Parametric modeling of the intervertebral disc space in 3D: Application to CT images of the lumbar spine

https://doi.org/10.1016/j.compmedimag.2014.04.008Get rights and content

Abstract

Gradual degeneration of intervertebral discs of the lumbar spine is one of the most common causes of low back pain. Although conservative treatment for low back pain may provide relief to most individuals, surgical intervention may be required for individuals with significant continuing symptoms, which is usually performed by replacing the degenerated intervertebral disc with an artificial implant. For designing implants with good bone contact and continuous force distribution, the morphology of the intervertebral disc space and vertebral body endplates is of considerable importance. In this study, we propose a method for parametric modeling of the intervertebral disc space in three dimensions (3D) and show its application to computed tomography (CT) images of the lumbar spine. The initial 3D model of the intervertebral disc space is generated according to the superquadric approach and therefore represented by a truncated elliptical cone, which is initialized by parameters obtained from 3D models of adjacent vertebral bodies. In an optimization procedure, the 3D model of the intervertebral disc space is incrementally deformed by adding parameters that provide a more detailed morphometric description of the observed shape, and aligned to the observed intervertebral disc space in the 3D image. By applying the proposed method to CT images of 20 lumbar spines, the shape and pose of each of the 100 intervertebral disc spaces were represented by a 3D parametric model. The resulting mean (±standard deviation) accuracy of modeling was 1.06 ± 0.98 mm in terms of radial Euclidean distance against manually defined ground truth points, with the corresponding success rate of 93% (i.e. 93 out of 100 intervertebral disc spaces were modeled successfully). As the resulting 3D models provide a description of the shape of intervertebral disc spaces in a complete parametric form, morphometric analysis was straightforwardly enabled and allowed the computation of the corresponding heights, widths and volumes, as well as of other geometric features that in detail describe the shape of intervertebral disc spaces.

Introduction

Chronic low back pain and musculoskeletal disorders are among the most common reasons for doctor visits worldwide [1], [2]. Degenerative lumbar disc disease, which is a gradual degeneration of intervertebral discs of the lumbar spine, has been identified as one of the most common generators of the low back pain [3], [4]. For the majority of the population, the gradual degeneration of intervertebral discs is a normal part of the aging process and does not represent a health problem. However, in some cases it eventually causes severe, chronic and debilitating low back pain. Although conservative treatment of the degenerative disc disease (e.g. management with analgesics, physical therapy, therapeutic injections) may provide relief to most individuals, surgical intervention may be required for individuals with significant continuing symptoms [5]. One of the promising surgical interventions for the degenerative disc disease is the total disc replacement surgery, where the degenerated intervertebral disc is replaced by an artificial implant. The use of artificial implants allows the restoration of the intervertebral disc space while maintaining normal physiological movement, which is advantageous over alternatives that usually involve the elimination of motion (e.g. spinal fusion) [6], [7]. The main post-operative complications of total disc replacement surgery depend on the type of the implant, but are generally related to device failure (e.g. metal fatigue), bone-implant failure (e.g. implant migration or dislocation, subsidence, vertebral body fracture) and/or host response (e.g. infection) [8], [9].

The majority of artificial implants for intervertebral discs are designed with endplates that are relatively flat in comparison to the concave endplate of vertebral bodies [10]. As a result, to fix and stabilize such type of implant between adjacent vertebral bodies, vertebral endplates are usually surgically reduced to a flat plane. Furthermore, the spikes on the sides and/or keels (oriented in the sagittal direction) in the center of each of the two endplates of the implant are driven into adjacent vertebral bodies to avoid rotational instability and promote bony ongrowth for additional fixation. However, these actions can compromise the strength of the strong cortical shell of the vertebral body and therefore reduce its ability to resist pressure, which can lead to artificial implant subsidence or vertebral fracture [11]. A better solution would be to leave the endplates of the vertebral body as intact as possible and adapt the shape of the implant to match the geometry of the vertebral body. Therefore, in designing and improving implants, geometrical data on the vertebral site is of considerable importance, especially the morphology of the intervertebral disc space (e.g. the volume that is required to house the implant) and vertebral body endplates (e.g. endplate shape) is valuable for designing artificial implants with good bone-implant contact, continuous force distribution and good bony ongrowth.

Several methods have been proposed to obtain the morphometry of the intervertebral disc space and vertebral body. van der Houwen et al. [12] reviewed 10 different studies that investigated the morphometry of vertebral bodies and their endplates using a variety of imaging techniques, e.g. radiography, computed tomography (CT) and magnetic resonance (MR). The outcome was that geometry data of vertebral surfaces is scarce, and therefore a new method was presented that consisted of manual positioning of 10 points on each endplate of adjacent vertebral bodies in arbitrarily chosen coronal and sagittal cross-sections of a CT image, and then performing morphometric analysis from measurements among these points. Hong et al. [13] obtained the morphometry of the intervertebral disc space by manually measuring horizontal and vertical lengths of intervertebral discs in mid-sagittal MR cross-sections of the vertebral body. According to the methods proposed by Bilgic et al. [14], Gocmen-Mas et al. [15] and Karabekir et al. [16], the morphometry of the vertebral body and intervertebral disc or intervertebral disc space was obtained from consecutive CT or MR cross-sections by applying the stereologic approach [17], which consists of counting points on a predefined grid.

Although the above mentioned approaches aimed for an accurate morphometric analysis of the vertebral body and intervertebral disc space that may help in improving the design of artificial implants, the measurements were performed in two-dimensional (2D) cross-sections that usually do not provide a complete insight into the three-dimensional (3D) shape representation, or they required extensive user interaction. On the other hand, several automated methods were proposed for segmentation of vertebral bodies and intervertebral discs from 3D CT or MR images [18], [19], [20], [21]. However, the shape of intervertebral discs that may correspond to intervertebral disc spaces was described as a point distribution model, for which a specific shape property is associated with several parameters. In this paper we propose an automated method for parametric modeling of the intervertebral disc space in 3D, meaning that each relevant 3D shape property of the intervertebral disc space (e.g. height, width, convexity of endplates, etc.) is quantitatively described by a single geometric parameter. The alignment of such parametric model to the intervertebral disc space in the 3D image allows a complete 3D morphometric analysis of the observed shape.

Section snippets

Parametric modeling in 3D

The modeling of the vertebral body and intervertebral disc space in 3D is carried out using the superquadric approach [20]. Superquadrics are a generalization of quadric surfaces and were already used for implicit modeling of 3D surface objects in computer vision and medical imaging [22], [23]. The inside–outside function of the general superquadric isF(x)=xa12/ɛ2+ya22/ɛ2ɛ2/ɛ1+za32/ɛ1,where x=(x,y,z)3 is a point in the 3D space, a1, a2 and a3 control the size of the superquadric along each

Images and ground truth

The proposed method for the determination of the intervertebral disc space in 3D was evaluated on CT images of the lumbar spine. The CT scans came from 20 subjects (12 males and 8 females, mean age ± standard deviation, SD, 52.2 ± 17.4 years, range 26–81 years) and were reconstructed as 3D images from axial cross-sections with 0.3–1.4 mm pixel size and 0.4–1.5 mm cross-sectional thickness. To quantitatively evaluate the proposed method, 10 anatomical points were manually placed on each vertebral

Discussion and conclusion

An automated method for modeling intervertebral disc spaces in 3D and their determination in CT images of lumbar spine was proposed. In comparison to existing methods that are based on measurements of different geometric features of the intervertebral disc space from 2D cross-sections and usually involve extensive user interaction [12], [13], [14], [15], [16], the proposed method provides a complete insight into the 3D shape representation of the intervertebral disc space with minimal user

Conflict of interest statement

The authors disclose that they have no financial or personal relationships with other people or organizations that could inappropriately influence their work.

Acknowledgements

This work has been supported by the Ministry of Higher Education, Science and Technology, Slovenia, under grants P2-0232, J7-2264 and J2-5473. The authors would like to thank D. Štern (University of Ljubljana, Faculty of Electrical Engineering, Slovenia; currently with the Institute for Computer Graphics and Vision, Graz University of Technology, Austria).

Robert Korez received his B.Sc. degree in mathematics from University of Ljubljana, Slovenia, in 2012. He is currently a Ph.D. student in the Laboratory of Imaging Technologies at the Faculty of Electrical Engineering, University of Ljubljana, Slovenia, and his research interests are in shape modeling and quantitative morphometry in the field of medical image analysis.

References (31)

  • C.W. Chen et al.

    CT volumetric data-based left ventricle motion estimation: an integrated approach

    Comput Med Imaging Graph

    (1995)
  • D.M. Elliott et al.

    Biomechanics of the intervertebral disc

  • W. Limthongkul et al.

    Volumetric analysis of thoracic and lumbar vertebral bodies

    Spine J

    (2010)
  • R. Bertagnoli

    Indications for total lumbar disc replacement

  • P.S. Sizer et al.

    Pain generators of the lumbar spine

    Pain Pract

    (2001)
  • Cited by (0)

    Robert Korez received his B.Sc. degree in mathematics from University of Ljubljana, Slovenia, in 2012. He is currently a Ph.D. student in the Laboratory of Imaging Technologies at the Faculty of Electrical Engineering, University of Ljubljana, Slovenia, and his research interests are in shape modeling and quantitative morphometry in the field of medical image analysis.

    Boštjan Likar received his B.Sc., M.Sc. and Ph.D. degrees in electrical engineering from University of Ljubljana, Slovenia, in 1995, 1998 and 2000, respectively, and his Ph.D. degree in medical sciences from Utrecht University, the Netherlands, in 2000. He is with the Faculty of Electrical Engineering, University of Ljubljana, Slovenia, where he is currently full professor in the Laboratory of Imaging Technologies, and his research interests concentrate on visual quality inspection, computer and machine vision systems, and on biomedical and hyperspectral imaging. He is the (co)author of over 80 SCI journal papers with over 700 clear citations, editor of two international conference proceedings, chair of two international conferences, associate editor of a special issue in Medical Image Analysis journal, associate editor of Image Analysis and Stereology journal, program committee member of over 15 international conferences, principal researcher of eight research projects, designer of more than 20 new computer vision products, and co-founder of Sensum, a company that supplies machine vision solutions for the pharmaceutical industry.

    Franjo Pernuš received his B.Sc., M.Sc. and Ph.D. degrees in electrical engineering from University of Ljubljana, Slovenia, in 1976, 1979 and 1991, respectively. Since 1976 he is with the Faculty of Electrical Engineering, University of Ljubljana, Slovenia, where he is currently full professor and head of the Laboratory of Imaging Technologies, and his research interests are in computer vision, medical imaging, and the application of pattern recognition and image processing techniques to various biomedical and industrial problems. He is the (co)author of over 100 SCI journal papers with over 700 clear citations, associate editor of the IEEE Transactions on Medical Imaging and of Computer Aided Surgery, and co-founder of Sensum, a company that supplies machine vision solutions for the pharmaceutical industry.

    Tomaž Vrtovec received his B.Sc. and Ph.D. degrees in electrical engineering from University of Ljubljana, Slovenia, in 2002 and 2007, respectively, and his Ph.D. degree in medical sciences from Utrecht University, the Netherlands, in 2011. He is with the Faculty of Electrical Engineering, University of Ljubljana, Slovenia, where he is currently assistant professor in the Laboratory of Imaging Technologies, and his research interests concentrate on biomedical imaging, with particular interest for the development and evaluation of techniques for segmentation and quantitative morphometry of three-dimensional spine images. He is the (co)author of over 20 SCI journal papers with over 50 clear citations, and program committee member of two international conferences.

    View full text