# A Sensor-Based Decision Support System for Transfemoral Socket Rectification

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## Abstract

**:**

## 1. Introduction

## 2. Socketsense DSS Concept

#### 2.1. Description of Socketsense Sensor Configuration

#### 2.2. DSS Architecture

## 3. Fuzzy Membership Functions and Rule Base

#### 3.1. Linguistic Variables as Fuzzy Membership Functions

#### Input Membership Function Normalisation

#### 3.2. The Rule Base

#### 3.2.1. Rule Description: The Distal-End of the Stump Should Not Experience High Pressures

**Physical mechanism:**Any pressure against the stump’s distal-end tissues (femoral relief) should be of low magnitude to prevent the development of edema in the region. High pressures at the distal-end can occur due to two reasons: (a) the length of the socket is too short and exerts high pressures on the stump; (b) the socket is loose and as a result the stump slides down into the socket and pushes against the bottom of the socket. An indication that the socket is loose is given by low pressure readings at Scarpa’s triangle region. In the latter case, the rectification action is the reduction of volume of the socket by inserting a silicon pad on the proximal areas of the socket. The result of the rectification is a tighter socket that holds and fastens the stump tissue relatively high in the socket so that the distal-end does not push against the socket wall and no high pressures are exerted, as is demonstrated in Figure 6.

- Antecedents:
- –
- P: High pressure at distal-end;
- –
- Q: Medium pressure at distal-end;
- –
- M: Low pressure at distal-end;
- –
- N: Low pressure at Scarpa’s triangle.

- Consequences:
- –
- R: Large volume reduction of anterior area at Scarpa’s area;
- –
- S: Medium volume reduction of anterior area at Scarpa’s area;
- –
- T: Low volume reduction of anterior area at Scarpa’s area;
- –
- U: Socket is too short and has to be replaced.

- Rule set I:$$\begin{array}{c}\hfill P\wedge N\Rightarrow R\end{array}$$$$\begin{array}{c}\hfill Q\wedge N\Rightarrow S\end{array}$$$$\begin{array}{c}\hfill M\wedge N\Rightarrow T\end{array}$$$$\begin{array}{c}\hfill P\wedge (\neg N)\Rightarrow U\end{array}$$

#### 3.2.2. Rule Description: Maintain Ischium in Place on the Ischial Seat

**Physical mechanism:**The socket, especially a ischial tuberosity (IT) socket, provides a definite ischial shelf to transmit the vertical load; this is called the ischial seat. If the ischial tuberosity is not properly seated on the ischial seat, high pressures may appear over the ischial and medial area which cannot be tolerated by the patient. If the socket is loose, the ischial tuberosity will slide inwards the socket, ride on the edge of the ischial shelf and wedge the stump into the anteromedial apex, generating high shear-forces on medial side and great discomfort to the patient [1]. To maintain the ischium in place properly, considerable counter pressure from the front of the socket is required. This is achieved by compressing the pressure tolerant soft tissues such as those of Scarpa’s triangle area along the anterior aspect of the stump, for example, by inserting a silicon pad of adjusted thickness over the anterior wall of the socket. The rules are expressed using propositional logic and include the following antecedents and consequences:

- Antecedents:
- –
- P: High pressures on pubic ramus on the medial wall of the socket;
- –
- Q: Low pressure at ischial seat;
- –
- N: Normal pressures at ischial seat.

- Consequences:
- –
- R: Insert silicon pad of high thickness over the anterior wall;
- –
- S: Insert silicon pad of medium thickness over the anterior wall.

- Rule set II:$$\begin{array}{c}\hfill P\wedge Q\Rightarrow R\end{array}$$$$\begin{array}{c}\hfill P\wedge N\Rightarrow S\end{array}$$

#### 3.2.3. Rule Description: Achieve Proper Degree of Tightness of Fit along the Length of the Stump

**Physical mechanism:**The lateral wall should be shaped to fit the stump accurately, and should, if necessary, be flattened to distribute the lateral support pressure over a large area so that it can be tolerated comfortably. If the force distribution is not uniform enough or does not offer the proper degree of tightness of fit along the length of the stump, the insertion of a silicon pad along the lateral wall is required in order to reduce the medio-lateral dimensions and increase socket fitness. The rule for the lateral wall is expressed using propositional logic as:

- Antecedent:
- –
- P: Pressure along the lateral side of the stump is not uniform (especially mid and proximal regions);
- –
- Q: The pressure along the lateral side is low;
- –
- R: The pressure along the lateral side is medium.

- Consequence:
- –
- T: Socket should be rectified by inserting normal thickness silicon pad on the lateral side;
- –
- U: Socket should be rectified by inserting large thickness silicon pad on the lateral side.

- Rule set III:$$\begin{array}{c}\hfill P\wedge Q\Rightarrow U\end{array}$$$$\begin{array}{c}\hfill P\wedge R\Rightarrow T\end{array}$$

## 4. Rectification of the 3D Digital Model

#### Deformation Algorithms

Algorithm 1: Constant value as normal displacement. |

Result: The rectified mesh ${m}^{\prime}$Input: The current mesh mThe constant normal displacement C The angle to start rectification ${\theta}_{start}$ The angle to finish rectification ${\theta}_{end};$ where ${\theta}_{end}>{\theta}_{start}$ |

- The edges of the region left-wise and right-wise (10%) are smoothed with a logistic function [23], so that there is a smooth transition between the fixed region and the controlled region.
- The two levels of the volume reduction (the FIS returns two outputs; reduction magnitude on anterior and lateral) are smoothed with a logistic function [23], so that there is a smooth transition between the two levels.
- The normal displacement of each point is normalized with respect to the maximum height found in the H region.

**Step 1:**

- ${f}_{l}$ is the logistic function:$${f}_{l}\left(x\right)=\frac{L}{1+exp(n\xb7k(x-{x}_{0}))}$$
- –
- ${x}_{0}$, the x value of the sigmoid’s midpoint.
- –
- L, the curve’s maximum value.
- –
- k, the logistic growth rate or steepness of the curve.
- –
- n, the direction of the curve (up-down or down-up).

The parameter values used for the logistic function are shown in Table A1. - $\theta \left({\mathit{p}}_{\mathit{i}}\right)$ is the angle of the point ${\mathit{p}}_{\mathit{i}}$.
- ${\theta}_{AS}$ is the starting angle on the anterior wall.
- ${\theta}_{AL}$ is the middle angle on the antero-lateral wall.
- ${\theta}_{LE}$ is the end angle on the lateral wall.
- ${m}_{A}$ is the magnitude of the rectification on the anterior wall.
- ${m}_{L}$ is the magnitude of the rectification on the lateral wall.
- $\mathsf{\Delta}{\theta}_{max}$ is the absolute maximum angle difference $|{\theta}_{AS}-{\theta}_{LE}|$.

**Step 2:**

- ${h}_{i}$ is the height of the point ${\mathit{p}}_{\mathit{i}}$.
- ${h}_{max}$ is the maximum height found in the H region.

## 5. Demonstration of Algorithmic Execution

#### 5.1. Finite Elements Simulation Setup

#### 5.2. Results

- 1.
- The pressure experienced at the distal-end (S5E3) reduces as the rectification thickness increases.
- 2.
- The pressure distribution on the proximal areas (S1E8, S1E7, S1E6, S2E7, S2E6, S3E7, S3E6, S3E5, S4E7, S4E6, S5E7) becomes higher as the rectification increases.
- 3.
- As the thickness of the rectification increases, a trade-off is observed between offloading pressure from the distal end and increasing the pressure at the proximal areas of the stump. This can be easily seen in Figure 10, Figure 11 and Figure 12. As a result, medium thickness rectification provides the best rectification results, since it balances between offloading the pressure distribution on the distal end of the stump while maintaining relevantly low pressures on the proximal regions.

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Appendix A

$\mathit{\theta}$ Range | ${\mathit{x}}_{0}$ | L | k | n |
---|---|---|---|---|

${\theta}_{AS}\le \theta \left({\mathit{p}}_{\mathit{i}}\right)\le {\theta}_{AS}+0.1\xb7\mathsf{\Delta}{\theta}_{max}$ | ${\theta}_{AS}+0.05\xb7\mathsf{\Delta}{\theta}_{max}$ | ${m}_{A}$ | $0.5$ | 1 |

${\theta}_{AL}-\frac{\mathsf{\Delta}{\theta}_{max}}{2}\le \theta \left({\mathit{p}}_{\mathit{i}}\right)\le {\theta}_{AL}+\frac{\mathsf{\Delta}{\theta}_{max}}{2}$ | ${\theta}_{AL}$ | $max({m}_{A},{m}_{L})$ | $0.5$ | $sign({m}_{A}-{m}_{L})$ |

${\theta}_{LE}-0.1\xb7\mathsf{\Delta}{\theta}_{max}\le \theta \left({\mathit{p}}_{\mathit{i}}\right)\le {\theta}_{LE}$ | ${\theta}_{LE}-0.05\xb7\mathsf{\Delta}{\theta}_{max}$ | ${m}_{L}$ | $0.5$ | $-1$ |

Sensor id | ${\mathit{z}}_{\mathit{max}}\left(\mathit{mm}\right)$ | ${\mathit{z}}_{\mathit{min}}\left(\mathit{mm}\right)$ | ${\mathit{\theta}}_{\mathit{min}}\left(\mathit{Degrees}\right)$ | ${\mathit{\theta}}_{\mathit{max}}\left(\mathit{Degrees}\right)$ | Anatomical Region |
---|---|---|---|---|---|

S1E8 | 0 | −50 | 0 | 30 | Proximal Lateral |

S1E7 | −50 | −100 | 0 | 30 | Proximal Lateral |

S1E6 | −100 | −150 | 0 | 30 | Proximal Lateral |

S1E5 | −150 | −200 | 0 | 30 | Proximal Lateral |

S1E4 | −200 | −250 | 0 | 30 | Distal Lateral |

S1E3 | −250 | −300 | 0 | 30 | Distal Lateral |

S2E8 | −50 | −100 | −150 | −120 | Ramus |

S2E7 | −100 | −150 | −150 | −120 | Proximal Medial |

S2E6 | −150 | −200 | −150 | −120 | Proximal Medial |

S2E5 | −200 | −250 | −150 | −120 | Distal Medial |

S2E4 | −250 | −300 | −150 | −120 | Distal Medial |

S3E8 | 0 | −50 | −30 | 0 | Lateral Gluteal Fold |

S3E7 | −50 | −100 | −30 | 0 | Lateral Gluteal Fold |

S3E6 | −100 | −150 | −30 | 0 | Lateral Gluteal Fold |

S3E5 | −150 | −200 | −30 | 0 | Proximal Posterior |

S3E4 | −200 | −250 | −30 | 0 | Distal Posterior |

S3E3 | −250 | −300 | −30 | 0 | Distal Posterior |

S4E8 | −50 | −100 | −120 | −90 | Ischium |

S4E7 | −100 | −150 | −120 | −90 | Proximal Adductor Magnus |

S4E6 | −150 | −200 | −120 | −90 | Proximal Adductor Magnus |

S4E5 | −200 | −250 | −120 | −90 | Distal Adductor Magnus |

S4E4 | −250 | −300 | −120 | −90 | Distal Adductor Magnus |

S5E8 | −50 | −100 | 150 | 180 | Scarpa’s Triangle |

S5E7 | −100 | −150 | 120 | 150 | Proximal Anterior |

S5E6 | −150 | −200 | 90 | 120 | Proximal Anterior |

S5E5 | −200 | −250 | 60 | 90 | Distal Anterior |

S5E4 | −250 | −300 | 30 | 60 | Distal Antero-lateral |

S5E3 | −335 | −350 | 0 | −90 | Femur Relief |

## References

- Radcliffe, C.W. Functional Considerations in the Fitting of Above-knee Prostheses. Artif. Limbs
**1955**, 2, 35–60. [Google Scholar] - Radcliffe, C.W. Above-knee prosthetics. Prosthetics Orthot. Int.
**1977**, 1, 146–160. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Paterno, L.; Ibrahimi, M.; Gruppioni, E.; Menciassi, A.; Ricotti, L. Sockets for Limb Prostheses: A Review of Existing Technologies and Open Challenges. IEEE Trans. Biomed. Eng.
**2018**, 65, 1996–2010. [Google Scholar] [CrossRef] - Muller, M.D. Transfemoral Amputation: Prosthetic Management. In Atlas of Amputations and Limb Deficiencies, 4th ed.; American Academy of Orthopaedic Surgeons: Rosemont, IL, USA, 2016; Chapter 46; pp. 537–554. [Google Scholar]
- Neumann, E.S.; Wong, J.S.; Drollinger, R.L. Concepts of Pressure in an Ischial Containment Socket: Measurement. J. Prosthetics Orthot.
**2005**, 17, 2–11. [Google Scholar] [CrossRef] - Polliack, A.A.; Sieh, R.C.; Craig, D.D.; Landsberger, S.; McNeil, D.R.; Ayyappa, E. Scientific validation of two commercial pressure sensor systems for prosthetic socket fit. Prosthetics Orthot. Int.
**2000**, 24, 63–73. [Google Scholar] [CrossRef] - Paterno, L.; Dhokia, V.; Menciassi, A.; Seminati, E. A personalised prosthetic liner with embedded sensor technology: A case study. Biomed. Eng. Line
**2020**, 19, 1–20. [Google Scholar] [CrossRef] - Jasni, F.; Hamzaid, N.A.; Muthalif, A.G.A.; Zakaria, Z.; Shasmin, H.N.; Ng, S.C. In-Socket Sensory System for Transfemoral Amputees Using Piezoelectric Sensors: An Efficacy Study. IEEE/ASME Trans. Mechatron.
**2016**, 21, 2466–2476. [Google Scholar] [CrossRef] - Hood, S.; Ishmael, M.K.; Gunnell, A.; Foreman, K.B.; Lenzi, T. A kinematic and kinetic dataset of 18 above-knee amputees walking at various speeds. Sci. Data
**2020**, 7, 150. [Google Scholar] [CrossRef] [PubMed] - Sanders, J. Interface mechanics in external prosthetics: Review of interface stress measurement techniques. Med. Biol. Eng. Comput.
**1995**, 33, 509–516. [Google Scholar] [CrossRef] [PubMed] - Travis, R.P.; Dewar, M.E. Computer-aided socket design for trans-femoral amputees. Prosthetics Orthot. Int.
**1993**, 17, 172–179. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Colombo, G.; Facoetti, G.; Rizzi, C. A digital patient for computer-aided prosthesis design. Interface Focus
**2013**, 3, 5–7. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Frillici, F.S.; Rotini, F. Prosthesis Socket Design through Shape Optimization. Comput. Aided Des. Appl.
**2013**, 10, 863–876. [Google Scholar] [CrossRef] - Ramasamy, E.; Avci, O.; Dorow, B.; Chong, S.Y.; Gizzi, L.; Steidle, G.; Schick, F.; Röhrle, O. An Efficient Modelling-Simulation-Analysis Workflow to Investigate Stump-Socket Interaction Using Patient-Specific, Three-Dimensional, Continuum-Mechanical, Finite Element Residual Limb Models. Front. Bioeng. Biotechnol.
**2018**, 6, 126. [Google Scholar] [CrossRef] [PubMed] - Trillas, E.; Eciolaza, L. Fuzzy Logic: An Introductory Course for Engineering Students; Springer Publishing Company, Incorporated: Berlin/Heidelberg, Germany, 2015. [Google Scholar]
- Zadeh, L. The concept of a linguistic variable and its application to approximate reasoning-III. Inf. Sci.
**1975**, 9, 43–80. [Google Scholar] [CrossRef] - Zhang, M.; Lee, W.C. Quantifying the regional load-bearing ability of trans-tibial stumps. Prosthetics Orthot. Int.
**2006**, 30, 25–34. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Lower Limb Prosthetic Sockets and Suspension Systems: Pressure Tolerant and Pressure-Sensitive Areas. Available online: https://www.physio-pedia.com/Lower_Limb_Prosthetic_Sockets_and_Suspension_Systems (accessed on 16 March 2021).
- JDWarner/Scikit-Fuzzy: Scikit-Fuzzy Version 0.4.2. 2019. Available online: https://doi.org/10.5281/zenodo.3541386 (accessed on 16 March 2021).
- Botsch, M.; Kobbelt, L.; Pauly, M.; Alliez, P.; Lévy, B. Polygon Mesh Processing; CRC Press: Boca Raton, FL, USA, 2010. [Google Scholar]
- Trimesh. 2021. Available online: https://trimsh.org/ (accessed on 16 May 2021).
- Cignoni, P.; Callieri, M.; Corsini, M.; Dellepiane, M.; Ganovelli, F.; Ranzuglia, G. MeshLab: An Open-Source Mesh Processing Tool. In Eurographics Italian Chapter Conference; Scarano, V., Chiara, R.D., Erra, U., Eds.; The Eurographics Association: Aire-la-Ville, Switzerland, 2008. [Google Scholar]
- Wikipedia Contributors. Logistic Function—Wikipedia, The Free Encyclopedia. 2021. Available online: https://en.wikipedia.org/wiki/Logistic_function (accessed on 16 April 2021).
- Quadrilateral Socket Model. Available online: https://www.thingiverse.com/thing:3233555 (accessed on 10 April 2021).
- Lacroix, D.; Ramírez Patiño, J.F. Finite element analysis of donning procedure of a prosthetic transfemoral socket. Ann. Biomed. Eng.
**2011**, 39, 2972–2983. [Google Scholar] [CrossRef] [PubMed] - Dickinson, A.S.; Steer, J.W.; Worsley, P.R. Finite element analysis of the amputated lower limb: A systematic review and recommendations. Med. Eng. Phys.
**2017**, 43, 1–18. [Google Scholar] [CrossRef] [PubMed] - Wang, G.G.; Deb, S.; Cui, Z. Monarch butterfly optimization. Neural Comput. Appl.
**2019**, 31, 1995–2014. [Google Scholar] [CrossRef] [Green Version] - Wang, G.G.; Deb, S.; Coelho, L.d.S. Elephant herding optimization. In Proceedings of the 2015 3rd International Symposium on Computational and Business Intelligence (ISCBI), Bali, Indonesia, 7–9 December 2015; IEEE: Piscataway, NJ, USA, 2015; pp. 1–5. [Google Scholar]
- Wang, G.G. Moth search algorithm: A bio-inspired metaheuristic algorithm for global optimization problems. Memetic Comput.
**2018**, 10, 151–164. [Google Scholar] [CrossRef]

**Figure 1.**Socket with sensors: (

**a**) CAD of sensors on the inner wall; (

**b**) CAD of liner with socket; (

**c**) actual socket with SocketSense sensors.

**Figure 3.**Membership functions for pressure measurements taken at: (

**a**) the distal-end, and (

**b**) at the Scarpa’s triangle. The two areas are indicated on the socket figure by the black dot.

**Figure 4.**Silicon pads for socket rectification and associated membership function: (

**a**) silicon pad; (

**b**) silicon pad inserted into the inner wall of the socket (sticks due to adhesives); (

**c**) membership function connecting the linguistic variable to pad thickness.

**Figure 6.**Illustration of rectification action based on silicon-pad insertion for avoiding the development of distal-end pressures. The forces developed by the silicon pad prevent the stump from sliding deep into the socket.

**Figure 9.**Pressure distribution over the entire stump after the donning process with the nominal socket.

**Figure 12.**Regional pressure values in the proximal posterior region of the stump for different sockets.

Body | Material Properties |
---|---|

Femur | Young’s Modulus $E=15$ GPa, |

Poisson’s Ratio $\gamma =0.3$ | |

Socket | Young’s Modulus $E=1.5$ GPa, |

Poisson’s Ratio $\gamma =0.3$ | |

Stump | 3 Parameter hyper-elastic (Mooney–Rivlin) |

${C}_{10}=4.25$ KPa, | |

${C}_{11}=0$ KPa, | |

${D}_{1}=2.36$ MPa${}^{-1}$ |

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**MDPI and ACS Style**

Karamousadakis, M.; Porichis, A.; Ottikkutti, S.; Chen, D.; Vartholomeos, P.
A Sensor-Based Decision Support System for Transfemoral Socket Rectification. *Sensors* **2021**, *21*, 3743.
https://doi.org/10.3390/s21113743

**AMA Style**

Karamousadakis M, Porichis A, Ottikkutti S, Chen D, Vartholomeos P.
A Sensor-Based Decision Support System for Transfemoral Socket Rectification. *Sensors*. 2021; 21(11):3743.
https://doi.org/10.3390/s21113743

**Chicago/Turabian Style**

Karamousadakis, Michalis, Antonis Porichis, Suranjan Ottikkutti, DeJiu Chen, and Panagiotis Vartholomeos.
2021. "A Sensor-Based Decision Support System for Transfemoral Socket Rectification" *Sensors* 21, no. 11: 3743.
https://doi.org/10.3390/s21113743