Abstract

Stereotactic neurosurgery requires careful a priori design and planning of cannula trajectories. Typically, an entry point on the skullcap is determined from which the target region inside the brain is approached on a straight line. Here, we focus on a novel approach to mitigate negative side effects due to the penetration of brain tissue. To this end, we propose the usage of a cannula that is composed of several pre-curved nickel-titanium tubes with decreasing diameter such that their construction allows for intertwining. Such actively deformable cannulas give raise to an infinite number of possible tube trajectories for which surgery planning, supported by mathematical optimization, is inevitable.

We model the design and planning problem as a constrained optimization problem. The optimization variables can be partitioned into design and control variables. Our approach is to use model-based optimization, more concretely, gradient-based nonlinear optimization techniques implemented in the software package WORHP. The optimal control problem is discretized by transcription methods. Medical and technical constraints are added to the problem.