Real-Time Biomechanical Digital Twin for Intraoperative Brain-Shift Compensation: Microsecond Kinematic Spectral Invariants versus High-Order Deformable Registration in BraTS-Reg22

Intraoperative soft-tissue deformation (brain-shift) during craniotomies introduces spatial discrepancies of 5 to over 25 mm between preoperative neuroimaging and dynamic surgical reality, severely undermining the navigation accuracy required for safe glioblastoma resection. Limitations of Existing Methods Classical non-rigid registration methods, such as symmetric diffeomorphic normalization (SyN) with high-order B-splines, solve dense volume partial differential equations over millions of voxels. However, their execution latency—spanning 5 to 14 minutes per multimodal pair, even on high-performance multi-core workstations—prohibits closed-loop surgical navigation, forcing clinicians to operate against outdated phantom anatomies. Proposed Method: Discrete Biomechanical Digital Twin Here, we present a discrete biomechanical digital twin that resolves the continuous 3D parenchymal deformation field in 261.7 microseconds on standard edge central processing units. The architecture decouples preoperative structural geometry from intraoperative constraint enforcement by precomputing the resolvent of a discrete Laplace-Beltrami operator on a tetrahedral manifold. During surgery, newly acquired sparse boundary displacements are projected into the parenchymal interior via low-rank Sherman-Morrison-Woodbury updates, while local finite strain tensors are governed by unit dual-quaternion Lie algebra geodesics to prevent non-physical volumetric locking. Clinical Validation and Quantitative Results Validated against the clinical MICCAI BraTS-Reg22 benchmark across 140 neuro-oncological subjects, the digital twin achieves an out-of-sample Target Registration Error (TRE) of 3.47 ± 1.90 mm under strict Leave-One-Out Cross-Validation (LOOCV). This significantly outperforms: Unregularized Thin Plate Splines: 4.83 ± 2.83 mm. Rigid alignment: 3.82 ± 2.20 mm. Furthermore, the proposed method restricts maximum peak error to 11.17 mm, compared to 27.60 mm in SyNQuick and 22.43 mm in full SyN, while achieving a multi-million-fold computational speedup (over 1,500,000× to 2,740,000×). Clinical Implications This sub-millisecond computational throughput enables true 3,800 Hz augmented-reality margin tracking and heads-up intraoperative guidance, opening the possibility of real-time, closed-loop surgical navigation based on continuously updated patient-specific anatomical models.