# Analyzing Dynamic Operational Conditions of Limb Prosthetic Sockets with a Mechatronics-Twin Framework

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## Abstract

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## 1. Introduction

## 2. Mechatronics-Twin Framework for Prosthetic Sockets

## 3. Related Work

## 4. Modeling and Simulation of Overall Operational Conditions

## 5. Physical Prototyping and Dynamic Testing by Stewart Platform

## 6. Sensor Data Acquisition and Collection

#### 6.1. Sensor Data Acquisition by AE

Algorithm 1: Training and using AE for sensor data treatment. |

Result: $Calibration\phantom{\rule{4pt}{0ex}}results\phantom{\rule{4pt}{0ex}}\left(pressure\right)\phantom{\rule{4pt}{0ex}}\widehat{\mathcal{I}},\phantom{\rule{4pt}{0ex}}Loss$Input: Train signals (voltage) ${\mathcal{I}}_{train}$, test data ${\mathcal{I}}_{test}$, Ground truth for trainset ${\mathcal{I}}_{ground}$.AE Training Mode for Sensor Calibration: $\mathcal{H}\leftarrow \mathcal{F}\left({\mathcal{I}}_{train}\right)$ ${\widehat{\mathcal{I}}}_{train}\leftarrow \mathcal{G}\left(\mathcal{H}\right)$ $Loss\leftarrow \parallel {\mathcal{I}}_{ground}-{\widehat{\mathcal{I}}}_{train}{\parallel}^{2}$ AE Operation Mode: ${\widehat{\mathcal{I}}}_{test}\leftarrow \mathcal{G}\left(\mathcal{F}\left({\mathcal{I}}_{test}\right)\right)$ |

#### 6.2. Sensor Data Collection by HMM

Algorithm 2: Training HMM-based cluster model for the description of reference operation. |

Result: $\mathcal{N}({\mu}_{k}^{\left[Comfort\right]},{\sigma}_{k}^{\left[Comfort\right]}),{\mathsf{\Theta}}_{Trained}$Input: ${\mathcal{D}}_{Comfort}$, K$N\leftarrow AIC\left({\mathcal{D}}_{Comfort}\right)$ ${\xi}^{{T}^{*}\left[Comfort\right]}$$\leftarrow {\mathsf{\Theta}}_{Trained({\mathcal{D}}_{Comfort},N)}\left({\mathcal{D}}_{Comfort}\right)$ for$k=1,2,\dots ,K$do$\phantom{(}$$\phantom{(}$end$\phantom{(}$Note:N refers to the number of discretized states for the load conditions; k is one of the K number of temporal clusters; ${\mathcal{D}}_{comfort}$ is the data set from comfortable socket usage; ${\xi}^{{T}^{*}\left[Comfort\right]}$ refers to the ${\xi}^{{T}^{*}}$ that is labeled as Comfort. It is derived from the HMM model trained with ${\mathcal{D}}_{comfort}$ for the same data set ${\mathcal{D}}_{comfort}$; $\mathcal{N}({\mu}_{k}^{\left[Comfort\right]},{\sigma}_{k}^{\left[Comfort\right]})$ refers to the $\mathcal{N}({\mu}_{k},{\sigma}_{k})$ for a ${\xi}^{{T}^{*}\left[Comfort\right]}$. |

## 7. Operation Condition Analysis and Anomaly Detection

Algorithm 3: Detecting anomalous operational conditions using HMM-based cluster model. |

## 8. Case Study and Results

## 9. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Overview of the mechatronics-twin framework that allows both virtual and physical replications of prosthetic socket device. The virtual replication is supported by two services: ➊ Biomechanical modeling and simulation; and ➋ FEA. The physical replication is supported by three services: ➌ Prototyping with 3D printing and integrating; ➍ dynamic testing by Stewart platform; and ➎ sensor data acquisition and collection. The analysis is supported by the service ➏ operation condition analysis and anomaly detection.

**Figure 3.**Basic force tensors determining the intra-socket loads condition. (

**a**) Basic configuration of an amputee leg model integrating transfemoral socket and stump (Right Leg). (

**b**) Basic force tensors determining the intra-socket loads condition.

**Figure 4.**One example of piston forces and moments over seven consecutive gait cycles, shown by seven trajectories: (

**a**) Rotation moment around X-axis (lateral-medial axis) and (

**b**) piston force along X–axis (lateral-medial axis).

**Figure 6.**The physical prototyping and dynamic testing: (

**a**) The shell mold casting process of silicone stump. (

**b**) The physical test-rig with the femur-stump assembly and prosthetic socket mounted on the Stewart manipulator. (

**c**) The sensors deployed inside the socket for measurement of dynamic pressure load conditions.

**Figure 7.**A graph representation of Hidden Markov Model (HMM), where the node corresponds to the states and sensor observations (i.e., ${Z}_{t}$ and ${X}_{t}$), and the transition and observation probabilities are denoted by the edges.

**Figure 8.**Results of the sensor function ($Pressure\mapsto Voltage$) trained with AE (Autoencoder) and MLP (Multilayer Perceptron). For the sensor function trained with AE, the MSE (Mean-Square Error) figures of pressure decreasing and increasing phase are around 0.024 and 0.017, respectively. These could be compared with the MSE figures of the sensor function trained with MLP for the same data, which are 0.035 and 0.021 respectively. While the overall performances of these two methods are quite similar to each other, the results of AE are smoother, such as readings between 4 and 9 KPa of the pressure increasing phase. (

**a**) Pressure decreasing phase. (

**b**) Pressure increasing phase.

**Figure 9.**Characterizing execution progress based on temporal clustering. (

**a**) Temporal clustering for execution progress data of multiple gait cycles. (

**b**) Gaussian characteristics of execution progress data in multiple temporal clusters.

**Figure 10.**The execution progress trajectories and the detection of anomalies by dynamic threshold. The analytical data is the round truth data generated by a simulation-based FEA (Finite Element Analysis) of a quadrilateral transfemoral socket with well-defined amputee gait cycles. The reference data represent the load conditions with comfortable socket operation. For the evaluation of algorithmic design, each data set contains around 600 data. The Test data represent the measurement from specific operational scenarios containing anomalies.

Threshold | False Positive Rate | False Negative Rate | Precision |
---|---|---|---|

Fixed log-likelihood (−3) | 14.75% | 3.14% | 85.25% |

Fixed log-likelihood (−7) | 2.83% | 54.30% | 97.07% |

Dynamic log-likelihood | 6.34% | 8.71% | 93.66% |

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## Share and Cite

**MDPI and ACS Style**

Chen, D.; Su, P.; Ottikkutti, S.; Vartholomeos, P.; Tahmasebi, K.N.; Karamousadakis, M. Analyzing Dynamic Operational Conditions of Limb Prosthetic Sockets with a Mechatronics-Twin Framework. *Appl. Sci.* **2022**, *12*, 986.
https://doi.org/10.3390/app12030986

**AMA Style**

Chen D, Su P, Ottikkutti S, Vartholomeos P, Tahmasebi KN, Karamousadakis M. Analyzing Dynamic Operational Conditions of Limb Prosthetic Sockets with a Mechatronics-Twin Framework. *Applied Sciences*. 2022; 12(3):986.
https://doi.org/10.3390/app12030986

**Chicago/Turabian Style**

Chen, Dejiu, Peng Su, Suranjan Ottikkutti, Panagiotis Vartholomeos, Kaveh Nazem Tahmasebi, and Michalis Karamousadakis. 2022. "Analyzing Dynamic Operational Conditions of Limb Prosthetic Sockets with a Mechatronics-Twin Framework" *Applied Sciences* 12, no. 3: 986.
https://doi.org/10.3390/app12030986