Optimized fiducial marker placement using B-spline surface modeling and graph theory for Cyberknife stereotactic body radiotherapy for superficial tumors

Abstract

CyberKnife, an established noninvasive stereotactic radiotherapy technology, has been extensively utilized to treat various malignancies because of its high precision and conformal dose delivery. The success of CyberKnife treatment is crucially dependent on optimal fiducial marker placement. This study introduces a novel fiducial marker placement planning algorithm tailored for superficial tumors, which are located 20–50 mm beneath the epidermis. A retrospective analysis was performed on the data collected from three patients with thymus, breast, and submandibular gland tumors. This algorithm generated potential implantation sites by constructing and optimizing a B-spline surface around the tumor. Candidate points were filtered using multi-criteria constraints: (1) a minimum of 18-mm inter-marker distance, (2) angular separation >30°, and (3) nonoverlapping visibility in 45° oblique digital reconstructed radiographs. To enhance the computational efficiency, a kd-tree spatial indexing structure was integrated with graph theory, specifically the Bron–Kerbosch algorithm for maximal clique detection. The proposed method achieved a time complexity of O(mlogm + m² + 3^{\frac{\text{n}}{3}}), demonstrating a significant improvement over the brute-force O(n³) approach. The experimental results showed that our algorithm could efficiently plan fiducial marker placement, thereby simplifying the planning process and providing valuable technical support for CyberKnife treatments.

Keywords

Fiducial Marker Placement / CyberKnife / Stereotactic Body Radiotherapy / Superficial Tumor

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2025 The Author(s). Precision Radiation Oncology published by John Wiley & Sons Australia, Ltd on behalf of Shandong Cancer Hospital & Institute.