Specimen acquisition and computer-assisted tool

A SOMATOM Definition Flash dual-source CT machine (Siemens Healthineers, Forchheim, Germany) was selected to scan the ankle joint of subjects from Shaanxi Province People’s Hospital. Scan parameters: 120 kV, 205.50 mAs, layer thickness: 0.5–1 mm, all DICOM images (521 px×512 px) in 336 layers for each subject, were imported into a standard segmentation software - MIMICS 17.0 software (Materialise, Leuven, Belgium), the region of interest (ROI) were extracted using both “Thresholding” and “region growing” module. All 3D models of the talus were automatically produced by the “calulate 3D from mask” functional block and then imported into Geomagic Stuido 12 to refine the model structure and improve the accuracy of the measurement results. Finally, the STL for the talar model was imported into 3 matic software for anatomical measurement. The computer workstation included a Lenovo thinkpad, Windows 7–64 bit operating system, Intel (R) Core(TM) i7-4600 processor, 8 GB of running memory, and 256 SSD hard disk. All the subjects signed the participant consent form. This research was approved by the Ethics Committee of Shaanxi Provincial People’s Hospital (No. SPPH-LLBG-17-3.2).

The CT data of the talus from subjects were collected in both outpatient and inpatient departments of Shaanxi Provincial People’s Hospital. The inclusion criteria were as follows: patients without/with a history of trauma but without fracture or dislocation of the talus. The exclusion criteria were as follows: (1) talar fracture; (2) congenital or acquired skeletal deformity; (3) necrosis of the talus caused by KBD/Rheumatoid arthritis; and (4) talar tumor from various pathological types.

Calibration of the coordinate system

To ensure that each talus model had the same three-dimensional position in the 3matic 11.0 software, the object coordinate system (OCS) was formatted to the world coordinate system (WCS) in the 3matic 11.0 software. Origin 0 (0,0,0) was defined as the centerpoint in the WCS and is an intersection point caused by 3 orthogonal planes. The XY plane (axial plane), YZ plane (sagittal plane), and ZX plane (coronal plane) were generated separately.

Definition of anatomical landmarks on the surface from the talus trochlea

According to a previously published method [16], the AM, PM, AL, and PL edges of the talar trochlea were defined, as shown in Fig. 1A. The anterior edge of the medial trochlea and anterior edge of the lateral trochlea were defined as the most anterior point of medial border and lateral border in trochlea, respectively. The posterior edge of the medial trochlea was defined as the most posterior point of the medial trochlea.

Fig. 1

Standardization of the talus model based on anatomical landmarks. (A. Seven anatomical top points on the talus trochlea; B. Determining the transverse plane α based on three anatomical points; C. Determining the sagittal plane and coronal plane based on the transverse plane α; D. Fitting the origin point of the talus by three points)

The transverse plane (α) was a datum plane created when passing through the anterior edges of the medial trochlea, posterior edges of the medial trochlea and anterior edge of the lateral trochlea (Fig. 1B). The coronal plane (β) was created as a datum plane perpendicular to α and passing through midpoint 1 (the anterior and posterior edges of the medial trochlea) and midpoint 2 (the anterior edge of the lateral trochlea and PL edge of the talar trochlea). The sagittal plane was set perpendicular to both the transverse plane (α) and coronal plane (β). (See Fig. 1C)

Centerpoint of talus

The intersection (origin 1) of the three coordinate planes (transverse plane, sagittal plane and coronal plane) was calculated by 3matic; then, the midpoint (point 1) of the AM and AL edges and the midpoint (point 2) of the PM and PL edges of the trochlea were defined; next, the midpoint of point 1 and point 2 was marked and projected onto the trochlea surface (point 3). A circle was created according to point 1, point 2 and point 3, and the center of the circle (origin 2) was set as the center of the talus (see Fig. 1D).

Origin 1 and origin 2 coincided with origin 0, and the centerpoint of the talus coincided with the origin of the WCS. The X axis is created through origin 0 and perpendicular to the sagittal plane, the Y axis is perpendicular to the coronal plane (β) through origin 0, and the Z axis is through origin 0 perpendicular to the transverse plane (α). All parts and analytical primitives in work area were rotated make sure X axis perpendicular to ZY plane, Y axis perpendicular to ZX plane, Z axis perpendicular to YX plane. The coordinate system of the talus is coincident with the WCS.

Top point on the trochlear surface

Six near coronal sections parallel to the ZY plane were produced, which passed through the AM edge, midpoint of the AM and PM edges, PM edges, AL edge, midpoint of the AL and PL edges, and PL edges previously determined [17]. The intersection top points between the trochlear surface and six near coronal sections were identified as the AM top, mid-medial top, PM top, AL top, mid-lateral top, and PL top. (Fig. 2A)

Five nearly sagittal sections

According to the principle of using three points to determine a plane, an AM section was established when it contained the AM top, mid-medial top, and midpoint between these two tops; in a similar way, a PM section, AL section, and PL section were defined. Each radius of curvature was calculated using the measure module in 3matic( Fig. 2B). Additionally, the midsagittal section is the sagittal section in the WCS in 3matic 11.0 software.

Fig. 2

Definition of the top point in six areas (A) and four sections (B)

Measured radius of talus curvature

First, the talus was cut by the AM section, the midpoint between the AM top and midmedial top was defined based on the length (AM midpoint), and then a circle was established through the three points. The radius was recorded as the anteromedial curvature of the talus (Fig. 3A). In the same way, the talus was cut by the AL section, the midpoint between the AL top and midlateral top was defined based on the length (AL midpoint), and the AL curvature of the talus was defined as the radius of the circle established through three points (Fig. 3B).

Second, the talus was cut by the PM section, the midpoint between the PM top and midmedial top was defined based on the length (PM midpoint), and the PM curvature of the talus was the radius of the circle established through three points (Fig. 3C). The talus was cut by the PL section, the midpoint between the PL top and midlataral top was defined based on the length (PL midpoint), and the PL curvature of the talus was the radius of the circle established through three points (Fig. 3D).

Third, the talus was cut by the midsagittal section, the anterior point/superior point/posterior point was marked, the anterior midpoint and posterior midpoint were calculated and marked, and the mid posterior curvature and mid anterior curvature were established through a circle containing three points (Fig. 3E and F).

Fig. 3

Curvature of talus in different areas(A,AM; B,AL; C,PM; D, PL; E,MA; F,MP.)

Fitted radius of talus curvature based on the cylinder

Following the normalized coordinate system of the talus, the trochlear surface of the talus was separated as a new part, and an analytical cylinder was fitted using the separated trochlea of the talus. The radius of the analytical cylinder shown on the properties page is similar to the talus curvature (Fig. 4).

Fig. 4

Schematic diagram for fitting the radius of curvature

Statistical analysis

All measurements of the 3D model in this study, including each trochlea of the talus, were measured by the same researcher. All data were collected and entered into Microsoft Excel 2016, SPSS17.0 statistical software package (SPSS Statistics for Windows, Version 17.0. Chicago: SPSS Inc.) was employed to identify significant differences. Independent sample t tests were used to identify the difference between two sets of data, paired t -tests were used to analyze the difference between the left and right trochlea of the talus, and the results are expressed as the mean ± standard deviation (‾x ± SD). The difference among multiple samples was tested by the LSD multiple comparison method; the relationship between the two variables was analyzed by bivariate correlation analysis. All statistical tests were two-sided, and P < 0.05 was considered statistically significant.