# Definition of a Global Coordinate System in the Foot for the Surgical Planning of Forefoot Corrections

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Requirements to Define a Global Coordinate System

- Be well defined. A well-defined coordinate system includes the definition of two axes and the position of the origin;
- Be robust. A robust coordinate system constructs the coordinate system consistently using the same definition, regardless of anatomical variations amongst patients (i.e., accessory ossicles);
- Be highly repeatable. A highly repeatable coordinate system implies the construction of exactly the same coordinate system within an individual foot if the protocol is repeated. This will enable the same foot orientation in the preoperative planning and independent analysis, regardless of the operator;
- Be clinically relevant with recognizable anatomical planes. This is necessary for the clinical interpretation of the deformity. When the virtual AP and lateral views of the coordinate system correspond with the corresponding radiographic images, a coordinate system is clinically relevant and has recognizable anatomical planes;
- Be compatible with CT scans of the foot. This will make it possible to construct the coordinate system regardless of the scanned section of the tibia and fibula;
- Not be sensitive to the ankle joint angle. This will enable the forefoot to be positioned clinically relevantly in the coordinate system, regardless of the ankle joint angle;
- Not include the shape and orientation of the bones in the forefoot by fitting an object since these bones might be deformed.

#### 2.2. Study Design and Subjects

^{2}, were included.

#### 2.3. Data Acquisition

#### 2.4. Coordinate System Definitions

#### 2.5. Coordinate System Evaluation

## 3. Results

## 4. Discussion

## 5. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Appendix A

**Figure A1.**CS1 and CS2 virtual anteroposterior (AP) images of the three 3D foot models without a splint compared to the corresponding conventional AP radiographic image: (

**a**) Foot model one virtual AP image CS1. (

**b**) Foot model one virtual AP image CS2. (

**c**) Corresponding conventional AP radiographic image. (

**d**) Foot model two virtual AP image CS1. (

**e**) Foot model two virtual AP image CS2. (

**f**) Corresponding conventional AP radiographic image. (

**g**) Foot model three virtual AP image CS1. (

**h**) Foot model three virtual AP image CS2. (

**i**) Corresponding conventional AP radiographic image.

**Figure A2.**CS1 and CS2 virtual lateral image of the three 3D foot models without a splint compared to the corresponding conventional lateral radiographic image: (

**a**) Foot model one virtual lateral image CS1. (

**b**) Foot model one virtual lateral image CS2. (

**c**) Corresponding conventional lateral radiographic image. (

**d**) Foot model two virtual lateral image CS1. (

**e**) Foot model two virtual lateral image CS2. (

**f**) Corresponding conventional lateral radiographic image. (

**g**) Foot model three virtual lateral image CS1. (

**h**) Foot model three virtual lateral image CS2. (

**i**) Corresponding conventional lateral radiographic image.

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**Figure 1.**The splint used to create a constant plantigrade foot and neutral ankle position across patients.

**Figure 2.**The construction of CS1: (

**a**) Axial view of the talus with the drawing of the facies superior of the trochlea tali. (

**b**) Illustration of the talus with the cylinder fitted on the identified facies superior of the trochlea tali defining the direction of the x-axis (red line) as the normal vector to a sagittal plane. (

**c**) Illustration of the talus and the Origin as the midpoint of the talar intersections (TI1 and TI2) of the axis of the cylinder, without the fitted cylinder and sagittal plane. (

**d**) Illustration of the talus and its longitudinal inertia axis without the fitted cylinder and sagittal plane. (

**e**) Illustration of the talus and its longitudinal inertia axis intersecting the cylinder (IPC) without the sagittal plane. An additional parallel to the x-axis was created. (

**f**) Illustration of the talus with the y-axis running from the Origin (O) to the intersection point of the additional line with the sagittal plane (IPS).

**Figure 3.**The axes of the global coordinate system of CS1 centered at the origin: x-axis (red), y-axis (yellow), z-axis (green).

**Figure 4.**The construction of CS2: (

**a**) Posterior–anterior view of the foot with the three automatically selected weight-bearing points: the most caudal point of the first metatarsal–sesamoid complex (M1), fifth metatarsal (M5), and calcaneus (C) in the original CT scan orientation. (

**b**) Illustration of the foot with the ground plane based on the three weight-bearing points. (

**c**) Illustration of the foot with the normal vector of the ground plane defining the direction of the z-axis. (

**d**) Illustration of the inertia axes of the talus with its intersection point serving as the Origin (O). (

**e**) Illustration of the foot with the projection of the longitudinal talus inertia axis on the ground plane, defining the direction of the y-axis. (

**f**) Illustration of the foot with the normal vector and projected longitudinal talus inertia axis translated towards the Origin to form the z-axis and y-axis.

**Figure 5.**The axes of the global coordinate system of CS2 centered at the origin: x-axis (red), y-axis (yellow), z-axis (green).

**Figure 6.**The absolute angle of rotation describing the smallest angle of rotation between the first coordinate system construction of the technical physician (TP1) and the orthopedic surgeon (OS).

**Figure 7.**CS1 and CS2 virtual anteroposterior (AP) (perpendicular view on the xy-plane (x-axis (red), y-axis (yellow)) and lateral (perpendicular view on the yz-plane (y-axis (yellow), z-axis (green)) images of Patient 2 were compared to the corresponding conventional AP and lateral radiographic images. For the exact generation of the virtual image, see the body text: (

**a**) CS1 virtual AP image; (

**b**) CS2 virtual AP image; (

**c**) corresponding conventional AP radiographic image; (

**d**) CS1 virtual lateral image; (

**e**) CS2 virtual lateral image; (

**f**) corresponding conventional lateral radiographic image.

**Table 1.**Overview of different studies that defined a global coordinate system in the foot, specifying the accompanying limitations.

Study | Limitations |
---|---|

Cappozo et al. [13] | Operator-dependent accuracy and repeatability |

Green et al. [4] | Dependent on the scanned section of the fibula |

Geng et al. [14] | Origin not explicitly defined |

Ortolani et al. [15] | Origin not explicitly defined |

Yoshioka et al. [16] | The ankle joint angle determines the location of the forefoot in the global coordinate system |

Modenese et al. [17] | No definition of how axes intersect the origin |

Helical Region of Interest | Just above the tibiotalar joint through to the carpal–metacarpal joints, dependent on the region of interest |

Collimation | Slice thickness: 1.25 mm or smaller Slice increment: 0.625 mm (50% overlap) |

kVp | 120 |

mAs | As given by the automatic system |

Pitch | Use 1 or smaller |

Field of View (FOV) | Fit the whole foot |

Matrix | Use a 512 × 512 matrix |

Kernel/Algorithm | Moderate/soft tissue |

**Table 3.**The absolute angle of rotation between the first (CS1) and second coordinate system (CS2) definition of the technical physician (TP1 and TP2) and between TP1 and the coordinate system definition of the orthopedic surgeon (OS).

Absolute Angle of Rotation | Patient 1 | Patient 2 | Patient 3 | Patient 4 | Patient 5 | Patient 6 | Mean (SD) |
---|---|---|---|---|---|---|---|

CS1 | |||||||

TP1–TP2 | 1.66° | 0.48° | 0.86° | 1.48° | 2.12° | 1.75° | 1.39° (0.61°) |

TP1–OS | 2.10° | 1.30° | 0.92° | 1.35° | 4.43° | 5.86° | 2.66° (2.01°) |

CS2 | |||||||

TP1–TP2 | 0° | 0° | 0° | 0° | 0° | 0° | 0° (0°) |

TP1–OS | 0° | 0° | 0° | 0° | 0° | 0° | 0° (0°) |

**Table 4.**The axis with angle magnitude between the first (CS1) and second coordinate system (CS2) definition of the technical physician (TP1 and TP2) and between TP1 and the coordinate system definition of the orthopedic surgeon (OS).

Axis with Angle Magnitude | Patient 1 | Patient 2 | Patient 3 | Patient 4 | Patient 5 | Patient 6 | |
---|---|---|---|---|---|---|---|

CS1 | |||||||

x-axis | 0.28° | 0.10° | 0.40° | 1.26° | −0.56° | −0.12° | |

TP1–TP2 | y-axis | −0.34° | −0.44° | −0.42° | 0.69° | −2.00° | −1.59° |

z-axis | 1.60° | −0.16° | 0.63° | −0.36° | −0.46° | 0.72° | |

x-axis | 0.50° | −1.1° | −0.40° | 0.82° | 0.36° | 0.88° | |

TP1–OS | y-axis | −2.00° | −0.08° | −0.23° | 0.75° | −4.03° | −5.69° |

z-axis | 0.38° | −0.72° | −0.79° | 0.76° | −1.81° | 1.12° | |

CS2 | |||||||

x-axis | 0° | 0° | 0° | 0° | 0° | 0° | |

TP1–TP2 | y-axis | 0° | 0° | 0° | 0° | 0° | 0° |

z-axis | 0° | 0° | 0° | 0° | 0° | 0° | |

x-axis | 0° | 0° | 0° | 0° | 0° | 0° | |

TP1–OS | y-axis | 0° | 0° | 0° | 0° | 0° | 0° |

z-axis | 0° | 0° | 0° | 0° | 0° | 0° |

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## Share and Cite

**MDPI and ACS Style**

Krakers, S.; Peters, A.; Homan, S.; olde Heuvel, J.; Tuijthof, G.
Definition of a Global Coordinate System in the Foot for the Surgical Planning of Forefoot Corrections. *Biomechanics* **2023**, *3*, 523-538.
https://doi.org/10.3390/biomechanics3040042

**AMA Style**

Krakers S, Peters A, Homan S, olde Heuvel J, Tuijthof G.
Definition of a Global Coordinate System in the Foot for the Surgical Planning of Forefoot Corrections. *Biomechanics*. 2023; 3(4):523-538.
https://doi.org/10.3390/biomechanics3040042

**Chicago/Turabian Style**

Krakers, Sanne, Anil Peters, Sybrand Homan, Judith olde Heuvel, and Gabriëlle Tuijthof.
2023. "Definition of a Global Coordinate System in the Foot for the Surgical Planning of Forefoot Corrections" *Biomechanics* 3, no. 4: 523-538.
https://doi.org/10.3390/biomechanics3040042