for causing the stretched exponential behavior may be due to the triple helices structure of collagen fibrils distributed randomly in bone, which can experience relatively large deformation under external loads. The deformation process may include self-deformation and relative slipping between the molecule chains. The relative slipping movements may change the dielectric constants and resistances of bone, which can lead to multiple relaxation time behaviors during the deformation process of bone.