Finite Element Analysis of Cervical Spinal Nerve Tolerance to Whiplash Injury

Finite Element Analysis of Cervical Spinal Nerve Tolerance to Whiplash Injury Chaoyang Chen 1, Bo Cheng 2, Dawei Chen 1, Chuanhua Huang 1, Binghui Jiang 3, Peter Mourelatos 1, Ian Bruce 1, Xin Jin 3, John M. Cavanaugh 1 Affiliations: 1. Department of Biomedical Engineering, Wayne State University, Detroit, MI, USA 2. State Key Laboratory of Automotive Safety and Energy, Tsinghua University, Beijing, China 3. Bioengineering Center, Wayne State University, Detroit, MI, USA Corresponding Author s name and complete mailing address: Chaoyang Chen, MD Department of Biomedical Engineering, Wayne State University, 818 West Hancock Ave, Detroit, MI, USA Email: cchen@wayne.edu Key Words: Whiplash, Cervical Spine, Nerve, Finite Element Analysis, Biomechanics Running Title: FEA of Cervical Nerve Tolerance to Whiplash Injury Acknowledgement: This research was support by State Key Laboratory of Automotive Safety and Energy Opening Fund (KF 11011) and a grant from the National Highway Transportation Safety Administration (NHTSA) (DTNH22-08-C-00082). 1

Abstract Neck whiplash injury is one of the most common injuries associated with motor vehicle accidents. These injuries produce acute and chronic neck pain, headache, paresthesia, or even paralysis. Whiplash injury can cause injuries to the cervical muscles, the ligaments, the joint capsules, the intervertebral disks and bone, and the nerve tissues. Among these tissues, the nerve is the most fragile tissue to be injured, which causes pain, paresthesia, and even paralysis. However the tolerance of the spinal nerves to stretch injury remains unknown. In this study, finite element analysis (FEA) methods were used to assess the threshold chest acceleration that causes spinal nerve injury. Three-dimensional cervical spine and nerve finite element (FE) models were built using Mimics software based on computed tomography (CT) scanned images. Strain of the spinal nerve was analyzed using HyperMesh and LS-Dyna software. Results demonstrated that using Mimics software to build an FE model is an effective and rapid approach. An increase of chest acceleration caused an increase of the strain in the spinal nerve. Seven G chest acceleration produced up to 39.8% strain of the spinal nerves resulting in a 40% probability of spinal nerve injury. In conclusion, Mimics software provides a rapid and accurate approach to build human cervical spine and spinal nerve model. FEA is an effective alternative approach for whiplash nerve injury biomechanical research. 2

Introduction Neck whiplash can occur in frontal, side and rear car collisions but most complaints occur after a rear-end collision by another vehicle. Whiplash occurs when the head lags behind the accelerated torso, producing relative acceleration between the head and thorax during motor vehicle collisions. Whiplash can produce acute and chronic neck pain, headache, dizziness, vertigo, paresthesia, or even paralysis (Ivancic et al., 2008; Sterner et al., 2004). The structures most likely to be injured during whiplash include the facet capsule, the intervertebral discs, the cervical ligaments, and the cervical spinal nerves, and spinal cord (Martin DH. 1998). MRI and autopsy studies have correlated chronic symptoms with injuries to the soft tissues in whiplash patients, such as cervical discs, ligaments and facet joints (Barnesley et al., 1995). Among these causative factors, injury to the nerve can result in more severe clinical symptoms, including motor, sensory, and sphincter disturbance. However what acceleration of the body during rear impact that can cause nerve injury is unknown. Clinical data, cadaveric specimens, anthropomorphic dummies, and computer modeling approaches have been used to investigate human injury mechanisms and tolerances (Bouquet 1994; Cavanaugh 1986; Hayashi 1996; Jager1994; Kang HS 1997; Lizee 998; Yoganandan 1999.) Clinical studies are useful in assessing the location of injury according to the treatment outcomes (Lord et al., 1996). Animal and cadaveric models have been used in injury biomechanical studies of musculoskeletal system (Luan et al., 2000, Winklestein et al., 2000, Lu et al 2004, Chen et al., 2006) to understand the mechanical of musculoskeletal pain, as well as the sub-failure injury and associated mechanical stimulation threshold value. But pain potentially 3

caused by nerve injury has not been addressed. Probability of spinal nerve injury from neck whiplash has not been investigated either. Conventional approaches including using cadaveric specimens and anthropomorphic dummies may not be able to address the sub-failure injury of the nerve. Animal model can be used to obtain the sub-failure and severe injury associated biomaterial property data, but can't better access whiplash-associated nerve injury. Human cadaveric specimens are rare, costly, and could present an ethical challenge to our society. Currently available anthropomorphic dummies provide limited information about crash injuries and might not accurately simulate the human body. The need for accurate modeling to analyze injury from automobile accident has led engineers to be interested in finding new and better methods for injury biomechanics research and designing of protection devices. Currently, computational finite element analysis (FEA) is a method that is cost-effective and provides accurate analysis outcomes and has been extensively used in the industry and bioengineering research. Once developed, a computer FEA model does not require the destruction of human tissues, crash test dummies, or automobiles. With computer modeling, tests could be repeated with alteration of only a single variable, allowing for the application of the scientific method to automotive safety engineering (Hedenstierna et al, 2008). It is well known that building a human FE model is time-consuming and tedious, for example, by using a common software called ANSYS (ANSYS, Inc. Canonsburg, PA). ANSYS is a powerful tool in industry and can be a FE model with neat elements. With the emergence of new MRI and CT techniques, as well as advanced software such as Materialise s Mimics 14.0, it is possible to build human FE models quickly and efficiently, especially for irregular geometry from the human anatomy. 4

The nerve is subjected to both strain and stress upon mechanical stimulation. However, analysis of the effects of strain on nerve injury is more common than analysis of stress. Overstretching of the nerve tissues leads to nerve dysfunction (Singh et al., 2006, 2009). The hypothesis of this study is that noxious whiplash movement of the cervical spine leads the spinal nerve to be mechanically stretched. Because the accelerations of jerk human body movement that may cause nerve injuries in whiplash has not yet been studied, the purpose of this study was to develop a neck finite element model to better understand the threshold acceleration of the shoulder that can cause spinal nerve injury under the dynamic conditions of whiplash. 5

Materials and Methods Establishment of finite element models: Computed tomography (CT) images of a de-identified adult male were used to construct the three-dimensional, geometrical surface model of the skull, C1-C7 vertebrae, intervertebral disks, and the shoulder using Mimics 14.0 (Materialise Inc., Leuven, Belgium). Multi-slice helical CT images with 1.25-mm distance between slices were imported into Mimics software by directly reading the consecutive CT Dicom format images of human cervical spine. The following procedures were performed: defining bone image threshold, withdrawing each outline, partitioning each edge of layer picture, editing selectively, and repairing by whole processing (Figure 2). Figure 2 shows the interface for 3-D geometry re-construction. The cervical 3-D geometry model of each anatomic component was then converted into the Nastran file format. The Nastran files were then imported into a FEA pre-processing software Hypermesh (Altair Inc, Troy, MI) to re-mesh the finite elements for quality control. Each element 6

size was controlled to be greater than 0.4 mm in order to reduce computer calculation time. All components loaded into the Hypermesh were assigned with biomechanical properties (Table 1). C1-T1 intervertebral bodies, intervertebral disks, and all other anatomic components were reconstructed individually to ensure proper anastomosis with parts connected based on actual anatomic features. The spinal cord and spinal nerve were then incorporated into the musculoskeletal model. A realistic and accurate 3-D finite element model of the cervical spine was thus established. The model was composed of the head, the seven cervical vertebrae (C1 C7), the first thoracic vertebra (T1) and shoulder, the intervertebral discs, muscles, facet joint capsules, ligaments including anterior longitudinal ligament (ALL) and posterior longitudinal ligament (PLL), spinal cord, and spinal nerves (Figure 3). Table 1. Material Properties Used for Various Components in the Model Components Young's Modulus (Mpa) Density (Kg/mm3) Poisson's ratio Bone 10000 1.83E 06 0.29 Disk 34 1.83E 06 0.4 ALL 30 1.20E 06 0.3 PLL 20 1.20E 06 0.3 Muscles 5 6.00E 07 0.4 Nerve 0.06 1.00E 07 0.5 The musculoskeletal component mechanical properties were adopted from Zhang et al. (2011) while the nerve mechanical property was adopted from our previous studies (Singh et al 2006 & 2009) 7

Figure 3 shows FE model of bone components and spinal nerve. The spinal cord and spinal nerves are covered by bone hence it is invisible in this picture. The muscles and ligaments are not shown in this figure. Loading conditions and constraints Horizontal kinematic chest acceleration data was extracted from Meyer's rear-impact volunteer s experiment (Figure 4B) (Meyer et al, 1998). The volunteer's chest acceleration curve was applied to the FE model at T1 and the shoulder to simulate the rear collision conditions. Figure 4. A shows acceleration curves of car, chest and head kinematics recorded by Meyer et al. during a rear impact test. Impact velocity was 13.5 kph and delta V was 7.5 kph. B shows the chest acceleration curve that was loaded into our FE model as horizontal Y orientation acceleration. Calculations for the finite element model were done by LS-DYNA s solver (Livermore Software Technology Corporation, Livermore, CA, USA). The first calculation was performed with chest acceleration loaded with Meyer s chest acceleration curve. The resultant d3plot file 8

was opened by LS-Dyna pre-post processing function to track nodal movement during whiplash. Head kinematic responses were derived and compared to Meyer s volunteer s head kinematics (acceleration) to determine model validation. After the model was validated through this procedure, different curves with increased acceleration (G) values (Figure 5) were applied to the chest to determine the consequent strain produced in the spinal nerve in response to increased acceleration to the shoulder. Figure 5 shows the increased acceleration curves that were applied to the chest in this study. Strain data on the spinal nerve were obtained using LS-Dyna LSTC pre-post processing function. The elements of the spinal nerve located between the foramen and spinal cord (or, the nerve root) were selected to track strain change over the time during neck whiplash dynamic movement. The outcome files were saved into Microsoft CSV format. These files were opened with Microsoft Excel for further data processing. All data obtained were input into SPSS statistical software for statically analysis. 9

Determination of nerve tissue tolerance to injury Maximum strain of the spinal nerve was quantitatively and qualitatively evaluated. Strain change over the time under different chest acceleration was analyzed. Strain rate of spinal nerve stretched was determined by dividing the measured strain by the time. Nerve injury criteria were setup based on from our recently published papers to determine the threshold acceleration at the shoulder that causes spinal nerve injury (Figure 5). The probability of nerve dysfunction caused by various strain under different strain rates was set up for criteria. For example, under 200 mm/s strain rate, 10.08% strain causes a 25% probability of nerve injury and 24.5% strain causes a 40% probability of nerve injury with conduction dysfunction. Figure 5. Probability of nerve dysfunction at different strain rate and strain. The nerve dysfunction was defined when conduction function dropped more than 56% of original capacity in a neurophysiologic study. 5.63% strain (in 800 mm/s group), 10.08% strain (200 mm/s group), and 18.73% strain (20 mm/s group) caused 25% probability of nerve injury respectively (Chen et al. 2011). 10

Results Finite Element Modeling The results shows that based on thin layer CT scanning technique, Mimics in combination with Hypermesh can reserve geometric features and make accurate three-dimensional finite element models quickly and efficiently. However the size of automatic-generated elements could be smaller than 0.3 mm. The small size of element can significantly increase the calculation time when using LS-Dyna software. Hence manual adjustment of element size was performed using Mimics software. Global responses Global kinematic responses from the model demonstrated a whiplash movement of neck as found in Meyer s volunteer s tests. The head moved backward, then moved forward just like a whiplash (Figure 6). Figure 6 shows head and neck kinematic movement from whiplash simulation. The simulation outcomes demonstrated similar trends of head kinematic movement during whiplash simulation (Figure 7A). Most of the response points from the FE model had the same trend as found in Meyer s (1998) experimental acceleration curve (Figure 7B). However, 11

there were differences in the moment of peak values. The peak value of horizontal acceleration of the head from the FE model was smaller than that of the head kinematic data recorded from the volunteer in Meyer's experiment. Using Hyperview, the strain change contour was viewed directly (Figure 7D). The elements at C1-C7 spinal nerve roots were selected to track strain change of the spinal nerve. Figure 7. A shows nodal points selected for tracking head acceleration during whiplash. B: Acceleration curves of selected nodes movement during whiplash simulation that were compared with volunteer head acceleration curve for model validation. C: Volunteer head acceleration curve measured by Meyer et al (1998). Figure 7D View of strain distribution on the spinal nerve and spinal cord using HyperView. Strain rate of the spinal nerve Using LS-Dyna s pre-post processing function, the strain rate was measured by displacement versus time. The strain rate ranged from 5-60 mm/s at different locations, average was 17.9±11.28% mm/s. 12

Spinal nerve strain change over the time Comparison of the left and right spinal nerve strain: There was not a statistical difference between the left and right spinal nerve strain when shoulder acceleration was 6 G (t test, p=0.997). In this study, the left spinal nerve strains caused by whiplash was greater than that of the right nerves when shoulder acceleration was greater than 6G (t test, p<0.00) (Figure 8). 7,0 Comparison Left and Right Spinal Nerve Strain 6,0 5,0 Strain (%) 4,0 3,0 2,0 left Right 1,0,0 6G 7G 9.21G 10.02G Acceleration Figure 8. When the shoulder acceleration was 6G, there was not statistical difference between left and right spinal nerve. When the shoulder accelerations were 7, 9.21, or 10.02 G, the left spinal nerves were stretched more than the right spinal nerves. In this study, higher acceleration did not cause higher strain of the nerve. Among the left spinal nerves, the highest strain was found in the C3 spinal nerve; while among the right nerves, the highest strain was found in the C5 spinal nerve (Figure 9, and figure 10-13). In this study, the most noxious acceleration was 7 Gs, which caused the spinal nerve to be stretched to a 39.8% strain. Further increase of shoulder acceleration did not cause increase of spinal nerve strain. 13

Figure 9 shows the maximum strain produced in each spinal nerve during neck whiplash dynamic movement. Among nerves, left C3 nerve was subjected to the highest strain. Figure 10. Distribution of strain on different level of spinal nerves. C1=1st cervical nerve, C7=7th cervical nerve. Applying 6 G (6x9.8m/s 2 ) acceleration to the chest produced up to 22% maximum principal strain on the both left and right spinal nerve. 14

Figure 11. Distribution of strain on different level of spinal nerves when 7 G acceleration was applied to the chest. Applying 7 G (7x9.8m/s 2 ) acceleration to the chest produced up to 38% maximum principal strain on the left C3 spinal nerve and 15% strain on the right C3 spinal nerve. Figure 12. Distribution of strain on different level of spinal nerves when 9.21 G acceleration was applied to the chest. The C3 was stretched to a maximum strain (27%) in the left C3 nerve, and 20% of maximum strain on right C5 spinal nerve. 15

Figure 13. Distribution of strain on different level of spinal nerves when 10.02 G acceleration was applied to the chest. The left C3 was stretched to 32% of the maximum strain, while the C5 spinal nerve was stretched to 17.5% maximum strain. Determination of spinal nerve injury Since the average strain rate in this study that was 17.9±11.28 mm/s, 20 mm/s was taken as the strain rate resulted from whiplash. Based on data showed in Figure 5, under 20 mm/s strain rate, 20% strain of the nerve caused 25% probability of nerve injury. The 20% strain was selected as cut-off value for binary logistic regression analysis. Binary logistic regression data analysis demonstrated that 7 G shoulder acceleration caused a higher probability of nerve injury than other accelerations of the shoulder. 16

Figure 14. Selecting 20% nerve strain as the criterion that causes nerve injury, the probability of nerve injury from 7 G shoulder acceleration was higher than other shoulder acceleration (horizontal acceleration). 17

Discussion The results demonstrate that finite element (FE) models of the human body can be a useful tool to for human injury biomechanics study, especially for the situation when other conventional methods are difficult to be adopted. Mimics 14.0 is a convenient software to build human FE models with accurate anatomic features. In this study, the size of the finite elements were controlled to be greater than 0.4 mm in order to reduce computer calculation time. This is because that as the size of the elements decreases, the results become increasingly accurate, however, smaller elements can significantly increase the calculation time. Only with further advancements in computation power can the elements become smaller and more precise. Neck injuries caused by whiplash results in substantial costs. In the United States, neck sprains are one of the most prevalent injuries as reported by 40% of insurance claimants (Spitzer et al, 1995). The vast majority of reported neck injuries are AIS I (Table 2) (Winkelstein, 1999). Their societal cost is enormous. Patients who report whiplash pain typically experience a moderate speed rear-end vehicular impact. Rear collisions cause pain in the neck almost twice as frequently as frontal collisions (Deans et al., 1987). Subjects typically complain of neck stiffness and pain in the neck muscles immediately after the impact. A minority of patients have severe pain indicative of nerve injury. Symptoms can become worse with time, and there is often an interval of little or no pain before the symptoms worsen (Jonsson et al., 1994). All these symptoms may result from nerve tissue injury to the cervical region, including the spinal nerve in addition to other soft tissue injury. However the threshold acceleration that causes nerve tissue injury during whiplash is unknown. There is no literature reports related to the spinal nerve injury caused by whiplash. This could re resulted from that it is difficult to assess spinal nerve injury using 18

conventional research approaches. Using Mimics software it is now readily to build sophisticated cervical spine FE model including nerve tissues. Based on our most recent spinal nerve biomechanical and neurophysiologic research outcomes (Singh 2006, 2009, Chen 2011), the nerve injury probability was first accessed using finite element analysis methods. The computer simulation outcomes demonstrated that the most noxious acceleration to the cervical nerve was 7 G. 7 G acceleration on the shoulder resulted in a 40% probability of spinal nerve injury. Increase of acceleration did not lead to higher strain of the spinal nerve, hence did not increase the probability of nerve injury. This is coincided with clinical findings in that human volunteer researches and clinical data showed that the higher impact acceleration did not cause worse clinical symptoms (Spitzer et al, 1995). Table 2. Whiplash-associated disease AIS Classification (Spitzer et al, 1995) 0 No complaint about the neck; no physical signs I Neck complaint pain, stiffness, or tenderness only II Neck complaint with musculoskeletal signs including decrease range of motion and point weakness III Neck complaint with neurological signs including decrease or absent deep tendon reflexes, weakness, and sensory deficits IV Neck complaint with fracture or dislocation The Finite Element Analysis (FEA) method allows experimental replication, the changing of parameters, and the possibility to study soft tissue injuries and impact responses. Using the FEA method, the cervical spinal nerve and cervical spinal cord tolerance to whiplash injuries has been determined by analyzing strain distribution on the nerve tissues. It was found in this study that the left spinal nerve was stretched more than the right spinal nerve. This may be resulted from the individual anatomy variance. Currently, most of human FE models have been built using ANSYS software with very neat but arbitrary elements according to one human anatomy image database from NIH. Hence that human FE model may not reflect that anatomic variance from different 19

individuals. The merit of using Mimics is it naturally and subjectively produce human FE anatomy. Since Mimics provides a rapid and accurate approach, it is possible to build multiple human FE models from different individuals image database in a short time period. Comparisons of different individual FE models become readily. The positive correlation between acceleration of the shoulder and strain of the spinal nerve was supported by the results. However, this study demonstrated that when acceleration on the shoulder reached 7 G, the spinal nerve was stretched to its maximum. 9 G and 10 G chest acceleration did not further increase the strain of the spinal nerve. After the chest acceleration reached 12 G, the model running was terminated during calculations due to the intervertebral disk element failure from being over-stretched. Hence, the model needs to be optimized in order to further evaluate the strain of the nerve that causes severe injury. It is possible that more severe injury occurs following musculoskeletal injuries. Conclusions A neck finite element model was developed to study the spinal nerve tolerance to whiplash injury using computer aided engineering (CAE) techniques plus statistical methods. The model validation was performed at the global level by tracking the head kinematics. The simulation outcomes demonstrate that whiplash can stretch the spinal nerve. The accelerations of 7 G (0.0686 mm/ms 2 ) on the shoulder can cause a 40% probability of cervical spinal nerve injury. Future work includes validating the FE model in human by installing a video monitoring system in a car s black-box to record human body kinematic movement during an automobile accident and follow up of the patient s symptoms. Another possible goal is to extend the human 20

FE model to the entire body rather than just the cervical region and test a wider variety of car collisions such as frontal-impact, side-impact, and rear-impact. Another area of interest is using the FE human model for Flying-Car driver safety research. The flying car was recently approved by the National Highway Transportation Safety Administration (NHTSA) as a transportation tool next year and the FEA method could investigate driver s comfort during taking off, landing and when drivers are exposed to vibration. 21

References Barnesley L, Lord SM, Wallis BJ, Bogduk N (1995) The prevalence of chronic cervical zygapophysial joint pain after whiplash. Spine 20:20 25. Chen C, Virk GS, Yaldo J, Guruprakash GK, Tanimoto K, Kallakuri S, Cavanaugh, JM. The Effects of Strain and Displacement Rate on Spinal Nerve Injury and Recovery. Transactions of Annual Meeting of Orthopaedic Research Society, San Francisco, CA 2012 (Accepted). Chen C, Lu Y, Kallakuri S, Patwardhan A, Cavanaugh JM.Distribution of A-delta and C-fiber receptors in the cervical facet joint capsule and their response to stretch. J Bone Joint Surg Am. 2006 Aug;88(8):1807-16. Deans, GT, Magalliard, JN, Kerr, M, Rutherford, WH: Neck sprain a major cause of disability following car accidents. Injury 1987,18:10-12. Ferrari R (2006). The Whiplash Encyclopedia, Second Edition. Jones & Bartlett Publishers: Boston; ISBN-10: 0763729345.P621-641. Hedenstierna S, Halldin P. How does a three-dimensional continuum muscle model affect the kinematics and muscle strains of a finite element neck model compared to a discrete muscle model in rear-end, frontal, and lateral impacts. Spine, 2008 Apr 15;33(8):E236-45. Ivancic PC, Ito S, Tominaga Y, Rubin W, Coe MP, Ndu AB, Carlson EJ, Panjabi MM (2008) Whiplash causes increased laxity of cervical capsular ligament. Clin Biomech 23:159 165. Jonsson H, Jr, Cesarini K, Sahlstedt B, et al. Findings and outcome in whiplash- type neck distortions. Spine 1994;19(24):2733 43. Lord SM, Barnsley L, Wallis BJ, McDonald GJ, Bogduk N (1996) Percutaneous radio-frequency neurotomy for chronic cervical zygapophyseal-joint pain. N Engl J Med 335:1721 1726. Lu Y, Chen C, Kallakuri S, Patwardhan A, Cavanaugh JM.Neural response of cervical facet joint capsule to stretch: a study of whiplash pain mechanism. Stapp Car Crash J. 2005 Nov;49:49-65. Luan F, Yang KH, Deng B, Begeman PC, Tashman S, King AI. Qualitative analysis of neck kinematics during low-speed rear-end impact. Clin Biomech (Bristol, Avon). 2000 Nov; 15 (9) :649-57. Martin DH. (1998). The acute traumatic central cord syndrome. In Whiplash Injury: Current Concepts in Prevention, diagnosis, and treatment of the servical whiplash syndrome. Edited by Robert Gunzburg and Marek Szpalski. Lippincott-Raven Published, Philadelphia, p129-133. Meyer et al. (1998) The minimal collision velocity for Whiplash. In Whiplash Injury: Current Concepts in Prevention, diagnosis, and treatment of the cervical whiplash syndrome. Edited by Robert Gunzburg and Marek Szpalski. Lippincott-Raven Published, Philadelphia, p107-109. 22

Singh A, Lu Y, Chen C, Cavanaugh JM. Mechanical properties of spinal nerve roots subjected to tension at different strain rates. J Biomech. 2006;39(9):1669-76. Singh A, Kallakuri S, Chen C, Cavanaugh JM.Structural and functional changes in nerve roots due to tension at various strains and strain rates: an in-vivo study. J Neurotrauma. 2009 Apr;26 (4): 627-40. Spitzer WO, Skovron ML, Salmi LR. Scientific monograph of the Quebec task force on whiplash-associated disorders: redefining whiplash and its management. Spine, 1995,20:1S 73S Sterner Y, Gerdle B (2004) Acute and chronic whiplash disorders a review. J Rehabil Med 36:193 209 quiz 210 Winkelstein BA, Nightingalse RW, Richardson WJ and Myers BS: Cervical facet joint mechanics: its application to whiplash injury. Proc. 43 rd Stapp Car Crash Conference. Paper #99SC15, 243-52, 1999. Winkelstein BA, Nightingale RW, Richardson WJ, Myers BS(2000) The cervical facet capsule and its role in whiplash injury: a biomechanical investigation. Spine 25:1238 1246 Zhang JG, Wang F, Zhou R, Xue Q. A three-dimensional finite element model of the cervical spine: an investigation of whiplash injury. Med Biol Eng Comput. 2011 Feb;49(2):193-201. 23