A chance-constrained programming approach to preoperative planning of robotic cardiac surgery under task-level uncertainty

Authors

Hamidreza Azimian, Hospital for Sick Children University of Toronto
Michael D. Naish, The University of Western OntarioFollow
Bob Kiaii, The University of Western Ontario
Rajni V. Patel, Lawson Health Research Institute

Document Type

Article

Publication Date

3-1-2015

Volume

19

Issue

2

Journal

IEEE Journal of Biomedical and Health Informatics

First Page

612

URL with Digital Object Identifier

10.1109/JBHI.2014.2315798

Last Page

622

Abstract

In this paper, a novel formulation for robust surgical planning of robotics-assisted minimally invasive cardiac surgery based on patient-specific preoperative images is proposed. In this context, robustness is quantified in terms of the likelihood of intraoperative collisions and of joint limit violations. The proposed approach provides a more accurate and complete formulation than existing deterministic approaches in addressing uncertainty at the task level. Moreover, it is demonstrated that the dexterity of robotic arms can be quantified as a cross-entropy term. The resulting planning problem is rendered as a chance-constrained entropy maximization problem seeking a plan with the least susceptibility toward uncertainty at the task level, while maximizing the dexterity (cross-entropy term). By such treatment of uncertainty at the task level, spatial uncertainty pertaining to mismatches between the patient-specific anatomical model and that of the actual intraoperative situation is also indirectly addressed. As a solution method, the unscented transform is adopted to efficiently transform the resulting chance-constrained entropy maximization problem into a constrained nonlinear program without resorting to computationally expensive particle-based methods.