of Manual and Computerized Measurements of Sagittal Vertebral Inclination in MR Images

vertebrae (T4-L5) from one normal and one scoliotic magnetic resonance (MR) spine image using six manual and two computerized measurements. Manual measurements were performed by superior and inferior tangents, anterior and posterior tangents, and mid-endplate and mid-wall lines. Computerized measurements were performed by automatically evaluating the symmetry of vertebral anatomy in sagittal cross-sections and volumetric images. The mid-wall lines were the manual measurements with the lowest intra- and inter-observer variability ($$1.4^\circ \!$$ and $$1.9^\circ \!$$ standard deviation, SD). The strongest inter-method agreement was found between the mid-wall lines and posterior tangents ($$2.0^\circ \!$$ SD). Computerized measurements did not yield intra- and inter-observer variability ($$2.8^\circ \!$$ and $$3.8^\circ \!$$ SD) as low as the mid-wall lines, but were still comparable to the intra- and inter-observer variability of the superior ($$2.6^\circ \!$$ and $$3.7^\circ \!$$ SD) and inferior ($$3.2^\circ \!$$ and $$4.5^\circ \!$$ SD) tangents.





1 Introduction


Spinal deformities are manifested in an altered orientation of vertebrae that can occur in sagittal, coronal and/or axial plane. Sagittal vertebral inclination (SVI) is the rotation of a vertebra projected onto the sagittal plane and is represented by kyphotic and lordotic spinal curvatures. A number of methods were proposed for its measurement in the form of sagittal spinal curvature, i.e. along multiple vertebrae [1–4], however, not all of them can be used to measure the sagittal inclination in the form of segmental vertebral angulation, i.e. for a single vertebra [5–8]. The inclination of superior and inferior vertebral endplates was proposed by Cobb [5] to measure the severity of scoliosis in coronal radiographs, and later adapted to measure SVI in sagittal radiographs. However, the “modified” Cobb angle measurements are strongly affected by endplate architecture [9], vertebral body shape [10] and deformities in the coronal plane [11]. Alternatively, measuring the inclination of vertebral body walls resulted in posterior [7] and anterior [8] tangents. A number of systematic analyses were performed to define reference SVI in normal spines [8, 12–14]. Stagnara et al. [12] concluded that “normal” sagittal curves do not exist, as the range of SVI in normal subjects was considerably large. Bernhardt and Bridwell [13] proposed to use ranges of inclination instead of mean values. Korovessis et al. [14] showed that thoracic kyphosis increases with age, whereas lumbar lordosis starts to decrease after the seventh decade of life. Schuler et al. [8] compared manual and computer-assisted measurements of SVI using seven different measurements on $$10$$ radiographs of L4/L5 and L5/S1 segments. The manual and computer-assisted measurements proved to be equivalent in terms of variability, the Cobb angle and posterior tangents were the least variable, and the anterior tangents were the most reliable measurements. Street et al. [15] evaluated the reliability of measuring kyphosis manually from different imaging modalities in the case of thoracolumbar fractures. For the Cobb angle measurements, they concluded that plain radiographs were the most reliable measurement modality, followed by computed tomography (CT) and finally by magnetic resonance (MR) imaging.

In the above mentioned studies, the measurements were performed in two-dimensional (2D) sagittal radiographs. Over the past years, MR has gained acceptance in spine imaging by providing high-quality three-dimensional (3D) images by a correct selection of imaging parameters. When compared to plain radiography or CT, MR is associated with higher costs and not suitable for imaging subjects with metal implants as they cause distortions in the acquired images, however, it does not deliver ionizing radiation to the patients. When MR is available or required, additional imaging can be therefore avoided to contain costs and limit exposure to unnecessary ionizing radiation. As a result, MR images of the spine were already used to measure various vertebral parameters [15–22]. A number of methods were proposed to measure SVI in lateral radiographic projections, but the variability of SVI measurements in MR images has not been investigated yet. The purpose of this study is therefore to systematically analyze the variability of manual and computerized measurements of SVI in MR images.


2 Methodology



2.1 Manual Measurements


The following six manual measurements were used to evaluate SVI (Fig. 1). The superior and inferior tangents represent the Cobb method [5] at the superior and inferior vertebral endplate, respectively. The anterior [8] and posterior tangents [7] represent the inclination of the anterior and posterior vertebral body wall, respectively. The mid-endplate and mid-wall lines are defined between the central points of the anterior and posterior vertebral body walls, and between the central points of the superior and inferior vertebral endplates, respectively. Each MR image was visualized by a specially developed computer program that allowed the observer to manually identify the vertebral centroid in 3D, and the coronal and axial vertebral rotation to extract a 2D oblique sagittal cross-section from the 3D image. In the oblique sagittal cross-section, the observer then manually identified the corners of each vertebral body that were used to determine the angles $$\omega _x$$ of SVI, measured against reference horizontal or vertical lines that are parallel to the coordinate system of the 3D image.

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Fig. 1
The corners of the vertebral body (points A, B, C and D) in the sagittal view define the manual measurements of sagittal vertebral inclination (SVI)


2.2 Computerized Measurements


Computerized measurements of SVI were performed by a method that determines vertebral rotation in 3D [23]. The rotation of a vertebra in a 3D image can be represented by the angles $$\mathbf {\omega }=(\omega _x, \omega _y, \omega _z)$$ of rotation of the local vertebral coordinate system $$V$$ (defined by Cartesian unit vectors $$\mathbf {e}_{V_x}$$, $$\mathbf {e}_{V_y}$$ and $$\mathbf {e}_{V_z}$$) around the axes of the global image coordinate system $$I$$ (defined by Cartesian unit vectors $$\mathbf {e}_{I_x}$$, $$\mathbf {e}_{I_y}$$ and $$\mathbf {e}_{I_z}$$). Both $$V$$ and $$I$$ are right-hand Cartesian coordinate systems, representing left-to-right ($$x$$-axis), anterior-to-posterior ($$y$$-axis) and cranial-to-caudal ($$z$$-axis) direction. The angles $$\omega _x$$ (i.e. SVI), $$\omega _y$$ (i.e. coronal vertebral inclination) and $$\omega _z$$ (i.e. axial vertebral rotation) then represent the rotation of the vertebral coordinate system $$V$$ around vectors $$\mathbf {e}_{I_x}$$ (pitch), $$\mathbf {e}_{I_y}$$ (roll) and $$\mathbf {e}_{I_z}$$ (yaw), respectively. If the origin of $$V$$ is located at the vertebral centroid and $$V$$ is rotationally aligned with the vertebra in $$I$$, anatomically corresponding symmetrical parts of the vertebra can be observed within volumes of interest (VOIs) along positive/negative directions of each axis $$\mathbf {e}_{V_j}$$, $$j = x, y, z$$. The angles $$\mathbf {\omega }$$ of vertebral rotation can be therefore determined by finding the planes of maximal symmetry, which divide the whole vertebra into symmetrical left/right ($${\pm }\mathbf {e}_{V_x}$$) halves, and the vertebral body into symmetrical anterior/posterior ($${\pm }\mathbf {e}_{V_y}$$) and cranial/caudal ($${\pm }\mathbf {e}_{V_z}$$) halves. For each axis $$\mathbf {e}_{V_j}$$, $$j = x, y, z$$, the symmetrical correspondences of the two halves ($$A$$ and $$B$$) of a VOI are measured by $$S_j({\text {VOI}})$$:


$$\begin{aligned} S_j({\text {VOI}}) = \frac{\sum _{i=1}^{N}{\left| \mathbf {v}_{A_i}\right| {\cdot }\left| \mathbf {v}_{B_i}\right| }{\cdot }f}{\sum _{i=1}^{N}{\left| \mathbf {v}_{A_i}\right| }{\cdot }\sum _{i=1}^{N}{\left| \mathbf {v}_{B_i}\right| }}; ~~~~~~ f = \left\{ \begin{array}{ll}1; &{} ~~\mathbf {v}_{A_i}{\cdot }\mathbf {v}_{B_i} < 0 \\ 0; &{} ~~{\text {otherwise}}, \end{array}\right. \end{aligned}$$

(1)


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Fig. 2
a Example of symmetrical anatomical correspondence in anterior/posterior direction ($$S_y$$), shown for a symmetrical pair of points $$\mathbf {p}_{A_i}$$ and $$\mathbf {p}_{B_i}$$ inside $${\text {VOI}}_2$$. b The vertebral coordinate system $$V$$ and the observed volumes of interest ($${\text {VOI}}_1$$ encompasses the whole vertebra, $${\text {VOI}}_2$$ encompasses the vertebral body)

where $$f$$ is the weighting function, and $$\mathbf {v}_{A_i}$$ and $$\mathbf {v}_{B_i}$$ are the projections of the intensity gradient vectors $$\mathbf {g}_{A_i}$$ and $$\mathbf {g}_{B_i}$$ in the coordinate system $$I$$ to the unit vector $$\mathbf {e}_{V_j}$$, $$j = x, y, z$$, of the coordinate system $$V$$ at symmetrical pair of points $$\mathbf {p}_{A_i}$$ and $$\mathbf {p}_{B_i}$$, respectively, and $$N$$ is the number of point pairs inside each VOI (Fig. 2a). By projecting the gradient vectors to $$\mathbf {e}_{V_j}$$, $$j = x, y, z$$, and by applying the weighting function $$f$$, we retain the gradient components $$\mathbf {v}_{A_i}$$ and $$\mathbf {v}_{B_i}$$ that are relevant for defining the vertebral symmetry in the direction of $$\mathbf {e}_{V_j}$$. Two variations of the computerized method were applied for each vertebra. The measurements in 3D automatically evaluated the vertebral rotation in 3D images by maximizing symmetrical correspondences:


$$\begin{aligned} \omega _x^{*} = \underset{\omega _x}{\arg }\big (\mathbf {\omega }\big );~~~~\mathbf {\omega }^{*} = \underset{\mathbf {\omega }}{\arg \max }\big (S_x({\text {VOI}}_1) + S_y({\text {VOI}}_2) + S_z({\text {VOI}}_2)\big ), \end{aligned}$$

(2)
where the VOI that encompasses the whole vertebra is denoted by $${\text {VOI}}_1$$, and the VOI that encompasses the vertebral body is denoted by $${\text {VOI}}_2$$ (Fig. 2b). On the other hand, the measurements in 2D automatically evaluated SVI in the same 2D oblique sagittal cross-sections that were used for manual measurements (Fig. 3) by considering only $${\text {VOI}}_2$$ that encompasses the vertebral body and reducing its dimensionality to the area of interest (AOI), and maximizing the remaining symmetrical correspondences:


$$\begin{aligned} \omega _x^*= \underset{\omega _x^*}{\arg \max }\big (S_y({\text {AOI}}) + S_z({\text {AOI}})\big ). \end{aligned}$$

(3)


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Fig. 3
An illustration of the computerized search for the coronal (anterior/posterior) and axial (cranial/caudal) planes of maximal symmetry, which define the sagittal vertebral inclination (SVI), in a 2D oblique sagittal MR cross-section of the L1 vertebra

The planes of symmetry are first manually initialized so that they are parallel to the 3D axes of the MR image, centered in the vertebral centroid in 3D, and $$50$$ mm in size to encompass the whole vertebral body of thoracic and lumbar segments. By rotating these planes in 3D, the rotation angles $$\omega _x^*$$ are obtained from the inclination of the planes, and the current symmetrical correspondences are evaluated by mirroring the edges of vertebral anatomical structures (obtained from image intensity gradients) over each plane and comparing them to the edges on the opposite side of that plane in an optimization procedure.

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Mar 17, 2016 | Posted by in COMPUTERIZED TOMOGRAPHY | Comments Off on of Manual and Computerized Measurements of Sagittal Vertebral Inclination in MR Images

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