# Development of a Knee Joint CT-FEM Model in Load Response of the Stance Phase During Walking Using Muscle Exertion, Motion Analysis, and Ground Reaction Force Data

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Participant

#### 2.2. Gait Analysis

#### 2.2.1. Motion Analysis

#### 2.2.2. Electromyography (EMG)

#### 2.3. Outline of the Model and Calculation Method

#### 2.3.1. CT Value (HU: Hounsfield Unit) Density Conversion Formula

^{3}] = (CT value × a) + b,

#### 2.3.2. Young’s Modulus

#### 2.3.3. Young’s Modulus Conversion Formula

#### 2.3.4. Poisson’s Ratio

_{1}is the transverse elastic strain and ε

_{2}is the longitudinal elastic strain.

#### 2.4. Modeling Construction and Procedure

#### 2.4.1. Determination of Material Properties

#### 2.4.2. Determination of Walking Posture

#### 2.4.3. Determination of Load and Restraint Conditions

## 3. Results

^{2}, the average contact pressure 2.50549 N/mm

^{2}, and the maximum contact pressure 8.95098 N/mm

^{2}.

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**A finite element model of the right knee of a walking posture in the load response (LR) phase in a healthy person. On the left is a front view and on the right is a side view. Bone elements are yellow, truss elements are pink, the meniscus is light blue, and articular cartilage is green. Articular cartilage was set on the femur, tibia, and patella.

**Figure 2.**The setting of load and restraint condition in the right knee model. The femoral side was restrained and the quadriceps muscle was forced displacement (↑). The muscle was input in each direction, the lower end of the lower leg was vertical, and the load obtained in the gait analysis was input.

**Figure 3.**Image (

**a**) shows the joint reaction force on the femoral joint surface, and (

**b**) shows the joint reaction force on the tibial joint surface. Arrows in the figure indicate the magnitude and direction of the reaction force.

**Figure 4.**Image (

**a**) shows the equivalent stress diagram on the femoral joint surface, and (

**b**) shows the equivalent stress diagram on the tibial joint surface. The left side of the figure is the medial side. The range of stress values is 0–5 MPa; it was displayed in blue, green, yellow, and red in the low- to high-stress side.

**Figure 5.**Simulated muscle activation patterns of the RF (

**a**), VM (

**b**), VL (

**c**), BF (

**d**), and ST (

**e**) muscles, and the measured EMG activity of RF (

**f**), VM (

**g**), VL (

**h**), BF (

**i**), and ST (

**j**).

Anatomy Element | Young’s Modulus (MPa) | Poisson’s Ratio |
---|---|---|

Femur, tibia, fibula, patella | Keyak’s conversion formula | 0.4 |

Cartilage | 20 (100 only on the fibula) | 0.4 |

Meniscal | 20 | 0.4 |

Ligament | 0.1 | 0.4 |

The angle between the leg bone and the floor (deg.) | ||

Inversion direction 11.5 | Bending direction 13.3 | Inward direction 7.7 |

The angle between the femur and tibia (deg.) | ||

Inversion direction 12.21 | Bending direction 14.62 | Inward direction −3.28 |

Anatomical Element | Strain Range | Tension (N) |
---|---|---|

Cruciate ligament, collateral ligament | ε < 0.0 0.0 < ε | 0.0 1000ε |

Patellar ligament, quadriceps tendon | ε < 0.0 0.0 < ε < 0.005 0.005 < ε | 0.0 172754ε 863.77 |

**Table 4.**The traction force of the muscle (calculated value) and floor reaction force (measured value).

Floor reaction force (N) | |

Inward direction | 26.08 |

Forward direction | −112.00 |

Upward direction | 808.95 |

Muscle traction (N) | |

Quadriceps | 863.77 |

Biceps femoris | 266.26 |

Semimembranosus | 99.99 |

Semitendinosus + gracilis | 61.11 |

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**MDPI and ACS Style**

Watanabe, K.; Mutsuzaki, H.; Fukaya, T.; Aoyama, T.; Nakajima, S.; Sekine, N.; Mori, K. Development of a Knee Joint CT-FEM Model in Load Response of the Stance Phase During Walking Using Muscle Exertion, Motion Analysis, and Ground Reaction Force Data. *Medicina* **2020**, *56*, 56.
https://doi.org/10.3390/medicina56020056

**AMA Style**

Watanabe K, Mutsuzaki H, Fukaya T, Aoyama T, Nakajima S, Sekine N, Mori K. Development of a Knee Joint CT-FEM Model in Load Response of the Stance Phase During Walking Using Muscle Exertion, Motion Analysis, and Ground Reaction Force Data. *Medicina*. 2020; 56(2):56.
https://doi.org/10.3390/medicina56020056

**Chicago/Turabian Style**

Watanabe, Kunihiro, Hirotaka Mutsuzaki, Takashi Fukaya, Toshiyuki Aoyama, Syuichi Nakajima, Norio Sekine, and Koichi Mori. 2020. "Development of a Knee Joint CT-FEM Model in Load Response of the Stance Phase During Walking Using Muscle Exertion, Motion Analysis, and Ground Reaction Force Data" *Medicina* 56, no. 2: 56.
https://doi.org/10.3390/medicina56020056