Accuracy assessment of CT-based outer surface femur meshes

Abstract

Objectives: Computer-aided bone surgery planning and implant design applications require accurate and compact representations of the patient's bone. The accuracy of bone segmentation from medical images has been studied extensively, with each study using a specific ground truth and a specific type and number of accuracy measurements. However, for convenience and practical reasons these three specifications have always been limited. The goal of this study is to thoroughly assess the absolute 3D accuracy of CT-based bone outer surface meshes, using femora as the examples.

Materials and Methods: Using dense and very accurate optical surface scans of 15 dried femora as an absolute ground truth, this paper reports on the absolute 3D geometric accuracy of triangulated bone outer surface meshes, which were segmented from the CT scans of the corresponding formalin-fixed intact cadaver specimens using the author's previously presented contour-based segmentation algorithm on the one hand, and the commercially available Mimics® software (Materialise N.V., Leuven, Belgium) on the other. The study incorporates the effect of soft tissue presence on hard tissue segmentation and simultaneously reveals the accuracy shift introduced as a result of boiling the cadaver bones by processing extra CT scans of the dried bones.

Results: The presented study demonstrates that, when using the optimal parameter settings for the respective segmentation procedures, sub-voxel mesh accuracies can be attained. Compact surface representations of femora can be generated with mean absolute accuracies of up to one fifth of the voxel size and Root Mean Square (RMS) error of half the voxel size.

Conclusions: The 3D accuracy of the contour-based segmentation previously presented by the author makes it most suitable for generating outer bone surface meshes for use in the aforementioned applications. The optimal parameter settings for this segmentation procedure have been identified. For the Mimics® bone surface meshes, a single, but excellent, pre-defined set of parameters was identified.

• CT
• bone segmentation accuracy
• surface meshes
• geometrical ground truth
• computer-aided implant design
• computer-aided bone surgery planning

Introduction

Computer-aided bone surgery planning and implant design applications require accurate and compact representations of the patient's bone [1–9]. The accuracy of bone segmentation from medical images has been studied extensively, with each study using a specific ground truth and a specific type and number of accuracy measurements.

For convenience and practical reasons, the geometrical ground truth is very often a software or hardware phantom [10–13], possibly abstract in shape, or a dry cadaver [14]. Studies on cadavers with soft tissue [15–18] are more elaborate, and are practically limited to a feasible number of measurements, especially if these are to be processed manually. A common example is the acquisition of distances between marked anatomical reference points, which are few by nature.

Measurements mostly come down to quantifying the Euclidean distance between two corresponding points, and correlate directly with the underlying application field. For example, in the case of cranio-maxillofacial implant position planning, the implant insertion length and thus the bone thickness of the bone models is investigated. Measurement points are retrieved manually or automatically from intensity profile lines [15] or visually from the voxel data [17], not from the calculated surface meshes, and possibly in specific anatomical planes [18].

In the case of personalized implant design for bone reconstructions, not only the orientation, but also the 3D shape accuracy of the implant is important, and this in absolute terms: A custom-made implant created from inaccurate models will simply not fit into the complementary bone defect. Fully 3D measurement approaches for triangulated surface meshes have been described in the literature [19], though in the clinical studies an absolute geometrical ground truth seemed to be unavailable. This is fully understandable in the case of in-vivo imaging of brain or other soft tissues, where opening up the cadaver for dissection and measurement causes a collapse of the soft tissue target structure. A possible solution is to perform relative comparisons, e.g., by comparing with another, clinically established, imaging technique [15]; by performing leave-one-out experiments when working with a statistical database approach and training set for testing the accuracy of deformable models data [20–22]; or by checking coherency within the same data set [23].

Measurements are mostly very limited in number, user-dependent, and assessed from only a small number of specimens. The first two shortcomings can be resolved by using fully automated computer-based measurement algorithms [15], [19]. To address the third shortcoming, however, an adequately enlarged specimen set is still needed.

Lascala et al. manually assessed 13 distances between marked skull landmarks on 8 dry skulls, using a caliper on the one hand, and a CT software indicating tool on the other [14]. Marmulla et al. built an abstractly shaped test cube with accurately known reference points, and assessed the 3D deviations for 172 corresponding–manually segmented–points in the CT data [13]. Cavalcanti et al. performed two specific linear measurements in all 2D resliced CT images of 8 cadaver maxillae [18]. The images–between 20 and 35 per cadaver–were oriented orthogonally to the bone, in accordance with the planning of dental implant placement. Caliper measurements made on the filmed images by four physicians were compared to electromagnetically digitized cadaver measurements.

Pinsky et al. performed 3D measurements for small simulated cylindrical defects in an acrylic mandible model (64), and on a dry mandible bone (21). Multiple examiners assessed the physical sample dimensions twice, while one examiner performed manual software measurements with the same frequency [16].

Loubele et al. presented an automated method for performing linear bone thickness measurements in CT images. This method was applied to both the maxilla and the mandible of two head phantoms to assess the measurement accuracy in cone beam CT images. As no absolute ground truth was available, they used the clinically established multi-slice spiral CT imaging technique as a reference [15]. Although prominent, this study once more shows that the general term “bone segmentation quality” should be treated carefully. In this method, a triangulated smoothed bone mesh is first extracted from the images (using the Marching Cubes algorithm [24]). The triangle normals then determine the measurement directions, which results in approximately 3800 to 5500 measurements per bone mesh. Subsequently, the measurements themselves are not retrieved from the mesh, but from voxel intensity profile lines along the measurement direction. This type of measurement specifically conforms to CT voxel-based planning software for dental implant placement.

Using dense and very accurate optical surface scans of 15 dried femora as a ground truth, the current paper reports on the 3D geometric accuracy of triangulated bone outer surface meshes, which were segmented from the CT scans of the corresponding intact formalin-fixed cadaver specimens by means of the previously presented contour-based segmentation algorithm [25] on the one hand, and by the commercially available Mimics® software (Materialise N.V., Leuven, Belgium) on the other. For each segmentation approach, the effect of different segmentation parameter settings on the mesh accuracy was analyzed. The study incorporates the effect of soft tissue presence on hard tissue segmentation and simultaneously reveals the accuracy shift introduced by boiling the cadaver bones by processing extra CT scans of the dried bones. Accuracies are reported for the entire femur bone mesh, as well as for proximal, diaphyseal and distal parts in particular.

In combination with data which describe the influence of formalin on the femoral bone geometry, the presented accuracy results offer an absolute validation of the meshes used in subsequent computer-aided surface-based bone surgery planning and implant design applications.

Materials and methods

Acquisition of the CT-based bone surface models

The lower extremities of nine formalin-fixed cadavers (Caucasian; mean age 85 ± 10 years; 1 male, 8 female) were scanned with a SOMATOM Sensation spiral CT scanner (Siemens AG, Erlangen, Germany) (voxel size: 1 mm × 1 mm ×1 mm). From these CT scans, the outer surface meshes of seven left and eight right healthy femora were extracted using the author's previously presented Filter & Mesh base platform [9], [25] on the one hand and the commercially available Mimics® software (Version 10.0) on the other.

The first method defines a bone Hounsfield window and applies a Marching Squares algorithm [24]–embedded in the Mimics® software–to obtain in-slice bone contour information. Subsequently, a set of automated Matlab® (Version 14, SP3, The MathWorks Inc., Natick, MA) routines only retains contour information representing the outer bone surface and removes noise, redundant (parts of) contours and shape irregularities. Subsequently, periodic least-squares approximating splines are calculated. The maximum deviation between a specific polyline point and its corresponding spline point is user-defined. Finally, the splines are uniformly sampled and a triangulated surface mesh of the outer bone surface is built. The surface mesh is exported to an STL (Standard Triangulation Language) file.

Using the same respective bone Hounsfield windows, the second method also starts with a Marching Squares algorithm, but in order to remove (most of) the internal information in an automated manner, a mask cavity fill operation is performed on the polyline set. Surface meshes are then obtained by applying a Marching Cubes algorithm for a specific resolution of the CT images (= matrix reduction–see below). In addition, a mesh smoothing and mesh triangle reduction can be applied. Note that this segmentation acquisition approach successfully removes contours which are fully internal, but does not separate internal information from contours which contain both internal (trabecular) and external (cortical) parts. For convenience, however, we further address these meshes–in parallel to the first segmentation approach–as outer surface meshes too.

Both segmentation methods were repeated, each with specific parameter settings as presented in Tables I and II. For the author's method [25], these were the number of points per spline (pps) and the spline accuracy value (spAcc). In addition, the interslice distance (IsDist) of the input image set was also varied; a parameter which was added to investigate the minimal specifications needed to obtain accurate meshes with a clinically acceptable CT scan protocol. This resulted in the CT mesh “classes” 1 to 7; “groups” of classes were defined to investigate the influence of one parameter setting when all others are kept unchanged. More specifically, these were groups 215, 316 and 347, which check the influence of a varying interslice distance (1, 2 or 3 mm, with spAcc of 1 mm and 35 pps), spline accuracy value (0.4, 1 or 1.6 mm, with IsDist of 2 mm and 35 pps) and points per spline (35, 50 or 75, with IsDist of 2 mm and spAcc of 0.4 mm), respectively.

Table I.  CT surface mesh classes, using the self-developed Filter & Mesh procedure of Gelaude et al. [25]. (pps: points per spline; spAcc: spline accuracy value; IsDist: interslice distance. Each class consists of 15 entire femur meshes; notice that a smaller spline accuracy value (spAcc) designates a higher spline accuracy.) Note: from this table, “groups” of classes were defined to investigate the influence of one parameter setting when all others were kept unchanged, e.g., groups 215, 316 and 347, which check the influence of a varying IsDist, spAcc and pps, respectively.

	Segmentation parameter settings			Number of triangulation faces
Class ID	pps	spAcc	IsDist	Mean	Std	Max	Min
1	35	1.0	2	15532	482	16693	14873
2	35	1.0	1	30387	960	32653	29013
3	35	0.4	2	15532	481	16693	14873
4	50	0.4	2	22186	688	23848	21247
5	35	1.0	3	10605	283	11303	10253
6	35	1.6	2	15535	481	16693	14872
7	75	0.4	2	33282	1031	35773	31873

For the Mimics® approach, the parameters were the matrix reduction, smoothing and triangle reduction, for which a specific combination is available to the user as one of the pre-defined STL export-settings low/medium/high/optimal (CT mesh classes L, m, h and o, respectively; see Table II for a detailed description). Matrix reduction designates a lowering of the CT resolution by combining voxels geometrically and averaging the voxel intensities. The underlying concept of matrix reduction is to speed up the computation and to obtain a smaller mesh size. The interslice distance for the Mimics® approach–being 1 mm–is kept unchanged.

Table II.  CT surface mesh classes, using Mimics® (Version 10.0). (resolution = with regard to matrix reduction, how many voxels were geometrically merged and averaged by their intensity value; * 2 iterations, smoothing factor 0.3; ^** advance edge reduction algorithm, tolerance (pixel size)/8, edge angle 10, iteration 3. All classes use the contour interpolation method (2D partial volume compensation) and an interslice distance of 1 mm; each class consists of 15 entire femur meshes).

	Segmentation parameter settings				Number of triangulation faces
Class ID	XY resolution	Z resolution	Smoothing	Triangle reduction	Mean	Std	Max	Min
L	6	2	no	no	15658	2086	20884	12582
m	3	2	no	no	32726	5023	44468	26136
h	2	1	no	no	95497	15466	130116	75972
o	1	1	yes*	yes^**	66367	17156	100160	48038

Acquisition of the optical bone surface scans

The soft tissues were initially removed from the cadavers manually, with the process then being completed by boiling and fat removal. Mounted on a rigid pin inserted distally in the intramedullary canal (Figure 1), the outside geometry of the dry femora was assessed using an optical measuring device (LC50 laser stripe scanner, Metris N.V., Leuven, Belgium). This device determines the distances between measurement points on the object and the scanning head, and combines it with the 3D information from a coordinate measuring machine (MC16, Coord3, S.p.A, Turin, Italy). The accuracy of the measuring system is–as specified by the manufacturer–between 15 and 35 microns. The (3D grid) sampling density for the measured point clouds was at least 0.2 mm.

Figure 1. Experimental set-up for optical surface scanning with the Metris LC50, mounted on a Coord3 MC16 coordinate measuring machine. The dry femur is mounted by inserting a rigid pin distally in the intramedullary canal, and is positioned obliquely with respect to the ground plane. Pre-drilling of the femur with a slightly smaller diameter than the pin diameter ensures rotational stability of the bone.

Assessing 3D deviations between CT-based and optical surface meshes

Using the Metris Focus Inspection® software (Version 8.2, Metris N.V., Leuven, Belgium), the optically scanned point cloud of each femur was (down)sampled using a uniform grid filter of size 1 mm and converted into a manageable STL surface mesh. The latter, also denoted as the “measured” set, was first manually aligned with the corresponding CT-based surface mesh (the “nominal” mesh) using anatomical landmarks distally at both condyles and proximally at the femoral head and the lesser and greater trochanter. A rigid matching algorithm (Iterative Closest Point [26]) then established the best match between the two meshes. In matched position, for each vertex of the measured triangulation, the projective 3D deviation to the nominal was calculated by projecting the measured vertex in surface normal orientation onto the nominal mesh, and calculating the Euclidean distance between the vertex and nominal intersection point. If the latter was located externally with respect to the measured mesh, the 3D deviation was assigned a negative value.

The 3D deviations between the optically scanned entire femora and each of the corresponding parameter-specific CT meshes (the aforementioned classes) were exported as ASCII text-files to the Matlab® environment for post-processing. For each bone, outliers were removed by applying an acceptance window of four standard deviations around the mean 3D deviation. In this study, outliers could originate from the CT acquisition as well as from the optical scanning technique, from small-scale bone defects introduced by boiling and handling of the cadaver bones, and–in the case of the Mimics® segmentation approach–from the presence of internal contour parts (see above). Outlier vertices were visualized and carefully inspected.

The 3D deviations between the uniformly sampled measured meshes and nominal CT meshes of the same class were merged and processed statistically. More precisely, the meanX, standard deviation σ, and maximum values of the 3D deviations were retrieved. For each of the CT mesh classes, Student t-tests were performed on the mean 3D deviations to check whether the CT meshes were significantly different from the ground truth geometry and from the other group members. Additionally, since the femur consists of three distinct shape-complex regions–being the proximal part with the femoral head and trochanters, the cylinder-like diaphyseal part and the distal condyles part, each related to clinically distinct applications–the above-described analysis for the entire femur was also run for the subportions of the bone (Table II). These are defined as the proximal and distal thirds of the femur, while the diaphyseal part encompasses the central 3/4 portion of the femur.

Assessing influence of soft tissue presence and boiling

As described in the previous section, the dry bones of the cadaver specimens were compared to the segmented CT-based bone meshes of the same specimens (Figure 2). As soft tissue is present in these CT data, and as boiling of the cadaver bones may have an impact on the resulting 3D deviation statistics, additional CT scans of the 15 dry bones were acquired and segmented with one of the aforementioned class segmentation algorithms. In this case, the resulting 3D deviations can only be attributed to the CT scanning machine and the CT segmentation algorithm; in the case described in the previous section some additional influence due to the soft tissue presence and boiling is possible. Comparing the additional dry bone CT scan deviation statisticsX_B ±σ_B with the above-described soft tissue CT scan deviation statistics X_A ±σ_A therefore allows quantification of the combined effect of soft tissue presence and boiling on the latter deviation statistics.

Figure 2. Comparison scheme. To assess the combined influence of soft tissue and boiling on the comparisons “A” between dry bone ground truths and bone meshes segmented from intact cadaver CT scans, additional dry bone CT scans are similarly processed (“B”) by one of the class L, m or h segmentation algorithms (Table II). Relative comparison of the 3D deviation statistics (mean X, standard deviation σ) for A and B then cancels out the contribution of the segmentation algorithm, and–if the same scanner and settings are used–of the CT machine as well.

Results

Fifteen cadaver femora were CT scanned and segmented, resulting in 165 CT-based triangulated outer surface meshes. Depending on the parameter settings used, the meshes were allocated in 11 classes (Tables I and II). The cadaver bones were dried and densely scanned on their outer surface by means of a laser scanner; these scans serving as the absolute geometrical ground truth. Using a uniform grid filter of size 1 mm, a sample of this point cloud was selected to determine the 3D deviations with the CT meshes of the corresponding bones. The resulting 3D deviations for each class were processed statistically and can be compared in groups for a specific femoral portion.

The statistics are tabulated in Table III, and graphs are presented for the entire femur in Figure 3.

Figure 3. Graphs showing 3D deviations of CT meshes for the entire femur. (pps = points per spline; spAcc = spline accuracy value; IsDist = interslice distance. Note that a smaller spline accuracy value (spAcc) designates a higher spline accuracy.) (See Tables I and II for class ID and Table III for statistics.) [Color version available online.]

Intact specimen CT scans: statistically significant differences (Comparisons A)

All classes of parameter settings resulted in CT meshes that were significantly different from and inflated with respect to the corresponding dried femora (P < 0.001). The same statement holds true for the proximal, diaphyseal and distal parts. Comparisons between classes of the same group indicate that all segmentation settings resulted in a significantly different mean 3D deviation (P < 0.005), except for class 1 versus class 5 in the proximal (P = 0.19) and distal (P = 0.12) parts, and that all variances are significantly different.

Table III.  Three-dimensional deviations of cadaver CT femur meshes (in mm). (X: mean; σ: standard deviation; A: see Figure 2; class ID: see Tables I and II; n: number of measurements; a negative 3D deviation indicates that the CT mesh is inflated.)

	Entire femur
Class ID	XA	± σA	Max	Min	n
1	−0.71	±0.56	4.39	−5.20	1111498
2	−0.69	±0.54	4.11	−5.08	1111290
3	−0.70	±0.55	4.34	−5.17	1111092
4	−0.72	±0.53	4.24	−5.30	1110876
5	−0.71	±0.58	4.78	−5.57	1111226
6	−0.72	±0.60	4.47	−5.34	1112331
7	−0.73	±0.52	4.16	−5.14	1110579
L	−3.10	±0.79	2.63	−8.15	1113160
m	−1.66	±0.55	3.29	−6.06	1111341
h	−1.14	±0.50	2.96	−5.26	1111555
o	−0.62	±0.49	3.40	−4.79	1112266
	Proximal femur
Class ID	XA	± σA	Max	Min	n
1	−0.77	±0.53	2.47	−3.99	432517
2	−0.74	±0.51	2.42	−3.89	432429
3	−0.76	±0.52	2.49	−3.98	432376
4	−0.78	±0.50	2.47	−4.02	432213
5	−0.77	±0.54	2.45	−4.02	432523
6	−0.78	±0.56	2.46	−4.07	432854
7	−0.79	±0.49	2.46	−4.02	432157
L	−3.14	±0.77	0.78	−6.72	432791
m	−1.71	±0.52	1.56	−4.77	432226
h	−1.18	±0.49	2.13	−4.36	432276
o	−0.67	±0.45	2.11	−3.43	432383
	Diaphyseal femur
Class ID	XA	± σA	Max	Min	n
1	−0.70	±0.32	1.91	−2.71	617847
2	−0.69	±0.31	1.84	−2.46	617962
3	−0.69	±0.29	1.78	−2.62	617288
4	−0.71	±0.28	1.94	−2.63	617198
5	−0.71	±0.32	1.88	−2.72	617866
6	−0.72	±0.38	2.12	−2.85	618728
7	−0.72	±0.28	1.90	−2.63	617256
L	−3.27	±0.47	−0.29	−5.38	618213
m	−1.73	±0.33	0.84	−3.73	617848
h	−1.18	±0.31	0.95	−2.71	618167
o	−0.62	±0.35	1.67	−2.25	618852
	Distal femur
Class ID	XA	± σA	Max	Min	n
1	−0.62	±0.80	6.98	−7.20	439270
2	−0.61	±0.76	6.55	−7.06	439091
3	−0.62	±0.79	6.93	−7.16	439150
4	−0.64	±0.76	6.75	−7.51	438854
5	−0.63	±0.83	7.57	−7.52	439242
6	−0.64	±0.83	7.05	−7.28	439542
7	−0.65	±0.75	6.66	−7.19	438890
L	−2.93	±0.99	5.14	−9.99	440391
m	−1.54	±0.75	5.74	−7.86	439248
h	−1.04	±0.68	4.99	−7.12	439384
o	−0.55	±0.67	5.43	−6.67	439591

Mutual comparison of the three femoral parts (proximal/diaphyseal/distal) reveals a significant difference for the mean 3D deviation. (Note: The mean 3D deviation of the diaphyseal part in classes 1 and 5 is not significantly different with respect to the corresponding mean of the entire bone mesh.) Maximum deviations were smallest for the diaphyseal part and largest for the distal part. The distal mean 3D deviation is better than the proximal value, but the dispersion is much higher.

Dry bone CT scans (Comparisons B)

The dry bone CT scans were segmented in Mimics® with a threshold slightly larger than the Hounsfield value for air (-1000 HU). STL surface meshes were created, for example, with the pre-defined “high” algorithm settings (class h - see Table II). The resulting 3D deviation statistics with respect to the sampled ground truth specimens (B), and the mean offset with respect to the intact specimen deviations (Δ X_AB) for each of the femoral portions are shown in Table IV. The difference in the means with respect to A amounts to approximately 0.5 mm (half the in-slice voxel dimensions), and is highly significant.

Table IV.  Three-dimensional deviations of dry bone CT meshes (in mm) using segmentation algorithm of class h (see Table II) (X: mean; σ: standard deviation; n: number of measurements; a negative 3D deviation indicates that the CT mesh is inflated. For “A” and “B”, see Figure 3).

	XB	± σB	Max	Min	n	Δ XAB
Entire femur	−0.65	±0.31	3.03	−3.84	1115113	+0.49
Proximal part	−0.65	±0.30	1.01	−2.17	433181	+0.53
Diaphyseal part	−0.68	±0.23	0.79	−2.08	619722	+0.50
Distal part	−0.62	±0.40	4.89	−4.84	440244	+0.42

Discussion

State-of-the-art CT-based computer-aided bone surgery planning and implant design applications require small-sized STL files of accurate meshes of the bone outer surface [1–9]. Unfortunately, such models are not directly available from standard segmentation algorithms (such as the Marching Cubes procedure [24]) since these include inside and outside information into the meshes. One solution is the use of statistically trained deformable models (ASM), in which a mean shape of the bone outer surface is deformed characteristically to best fit the patient CT data [20–22], [27]. Using leave-one-out experiments, these studies typically report mean 3D surface deviations of 1.5 mm (max: 3 mm) [22] and 1.79 mm (max: 5.75 mm) [21] for the proximal femur.

As an alternative, the author developed a contour-based segmentation algorithm to retrieve bone outer surface meshes from clinical CT image data [25]. In view of the surface-based implant design, this algorithm makes small- and large-scale adaptations to the bone contours only if these are directed to the outside, which is an important difference with any best-fit algorithm.

For the intended applications, the mean 3D deviation should be in the range of 1 mm, while peak deviations should be local–as a form of noise which can be easily neglected during subsequent planning or design applications. In a preliminary evaluation, the accuracy of the aforementioned algorithm was estimated at 1.20 mm for a typical pelvis mesh [25]. The study performed fully validates the geometrical accuracy using dense and very accurate optical surface scans of 15 dried femora as an absolute geometrical ground truth. Femoral shapes were chosen as they contain different degrees of shape complexity: a spherical head shape proximally, a cylindrical diaphysis, and convex/concave condyles.

For comparison purposes, a parallel–yet unconventional–segmentation approach was included in the study by using manual mask-filling tools in the commercially available Mimics® software to generate bone outer surface models. Standard Marching Cubes models could not be used since internal bone information is still present in those models and this would prevent a correct calculation of the 3D deviations in the Focus Inspection® software.

It should be mentioned that, using the aforementioned tools, fully internal information is removed from the Mimics® meshes, but internal loops–where a cortical bone contour turns inside the bone to include a trabecular contour part–are not. On the one hand, this makes the generated Mimics® outer surface meshes as such–without further manual editing–not yet suitable for the intended surface-based design applications, in which implant designs and/or muscle attachment regions are directly extracted from the bone surface mesh [8–9], [28]. On the other hand, these meshes can still be used for assessing the 3D deviations, on condition that the internal information is removed as outliers, for example. This is accomplished by the acceptance window, previously described in the section headed Assessing 3D deviations between CT-based and optical surface meshes.

In the following paragraphs, the validation results are analysed for the above-defined (groups of) classes of CT meshes (Tables I and II). From this analysis, the best parameter settings are selected.

General trends

By inspecting the graphs and tables of results, some general trends can be observed for the 3D deviations between CT meshes and the geometrical ground truth:

• The mean 3D deviations of all CT mesh classes are significantly different from the ground truth (P < 0.001), being the dry bone geometries.

• Using the method previously developed by the author [25], the interslice distance has only a very small influence on the accuracy of the femoral CT meshes (group 215, all parts). As mentioned above, increasing the IsDist causes only a small extra negative shift and slightly enlarges the standard deviation of the 3D deviations. For the proximal and distal parts, a significant difference for class 1 versus class 5 could not even be proven. The maximal 3D deviations (in absolute value) increase accordingly.

• The spline accuracy has a more pronounced effect on the 3D deviations (group 316, all parts). A smaller spAcc value (higher accuracy) generates a graph with a less negative shift (smaller mean deviation with respect to the ground truth) and a smaller dispersion. The maximal 3D deviations (in absolute value) decrease accordingly.

• The number of points per spline has a moderate effect on the 3D deviations (group 347, all parts). Increasing the pps causes an increase in negative shift of the mean and a smaller dispersion. This effect most probably results from the fact that, when more detail is incorporated by higher sampling of the spline, more unwanted noise is added. The maximal 3D deviations (in absolute value) are hardly influenced.

• Using the Mimics® segmentation approach, considerable shifts are observed depending on the STL export settings (group Lmho, all parts). The higher the matrix reduction (Table II), the larger the negative shift of the mean 3D deviation, and the larger the dispersion. Compared to class 2 (which has equal IsDist of 1 mm), the optimal class has a less negative mean and a smaller dispersion, but requires on average twice the number of triangles (Table I). Mimics® classes with comparable numbers of triangles (i.e., the Low STL export quality setting) perform very poorly. Only the optimal class is comparable to any of the classes 1 to 7.

Influence of soft tissue removal–dry bones: offset value

All graphs of the 3D deviations show a statistically significant negative shift, meaning that all CT meshes are inflated with respect to the accurately scanned dry bones. Boiling the cadavers–the only efficient method to properly remove the soft tissues of multiple cadavers–causes shrinkage of the bones, and therefore contributes to this shift. This hypothesis was formulated after a preliminary analysis of the most distal and proximal CT table positions (not shown). Subsequently, a subtractive calculation method was set up to actually characterize the combined effect of boiling and soft tissue presence, by analogously processing extra CT scans of the dried bones (Figure 2).

The shift Δ X_AB in 3D deviations between the CT mesh and ground truth due to soft tissue presence and boiling was determined by means of the h-class Mimics® segmentation (Figure 4a). As expounded in the section headed Assessing influence of soft tissue presence and boiling (Figure 2), this positive offset is to be applied to all graph curves (Figure 4b).

Figure 4. Influence of soft tissue removal and boiling of the cadaver bones. (a) For class h (see Table II and the section headed Assessing influence of soft tissue presence and boiling), the dry bone CT scans (B) as well as the intact specimen CT scans (A) of all specimens are segmented and compared to the MetrisScan ground truths (entire femora). The mean 3D deviation X_B is attributed to the CT machine and segmentation algorithm; apart from the same CT machine and segmentation algorithm, the mean 3D deviation X_A is attributed to soft tissue presence (setting the bone Hounsfield window for cortical bone) and boiling of the cadaver bones. (b) Graphs of the 3D deviations for all intact specimen CT-based meshes, all classes (entire femora). A positive shift Δ X_AB should be applied to the graphs to counteract the combined effect of soft tissue presence and boiling. The dotted vertical line should serve as new zero line. [Color version available online.]

Optimal choice of segmentation parameters

Based on the aforementioned findings, the optimal parameter settings for the segmentation approaches can be determined (Table V). When entire mesh accuracy is envisaged, the approach with the self-developed Filter & Mesh base platform [25] preferably requires the class 3 settings, being an interslice distance of 2 mm, a small spline accuracy value–e.g., 0.4 mm, meaning high accuracy–and 35 points per spline. Using the dried femora as the ground truth, this results in an STL surface mesh consisting of 15532 ± 481 triangles with a 3D accuracy of −0.70 ± 0.55 mm (the minus sign indicates an inflated CT mesh). Incorporating more CT slices (smaller IsDist, e.g., class 2 in particular) has only a tiny effect on the mesh accuracy, increases the STL file size (Table I), and is practically undesirable as it would extend the duration of the acquisition. The spline accuracy value (spAcc) should be as low as possible in order to lower the dispersion of the 3D deviations; the value of 0.4 mm is only indicative. In practice, a compromise should be made between high accuracy and short calculation duration.

Table V.  Optimal choice of segmentation parameters for outer surface mesh generation for femoral CT scans with soft tissue, as in clinical practice. (See Tables I and II for class definitions; voxel in-slice dimension = 1 mm × 1 mm; a negative 3D deviation indicates that the CT mesh is inflated; Δ X_AB = compensation for combined effect of soft tissue presence during bone Hounsfield windowing and shrinkage of the ground truth femora by boiling [see Table IV].)

	Filter & Mesh base platform [25](mm)	Mimics® approach(mm)	Δ XAB (mm)
Entire femur mesh	class 3	class o
	−0.70 ± 0.55 (15532 ± 481 triangles)	−0.62 ± 0.49 (66367 ± 17156 triangles)	+0.49
Proximal part	class 2	class o
	−0.74 ± 0.51 (10770 ± 452 triangles)	−0.67 ± 0.45 (30816 ± 10957 triangles)	+0.53
Diaphyseal part	class 3	class o
	−0.69 ± 0.29 (10967 ± 356 triangles)	−0.62 ± 0.35 (21981 ± 3727 triangles)	+0.50
Distal part	class 2	class o
	−0.61 ± 0.76 (9750 ± 271 triangles)	−0.55 ± 0.67 (28083 ± 7912 triangles)	+0.42

Using similar argumentation, class 2 settings are required for bone pieces from which the geometry is comparable to the proximal and distal femur, particularly because of the smaller interslice distance (1 mm) at these rounded epiphyses. Diaphyseal-like geometries–a cylindrical structure with a protruding linea aspera–require class 3, which is slightly better than class 2 because of the smaller spline accuracy value.

For the Mimics® approach, the “optimal” quality setting should be used to generate the bone surface models (all parts). Using the dried femora as the ground truth, this results in an STL surface mesh consisting of 66367 ± 17156 triangles with a 3D accuracy of −0.62 ± 0.49 mm. The slightly smaller standard deviation implies that even better looking, smooth bone surfaces were obtained. Other settings (low-, medium- and high-quality classes) generate a mean 3D deviation of much more than 1 mm, which is–after also compensating for the shrinkage of the dry bones (see section entitled Influence of soft tissue removal–dry bones: offset value)–unacceptable for the intended applications.

Conclusion

Computer-aided bone surgery planning and implant design applications require accurate and compact representations of the patient's bone. Accordingly, the authors previously developed a contour-based segmentation algorithm to retrieve bone outer surface meshes from clinical CT image data (the Filter & Mesh base platform) [25]. Using a geometrical ground truth of no less than 15 dry cadaver femora (1 mm × 1 mm in-slice voxel size), the optimal parameter settings for the outer surface bone segmentation from clinical CT data have been revealed.

In summary, the presented study demonstrates that, when using the optimal parameter settings for the respective segmentation procedures, sub-voxel mesh accuracies can be attained. Compact surface representations of femora can be generated with mean absolute accuracies of up to one fifth of the voxel size and Root Mean Square (RMS) error of half a voxel size. In parallel, a segmentation approach with the commercially available Mimics® software has been investigated. A single–though excellent–pre-defined set of parameters was identified. For surface-based design purposes, however, the created meshes need some further manual processing to remove internal bone information which is linked to the outside.

Acknowledgments

We wish to thank Jo Verbinnen (Department of Anatomy, K.U. Leuven) for helping with the cadavers, and the Materialise company for putting at our disposal the Mimics® 3D image processing and editing software. This research is funded by a PhD grant to Dr. Gelaude from the Institute for the Promotion of Innovation through Science and Technology in Flanders (IWT-Vlaanderen) (SB-33312).

Declaration of interest: The authors report no conflicts of interest. The authors alone are responsible for the content and writing of the paper.