Measurement of acetabular inclination and anteversion via CT generated 3D pelvic model

The research was approved by Ethics Committee of Tongji medical college, Huazhong University of Science and Technology. Patients according to the inclusion criteria were retrospectively included into the research. CT data of healthy cases were collected from imaging database of Union Hospital from January to October in the year 2014. The inclusion criteria were bilateral iliac crest to proximal femur whose radiological diagnosis reported no disease. Patients with particular diseases such as pelvic fracture, ONFH, THA, DDH, ankylosing spondylitis as well as lumbar intervertebral fusion were excluded. Data that fit the criteria was saved in DICOM format.

Murray in 1993 determined three methods for acetabular measurement, anatomical, operational and radiographic measurements of inclination and anteversion [9]. Anatomical inclination (AI) was the angle between the plane of acetabular face and the transverse plane, whose mathematical model was the angle between the acetabular axis of the patient and the longitudinal axis (Fig. 1b ∠AOC). Anatomical anteversion (AA) was the angle between the acetabular axis and the coronal plane when viewed in cranio-caudal direction. The mathematic model of AA was the angle between the acetabular axis that was projected to transverse plane and transverse axis (Fig. 1b ∠COF). Operative inclination (OI) was defined as the angle between the rod and operational bed in lateral position whose mathematical model was the angle between the acetabular axis and sagittal plane (Fig. 1c ∠AOB) [9]. Operative anteversion (OA) was known as the rotation of the rods around the transverse axis when inclination was determined. The mathematical model was the angle between the acetabular axis that was projected on to the sagittal plane and longitudinal axis (Fig. 1c ∠BOE) [9]. The radiographic inclination (RI) was defined as the face of the cup and transverse axis when projected on anterior-posterior view. It was the same angle between the acetabular axis projected on the coronal plane and longitudinal axis, alternatively (Fig. 1 ∠DOE). The radiographic anteversion (RA) was calculated by major and minor diameters of the ellipse which could be defined as the angle between the acetabular axis and the coronal plane (Fig. 1 ∠AOD) [10].

After loading the DICOM data, 3D pelvic model was rebuilt by 3D–Slicer software (http://​www.​slicer.​org/​) and all landmarks on the pelvis were marked. (1) Acetabular rim: The rim of acetabulum except the gap of transverse acetabular ligament should be labeled, at least 30 points starting from the rim. Further, the distance between the adjacent points should be maintained in a coincident manner. (2) Bilateral anterior superior iliac spine (ASIS) and pubic tubercle. (3) Sacral crest: At least 3 points of sacral crest were labeled (Fig. 2). Landmarks were judged and labelled manually. One case was labelled by two orthopedists independently and the results were compared. If each landmark labelled by the orthopedists had a divergence less than 2 mm in case, the labelling work was considered as validation, otherwise another orthopedist was engaged for labelling. All bony landmarks were marked and the coordinates of each point (x, y, z) were exported for calculation.

Hip joint was a hemisphere joint and normal vector of acetabular face (bottom) was named as the axis of acetabulum [16, 17]. The bottom of acetabulum was not flat. At least 30 points of acetabular rim were collected and these points were used to fit the acetabular bottom. Thus, the normal vector calculated was regarded as the axis of acetabula. The bias between the norm vector and acetabular axis was reported by Lubovsky, but did not show any significant result [18].

The method to calculate norm vectors was by minimizing the sum of the squares of the distances of all collection points. The Matlab software (MathWorks Inc., USA) used a formula called “fitNorm” which could be utilized to calculate the norm vector.

Coronal plane was immeasurable in the pelvic CT model. However, when a body was placed in erect and supine position, anterior pelvic plane (APP) was almost parallel to the coronal plane [19]. As all cases were examined in supine position, we demarcated APP by bilateral ASIS and pubic tubercles (Fig. 3) [20]. Sagittal plane was much easier to determine as the plane was enclosed by midpoint of bilateral ASIS, and sacral crests were coincided with the sagittal plane (Fig. 3). Therefore, these coordinates were imported into the Matlab software. Norm vectors of coronal plane and sagittal plane were calculated by “fitNorm”.

Transverse plane was immeasurable in pelvic CT model either. As transverse plane was perpendicular to the coronal plane; mathematically, it meant normal vector of transverse plane was vertical to the normal vector of coronal. Using arrhythmic method, we subsequently calculated the formula of transverse plane:

The perpendicular plane was calculated by three reference planes, which might due to APP that was almost paralyzed to the coronal plane. The angle between the two planes was calculated by [21]:

\( \overrightarrow{n} \) and \( \overrightarrow{m} \) were two norm vectors of reference planes. If two planes were vertical, the angle calculated was 90°. The angle θ was examined by statistical methods with 90°.

We calculated these parameters strictly by definition and by manipulating the Matlab software. Normality test of each parameter was then examined to investigate whether these data could be used for further statistical tests, which were undetermined. Moreover, patients were classified by age and gender to confirm whether these factors affect distribution of acetabular degrees.

The angle was calculated by formula (1). For instance, OI was the angle between the acetabular axis and sagittal plane. Thus, \( \overrightarrow{n} \) was vector of acetabular axis and \( \overrightarrow{m} \) was vector of sagittal plane. For RI, which was the angle between the acetabular axis projected onthe coronal plane and longitudinal axis, the vector of acetabular axis should be projected to the coronal plane firstly. Vector of acetabular axis was regarded as two coordinates that started from P₁(0, 0, 0) and ended with P₂(x ₂, y ₂, z ₂). The formula of coronal plane was Ax + By + Cz + D = 0. Thus, the vector projected to the coronal plane was started from \( {\mathrm{P}}_1^{\prime}\left(0-\mathrm{A}\bullet {\mathrm{t}}_1,0-\mathrm{B}\bullet {\mathrm{t}}_1,0-\mathrm{C}\bullet {\mathrm{t}}_1\right) \) and ended with \( {\mathrm{P}}_2^{\prime}\left({x}_2-\mathrm{A}\bullet {\mathrm{t}}_2,{y}_2-\mathrm{B}\bullet {\mathrm{t}}_2,{z}_2-\mathrm{C}\bullet {\mathrm{t}}_2\right) \) [22].

A total of 100 cases were involved in the study and after excluding the ineligible cases a total of 61 cases continued further study. Five cases were excluded because of pool structure of ASIS caused by iliac crest graft. Seven cases were excluded after 3D reconstruction due to blurred anatomical structure by poor CT filming. Forty-nine cases (98 hips) were finally chosen.

The characteristics of gender and age distribution were presented in Table 1. In age distribution, we classified the patients based on age into sub-groups, less than 30 years old, 30–40 years old (40 excluded), 40–50 years old (50 excluded) and more than 50 years old.

To examine whether these three reference planes were perpendicular, we analyzed the angles of three groups of reference planes, APP with sagittal, APP with transverse and sagittal with transverse. The angle between transverse and sagittal was 90° because transverse plane was transformed by sagittal plane. The angle between APP and sagittal was 88.4° ± 6.0° (P > 0.05). The angle between APP and APP and transverse was 83.2° ± 13.6° (P > 0.05). Therefore, all three reference planes were statistically perpendicular.

After normality test, we then calculated the inclination and anteversion of different measurements with mean and standard deviations (SD). Transformed RI was involved in the calculation. Inclination and anteversion measurements were presented in Table 2.

Inclination and anteversion were tested with gender classification. The results indicated that inclination and anteversion in both male and female showed no significant differences (P > 0.05). This illustrated that gender classification did not influence the distribution of inclination and anteversion. Test of divergence with age span was also calculated, which showed that the age span mentioned above did not interfere with the distribution either. All these results proved that the parameters of acetabula were kept stable in population. Inclinations and anteversions in gender and age distribution were presented in Table 2.

Subsequently, the difference among the inclinations in anatomic, operative and radiographic measurements was confirmed. Results of ANOVA illustrated significant differences within AI, OI and RI (P < 0.01). Comparison of LSD found that AI showed significant differences with OI and RI (P < 0.05), while no significant differences between OI and RI (P > 0.05) were observed (Fig. 4). We also tested the divergence in anteversions by three measurements, which showed significant difference among AA, OA and RA (P < 0.01) and with a significant divergence in LSD (Fig. 4).