# Pressure Ulcers and Dressings: A Strain Sensitivity Analysis of the Boundary Conditions of a Finite Element Model

^{1}

^{2}

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^{5}

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Reference Finite Element Model

_{10}parameters of the skin and the adipose tissue by a coefficient of 1.0, 1.5, and 2.0 for the soft, medium, and stiff areas, respectively, as detailed in Figure 2.

#### 2.2. Sensitivity Analysis

**, λ**

_{1}**, and λ**

_{2}**were extracted to compute the Green–Lagrange principal strains (Equation (4)). The maximal shear strain, E**

_{3}_{shear}, was calculated as detailed in Equation (5).

_{shear}was below this threshold for healthy tissues.

_{i}the value of the ith parameter, and θ the vector of the adjustable coefficients, which was estimated with ordinary least squares. The value of two for the degree will be further justified in the results section. The sensitivity of the model to each input (linear term, square, order-two interaction) can be simply defined as the percentage of variance due to this input. Assuming, for simplicity, the m = 4 parameters independent and uniformly distributed in [−1, 1] (i.e., with second- and fourth-order moments of respectively 1/3 and 4/45), it becomes:

## 3. Results

## 4. Discussion

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 3.**Minimal, intermediate, and maximal levels of the alveoli cutting (

**a**) and wound deepness (

**b**) parameters.

**Figure 4.**Effect of the four parameters on the volume of healthy tissues (i.e., tissues with strains lower than 0.3), with the other three parameters being set to their intermediary value.

**Figure 5.**Green–Lagrange maximal shear strains in the ROI of some experiments. All parameters were set to the intermediate values except for one that varied according to the defined levels: (

**a**) changes in the gauze pressure, (

**b**) changes in the alveoli cut, (

**c**) changes in the wound deepness, and (

**d**) changes in the mattress stiffness. The ROI appears in grey in (

**e**).

Component | C_{10} (MPa) | C_{20} (MPa) | C_{30} (MPa) | µ (MPa) | E_{X} (MPa) | E_{Y} (MPa) | E_{Z} (MPa) | d_{1} (MPa^{−1}) | ν |
---|---|---|---|---|---|---|---|---|---|

Adipose tissue | 1.3 × 10^{−4} | 0.0 | 12.2 × 10^{−3} | - | - | - | - | 1.6 | 0.4999 |

Skin | 2.7 × 10^{−1} | 1.9 | - | - | - | - | - | - | 0.4999 |

Dressing layer 1 | - | - | - | 1.0 × 10^{−3} | - | - | - | - | - |

Dressing layer 2 | - | - | - | - | 4.4 | 1.8 | 2.6 × 10^{−2} | - | 0.2560 |

Mattress | - | - | - | - | 2.3 × 10^{−1} | - | - | - | 0.3000 |

**Table 2.**Parameters’ minimal, intermediate, and maximal values used as levels for the experimental points of the sensitivity analysis.

Parameters | Minimal Level | Intermediate Level | Maximal Level |
---|---|---|---|

Wound deepness | 1.30 mm | 3.20 mm | 5.00 mm |

Alveoli cut | Recommended +1 layer | Recommended | Recommended −1 layer |

Mattress stiffness | 0.03 MPa | 0.23 MPa | 0.43 MPa |

Gauze pressure | 0.00 MPa | 0.02 MPa | 0.04 MPa |

**Table 3.**Parameter coefficients and polynomial model sensitivities (>1%) in decreasing order of magnitude.

Parameters | Coefficients θi and θii or θij | Sensitivities Si or Sij (%) |
---|---|---|

Gauze pressure | −3.9, −10.7 | 60 |

Wound deepness | −4.3, −3.3 | 28 |

Wound deepness∗Gauze pressure | +4.6 | 10 |

Mattress stiffness | +1.1, −0.9 | 1 |

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**MDPI and ACS Style**

Fougeron, N.; Rivals, I.; Connesson, N.; Chagnon, G.; Alonso, T.; Pasquinet, L.; Auguste, S.; Perrier, A.; Payan, Y.
Pressure Ulcers and Dressings: A Strain Sensitivity Analysis of the Boundary Conditions of a Finite Element Model. *Biomechanics* **2023**, *3*, 1-12.
https://doi.org/10.3390/biomechanics3010001

**AMA Style**

Fougeron N, Rivals I, Connesson N, Chagnon G, Alonso T, Pasquinet L, Auguste S, Perrier A, Payan Y.
Pressure Ulcers and Dressings: A Strain Sensitivity Analysis of the Boundary Conditions of a Finite Element Model. *Biomechanics*. 2023; 3(1):1-12.
https://doi.org/10.3390/biomechanics3010001

**Chicago/Turabian Style**

Fougeron, Nolwenn, Isabelle Rivals, Nathanaël Connesson, Grégory Chagnon, Thierry Alonso, Laurent Pasquinet, Stéphane Auguste, Antoine Perrier, and Yohan Payan.
2023. "Pressure Ulcers and Dressings: A Strain Sensitivity Analysis of the Boundary Conditions of a Finite Element Model" *Biomechanics* 3, no. 1: 1-12.
https://doi.org/10.3390/biomechanics3010001