Methods to Calculate Stresses Resultingfrom Whiplash Injuries
Harold Franck*, Darren Franck
Advanced Engineering Associates, Maccorkle Ave Se in Charleston, West Virginia, USA
*Correspondingauthor:Harold Franck, Advanced Engineering Associates, Maccorkle Ave Se in Charleston, West Virginia, USA. Tel: +3049258565; Email: harold@aeawv.com
Received Date:
26 May, 2017; Accepted Date: 06 July, 2017; Published Date: 17
July, 2017
Citation: Franck H and Franck D (2017) Methods to Calculate Stresses Resulting from Whiplash Injuries. Forensic Stud: FSTD-109.
1. Abstract
Rear end vehicular collisions can result in whiplash type injuries to the occupants of the target vehicle. Standard accident reconstruction techniques may be utilized to calculate the respective velocity changes of the bullet and target vehicles. Once the delta-v’s are determined, maximum and minimum limits may be placed on the critical stresses that are imparted on the spinal column of the occupants of the target vehicle that may be subjected to whiplash injuries. These stresses can then be compared to the known ultimate compressive, tensional, and torsion ultimate stresses on the soft tissue structures of the spinal column. This treatise develops three methods of analysis for the investigative forensic biomechanical engineer.
2.
Keywords: Injury Mechanism; Ultimate strength;Whiplash
1.
Introduction
There is a significant divergence of opinions on the probability and potential for injury to the spinal column resulting from rear-end vehicular collisions. Some experts claim that injuries may occur as a result of any speed change. We do not agree with such a position because, the principles of material mechanics are well understood and utilized in design and failure analysis irrespective of the material being studied. Therefore, this treatise affords the forensic biomechanical engineer a basis for calculating the potential for failure and injury based on known scientific data.
Generally, these spinal injuries are referred to as whiplash type maladies that are often claimed to result to the cervical, thoracic, and lumbar sections of the spine. It should be noted that the modern vehicle has substantial padding that affects the lumbar and thoracic spine. Consequently, significant speed changes are required to overcome the supportive cushioning effect of the seat back. Furthermore, the seats, especially for the front passengers, are designed to give or collapse beyond a certain limit. Please note that in this analysis we are not concerned with the crashworthiness of the vehicles, seats, and restraint systems.
Similarly, vehicles are equipped with head rests that also offer some degree of protection when the head and the neck of the occupant is thrust rear-ward in the collision. Depending on the seat configuration and the physical structure of the occupant, the head rest may offer little or no protection. As a further caveat for this analysis we note that the supportive structure of the head rest is simply not considered.
(Figure 1) represents a spinal column superimposed on a typical seat. Two important features are noted. One, the spinal column is much more robust in the lower thoracic and lumbar regions. Two, the maximum exposure to whiplash can occur to the cervical and portions of the upper thoracic regions.
1.1. Data on Injury to Soft Tissue Spinal Structures
(Tables 1&2) show spinal column dimensions that are necessary for most biomechanical whiplash calculations. From a mechanical standpoint, it is well understood that larger structures, whether biological or not, are more resilient and require greater forces to overcome their failure limits.
The
data above was taken from H Yamada, and H Franck and D Franck. (Figure
2) shows the stress-strain curves for wet
intervertebral discs in tension for various portions of the spine for
individuals between the ages of 20 and 39 years of age corresponding to the
data on (Table 3). Note that the cervical
discs exhibit the greatest stress capability simply because they must allow for
the greatest movement in the neck and head area. I fact the cervical discs
allow up to a 40-degree angle of twist while the lumbar and thoracic vertebrae
restrict the angle of twist to about 20 degrees.
2. Hooke’s Law
(Figure 2)requires some explanation and review. Analysis of
structural elements, in this case the stresses on the spinal disc structures,
requires a determination of the forces acting on the structure. The forces that
affect the structure and the resistance of the particular structure to
separation of movement within the structure are considered internal. The forces
that transmit the loads are considered external and are dependent on the motion
produced on the entire body by an event such as a rear-end collision.
Generally, the force acting on the body is proportional to the stress times the
cross-sectional area or
The Second Method is that of a couple which
is produced by the movement of the head resulting from the collision. This is a
two-dimensional problem. Consider Figure 3 below.
In the
Couple Model
The
cross section of the disc for this model is not the average of all the discs
but the value for the average of the cervical and thoracic discs which is
approximately 350
The Third Method is produced by a torque on the discs. One argument that is proposed states that the rotation of the head relative to the direction of the force makes a difference whether injury might occur. (Figure 4) represents the torque produced by such motion. The pertinent equations follow,
For
the torque equations t is the pulse width but the 2r term is different as
follows. The separation between the vertebrae at mid line is approximately 20
mm and the area of the cervical discs is about 350 mm2 with a diameter of approximately 18 mm. Consequently, the 2r term is
about 0.176 ft.
3.1. Summary of Whiplash Tests
3.2. The Graphs for the Previous
Tests are Shown Below
3.3. The Graphs for the Tests on
Table 7 are Shown below
For each of the test graphs, the top graph in red corresponds to the
head acceleration and the bottom graph represents the measurement of the chest
acceleration.
The data from Table 8 is plotted below.The Couple Model yields the
greatest stress shown in yellow. The Damask and Torque Models yield essentially
the same results.
4. Conclusions
In order to assess the potential for injury to the upper spinal column,
calculations are required in scientifically correct terms
Figure 1: Spinal Column and Seat.
Figure 2: Elongation Tensile Properties of Discs.
Figure 3: Couple Model.
Figure 4:Torque Model.
Figure
5: Stress Comparison.
Section |
20-39 yrs. |
40-59 yrs. |
60-79 yrs. |
Average |
Cervical |
16.7 ± 0.78 |
14.6 ± 0.24 |
11.0 ± 0.11 |
14.1 |
Upper Thoracic |
18.0 ± 0.31 |
17.5 ± 0.22 |
14.2 ± 0.27 |
16.6 |
Middle Thoracic |
20.2 ± 0.41 |
20.0 ± 0.31 |
18.1 ± 0.36 |
19.4 |
Lower Thoracic |
23.6 ± 0.80 |
22.3 ± 0.30 |
21.6 ± 0.22 |
22.5 |
Lumbar |
27.9 ± 0.43 |
27.0 ± 0.33 |
23.6 ± 0.26 |
26.2 |
Table 1: Height of Human Vertebraeby Age and Section (mm).
Section |
20-59 yrs. |
60-79 yrs. |
Average |
Cervical |
326 ± 7 |
264 ± 10 |
305 |
Upper Thoracic |
432 ± 13 |
380 ± 12 |
415 |
Middle Thoracic |
556 ± 18 |
525 ± 14 |
546 |
Lower Thoracic |
870 ± 34 |
749 ± 22 |
830 |
Lumbar |
1088 ± 18 |
990 ± 21 |
1055 |
Table 2: Cross Sectional Area of Human Vertebrae by Age and Section (mm2).
(Tables 3,4&5) relate the ultimate strengths in tension, torsion, and compression for various sections of the spine and for various age groups.
Section |
20-39 yrs. |
40- 79 yrs. |
Average |
Cervical |
0.33 ± 0.02 |
0,29 ± 0.03 |
0.30 |
Upper Thoracic |
0.24 ± 0.01 |
0.20 ± 0.03 |
0.21 |
Lower Thoracic |
0.26 ± 0.02 |
0.22 ± 0.01 |
0.21 |
Lumbar |
0.30 ± 0.01 |
0.24 ± 0.01 |
0.26 |
Table 3: Ultimate Tensile Strength of Human Intervertebral Discs (Kg/mm2).
Section |
20-39 yrs. |
40-79 yrs. |
Average |
Cervical |
0.52 ± 0.07 |
0.46 ± 0.05 |
0.48 |
Upper thoracic |
0.46 ± 0.03 |
0.38 ± 0.04 |
0.41 |
Middle Thoracic |
0.47 ± 0.02 |
0.42 ± 0.03 |
0.44 |
Lower Thoracic |
0.48 ± 0.02 |
0.44 ± 0.04 |
0.45 |
Lumbar |
0.51 ± 0.03 |
0.46 ± 0.03 |
0.48 |
Table 4:Ultimate Torsional Strength of Human Intervertebral Discs (Kg/mm2).
Section |
40-59 yrs. |
Cervical |
1.08 |
Upper Thoracic |
1.02 |
Lower Thoracic |
1.08 |
Lumbar |
1.12 |
Average |
1.08 |
Table 5: Ultimate Compressive Strength of Human Intervertebral Discs (Kg/mm2).
Test |
Time (sec) |
Accel (g) |
Area (g-s) |
Del V (ft./s) |
Del V (mph) |
10A |
0.14 |
5.62 |
0.3929 |
12.62 |
8.63 |
11A |
0.16 |
4.84 |
0.3850 |
12.40 |
8.46 |
12A |
0.14 |
3.62 |
0.2862 |
9.22 |
6.29 |
13A |
0.18 |
5.14 |
0.3661 |
11.79 |
8.04 |
14A |
0.14 |
5.46 |
0.3373 |
10.86 |
7.41 |
15A |
0.16 |
9.28 |
0.6746 |
21.72 |
14.82 |
Averages |
0.15 |
5.66 |
0.4070 |
13.11 |
8.94 |
Table 6: Whiplash Tests and Head Accelerations 40-year-old Female.
Test |
Time (sec) |
Accel (g) |
Area (g-s) |
Del V (ft/s) |
Del V (mph) |
16H |
0.14 |
3.91 |
0.2487 |
8.01 |
5.46 |
17H |
0.14 |
5.75 |
0.2827 |
9.10 |
6.21 |
18H |
0.10 |
9.34 |
0.4467 |
14.38 |
9.81 |
19H |
0.14 |
4.31 |
0.2675 |
8.61 |
5.88 |
20H |
0.14 |
4.34 |
0.2678 |
8.62 |
5.88 |
21H |
0.14 |
2.86 |
0.2614 |
8.42 |
5.74 |
Averages |
0.13 |
5.09 |
0.2958 |
9.52 |
6.50 |
Table 7: Whiplash Tests and Head Accelerations 66-year-old Male.
test
|
weight |
v(mea) |
a(mea) |
pulse (t) |
A(da) |
A(co) |
A(to) |
sig(da) |
sig(co) |
sig(to) |
10A |
130 |
12.65 |
5.62 |
0.14 |
12.424 |
37.869 |
28.237 |
0.032 |
0.040 |
0.030 |
11A |
130 |
12.4 |
4.84 |
0.16 |
11.938 |
36.387 |
27.132 |
0.030 |
0.039 |
0.029 |
12A |
130 |
9.22 |
3.62 |
0.14 |
6.600 |
20.117 |
15.000 |
0.017 |
0.021 |
0.016 |
13A |
130 |
11.79 |
5.14 |
0.18 |
10.792 |
32.895 |
24.528 |
0.028 |
0.035 |
0.026 |
14A |
130 |
10.86 |
5.46 |
0.14 |
9.157 |
27.910 |
20.811 |
0.023 |
0.030 |
0.022 |
15A |
130 |
21.72 |
9.28 |
0.16 |
36.627 |
111.639 |
83.244 |
0.093 |
0.118 |
0.088 |
Av(A) |
130 |
13.11 |
5.66 |
0.15 |
13.344 |
40.673 |
30.328 |
0.034 |
0.043 |
0.032 |
16H |
155 |
8.01 |
3.91 |
0.14 |
4.981 |
15.183 |
11.321 |
0.015 |
0.019 |
0.014 |
17H |
155 |
9.1 |
5.75 |
0.14 |
6.429 |
19.597 |
14.612 |
0.020 |
0.025 |
0.018 |
18H |
155 |
14.38 |
9.34 |
0.1 |
16.055 |
48.935 |
36.488 |
0.049 |
0.062 |
0.046 |
19H |
155 |
8.61 |
4.31 |
0.14 |
5.756 |
17.543 |
13.081 |
0.017 |
0.022 |
0.017 |
20H |
155 |
8.62 |
4.34 |
0.14 |
5.769 |
17.584 |
13.111 |
0.018 |
0.022 |
0.017 |
21H |
155 |
8.42 |
2.86 |
0.14 |
5.504 |
16.777 |
12.510 |
0.017 |
0.021 |
0.016 |
Av(H) |
155 |
9.52 |
5.09 |
0.13 |
7.037 |
21.447 |
15.992 |
0.021 |
0.027 |
0.020 |
Table 8:Comparison of Methods.
1.
Damask AC, Damask J (1990) InjuryCausation Analysis: Case
Studies and Data Sources.The Michie Company,Charlottesville, VA.
3.
Yamada H (1970)The Strength of Biological Materials.
Williams and Wilkins,Philadelphia, PA.