A novel parameter decomposition based optimization approach for automatic pose estimation of distal locking holes from single calibrated fluoroscopic image
Introduction
Femoral shaft fractures belong to one of the most common injuries encountered in clinical routine trauma surgeries. Most of them are displaced and need to be surgically reduced. Intramedullary nailing with/without reaming is an excellent operative procedure that has revolutionized the treatment of fractures of the femoral shaft. The efficacy of statically/dynamically locked intramedullary nails for the treatment of the femoral shaft fractures has been well established (Brumback et al., 1988, Wiss et al., 1986). The surgical procedure involves the fixation of the long-bone fractures by inserting an intramedullary nail (IMN), which is a prefabricated, metal rod, into the medullary canal of the damaged bone. The surgeon introduces the implant by making an incision in the proximal femur, reducing the bone fragments, inserting the IMN through the fragments, and finally locking the IMN with screws to create a means for the internal support. The transverse interlocking screws are essential to control the rotation and the translation of the bone fragments with respect to each other. In comminuted fractures, these interlocking screws also bear the transmitted load until the fracture has consolidated (Wiss et al., 1986). To insert the transverse, interlocking screws, it is necessary to align and drill through the bone to meet the proximal and distal interlocking screw openings of the IMN.
It has been recognized that one of the most difficult steps in intramedullary nailing of femoral shaft fractures is the distal locking – the insertion of distal interlocking screws (Winquist, 1993, Whatling and Nokes, 2006), for which it is necessary to know the positions and the orientations of the distal locking holes (DLHs) of the IMN. Complicating the process of locating and inserting the distal interlocking screws is the nail deformation resulted from the insertion, and therefore a simple aiming arm, mounted on the proximal end of the nail alone, will not sufficiently provide accurate aiming (Krettek et al., 1998). It has been reported that the deformation occurs in several planes due to medial–lateral (ML) and anterior–posterior (AP) flexions of the distal nail after it has been inserted (Whatling and Nokes, 2006, Krettek et al., 1998). Deformation analyses of solid 9 mm femoral nails using a magnetic tracking system in a cadaveric study has shown lateral translations of 18.1 ± 10.0 mm, dorsal translations of −3.1 ± 4.3 mm, and rotational deformation of −0.1 ± 0.2° for the center of the distal transverse locking holes (Krettek et al., 1998). The reason for the wide variations of the insertion related femoral nail deformation is due to the fact that the nail has to deform to the shape of the medullary canal upon insertion. The shape of the canal varies widely from person to person. Therefore, it is very difficult to determine where the resulting locations and orientations of the DLHs will be relative to their initial position before it is deformed. The surgeon depends heavily on an intra-operative X-ray means in a conventional surgical procedure for providing precise locations and orientations of the DLHs. It requires positioning the axis of the fluoroscope parallel to the locking holes so that these holes appear perfectly circular in the image and then placing the tip of a drill in the center of this circle (Whatling and Nokes, 2006). This is achieved through a trial-and-error method and requires long X-ray exposure time for both the surgical staff and the patient. A free hand technique or a radiolucent drill is then used to drill a hole through the bone to meet the opening of the nail hole so that an interlocking screw can be inserted later. It has been reported that the placement of the distal screws usually takes half of the total operation time and that the surgeon’s direct exposure to radiation for each conventional surgical procedure was 3–30 min, of which 31–51% was used for the distal locking (Skjeldal and Backe, 1987, Levin et al., 1987).
This paper presents a novel parameter decomposition based optimization approach for solving this problem using single calibrated fluoroscopic image. We do not ask for an image with perfectly circular holes but we do put a constraint on its acquisition, i.e., the reduced femur shaft should be put roughly parallel to the image intensifier of the fluoroscopy machine, which is much easier to be achieved intraoperatively. We then formulate the pose recovery as a model-based fitting problem and decompose the to-be-optimized parameters into two sets: (a) the angle between the nail axis and its projection on the imaging plane, and (b) the translation and rotation of the geometrical models of the locking holes around the nail axis. By using a hybrid optimization technique coupling an evolutionary strategy and a local search algorithm to find the optimal values of the latter set of parameters for each given value of the former one, we reduce the multiple-dimensional optimal fitting problem to an one-dimensional search along a finite interval.
The paper is organized as follows: Section 2 reviews the related works. Section 3 describes image calibration and geometrical models. In Section 4, we describe the proposed approach in details. Section 5 presents our comprehensive experimental results, followed by discussions and conclusions in Section 6.
Section snippets
Related works
The desire to target accurately with as little as possible X-ray exposure has led to various attempts to develop image-based methods for recovering the positions and the orientations of the DLHs. Multiple fluoroscopic images (normally 2) based methods as well as single image based methods have been presented before (Viant et al., 1997, Zhu et al., 2002, Malek et al., 2005, Leloup et al., 2004, Leloup et al., 2005, Yaniv and Joskowicz, 2005).
In (Viant et al., 1997, Zhu et al., 2002, Malek et
Image calibration
In reality, the proximal fragment, the distal fragment, and the nail may be treated as three rigid bodies and registered independently. The rigid transformations between these three rigid bodies can be trivially obtained from a navigator such as an optoelectronic tracker, a magnetic tracker, or even a medical robot. As this is not our focus in this paper, here we assume that the fractured femur has already been reduced and the proximal fragment and the distal fragment are kept fixed relative to
Preprocessing
The task of this step is to locate the projections of the distal locking holes. It is achieved by first applying a Hough transform (Jain et al., 1995) to find the two mostly parallel edge lines of the projection of the distal part of the nail from the C-arm image and then by sweeping a parallelpiped window along the axis of the nail projection to locate the projections of the distal locking holes. To improve the robustness of the nail detection, we proposed a nail edge detector as described
Experimental results
We have designed and conducted following comprehensive experiments to validate the robustness and the accuracy of the present approach:
- (1)
Experiment on evaluating the working range of the present approach.
- (2)
Experiment on evaluating the robustness of the present approach to outliers.
- (3)
In vitro experiment on evaluating the overall accuracy.
The first two experiments were performed on fluoroscopic images of a test bench, which was designed to allow rotation and tilt of the test subject, as shown by the
Discussions and conclusions
We have presented a novel parameter decomposition based optimization approach for automatic pose recovery of distal locking holes from single calibrated fluoroscopic image. We designed and conducted comprehensive experiments to validate the robustness and the accuracy of the present approach. The valid working range of the present approach were experimentally determined. Using a simulation environment, we validated the robustness of the present approach to outliers. Finally, the overall
Acknowledgements
This work was supported in part by Swiss National Science Foundation through Project NCCR CO-ME. The authors are grateful to the anonymous reviewers whose comments and suggestions helped improve the original manuscript.
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2018, Medical Engineering and PhysicsCitation Excerpt :Such solutions, however, are technically demanding and require extra equipment and trained staff that might not be affordable for many operating rooms. There have been also attempts to develop improved image-based techniques in order to recover the axis of a distal hole using two [18,19] or even one fluoroscopic shot [20,21]. Although these techniques are claimed to reduce the dosage of exposure, their efficacy for practical use has not been verified yet.
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