Expansion of stereotactic work envelope using transformation matrices and geometric algebra for neurosurgery

Abstract

Stereotactic systems have traditionally used Cartesian coordinate combined with linear algebraic mathematical models to navigate the brain. Previously, the development of a novel stereotactic system allowed for improved patient comfort, reduced size, and carried through a simplified interface for surgeons. The system was designed with a work envelope and trajectory range optimized for deep brain stimulation applications only. However, it could be applied in multiple realms of neurosurgery by spanning the entire brain. To this end, a system of translational and rotational adapters was developed to allow total brain navigation capabilities. Adapters were designed to fit onto a Skull Anchor Key of a stereotactic frame system to allow for rotation and translation of the work envelope. Mathematical formulas for the rotations and translations associated with each adapter were developed. Mechanical and image-guided accuracies were examined using a ground truth imaging phantom. The system's clinical workflow and its ability to reliably and accurately be used in a surgical scenario were investigated using a cadaver head and computed tomography guidance. Eight adapters designed and 3D-printed allowed the work envelope to be expanded to the entire head. The mechanical error was 1.75 +/- 0.09 mm (n = 20 targets), and the cadaver surgical targeting error was 1.18 +/- 0.28 mm (n = 10 implantations). The novel application of conventional and geometric algebra in conjunction with hardware modifications significantly expands the work envelope of the stereotactic system to the entire cranial cavity. This approach greatly extends the clinical applications by the system.