# Preoperative Prediction of Optimal Femoral Implant Size by Regularized Regression on 3D Femoral Bone Shape

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## Abstract

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## 1. Introduction

## 2. Materials and Methods

#### 2.1. Data Preprocessing

#### 2.2. Hypergraph Representation of a Triangular Mesh

#### 2.3. Hypergraph Regularized Group Lasso

Algorithm 1: Hypergraph regularized group Lasso. |

#### 2.4. Baseline Method

## 3. Results

^{®}Xeon

^{®}E5-1620 v3 CPU and 64 GB RAM memory.

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 2.**Graph and hypergraph structure for a mesh in 3D space. (

**a**) Graph structure. (

**b**) Hypergraph structure.

**Figure 3.**The average model performance over the cross-validation folds for different values of ${\lambda}_{G}$, ${\lambda}_{L}$, and ${\lambda}_{R}$ in terms of accuracy and MSE. (

**a**) Accuracy as a function of ${\lambda}_{L}$ and ${\lambda}_{G}$ with ${\lambda}_{R}=1$. (

**b**) MSE as a function of ${\lambda}_{L}$ and ${\lambda}_{G}$ with ${\lambda}_{R}=1$. (

**c**) Accuracy as a function of ${\lambda}_{R}$ with ${\lambda}_{G}=100$ and ${\lambda}_{L}=10$. (

**d**) MSE as a function of ${\lambda}_{R}$ with ${\lambda}_{G}=100$ and ${\lambda}_{L}=10$.

**Figure 4.**A medial, anterior, lateral, posterior, and distal view of the vertex importance for the model.

**Figure 6.**A medial, anterior, lateral, posterior, and distal view of the directions of the ${\beta}_{\mathbf{g}}$ vectors for the vertices with non-zero coefficients.

Parameter | Value |
---|---|

Scanner | GE Optima^{TM} MR450w |

Field strength | 1.5 T |

Scan type | 3D |

Scan direction | Sagittal |

Sequence | Fat saturated T1 spoiled gradient echo |

Slice thickness | 1 mm |

Pixel size | 0.4 mm |

**Table 2.**Comparison of manual methods for predicting the required femoral implant size in terms of their accuracy. Bold values indicate the best performance per metric.

Study | Absolute Accuracy | +1/−1 Size Accuracy | Modality |
---|---|---|---|

Trickett et al. 2009 [3] | 48% | 98% | 2D: X-ray |

Miller et al. 2012 [4] | 64% | 100% | 2D: X-ray |

Unnanuntana et al. 2007 [5] | 50.4% | 97.3% | 2D: X-ray |

Pietrzak et al. 2019 [6] | 52.9% | - | 2D: X-Ray |

Ettinger et al. 2016 [7] | 59.6% | 97.9% | 2D: X-ray |

Pietrzak et al. 2019 [6] | 96.6% | - | 3D: CT |

Ettinger et al. 2016 [7] | 100% | 100% | 3D: MRI |

Schotanus et al. 2016 [8] | 93.9% | - | 3D: MRI |

**Table 3.**Comparison of automatic methods for predicting femoral implant size in terms of their accuracy. Bold values indicate the best performance per metric.

Study | Absolute Accuracy | +1/−1 Size Accuracy | Modality |
---|---|---|---|

Seaver et al. 2020 [37] | 19.2% | 51.2% | 2D: X-ray |

Trainor et al. 2018 [11] | 56% | 99% | Shoe size |

Sershon et al. 2017 [17] | - | 85–95% (implant dependent) | Demographics |

Bhowmik-Stoker et al. 2018 [19] | - | 94% | Demographics |

Sershon et al. 2019 [18] | - | 76% | Demographics |

Blevins et al. 2020 [22] | - | 94.4% | Demographics |

Wallace et al. 2020 [2] | 43.7% | 90.1% | Demographics |

Kunze et al. 2021 [16] | 48.4% | 95% | Demographics |

Naylor et al. 2022 [21] | - | 83.09% | Demographics |

Lambrechts et al. 2022 [23] | 82.2% | - | 3D: MRI |

Manufacturer’s default plan | 23.1% | 99.11% | 3D: MRI |

Shape coefficient regression | 58.93% | 98.21% | 3D: MRI |

Hypergraph regularized group lasso | 70.08% | 99.11% | 3D: MRI |

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**MDPI and ACS Style**

Lambrechts, A.; Van Dijck, C.; Wirix-Speetjens, R.; Vander Sloten, J.; Maes, F.; Van Huffel, S. Preoperative Prediction of Optimal Femoral Implant Size by Regularized Regression on 3D Femoral Bone Shape. *Appl. Sci.* **2023**, *13*, 4344.
https://doi.org/10.3390/app13074344

**AMA Style**

Lambrechts A, Van Dijck C, Wirix-Speetjens R, Vander Sloten J, Maes F, Van Huffel S. Preoperative Prediction of Optimal Femoral Implant Size by Regularized Regression on 3D Femoral Bone Shape. *Applied Sciences*. 2023; 13(7):4344.
https://doi.org/10.3390/app13074344

**Chicago/Turabian Style**

Lambrechts, Adriaan, Christophe Van Dijck, Roel Wirix-Speetjens, Jos Vander Sloten, Frederik Maes, and Sabine Van Huffel. 2023. "Preoperative Prediction of Optimal Femoral Implant Size by Regularized Regression on 3D Femoral Bone Shape" *Applied Sciences* 13, no. 7: 4344.
https://doi.org/10.3390/app13074344