Directional Tissue Stiffness Deflects Symmetric Rotating Magnetic Microdrillers: A Verified Model and Field-Tilt Compensation Strategy

Needle-steering literature is well developed for deflection caused by an asymmetric bevel tip, but this mechanism does not apply to symmetric, rotating actuators such as magnetically-driven auger microdrillers. White matter is mechanically anisotropic — stiffer along fiber tracts than across them — raising a distinct question that does not appear to have been previously addressed: does directional tissue stiffness alone deflect a symmetric rotating tip, independent of its shape? We model the tip as a small cavity expanding into a transversely-isotropic incompressible neo-Hookean solid, verify the isotropic limit against the classical Gent-Lindley cavitation result, and show the resulting lateral force vanishes exactly along and across the fiber axis and peaks at 45°, as symmetry requires. Using published anisotropy measurements (15% via in vivo MRE, up to ~3× via ex vivo tensile testing) and real photoresist material data for the drilling shaft, we find the shaft's own bending stiffness dominates over magnetic realignment torque by two to three orders of magnitude, limiting predicted deflection to 0.24–4.72° of tip tilt. We then derive and verify a compensation strategy: pre-tilting the driving field's rotation axis by an angle numerically equal to the uncompensated deflection, in the opposite direction, drives the net predicted trajectory error to zero in the linearized model. This compensation law can be driven by pre-operative diffusion tensor imaging (DTI), an established clinical technique for mapping fiber orientation. Simulating a curving fiber path under realistic DTI angular measurement uncertainty (6–11°, from published validation studies), the compensation strategy remains effective, removing 91–95% of trajectory drift despite imperfect, real-world imaging information.