Preliminary evaluation of an MRI-based technique for displaying and ...

Int J CARS (2013) 8:967–975 DOI 10.1007/s11548-013-0837-3

ORIGINAL ARTICLE

Preliminary evaluation of an MRI-based technique for displaying and quantifying bony deformities in cam-type femoroacetabular impingement Xiumei Kang · Honglin Zhang · Donald Garbuz · David R. Wilson · Antony J. Hodgson

Received: 17 December 2012 / Accepted: 18 March 2013 / Published online: 3 April 2013 © CARS 2013

Abstract Purpose Characterizing aspheric deformities of the femoral head–neck junction in cam-type femoroacetabular impingement (FAI) requires representing the location, size, or extent of the bony lesion. The objectives of this work are to (1) assess the feasibility of creating 3D models of cam deformities from MRI sets, (2) present a standardized 2D visualization of the lesion, and (3) present and evaluate the potential utility of summary metrics in distinguishing between FAI patients and control subjects. Methods Using MRIs from five subjects with diagnosed camtype FAI and four healthy subjects, we developed a technique based on subtracting an estimated normal surface from each subject’s actual bone surface in order to generate a subjectspecific 2D “diagnosis graph” that characterized the femoral deformity. The models from three control subjects were combined to create the baseline model. Results The RMS fitting error between the surface models of individual control subjects and their corresponding baseline models was 1.05 mm across the head and the head-to-neck X. Kang · A. J. Hodgson (B) Centre for Hip Health and Mobility, Vancouver Coastal Health Research Institute, Department of Mechanical Engineering, University of British Columbia, 6250 Applied Science Lane, Vancouver, BC V6T 1Z4, Canada e-mail: [email protected] H. Zhang · D. R. Wilson Centre for Hip Health and Mobility, Vancouver Coastal Health Research Institute, Department of Orthopaedics, University of British Columbia, 7/F, 2635 Laurel Street, Vancouver, BC V5Z 1M9, Canada D. Garbuz Division of Lower Limb Reconstruction and Oncology, Department of Orthopaedics, University of British Columbia, 3114-910 West 10th Avenue, Vancouver, BC V5Z 1M9, Canada

transition region. In the anterosuperior region of the 2D diagnosis graphs, the mean height of the detected cam deformities relative to the estimated baseline normal shape was 17.9 % of the head radius for the five FAI subjects (95 % CI 8.5– 27.3 %) and 7.0 % (95 % CI 2.9–11.1 %) for the four control subjects. A binary logistic regression analysis indicated that an h/r ratio larger than a threshold of ε = 10.7 % (equivalent to approximately 2.3 mm in height) yielded the best discrimination between cam-type FAI subjects and normal subjects. Conclusions Our 2D diagnosis graph qualitatively enabled the cam-type lesions in four of our five diagnosed patients to be clearly visualized on MRI-derived models. We believe this visualization tool may be helpful in better characterizing cam-type lesions for diagnosis and for developing more precise plans for surgical treatment.

Keywords Hip · Femoroacetabular impingement · Alpha angle · Computer-assisted diagnosis · Magnetic resonance imaging

Introduction Cam-type femoroacetabular impingement (FAI) is a mechanical hip disorder that is thought to be caused by abnormal contact between a deformed femur and the acetabular rim, which normally occurs at the anterolateral head–neck junction when the hip is flexed and internally rotated. This abutment is thought to cause damage to the acetabular labrum and the articular cartilage of the femoral head and acetabulum [1,2]. FAI is the main cause of groin pain, hip pain, and decreased hip range of motion (ROM) in athletes, and camtype FAI has a prevalence on the order of 24 % in high-activity

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athletes and 10–15 % of the general population according to [3], though cam-type FAI appears to be markedly more prevalent in young males than young females (27 vs. 0 % in a pair of population studies) [4,5]. Cam-type FAI is an important predisposing factor for the development of hip osteoarthritis (OA) in young adults. It is believed that early surgical intervention in patients with FAI will postpone or prevent the development of hip OA [6]. One of the challenges in FAI diagnoses and treatment is detecting and characterizing the location and size of the cam deformity. Morphological studies have shown that the femoral head is approximately spherical and that the crosssections of the femoral neck are approximately elliptical in shape [7]. The term alpha angle was first proposed by Notzli to describe the angle from the neck axis where the femoral head first departs from sphericity as seen in an oblique axial view containing the femoral neck axis [8]. The alpha angle has become and remains the most frequently used index for measuring the aspheric deformity of the femoral head–neck junction and for quantitatively distinguishing between camtype FAI and normal hip joints. It is also significantly correlated with the extent of cartilage defects within the hip joint [8,9]. Patients with confirmed cam-type FAI had an alpha angle greater than or equal to 55◦ [10], and it has been shown that surgery aimed at reducing the lesion results in a reduced alpha angle and increased hip ROM [11]. Due to natural anatomical variability, the alpha angle measured in a single pre-determined place may not represent the most significant plane of deformity. Audenaert et al. [7] found that the maximum alpha angle measured from multiple radial planes provided higher accuracy and diagnostic relevance than the alpha angle measured on the oblique axial view of the femoral head. Their technique was based on fitting a simplified geometric model (based on a sphere to represent the femoral head and an elliptical cylinder to represent the femoral neck) to the subject-specific bone surfaces derived from CT images. The cam deformity was defined as the portion of the subject’s bone volume that protruded beyond the fitted geometric model. Although this technique was shown to be more reliable than previous techniques, more recent and more detailed morphological models have suggested that the femoral head surface is better modeled as a rotational ellipsoid than a sphere [12], so this approximation assumption may limit the reliability of the measure. Lohan found that the alpha angle had considerable intraobserver variability and was statistically of no value in predicting the presence of cam-type FAI [13]. They presented an alternative measurement called anterior femoral distance (AFD), defined as the greatest perpendicular depth of epiphyseal overgrowth at the anterior femoral head–neck junction. Using AFD as the diagnosis indicator of cam-type FAI resulted in a performance measure of 0.67 (defined as the

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area under a receiver operator characteristic (ROC) curve describing the tradeoff between sensitivity and specificity). Even if measured on 3D image sets, the alpha angle or alternative measures such as the AFD are nonetheless single, summary measures of a spatially complex deformity and cannot be expected to correlate well with the actual limitations of motion experienced by a patient, nor can such summary measures be directly used to plan a surgical intervention. For such purposes, a more detailed model of the deformity is required. Due to the near-spherical geometry of the femoral head, it is convenient to represent its shape using a spherical coordinate system. Spherical representations have been successfully used for calculating the thickness of cartilage on the acetabulum and the femoral head for comparing the hips of non-osteoarthritic and osteoarthritic subjects [14]. A spherical medial representation (SM-Rep) was used for describing the ROMs of the hip joint [15]. Similarly, a spherical representation has been used to describe the ROM of the shoulder [16]. However, to date, the bony deformities found in FAI have not been characterized using a spherical representation. We are particularly interested in whether improved models of the deformity can be reliably obtained from MRI scans because many FAI patients are relatively young, so it is desirable to minimize these patients’ exposure to radiation. For this reason, there is interest in referring these patients for MRI scans rather than CT scans. Our laboratory has significant experience segmenting cartilage and bone in MRI scans, so we believe this approach is feasible. The objectives of the work presented here are therefore to (1) assess the feasibility of creating 3D models of cam deformities from MRI sets, (2) present a standardized 2D visualization of the lesion, and (3) present and evaluate the potential utility of summary metrics in distinguishing between FAI patients and control subjects. Methods Data acquisition MRIs of the right hip joint were acquired from five subjects with diagnosed cam-type FAI (mean age ± SD, 41.4 ± 7.7 years) and four subjects with no hip symptoms (mean age ± SD, 37±7.6 years) using a Philips Achieva 3.0 Tesla MRI scanner. Ethics approval was obtained from the UBC Clinical Research Ethics Board for the study protocol, and informed consent was obtained from the research subjects. Transverse images along the oblique axis of the femoral neck were taken using a high-resolution T1-weighted Dual Sense Spin Echo protocol. The in-plane resolution was 0.39 × 0.39 mm and the slice thickness was 1.997 mm. The scanning data were manually segmented using the image edit module in the biomedical image processing software, Analyze 10.0, to

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Fig. 1 The oblique axial MRI of the femoral head and neck region for a a normal subject with an alpha angle of 45◦ , and b a FAI subject with an alpha angle of 68◦ . c The corresponding surface model of the normal subject, and d the FAI subject

obtain the femoral bone surface models. We applied a defined protocol to edit and smooth the images (Fig. 1). Definition of hip spherical coordinate system To build the reference coordinate system, three landmarks were acquired from the 3D surface model of the femur: the femoral head center (FHC), the femoral neck center (NC), and the femoral center (FC) (see Fig. 2). The FHC was defined by applying a least-squares sphere-fitting algorithm to a 30 mm thick slice centered approximately on the equator of the femoral head which was initially identified on the 3D surface model. The NC was defined as the fitted center of the cross-section on the mid-neck plane perpendicular to the femoral neck axis at the point of greatest constriction. The FC was determined by estimating the centroid of the most distal slice of the distal femur (approximately at the proximal end of the lesser trochanter). A right-handed reference coordinate system is defined by the three landmarks, as shown in Fig. 2. The FHC is taken as the origin of the reference coordinate system. The line from NC through FHC corresponds to the Z axis. The X axis is perpendicular to the Z axis and lies in the plane defined by three landmarks of FHC, NC, and FC; it points roughly superiorly. The Y axis is orthogonal to the resulting Z and X axes and points anteriorly. We define a spherical coordinate system centered at the FHC, with the same Z and X axes as the reference coordinate system. It is parameterized by the radius r , inclination angle

Fig. 2 Definition of reference and spherical coordinate system on a right hip

θ , and azimuth angle ϕ. Any point (x, y, z) on the femoral surface model can be expressed using spherical coordinates (r, θ, ϕ). Registration of normalized femoral models to a baseline model In order to compare or combine different femoral head/neck models, as described in the following sections, we need to align the models with one another. A landmark identification process enables us to calculate a rough initial correspondence between different models, but to improve the registration, we apply the iterative closest point (ICP) algorithm implemented

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in the ITK package v3.20.0 [17]. When performing the ICP, we truncated each model at the level of the greater trochanter to minimize the influence of size differences between different models and applied a scaling factor based on the diameter of the femoral head. The resulting pointsets had different numbers of points and their point-to-point correspondences were unknown. When aligning a model from a subject with FAI to one without, we excluded the anterosuperior region of the FAI subject’s surface model so that the registration was based solely on the presumably undeformed portions of the bone surface. We defined the anterosuperior region as lying in the range of ϕ = 0◦ –90◦ and θ = 80◦ –140◦ where cam deformities typically occur. Generating two-dimensional (2D) shape maps A 2D shape map was developed to represent the 3D shape of the femoral head and neck based on a spherical representation. The spherical representation is similar to the concept of discrete global accessibility cones (GACs) and the global accessibility cone with depth of a truncated half-line (GACd(R) ) used in manufacturing automation to represent the workspace around a center [18,19]. By projecting directional vectors to the surface and calculating the distance from the FHC to the points of intersection with the surface, a shape map was generated in which radial distances to the surface are represented as a function of θ and ϕ. The 3D femoral head and neck surface was represented as a matrix of 180 × 360 elements, in which each element represented a direction from the FHC as a coordinate pair (θ, ϕ), where θ = 1◦ , 2◦ , . . . , 180◦ ; ϕ = 1◦ , 2◦ , . . . , 360◦ . The intensity at a pixel represents the distance from the FHC to the intersection point on the femoral surface. Figure 3 shows the generation of a 2D shape map using a ray-polygon

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Fig. 3 The generation of a 2D shape map. a A directional vector T (θ, ϕ) intersects with a triangular patch (in yellow), and is projected to a pixel p(θ, ϕ) on the 2D shape map (b)

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intersection algorithm. The triangulated mesh surface model of the femur consists of many triangular patches. Each patch consists of three vertexes. For a given patch (shown in yellow) in Fig. 3a, we determined four spherical boundaries θmin , θmax , ϕmin , ϕmax which corresponded to a small area on the 2D shape map shown in Fig. 3b. All vectors (θ, ϕ) within the boundaries of θmin , θmax , ϕmin , ϕmax were projected to the plane of the triangular patch. The intersection points inside the triangular patch and the corresponding distances to the FHC were recorded. Based on the definition of the coordinate frame described above, we divided the femoral head into four sub-regions: superior (ϕ = 315◦ –360◦ and ϕ = 0◦ –45◦ ), anterior (ϕ = 45◦ –135◦ ), inferior (ϕ = 135◦ –225◦ ), and posterior (ϕ = 225◦ –315◦ ). The alpha angle is calculated as 180◦ less the smallest inclination angle θ at which the radial distance to the bone surface exceeds the fitted spherical radius R by a specified threshold value that represents a small multiple of the typical variation of the femoral head radius in the spherical portion of the head. Generating a 2D diagnosis graph Although a 2D shape map accurately represents the shape of the femoral head and neck region, it is difficult to distinguish abnormal cam deformities from the shape map alone as there is no built-in reference for what is considered “normal.” However, since the anatomical structure of the femur is similar to control subjects and subjects with FAI outside of the region of the cam deformities, we constructed a 2D diagnosis graph by subtracting a subject-specific estimate of the shape map for a non-deformed bone from the subject’s actual shape map derived from the MRI segmentation process. In principle, one would wish to use as much information as possible in constructing the estimate of the non-deformed bone. For example, it would be ideal to generate a normal shape map using the subject’s own contralateral hip if it is lesion-free. Another plausible approach might be to construct a statistical shape model of the proximal femur. However, since our goals are more modest—namely, to demonstrate the feasibility of our approach—and since we have not yet built up a sufficiently large MRI library of proximal femur models, we have adopted a simpler technique for use in the current study; we have simply averaged the shape maps derived from a small number of control (normal) subjects, after scaling based on the radius of the best-fit of a sphere to the femoral head and registering the surface models to one another using the previously described ICP algorithm. The resulting averaged shape map becomes the baseline normal shape map. This baseline “normal” shape map was then compared with the subject’s shape map derived after registering the subject’s 3D surface model to a reference model in the set

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of control subjects by applying a scaling factor based on the ratio of femoral head diameters, roughly aligning the models based on matching the coordinate frames defined for each model, and performing a final fine registration using the ICP algorithm with the anterosuperior region deleted from the subject’s shape. Following subtraction of this normalized baseline normal shape map from the subject’s shape map, any negative values are set to zero. We call the resulting difference distribution (expressed as a normalized height/radius ratio in %) a diagnosis graph, and plot it on a polar plot with the radial distance corresponding to the inclination angle θ ; however, since the proximal portion of the femoral head is essentially unaffected, the diagnosis graph is more informative if we start the plot at θ = 70◦ (i.e., the radial distance is proportional to θ − 70◦ ). Following this processing, the height ratios on the diagnosis graph can be multiplied by the femoral head radius in order to calculate lesion height, surface area, and volume. The apex of the cam lesion can be easily identified on the 2D diagnosis graph as the point of maximum height of the cam lesion. The surface area of the lesion can be estimated as the total number of nonzero pixels in the anterosuperior region multiplied by the surface area represented by each pixel. The volume of the lesion is calculated as the sum of the products of the surface area and height represented by each nonzero pixel in the anterosuperior region of the 2D diagnosis graph. A height/radius (h/r ) ratio representing the ratio of the lesion’s maximum height to the estimated radius of the spherical portion of the femoral head is computed to characterize the degree of protrusion of the cam lesion. Due to shape variations among subjects, the values in the 2D diagnosis graph of a control subject may not be all zero, though the maximum height will normally be much smaller than that of a FAI subject. To focus attention on significant lesions rather than normal minor variations in the diagnosis graph, we used a binary logistic regression analysis on the ROC graph to select the optimal h/r ratio threshold, ε, for distinguishing FAI subjects from control subjects. We then computed a thresholded version of the diagnosis graph by subtracting the baseline shape map plus the threshold value, ε, from a specific subject’s shape map and setting any negative values to zero.

Results Nine femoral head models consisting of an average of 5,003 triangular patches were generated from the scanned MRI of the hip joints. The mean estimated femoral head radius for the nine models was 22.3 mm, and the average SD of the residuals relative to a pure sphere was 1.1 mm. The diagno-

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sis graphs of the five FAI subjects were generated relative to the baseline shape map formed by averaging three control subjects (subjects 1, 2, and 4). The diagnosis graphs of each of the four control subjects were generated relative to the baseline map formed by averaging the remaining three control subjects (i.e., using a “leave 1 out” strategy). The mean difference for our four control subjects relative to the corresponding baseline shapes ranged from −0.9 % (−0.2 mm) to 1.9 % (0.4 mm), and the individual RMS deviations ranged from 3.6 % (0.8 mm) to 7.0 % (1.5 mm); the overall average RMS deviation across all four subjects was 1.05 mm. The 2D diagnosis graphs clearly show the location and extent of the cam deformity. In two subjects, the cam deformity is located in the anterosuperior area (Fig. 4b, c), while in two others, the cam deformity is primarily distributed in the superior area (Fig. 4a, e). In one specimen, only a slight deformity can be seen (Fig. 4d). In the control subjects, there is only a small indication (the small, light blue regions) of any difference between the control subject and the scaled, averaged, registered baseline shape map (Fig. 4f–i). Although the number of subjects is too small to draw definitive statistical conclusions, the five FAI subjects had significantly larger mean maximal h/r ratios (17.9 vs. 7.0 %), heights (3.9 vs. 1.6 mm), and volumes (346 vs. 170 mm3 ) for the cam deformity than the four control subjects, though the mean surface areas were similar in the two groups (247 vs. 228 mm2 ) (Table 1, see columns for ε = 0). The 95 % confidence interval for the mean h/r ratio in the FAI group was 8.5–27.3 % versus 2.9–11.1 % in the control group. On average, the FAI subjects had a h/r ratio 10.9 % higher than control subjects ( p = 0.037, Student’s t test). When diagnosing FAI on the basis of the alpha angle, it is common to use a threshold value of 55◦ [9]. Based on this criterion, two of the FAI subjects would be misdiagnosed, so we explored whether or not an alternative measure might provide improved discrimation performance. The ROC curve corresponding to the height/radius ratio (shown in Fig. 5) had an area under the curve of 85 %. A binary logistic regression analysis indicated that a threshold of ε = 10.7 % (equivalent to approximately 2.3 mm in height) yielded the best discrimination performance, as measured by Youden’s Index (Se + Sp − 100 %); for this value of ε, the sensitivity was 80 %, the specificity was 100 %, and Youden’s Index was 80 %. Using this threshold, we computed the thresholded diagnosis graphs for all subjects (see example in Fig. 6). As shown in the columns labeled ‘ε = 10.7 %’ in Table 1, the surface area of the lesions was reduced in all subjects; for the control subjects, all lesions were eliminated, while for the five FAI subjects, only one lesion was eliminated. By excluding those areas where the subject’s shape map was within the

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Fig. 4 2D diagnosis graphs (height/radius ratio in %, prior to subtracting threshold value ε) in the femoral head and neck area for subjects with FAI (a–e), and normal subjects (f–i). j indicates the color coding associated with images (a–i) (in % of h/r ratio). The cam deformi-

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Table 1 The alpha angle, maximum height, h/r ratio, surface area, and volume of identified cam lesions Group

α (◦ )

Subject

FAI

h/r (%)

Surface area (mm2 )

Volume (mm3 )

ε=0

ε = 10.7 %

ε=0

ε = 10.7 %

161

55

1

43.8

4.0

18.0

127

17

2

68.1

6.7

31.4

446

155

875

618

3

61.9

3.2

14.5

353

46

377

121

4

54.9

1.0

4.4

101

0

44

0

5

63.3

4.8

21.3

211

45

275

148

58.4 ± 9.4

3.9 ± 2.1

17.9 ± 9.8

247 ± 148

52 ± 60

346 ± 320

188 ± 247

1

44.9

2.3

10.7

373

368

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44.3

0.6

2.8

130

24

3

48.4

2.1

8.8

211

175

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38.5

1.3

5.6

197

104

44.0 ± 4.1

1.6 ± 0.8

7.0 ± 3.5

228 ± 103

Mean ± SD Control

Height (mm)

Mean ± SD

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170 ± 142

0

Surface areas represent the total area of the diagnosis graph with positive values after applying either a zero (ε = 0 %) or a non-zero (ε = 10.7 %) threshold. Volumes represent the total volume of the lesion lying above the baseline shape map in the nonzero regions of the diagnosis graphs

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Fig. 5 Receiver operating characteristic curve for discriminating between FAI and control subjects based on the height/radius ratio (in %). The larger square indicates the optimal threshold value

threshold value of the baseline shape map, the total lesion size was reduced by an average of nearly 50 % from 346 to 188 mm3 . To assess the sensitivity of the lesion measures to the selection of control subjects included in the underlying “normal” model, we computed five different baseline shapes formed by alternative sets of control subjects. The standard deviations of the resulting deformity measures for the FAI subjects were all less than 5 % of the nominal value (e.g., the mean h/r ratio was 18.1 ± 0.7 % across the five sets). We therefore conclude the lesion measures are not particularly sensitive to the choice of baseline normal subjects used to compute the averaged baseline shape map.

In this paper, we have demonstrated the feasibility of characterizing cam-type FAI lesions by comparing a bone surface model derived from an MRI scan of a subject with FAI to a model derived from subjects without FAI. The 2D diagnosis graph that arises following scaling, alignment, and subtraction succeeded in clearly identifying the lesion in four of the five subjects with clinically identified cam-type lesions. However, because this is primarily a feasibility study with a relatively small number of subjects, we are not yet able to draw any substantive conclusions as to the relative reliability of the various summary measures we propose compared with the existing alpha angle measure. Our quantitative results for MRI-derived models are comparable to those from an earlier study based on CT imaging. Audenaert et al. used a similar technique of subtracting a model of the undeformed head and neck region (based on fitting a sphere and an elliptical cylinder to the femoral head and mid-neck regions) to identify the extent and shape of the cam lesion [11]. They report the average fitting error to be 0.37 mm in the region of the proximal femoral head and 0.68 mm in the mid-neck region. By way of comparison, our average fitting error across the spherical portion alone was 1.1 mm and across the entire model (i.e., including both the head and the head-to-neck transition region) was 1.05 mm, or slightly larger than what Audenaert et al. found. Although our accuracy was marginally lower than Audenaert et al.’s results, this is understandable given that our models were derived from MRI scans in which the slice thickness was significantly larger than in CT scans (2.0 vs. 0.63 mm). We also found results similar to Audenaert’s [11] in terms of typical lesion height (3.9 mm in our study vs. 3.2 mm in

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Fig. 6 The 2D diagnosis graph (height/radius ratio in %) after subtracting the baseline shape map (from subject 1, 2, and 4) plus a threshold value ε = 10.7 % for a FAI subject with a cam lesion (a), and a control subject without a cam lesion (b), which correspond to subjects (b) and

(f), respectively, in Fig. 4. The corresponding 3D models of (a) and (b) show the detected cam lesion (c) and no cam lesion (d) by the diagnosis graph analysis

Audenaert’s), and surface area for the non-thresholded diagnosis graphs (247 vs. 326 mm2 ). The ROC area metric in our study of 85 % (based on the maximum lesion height/radius ratio) had a larger value than their metric based on the Anterior Femoral Distance (85 vs. 67 %), though we could not demonstrate statistical significance for this difference due to the relatively small number of samples in our data set. We believe that the errors involved in calculating 2D diagnosis maps are small relative to the size of FAI cam deformities. There are three main sources of error and/or variability: producing a segmented and smoothed model from MRIs, approximating the spherical surface with triangular patches, and registering the femoral models. The manual segmentation process introduces both intra- and inter-observer variability. Reinbacher evaluated the variability of segmenting knee cartilage using a semi-automatic segmentation method. The intra-observer variability based on Dice’s similarity coefficient (DSC) for two datasets was 0.936 and 0.932, respectively, and the corresponding inter-observer variability was 0.914 and 0.925 [20]. Since it is somewhat easier to segment bone than cartilage, we anticipated a higher DSC for our approach. We reanalyzed one specimen with both a primary and a secondary analyst and found that the intra- and inter-observer variabilities were 0.984 and 0.982, respectively (DSC scores), which implies that the volumetric discrepancy due to the segmentation process is under 2 %. The triangular patch approximation process created a distance

error with a standard deviation of approximately 0.04 mm, which is an order of magnitude smaller than the errors associated with segmentation, so this error can likely be ignored. The registration process introduces errors due to variability in selecting landmarks; these errors were reduced by following the initial registration with a fine registration step based on surface matching. Fine registration was affected by how much of the model could be used in the fine alignment step. We used the femoral head and neck portion of the model and excluded the greater trochanter in the fine registration step to minimize the influence of shape and size differences more remote from the areas of interest in this study. The fine registration error was estimated by displacing a selected model by the maximal angles and distances between the initial coarse and final registrations found among the remaining eight models, re-registering the transformed model to the original model, and comparing the difference in the final transformation parameters. The registration error was less than 0.5◦ (around the z axis) and 0.04◦ (around the x and y axes) in rotation, and less than 0.0003 mm in translation. Our method has potential application in preoperative surgical planning, which is required for to accurately resect the cam lesion. Brunner et al. proposed a CT-based navigation system to improve resection accuracy in arthroscopic surgery [10]. However, their system was unable to improve the accuracy of lesion resection—24 % of their patients ended up with insufficient correction of the alpha angle. The likely

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reason is that their system did not incorporate a preoperative surgical plan with a marked resection for the cam lesion; instead, the system only displayed the position of the surgical tools relative to the femoral head. In contrast, Audenaert et al. proposed a protocol for navigated surgical resection of the cam resection using a preoperatively computed surgical plan. Using three artificial Sawbone models, they demonstrated that the accuracy of their system, defined as the RMS error between the planned cam resection and the resulting surface, was excellent at only 0.14 mm [21]. Given the similarity in fitting error between our approach and Audenaert’s, our method could therefore likely enable MRI-derived models to be used for diagnosis, preoperative planning, visualization of the cam lesions during the surgery, and postoperative assessment of the resection accuracy of cam lesions. Combined with a real-time update of the position of surgical tools, the location and depth of cam lesions could be updated and visualized dynamically on both a 2D diagnosis graph and a 3D femoral model during a computerassisted surgery procedure.

Conclusion This study has presented a novel diagnosis graph for detecting and visualizing the location and size of cam lesions. Qualitatively, our 2D diagnosis graph enabled the cam-type lesions in four out of five clinically diagnosed patients to be clearly visualized using MRI-derived models, while no control subjects were misclassified. This visualization tool may help surgeons better characterize cam lesions for diagnosis and develop more precise surgical plans for treatment and may be incorporated into future computer-assisted surgical procedures.

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Acknowledgments Dr. Kang was supported by the Natural Sciences and Engineering Research Council of Canada (NSERC) through a Postdoctoral Fellowship and conducted her research at the Center for Hip Health and Mobility at Vancouver General Hospital, Canada.

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Conflict of interest The authors declare that they have no conflict of interest.

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