Sánchez-Molina D, Arregui-Dalmases C, Velázquez-Ameijide J, Angelini M, Kerrigan J, Crandall J
UPC-RMEE-EEBE, Barcelona, Spain.
UPC-EM-EEBE, Barcelona, Spain; CAB, Charlottesville, VA, USA.
Comput Methods Programs Biomed. 2016 Nov;136:55-64. doi: 10.1016/j.cmpb.2016.08.007. Epub 2016 Aug 20.
Abrupt accelerations or decelerations can cause large strain in brain tissues and, consequently, different forms of Traumatic Brain Injury (TBI). In order to predict the effect of the accelerations on the soft tissues of the brain, many different injury metrics have been proposed (typically, an injury metric is a real valued functional of the accelerations). The objective of this article is to make a formal and empirical comparison, in order to identify general criteria for reasonable injury metrics, and propose a general guideline to avoid ill-proposed injury metrics.
A medium-sized sample of vehicle-pedestrian collisions, from Post Mortem Human Subject (PMHS) tests, is analyzed. A statistical study has been conducted in order to determine the discriminant power of the usual metrics. We use Principal Component Analysis to reduce dimensionality and to check consistency among the different metrics. In addition, this article compares the mathematical properties of some of these functionals, trying to identify the desirable properties that any of those functionals needs to fulfill in order to be useful for optimization.
We have found a pair-wise consistency of all the currently used metrics (any two injury metrics are always positively related). In addition, we observed that two independent principal factors explain about 72.5% of the observed variance among all collision tests. This is remarkable because it indicates that despite high number of different injury metrics, a reduced number of variables can explain the results of all these metrics. With regard to the formal properties, we found that essentially all injury mechanisms can be accounted by means of scalable, differentiable and convex functionals (we propose to call minimization suitable injury metric any metric having these three formal properties). In addition three useful functionals, usable as injury metrics, are identified on the basis of the empirical comparisons.
The commonly used metrics are highly consistent, but also highly redundant. Formal minimal conditions of a reasonable injury metric has been identified. Future proposals of injury metrics can benefit from the results of this study.
突然加速或减速会导致脑组织产生较大应变，进而引发不同形式的创伤性脑损伤（TBI）。为了预测加速度对脑软组织的影响，人们提出了许多不同的损伤指标（通常，损伤指标是加速度的实值函数）。本文的目的是进行形式和实证比较，以确定合理损伤指标的一般标准，并提出避免不当损伤指标的一般指南。
分析了来自尸体人体受试者（PMHS）测试的中等规模的车辆与行人碰撞样本。进行了一项统计研究，以确定常用指标的判别能力。我们使用主成分分析来降低维度并检查不同指标之间的一致性。此外，本文比较了其中一些函数的数学性质，试图确定任何这些函数为了对优化有用而需要满足的理想性质。
我们发现所有当前使用的指标都具有成对一致性（任意两个损伤指标总是正相关）。此外，我们观察到两个独立的主因子解释了所有碰撞测试中约72.5%的观测方差。这很显著，因为它表明尽管有大量不同的损伤指标，但较少数量的变量可以解释所有这些指标的结果。关于形式性质，我们发现基本上所有损伤机制都可以通过可扩展、可微和凸函数来描述（我们建议将具有这三个形式性质的任何指标称为合适的损伤指标）。此外，在实证比较的基础上确定了三个可用作损伤指标的有用函数。
常用指标高度一致，但也高度冗余。已确定合理损伤指标的形式最小条件。损伤指标的未来提议可受益于本研究的结果。
