Design Optimization of a Magnetic Field-Based Localization Device for Enhanced Ventriculostomy

Magnet dipole model. Pm and P_s,i are the position coordinates of, respectively, the magnet and ith sensor with regard to the origin O. U is the magnet's magnetization vector.

Approaches in spatial sensor configuration in bounded 2D space. (a) Rectangular array: the parameters xspacing and yspacing are the spatial spacing between two sensors, and nbs in x and nbs in y are the number of sensors in x and y directions, respectively. (b) Circular pattern: n sensors are equally spaced along a circle defined by the parameters center and radius. (c) GA pattern: Each node in a predefined spatial grid is a possible sensor location.

Flow chart of a GA optimization algorithm and genetic operators used to vary the programing of individuals from one generation to the next: (a) crossover and (b) mutation

Influence of the initial population diversity on the GA convergence and performance. Two different initial populations are tested here for a nine-sensor configuration. The initial populations in (a) has a lower diversity than in (b) and appears to stagnate to a local minimum and results in a higher objective function value.

CT scan-rendered model of the head with fitted ellipsoid shape. The GA-optimized sensor position for a nine-sensor configuration is shown on the ellipsoid mesh. The sensors are oriented so that their Z_s axis is normal to the ellipsoid surface and Y_s axis aligned with the longitude of the mesh. The dots on the mesh represent the spatial position of individual sensors through GA optimization.

Absolute positional estimation error at various distances from the insertion point of the catheter across the trajectory path, in presence of 2.5 μT RMS Gaussian measurement noise

Experimental setup comprising of six-axis robot arm with N52 cylindrical magnet at end-effector and magnetic sensor board affixed onto the worktable

Experimental error comparison at various z displacements along the trajectory points

(a) Experimental setup with the 3D measurement device. (b) Experimental localization. The reference trajectory performed by the robot arm aims at targeting the ventricles (in gray) in the patient's brain.