Towards collision detection in foot and ankle deformity correction using parallel external fixator: A novel analytical approach

• Published in: Applied mathematical modelling 2022-12, Vol.112, p.324-340
• Main Authors: Zuo, Shiping, Li, Jianfeng, Dong, Mingjie, Tao, Chunjing, Jiao, Ran, Li, Guotong
• Format: Article
• Language: English
• Subjects: Collision detection; Correction path; Foot and ankle deformity correction; Parallel external fixator
• ISSN: 0307-904X
• DOI: 10.1016/j.apm.2022.07.039

•A mathematical model-based analytical approach is proposed for collision detection in foot and ankle deformity correction.•Basic mathematical functions are used to reproduce the contours of bone cross-section, soft tissue, and distraction rods.•Algorithms are proposed for bone cross-section and soft tissue-distraction rod collisions by judging the spatial relations.•Adjustment strategy is provided to resolve algorithm anomalies and obtain the final correction path and assembly positions.•The effectiveness and applicability of the proposed approach and algorithms are verified via a clinical case simulation. Gradual correction using external fixator has been advocated as a minimally invasive solution for limb deformity and is widely used in the clinic. This treatment manner requires a long-term distraction process, which is guided by a preplanned correction path. However, bone cross-section (BCS) collision and soft tissue (ST)-distraction rod (DR) collision may occur on the path and then affect the continuity of the process. Thus, collision detection should be carried out before performing distraction. Existing detection solutions do not simultaneously consider these two types of collisions, and primarily target long-bone deformity. To solve these issues, taking more complex foot and ankle deformity as the research object, a novel analytical detection approach is proposed in this paper. By modelling the contours of BCS, ST, and DRs as convex envelope planes/bodies using different spatial line styles, the spatial posture relations of their boundaries can be reproduced on the correction path, and collision detection can be transformed into the mathematical problem of calculating point-plane and point-line distances. Subsequently, two algorithms are proposed for BCS and ST-DR collision detections, and adjustment strategies are provided to resolve algorithm anomalies. Clinical case simulation proves the effectiveness and applicability of the approach. Since the detection is used for pre-distraction prediction rather than real-time monitoring, the correction path with potential collision risk can be re-planned before distraction, and finally, guarantees the safety of gradual correction.