## Assessing the Relative Positioning of an Osteosynthesis Plate to the Patient-Specific Femoral Shape from Plain 2D Radiographs

Please always quote using this URN: urn:nbn:de:0297-zib-54268
• We present a novel method to derive the surface distance of an osteosynthesis plate w.r.t. the patient­specific surface of the distal femur based on 2D X­ray images. Our goal is to study from clinical data, how the plate­to­bone distance affects bone healing. The patient­specific 3D shape of the femur is, however, seldom recorded for cases of femoral osteosynthesis since this typically requires Computed Tomography (CT), which comes at high cost and radiation dose. Our method instead utilizes two postoperative X­ray images to derive the femoral shape and thus can be applied on radiographs that are taken in clinical routine for follow­up. First, the implant geometry is used as a calibration object to relate the implant and the individual X­ray images spatially in a virtual X­ray setup. In a second step, the patient­specific femoral shape and pose are reconstructed in the virtual setup by fitting a deformable statistical shape and intensity model (SSIM) to the images. The relative positioning between femur and implant is then assessed in terms of displacement between the reconstructed 3D shape of the femur and the plate. A preliminary evaluation based on 4 cadaver datasets shows that the method derives the plate­to­bone distance with a mean absolute error of less than 1mm and a maximum error of 4.7 mm compared to ground truth from CT. We believe that the approach presented in this paper constitutes a meaningful tool to elucidate the effect of implant positioning on fracture healing.

• ERRATUM - A previous version of the ZIB-Report 15-21 (urn:nbn:de:0297-zib-54268) wrongly gave the impression that specimens were provided by the Department of Trauma Surgery, Medical University of Innsbruck, Austria. For the presented study, neither experiments were performed nor specimens provided by the Medical University of Innsbruck. The authors of the report instead re-used CT data that was gathered for a different (independent) experimental study, described in: Märdian, S., Schmölz, W., Schaser, K. D., Duda, G. N., & Heyland, M. (2015), "Interfragmentary lag screw fixation in locking plate constructs increases stiffness in simple fracture patterns", Clinical Biomechanics, 30(8), 814-819. Parts of the text have been edited in the revised version to prescind from any direct involvement of the Medical University of Innsbruck in the presented work.

Author: Moritz Ehlke, Mark Heyland, Sven Märdian, Georg N. Duda, Stefan Zachow ZIB-Report 3d-­reconstruction from 2d X­rays; fracture fixation of the distal femur; pose estimation; statistical shape and intensity models 68-XX COMPUTER SCIENCE (For papers involving machine computations and programs in a specific mathematical area, see Section -04 in that area) / 68-06 Proceedings, conferences, collections, etc. I. Computing Methodologies / I.4 IMAGE PROCESSING AND COMPUTER VISION (REVISED) / I.4.5 Reconstruction J. Computer Applications / J.3 LIFE AND MEDICAL SCIENCES / Health 2015/01/04 ZIB-Report (15-21) 1438-0064 Appeared in: Proceedings of the 15th Annual Meeting of CAOS-International (CAOS)

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