Ninety-six lower leg cadavers provided by the Institute of Forensic Medicine of the University of Zurich and previously analyzed in former studies [13, 16], were included in the study. The inclusion criterion was an existing CT assessed by the first author that included the entire tibia and fibula of both sides. Exclusion criteria comprised radiologically apparent previous trauma, surgery, advanced degenerative changes, or deformity of the tibia or fibula. Due to the well-known radiological criteria for osteoarthritis and clearly identifiable posttraumatic deformities, no inter-reader reliability was performed.

Thirty-four male and twelve female donors (two samples lacked gender information) were included with a mean age of 52 ± 17.7 years (range: 21 to 95 years). Mean weight was 83.1 ± 16.5 kg (range: 55 to 111 kg), and mean height was 176.2 ± 8.6 cm (range: 154 to 195 cm). High-resolution CT data were acquired using a Somatom Definition Flash CT scanner (Siemens®, Erlangen, Germany) with a slice thickness of 0.5 to 0.6 mm. 3D triangular surface models of 96 paired (48 left, 48 right) healthy tibiae and fibulae were created with manual threshold segmentation and region growing using MIMICS software (MIMICS Medical, Materialise NV, Leuven, Belgium). The bone models were imported into the surgical planning software CASPA (Balgrist CARD AG), developed in-house. To approximate the original distal fibula from the mirrored contralateral side, an iterative point proximity (ICP) algorithm [18, 19] was used to superimpose the mirrored contralateral model on the original model as described in previous studies [13, 17]. A 3D coordinate system was defined according to Wu et al. [20]; y-axis same direction vector as the anatomical tibial axis defined by an oriented bounding box (OBB) [21], z-axis: lateral, x-axis: anterior (Fig. 1).

Fig. 1
figure 1

Definition of the anatomical coordinate system. The origin was located in the geometric center of the tibia, the X-axis (red) points from posterior to anterior, the Y-axis (green) points from distal to proximal, and the Z-axis (blue) points from medial to lateral

Definition of tibia and fibula segments for contralateral registration

As segment selection and registration of anatomical structures potentially improve the accuracy of approximation to the premorbid anatomy [17], four different lower limb segments were defined to restore the distal fibula, excluding the possibly deformed distal 25% of the fibula. The contralateral lower leg model was mirrored, and four anatomic segments were defined (Fig. 2).

  • 25% tibia: the segment was defined as 25% of the distal tibial length.

  • 50% tibia: the segment was defined as 50% of the distal tibial length.

  • 75% fibula: the segment was defined as 75% of the proximal fibula length.

  • 75% fibula and tibia: the segment included the whole tibia model and 75% of the proximal fibula length (Fig. 2).

Fig. 2
figure 2

Definition of tibia and fibula segments for contralateral registration. The contralateral model was mirrored and four anatomical segments were defined and depicted from left to right: 25% tibia: including 25% of the tibia length; 50% tibia: including 50% of the tibia length; 75% fibula: including 75% of the fibula length; 75% fibula and tibia: including 75% of the fibula length and the complete tibia model

The surface registration algorithm for superimposing the mirrored contralateral models on the original model was performed for all four defined segments of the tibia and fibula with specified length, as described above.

Accuracy of distal fibula restoration

Translation and rotation of the distal contralateral fibula were measured in comparison to the original distal fibula and reported as errors. Translation was measured in mm (positive values indicate lengthening of the distal fibula, negative values indicate shortening), and rotation was measured in degrees (positive values indicate external rotation, negative values indicate internal rotation) around the anatomical axis (y-axis) (Fig. 3). Furthermore, the 3D distance (Euclidean distance) between the target ipsilateral distal fibula and the contralateral mirrored distal fibula was calculated. Similarly, the 3D angle (Euler’s angle) was calculated between the target ipsilateral distal fibula and the contralateral mirrored distal fibula to quantify positional deviation. In addition, the median absolute error of the distal fibula (translation, rotation, Euclidean distance, Euler’s angle) was defined for each segment. Bilateral models without pathology were used for the calculations. Accordingly, the error would be 0 mm or 0° if the anatomy were perfectly reconstructed.

Fig. 3
figure 3

25% tibia segment (blue, contralateral mirrored) to restore the distal fibula. The blue tibia is superimposed to the white ipsilateral tibia using the ICP method. Red fibula = target ipsilateral fibula; white fibula = contralateral mirrored fibula. Using the 25% tibia segment as a reference result in a distalization of the white contralateral fibula by 0.5 mm and an internal rotation of − 0.6°

Measurement of the tibia and fibula length

The length of the tibia and fibula model was defined by the OBB [13]. Side-to-side differences are reported as median absolute differences.

Due to the highly standardized definition of the surfaces and the largely automated measurement procedure, no inter- and intra-reader reliability was performed.

Statistical analysis

Statistical analysis was conducted with SPSS software v26.0 (IBM, New York, USA).

The Shapiro-Wilk test was applied to test the data for normal distribution. The variables are reported as median and range. As the data were not normally distributed, the Friedmann’s test (nonparametric ANOVA for related samples) was applied to study between-level differences. Outcomes with significant differences were further analyzed in a pairwise comparison using Wilcoxon signed rank tests. The respective p-values were Bonferroni-corrected as applicable. To identify patient-specific factors, including age, sex, BMI and tibia and fibula side-to-side differences, associated with the outcomes of interest, a stepwise linear regression model was applied. In this analysis, missing values (weight and height information were missing in nine donors; gender information was lacking in two cases) were not taken into account, and the corresponding cases were excluded from the analysis. The alpha level was set at 0.05, and all p-values were two-tailed.

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