Nonparametric bootstrap technique for calibrating surgical SmartForceps: theory and application

Knowledge of forces, exerted on the brain tissue during the performance of neurosurgical tasks, is critical for quality assurance, case rehearsal, and training purposes. Quantifying the interaction forces has been made possible by developing SmartForceps, a bipolar forceps retrofitted by a set of strain gauges. The forces are estimated using voltages read from strain gauges. We therefore need to quantify the force-voltage relationship to estimate the interaction forces during microsurgery. This problem has been addressed in the literature by following the physical and deterministic properties of the force-sensing strain gauges without obtaining the precision associated with each estimate. In this paper, we employ a probabilistic methodology by using a nonparametric Bootstrap approach to obtain both point and interval estimates of the applied forces at the tool tips, while the precision associated with each estimate is provided. To show proof-of-concept, the Bootstrap technique is employed to estimate unknown forces, and construct necessary confidence intervals using observed voltages in data sets that are measured from the performance of surgical tasks on a cadaveric brain. Results indicate that the Bootstrap technique is capable of estimating tool-tissue interaction forces with acceptable level of accuracy compared to the linear regression technique under the normality assumption.