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

Highlights

• 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.

Abstract

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.

Introduction

Foot and ankle play critical roles in the human musculoskeletal system to maintain proper lower extremity mechanics [1]. However, morphological abnormalities and functional disabilities of the foot and ankle can be induced by congenital anomalies (or sequal), neurological disorders, trauma, or burn [2], [3], [4]. These causes lead to abnormal changes in biomechanical mechanisms and, consequently, foot and ankle deformity, which affects the quality of life and personal dignity of patients in each age stratum.

Compared with the conventional one-stage acute correction with the key features of bone-sacrificing and hand-manipulating [5,6], gradual correction has been proposed as an alternative option. This minimally invasive treatment is founded upon the principle of distraction histogenesis [7], i.e., both ST and bone can regenerate under the stress stimulation produced by distraction manipulation. The optimum distraction rate at the target bone/ST has been summarized as 1 mm per day in four steps [8], and thus gradual correction features a long-term process and requires ongoing management. Facing different preoperative conditions, ST procedure (i.e., ST and joint distraction with or without release) and bone procedure (i.e., osteotomy distraction with or without arthrodesis) can be used as surgical techniques [9,10]. For younger patients before maturity (under 8 years), pure ST procedure is sufficient to balance deforming force and remodel anatomical structure [3,4]; for patients with fixed bone deformity, bone procedure (or in conjunction with ST procedure) is required to separate bone segment and realize appropriate correction [11,12]. After performing surgical operation, the parallel external fixator (PEF) has become the recognized medical device to assist subsequent distraction and then accomplish histogenesis in a gentle and process-controllable manner [13,14]. By connecting with the body segments in a surrounding manner, the PEF can move the deformed segment relative to the non-deformed one via its DRs, and the posture transformation should be guided by a preplanned deformity-specific correction path [15,16]. To date, the ideal correction path in the clinic is generated using the simultaneous or sequential end-posture equipartition discretization method (daily distraction quantity of each deformity component shows a linear relationship in mathematics with the number of correction days) [16], in which the total correction quantity at the end approximates 1 mm per day.

Notably, although the ideal correction path is smooth and brings short fixation time, its plausibility should be pre-verified, otherwise collision phenomena may occur in the body segment-PEF system and affect the continuity and safety of correction. Firstly, high risk of detached BCS collision was reported in fracture reduction, and different correction paths (e.g., staged trajectory of extension-rotation-reduction [17,18], shortest linear distance-based planning [19], and fracture classification-based planning [20]) were proposed to resolve the interference. Moreover, some three-dimensional (3D) software programs were used or developed in these studies to simulate and visualize the distraction process (Fig. 1a) and then acted as the tool for collision detection. Analogously, after performing osteotomy in deformity correction, since the initial whole bone is separated into two detached parts, the BCSs may also collide with each other on the ideal correction path. Secondly, regardless of ST procedure and bone procedure, the collision may occur between ST and DR. In [21], proper frame size (approximately 4 cm larger than the ST) was preoperatively determined using sizing templates to avoid this interference. However, this experience-based method cannot guarantee complete safety for those patients with large changes in ST appearances, which may cause ST-DR collision. This phenomenon was also mentioned in [22], to evaluate the motion limits of the PEF, the ST was modelled using polymer discs, and the collision was measured when any DR touches the modelled ST substantiation (Fig. 1b). However, it is time-consuming to customize physical models, assemble a body segment-PEF system, and simulate distraction for patients with varying body sizes and preoperative conditions. Moreover, the consistency of mounting parameters between the physical model and the actual clinic cannot be guaranteed, leading to inaccurate results. Analogously, the artificial bone model was used in [13] to evaluate the ability of different assembly types, in which the collision was reported as an important factor limiting the correction range. In [23], a cone-cylinder model-based detection algorithm was constructed for the tibial deformity (Fig. 1c). However, facing the diverse shank morphologies, it is not accurate enough to simply express the ST as a truncated cone, which in turn may lead to incorrect detection results.

According to the above discussion, existing researches on BCS and ST-DR collision detections are few, and are mainly orientated to the treatment of those body segments with long bones (e.g., femur [19,20,22] and tibia [18,21,23]). To the authors' knowledge, few targeted studies have been carried out for foot and ankle that possess a more complex anatomical structure. Additionally, simultaneous detection of BCS and ST-DR collisions on the correction path has not been found in the authors' literature search, and thus there is still a lack of effective and applicable detection methods for them. Finally, the accuracy of existing methods has more room for improvement, in which the detection results of the software-based and substantiation model-based methods rely more on visual detection while the cone-cylinder model-based method cannot cope with complex ST appearances (especially the swollen ones [13]). To cope with these problems, taking foot and ankle as the research objects, a novel analytical detection approach is proposed in this paper, detection algorithms are introduced for both BCS and ST-DR collisions. When the ideal correction path passes collision detection, it can be identified as the final scheme, otherwise the path and/or assembly adjustments need to be performed.

The main contribution of this article lies in the following aspects:

• An analytical collision detection approach is proposed for the correction path in foot and ankle deformity;

• Basic mathematical functions are used to reproduce the contours of the BCS, ST, and DRs, which can achieve relatively good accuracy and short execution time;

• Algorithms are proposed for BCS and ST-DR collision detections based on their spatial distances, the detection result can be obtained without visual detection, as well as customizing and assembling models;

• Adjustment strategies are provided to resolve algorithm anomalies, and then obtain the final assembly positions and collision-free correction path.

The remainder of this paper is organized as follows. Section 2 introduces the detection requirements in foot and ankle deformity correction. Section 3 presents a novel analytical detection approach, including the basic mathematical functions and two algorithms for BCS and ST-DR collision detections. In Section 4, adjustment strategies are provided for algorithm anomalies, clinical case is used to simulate deformity correction and verify the effectiveness and applicability of the approach and algorithms. Section 5 compares the proposed approach with existing solutions. Finally, the paper is concluded in Section 6.