# Joint Torques and Tibiofemoral Joint Reaction Force in the Bodyweight “Wall Squat” Therapeutic Exercise

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## Abstract

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## Featured Applications

**With the results of this study, therapists can manage the wall squat exercise and its variants to finely modulate the lower-limb joint torques and to minimize the shear component of the tibiofemoral joint reaction force.**

## Abstract

_{GR}) of the ground reaction force; back supported via the scapular or pelvic zone. The ankle and hip angles corresponding to a given knee angle can be modulated, changing the distance d, to manage limitation in lumbopelvic and ankle mobility. The knee-extensor muscles can be overloaded (250 Nm muscle torque) with knees flexed at 90°, back supported through the pelvic zone, and feet away from the wall (d = 50 cm). Scapular support, x

_{GR}at forefoot, and d = 50 cm, yield a higher level of muscle-torque for hip-extension (130 Nm) and knee-flexion (65 Nm), with knees at 90° of flexion or near full extension, respectively. Ankle-dorsiflexion (plantarflexion) muscle torque up to 40 Nm is reached with x

_{GR}at the forefoot (rearfoot). This study may aid trainers and therapists to finely modulate the muscle torques (up to the above-mentioned levels) by an appropriate selection of exercise variants for training or rehabilitation purposes. Low levels (60 N) of anterior tibial pull may occur near 25° of knee flexion with ${x}_{\mathrm{GR}}$ at the rearfoot.

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Biomechanical Modelling

#### 2.2. Participants

#### 2.3. Testing Session

#### 2.4. Data Recording and Processing

#### 2.5. Statistical Analysis

## 3. Results

#### 3.1. Kinematics

#### 3.2. Ground Reaction Force

#### 3.3. Joint Torques and TF Shear Force

#### 3.4. TF Shear Force

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**Mechanical diagram of the bodyweight wall-squat exercise that includes the external forces acting on the exerciser (body weight $M\overrightarrow{g}$, ground reaction force ${\overrightarrow{R}}_{\mathrm{GR}}$, supporting force exerted by the wall on the back ${\overrightarrow{F}}_{\mathrm{wall}}$), the hip, knee, and ankle angle (${\mathsf{\theta}}_{\mathrm{hip}}$, ${\mathsf{\theta}}_{\mathrm{knee}}$, ${\mathsf{\theta}}_{\mathrm{ankle}}$), the shank and thigh inclination angle (${\mathsf{\theta}}_{\mathrm{shank}}$, ${\mathsf{\theta}}_{\mathrm{thigh}}$), and the horizontal distance (d) of the ankle from the hip. $\widehat{i}$ and $\widehat{j}$ are the unit vectors codirectional with the x-axis and y-axis, respectively.

**Figure 2.**Dependence of the hip and ankle angle $({\mathsf{\theta}}_{\mathrm{hip}}$ and ${\mathsf{\theta}}_{\mathrm{ankle}}$) on the knee angle (${\mathsf{\theta}}_{\mathrm{knee}}$) for different values of the horizontal ankle-to-hip distance $d$ (d = 0.2, 0.3, 0.4, 0.5 m). The knee flexion angle is given by $180\xb0-{\mathsf{\theta}}_{\mathrm{knee}}$. Data refer to a subject 175 cm tall.

**Figure 3.**Dependence of the knee muscle torque ${\tau}_{\mathrm{knee}}$ on the knee angle ${\mathsf{\theta}}_{\mathrm{knee}}$ for different values of the horizontal ankle-to-hip distance $d$ (d = 0.2, 0.3, 0.4, 0.5 m), two positions of the centre of pressure ${y}_{\mathrm{wall}}$ of the force exerted by the wall on the back (scapular support,${y}_{\mathrm{wall}}={y}_{\mathrm{shoulder}}$, and pelvic support, ${y}_{\mathrm{wall}}={y}_{\mathrm{hip}}$), and two positions of the centre of pressure ${x}_{\mathrm{GR}}$ of the ground reaction force (${x}_{\mathrm{GR}}$ at rearfoot, ${x}_{\mathrm{GR}}={x}_{\mathrm{ankle}}$, and ${x}_{\mathrm{GR}}$ at forefoot, ${x}_{\mathrm{GR}}={x}_{\mathrm{ankle}}+13\mathrm{cm}$). Positive values of ${\tau}_{\mathrm{knee}}$ reflect a knee-extension muscle torque, whereas negative values reflect a knee-flexion muscle torque. Data refer to a subject 175 cm tall with a body mass of 75 kg.

**Figure 4.**Dependence of the hip muscle torque ${\tau}_{\mathrm{hip}}$ on the knee angle ${\mathsf{\theta}}_{\mathrm{knee}}$ for different values of the horizontal ankle-to-hip distance $d$ (d = 0.2, 0.3, 0.4, 0.5 m), scapular support (${y}_{\mathrm{wall}}={y}_{\mathrm{shoulder}}$), and two positions of the centre of pressure ${x}_{\mathrm{GR}}$ of the ground reaction force (${x}_{\mathrm{GR}}$ at rearfoot, ${x}_{\mathrm{GR}}={x}_{\mathrm{ankle}}$, and ${x}_{\mathrm{GR}}$ at forefoot, ${x}_{\mathrm{GR}}={x}_{\mathrm{ankle}}+13\mathrm{cm}$). ${\tau}_{\mathrm{hip}}~0$ for ${y}_{\mathrm{wall}}={y}_{\mathrm{hip}}$ (pelvic support). Positive values of ${\tau}_{\mathrm{hip}}$ reflect a hip-extension muscle torque, whereas negative values reflect a hip-flexion muscle torque. Data refer to a subject 175 cm tall with a body mass of 75 kg.

**Figure 5.**Dependence of the ankle muscle torque ${\tau}_{\mathrm{ankle}}$ on the knee angle ${\mathsf{\theta}}_{\mathrm{knee}}$ for different values of the horizontal ankle-to-hip distance $d$ (d = 0.2, 0.3, 0.4, 0.5 m), two positions of the centre of pressure ${y}_{\mathrm{wall}}$ of the force exerted by the wall on the back (scapular support,${y}_{\mathrm{wall}}={y}_{\mathrm{shoulder}}$, and pelvic support, ${y}_{\mathrm{wall}}={y}_{\mathrm{hip}}$), and two positions of the centre of pressure ${x}_{\mathrm{GR}}$ of the ground reaction force (${x}_{\mathrm{GR}}$ at rearfoot, ${x}_{\mathrm{GR}}={x}_{\mathrm{ankle}}$, and ${x}_{\mathrm{GR}}$ at forefoot, ${x}_{\mathrm{GR}}={x}_{\mathrm{ankle}}+13\mathrm{cm}$). Positive values of ${\tau}_{\mathrm{ankle}}$ reflect a plantarflexion muscle torque, whereas negative values reflect a dorsiflexion muscle torque. Data refer to a subject 175 cm tall with a body mass of 75 kg.

**Figure 6.**Dependence of the tibiofemoral shear force ${\mathsf{\phi}}_{\mathrm{TF},\text{}\mathrm{shear}}$ on the knee angle ${\mathsf{\theta}}_{\mathrm{knee}}$ for different values of the horizontal ankle-to-hip distance $d$ (d = 0.2, 0.3, 0.4, 0.5 m), two positions of the centre of pressure ${y}_{\mathrm{wall}}$ of the force exerted by the wall on the back (scapular support,${y}_{\mathrm{wall}}={y}_{\mathrm{shoulder}}$, and pelvic support, ${y}_{\mathrm{wall}}={y}_{\mathrm{hip}}$), and two positions of the centre of pressure ${x}_{\mathrm{GR}}$ of the ground reaction force (${x}_{\mathrm{GR}}$ at rearfoot, ${x}_{\mathrm{GR}}={x}_{\mathrm{ankle}}$, and ${x}_{\mathrm{GR}}$ at forefoot, ${x}_{\mathrm{GR}}={x}_{\mathrm{ankle}}+13\mathrm{cm}$). Positive values of ${\mathsf{\phi}}_{\mathrm{TF},\text{}\mathrm{shear}}$ reflect a posterior (PCL loading) tibial pull, whereas negative values reflect an anterior (ACL loading) tibial pull. ${\mathsf{\phi}}_{\mathrm{TF},\text{}\mathrm{shear}}$ has been plotted only at knee angles where a knee-extension muscle torque is developed (${\tau}_{\mathrm{knee}}>0$), and under the condition that ${\tau}_{\mathrm{knee}}$ is produced by the quadriceps in absence of hamstring cococntraction. Thus, negative values of ${\mathsf{\phi}}_{\mathrm{TF},\text{}\mathrm{shear}}$ represent the maximum theoretic limit of anterior TF force that may occur in the wall-squat exercise.

**Table 1.**Maximum lower-limb joint torques developed during the static wall squat and corresponding exercise conditions. The maximum isokinetic concentric torques developed by males and females are also reported for comparison [15].

Torque Type | Maximum Torque | Conditions for Maximum Torque | Peak Isokinetic Torque of Males (Females) | |||
---|---|---|---|---|---|---|

Knee Angle | Distance d | Type of Support | Body Weight at Forefoot/Rearfoot | |||

Hip extension torque | 130 Nm | 80° | 50 cm | scapular | forefoot | 177 Nm (110 Nm) |

Knee extension torque | 250 Nm | 80° | 50 cm | pelvic | forefoot | 268 Nm (176 Nm) |

Knee flexion torque | 65 Nm | 0° | 50 cm | scapular | forefoot | 171 Nm (110 Nm) |

Ankle plantar-flexion torque | 40 Nm | 0° | 50 cm | scapular/pelvic | forefoot | 171 Nm (108 Nm) |

Ankle dorsi-flexion torque | 40 Nm | 80° | 20 cm | pelvic | rearfoot | 33 Nm (26 Nm) |

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**MDPI and ACS Style**

Biscarini, A.; Contemori, S.; Dieni, C.V.; Panichi, R. Joint Torques and Tibiofemoral Joint Reaction Force in the Bodyweight “Wall Squat” Therapeutic Exercise. *Appl. Sci.* **2020**, *10*, 3019.
https://doi.org/10.3390/app10093019

**AMA Style**

Biscarini A, Contemori S, Dieni CV, Panichi R. Joint Torques and Tibiofemoral Joint Reaction Force in the Bodyweight “Wall Squat” Therapeutic Exercise. *Applied Sciences*. 2020; 10(9):3019.
https://doi.org/10.3390/app10093019

**Chicago/Turabian Style**

Biscarini, Andrea, Samuele Contemori, Cristina V. Dieni, and Roberto Panichi. 2020. "Joint Torques and Tibiofemoral Joint Reaction Force in the Bodyweight “Wall Squat” Therapeutic Exercise" *Applied Sciences* 10, no. 9: 3019.
https://doi.org/10.3390/app10093019