Elsevier

Medical Image Analysis

Volume 31, July 2016, Pages 88-97
Medical Image Analysis

Regression forest-based automatic estimation of the articular margin plane for shoulder prosthesis planning

https://doi.org/10.1016/j.media.2016.02.008Get rights and content

Highlights

  • We present a fully automated method for estimating the articular margin plane of the proximal humerus from computed tomography images.

  • The two-step approach consists of a coarse estimation stage followed by a refinement step which permits to considerably reduce the overall processing time.

  • The algorithm achieves accuracy comparable to manual annotation.

  • We present novel feature types that combine a bone enhancing sheetness-measure with ray features.

  • The method has the potential to automate time-consuming preoperative planning tasks.

Abstract

In shoulder arthroplasty, the proximal humeral head is resected by sawing along the cartilage-bone transition and replaced by a prosthetic implant. The resection plane, called articular margin plane (AMP), defines the orientation, position and size of the prosthetic humeral head in relation to the humeral shaft. Therefore, the correct definition of the AMP is crucial for the computer-assisted preoperative planning of shoulder arthroplasty.

We present a fully automated method for estimating the AMP relying only on computed tomography (CT) images of the upper arm. It consists of two consecutive steps, each of which uses random regression forests (RFs) to establish a direct mapping from the CT image to the AMP parameters. In the first step, image intensities serve as features to compute a coarse estimate of the AMP. The second step builds upon this estimate, calculating a refined AMP using novel feature types that combine a bone enhancing sheetness measure with ray features. The proposed method was evaluated on a dataset consisting of 72 CT images of upper arm cadavers. A mean localization error of 2.40 mm and a mean angular error of 6.51° was measured compared to manually annotated ground truth.

Introduction

Treatment of primary and secondary degenerative conditions of the shoulder with joint replacement surgery has substantially increased over the past decade, resulting in an annual growth rate of about 10% (Day et al., 2010). While approximately 7000 shoulder joint replacement surgeries were performed in the United States in the year 2002 (Bohsali et al., 2006), today more than 50,000 patients are treated per year (Ponce et al., 2015). The growing number of shoulder arthroplasty procedures also promoted the development of computer assisted preoperative planning and intraoperative navigation techniques (Iannotti et al., 2014, Kircher et al., 2009, Nguyen et al., 2009). The improved accuracy of component positioning in presence of osteoarthritis (Edwards et al., 2008, Iannotti et al., 2014, Kircher et al., 2009, Nguyen et al., 2009) as well as the more precise reconstruction of comminuted proximal humeral fractures (Bicknell et al., 2007, Fürnstahl et al., 2012) do often justify the increased planning effort preoperatively. One important step during shoulder arthroplasty is the resection of the humeral head along the anatomical neck (Fucentese et al., 2010). Resection is performed by sawing along the so-called articular margin plane (AMP) which lies on the cartilage to bone transition (Boileau and Walch, 1997). The AMP defines the orientation, position and size of the prosthetic humeral head in relation to the humeral shaft and influences the selection of humeral head component size (Fig. 1a). As the AMP varies from patient to patient (Iannotti et al., 1992), it must be defined individually for each case. Therefore, the estimation of the AMP based on preoperative computed tomography (CT) data is a crucial step for the preoperative planning of arthroplasty. The current standard procedure for determining the AMP preoperatively relies on manually defined reference points (DeLude et al., 2007, Johnson et al., 2013). Because the reference points are difficult to identify in the CT image, annotation is often carried out using a 3D triangular surface model, reconstructed from the CT data. Fig. 1b shows an example of a humerus model with manually annotated reference points. However, the procedure of manually annotating the AMP is tedious, time consuming (i.e., 20 min) and, dependent on the experience of the surgeon, the AMP parameters may vary considerably between different persons (Vlachopoulos et al., 2016).

Therefore, an automatic approach for determining the AMP would be desired to reduce manual effort. However, classical image processing techniques, such as template matching or spherical Hough transform, are likely to yield poor performance due to the lack of obvious landmarks or unambiguous geometries. Contrary, supervised machine learning algorithms allow for more versatile models and – depending on the chosen algorithm – are able to select a small number of discriminative features from a large set of candidates to effectively tackle the problem at hand.

In this paper, we present a random regression forest (RF)-based method to estimate the AMP from upper arm CT images. To the best of our knowledge, there is no prior work addressing this problem. A key aspect of our method is to take a two-step approach with novel feature types that combine a bone-enhancing sheetness measure (Descoteaux et al., 2006) with ray features (Smith et al., 2009). As our method is fully automatic, it can be seamlessly integrated into the existing workflows.

In the remainder of this section we briefly review prior work addressing similar problems. Section 2 provides the relevant background and gives a detailed description of our algorithm. Sections 3 and 4 are dedicated to the experimental evaluation of the proposed method. Finally, in Section 5 we discuss the results of the experimental evaluation and conclude with indications for future work in Section 6.

In the discussion of related work, we will focus on methods related to estimating position, orientation, anatomical landmarks, and orthopedic parameters from CT images. These methods may be roughly categorized into template matching, Hough transform and learning-based methods.

In (Ehrhardt et al., 2003), an atlas-based automatic segmentation and landmark localization framework for hip operation planning was proposed. In their method, a landmark-annotated gray value atlas was first registered to a CT image of the hip. Thereafter, the landmark locations were transferred from the atlas coordinate system to the CT coordinate system. The so-obtained coarse estimates of the landmark positions were then refined by locally registering surface atlases to the bone surface. A mean localization error below 1 mm was reported. However, no detailed performance evaluation was presented. Casciaro and Craiem (2014) described an automatic method for estimating anatomical bone axes in CT scans of ex-vivo femora. To do so, the bone surface was extracted from CT using a Laplacian filter, followed by portioning of the surface points into different bone segments. The axis of each segment was then obtained by fitting a cylinder to each point cloud.

Due to the absence of salient anatomical structures on the surface of the humeral head and its symmetric shape, simple atlas registration may yield inaccurate results (Fürnstahl et al., 2012).

van der Glas et al. (2002) applied spherical Hough transform to CT and magnetic resonance (MR) images for determining center and radius of the shoulder joint. Ruppertshofen et al. (2011) generated discriminative shape models in an iterative procedure and combined these models with generalized Hough transform to localize hip, knee and ankle joints in CT images. The mean localization error achieved for hip, knee, and ankle was 12.5 mm, 4.3 mm, and 9.8 mm, respectively. In our case, determining the shoulder joint center via spherical Hough transform would not help calculating the AMP, as the AMP is considerably offset with respect to the joint center. Moreover, the computational complexity of Hough transform scales badly with respect to the number of model parameters and image size.

The works of Glocker et al. (2012) and Kelm et al. (2013) addressed the problem of estimating position and angulation of vertebrae in CT and MR images. In (Glocker et al., 2012), the authors used RF to localize the vertebrae centroids with a mean error of 18.4 mm. The estimates were then refined using a probabilistic graphical model. Kelm et al. (2013) used marginal space learning and a global probabilistic spine model to simultaneously determine pose and labeling of all vertebral discs. After refinement, a mean error of 3.2 mm and 4.5° was reported.

In (Donner et al., 2013) a method combining a landmark classifier with a Hough RF and a parts-based model of the global landmark topology was proposed to simultaneously localize multiple landmarks. The method was trained and tested for localizing landmarks in hand radiographs, hand CTs, and whole body CTs (corresponding mean localization errors: 0.99 mm, 1.45 mm, 5.25 mm).

Han et al. (2015) considered the problem of landmark localization in brain MR images for registration and devised an algorithm that iteratively refines the landmark locations via a cascade of RFs (mean landmark localization error: 2.22 mm). A cascade of RFs, together with a local feature-weighting scheme, was also proposed by Ebner et al. (2014) for localizing landmarks in hand CTs (mean landmark localization error: 1.44 mm) and by Gao and Shen (2014) for landmark localization in prostate CT images (mean landmark localization error: 4.67 mm).

The works of Chen and Zheng (2013) and Lindner et al. (2013) targeted anatomical landmark detection for the segmentation of the pelvic bone in radiographs. In (Chen and Zheng, 2013), the authors repeatedly determined anatomical landmarks on femur and pelvis via RFs, regularizing the landmark positions using active shape models (mean point-to-curve error: 2.2 mm). A similar approach was proposed in Lindner et al. (2013), where a voting-based RF scheme was used to calculate the bounding box of proximal femora. Afterward, the bounding box was used to constrain the search area for the landmarks that were also localized with RFs. Lindner et al. (2013) reported a mean point-to-curve error below 0.9 mm for 99% of the test images.

Calculating the AMP may be considered as a pose estimation problem as well, because the AMP encodes the pose of the humeral head with respect to the shaft. Employing RFs to estimate pose in terms of position and orientation simultaneously was mainly considered outside the field of medical image analysis, e.g., in (Fanelli et al., 2011), where a RF framework is used to extract the human head pose from depth images in real time, and in (Shotton et al., 2013), where the authors proposed RFs to simultaneously localize 16 body joints in depth images.

Learning-based methods, in particular RFs, have proven to be effective in many related applications of medical image processing (Criminisi and Shotton, 2013a) and are therefore considered here for estimating the AMP.

Section snippets

Method

In this section, we present a fully automatic algorithm for estimating the AMP in CT images of the upper arm. Fig. 2 gives an overview of our algorithm, consisting of two consecutive steps, both divided into training and test phases. In a first step, a RF is employed to determine a coarse estimate of the AMP parameters based on the intensity neighborhood of voxels located on a regular grid by averaging over candidates with high confidence. More specifically, the RF computes offsets describing

Dataset

A total of 72 cadaveric whole body CT scans were provided by the Institutes for Forensic Medicine of the Universities of Bern and Zurich, Switzerland. The data were acquired using a Siemens Emotion 6® and a Siemens Somatom Definition Flash® CT scanner, respectively, with in-plane resolutions between [0.92, 1.37] mm (mean: 1.22 mm) and an axial resolution between [0.50, 0.70] mm (mean: 0.55 mm).

Our dataset was generated from the full body scan by extracting a subset with a field of view similar to

Results

We measured the position error as the Euclidean distance between c and the estimate found by our method. The angular error was expressed by the angle between the ground-truth AMP normal vector and its estimate. In Table 1, position and angular errors are given after coarse estimation (step 1) and refinement (step 2).

The optimal parameters found for step 1 of our algorithm were D=9, ɛ=0.04, and in step 2 the best parameters were D=12 and ɛ=0.52 for FR1 as well as D=12 and ɛ=0.78 for FR2. As part

Discussion

In this work, an algorithm was described for estimating the AMP in full-size upper arm CT scans in an automated fashion. The stepwise approach, comprising coarse estimation followed by refinement, has proven to be effective, i.e., the average position error of 7.77 mm and angular error of 10.19 achieved after step 1, decreased in step 2 by 69.1% and 36.1% for position and angulation, respectively. This observation is well aligned with the intuition that the local neighborhood of the humeral head

Conclusion and future work

We proposed and evaluated a two-step algorithm to estimate the AMP in CT images in a fully automated fashion. The algorithm already outperforms a human expert with respect to position error and has potential to achieve the accuracy of a human expert in terms orientation error when further refined. Future work includes the enhancement of sheetness-based ray features to provide better orientation information. It will be interesting to explore the behavior of ray features in combination with other

Acknowledgments

M.T. would like to thank Markus Rempfler for insightful discussions about RFs. This work was funded by the Balgrist Foundation Switzerland and by the Swiss Canton of Zurich through a Highly-Specialized Medicine grant. The authors would like to thank the Swiss Institute for Computer Assisted Surgery (SICAS) for the permission of using the cadaver data for this research.

References (45)

  • HertelR. et al.

    Geometry of the proximal humerus and implications for prosthetic design

    J. Shoulder Elbow Surg.

    (2002)
  • HuffmanG.R. et al.

    Neer award 2006: biomechanical assessment of inferior tuberosity placement during hemiarthroplasty for four-part proximal humeral fractures

    J. Shoulder Elbow Surg.

    (2008)
  • KircherJ. et al.

    Improved accuracy of glenoid positioning in total shoulder arthroplasty with intraoperative navigation: a prospective-randomized clinical study

    J. Shoulder Elbow Surg.

    (2009)
  • NguyenD. et al.

    Improved accuracy of computer assisted glenoid implantation in total shoulder arthroplasty: an in-vitro randomized controlled trial

    J. Shoulder Elbow Surg.

    (2009)
  • PonceB.A. et al.

    Comparative analysis of anatomic and reverse total shoulder arthroplasty: in-hospital outcomes and costs

    J. Shoulder Elbow Surg.

    (2015)
  • VlachopoulosL. et al.

    Computer algorithms for three-dimensional measurement of humeral anatomy: analysis of 140 paired humeri

    J. Shoulder Elbow Surg.

    (2016)
  • BohsaliK.I. et al.

    Complications of total shoulder arthroplasty

    J. Bone Joint Surg. Am.

    (2006)
  • BoileauP. et al.

    CT scan method accurately assesses humeral head retroversion

    Clin. Orthop. Relat. Res.

    (2008)
  • BoileauP. et al.

    The three-dimensional geometry of the proximal humerus. Implications for surgical technique and prosthetic design

    J. Bone Joint Surg. Br.

    (1997)
  • BreimanL.

    Random forests

    Mach. Learn.

    (2001)
  • CasciaroM.E. et al.

    Towards automatic measurement of anteversion and neck–shaft angles in human femurs using CT images

    Comput. Methods Biomech. Biomed. Eng.

    (2014)
  • ChenC. et al.

    Fully automatic segmentation of AP pelvis x-rays via random forest regression and hierarchical sparse shape composition

    Computer Analysis of Images and Patterns

    (2013)
  • Cited by (12)

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

      2020, Medical Image Analysis
      Citation Excerpt :

      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.

    • A review of advances in image-guided orthopedic surgery

      2023, Physics in Medicine and Biology
    View all citing articles on Scopus

    This paper was recommended for publication by “Nicholas Ayache”.

    View full text