Generalized Approach for Modeling Minimally Invasive Surgery as a Stochastic Process Using a Discrete Markov Model

Abstract

Minimally invasive surgery (MIS) involves a multidimensional series of tasks requiring a synthesis between visual information and the kinematics and dynamics of the surgical tools. Analysis of these sources of information is a key step in defining objective criteria for characterizing surgical performance. The Blue DRAGON is a new system for acquiring the kinematics and the dynamics of two endoscopic tools synchronized with the endoscopic view of the surgical scene. Modeling the process of MIS using a finite state model [Markov model (MM)] reveals the internal structure of the surgical task and is utilized as one of the key steps in objectively assessing surgical performance. The experimental protocol includes tying an intracorporeal knot in a MIS setup performed on an animal model (pig) by 30 surgeons at different levels of training including expert surgeons. An objective learning curve was defined based on measuring quantitative statistical distance (similarity) between MM of experts and MM of residents at different levels of training. The objective learning curve was similar to that of the subjective performance analysis. The MM proved to be a powerful and compact mathematical model for decomposing a complex task such as laparoscopic suturing. Systems like surgical robots or virtual reality simulators in which the kinematics and the dynamics of the surgical tool are inherently measured may benefit from incorporation of the proposed methodology.