Determination of converge parameters for Monte Carlo experiments in the simulation of the failure of bone tissue

Abstract

The Monte Carlo method is widely used in the field of biomechanics to study the variability of diverse parameters, like tissues properties, magnitude and direction of loads, kinematic of joints, among others. In particular, the failure of bone tissue, which is the target of this investigation, has been extensively studied; however, it is common to find in the literature realizations of Monte Carlo experiments with arbitrary sample size, or with a convergence criterion for which a statistically valid confidence level, or interval, is not defined. These strategies lead to results with presumed low, but unknown uncertainty. One option to address this problem is the acceptable shifting convergence band rule which, if appropriately configured and applied, serves as a convergence criterion with an implicit confidence level. However, in order to ensure a desired confidence level, it is necessary to determine the correct parameters for the method. As the typical biomechanical simulation is very time consuming, it is not advisable to calculate these parameters with the full model. Therefore, it is recommended to run a Monte Carlo experiment with a simpler, faster to simulate, model that is probabilistically similar to the full model. In this work, a pilot experiment is developed in order to compute the parameters required to stop the Monte Carlo simulation of the failure of bone tissue, with a desired confidence level. Two different failure criteria are applied, one with two and the other with three input probabilistic variables. Also, the variation of the convergence parameter with the desired precision of the mean is explored. Results led to determine suitable parameters for the different combinations of desired confidence level, precision of the mean and failure criterion. It was also found that when three input variables were involved, or when a three significant digits precision of the mean was required, the number of trials needed to attain convergence was greater than when two inputs variables were involved or when two significant digits precision was required.