# A Review of Validation Methods for the Intracranial Response of FEHM to Blunt Impacts
## 3 Prominent FEHM and Their Validation
### Assessment of FEHM Performance and Validation  
Once the empirical scenario has been replicated in the numerical environment, the performance of the FEHM needs to be assessed compared to observations from testing. Impact responses are presented in a number of ways, including discrete point histories, absolute peaks, area fraction measures and spacial plots. In the majority of cases, particularly although not exclusively for the earlier FEHM, this has been through a qualitative comparison of the simulated and empirical outputs [21; 44; 47; 72; 74; 75; 76; 77; 80; 82; 86]. Others have supplemented this with peak value comparisons [44; 77; 80].  
More recently, statistical measures have also been applied to quantitatively analyse the similarity of numerical outputs to empirical data. [PERSON] et al. [78] used Pearson correlation to objectively compare how well two variations of their FEHM performed during validation simulations. There is, however, no benchmark value or rating system to judge the quality of either model against empirical data. Pearson correlation is limited to considering the linear correlation between points of data sets. The Normalized Integral Square Error (NISE) method separately compares the differences in phase, amplitude and shape of two time series that are then summed to give an overall measure [100]. Based on generally accepted coefficients of variation (e.g., ratio of standard deviation to mean), acceptable NISE limits are proposed for each of phase, amplitude and shape in terms of the repeatability and reproducibility. While the limits of NISE were proposed for determining the quality of experimental procedures and results, the line comparison equations have been applied in judging FEHM validation. [PERSON] et al. [101] and [PERSON] et al. [56] calculated a correlation score between 0 and 100 by subtracting the NISE from 1 and multiplying by 100 during the validation of THUMS (Total HUman Model for Safety) and WHIM FEHM. These were then related to bio-fidelity ratings aligned with the classifications detailed in ISO/TR-9790 [102], as shown in Table 5. The CORA method ([PERSON] et al. [48]) combines corridor and cross-correlation rating methods to rate the similarity of curves between 0 and 1. As with NISE, the cross-correlation aspect of CORA considers the shape, amplitude and phase of responses. The parameters used within each analysis stage can be adjusted to fit the scenario being considered and its limits. Research into to the validation of full body FE models found CORA to be the most comprehensive of analysis methods available, although it was recommended to keep the evaluated aspects separate rather than combining to a single rating for the model [103]. CORA has since been included in the investigative technical report ISO/TR16250:2013 [104], providing recommendations on the analysis of time-history signals in the testing of vehicle safety and computer model validation. In a study focused on FEHM, [PERSON] and [PERSON] [105] found CORA more reliably evaluated validation signals than NISE (see Section 4.2). During the development of FEHM, CORA has been used by [PERSON] et al. [25], [PERSON] et al. [83], [PERSON] et al. [85] and [PERSON] et al. [90] for the validation of ABM (Atlas-based Brain Model), THUMS (a version superseding the model previously analysed using NISE [101]), Tokyo and UCDBTM V2.0 (University College Dublin Brain Trauma Model) models,respectively. Several parts of the GHBMC full body model have been validated against CORA and the tools recommended in ISO/TR16250:2013 (e.g., [106; 107; 108; 109]). However, [PERSON] et al. [44] is the most recently published record of the head intracranial response validation found and CORA is not employed.