Towards a probabilistic approach for quantifying uncertainty in robot soft tissue indentation via computational biomechanics models

In surgical robot simulation and motion planning a forward (or predictive) model is critical. This paper considers an initial approach to estimate the effect of the variation of parameters on the overall statistical distribution for the total strain and stress as predicted by a non-linear biomechanical model. This considers the statistical distribution, as compared to a single mean value, of the predicted variables. For example, if the material were an ideal a Hookean spring (i.e., F = kx), then Gaussian variations in force (F ∼ N (μ_F , σ_F² )) and material stiffness (k ∼ N (μ_k, σ_k² )) would give a Ratio distribution in displacement x (i.e., the distribution formed from the ratio of two Gaussians). In order to evaluate the case when the material properties are non-linear, such as those for brain tissue, this paper explores an empirical approach based around a sequence of multiple cases where the strain was determined via FEA. When assuming an Ogden hyperelastic constitutive model, results show a Normal variation of displacement for Normal varying moduli, but a Bimodal distribution of displacement for Normal varying forces.