# Finite Element Analysis of Customized Acetabular Implant and Bone after Pelvic Tumour Resection throughout the Gait Cycle

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## Abstract

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## 1. Introduction

## 2. Materials and Methods

#### 2.1. Finite Element Models

#### 2.2. Material Properties

#### 2.3. Loads and Boundary Conditions

#### 2.4. Model Validation

## 3. Results

#### 3.1. Results for the Stage of Tightening the Screw Simulation

#### 3.2. Results of the Walking Cycle Simulation

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**A virtual resection of the pelvic bones for pelvic tumour surgery: (

**a**) resection planes; (

**b**) the pelvis reconstructed with the individual endoprosthesis.

**Figure 2.**Developed design of the individual endoprosthesis considered in this paper: (

**a**) design and main components of the implant: the cup (1), the bearing flange on the iliac bone (2), the bearing flange on the pubic bone (3), and the bearing flange on the ischiatic bone (4). (

**b**) Implant position and fixation by seven screws.

**Figure 3.**Implant fixation: (

**a**) the screws numbered from 1 to 7 and their positions (the implant is hidden); (

**b**) the holes numbered from 1 to 7 in the bone parts, the same numeration as this for the screws.

**Figure 4.**Finite element model of the “bone–endoprosthesis” system: (

**a**) finite element mesh on the pelvis; (

**b**) finite element mesh on the implant.

**Figure 5.**Boundary conditions and applied forces: (

**a**) model with boundary conditions and loads including screw pretension and reaction forces applied to the centres of the left and right joints; (

**b**) reaction force curves for walking simulation measured as a percentage of body weight (BW).

**Figure 6.**Total displacement in the “bone–endoprosthesis” system for the walking condition and a screw load of 1000 N: (

**a**) typical displacement distribution (mm); (

**b**) displacement values for the full gait cycle at the spherical center of the left femoral head.

**Figure 7.**Dependence of the maximum von Mises stress in the screws as a function of the applied preload values.

**Figure 8.**Equivalent von Mises stress (MPa) distribution caused by a pretension load of 1000 N: (

**a**) in the screw system; (

**b**) in the implant.

**Figure 9.**Comparative graphs of the maximum von Mises stresses occurring in the reconstructed pelvis bone on the hole boundaries: (

**a**) the spongy tissue; (

**b**) the cortical tissue.

**Figure 10.**Equivalent von Mises stress (MPa) distribution in the bone tissue caused by a pretension load of 1000 N: (

**a**) the upper part of the resected pelvic bone; (

**b**) the lower part of the resected pelvic bone. The images on the left show the stresses in the cortical tissue, and the images on the right show the stresses in the spongy tissue.

**Figure 11.**Maximum von Mises stress in each of the screws with pretension in the walking cycle phases: (

**a**) pretension force equal to 500 N; (

**b**) pretension force equal to 1000 N.

**Figure 12.**Maximum von Mises stress in the implant on the boundaries of the holes in the walking cycle phases: (

**a**) pretension force equal to 500 N; (

**b**) pretension force equal to 1000 N.

**Figure 13.**Equivalent von Mises stress (MPa) distribution in the endoprosthesis titanium parts caused by the pretension load of 1000 N and joint reaction forces at 45% of the gait cycle: (

**a**) screw system; (

**b**) implant body.

**Figure 14.**Maximum von Mises stress in the bone tissue on the boundaries of the holes шт in the walking cycle phases: (

**a**) the pretension force equal to 500 N; (

**b**) the pretension force equal to 1000 N.

**Figure 15.**Equivalent von Mises stress (MPa) distribution in the bone tissue caused by the pretension load of 1000 N and joint reaction forces at 45% of the gait cycle: (

**a**) the upper part of the resected pelvic bone; (

**b**) the lower part of the resected pelvic bone. The images on the left show stresses in the cortical tissue, and the images on the right show stresses in the spongy tissue.

Part | Number of Finite Elements | Finite Element Type | FEM Verification | ||
---|---|---|---|---|---|

Aspect | Skewness | Warping | |||

Top of the damaged half of the pelvic bone | 77,392 | Four-node linear solid tetrahedral C3D4 type | No violations | 2892 elements off | No violations |

Bottom of the damaged half of the pelvic bone | 122,131 | 3031 elements off | |||

Healthy pelvic bone | 265,775 | 8807 elements off | |||

Sacrum | 44,746 | 2009 elements off | |||

Implant | 329,828 | 12,615 elements off |

Material | Young’s Modulus, GPa | Poisson’s Ratio | Ultimate Stress, MPa | |
---|---|---|---|---|

Yield | Fatigue | |||

Cortical tissue [9,18] | 17 | 0.3 | 80–150 [18] | the same as the yield stress |

Spongy tissue [14,20] | 0.07 | 0.2 | 1.4–2.1 [20] | |

Normal Ti-6Al-4V [21] | 113.8 | 0.34 | 950 | 310–610 [21] |

3D printed Ti-6Al-4V [22,23] | 123.4 | 0.26 | 910 | 200–500 [23] |

Polyethylene [24] | 1 | 0.35 | 26 | - |

**Table 3.**Summary of the maximum von Mises stresses occurring in the endoprosthesis parts and bone tissue for screw pretension loads equal to 500 N and 1000 N.

Assembly Components | Maximum Von Mises Stresses (MPa) and Their Location | |||
---|---|---|---|---|

Pretension Force of 500 N | Pretension Force of 1000 N | |||

Pretension Stage | Walking Cycle (45% Phase) | Pretension Stage | Walking Cycle (45% Phase) | |

Screw system | 122 MPa, screw 7 | 192 MPa, screw 7 | 212 MPa, screw 7 | 263 MPa, screw 7 |

Implant | 151 MPa, hole 1 | 197 MPa, hole 1 255 MPa, hole 1 (65% phase) | 253 MPa, hole 4 | 335 MPa, hole 1 |

Pelvic cortical tissue, top part of resected bone | 29 MPa, hole 7 | 171 MPa, hole 7 168 MPa, hole 5 | 48 MPa, hole 7 | 168 MPa, hole 7 162 MPa, hole 5 |

Pelvic spongy tissue, top part of resected bone | 0.68 MPa, hole 4 | 4.98 MPa, hole 1 4.3 MPa, hole 4 | 1.25 MPa, hole 4 | 5.0 MPa, hole 1 4.1 MPa, hole 4 |

Pelvic cortical tissue, bottom part of resected bone | 2.7 MPa | 19 MPa | 4.5 MPa | 19 MPa |

Pelvic spongy tissue, bottom part of resected bone | 0.28 MPa, hole 3 | 1.1 MPa, hole 3 | 0.47 MPa, hole 3 | 1.2 MPa, hole 3 |

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**MDPI and ACS Style**

Maslov, L.; Borovkov, A.; Maslova, I.; Soloviev, D.; Zhmaylo, M.; Tarasenko, F. Finite Element Analysis of Customized Acetabular Implant and Bone after Pelvic Tumour Resection throughout the Gait Cycle. *Materials* **2021**, *14*, 7066.
https://doi.org/10.3390/ma14227066

**AMA Style**

Maslov L, Borovkov A, Maslova I, Soloviev D, Zhmaylo M, Tarasenko F. Finite Element Analysis of Customized Acetabular Implant and Bone after Pelvic Tumour Resection throughout the Gait Cycle. *Materials*. 2021; 14(22):7066.
https://doi.org/10.3390/ma14227066

**Chicago/Turabian Style**

Maslov, Leonid, Alexey Borovkov, Irina Maslova, Dmitriy Soloviev, Mikhail Zhmaylo, and Fedor Tarasenko. 2021. "Finite Element Analysis of Customized Acetabular Implant and Bone after Pelvic Tumour Resection throughout the Gait Cycle" *Materials* 14, no. 22: 7066.
https://doi.org/10.3390/ma14227066