# Quantitative Assessment of the Restoration of Original Anatomy after 3D Virtual Reduction of Long Bone Fractures

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## Abstract

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## 1. Introduction

## 2. Materials and Methods

#### 2.1. Material Preparation and CT Scanning

#### 2.2. Virtual Reduction and Accuracy Evaluation

#### 2.3. Statistical Analysis

## 3. Results

#### 3.1. Ultimate Shape of the Virtual Reduction

#### 3.2. Length Variation

#### 3.3. Apposition Variation

#### 3.4. Alignment Variation

#### 3.5. Rotation Variation

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Experimental fracture models for 19 ORTHObone tag numbers. The simple fractures (11 cases) involved only two fragments, while the comminuted fractures (8 cases) involved three or more fragments. Each classification included both transverse fractures (4 cases) and spiral fractures (15 cases).

**Figure 2.**Scheme of the workflow for virtual reduction and image registration between the virtually reduced object and the original object. (1) CT scanning of the original bone, (2) assignment of patches at the cortical marking holes, (3) fracture of the ORTHObone, (4) CT scanning of the fractured bone, (5) virtual reduction, and (6) image registration.

**Figure 3.**3D-based method of accuracy evaluation for virtual reduction. (

**A**) There were three cortical marking holes on the distal part and three points on the proximal part. The three original lengths only in the Z-axis were measured as Length 1 (between Point 1 and Point 4), Length 2 (between Point 2 and Point 5) and Length 3 (between Point 3 and Point 6). The length variation was calculated using the change in length (Length 1′, Length 2′, and Length 3′). (

**B**) When the 2D sky blue color triangles for both the original object and the virtually reduced object were fixed at the same position, the location of the deep 2D blue triangle belonging to the original object was converted to the location of the 2D red triangle in the virtually reduced object. The variation of apposition was calculated by measuring the variation of the X and Y coordinates from the central point of the triangles (from deep blue to red) (

**C**) The three marking holes on the distal part generated Normal Vector 1 via Plane 1, and the other three marking holes on the proximal part generated Normal Vector 2 via Plane 2 (from original object), and Normal Vector 2′ via Plane 2′ (from the virtually reduced object). AP angulation and Lateral angulation indicate the difference in the angle between Normal Vector 2 and Normal Vector 2′ on the AP plane and the lateral plane, respectively. The angle difference in the rotation was measured by the variation in the angle between Normal Vector 2 and Normal Vector 2′ on the axial plane.

**Figure 4.**The original shapes of the 19 ORTHObones (top line) and the virtually reduced objects for all ORTHObones. The bone fragments in the virtually reduced object are represented by different colors (bottom line).

**Figure 5.**Results of the measured length and length variations between the original object and the virtually reduced object. (

**A**) The measured lengths of specific distances (Length 1(′), Length 2(′), and Length3(′)) from the original object and the virtually reduced object. (

**B**) The length variation in 19 ORTHObones before and after virtual reduction. VR: virtual reduction, M: mean, SD: standard deviation, H: null hypothesis, P: p-value.

**Figure 6.**Apposition variation results after virtual reduction (the central position of the red triangle in Figure 3B) of the fractured bone. The central point of the deep blue triangle in Figure 3B was set at the central coordinate of the graph (X = 0, Y = 0). Left: Cases 1 to 7; middle: Cases 8 to 14; and right: Cases 15 to 19.

**Figure 7.**The measured 2D AP angulation on the YZ plane and the variation between the original object and the virtually reduced bone. (

**A**) AP angulations measured from the angle between Normal Vector 1 and Normal Vector 2 (the original object), (

**B**) AP angulations measured from the angle between Normal Vector 1 and Normal Vector 2′ (the virtually reduced object), (

**C**) overlapped results for (

**A**) with blue lines and (

**B**) with red lines, and (

**D**) the difference (black line) in AP angulation between (

**A**) with blue lines and (

**B**) with red lines.

**Figure 8.**2D lateral angulation measured on the XZ plane and the variation between the original object and the virtually reduced bone. (

**A**) The lateral angulations measured from the angle between Normal Vector 1 and Normal Vector 2 (the original object), (

**B**) the lateral angulations measured from the angle between Normal Vector 1 and Normal Vector 2′ (the virtually reduced object), (

**C**) overlapped results of (

**A**) with blue lines and (

**B**) with red lines, and (

**D**) the difference (black line) in lateral angulation between (

**A**) with blue lines and (

**B**) with red lines.

**Figure 9.**The measured 2D angle of axial rotation in the XY plane using 3D angulation and the variation between the original object and the virtually reduced bone. (

**A**) The axial rotation measured from the angle between Normal Vector 1 and Normal Vector 2 (the original object), (

**B**) the axial rotation measured from the angle between Normal Vector 1 and Normal Vector 2′ (the virtually reduced object), (

**C**) the overlapped results for (

**A**) with blue lines and (

**B**) with red lines, and (

**D**) the difference (black line) in axial rotation between (

**A**) with blue lines and (

**B**) with red lines.

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**MDPI and ACS Style**

Kim, M.-S.; Yoon, D.-K.; Shin, S.-H.; Choe, B.-Y.; Rhie, J.-W.; Chung, Y.-G.; Suh, T.S.
Quantitative Assessment of the Restoration of Original Anatomy after 3D Virtual Reduction of Long Bone Fractures. *Diagnostics* **2022**, *12*, 1372.
https://doi.org/10.3390/diagnostics12061372

**AMA Style**

Kim M-S, Yoon D-K, Shin S-H, Choe B-Y, Rhie J-W, Chung Y-G, Suh TS.
Quantitative Assessment of the Restoration of Original Anatomy after 3D Virtual Reduction of Long Bone Fractures. *Diagnostics*. 2022; 12(6):1372.
https://doi.org/10.3390/diagnostics12061372

**Chicago/Turabian Style**

Kim, Moo-Sub, Do-Kun Yoon, Seung-Han Shin, Bo-Young Choe, Jong-Won Rhie, Yang-Guk Chung, and Tae Suk Suh.
2022. "Quantitative Assessment of the Restoration of Original Anatomy after 3D Virtual Reduction of Long Bone Fractures" *Diagnostics* 12, no. 6: 1372.
https://doi.org/10.3390/diagnostics12061372