g i n a l Article An optimised method for quantifying glenoid orientation

A robust quantiﬁ cation method is essential for inter-subject glenoid comparison and planning of total shoulder arthroplasty. This study compared various scapular and glenoid axes with each other in order to optimally deﬁ ne the most appropriate method of quantifying glenoid version and inclination. Six glenoid and eight scapular axes were deﬁ ned and quantiﬁ ed from identiﬁ able landmarks of twenty-one scapular image scans. Pathology independency and insensitivity of each axis to inter-subject morphological variation within its region was tested. Glenoid version and inclination were calculated using the best axes from the two regions. The best glenoid axis was the normal to a least-square plane ﬁ t on the glenoid rim, directed approximately medio-laterally. The best scapular axis was the normal to a plane formed by the spine root and lateral border ridge. Glenoid inclination was 15.7° ± 5.1° superiorly and version was 4.9° ± 6.1°, retroversion. The choice of axes in the present technique makes it insensitive to pathology and scapular morphological variabilities. Its application would effectively improve inter-subject glenoid version comparison, surgical planning and design of prostheses for shoulder arthroplasty.


INTRODUCTION
Effective surgical planning for total shoulder arthroplasty requires a clear understanding of a patient' s glenoid version and inclination, [1][2][3][4][5][6] Quantifi cation of these parameters even in the presence of osseous pathology requires a robust and reproducible technique. [7] Several methods have been proposed for in vivo quantifi cation of glenoid version; from the use of conventional roentgenograms to axial-tomographic scans. [4,8,9] Computed tomographic (CT) methods are more reproducible and reliable compared to conventional X-ray methods. [10,11] Friedman et al., [8] used a method that requires three landmarks to defi ne glenoid version. They used CT scans in the axial plane from the acromion to the inferior border of the glenoid. Glenoid version was measured on the slice corresponding approximately to the mid-glenoid level [ Figure 1]. Although an improvement on conventional X-ray methods [10] there remain limitations to this technique in that the results are scanningorientation dependent; [3,9,12] it is essential that the glenoid surface is perpendicular to the plane of the CT slice. An improvement is to use ultrasound to defi ne the perpendicular to the glenoid face. [12] It is known that the glenoid face is twisted in a superiorinferior direction [3,4] and therefore the use of two points from a subjective mid-glenoid slice will be susceptible to inherent errors. Others have used methods with either surface scanning [4] or direct physical measurements [6] of ex vivo scapulae. These methods suffer from scanning orientation dependency that is set by eye, [4] or use of only two points to defi ne an angle. [6] In another study, Couteau et al. [9] carried out a 3-D morphological and mechanical analysis of twelve shoulders  Friedman et al. 1992 and four cryosectional image datasets. Sixteen of the specimens were left shoulders, mean age was 60 years, range (57 years to 79 years). Nine of the image scans were of 1.00 mm slice thickness, six (1.50 mm), four (1.40 mm) and two (1.25 mm).
Features or regions of interest within the fi eld of view of any standard shoulder or chest scan were defi ned. This includes regions within the scapular distal half and the supraglenoid tubercle. AMIRA image processing software (Mercury Computer Systems Inc, Chelmsford, MA, USA) was applied to segment and extract the three-dimensional locations describing each feature of interest.
Least-square basic geometric shapes such as an ellipse, plane, line or triangle were numerically fi tted on a given set of points to quantify axes on each specimen. These include those normally applied by classical techniques for glenoid quantifi cation and some novel ones. The specifi c axes that were defi ned are described below: I. Glenoid rim normal (GNrim): This is the normal unit vector to the best-fi t plane over the rim of the glenoid. The outline of the glenoid rim was segmented, reconstructed and applied to mathematically quantify the least square plane-fi t over the points and the normal unit vector to it [ Figure 2]. II. Glenoid fossa normal (GNfos): The normal unit vector to the best-fi t plane over the glenoid fossa. [9] The entire glenoid fossa was segmented, reconstructed and applied to quantify the plane and its normal [ Figure 2]. III. Glenoid equatorial line (GEL): A line joining the anterior and posterior margins of the mid-glenoid slice. [4,8,10] This is the axial slice midway along the glenoid height [ Figure 3]. IV. Coronal mid-glenoid superior axis (CMGS): A line joining the inferior and superior margins of the mid-glenoid slice from the coronal frames of an image scan [ Figure 3]. This is the coronal slice midway along the glenoid width. V. Bokor glenoid equatorial line (BGEL): This is a GEL based on the proposals of Bokor et al., [12] that scan orientation should be such that the glenoid surface is perpendicular to the plane of the CT axial cut [ Figure 3]. This was achieved using image processing software. VI. Glenoid superior axis (GSA): A line directed superiorly from the most inferior aspect of the glenoid to the biceps tendon insertion. [5,6,15] For the scapula, the axes were: I. Lateral border line (LBL): The best-fi t inferior-superior line along the ridge of the scapular lateral border [ Figure 4]. II. Spine root line (SRL): The best-fi t long-axis along the root of the scapular spine [ Figure 4]. III. Scapular normal (SN): The cross-product (unit vector) between LBL and SRL [ Figure 4]. This is directed anteriorly. IV. Scapular transverse axis (STA): A line drawn from the using CT scans. In their method, the points defi ning the glenoid articular surface were extracted and their centroid calculated. A least-square (LS) plane was mathematically fi tted on the extracted points and a normal unit vector to this quantifi ed. This represented the glenoid axis. A mid-transverse section of the glenoid was defi ned as the axial slice corresponding to the location of the centroid. The central axis of inertia of this slice was quantifi ed to represent the scapular axis. The version angle was fi nally calculated as the angle between the two representative axes.
Fundamentally, glenoid quantifi cation can be seen as the measurement of the glenoid plane orientation relative to the scapular plane. All the earlier techniques achieved this by applying two axes, one each to represent the planes. Most of these techniques rely on three or fewer landmark points that are susceptible to failures in the presence of pathologies. Again, it is known that inter-subject variability in the morphology of the scapula exists which none of these techniques addressed. [13,14] Therefore, comparison of glenoid quantifi cation between individuals using these techniques might not be reliably accurate. A more reliable technique could be developed based on axes that address the known limitations, having minimal inter-subject variability as well as being pathologyindependent.
The aim of this work was to: 1. Compute the axes of the glenoid and scapula as defi ned in the literature as well as other axes defi ned here from clearly identifi able landmarks, 2. To use weighting criteria to compute the best axes that are least susceptible to morphometric variability to defi ne glenoid version and inclination.

MATERIALS AND METHODS
Three-dimensional image datasets from standard shoulder scans were assessed for obvious osseous pathology and twenty-one of them selected. This comprised seventeen CT image scans  [8] [ Figure 1]. V. V. Bokor scapular transverse axis (BSTA) as proposed by Bokor et al. [12] VI. Second Moment of Area transverse Axis (SMATA): The medio-laterally directed principal axis of the second moment of area quantifi ed on the closest axial slice to the centroid of the glenoid fossa. VII. Wong scapular transverse axis (WSTA): This is a line joining the spinoglenoid notch and the spine/medial border intersection. [5] VIII. Churchill scapular transverse axis (CSTA): This is a line joining the centre of the glenoid fossa and the spine/ medial border intersection. [6] The corporate morphology of the glenoid or scapula was characterized by these axes that were defi ned from landmarks. It is therefore essential to identify a glenoid axis that integrates the variations in the remaining axes in its make-up. Such an axis would therefore be relatively insensitive to changes in glenoid morphology represented by inter-subject variations in the remaining axes. For the scapular body also, the best axis capable of refl ecting this quality was required.
The angles between all the glenoid axes were calculated in all the specimens. The means and standard deviations (SD) for these were quantifi ed. A relatively insensitive axis would result in a smaller sum total of its SDs from the specimens compared to the rest of the axes. The insensitivity index of an axis was defi ned as the sum of its SDs from the 21 specimens. All the insensitivity indices were normalized relative to the smallest index which assumed a weighting value of 1. 'Relative Insensitivity' of the rest of the axes was thus quantifi ed. These were also done for the scapular axes. In addition to high insensitivity, the fi nal criterion for the selection of the best axes was based on pathology-independency. An axis of which quantifi cation was based on two or three points only had a risk of pathological failure if any of the quantifi cation landmarks was associated with any regular osseous pathology. Such an axis was assigned a weighting of 1, otherwise this was 0. Optimal glenoid version was defi ned as a measure of the angle between the best glenoid axis and that of the scapula on the approximate transverse plane. Optimal glenoid inclination was defi ned as a measure of the angle between the best glenoid and scapular axes on the approximate coronal plane. Four different classical techniques were also applied to quantify version of each specimen. These were: (I) Friedman et al., [8] angle between GEL and STA; (II) Bokor et al., [12] angle between BGEL and BSTA; (III) Couteau et al., [9] (modifi ed) angle between GNfos and SMATA; (IV) Churchill et al., [6] angle between BGEL and CSTA. Glenoid inclination was quantifi ed using two other methods: (I) Wong et al., [5] method as the included angle between WSTA and GSA; (II) Churchill et al., [6] method as the angle between CSTA and GSA. The correlation coeffi cients between these and the optimal methods were also calculated.

RESULTS
The most insensitive axis of the glenoid is the normal to a LS plane fi t on the glenoid rim (GNrim) while that of the scapula is the normal to the plane formed by LBL and SRL (SN). These have Relative Insensitivity of 1.00 respectively [ Tables 1 and 2]. Quantifi cation of these involved multitudes of points over their landmarks. Optimal glenoid version is therefore a measure of the angle between GNrim and SN. This produced a mean value of 4.9 ± 6.1°, retroversion; range: -16.4° to 10.7°. Mean glenoid version using Friedman et al. [8] technique was 12.2° ± 8.4°,   retroversion; range: -30.6° to 0°; having correlation coeffi cient of 0.08 with the optimal method. Bokor et al., [12] technique on the same specimens produced mean glenoid version of 3.5° ± 4.8°, anteversion; range: -4.5° to 14.5°; and correlation coeffi cient of 0.26 with the optimal method. By Cauteau et al., [9] parallel technique, this was 15.8° ± 38.2°, anteversion and correlation coeffi cient of 0.12. Churchill et al., [6] method produced 3.3° ± 4.6°, anteversion; range: -4.6° to 13.1°; and correlation coeffi cient of 0.23. The CSTA and WSTA with equal Relative Insensitivity of 1.02 are the most insensitive scapular axes on the approximate coronal plane. These were followed closely by SRL (relative insensitivity, 1.03). By pathology-independency criterion, the SRL was quantifi ed with numerous points as against the two-point and pathology-dependent CSTA and WSTA. This was therefore chosen as the best. This combines with the glenoid' s GNrim to produce an 'optimal' mean glenoid inclination of 15.7° ± 5.1°, superiorly; range: -7° to 27.4°. Wong et al., [5] method quantifi ed a mean inclination of 0.9° ± 4.3°, superiorly; range: -7.1° to 11.2°. Churchill et al., [6] method produced 5.2° ± 3°, superiorly; range: 0.8° to 11.5°.

DISCUSSION
The classical methods of glenoid version quantifi cation have been associated with various limitations such as scanning orientation dependency. [3,4,9,12] More recent studies have proposed other methods that addressed the orientation factor. However, these are also fl awed for being sonographerdependent in ensuring preferred scanning orientation. The technique proposed in the present study was based on thousands of vectors to form the SRL, SN and GNrim axes. GNrim integrates the corporate morphology of the glenoid rim rather than two points only compared to other methods. [6,8,12] This would therefore remain stable irrespective of the scanning orientation unlike the techniques of Friedman et al. [8] and Monk et al. [4] and hence avoids the subjective opinion of the sonographer. The rim of the glenoid has been reported to be superoinferiorly twisted and might have the presence of osseous pathology. [3,7,9] The fi tting of LS plane over the glenoid face using over two thousand points across the glenoid rim constitutes a better approximation of glenoid defi nition irrespective of the presence of the aforementioned complications. The SN axis integrates most of scapular morphology represented in over 5000 points from its parent axes (SRL and LBL). This is therefore a better representation of the scapular body compared to only two points applied by the classical methods. None of the earlier techniques produced a good correlation with the present technique because of its unique approach. This used an 'anterior-posterior' axis for the scapula instead of 'medio-lateral' axis applied by others.
Glenoid inclination has not been as extensively discussed in the literature as the version. This might suggest that the parameter is not seen to be so important during shoulder arthroplasty. However, it is known that a more upward-facing glenoid increases the risk of superior humeral head migration, possibly associated with the genesis of rotator cuff disease. [5] Similar to the classical method of version calculation, inclination is based on defi ning a line joining two points only on the glenoid rim. [5,6] The second line has been differently defi ned in the literature. Churchill et al., [6] line joined the spine-medial border intersection to the glenoid fossa centre while Wong et al., [5] joined this to the spinoglenoid notch. The present study however, has demonstrated glenoid inclination based on a multipoint approach, using GNrim and SRL.
Quantifi cations based on the present proposals are easily realized using any standard shoulder or chest scans and do not require any special radiological scan of the patient. The derivation and application of subject-invariant axes in this   study would allow a more accurate inter-subject comparison of glenoid quantifi cation. This could allow better design of prostheses and ensure a more effective surfacing of the glenoid during total shoulder arthroplasty. The present technique' s sensitivity to numerically describing version and inclination and its insensitivity to scanning orientation suggest that this has the potential to be a clinical tool in assessing glenohumeral function. As a numerical technique, this can be automated and considerable time saved for the quantifi cation of these parameters. Further studies will have to be conducted to relate these parameters of version and inclination to clinical outcome.