Prediction of elasticity constants in small biomaterial samples such as bone. A comparison between classical optimization techniques and identification with artificial neural networks

Measuring the elasticity constants of biological materials often sets important constraints, such as the limited size or the irregular geometry of the samples. In this paper, the identification approach as applied to the specific problem of accurately retrieving the material properties of small bone samples from a measured displacement field is discussed. The identification procedure can be formulated as an optimization problem with the goal of minimizing the difference between computed and measured displacements by searching for an appropriate set of material parameters using dedicated algorithms. Alternatively, the backcalculation of the material properties from displacement maps can be implemented using artificial neural networks. In a practical situation, however, measurement errors strongly affect the identification results, calling for robust optimization approaches in order accurately to retrieve the material properties from error-polluted sample deformation maps. Using a simple model problem, the performances of both classical and neural network driven optimization are compared. When performed before the collection of experimental data, this evaluation can be very helpful in pinpointing potential problems with the envisaged experiments such as the need for a sufficient signal-to-noise ratio, particularly important when working with small tissue samples such as specimens cut from rodent bones or single bone trabeculae.