Documentation:FIB book/problems/brain injury

In this assignment, we will look into various brain injury predictors that fall into four major categories: (1). linear acceleration based, (2). angular acceleration based, (3). linear and angular acceleration combined, and (4). stress and strain based. We will use data collected in one of the Honda CR-V tests from National Highway Traffic Safety Administration (NHTSA). Videos of the crash test can be downloaded here. You can use MATLAB to import the data and process it. Please include the MATLAB code (or other source code if you choose to use other software for data analyzing), relevant formulas and calculations, etc. with your submission.

Question 1 Raw data processing

Steps to download the raw data:

(1). The raw collected data is from this website here .

(2). There is a section called 'Supporting files' near the bottom.

(3). Click on 'Crash test data' to download the data.

It is stored as a .mat file. It consists of:

(1). timestamp - tdata.

(2). linear acceleration - a1, a2, a3 for x, y, z-axis, respectively, in gravity g.

(3). angular velocity - omega1, omega2, omega3 for x, y, z-axis, respectively, in degree/s.

Plot linear accelerations in unit: g, and angular velocities in unit: rad/s, in two figures. Since we will also be using angular acceleration in this assignment, you can extract them from the angular velocity numerically by $\alpha ={\frac {\Delta \omega }{\Delta t}}$, and plot them individually in three figures in unit: rad/s^2.

SOLUTION (expand to show)
Figure 1. Resultant linear acceleration Figure 2. Resultant angular velocity Figure 3. Angular acceleraion: x-axis Figure 4. Angular acceleraion: y-axis Figure 5. Angular acceleraion: z-axis

Question 2 Linear acceleration based brain injury criteria

Peak linear resultant acceleration (PLA)

Compute peak linear resultant acceleration and find the corresponding estimated risk of brain injury according to the table below:

Table 1. PLA thresholds, adapted from Fernandes FA, et al. (2015)

Injury	Tolerance
Brain injury	50% probability: AIS 4: 200 - 250 g AIS 5: 250 - 300 g AIS 6: > 300 g
Mild Traumatic Brain Injury (MTBI)	25% probability: 559 m/s^2 50% probability: 778 m/s^2 75% probability: 965 m/s^2
Concussion	50% probability: 65.1 g 75% probability: 88.5 g
Skull fracture	50% risk: 135 g

Head injury criterion (HIC)

HIC is computed using the following equation :

$HIC=\max _{t_{1},t_{2}}\left({\frac {1}{t_{2}-t_{1}}}\int _{t_{1}}^{t_{2}}a(t)dt)\right)^{2.5}(t_{2}-t_{1})$

Calculate HIC15 by checking three different time intervals: 5 ms, 10 ms, and 15 ms. Then assess its associated head injury risk using the following table:

Table 2. HIC thresholds, adapted from Fernandes FA, et al. (2015)

Injury	Tolerance
Brain injury	8.5% probability of death: 1000 31% probability of death: 2000 65% probability of death: 4000

SOLUTION (expand to show)
Peak linear resultant acceleration is equal to 49.0276 g (480.9611 m/s^2). This number does not reach any threshold listed in Table 1. The HIC15 value is 280.5993 by a window of 10 ms. Plot of HIC using three different time intervals: Figure 6. HIC values using 5 ms, 10 ms, and 15 ms time intervals The HIC value does not reach any threshold listed in Table 2 either.

Question 3 Angular acceleration based brain injury criteria

Peak rotational acceleration

Gennarelli et al. proposed a relationship between AIS and angular acceleration ($\alpha =2887.8\times AIS$), which can be summarized in Table 3:

Table 3. Relationship between AIS and angular acceleration/velocity, adapted from Fernandes FA, et al. (2015)

AIS Level	Injury severity	Angular acceleration (rad/s^2)
1	Mild cerebral concussion	2877.8
2	Classical cerebral concussion	5755.6
3	Severe cerebral concussion	8633.4
4	Mild diffuse axonal injury (DAI)	11511.2
5	Moderate DAI	14389
6	Severe DAI	17266.8

Find peak rotational acceleration and estimate corresponding AIS level.

Rotational injury criterion (RIC)

Kimpara and Iwamoto proposed a rotational injury criterion (RIC), which was done by simply replacing the resultant linear acceleration in HIC with resultant angular acceleration:

$RIC=[(t_{2}-t_{1})\{{\frac {1}{t_{2}-t_{1}}}\int _{t_{1}}^{t_{2}}\alpha (t)dt\}^{2.5}]_{max}$

They also proposed that RIC values at or above $1.03\times {10^{7}}$indicate a 50% MTBI probability.

Estimate RIC by checking a time window of 5 ms, 10 ms, 15 ms respectively. Check if the computed value goes beyond the 50% MTBI probability.

SOLUTION (expand to show)

Peak angular acceleration is 6.006*10^3. Peak angular velocity is 29.7796 rad/s. According to Table 3, the peak angular acceleration value represents a classical cerebral concussion. Plot: Figure 7. RIC values computed from 5 ms, 10 ms, and 15 ms time intervals According to the plot, the estimated RIC value is 0.9730*10^7 (< 1.03*10^7) using a 10 ms window. This number does not pass the threshold of a 50% probability of MTBI.

Question 4 Combined linear and angular acceleration based brain injury criteria

Generalized acceleration model for brain injury threshold (GAMBIT)

Newman tried to combine linear and angular acceleration together to create a mixed brain injury criteria named generalized acceleration model for brain injury threshold (GAMBIT):

$G(t)=[({\frac {a(t)}{a_{c}}})^{n}+({\frac {\alpha (t)}{\alpha _{c}}})^{m}]^{1/s}$

where $a(t)$and $\alpha (t)$represent linear and angular acceleration, in unit g and rad/s^2 at time $t$, respectively. This equation assumes that linear and angular acceleration contributes to the brain injury equally and independently. Researchers have attempted to develop thresholds for GAMBIT, which is shown below in Table 4:

Table 4. GAMBIT parameters and critical values, adapted from Fernandes FA, et al. (2015)

Reference	n	m	s	$a_{c}$(g)	$\alpha _{c}$(rad/s^2)
Newman	2	2	2	250	25000
Chinn B, et al. Mellor A, St Clair	2	2	2	250	10000

Thresholds are summarized in Table 5 from two resources.

Table 5. GAMBIT thresholds for injury risk probability, adapted from Fernandes FA, et al. (2015)

Injury	Threshold
Brain injury	50% probability of AIS > 3: G = 1 or 1.5 <= G <= 2
Concussion	50% probability: G >= 0.4 95% probability: G >= 0.56

Although there are multiple versions of GAMBIT parameters and GAMBIT thresholds, in this assignment, we will use the Newman version of calculation and the injury risk from reference [12] version to calculate GAMBIT, as a practice to see how linear and angular acceleration can be mixed to assess injury risk. Compute GAMBIT with our crash-test data based on the Newman version in Table 4 and assess what injury risk it may represent according to reference [12] in Table 5.

SOLUTION (expand to show)
Peak G is 0.2884. Therefore, it does not reach any threshold values listed in Table 5.

Question 5 Stress and strain based brain injury criteria

Strain correlated with linear and angular accelerations

Aare et al. have attempted to associate linear and angular accelerations with strains in brain tissues. They combined the findings from Kleiven and Von Holst that the change of angular velocity is best correlated with intracranial strains and the correlation between HIC and strain levels :

$\varepsilon =k_{1}\Delta \omega +k_{2}HIC$

where $\varepsilon$stands for the maximum strain component in brain tissues, $\Delta \omega$ is the maximum change in angular velocity (rad/s^2), HIC is the head injury criterion, and $k_{1}$and $k_{2}$are constant coefficients, which were obtained by regression analysis .

Compute strain using $k_{1}=7.26\times 10^{-3}$, $k_{2}=3.50\times 10^{-5}$ , and the estimated HIC value from question 2. Map the computed number to possible brain tissue damage injuries, cerebral contusions, and DAI:

Table 6. Strain thresholds, adapted from Fernandes FA, et al. (2015)

Injury	Thresholds
Brain tissue damage	0.5
Cerebral contusions	50% risk: 0.19
DAI	0.1

SOLUTION (expand to show)

1. $\Delta \omega$(maximum change in angular velocity) is equal to the difference between the maximum and minimum angular velocity, which is 29.7487 in the crash-test data. 2. The estimated HIC value is 280.5993 from question 2. Therefore, the maximum $\varepsilon$is calculated as 0.2258 (< 0.5, > 0.19, and > 0.1), which means that: (1). It does not indicate brain tissue damage according to reference [15]. (2). It creates a 50% risk of cerebral contusions according to reference [16]. (3). It indicates a DAI injury according to reference [17].

Question 6 Compare and illustrate any thoughts on the various brain injury criteria

Document your observations or thoughts after completing all the questions above. List at least two major reflections.

SOLUTION (expand to show)

There are no standard answers for this section, as long as they are reasonable. This question is mainly for the student's use. The purpose is to reflect on what they have done after doing all these calculations. Potential aspects to reflect on include: (1) if there is any inconsistency in the injury prediction, (2) if you have any criticisms on any of the injury criteria listed above, and (3) what are some of the trade-offs between using these injury criteria.