**4. Probability of risk**

122 Injury and Skeletal Biomechanics

Each of the curves for compression, tension and shear loading were analyzed. From these curves, specific data points were extrapolated and both standard deviations and standard error for each point were calculated. The extrapolated data for compression, tension and

**Extrapolated Data for Compression Loading**

Large Mid Small 6YrOld 3YrOld

LargeAdult MidSize Small 6YrOld 3YrOld

0 5 10 15 20 25 30 35

**Extrapolated Tension Loading Curves**

From the standard deviations, ranges of loading were developed for each of the following three scenarios: (i) no injury or minor injury will occur, (ii) A moderate injury is likely to occur and (iii) an unsurvivable injury is likely to occur. For the purposes of comparison, no/minor injury in this analysis refers to an injury that rates from 0 to 1 on the AIS scale.

0 10 20 30 40 50 60 70

shear loading are illustrated in Figures 8, 9, and 10 respectively.

**Figure 8.** Extrapolated Compression Loading Data

0

1000

2000

3000

4000

5000

6000

**Figure 9.** Extrapolated Tension Loading Data

0

1000

2000

3000

4000

5000

6000

With the assistance of an Excel Add-In called RiskAmp, numerous Monte Carlo Simulations were set up to study the probability of the five different dummy types being exposed to various compressive, tensile and shear forces. Because of their reliance on repeated computation of random or pseudo-random numbers, these methods tend to be used when it is unfeasible or impossible to compute an exact result with a deterministic algorithm [22]. Applied forces were randomly generated for 1000 simulations. The simulation means and standard deviations were studied. Ranges of force values known to produce responses in the 3 "Injury Zones" were tested against the simulation means to determine the probability of exposure to the varying degrees of compressive, tensile and shear forces.

The risk of injury of being exposed to a force that would place the dummy in each of the three previously discussed injury zones (No Injury Likely, Moderate Injury Likely and Unsurvivable Injury Likely) were developed thereafter.

### **5. Results**

Axial loading, whether tension or compression, can pose a significant risk of injury as seen by the ISO-13232 (Figure 11) testing and analysis procedures [23]. Figure 12 shows the axial neck force time responses as measured in a laboratory head impact test and computer simulation. In figure 12, it can be seen that after only 5 milliseconds, the largest compressive force is exerted on the neck of the rider. After only 15 milliseconds, the rider is then exposed to the highest tensile forces; a direct result of the neck rebounding from compression. And finally, after approximately 30-35 milliseconds, the reactive forces level off. This plot illustrates that the majority of force exposure in impact scenarios occurs within the first 30 milliseconds. It is thus important to focus on the risk of injury during that time frame.

Cervical Spinal Injuries and Risk Assessment 125

Trends are apparent when the five mannequins are all compared under the same type of loading. Under compression, they all exhibit a linear tolerance to loading. For the mid size adult, an instantaneous force between 3700 and 4300 N indicates a significant injury is likely. Anything above 4300 N, illustrates a higher risk of an unsurvivable injury. The linear descending trend remains apparent throughout the first 32 milliseconds of force duration. At 32 milliseconds, it only takes a force between 1000 N and 1600 N to expose the adult to a risk of significant injury. At 1600 N, applied for 32 ms means that an adult is at very high risk of an unsurvivable injury. As the applied compressive load increases with respect to

When exposed to tension, a descending, "bi-linear" relationship is seen. Instantaneous forces below 3900 N pose no significant risk of injury. Anything between 3900 N and 4500 N indicates a considerable risk of injury. Finally anything above 4500 N illustrates a dangerous risk of unsurvivable injury. A slightly decreasing linear trend occurs between 0 and 35 ms. At this point in load duration, the linearity changes, the decreasing slope becomes aggressive and the risk of injury becomes more severe. At 35 ms, it takes between 3500 N and 4100 N to see a significant risk of injury, but as time increases to 60 milliseconds, only a force of 1100 N is needed to generate a significant risk of moderate injury. In the first half of the plot, a very gradual decrease in load tolerance with respect to time is evident, but after a load duration of 35 milliseconds, the slope of linearity significantly decreases, indicating

The shear loading relationship increases in complexity, as it is "tri-linear" in nature. The first third of the plot demonstrates a strong descending linear relationship. An instantaneous force of 2900 N poses a good chance for a moderate to severe injury. Any force above 3300 N instantaneously applied shows a very high risk for an unsurvivable injury. Initially, as with all the mannequin types, a gradual decrease in shear loading tolerance is evident. After approximately 25 milliseconds, the tolerance to shear force plateaus. From 25 to 35 milliseconds of load duration, a force of only 1300 N is needed to substantiate the chance for a moderate injury. Anything above 1800 N indicates that the risk of an unsurvivable injury occurring is quite high. Any load duration beyond 35 ms, sees another decreasing linear trend. It is at the point of 45 ms, that a force of only 900 N is needed to pose significant threat of injury on the neck. This curve behavior illustrates the neck's ability to resist

Because the probability of injury trends for the five mannequins were similar, only the

Injury due to shear loading seems to happen at much smaller loads for all body types than injuries caused by the other types of loading. For example, the 3 year old experiences instantaneous injury from a tension or a compression load of approximately 1400 N; however the shear load needed to induce injury is only approximately 1000 N. As age and physique increase, a body's tolerance to loading also increases. For example, the 6 year old mannequin does not experience instantaneous injury due to compressive

time, the probability of injury linearly increases.

that a much higher probability of injury exists.

twisting just prior to complete fracture.

loading curves for the mid size adult are shown (Figures 12).

**Figure 11.** ISO-13232 Axial neck Force Time Responses Measured in a Laboratory Head Impact Test and Computer Simulation [23]

**Figure 12.** Mid Size Adult Risk of Injury Criteria

Trends are apparent when the five mannequins are all compared under the same type of loading. Under compression, they all exhibit a linear tolerance to loading. For the mid size adult, an instantaneous force between 3700 and 4300 N indicates a significant injury is likely. Anything above 4300 N, illustrates a higher risk of an unsurvivable injury. The linear descending trend remains apparent throughout the first 32 milliseconds of force duration. At 32 milliseconds, it only takes a force between 1000 N and 1600 N to expose the adult to a risk of significant injury. At 1600 N, applied for 32 ms means that an adult is at very high risk of an unsurvivable injury. As the applied compressive load increases with respect to time, the probability of injury linearly increases.

124 Injury and Skeletal Biomechanics

and Computer Simulation [23]

**Figure 12.** Mid Size Adult Risk of Injury Criteria

0 5 10 15 20 25 30 35 40 45 50 55 60

Injury LIkely No Injury Unsurvivable Injury

**MidSize Adult Risk of Injury - Tension Loading**

finally, after approximately 30-35 milliseconds, the reactive forces level off. This plot illustrates that the majority of force exposure in impact scenarios occurs within the first 30 milliseconds. It is thus important to focus on the risk of injury during that time frame.

**Figure 11.** ISO-13232 Axial neck Force Time Responses Measured in a Laboratory Head Impact Test

0 4 8 12 16 20 24 28 32

Injury Likely No Injury Unsurvivable Injury

0 5 10 15 20 25 30 35 40 45

Injury Likely No Injury Unsurvivable Injury

**MidSize Adult Risk of Injury - Shear Loading**

**Mid Sized Adult Risk of Injury - Compression Loading**

When exposed to tension, a descending, "bi-linear" relationship is seen. Instantaneous forces below 3900 N pose no significant risk of injury. Anything between 3900 N and 4500 N indicates a considerable risk of injury. Finally anything above 4500 N illustrates a dangerous risk of unsurvivable injury. A slightly decreasing linear trend occurs between 0 and 35 ms. At this point in load duration, the linearity changes, the decreasing slope becomes aggressive and the risk of injury becomes more severe. At 35 ms, it takes between 3500 N and 4100 N to see a significant risk of injury, but as time increases to 60 milliseconds, only a force of 1100 N is needed to generate a significant risk of moderate injury. In the first half of the plot, a very gradual decrease in load tolerance with respect to time is evident, but after a load duration of 35 milliseconds, the slope of linearity significantly decreases, indicating that a much higher probability of injury exists.

The shear loading relationship increases in complexity, as it is "tri-linear" in nature. The first third of the plot demonstrates a strong descending linear relationship. An instantaneous force of 2900 N poses a good chance for a moderate to severe injury. Any force above 3300 N instantaneously applied shows a very high risk for an unsurvivable injury. Initially, as with all the mannequin types, a gradual decrease in shear loading tolerance is evident. After approximately 25 milliseconds, the tolerance to shear force plateaus. From 25 to 35 milliseconds of load duration, a force of only 1300 N is needed to substantiate the chance for a moderate injury. Anything above 1800 N indicates that the risk of an unsurvivable injury occurring is quite high. Any load duration beyond 35 ms, sees another decreasing linear trend. It is at the point of 45 ms, that a force of only 900 N is needed to pose significant threat of injury on the neck. This curve behavior illustrates the neck's ability to resist twisting just prior to complete fracture.

Because the probability of injury trends for the five mannequins were similar, only the loading curves for the mid size adult are shown (Figures 12).

Injury due to shear loading seems to happen at much smaller loads for all body types than injuries caused by the other types of loading. For example, the 3 year old experiences instantaneous injury from a tension or a compression load of approximately 1400 N; however the shear load needed to induce injury is only approximately 1000 N. As age and physique increase, a body's tolerance to loading also increases. For example, the 6 year old mannequin does not experience instantaneous injury due to compressive loading until a load of 1700 N is applied. This is higher than the load that a 3 year can forebear, but much less than the 4400 N needed to cause compressive injury to a large adult.

Cervical Spinal Injuries and Risk Assessment 127

**Table 5.** Probability of Injury Caused by Tension

**Table 6.** Probability of Injury Caused by Shear Force

In each of the five cases, for the five different body types, data was compiled from previously published loading curves to determine what type of loading has the chance to cause a significant cervical spinal injury. Shear loading produces a much higher risk of injury on the neck at much lower loads when compared to compressive and tensile loading. If, for example, a compressive load were instantaneously applied to a mid size adult, but wasn't maintained, it takes approximately 3600 N to even enter the region that indicates there is a potential for significant injury. If that force were, however, a shear force, it only takes approximately 2900 N to enter that region (Figure 12). In each of the five body types, the safe and seriously injured regions are well defined. The middle regions, however are those most uninvestigated. They illustrate that injury is fairly likely to occur, but do not illustrate the severity of the injury depending on where one lies within that region. The probability definitions (Tables 4-6) supplement these risk injury curves by providing some scenarios in which various compressive, tensile and shear forces can cause significant injury. It was important to recognize that not all body types are commonly subjected to forces of dangerous magnitude. For example, a 3 year old would most likely be secluded from

Dummy No Injury Injury Likely Unsurvivable

Dummy No Injury Injury Likely Unsurvivable

*Probability of Shear Injury*

3 Yr Old 24/100 9/100 67/100 6 Yr Old 30/100 10/100 60/100 Small 35/100 11/100 55/100 Midsize 45/100 15/100 40/100 Large 48/100 14/100 38/100

*Probability of Tensile Injury*

3 Yr Old 39/100 7/100 54/100 6 Yr Old 41/100 11/100 49/100 Small 61/100 12/100 27/100 Midsize 67/100 11/100 23/100 Large 79/100 7/100 14/100

**6. Discussion** 

The risk of injury has been presented graphically with respect to the types and magnitudes of forces that are more likely to cause injury, based on age and load duration. The succeeding tables depict the average probability of injury, based on body and loading types. For each Monte Carlo Simulation performed, probability of injury was calculated for a variety of time steps, starting with 0 milliseconds and concluding with a time value known to cause serious injury (i.e. for compressive loads, a concluding time of 32 milliseconds was used for all five mannequin types). The probabilities listed in Tables 3-6 were calculated by averaging the results of the Monte Carlo Simulations for each time step. These values were averaged for the purpose of data consolidation. As can be seen in Tables 4-6, the bigger the mannequin, or human body type, the higher the probability that no injury will occur, and the less likely that an unsurvivable injury will take place.


**Table 3.** The Hybrid III Family of Mannequins Data


**Table 4.** Probability of Injury Caused by Compression


**Table 5.** Probability of Injury Caused by Tension


**Table 6.** Probability of Injury Caused by Shear Force

### **6. Discussion**

126 Injury and Skeletal Biomechanics

adult.

take place.

**Table 3.** The Hybrid III Family of Mannequins Data

**Mannequin Height**

3 Yr Old -- 33 15 6 Yr Old -- 47 21 Small Adult 5'0'' 110 50 Midsize Adult 5'10'' 170 77 Large Adult 6'2'' 223 100

Dummy No Injury Injury Likely Unsurvivable

*Probability of Compressive Injury*

3 Yr Old 27/100 9/100 64/100 6 Yr Old 32/100 11/100 57/100 Small 29/100 12/100 59/100 Midsize 45/100 17/100 38/100 Large 49/100 18/100 32/100

**Hybrid III Family**

**Table 4.** Probability of Injury Caused by Compression

loading until a load of 1700 N is applied. This is higher than the load that a 3 year can forebear, but much less than the 4400 N needed to cause compressive injury to a large

The risk of injury has been presented graphically with respect to the types and magnitudes of forces that are more likely to cause injury, based on age and load duration. The succeeding tables depict the average probability of injury, based on body and loading types. For each Monte Carlo Simulation performed, probability of injury was calculated for a variety of time steps, starting with 0 milliseconds and concluding with a time value known to cause serious injury (i.e. for compressive loads, a concluding time of 32 milliseconds was used for all five mannequin types). The probabilities listed in Tables 3-6 were calculated by averaging the results of the Monte Carlo Simulations for each time step. These values were averaged for the purpose of data consolidation. As can be seen in Tables 4-6, the bigger the mannequin, or human body type, the higher the probability that no injury will occur, and the less likely that an unsurvivable injury will

(ft, in) (lbs) (kg)

**Weight**

In each of the five cases, for the five different body types, data was compiled from previously published loading curves to determine what type of loading has the chance to cause a significant cervical spinal injury. Shear loading produces a much higher risk of injury on the neck at much lower loads when compared to compressive and tensile loading. If, for example, a compressive load were instantaneously applied to a mid size adult, but wasn't maintained, it takes approximately 3600 N to even enter the region that indicates there is a potential for significant injury. If that force were, however, a shear force, it only takes approximately 2900 N to enter that region (Figure 12). In each of the five body types, the safe and seriously injured regions are well defined. The middle regions, however are those most uninvestigated. They illustrate that injury is fairly likely to occur, but do not illustrate the severity of the injury depending on where one lies within that region. The probability definitions (Tables 4-6) supplement these risk injury curves by providing some scenarios in which various compressive, tensile and shear forces can cause significant injury.

It was important to recognize that not all body types are commonly subjected to forces of dangerous magnitude. For example, a 3 year old would most likely be secluded from

#### 128 Injury and Skeletal Biomechanics

situations that could cause him or her to endure such forces, unless the situation was unexpected such as an automobile accident. A large adult, however might perform everyday lifting and pushing tasks that make him or her more likely to encounter high compressive, tensile or shear forces. To take this form of exposure into consideration, Pert distributions (instead of normal distributions) were utilized in the Monte Carlo simulations. Pert distributions help identify associated risk and the likelihood of particular situations occurring, such as various types of people enduring any of a combination of applied loads. This made the results of the simulations more accurate and appropriate for this particular study.

Cervical Spinal Injuries and Risk Assessment 129

Dummy\_AIS2 Dummy\_AIS3 Dummy\_AIS4 Dummy\_AIS5 Cadaver\_AIS2 Cadaver\_AIS4 Cadaver\_AIS5 Cadaver\_AIS3

Dummy\_AIS2 Dummy\_AIS3 Dummy\_AIS4 Dummy\_AIS5 Cadaver\_AIS2 Cadaver\_AIS3 Cadaver\_AIS4 Cadaver\_AIS5

This collection of plots sets a solid foundation for understanding what types of loading over what periods of time can injure someone, as well as the probability of someone experiencing different magnitudes of force over different time intervals. It is evident in the comparison of mannequin to cadaver data that mannequin testing does supply an accurate representation of a body's response to the various types of loading. Additionally it provides a more realistic means for studying a person's tolerance to force. The graphic schemes defined in this research have helped to identify the most common mechanisms of

> **Cadaveric and Mannequin Data Compared for Mid Size Adults under Compression**

**Figure 13.** Figure 13: Cadaver and Mannequin Compression Loading Data

0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000

**Applied Force (N)**

**Cadaveric and Mannequin Data Compared For Mid Size Adults under Tension**

0 500 1000 1500 2000 2500 3000 3500 4000 4500

**Applied Force (N)**

**Figure 14.** Figure 14: Cadaver and Mannequin Data for Tension Loading

cervical spine injury.

**Probability of Injury (%)**

**Probability of Injury (%)**

Verifying these Monte Carlo simulations with experimental data was the next step with respect to this research. Cadaveric data was obtained from the literature to validate the accuracy of the Monte Carlo models [9]. As can be seen in Figure 12, the higher the applied force, the greater the probability of injury. Probability of injury was therefore plotted with respect to applied force for all five mannequin types under all three types of loading. A relationship was developed that indicated how probability of injury changed with respect to applied force. To relate the mechanisms of injury to a more common means of risk evaluation, equations were developed relating the applied force to the Abbreviated Injury Scale (AIS). The probability of achieving an injury with an AIS score between 2 and 5 can now be determined simply by knowing the applied force and using the following equations:

$$P(AIS \ge 2) = \left(\frac{1}{1 + e^{\left(2.056 - 1.1955(N\_{lj})\right)}}\right) \times 100\%$$

$$P(AIS \ge 3) = \left(\frac{1}{1 + e^{\left(3.227 - 1.969(N\_{lj})\right)}}\right) \times 100\%$$

$$P(AIS \ge 4) = \left(\frac{1}{1 + e^{\left(2.693 - 1.196(N\_{lj})\right)}}\right) \times 100\%$$

$$P(AIS \ge 5) = \left(\frac{1}{1 + e^{\left(3.817 - 1.196(N\_{lj})\right)}}\right) \times 100\%$$

In the above equations, Nij refers to the normalized force. For the purposes of risk analysis, the normalized force is identified as the applied force, divided by the critical force, or forced deemed as having the minimum magnitude needed to induce injury.

Both cadaveric and mannequin data of applied force and the resulting probability of various AIS scores was plotted for each type of force. The results of these plots can be seen in Figures 13-15 for compression, tension and shear loading, respectively. In Figure 13, it can be seen that it takes approximately 4000 N of compressive force to generate a 30% risk of an AIS≥2 injury.

Comparatively, from Figure 15, it only takes approximately 3000 N of shear to generate that same 30% risk of an AIS≥2 injury. This again confirms that shear force poses a much higher probability of significant injury over the other types of forces at much lower magnitudes. This collection of plots sets a solid foundation for understanding what types of loading over what periods of time can injure someone, as well as the probability of someone experiencing different magnitudes of force over different time intervals. It is evident in the comparison of mannequin to cadaver data that mannequin testing does supply an accurate representation of a body's response to the various types of loading. Additionally it provides a more realistic means for studying a person's tolerance to force. The graphic schemes defined in this research have helped to identify the most common mechanisms of cervical spine injury.

128 Injury and Skeletal Biomechanics

the following equations:

AIS≥2 injury.

study.

situations that could cause him or her to endure such forces, unless the situation was unexpected such as an automobile accident. A large adult, however might perform everyday lifting and pushing tasks that make him or her more likely to encounter high compressive, tensile or shear forces. To take this form of exposure into consideration, Pert distributions (instead of normal distributions) were utilized in the Monte Carlo simulations. Pert distributions help identify associated risk and the likelihood of particular situations occurring, such as various types of people enduring any of a combination of applied loads. This made the results of the simulations more accurate and appropriate for this particular

Verifying these Monte Carlo simulations with experimental data was the next step with respect to this research. Cadaveric data was obtained from the literature to validate the accuracy of the Monte Carlo models [9]. As can be seen in Figure 12, the higher the applied force, the greater the probability of injury. Probability of injury was therefore plotted with respect to applied force for all five mannequin types under all three types of loading. A relationship was developed that indicated how probability of injury changed with respect to applied force. To relate the mechanisms of injury to a more common means of risk evaluation, equations were developed relating the applied force to the Abbreviated Injury Scale (AIS). The probability of achieving an injury with an AIS score between 2 and 5 can now be determined simply by knowing the applied force and using

1��(������������(���)

1��(�����������(���)

1��(�����������(���)

1��(�����������(���)

In the above equations, Nij refers to the normalized force. For the purposes of risk analysis, the normalized force is identified as the applied force, divided by the critical force, or forced

Both cadaveric and mannequin data of applied force and the resulting probability of various AIS scores was plotted for each type of force. The results of these plots can be seen in Figures 13-15 for compression, tension and shear loading, respectively. In Figure 13, it can be seen that it takes approximately 4000 N of compressive force to generate a 30% risk of an

Comparatively, from Figure 15, it only takes approximately 3000 N of shear to generate that same 30% risk of an AIS≥2 injury. This again confirms that shear force poses a much higher probability of significant injury over the other types of forces at much lower magnitudes.

� � 1���

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� � 1���

� � 1���

�(��� � �) � � <sup>1</sup>

�(��� � �) � � <sup>1</sup>

�(��� � �) � � <sup>1</sup>

�(��� � �) � � <sup>1</sup>

deemed as having the minimum magnitude needed to induce injury.

**Figure 13.** Figure 13: Cadaver and Mannequin Compression Loading Data

**Figure 14.** Figure 14: Cadaver and Mannequin Data for Tension Loading

Cervical Spinal Injuries and Risk Assessment 131

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[3] Clemens HJ., B. K. (1972). Experimental Investigation on Injury Mechanisms of Cervical

[4] Doherty, B. E. (1993). A Biomechanical Study of Odontoid Fractures and Fracture

[5] Fielding JW., C. G. (1974). Tears of the Transverse Ligament of the Atlas. Journal of Bone

[6] Goel VK., W. J. (1990). Ligamentous Laxity Across the C0-C1-C2 Complex: Axial Torque-

[7] Goldberg W., M. C. (2001). Distribution and Patterns of Blunt Traumatic Cervical Spine

[8] Lars, B. K. (2006). Acute Spinal Injuries: Assessment and Management. Emergency

[9] Liu, Y. King, Krieger, K.W., Njus, G., Ueno, K., Connors, M.P., Wakano, K., Thies, D. Cervical Spine Stiffness and Geometry of the Young Human Male. Air Force Aerospace Medical Laboratory. Tulane University School of Medicine, New Orleans, LA.

[10] Maiman DJ., S. A. (1983). Compression Injuries of the Cervical Spine: A Biomechanical

[11] Mertz HJ., P. L. (1971). Strength and Response of the Human Neck. Proceedings of the

[12] Myers BS., M. J. (1991). The Influence of End Condition on Human Cervical Spine Injury Mechanisms. Proceedings of the 35th Stapp Car Crash Conference , 391-400. [13] Myers BS., M. J. (1991). The Role of Torsion in Cervical Spinal Injuries. Spine , 16 (8),

[14] Nahum Alan M., M. J. (2002). Accidental Injury: Biomechanics and Prevention. New

[15] Pintar FA., Y. N. (1995). Cervical Vertebral Strain Measurements under Axial and

[16] Portnoy HD., M. J. (1972). Mechanism of Cervical Spine Injury In Auto Accident. Proceedings of the 15th Annual Conference of the American Association for

[17] Reid DC., S. L. (1989). Spine Fractures in Winter Sports. Sports Medicine , 7 (6), 393-399. [18] Sekhon, L. F. (2001, December 15). Epidemiology, Demographics and Pathophysiology

[19] Shea M., W. R. (1992). In Vitro Hyperextension Injuries in Human Cadaveric Cervical

Eccentric Loading. Journal of Biomechanical Engineering , 474-478.

Spine at Frontal and Rear Front Vehicle Impacts. SAE Paper 720960 , 78-104.

**8. References** 

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rotation Characteristics Until Failure. Spine , 15, 990-996.

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Approved for Public Release January 19, 1983.

Analysis. Neurosurgery , 13 (3), 254-260.

15th Stapp Car Crash Conference , 207-255.

Survivors. Retrieved on December 9th, 2010

**Figure 15.** Cadaver and Mannequin Data for Shear Loading
