An automatic genetic algorithm framework for the optimization of three-dimensional surgical plans of forearm corrective osteotomies

Highlights

• Automatic diagnosis strategy based on bony landmarks.

• Two-stage weighted multi-objective optimization based on a genetic algorithm.

• Novel bone protrusion evaluation considering bone contact and surfaces gaps.

• Patient-specific screw optimization based on bone density information.

• Capability of considering all types of common osteotomies: single-cut, opening wedge, closing wedge.

Abstract

Three-dimensional (3D) computer-assisted corrective osteotomy has become the state-of-the-art for surgical treatment of complex bone deformities. Despite available technologies, the automatic generation of clinically acceptable, ready-to-use preoperative planning solutions is currently not possible for such pathologies. Multiple contradicting and mutually dependent objectives have to be considered, as well as clinical and technical constraints, which generally require iterative manual adjustments. This leads to unnecessary surgeon efforts and unbearable clinical costs, hindering also the quality of patient treatment due to the reduced number of solutions that can be investigated in a clinically acceptable timeframe. In this paper, we propose an optimization framework for the generation of ready-to-use preoperative planning solutions in a fully automatic fashion. An automatic diagnostic assessment using patient-specific 3D models is performed for 3D malunion quantification and definition of the optimization parameters’ range. Afterward, clinical objectives are translated into the optimization module, and controlled through tailored fitness functions based on a weighted and multi-staged optimization approach. The optimization is based on a genetic algorithm capable of solving multi-objective optimization problems with non-linear constraints. The framework outputs a complete preoperative planning solution including position and orientation of the osteotomy plane, transformation to achieve the bone reduction, and position and orientation of the fixation plate and screws. A qualitative validation was performed on 36 consecutive cases of radius osteotomy where solutions generated by the optimization algorithm (OA) were compared against the gold standard solutions generated by experienced surgeons (Gold Standard; GS). Solutions were blinded and presented to 6 readers (4 surgeons, 2 planning engineers), who voted OA solutions to be better in 55% of the time. The quantitative evaluation was based on different error measurements, showing average improvements with respect to the GS from 20% for the reduction alignment and up to 106% for the position of the fixation screws. Notably, our algorithm was able to generate feasible clinical solutions which were not possible to obtain with the current state-of-the-art method.

Introduction

Post-traumatic healing in non-anatomical positions (malunions) or congenital deformations of bones can cause limitations in the range of motion (ROM) of the patient, generate pain and, if not treated properly, result in severe degenerative pathologies such as osteoarthritis (Nagy et al., 2008). The current gold standard for surgical treatment of these pathologies is the restoration of the normal anatomy in a surgical procedure known as a corrective osteotomy. In this procedure, the pathological bone is cut into two or more fragments, the fragments are realigned (clinical term: reduced) to their physiological position and stabilized with an osteosynthesis implant (Schweizer et al., 2010). However, the correction of bone malunions is highly patient-specific, requiring performing a complex 6-degree-of-freedom (DoF) correction (rotation and translation) for each bone fragment, in order to restore the physiological anatomy of the patient. Therefore, corrective osteotomies are technically challenging to perform without careful diagnosis and detailed preoperative planning of the procedure. Moreover, the successful outcome of a corrective osteotomy depends also on precise intraoperative navigation of the bone reduction (Fürnstahl et al., 2016).

Conventional two-dimensional (2D) preoperative planning approaches based on X-ray and Computed Tomography (CT) images fail to correctly assess the inherently three-dimensional (3D) nature of bone malunions (Schweizer et al., 2010). Another drawback of 2D preoperative planning is that it cannot be used for surgical navigation, and surgeons must rely mainly on outdated, rudimentary surgical techniques to achieve the desired bone correction. Computer-assisted 3D preoperative planning addresses those problems. Several works have established 3D preoperative planning as the state-of-the-art technique for corrective osteotomies (Athwal et al., 2003; Dobbe et al., 2011; Fürnstahl, 2010; Fürnstahl et al., 2016), due to its clear benefits in patient treatment. It allows the quantification of malunions and its corrections in all 6 DoF. 3D preoperative planning offers also the possibility of precise pre-calculation of the osteotomy fixation using 3D representations of the fixation plates and fixation screws (Dobbe et al., 2011; Miyake et al., 2012a; Schweizer et al., 2010, 2013). Lastly, it enables the translation of the preoperative planning intraoperatively by means of surgical navigation, based either on patient-specific instruments (PSI) (Fürnstahl et al., 2016; Miyake et al., 2011; Murase et al., 2008; Omori et al., 2014) or on optical navigation systems (Andress et al., 2018). Thus, the introduction of 3D preoperative planning techniques marked a paradigm shift in patient treatment, allowing performing complex surgical procedures that would not be possible using conventional techniques (Athwal et al., 2003; Dobbe et al., 2014; Fürnstahl et al., 2016; Kunz et al., 2013; Roner et al., 2017; Schweizer et al., 2013, 2016; Zdravkovic and Bilic, 1990).

In our institution, the current state-of-the-art preoperative planning of long-bone osteotomies encompass the following steps: in a first step, patient-specific 3D triangular surface models (hereinafter: 3D models) of the bones are generated based on the segmentation of the CT data of the patient (Fürnstahl et al., 2008), which is part of our standard clinical procedure (Fürnstahl et al., 2008). After obtaining the patient-specific 3D bone models, a diagnosis of the malunion is performed by comparison of the pathological bone model to a reconstruction target (Fig. 1A). Usually, a mirrored model of the contralateral healthy side is used as the reconstruction target. The deformity analysis allows the definition of the needed osteotomy cuts along the pathological bone model, which are simulated as shown in Fig. 1B. The resulting bone fragments can then be realigned into their anatomical position by realigning the bone fragments to fit the reconstruction target (Fürnstahl, 2010; Fürnstahl et al., 2016; Murase et al., 2008). The final step of the preoperative planning procedure is the simulation of the fixation of the osteotomy by integrating 3D models of the fixation plate and screws (Fig. 1C). In total, the planning process for corrective osteotomies requires the definition of 18 DoF, without including the orientation and position of the screws. This preoperative plan can be translated into the operation room by means of patient-specific navigation instruments, designed according to the preoperative plan and later 3D-printed, allowing the surgeons to perform intraoperatively step-by-step the previously simulated procedure (Fürnstahl et al., 2016; Omori et al., 2014; Rosseels et al., 2019).

Despite clear advantages of 3D preoperative planning, the generation of preoperative planning solutions requires the manual calculation of the aforementioned steps by trial and error, even when using dedicated 3D planning software (Fürnstahl et al., 2016; Roner et al., 2017; Schweizer et al., 2010). The development of a clinically feasible solution also requires close collaboration between surgeons, providing the clinical knowledge, and engineers, who have the technical expertise. As the availability of surgeons needed for consultancy is often very limited, the generation of an optimal preoperative solution for extra-articular long-bone osteotomies can add up to 4 h (Fürnstahl et al., 2016) and might involve several iterations of manual adjustments. This incurs unwanted clinical costs as a consequence of the human workload spent on manual processes. Moreover, only a reduced number of clinically feasible solutions can be investigated due to the constrained clinical timeframe.

One possibility to overcome those challenges is the implementation of a computer-based planning approach, able to systematically and automatically generate optimal preoperative planning solutions. The automatic generation can significantly decrease clinical costs and reduce unnecessary interaction times of the collaborators. It could also improve the quality of patient treatment by considering a larger range of parameters and solutions in order to generate better preoperative planning solutions than those obtained by a human planner. Moreover, with the current trend of the health industry towards digitalization of patient data and treatment solutions, automatic methods become an essential asset for optimal clinical treatments.

However, the implementation of an automatic optimization approach is a challenging task. Early on, Zdravkovic and Bilic (1990) proposed a computer-assisted preoperative planning framework for orthopedic surgeries in order to handle the complex tasks involved in the preoperative planning process. The latter, includes multiple nonlinear, discontinuous and non-differentiable planning objectives, making their mathematical manipulation difficult. Some objectives are contradicting and tightly associated with each other, which can cause the worsening of one objective while trying to improve another one.

In the field of corrective osteotomies of long bones, only a few works have tried to tackle the automatic optimization problem (Belei et al., 2007; Carrillo et al., 2017; Schkommodau et al., 2005). Although these approaches have been promising and are pioneers in the filed of automatic optimization for surgical planning of orthopedic surgeries, they still lack of solutions that can be readily applied in clinical practice without further modifications.

In this paper, we present a multi-staged, multi-objective optimization approach based on the artificial intelligent methods for the generation of ready-to-use preoperative planning solutions. The system is capable of calculating solutions considering all common bone malunions, osteotomy types, and surgical approaches. We have introduce the following key contributions with respect to our previous work (Carrillo et al., 2017):

• An automatic diagnosis of bone deformation based on bony landmarks, which allows automatic narrowing of the optimization search space. In our previous work, the diagnosis of the bone deformation was assumed as given.

• Automatic placement of the fixation plate using information provided by statistical shape models (SSM), in contrast to the manual definition of the feasible fixation areas used in Carrillo et al. (2017).

• A novel bone protrusion evaluation that supports the generation of better solutions by considering bone contact and surfaces gaps. The use of bone protrusion represents a more realistic clinical metric than the minimization of the cut surface used in our previous work.

• In contrast to the heuristic approach employed in our previous work, in this paper, we have developed a patient-specific screw purchase optimization based on bone density information extracted from CT data.

• The capability of considering all types of common osteotomies (single-cut, opening wedge, closing wedge) along the entire Radius, in order to generate solutions that would be difficult to achieve for a human planner within a reasonable time. The algorithm presented in Carrillo et al. (2017) was only able to handle distal radius osteotomies and was not capable of generating single-cut solutions.

• We have also reduced the computational effort of the strategy presented in Carrillo et al. (2017) by applying a different multi-stage approach.

• Finally, we have provided a profound clinical and mathematical explanation of all the optimization objectives, which was previously missing.

The developed optimization framework was validated clinically against state-of-the-art preoperative planning solutions on a consecutive series of patients with forearm malunions, previously treated at our institution. In the following, we will give a brief overview of existing preoperative planning approaches for orthopedic surgeries. In Section 2, we describe in detailed the proposed optimization framework. In Section 3, dataset, experimental set-up, and results are presented. In Section 4 a discussion about results, impact, and limitations of this work is given. Finally, in Section 5, we draw final conclusions and give an outlook about future work.

The first step towards the generation of a complete 3D preoperative planning is the patient diagnosis done through the analysis of the bone malunion. In 3D preoperative planning, patient-specific 3D bone models generated from the segmentation of multi-planar data (Lorensen and Cline, 1987) are superimposed over a healthy reconstruction template using semi-automatic registration methods (Kawakami et al., 2002; Schenk et al., 2016; Schweizer et al., 2010; Vlachopoulos et al., 2017). Afterward, the bone deformation is quantified by means of clinical and mathematical measurements (Fürnstahl et al., 2016; Gosse et al., 1997; Murase et al., 2008; Subburaj et al., 2010), providing the basis for the preoperative planning of the surgical correction. Here, 4 main objectives have to be considered: osteotomy cut plane, reduction of the bone fragments, position of the fixation plate and direction and position of fixation screws.

Current state-of-the-art of 3D preoperative planning for corrective osteotomies uses dedicated planning software for the manual calculation of each of these objectives. We refer the interested readers to Fürnstahl (2010), Fürnstahl et al. (2016), Schweizer et al. (2016), Vlachopoulos et al. (2015) for more information about the 3D planning tool. The latter facilitates the process of generation of a 3D preoperative plan, however the basic primitives operations needed for creating a preoperative plan are cutting Boolean operations and the possibility for interactive transformation, which would be also available in any dedicated CAD software.

The process of creating each of the steps involved in the preoperative plan is difficult to control even by skilled engineers, as any change done to one of the parameters (e.g., position of fixation screws, inclination of osteotomy plane) must be manually propagated across the different objectives (Athwal et al., 2003; Belei et al., 2007; Bilic et al., 1994; Carrillo et al., 2017; Fürnstahl, 2010). Current-state-of-the-art planning (Fürnstahl et al., 2016; Roner et al., 2017; Vlachopoulos et al., 2015) is also incapable of handling contradicting objectives, meaning for example that an improvement in the accuracy of the bone reduction can subsequently deteriorate the position of the fixation plate or generate solutions with non-feasible osteotomy cuts. Similarly, an improvement in the position of the osteotomy cut can cause a less fitting position for the placement of the fixation plate.

Existing automatic methods have only solved a reduced problem set, failing to include all objectives needed for a ready-to-use clinical solution, i.e., osteotomy cut plane, reduction of the bone fragments, position of the fixation plate and direction and position of fixation screws. Such is the case of previously described methods (Eck et al., 1990; Menetrey and Paul, 2004), where an automatic calculation was performed only for the osteotomy plane. Eck et al. (1990) calculated the osteotomy plane in femoral head reduction planning using a nonlinear optimization algorithm, based on a least-square-approximation solver. Menetrey and Paul (2004) did a similar parametrization of the osteotomy plane and wedge size for osteotomies around the knee, optimizing only the reduction alignment.

Schkommodau et al. (2005) developed a multi-objective optimization strategy for corrective osteotomies of lower extremities that considered the following optimization objectives: leg length, translation, antetorsion, and angulation. Their method solved a simplified osteotomy sub-problem with only 12 DoF, which did not include the position of the fixation plate or the fixation screws into the optimization process. The multi-objective problem was solved by a sequential quadratic programming algorithm and considered the influence of all these objectives in the preoperative planning. The approach was later extended by Belei et al. (2007) to account for different osteotomy types (closing wedge, opening wedge, single cut) and to consider also double osteotomy solutions. These approaches represent the first attempt to automate the planning of corrective osteotomy. However, the planning was based on simplified geometry rather than on patient anatomy and it relied on intraoperatively calibrated fluoroscopic datasets.

Learning-based methods have proven to be effective in similar applications of medical image processing techniques (Criminisi and Shotton, 2013; Esfandiari et al., 2018; Tschannen et al., 2016). In the field of shoulder arthroplasty, Tschannen et al. (2016) presented an automatic algorithm for preoperative planning of the resection plane for arthroplasty of the proximal humeral head, based on random regression forests. The approach allowed controlling the orientation, position, and size of the prosthetic humeral head in relation to the humeral shaft, using a direct mapping between the CT image and the parameters of the resection plane. The estimation of the plane position using CT data could be of interest to speed-up the convergence of optimization algorithms. Another interesting application is found in the field of spine surgery, where the problem of pedicle screw placement and pose estimation has been extensively studied (Farshad et al., 2017; Scheufler et al., 2011). Also, Esfandiari et al. (2018) proposed an algorithm based on convolutional neural networks for the 6-DoF estimation of the screw position and direction using intraoperative fluoroscopy data and estimation of the bone density. Similar approaches, taking into account the bone density information of the patient, should be considered in long-bone osteotomies to increase the quality of the osteotomy fixation.

To the best of our knowledge, only our previous work (Carrillo et al., 2017) deals with an 18-DoF optimization problem for the generation of preoperative planning solutions of corrective osteotomies. The optimization approach presented in Carrillo et al. (2017) has been taken as the basis for the core optimization algorithm (Section 2.3.3) of the herein presented framework.