Calibration of surgical tools using multilevel modeling with LINEX loss function: Theory and experiment

Quantifying the tool-tissue interaction forces in surgery can be used in the training process of novice surgeons to help them better handle surgical tools and avoid exerting excessive forces. A significant challenge concerns the development of proper statistical learning techniques to model the relationship between the true force exerted on the tissue and several outputs read from sensors mounted on the surgical tools. We propose a nonparametric bootstrap technique and a Bayesian multilevel modeling methodology to estimate the true forces. We use the linear exponential loss function to asymmetrically penalize the over and underestimation of the applied forces to the tissue. We incorporate the direction of the force as a group factor in our analysis. A weighted approach is used to account for the nonhomogeneity of read voltages from the surgical tool. Our proposed Bayesian multilevel models provide estimates that are more accurate than those under the maximum likelihood and restricted maximum likelihood approaches. Moreover, confidence bounds are much narrower and the biases and root mean squared errors are significantly smaller in our multilevel models with the linear exponential loss function.