Abstract: Determination of Unknown Biomechanical Parameters of a Screw-vertebra MBS Model

Abstract

In this study, we show that parameters for which values are not known a priori can be determined with sufficient accuracy using a multibody simulation (MBS) model. We propose a sensitivity analysis method that allows us to approximate these unknown parameters without the need for long simulation times. Furthermore, this method allows the MBS model to be optimized to a high degree using an iterative process. The sensitivity analysis method is applied to a simplified screw-vertebra model, consisting of an anterior anchor implant screw and vertebral body of C4. The main focus is on determining stiffness (c) and damping (d) characteristics to analyze the interaction between the implant anchor screw and the vertebral body. In the two-stage algorithm, we aim to find a tuple of the minimum stiffness and damping coefficients from the predefined values so that the maximum screw translation and the maximum screw velocity are constrained by the selected thresholds when the pullout force is applied to the cervical screw. In addition, we analyze when the static equilibrium state of the model is reached in each iteration. The proposed parameter determination is performed in two phases. In the first step, two initial sets of parameters, one set for c-values and one containing d-values, were collected. Then, for each pair of parameter values, the model simulation is executed, and the final search intervals for both parameters are determined. In the final step, a binary search is used to minimize the parameters. The optimal model parameters for the MBS model are determined to be c = 823224N/m for stiffness and d = 488Ns/m for damping. The presented method of parameter identification can be used in studies including more complex MBS spine models or to set initial parameter values that are not available as initial values for FE models [1].