# Injury Metrics for Assessing the Risk of Acute Subdural Hematoma in Traumatic Events

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## Abstract

**:**

## 1. Introduction

## 2. Data and Methods

#### 2.1. Materials and Data

#### 2.2. Injury Metrics

#### 2.3. Proposed Injury Metric

## 3. Results

#### 3.1. Dependence of Ultimate Stress on Strain Rate

#### 3.2. Distribution of the Intrinsic Ultimate Stress

#### 3.3. Comparison of the Metrics in a Fall from a Height

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

ASDH | Acute Subdural Hematoma |

BVDM | Bridging Vein Damage Metric |

CBV(s) | Cerebral Bridging Vein(s) |

CDF(s) | Cumulative Distribution Function(s) |

EVT | Extreme Value Theory |

FEHM | Finite Element Head Model |

GEV | Generalized Extreme Value |

PMHS | Post-Mortem Human Subject |

RMDM | Relative Motion Damage Measure |

SRDF | Strain Rate Dependence Function |

TBI | Traumatic Brain Injury |

## Appendix A. Suitability of BVDM

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**Figure 1.**Scatterplot of ultimate stress vs. strain rate for low values of strain-rate a significant relation exists (p-value < 0.001).

**Figure 2.**The nonlinear relation of ultimate stress and strain rate, for higher values of strain-rate $\dot{\epsilon}>10$ s${}^{-1}$ the ultimate stress seems independent of the strain rate. The SRDF $\phi \left(\dot{\epsilon}\right)$ is proportional to the black dotted line.

**Figure 3.**Comparison of the distributions for the ultimate axial force (${F}_{u}$) and the intrinsic ultimate force (${F}_{u}^{*}$).

**Figure 4.**Comparison of the Cumulative Distribution Function (CDF) for the ultimate axial force (${F}_{u}$) and the intrinsic ultimate force (${F}_{u}^{*}$), red line: Weibull distribution, green line: empirical distribution function.

**Figure 5.**Axial Forces on the CBVs of the SIMon model (FEHM), computed for the described fall from a height of 2.5 m against a ground of ballast stiffness ${k}_{b}=40\phantom{\rule{4pt}{0ex}}{\mathrm{N}/\mathrm{cm}}^{3}$. One line is presented for each pair of CBVs of the FEHM. Each color line represents a different CBV, the forces differ because the CBVs are located in different parts of the brain.

**Figure 6.**Comparison of the predictions of RMDM${}_{eq}^{*}$ and the BVDM, at the beginning of the traumatic event both metrics make similar predictions, but towards the end, when the head rebounds and the axial forces stabilize, the predictions differ considerably.

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**MDPI and ACS Style**

García-Vilana, S.; Sánchez-Molina, D.; Velázquez-Ameijide, J.; Llumà, J.
Injury Metrics for Assessing the Risk of Acute Subdural Hematoma in Traumatic Events. *Int. J. Environ. Res. Public Health* **2021**, *18*, 13296.
https://doi.org/10.3390/ijerph182413296

**AMA Style**

García-Vilana S, Sánchez-Molina D, Velázquez-Ameijide J, Llumà J.
Injury Metrics for Assessing the Risk of Acute Subdural Hematoma in Traumatic Events. *International Journal of Environmental Research and Public Health*. 2021; 18(24):13296.
https://doi.org/10.3390/ijerph182413296

**Chicago/Turabian Style**

García-Vilana, Silvia, David Sánchez-Molina, Juan Velázquez-Ameijide, and Jordi Llumà.
2021. "Injury Metrics for Assessing the Risk of Acute Subdural Hematoma in Traumatic Events" *International Journal of Environmental Research and Public Health* 18, no. 24: 13296.
https://doi.org/10.3390/ijerph182413296