APPENDIX A: EXPERIMENT RECONSTRUCTIONS WITH THUMS
Table A1. Reported and predicted peak values for lateral head impact.
Physical test1
Measurement
Physical test1
THUMS
Unpadded-9221
HIC
Head CG resultant acceleration (g)
Angular acceleration about X
THUMS
Padded-9217D
1894-3850
3141
473-690
741
276-502
402
115-196
164
2324-6035
8206
3390-4677
3610
11441-14175
1230
2312-5676
5078
7546-11662
10498
6868-7409
5582
33.3-42.5
40.3
25-27
20
(rad/s^2)
Angular acceleration about Z
(rad/s^2)
Impactor force (N)
Impactor linear acceleration (g)
1
Reported in McIntosh et al. (1993)
150
McIntosh et al.
Simulation
300
Acceleration (g)
Acceleration (g)
375
225
150
75
McIntosh et al.
Simulation
125
100
75
50
25
0
0
0
0.002
a)
0.004
0.006
0.008
0
0.01
Time (s)
0.002 0.004 0.006 0.008 0.01 0.012
Time (s)
b)
Figure A1. Head CG resultant accelerations obtained experimentally (one subject per curve) and predicted for
THUMS for a) unpadded (9221) and b) padded (9217D) lateral head impacts after McIntosh et al. (1993).
Table A2. Cross-correlation analysis results for lateral head impact
THUMS vs McIntosh1
Signals compared
Response curve
Evaluation metric
Unpadded-9221
Padded-9217D
Head resultant cg acceleration
Head resultant cg acceleration
Magnitude
0.79
0.75
Shape
0.91
0.96
Phase (ms)
0.05
-0.17
1
Reported in McIntosh et al. (1993)
a)
b)
c)
d)
Figure A2. Resultant head cg acceleration (a,c) and T1 force (b,d) traces and corridors obtained experimentally
and predicted using FEM for inverted head impacts against a horizontal (a,b) (0) and anteriorly inclined (c,d)
(15) rigid surface after Nightingale et al. (1996) and reported by Camacho et al. (1997).
Table A3. Cross-correlation analysis results for inverted impact
THUMS vs Nightingale corridor mean1,2
Signals compared
0 inclination
Response curve
15 anterior inclination
Head resultant cg accel
T1 resultant force
Head resultant cg accel
T1 resultant force
Magnitude
0.26
0.83
0.88
0.79
Shape
0.96
0.92
0.84
0.94
Phase (ms)
0.48
0.01
0.67
0.10
Corridor
0.08
0.50
0.10
0.63
Evaluation metric
1
Test performed by Nightingale et al. (1996)
2
Corridors calculated in Camacho et al. (1997)
Toomey et al.
Simulation
Toomey et al.
Simulation
5
75
4
Force (kN)
Moment (Nm)
100
50
25
3
2
1
0
0
-25
0
0.004
a)
0.008
0.012
Time (s)
0.016
0
0.02
0.004
0.008
b)
0.012
0.016
0.02
Time (s)
Figure A3. T1 sagittal plane moment (a) and resultant force (b) traces obtained experimentally (one subject per
curve) and predicted using FEM for inverted head impacts against a laterally inclined (15) rigid surface after
Toomey et al. (2009)
Table A4. Cross-correlation analysis results for laterally inclined inverted impact
THUMS vs Toomey 15 lateral inclination1
Signals compared
Test 1
Test 3
T1 sagittal moment
T1 resultant force
Magnitude
0.79
0.75
Shape
0.85
0.91
Phase (ms)
-0.05
-1.2
Response curve
Evaluation metric
1
Reported in Toomey et al. (2009)
APPENDIX B: SIGNAL CORRELATION ANALYSIS METHODOLOGY
The following definitions were used to quantify the similarity between two signals, x(t) and y(t).
Magnitude correlation:
∞
𝑀=
‖𝑥‖ ∫−∞ 𝑥 2 (𝑡)𝑑𝑡
=
‖𝑦‖ ∫∞ 𝑦 2 (𝑡)𝑑𝑡
−∞
where M = 1 corresponds to identical magnitudes.
Shape correlation:
𝑆 = 𝑠 2 (𝑥, 𝑦, ℎ)
for which h is chosen to maximize s(x,y,h) and where
∞
𝑠(𝑥, 𝑦, ℎ) =
∫−∞ 𝑥(𝑡)𝑦(𝑡 + ℎ)𝑑𝑡
∞
∞
√∫−∞ 𝑥 2 (𝑡)𝑑𝑡 ∫−∞ 𝑦 2 (𝑡)𝑑𝑡
Phase shift:
P=h
where h is chosen for which s(x,y,h) reaches its maximum value.
Corridor rating:
𝑖𝑓 |𝑦(𝑡𝑖 ) − 𝑥(𝑡𝑖 )| < 𝛿𝑖 (𝑡)
1
𝛿𝑜 (𝑡) − |𝑦(𝑡𝑖 ) − 𝑥(𝑡𝑖 )|
)
𝛿𝑜 (𝑡) − 𝛿𝑖 (𝑡)
0
{
𝑘
𝑐𝑖 = (
𝐶=
𝑤𝑖𝑡ℎ 𝑘 ∈ 𝑁>0
𝑖𝑓 |𝑦(𝑡𝑖 ) − 𝑥(𝑡𝑖 )| > 𝛿𝑜 (𝑡)
∑𝑛𝑖=1 𝑐𝑖
𝑛
Figure 1. Impact vectors (left) and 45 anterolateral setup (right).
Figure 2. Boxplots of injury measure outputs (rows) according to impact parameters (columns). Statistical
significance (p < 0.05) is identified with grey shading.
Figure 3. Boxplots of injury measure outputs (rows) according to impact orientation (columns). Statistical
significance (p < 0.05) is identified with grey shading.
BrIC lateral
BrIC anterolateral
T1 axial force anterior
BrIC anterior
T1 axial force lateral
T1 axial force anterolateral
Percent of maximum
100%
80%
60%
40%
20%
0%
0
15
30
45
Lateral/Anterior/Anterolateral angle (deg)
Figure 4. Peak brain and cervical-spine injury measures according to impact orientation in impacts at 6m/s and
127 mm of displacement.
Maximum principal strain
Cerebrum
0.5
Cerebellum
Brainstem
CSDM0.1=0.636
0.4
0.3
0.2
0.1
0
Maximum principal strain
0.5
CSDM0.1=0.131
0.4
0.3
0.2
0.1
0
0
0.02
Time (s)
0.04
Figure 5. Scatter plot of peak strain values recorded for each brain element (n=15212) in simulations with the
greatest (top) and least (bottom) CSDM0.1 values.
Table 1. Magnitude of factor levels for impact conditions
Factor
Levels
Velocity (m/s)
4, 5, 6
Displacement (mm)
31.75, 63.5, 127
Orientation (deg)
Anterior
Lateral
0, 15, 30, 45
Anterolateral
Note that the 0 angle for each orientation represents the same condition.