DYNAMIC ANALYSIS OF WHIPLASH

Transcription

1 DYNAMIC ANALYSIS OF WHIPLASH by JEFFERY HOOVER A thess submtted n conformty wth the requrements for the degree of Masters of Appled Scence Mechancal and Industral Engneerng Unversty of Toronto Copyrght by Jeffery Hoover 2012

2 Dynamc Analyss of Whplash Jeffery Hoover Masters of Appled Scence Mechancal and Industral Engneerng Unversty of Toronto 2012 Abstract Ths study s concerned wth whplash njures resultng from the sudden acceleraton and deceleraton of the head relatve to the torso n vehcle collsons. Whplash s the most common automoble njury, yet t s poorly understood. The objectve of ths thess s to develop a representatve rgd lnkage lumped parameter model usng Lagrangan mechancs to capture the relatve moton of the head and cervcal spne. Jont locatons correspondng to the ntervertebral centers of rotaton are used to smulate the normal spnal movements and an nverse analyss s appled to determne the vscoelastc parameters for the spne, based on cadaver test results. The model s further valdated usng ANSYS dynamc fnte element analyss and expermentally valdated usng a newly desgned and fully nstrumented whplash test fxture. Our fndngs reveal the effectveness of the smplfed model whch can be easly scaled to accommodate dfferences n collson severty, posture, gender, and occupant sze.

3 Acknowledgments I extend my apprecaton and grattude to Dr. S.A. Megud for hs expert advce, techncal gudance and fnancal assstance throughout the course of my research. I also wsh to acknowledge the assstance of Professors J. Zu and C. Smmons for ther knd advce as well as Ben Cornwell-Mott for hs expermental contrbutons. I would also lke to pay specal thanks to the members of the Mechancs and Aerospace Desgn Laboratory for ther frendshp and help durng ths research. Furthermore, the fnancal support of the Unversty of Toronto s gratefully acknowledged.

4 Table of Contents Abstract... Acknowledgments... Table of Contents... v Lst of Tables... v Lst of Fgures... v Notaton... x Glossary... xv Chapter 1 Introducton and Justfcaton Problem Statement Objectves Method of Approach Layout of Thess... 7 Chapter 2 Lterature Revew Background Injury Crtera Dynamc Models Testng In Vvo Human Testng In Vtro Cadaver Testng Testng of Anthropomorphc Test Dummes Opportuntes for Model Improvements Chapter 3 Rgd Lnkage Model of Whplash Jont Locatons for Intervertebral Moton v

5 3.2 Consttutve Equatons for Rgd Lnkage Model Determnng Vscoelastc Jont Parameters Dynamc Response for Rgd Lnkage Model Chapter 4 Fnte Element Model of Whplash Overvew of Fnte Element Method Rgd Lnkage Model Beam Model Chapter 5 Expermental Investgatons Test Fxture Desgn Head and Neck Desgn Imagng and Instrumentaton Moton Capture Software Typcal Dynamc Results Chapter 6 Results and Dscusson Outlne of Results and Dscusson Comparson of Developed Models Effect of Neck Stffness on Whplash Response Effect of Gravty on Whplash Response Effect of Acceleraton Profle on Whplash Response Effect of Acceleraton Magntude on Whplash Response Chapter 7 Conclusons and Future Work Conclusons Future Work References Appendx A Tssue and Vertebrae Characterstcs for the Head and Neck v

6 A.1 Vertebrae A.2 Intervertebral Dscs and Facet Jonts A.3 Lgaments A.4 Muscles A.5 Spnal Cord Appendx B Expermental Crcut Dagrams v

7 Lst of Tables Table 1.1: Symptoms of Whplash [15]... 2 Table 2.1: Collson factors for whplash njury Table 2.2: Human factors for whplash Table 2.3: Spnal unt stffness coeffcents [48] Table 2.4: Whplash njury crtera Table 2.5: Human adult male head and neck nertal propertes Table 3.1: Important characterstcs for modelng whplash Table 3.2: Instantaneous axs of rotaton locatons for a 50th percentle male Table 3.3: Rgd lnkage whplash models and nput parameters Table 3.4: Optmzaton crtera for determnng vscoelastc parameters Table 3.5: Optmzed rgd lnkage lumped parameter values Table 4.1: Fnte element beam model parameters Table 5.1: Whplash test fxture parameters Table 5.2: Expermental neck sample mass and heat treatment summary Table 5.3: Expermental neck sample geometry and mechancal propertes v

8 Lst of Fgures Fgure 1.1: Typcal cadaver whplash moton for 8.5 g rear-end collson acceleraton [4]... 1 Fgure 1.2: RCAR head restrant poston requrements [29]... 4 Fgure 1.3: Desgn strateges for reducng whplash... 5 Fgure 1.4: Head restrant optmzaton methodology... 6 Fgure 1.5: Outlne of the method of approach... 7 Fgure 2.1: Bomechancal axs system [45] Fgure 2.2: Vertebrae, ntervertebral dscs, and lgaments of the spnal unt [48] Fgure 2.3: Anatomcal head movements [49] Fgure 2.4: RCAR dynamc rear-end collson sled acceleraton [29] Fgure 2.5: 50th percentle male n seated posture [81] Fgure 2.6: Instantaneous centers of rotaton for the cervcal spne Fgure 2.7: In vtro expermental test apparatus [4] Fgure 2.8: In vtro head response relatve to the T 1 vertebra [4] Fgure 2.9: In vtro ntervertebral neck response durng whplash [4] Fgure 3.1: Rgd lnkage model for whplash Fgure 3.2: Dynamc rgd lnkage model IAR assessment Fgure 3.3: Rotatonal Vogt element Fgure 3.4: Rgd lnkage 8.5 g whplash acceleraton appled at the T 1 vertebra Fgure 3.5: Inverse method to determne vscoelastc parameters v

9 Fgure 3.6: Intervertebral extenson of the cervcal spne Fgure 3.7: Rgd lnkage model comparson of relatve head to T 1 vertebra horzontal dsplacement durng whplash Fgure 3.8: Rgd lnkage model comparson of relatve head to T 1 vertebra vertcal dsplacement durng whplash Fgure 3.9: Rgd lnkage model comparson of head rotaton durng whplash Fgure 3.10: Rgd lnkage model comparson of ntervertebral extensons durng whplash Fgure 3.11: Rgd lnkage model performance summary for cadaver ft results Fgure 4.1: Rgd lnkage FE model wth revolute jonts and rgd beam elements Fgure 4.2: Rgd lnkage FE 8.5g whplash acceleraton appled at the T 1 vertebra Fgure 4.3: Rgd lnkage FE tme varaton of head response durng whplash Fgure 4.4: Rgd lnkage FE tme response of head acceleraton durng whplash Fgure 4.5: Rgd lnkage FE tme varaton of ntervertebral extenson durng whplash Fgure 4.6: Beam FE model wth contnuous beam mass, head mass, and nerta Fgure 4.7: Equvalent beam element Fgure 4.8: Beam FE whplash acceleraton appled at the T 1 vertebra Fgure 4.9: Beam FE tme varaton of head response durng whplash Fgure 4.10: Beam FE tme varaton of head acceleraton durng whplash Fgure 4.11: Beam FE tme varaton of ntervertebral extenson durng whplash Fgure 5.1: Expermental whplash test fxture Fgure 5.2: Fxture sled assembly desgn x

10 Fgure 5.3: Heat treated 4130 steel neck sample desgn Fgure 5.4: Neck materal propertes Fgure 5.5: Head assembly Fgure 5.6: Moton capture nstrumentaton for whplash test fxture Fgure 5.7: Expermental reflectve targets for hgh-speed moton capture Fgure 5.8: Typcal moton trackng frame for head, neck, and sled durng whplash Fgure 5.9: Typcal expermental sled acceleraton for the wde neck Fgure 5.10: Expermental head response for the wde neck durng whplash Fgure 5.11: Expermental segment angles for the wde neck durng whplash Fgure 5.12: Expermental ntervertebral extenson for the wde neck durng whplash Fgure 5.13: Expermental relatve head acceleraton for the wde neck durng whplash Fgure 6.1: Comparson of acceleraton profles for rgd lnkage (RL), fnte element rgd lnkage (FE-RL), fnte element beam (FE-beam), experments (exp), Van Lopk et al. model (model) [69], and Grauer et al. cadaver testng [4] Fgure 6.2: Relatve head to T 1 vertebra comparson between rgd lnkage (RL), fnte element rgd lnkage (FE-RL), fnte element beam (FE-beam), experments (exp), Van Lopk et al. model (model) [69], and Grauer et al. cadaver testng [4] durng whplash Fgure 6.3: Head rotaton comparson between rgd lnkage (RL), fnte element rgd lnkage (FE-RL), fnte element beam (FE-beam), experments (exp), Van Lopk et al. model (model) [69], and Grauer et al. cadaver testng [4] durng whplash Fgure 6.4: Intervertebral extenson comparson between rgd lnkage (RL), fnte element rgd lnkage (FE-RL), fnte element beam (FE-beam), experments (exp), Van Lopk et al. model (model) [69], and Grauer et al. cadaver testng [4] durng whplash x

11 Fgure 6.5: Expermental neck stffness assessment durng whplash Fgure 6.6: FE beam gravty assessment durng 8.5g whplash Fgure 6.7: FE beam acceleraton profle assessment durng whplash Fgure 6.8: FE beam acceleraton magntude assessment durng whplash Fgure A.1 Human spne segments [99] Fgure A.2: Typcal cervcal (C 4 ) vertebra [104] Fgure A.3: Intervertebral dscs and facet jonts [104] Fgure A.4: Cervcal vertebra and ntervertebral dsc [107] Fgure A.5: Lgaments of the spne [48] Fgure A.6: Muscles of the neck. Adapted from Gray [52] Fgure A.7: Actve and passve muscle force characterstcs [48, 111, 112] Fgure B.1: ACH001 accelerometer crcut dagram Fgure B.2: Kstler 8632C50 accelerometer crcut dagram Fgure B.3: Wheatstone brdge crcut dagram Fgure B.4: Instrumentaton amplfer x

12 Notaton C 1 C 7 T 1 cervcal vertebrae frst thoracc vertebra m head head mass Izz head moment of nerta of the head about the center of mass n the sagttal plane L rgd lnkage length, rgd lnkage angle, angular velocty,ntal ntal rgd lnkage angle k rgd lnkage angular velocty jont stffness c jont dampng m jont mass (note: m8 mhead ) T V v total knetc energy total potental energy net jont velocty x, x component of jont poston, velocty x y, y component of jont poston, velocty y Q M V C generalzed force mass matrx gyroscopc matrx dampng matrx x

13 K e stffness matrx Q generalzed force vector, generalzed coordnate vector for jont angle, angular velocty, and angular, acceleraton m sum of jont masses m to h m head ft extft headft headposft headrotft row vector of angular acceleraton and angular velocty row vector of angular velocty and jont angle ft for overall head and neck moton ft for neck moton ft for head moton ft for head poston ft for head rotaton x ( t) expermental head poston n x drecton exp y ( t) expermental head poston n y drecton exp x head (t) model head poston n x drecton y head (t) model head poston n y drecton ( t) expermental head rotaton exp head (t) model head rotaton (t) model ntervertebral extenson ( t) expermental ntervertebral extenson exp, tsteps total number of tme steps x

14 seg segment rotaton M jont moment M bend beam bendng moment E I EI d beam dl modulus of elastcty second moment of area bendng stffness beam curvature k sprng sprng stffness m sled sled mass y beam stress dstance from neutral axs smoothng factor smoothed 1 smoothed data pont at new tme smoothed smoothed data pont at prevous tme x 1 orgnal data pont at new tme x orgnal data pont at prevous tme xv

15 Glossary Abducton Acute symptoms Adducton Anthropometry Bofdelty Cervcal spne Chronc symptoms Extenson Facet jonts Flexon In vtro In vvo Instantaneous axs of rotaton (IAR) Instantaneous center of rotaton (ICR) Interndvdual The movement of a lmb away from the mdlne or axs of the body Symptoms of short duraton but typcally severe The movement of a lmb toward the mdlne or axs of the body The scentfc study of the measurements and proportons of the human body The qualty of beng lfelke n appearance or responses and often refers to dummes used n safety nvestgatons of motor vehcles Of or pertanng to the neck. Cervcal vertebrae C1-C8 Symptoms that are ongong. Pan that extends beyond the expected perod of healng Act of stretchng or straghtenng out a flexed lmb Any of the four projectons that lnk one vertebra of the spne to an adjacent vertebra. Facet jonts (also known as zygopophyseal jonts) are the small jonts that connect vertebral bodes to each other. Act of bendng a jont; especally a jont between the bones of a lmb so that the angle between them s decreased A bologcal process made to occur n a laboratory vessel or other controlled experment rather than wthn a lvng organsm or natural settng. A bologcal process or experment occurrng n a lvng body See nstantaneous center of rotaton Defnes the pont about whch the object rotates. When an object moves t s subject to a combnaton of rotaton and translaton. A pont may be determned about whch the object s only subject to a rotaton. Ths pont, called the nstantaneous center of rotaton or nstantaneous axs of rotaton, wll be defned at a specfc pont for each movement the object makes. Between dfferent ndvduals xv

16 Intervertebral dscs Kyphoss Lgament Lordoss Morphometry Muscle Nervous system Parestesas Pathophysology Revolute jont Sagttal plate Soft tssue Spnal cord Le between each adjacent vertebrae n the spne. Forms a cartlagnous jont to allow movement between vertebrae. Exaggerated curvature of the thoracc spne. Also called a hunchback. Fbrous tssue that connects bones to other bones Exaggerated lumbar curvature of the spne The measurement of the shape of objects. Morphometry ncludes a large range of measurements ncludng numbers, length, surface area, volume, angles, and curvature. Is a contractle tssue whose purpose s to produce force and moton An organ contanng a network of specalzed cells called neurons that coordnate the actons and transmt sgnals between dfferent parts of the body. The central nervous system contans the bran, spnal cord, and retna. A sensaton of tnglng, prckng, or numbness of a person s skn wth no apparent long-term physcal effect. More generally known as the feelng of pns and needles The study of changes of normal mechancal, physcal, and bochemcal functons, ether caused by dsease, or resultng from an abnormal syndrome. Pathophysology emphaszes quantfable measurements Allows only relatve rotaton between two bodes (also called a pn or hnge jont) A vertcal plane passng through the standng body from front to back. The md-sagttal, or medan, plane splts the body nto left and rght halves. Refers to tssues that connect, support, or surround other structures and organs of the body, not ncludng bone. Soft tssue ncludes tendons, lgaments, fasca, skn, fbrous tssues, fat, synoval membranes, muscles, nerves, and blood vessels. A long, thn, tubular bundle of nervous tssue and support cells that extends from the bran. The bran and spnal cord together make up the central nervous system. The spnal cord has three man functons ncludng communcatng motor nformaton, communcatng senses, and coordnatng reflexes xv

17 Vertebrae (vertebra sngular) Vscoelastc Any of the bones or segments composng the spnal column, consstng typcally of a cylndrcal body and an arch wth varous processes, and formng a foramen, or openng, through whch the spnal cord passes. A property of materals that exhbt both vscous and elastc characterstcs when undergong deformaton. xv

18 Chapter 1 Introducton and Justfcaton In ths chapter, we defne the problem and justfy the undertakng of the study. The method of approach to acheve the stated objectves s outlned, followed by a summary of the layout of the thess. 1.1 Problem Statement Whplash s defned by the Quebec Task Force as, an acceleraton-deceleraton mechansm of energy transferred to the neck [1]. Durng a rear-end automotve collson the torso s accelerated forward as the energy from the collson s transferred to the human body. For unrestraned moton the head s approxmately statonary as the torso s ntally accelerated forward. Ths leads to an S-shaped curvature of the cervcal spne (see Appendx Fgure A.1) wth the upper segments flexed and the lower segments extended as shown n Fgure 1.1. After ths the head begns to rotate rearward untl the upper and lower segments of the cervcal spne are extended. Ths s followed by the head reboundng forward nto a flexed confguraton. Although whplash njures are stll poorly understood research has suggested they may be assocated wth abnormal motons n the lower cervcal vertebrae early n the collson sequence [2] and the dfferental moton between the head and the torso [3]. Fgure 1.1: Typcal cadaver whplash moton for 8.5 g rear-end collson acceleraton [4] Whplash njures are the most common type automoble njury [5], wth 85% of all whplash njures occurng durng rear-end collsons [6]. More than 65% of all whplash njures occur at 1

19 speeds below 30 km/h [7] wth some njures even occurrng where there s no vehcle damage at all [8]. Ths hgh prevalence, coupled wth human vulnerablty, leads to more than 1 mllon cases of whplash reported annually n the U.S. alone [7]. These njures lead to sgnfcant costs, panful symptoms, and reduced qualty of lfe for ndvduals wth chronc symptoms. There are many acute and chronc symptoms assocated wth whplash as shown n Table 1.1, ncludng neck, back, and shoulder pan and headaches whch can range from mld to severe [9]. These njures are dffcult to assess and treat, owng to the complex behavour of soft tssue and the nervous system n the head and neck and the nablty of modern X-Ray, MRI, and CT scan technques to detect njury [6, 10, 11]. These factors have led to costs of whplash assocated dsorders estmated at 10 bllon dollars/euros annually n the U.S. and Europe [12-14]. In the U.S. these fgures refer to the costs of healthcare and nsurance alone. The addton of lost work tme due to whplash assocated dsorders would make ths fgure even larger. Symptom Table 1.1: Symptoms of Whplash [15] Acute Prevalence (%) Chronc 3 months Symptom Prevalence (%) Neck Pan 94 Neck Pan 100 Neck Stffness 96 Shoulder Pan 88 Headache 44 Neck Stffness 83 Interscapular Pan 35 Headache 68 Sleepng Problems 35 Back Pan 64 Intruson/Avodance 30 Dzzness 43 Numbness/Parestesas 22 Numbness 40 Dzzness 15 Sleepng Problems 34 Vsual Symptoms 12 Concentraton Problems Audtory Symptoms 13 Memory Problems 25 Memory Problems 15 Audtory Symptoms Vsual Symptoms 14 Wth these statstcs, much research has focused on studyng the many facets of whplash to understand, treat, and prevent t wth mproved vehcle safety. Unfortunately, mprovements n vehcle safety have only resulted n nomnal gans n whplash preventon. The addton of the 2

20 frst vehcle head restrants n the late 1960 s only resulted n a 14-18% reducton n whplash njures [16, 17]. Ths was lkely due to mproper head restrant adjustment and excessve backset dstance between the head restrant and the ndvdual. About 75% of all head restrants were found to be left n the down poston n an early study [18], whch s stll a common trend today. Current global Research Councl for Automotve Repars (RCAR) standards requre that the head restrant s postoned close to the back of the head (backset) and top of the head (topset) as shown n Fgure 1.2, whch has been correlated wth reduced njures n rear-end collsons [19, 20]. Even properly adjusted passve head restrants have been found to only provde a 24% reducton n the ncdence of neck pan n rear-end collsons [6]. Many dfferent desgn strateges have been proposed to reduce whplash njury. The strateges for reducng whplash njury n the event of a collson can be lumped nto 3 man categores: () reduce energy transferred to the occupant, () restrct occupant head movement, and () alert the occupant to look forward and engage neck muscles as shown n Fgure 1.3. The novel deas proposed by the author are talczed n ths fgure. Opportuntes for reducng the energy transferred to the occupant are lmted because of hgh speed collson safety requrements and space restrctons wthn the vehcle. Volvo has desgned a system that allows the seat to swvel backwards when the torso s pushed back nto the seat durng a rear-end collson [21-23]. Ths absorbs some of the energy of the collson and encourages a flexed cervcal spne durng the collson. Ths desgn s consdered an actve system because t s actvated durng a collson to protect the occupant from njury. Other actve systems have focused on restrctng the occupant head movement to prevent njury. For these systems, the head restrant wll move forward to close the gap between the head and the head restrant to provde support early n the collson. It should be noted that the head restrant cannot be desgned to have no ntal gap wth the passengers head because t must not nterfere wth passengers wth dfferent drvng postures and durng movements to check mrrors etc. The Saab Actve Head Restrant (SAHR) and Mercedes Neck-Pro are two examples of actve head restrant systems [24, 25]. These types of actve systems have been found to reduce whplash clams by 31-75% compared wth typcal desgns [26-28]. There s potental for further gans as well. These actve head restrant desgns are only 'sem-actve' n that they are only actvated once n the collson sequence (movng forward to close the gap between the passenger and the head). A truly actve system, as lsted n Fgure 1.3, would allow the head restrant movement pror to and durng the collson sequence to produce the optmal response for 3

21 passenger safety. Durng normal drvng the condtons the actve head restrant would move to mantan the desred topset and backset between the head and head restrant wthout nterferng wth passenger motons. Upon sensng a collson, the actve head restrant would actvate to close gap between head restrant and head and then move n the optmal way to mnmze njury. Fgure 1.2: RCAR head restrant poston requrements [29] 4

22 Fgure 1.3: Desgn strateges for reducng whplash Further safety mprovements to provde the optmal head restrant characterstcs (for standard and sem-actve desgns) and response (for actve desgns) have been lmted by the development of robust human dynamc smulaton models and the understandng of whplash njury. Most computer smulaton models provde poor accuracy for cervcal and head motons durng whplash due to the dffculty of capturng the moton and propertes of the ntervertebral dscs, facet jonts, lgaments, muscles, etc. throughout the dynamc whplash moton. Complex fnte element models have been able to approxmate the ntervertebral moton at great computatonal expense [30]. Effcent and accurate head/neck models are requred to determne the optmal head restrant desgn for the gven collson severty, passenger sze, gender, and posture as shown n Fgure 1.4. An effcent model wth fast soluton tme s benefcal to allow for head restrant optmzaton over many teratons and desgn parameters. Ths model must also provde an accurate response for both the head and ntervertebral motons to enable an accurate assessment of njury gven our current understandng of whplash trauma. 5

23 Fgure 1.4: Head restrant optmzaton methodology 1.2 Objectves The objectve of ths thess s to develop a representatve rgd lnkage lumped parameter model usng Lagrangan mechancs to capture the relatve moton of the head and cervcal spne durng whplash. Jont locatons correspondng to ntervertebral centers of rotaton are used to smulate the normal spnal movements and an nverse analyss s appled to determne the vscoelastc parameters for the spne based on cadaver test results. The model s further valdated usng hgh resoluton dynamc fnte element analyss (ANSYS) and expermental results. 1.3 Method of Approach Fgure 1.5 shows the schematc of the method of approach adopted for ths work. Two types of dynamc models (analytcal and fnte element) are developed to capture the whplash moton durng rear-end collsons. These models attempt to capture the dynamc whplash response for a healthy 50th percentle male lookng forward n normal seated posture. 6

24 Fgure 1.5: Outlne of the method of approach 1.4 Layout of Thess The remander of the thess s organzed as follows. Chapter 2 revews the state of the avalable lterature for whplash. It ncludes the background nformaton for whplash; whplash njury assessment crtera; dynamc models for whplash; and human, cadaver, and test dummy whplash results. Chapter 3 descrbes the development of the analytcal rgd lnkage model for whplash. It covers the anthropometrc and mass values for the head and neck, the modelng approach for the ntervertebral moton of the cervcal spne, the Lagrange method for determnng the equatons of moton, and the nverse method for determnng the vscoelastc parameters of the head and neck. Chapter 4 descrbes the two dfferent dynamc fnte element models used to model whplash. Chapter 5 dscusses the expermental results for whplash ncludng the development of a whplash test fxture, smulated head and neck, and the dynamc response of the system. Chapter 6 demonstrates the performance of the rgd lnkage and fnte element models and ther valdaton wth expermental results. The strengths and weaknesses of the dfferent approaches are dscussed as well as a revew of the mportant factors nfluencng whplash. Chapter 7 presents the conclusons of the work and future work for mprovng the model. 7

25 Expermental data currently mssng n the feld of whplash to date s dscussed as well. Followng the man body of the thess are the lst of references and appendces. Glossary terms are placed n the front of the thess. 8

26 Chapter 2 Lterature Revew Ths thess s concerned wth the dynamc analyss of whplash. As such, the lterature revew wll cover the tssue propertes of the head and neck, the causes and pathophysology of whplash, njury crtera for whplash, dynamc models for whplash, expermental results for whplash testng, and opportuntes for model mprovements. These sectons are ncluded to provde the reader wth a bref summary of these topcs as they relate to ths thess. 2.1 Background There are many factors that nfluence the dynamc response durng whplash. The man collson factors are summarzed n Table 2.1. Rear-end collsons are of the greatest nterest n the study of whplash because they lead to 85% of all whplash njures [6]. Durng a rear-end collson the bullet vehcle colldes wth the target vehcle, causng t to accelerate forward. The crash severty corresponds to the net change n the velocty of the target vehcle n such a collson. Ths s related to the energy transferred durng the collson and, not surprsngly, to the rsk of whplash njury [31]. Based on the crash severty, vehcle, and seat characterstcs, a gven acceleraton of the target passenger s produced. Stffer vehcles, wth less energy absorbng bumpers, produce shorter collson profles wth hgher peak acceleratons. Ths peak acceleraton s found to be an ndcator for whplash njury as well as crash severty [32, 33]. In some cases, ndvduals can be njured even n low-speed collsons where there s no vehcle damage [8]. The seat nclnaton and stffness also determnes the net acceleraton profle and drecton of the occupant. For typcal seat nclnatons, the occupant s accelerated upwards as well as forward, leadng to an axal compresson of the cervcal spne durng the whplash moton [34]. The propertes of the seat also affect the acceleraton of the occupant and the relatve head and torso moton assocated wth njury [35, 36]. 9

27 Table 2.1: Collson factors for whplash njury Collson Factors Collson Type Crash Dynamcs Vehcle Characterstcs Seat Head Restrant Descrpton Front-End, Rear-End, Sde-Impact Crash severty ( V), Acceleraton, Deceleraton Mass, Stffness, Energy Absorpton, Coeffcent of Resttuton Profle, Inclnaton, Stffness, Dampng Standard, Sem-Actve, Actve, Topset, Backset, Stffness, Dampng In addton to the collson factors there are many human factors that affect the dynamc response and nfluence the outcome of whplash njury. All of the human factors lsted n Table 2.2 play a role n the whplash response. Indvduals lookng to the sde to check ther mrrors or vehcle blnd spots are partcularly susceptble to chronc whplash njury n the case of a collson. In ths head-turned posture the facet jonts are n a vulnerable poston wth the potental for excessve facet capsular lgament strans n the event of a rear-end collson [37]. In the most common scenaro the passenger s lookng forward n the vehcle, leadng to a 2-dmensonal whplash moton n the sagttal plane (see Fgure 2.1) durng a rear-end collson. Varatons n ntal posture affect the dynamcs of the whplash moton, wth kyphotc spne curvatures more susceptble to njury due to greater extenson of the lower cervcal vertebrae durng normal posture [34, 38]. Varatons n heght and weght have an effect on the forces and motons sustaned durng the whplash moton, wth greater mass leadng to greater loadng [39]. Gender has also been suggested as a rsk factor for whplash [40, 41]. Females may be more vulnerable to whplash njury due to anthropometrc and strength dfferences n the head and neck [42]. It has also been suggested that chldren and the elderly may be more susceptble to whplash njury [6, 43, 44]. 10

28 Fgure 2.1: Bomechancal axs system [45] Most people n rear-end collsons are unaware of the mpendng collson and are not bracng for the mpact. In ths scenaro, very lttle muscle actvaton s requred to hold the head uprght, and the neck provdes mnmal resstance to the collson acceleraton. Even f the muscles are not hghly actvated ntally, they wll become actvated durng a rear-end collson as the natural response to resst the whplash moton. The sternocledomastod, splenus capts, and trapezus muscles are all actvated durng whplash wth the greatest muscle force comng from the sternocledomastod muscle group. These muscles are typcally actvated late n the collson sequence, wth muscle actvaton begnnng approxmately 120 ms after mpact and peak actvaton occurrng at approxmately ms, ms, and ms for the sternocledomastod, splenus capts, and trapezus muscles, respectvely [7]. The awareness of an ndvdual to the mpendng collson can lead to ncreased muscle actvaton pror to the collson, whch can alter the dynamcs and loadng of the cervcal spne. Subject awareness and bracng for mpact can alter the tme to peak muscle contracton and peak muscle contracton levels durng whplash [7]. Ths was found to reduce the peak head acceleraton by 40%, as well [46]. It s stll unclear whether ths altered loadng and dynamc response would reduce, exacerbate, or create new mechansms of whplash njury. The human head and neck wegh approxmately kg and kg respectvely [47]. The vertebrae, ntervertebral dscs, facet jonts, lgaments, and muscles of the head and neck all work together to support ths load and provde excellent range of moton n the sagttal, transverse, and frontal planes. The general arrangement of the vertebrae, ntervertebral dscs, and 11

29 lgaments s shown n Fgure 2.2. The vertebrae are stff bony structures wth a complex threedmensonal structure. They protect the spnal cord and provde connecton ponts for the ntervertebral dscs, facet jonts, and lgaments of the spne. There are seven vertebrae of the cervcal spne (C 1 -C 7 ). The upper two vertebrae (C 1 atlas and C 2 axs) have a unque geometry that allow for rotaton of the head about the vertcal axs ( no movement). The lower vertebrae, from C 2 down to C 7, are separated by ntervertebral dscs and facet jonts that allow them to slde and rotate past one another durng flexon/extenson, abducton/adducton, and axal rotatons as shown n Fgure 2.3. Table 2.2: Human factors for whplash Human Factors Head Poston Posture Anthropometrc and Weght Varatons Gender Age Awareness Vertebrae Intervertebral Dscs Lgaments Muscles Spnal Cord Cervcal Moton Tssue Varaton Body Functon Descrpton Lookng Forward, Rotated Left / Rght, Inclned Up / Down Normal, Slouchng, Head Fore / Aft, Cervcal Lordoss / Kyphoss Heght, Sze, Weght Male, Female Chld, Adult, Elderly Unaware / Aware of Collson (Intal Muscle Actvaton) Complex Geometry, Stffness, Mass Vscoelastc, Non-Homogeneous, Non-Isotropc, Mass Non-lnear Stffness, Path, Attachment, Mass Vscoelastc, Actvaton, Morphometry, Path, Attachment, Mass Vscoelastc, Attachment, Mass Intervertebral Moton durng Whplash Interndvdual Tssue Stffness and Dampng Fractures, Injures, Dsease 12

30 Fgure 2.2: Vertebrae, ntervertebral dscs, and lgaments of the spnal unt [48] 13

31 Fgure 2.3: Anatomcal head movements [49] The ntervertebral dscs support the large compressve loads transferred through the vertebrae whle producng very lttle resstance to shear. The ntervertebral dscs are composed of a nucleus pulposs gel wth a hgh water content (70-90%) [48], surrounded by a fbrous annulus fbross tssue around the outsde of the dsc. Ths structure gves the ntervertebral dscs ther ansotropc and vscoelastc propertes. The facet (or zygapophyseal) jonts also act to mantan spacng between the vertebrae to facltate moton and mantan stablty n the spne. Two facet jonts are located between each cervcal vertebra below C 2, dorsal to the ntervertebral dsc and symmetrc about the sagttal plane. The facet jont acheves large shear motons by the unfoldng of the fbroadpose menscod between the nferor and superor artcular processes of each adjacent 14

32 vertebra. The lgaments of the spne connect between the vertebrae to support the spne. Lgaments dsplay a hghly non-lnear stress-stran relatonshp wth very low stffness for low stran levels. They also dsplay vscoelastc propertes due to ther hgh (~2/3) water content [45]. Hgher stress values wll occur for hgher stran rates due to ths vscoelastcty. As s the case wth most bomechancal tssue, sgnfcant varatons n lgament stffness are observed between ndvduals and age groups [50]. The muscles of the spne provde support and facltate movement. Durng normal seated posture, a small level of muscle actvaton s requred to hold the head uprght. In ts passve state muscle stretched beyond ts restng length wll dsplay a nonlnear ncrease n load wth deflecton. In ts contracted state the muscle wll be shortened, thereby producng a greater ncrease n load wth deflecton. As a result, a subject bracng for a collson wll contract the muscles of the neck, ncreasng ther resstance to loadng and decreasng overall head moton durng whplash [51]. At the same tme, the loads appled to the cervcal spne wll be ncreased because of hgher muscle forces. The spnal cord s protected by the vertebrae and acts to communcate motor, sensory, and reflex sgnals to the body. Durng the flexon and extenson motons of the spne, the length and cross sectonal area of the spnal cord s forced to change as the vertebrae slde and rotate past one another. The spnal cord accounts for these deflectons by mantanng very low resstance to deformaton for stran values up to 5%. The spnal flud wthn the spnal cord gves t a hghly vscoelastc response whle makng t susceptble to developng pressure waves under rapd deformatons [3]. For a more detaled descrpton of these tssues the reader s referred to the appendx and the work of Ether [45], Whte [48], and Gray [52]. In addton to understandng the mechancal propertes of the ndvdual structures of the spne, some studes have been performed on the propertes of the spnal unt n vvo and n vtro. Table 2.3 shows the resstance to spnal rotaton for flexon and extenson motons of cadaver samples. These propertes provde a rough estmate of the net stffness of the spne to resst whplash moton and demonstrate the vulnerablty of the cervcal spne to external loadng due to ts lower stffness. Smlar studes have been performed to quantfy the flexblty of the spne and ntervertebral range of moton [48, 53, 54]. In order to understand the relatve moton of the vertebrae durng flexon/extenson and whplash moton, a number of studes have examned the locatons of the nstantaneous axes of rotaton at each vertebral level [2, 55, 56]. Usng x-ray cnematography, the vertebrae can be mapped to understand the moton of each vertebra relatve 15

33 to the vertebra nferor to t. The nstantaneous axs of rotaton defnes the axs perpendcular to the sagttal plane about whch the superor vertebra has rotated from one tme step to the next. Pennng [53] found these centers of rotatons to be repeatable for voluntary flexon/extenson motons across multple ndvduals and over the entre voluntary range of moton. Ths approach smplfes the complex ntervertebral moton of the spne consderably, allowng the moton of the spne to be approxmated by one angular degree of freedom at each vertebral level nstead of three degrees of freedom for shear, compresson, and rotaton. Table 2.3: Spnal unt stffness coeffcents [48] Spnal Unt Stffness (Nm/deg) Flexon Extenson Cervcal Thoracc Injury Crtera Many njury crtera are used to assess whplash trauma. The most establshed njury crtera are summarzed n Table 2.4. The presence of multple njury crtera speaks to the complex nvolvement of the dfferent soft tssues n the cervcal spnal unt assocated wth whplash. In order to capture the njury rsk due to multple potental njury modes, more than one njury crteron s requred. For example, the development of Boström s Neck Injury Crteron (NIC) ensures that the pressure effects n the spnal canal do not exceed threshold levels assocated wth njury to the dorsal root ganglon [3]. The Intervertebral Neck Injury Crteron (IV-NIC) developed by Panjab et al. [57] analyses the extenson at each of the ntervertebral jonts throughout the whplash moton. Injury s assessed based on the rato of the ntervertebral extensons to ther physologc values. Ths njury crteron provdes an assessment of soft-tssue njury to the facet jonts and ntervertebral dscs by capturng the moton beyond the physologc lmt of the spne. Facet jont njury has also been lnked to the S-shaped curvature of spne occurrng early n the collson sequence [2]. The normalzed Neck Injury Crteron (N j ) and Neck Protecton Crteron (N km ) consder the forces and moments durng the whplash moton to assess the njury severty. The N j crteron was developed for assessng the abbrevated njury 16

34 scale, level 2 njury (AIS2) n frontal mpacts and s applcable n hgh-speed rear-end collsons [58, 59]. The N km crteron requrement has been proposed to assess njures n rear mpacts by reducng njurous loads and moments actng on the spne. The ntercept values for these N j and N km crtera are based on the BoRIDII test dummy to assess the whplash response n hgh-speed rear-end collson scenaros. The Neck Dsplacement Crteron (NDC) developed by Vano et al. [60] ensures the head extenson, posteror dsplacement of the head (at the occptal condyles) relatve to the torso, and axal compresson of the cervcal spne from T 1 to the occptal condyles are below threshold values. Based on these crtera t s clear that an accurate model of whplash must capture not only the realstc motons of the head relatve to the torso but also the ndvdual ntervertebral rotatons throughout the whplash moton. 17

35 Table 2.4: Whplash njury crtera Neck Injury Crteron (NIC) [3] Normalzed Neck Injury Crteron (N j ) [58, 59] Neck Protecton Crteron (N km ) [58, 59] Neck Dsplacement Crteron (NDC) [60] Injury Crtera NIC 2 0.2a rel vrel a relatve acceleraton T 1 /C 1 rel v relatve velocty T 1 /C 1 N rel Fz j F nt M z M nt N Fz Fz F M y nt M nt axal force km F nt M z M nt +6806N/-6160N Ext bendng moment 125Nm F F x M y nt M nt shear force +845N/-845N Ext bendng moment 47.5Nm Peak Head/T1 extenson Posteror shear dsplacement Axal compresson dsplacement Intervertebral Neck-Injury whplash, Crteron (IV-NIC) IV NIC physologcal, [57] NIC [61] N j [61] N km [61] Threshold m s Mnmum excellent ratng: Extenson < 25 o Posteror Shear < 3.5cm Axal Compresson < 1.5cm Head / C C C C C C / C / C / C / C / T

36 2.3 Dynamc Models A great varety of computatonal dynamc models have been developed usng mult-body dynamcs and fnte element approaches to date. Both full-body and head and neck models have been developed, although most recent models have focused on the head and neck alone n an effort to capture the complex dynamc response n ths area. The smplest mult-body models use rgd lnkages wth jonts and lumped parameters to capture the net effect of the muscles, lgaments, ntervertebral dscs etc. These models have been developed wth varyng levels of success [62-64]. The major lmtatons of these models have been the dffculty to capture the complex vertebral geometry and ntervertebral movements and the dffculty n obtanng realstc lumped parameter values. In some scenaros these smplfed models have been found to accurately determne the human head response durng rear-end whplash loadng wth very low soluton tmes [62]. More complex mult-body models have been developed to capture the geometry of the ndvdual vertebrae and head and model each ntervertebral dsc, facet jont, lgament, and muscle. The most proven mult-body model s probably the De Jager model used n the MADYMO software package [65]. Ths model has been studed n a number of dfferent scenaros and has been refned over tme [65-68]. Most recently Lopk et al. [69] presented a head and neck mult-body model wth very good head and ntervertebral response over a range of acceleraton profles. Ths model used the vsualnastran4d software package n combnaton wth Matlab to model the muscle response. In ths model, ntervertebral dscs were modeled by nonlnear vscoelastc constrants connectng adjacent vertebrae, lgaments were modeled by nonlnear vscoelastc elements, and facet jonts were modeled by frctonless contact. Muscles are typcally modeled wth passve and actve components usng Hll muscle elements [70]. These models dsplay relatvely fast computaton tmes (~20 mnutes) [69] but are stll lmted n ther ablty to accurately capture ntervertebral rotatons and motons. Ths s due to the lack of understandng of the vscoelastc propertes of the ntervertebral dsc and facet jonts to characterze the ntervertebral response and a lack of data for the knematc response of the cervcal spne durng whplash. A number of fnte element (FE) models of the head and neck have also been developed n an effort to assess the dynamc response and susceptblty for njury durng rear-end collsons. These fnte element models attempt to accurately model the geometry and materal propertes of 19

37 the head and neck. Ths approach tends to be computatonally ntensve, wth Hallden et al. [71] developng a FE model wth run tmes of up to 45 hours to solve [69]. The fnte element approach s also lmted by the applcaton of accurate materal propertes for all of the soft tssue of the neck and head. Recently, Fce et al. [30] demonstrated the use of a FE model to capture the overall dynamc whplash response and assess the potental for njury to the facet jonts durng whplash loadng. Other FE models have been presented as well [72-75]. Compared to the multbody modelng approach, the FE approach has the ablty to produce a more complete pcture of the stresses and strans observed durng the whplash moton [76], but s stll lmted by the accurate materal propertes requred to capture the moton of the ntervertebral jonts. 2.4 Testng The expermental testng of whplash can be broken nto three major groups: n vvo testng of human subjects durng low-speed rear-end collsons; n vtro testng of cadaver specmens (head/neck or head/neck/torso); and testng usng anthropometrc test dummes. Human testng provdes the most realstc response to the whplash moton but t s lmted to low-speed testng to avod chronc njury to the test subjects. In vtro cadaver testng s performed at all mpact veloctes, but muscle tssue propertes tend to be stffer than n vvo test subjects [77] and muscle actvaton s typcally gnored wth ths type of testng. Anthropomorphc test dummes (ATDs) are full sze physcal specmens made to match the geometry and mass of ndvdual body parts. These dummes have been valdated aganst n vvo, n vtro and computatonal models wth lmted bofdelty n low-speed rear-end collsons [78]. A hybrd ATD (HUMON) wth a cadaver head and neck on an ATD body has been developed as well [79]. In the motor vehcle ndustry, ATDs are used for vehcle valdaton of statc and dynamc whplash crtera [29, 80]. The dynamc acceleraton profle specfed by the RCAR seat/head restrant evaluaton standard s shown n Fgure 2.4. Ths s a global standard adopted by the Insurance Insttute of Hghway Safety (IIHS) and others to assess njury usng the BoRID ATD. Ths acceleraton profle s based on typcal collson characterstcs [8] and s commonly used n assessng the dynamc response durng whplash. 20

38 Fgure 2.4: RCAR dynamc rear-end collson sled acceleraton [29] Another crtcal aspect n the dynamc analyss of whplash s the determnaton of the anthropometrc values, mass, and nerta for the neck and head. These parameters wll be dependent on subject sze, age, gender, and ethncty. The anthropometrc data for the 50th percentle male (average heght and mass of North Amercan male) n normal seated posture s shown n Fgure 2.5. A more detaled three-dmensonal model of a 50th percentle male has also been presented by Vasavada usng the OpenSm software for vsualzaton [42, 49]. Varous other complatons of anthropometrc data exst to defne mass, nerta, and geometry values for male and female subjects wth a summary of these values shown n Table 2.5. Measurements of the range of moton for the cervcal spne have also been completed n vvo and n vtro to understand the lmtatons of the cervcal spne [54, 57]. These measurements have led to an mproved understandng of the range of moton for the cervcal spne and have led to the development of the Intervertebral Neck Injury Crteron (IV-NIC) [57]. 21

39 Source Fgure 2.5: 50th percentle male n seated posture [81] Table 2.5: Human adult male head and neck nertal propertes Adult Male Sze (%) Body Mass (kg) Head Mass (kg) Neck Mass (kg) Head Inerta (about center of mass) (kg-m 2 ) Ixx (forward) Iyy (cross-car) Grosso et al. [82] 50th NASA 1 [83] 50th NASA 2 [82] 50th Walker et al. [47] Izz (up) In Vvo Human Testng A varety of n vvo human low-speed rear-end collson experments have been performed over the past 30 years. They have been performed usng subjects n both vehcle and sled test scenaros [41, 84]. Testng has been performed on male and female subjects, wth and wthout head restrants, but the test results performed wthout head restrants are of the greatest nterest to ths research n order to understand the unnhbted moton and mechancal propertes of the head and 22

40 neck durng whplash. Most studes nvolve subjects lookng forward wth normal ntal posture durng the collson, but head-turned postures have also been examned [37]. Human testng has focused on both the knematc and electromyographc (EMG) response durng whplash. To determne the knematc response, accelerometers and reflectve targets are commonly used to track the locatons of nterest on the head and neck. In most cases, the poston, velocty, acceleraton, and rotaton of the head center of gravty and torso (T 1 ) are reported [32, 39, 51, 85]. Whle ths nformaton s useful, the ntervertebral rotatons, vertebral nstantaneous axes of rotaton, and vertebral motons are requred for assessng facet jont njury and for understandng the complex moton of the spne durng whplash. Unfortunately, ths nformaton s lmted. Kaneoka et al. [2] performed a groundbreakng test on male volunteers usng hgh-speed x-ray cnematography to track the moton of the ndvdual vertebra durng low-speed whplash testng. Ths study found an abnormal shft n the nstantaneous axs of rotaton of the C 5 vertebra assocated wth facet jont njury durng the S-shaped curvature of the spne. However, the motons of the nstantaneous axs of rotaton at each vertebral level through the entre whplash moton were not reported. EMG sgnals have been used to measure the level of muscle actvaton durng whplash to understand the level and tme of muscle actvaton durng whplash [2, 7, 46]. Ths testng has demonstrated the lack of muscle actvaton early n the collson, beleved to be assocated wth the tme of whplash njury. X-ray cnematography has also been used to capture the moton of the cervcal spne durng voluntary flexon/extenson motons n the sagttal plane. Fgure 2.6A shows the concept of the nstantaneous axs of rotaton appled to flexon/extenson movements of the cervcal spne. In ths fgure, two x-ray mages are supermposed from two dfferent flexon/extenson postons. By overlayng the x-rays such that the vertebra at a gven level s overlad, the moton of the superor vertebra relatve to ths vertebra can be observed. The pont correspondng to the axs of rotaton for ths vertebra and tme step can then be defned. Ths analyss can be carred out for each vertebra, tme step, and ndvdual to determne the varablty n ths approach. These results are shown n by the dots n Fgure 2.6b provded by Amevo et al. [55]. The localzed postons of these dots show that ths approach provdes a relable means for nterpretng the complex moton of the cervcal spne durng flexon and extenson movements. It should be noted that the lack of dots on the C 2 vertebrae s due to the altered geometry of the C 1 and C 2 neck regon allowng the head to rotate about the occptal condyles and rotaton to occur about the C 1 vertebra. These 23

41 locatons are also for voluntary flexon/extenson movements whch may dffer from that for the dynamc whplash response. Fgure 2.6: Instantaneous centers of rotaton for the cervcal spne (A) ICR locatons [53] (B) varablty [55] In Vtro Cadaver Testng In vtro dynamc testng allows cadavers to be tested n rear-end collsons at acceleraton levels assocated wth whplash njury. Ths provdes the most realstc human response to whplash avalable at hgh levels of acceleraton (>6.5 g). A number of dfferent n vtro studes have been performed to assess the dynamc response durng rear-end collsons ncludng Stemper [68, 86], Panjab [57, 87], Grauer [4], and others [61, 88-90]. These tests have been performed on both full-body and head-neck complexes. Testng on head-neck complexes s most commonly performed by applyng a unaxal acceleraton to the upper thoracc vertebrae whle observng the response of the head and neck. Ths testng gnores the effects of axal spne loadng that occurs due to the upward force on the occupant as a result of seat nclnaton. Muscle smulaton s another area of concern wth n vtro testng due to ts ncreased stffness compared wth n vvo propertes [77] and the dffculty to smulate muscle actvaton to hold the head n normal posture. Two approaches have been used to deal wth ths lmtaton: () removng muscle tssue and supportng the head n normal ntal posture pror to the collson, and () usng a muscle 24

42 force replcaton system to capture the muscle propertes of the neck and hold the head uprght pror to the collson. The frst approach, used by Grauer et al. [4], fals to capture the passve stffness of the muscles of the neck, producng what should be a slghtly more flexble specmen. The second approach, used by Panjab et al. [91], uses a muscle force replcaton system to support the head and capture the passve muscle propertes n the neck. Ths system benefts from a more complete test specmen, wth the potental for the most realstc whplash response, but adds the uncertanty of the overall performance of the muscle replcaton system to accurately capture the muscle response. Both of these types of cadaver tests have been able to duplcate the typcal S-shaped curvature characterstc of the n vvo whplash moton, whch supports ther valdty [4, 91]. Fgure 2.7: In vtro expermental test apparatus [4] The test setup used by Grauer et al. s shown n Fgure 2.7. For ths test the T 1 vertebra was fxed to the test sled at a 20 degree angle correspondng to that of normal posture. The head was replaced by a surrogate head wth a mass of 5.5 kg and moment of nerta of kg m 2 to represent a 50th percentle human head. The surrogate head was supported by a magnetc pston holdng the foramen magnum (base of skull) at a horzontal orentaton correspondng to an ndvdual lookng straght ahead whle drvng. The magnet was used to rapdly remove the support at the start of the experment, allowng the head and neck to move freely durng the collson. Muscle and external soft tssue was removed and moton-montorng flags were secured to each vertebra to track ther moton and rotaton. Ths allowed for the moton capture of the 25

43 vertebrae n addton to that of the head, whch s very mportant for understandng the complex ntervertebral moton of the neck. A horzontal acceleraton was appled to the trauma sled to perform the test. The results of ths testng are shown n Fgures 2.8 and 2.9 for an 8.5 g acceleraton profle. Head rotaton s seen to ncrease sharply after approxmately 50 ms wth the horzontal moton of the neck startng approxmately 25 ms before ths. Ths s characterstc of the S-shaped curvature and moton of the neck durng whplash, where the head ntally moves backwards relatve to the torso (S-shaped curvature) before rotatng backwards and reboundng forward as shown n Fgure 1.1. Fgure 2.9 also demonstrates the S-shaped curvature response wth C 0 -C 1 and C 1 -C 2 ntervertebral flexon occurrng whle the lower ntervertebral jonts are extended around ms. After ths tme the upper ntervertebral jonts transton from flexon to extenson as the head rotates backwards. As such, these results provde a realstc response of the head and neck durng whplash njury. Fgure 2.8: In vtro head response relatve to the T 1 vertebra [4] 26

44 Fgure 2.9: In vtro ntervertebral neck response durng whplash [4] Testng of Anthropomorphc Test Dummes Anthropomorphc test dummes (ATDs) are full-body human replcas that can be used to smulate the whplash response durng rear-end collsons. HybrdIII-TRID, RID2, and BoRID2 are three such ATDs that have been specfcally desgned for rear-end collsons. By capturng segment masses and geometry representng 50th percentle human propertes, these dummes attempt to duplcate the human response durng whplash. Although ATDs have been shown to approxmate the head moton and loadng durng whplash, the bofdelty of the neck s lmted [78, 92]. Ths s lkely due to the pn jonts and other attachments used to smulate the complex moton of the vertebrae and soft tssue. Ths lmts the potental for ATDs to assess njury due to the IV-NIC and makes them a poor choce n supportng the development of a fundamental dynamc model for whplash. There are stll many applcatons for ATDs and they have been used to valdate vehcle safety mprovements for over 20 years usng the NIC and other njury crteron for whplash [32, 93-95]. 27

45 2.5 Opportuntes for Model Improvements In order to facltate njury assessment durng whplash, dynamc models must accurately capture both the head moton relatve to the T 1 vertebra and the ntervertebral rotatons of the cervcal spne [3, 57]. Current lumped-parameter models have been lmted n ther ablty to capture the dynamc ntervertebral response of the cervcal spne due to: () () the complex sldng and rotaton moton of the vertebrae relatve to one another and the dffculty n determnng accurate lumped-parameter values to nclude the net effects of the ntervertebral dscs, facet jonts, lgaments, muscles, and other soft tssue. By addressng these areas of concern, a smplfed lumped parameter model capable of capturng the complex whplash moton n the cervcal spne and head may be acheved. 28

46 Chapter 3 Rgd Lnkage Model of Whplash Ths chapter descrbes the development of a rgd lnkage dynamc model of whplash. It covers the development of realstc jont locatons, the Lagrange method for developng the equatons of moton for the system, the fttng method for determnng the lumped parameter values for the system, and the results for the rgd lnkage model. Fgure 3.1: Rgd lnkage model for whplash 29

47 The rgd lnkage model of whplash s shown n Fgure 3.1. The segment lengths are defned by L 1 to L 8 for the T 1 to C 7 segment up to the uppermost segment endng at the center of gravty of the head. The segment angles correspondng to ntal posture are gven by 1 to 8, startng from the bottom to top locatons shown n Fgure 3.1. These angles are measured n the counterclockwse drecton from the vertcal. There are 8 degrees of freedom for the system correspondng to each of the segments angles 1 to 8, whch are measured n the CCW drecton and allowed to vary over tme. The rotatonal stffness at each of the jonts s gven by k 1 to k 8 and the rotatonal dampng s gven by c 1 to c 8. Segment masses, startng at the second ntervertebral jont, are gven by the values m 1 up to m head. At ths top m head locaton the moment of nerta of the head I head s also defned at the center of gravty of the head. Whplash njury s characterzed by the moton of the head and cervcal spne [3, 57, 61], so ths model wll focus on the response n ths regon. The mportant characterstcs for modelng whplash are shown n Table 3.1. The rgd lnkage model s developed to model the most common whplash scenaro. For example, the model wll assume the subject s lookng forward wth normal posture durng the rear-end collson, leadng to a 2-dmensonal whplash response n the sagttal plane. The model mass and lnkage values correspond to that of the average North Amercan male. Muscle actvaton s gnored as most ndvduals are unaware of an mpendng collson and nvoluntary muscle actvaton s beleved to occur after whplash njury s sustaned [2, 7, 46]. Passve muscle stffness s gnored n accordance wth the expermental results of Grauer et al. [4]. Lumped parameters are used to capture the net effects of the vertebrae, ntervertebral dscs, facet jonts, lgaments, and spnal cord n accordance wth Grauer et al. s [4] testng on healthy cadaver subjects. In order to acheve an acceptable level of accuracy, the model s formulated to handle the large deflectons whch occur durng whplash. 30

48 Table 3.1: Important characterstcs for modelng whplash Characterstc Descrpton Model Head Poston Lookng Forward, Left, Rght, Up / Down Lookng Forward Posture Anthropometrc and Weght Varatons Normal, Slouchng, Head Fore / Aft, Cervcal Lordoss / Kyphoss Heght, Sze, Weght Gender Male, Female Male Age Chld, Adult, Elderly Adult Normal Seated Posture 50th Percentle Awareness Unaware / Aware of Collson Unaware Vertebrae Intervertebral Dscs Lgaments Spnal Cord Muscles Complex Geometry, Stffness, Mass Vscoelastc, Non-Homogeneous, Non-Isotropc, Mass Non-lnear Stffness, Path, Attachment, Mass Vscoelastc, Attachment, Mass Vscoelastc, Actvaton, Morphometry, Path, Attachment, Mass Lumped Parameters for Mass, Lnear Stffness and Dampng None Cervcal Moton Intervertebral Moton durng Whplash Center of Rotaton Tssue Varaton Interndvdual Tssue Stffness and Dampng Body Functon Fractures, Injures, Dsease Healthy Large Deformatons Head and Cervcal Vertebrae Motons durng Whplash Expermental Tssue Propertes Large Deformatons 3.1 Jont Locatons for Intervertebral Moton For ndvduals lookng forward durng a rear-end collson the moton of the head and vertebrae can be approxmated by a 2-dmensonal moton n the sagttal plane. Assumng no addtonal constrants are appled, ths allows for 3 degrees of freedom (x poston, y poston, and rotaton) for the moton of each vertebra. The relatve moton of each vertebra can be smplfed further by understandng the moton of the spne durng normal flexon/extenson movements. Durng these movements the vertebrae slde and rotate past one another n such a way that ther moton can be approxmated by a rotaton of each superor vertebra about a specfc locaton on each adjacent nferor vertebra. As dscussed n secton 2.4.1, ths approach has been found to provde a good 31

49 approxmaton for voluntary flexon/extenson motons through the entre cervcal range of moton and across multple ndvduals [53, 55]. The mean locatons of the centers of rotaton are a functon of vertebra sze, allowng them to be defned for a range of ndvdual szes [55]. For the 50th percentle North Amercan male, the sze and locaton of each vertebra can be defned usng the anthropometrc data shown n Fgure 2.5 [81]. The resultng locatons for the IAR s are shown n Table 3.2. The skull center of gravty (CoG) does not correspond to an nstantaneous axs of rotaton but s ncluded for completeness. The skull rotaton IAR locaton corresponds to the rotaton center for the skull as t moves about the occptal condyles of the atlas. The C 1 /C 2 IAR locaton captures the rotaton of the atlas about the axs and the followng locatons defne the IAR s for C 3 through to T 1. Table 3.2: Instantaneous axs of rotaton locatons for a 50th percentle male IAR Locaton X Poston (mm) Y Poston (mm) Mass (kg) Inerta (kg m 2 ) Lnkage Length (mm) Intal Angle (Deg) Skull CoG L 8 (top) Skull Rotaton L C 1 /C L C L C L C L C L C L T Total The concept of usng IAR s to defne the movements of the vertebrae s analogous to that of a rgd lnkage structure wth revolute jonts at the IAR locatons. In both cases, the dstance between the centers of rotaton for adjacent vertebrae s conserved and rotatons are only permtted about the IAR locatons. The resultng revolute jonts and rgd lnkages are shown n Fgure 3.1, overlad on the fgure for the 50th percentle male. Revolute jont locatons are shown by + sgns wth dashed lnes ndcatng lnkages between these jonts. Lnkage values for the length and ntal angle (correspondng to ntal posture) are provded n Table 3.2. Table 3.2 also shows the mass and nerta values defned at each of the jont locatons. The mass and nerta values for the head were chosen to match those of Grauer et al. [4] and approxmate those of a 32

50 50th percentle male as shown n Table 2.5. The mass values at the other jont locatons were calculated based on the percentage of the nferor vertcal segment length to the total vertcal neck length. The total neck mass was taken to be 1.8 kg, correspondng to that of a 50th percentle male as shown n Table 2.5. The nerta of the neck at each of the neck jonts s neglected because the soft tssue of the neck does not tend to rotate durng ntervertebral rotatons, but nstead translates n a more lnear fashon durng ths moton. Although the locaton of IAR s are well establshed for voluntary motons, ther applcaton n the dynamc whplash response s stll largely unknown. To the authors knowledge, only one expermental study has been performed nvolvng IAR analyss at the C 5 /C 6 level durng whplash. Ths research found a shft n the C 5 /C 6 IAR locaton durng whplash, beleved to be assocated wth facet jont njury [2]. The motons of the IAR locatons at all of the vertebral locatons throughout the whplash moton were not reported, however. In order to assess the valdty of the IAR approxmaton durng whplash, the expermental ntervertebral rotatons of Grauer et al. [4] can be appled to the rgd lnkage model to compare the resultng head response wth that found expermentally. The Grauer expermental results capture both the ntervertebral extensons of the neck and the relatve moton of the head to the T 1 vertebra, so f the IAR approxmaton s reasonable t should provde a lnk between these two sets of results. It should be noted that the IAR locatons of cadaver samples cannot be expected to be the same as those of the rgd lnkage model because of dfferences n heght, sze, etc. The comparson between the rgd lnkage model (shown n Fgure 3.1), usng IAR locatons for a 50th percentle male, and the expermental results of Grauer et al. [4] are shown n Fgure 3.2 below. The results show a very good ft for both head rotaton and head poston usng ths IAR rgd lnkage approach. Ths supports the valdty of usng IAR jont locatons to approxmate the cervcal spne moton durng whplash. 33

51 Head Rotaton (deg) Relatve Head Dsplacement (m) 80 A 0.02 B Exp IAR Tme (s) Exp X Exp Y IAR X IAR Y Tme (s) Fgure 3.2: Dynamc rgd lnkage model IAR assessment (A) head rotaton (B) head dsplacement relatve to T 1 vertebra 3.2 Consttutve Equatons for Rgd Lnkage Model The rgd lnkage dynamc model of the head and neck s shown n Fgure 3.1. The model conssts of 8 rgd lnkages runnng from the T 1 vertebra up to the center of gravty of the head. Revolute jonts wth mass, stffness, and dampng lumped parameters are defned at each of the jont locatons from the T 1 jont upwards. Jont rotatonal stffness and dampng values are appled n a Vogt element as shown n Fgure 3.3. The nerta of the head s defned at the center of gravty of the head, as well. The nput acceleraton, appled at the T 1 vertebrae, n both the x (forward) and y (upward) drectons wll defne the response of the system over tme. For ths rgd lnkage confguraton, the knetc energy T of the system can be defned as a functon of the jont mass m and velocty v, as shown n equaton 3.1. Ths summaton starts at the frst jont above the T 1 jont and contnues up to the center of mass of the head accordng to 34

52 Fgure 3.1. The velocty vector, whch les n the sagttal plane, can be further decomposed nto x and y components as provded n equaton 3.2. k c Fgure 3.3: Rotatonal Vogt element T I head 8 mv (3.1) T 1 2 I head m x y (3.2) 2 The jont mass locatons n the forward x and upward y drectons are a functon of the lnkage lengths L and angles (measured n the CCW drecton from the vertcal) as shown n equatons 3.3 and 3.4. Takng the dervatve of equatons 3.3 and 3.4 wth respect to tme gves the x and lnkage lengths y jont veloctes n equatons 3.5 and 3.6. These veloctes are a functon of the L, angles, and angular veloctes for fxed segment lengths L. Equatons 3.2, 3.5, and 3.6 can be combned to defne the knetc energy of the rgd lnkage system n terms of the generalzed coordnates and. j 1 x L j sn (3.3) j 35

53 j 1 y L j cos (3.4) j j 1 x L j j cos (3.5) j j 1 y L j j sn (3.6) j The potental energy V for the system s a functon of the stored sprng energy at each of the jonts, gnorng the effects of gravty. Equaton 3.7 shows the potental energy as a functon of the rotatonal sprng stffness counterclockwse drecton. k and lnkage angle, measured from the vertcal n the V k 2 1 k (3.7) 1 1 Once the knetc and potental energy have been defned n terms of the generalzed coordnates and the Lagrange method can be used to determne the equatons of moton for the system. Lagrange s equatons are gven by equaton 3.8 where the generalzed force equaton 3.9. The generalzed force s a functon of the jont mass acceleraton Q s shown n m, horzontal external a xref, vertcal external acceleraton a yref, partal dervatve of the jont horzontal poston wth respect to the generalzed coordnate x k, and partal dervatve of the jont vertcal poston wth respect to the generalzed coordnate y k. d dt T T V Q (3.8) 36

54 Q 8 k 1 mka xref xk mka yref yk (3.9) There are 8 degrees of freedom for the rgd lnkage system correspondng to the angles of the 8 segments n the model. Equaton 3.8 defnes Lagrange s 8 equatons of moton for ths system whch can be arranged usng matrx algebra nto the format of equaton In ths equaton the 8 by 8 mass matrx M s multpled by the 8 by 1 angular acceleraton row vector of segment angular acceleratons 1 down to 8. The V matrx characterzes the dampng n the system due to corols forces and the C matrx defnes the dampng n the system as a result of the jont dampng. In most cases, the V and C matrces are combned but they have been separated here for clarty. These matrces are multpled by the segment angular velocty row vector. The stffness matrx K arses from the jont stffness parameters k and defnes the moment produced for a gven change n the generalzed coordnates. The generalzed force vector e Q defnes the generalzed external forces actng on the system due to the external acceleratons appled at the T 1 vertebra. Equaton 3.10 can be modfed to that of equaton 3.11 where the rgd lnkage model s gven an ntal confguraton about whch t wll resst ntal movement. Ths ntal confguraton corresponds to the normal seated posture of the average 50 th percentle male. M V C K (3.10) Q e M V C K (3.11) ntal Q e Each of the matrces defned n equaton 3.11 are shown explctly n equatons 3.12 to The mass matrx n equaton 3.12 s a functon of the jont masses, segment lengths, and segment angles. The notaton mass m 1 h defnes the addton of the jont masses m 1, m 2, m 3 up to the head m h. The corols matrx n equaton 3.13 s a functon of the jont masses and segment lengths, angles, and angular veloctes. The dampng matrx n equaton 3.14 s a functon of each 37

55 of the jont dampng values correspondng to the rotatonal Vogt elements. The stffness matrx n equaton 3.15 s a functon of the jont stffness values correspondng to the rotatonal Vogt elements. In equaton 3.16 the generalzed force vector s a functon of the jont masses, segment lengths, and nput acceleraton for the system. (3.12) 38

56 (3.13) (3.14) (3.15) 39

57 (3.16) Substtutng the jont and lnkage values for each of the matrx varables above produces a matrx equaton whch s a functon of the angular poston, velocty, and acceleraton of each segment accordng to equaton Equaton 3.11 can then be rearranged to obtan the angular acceleraton n terms of the angular velocty and poston as shown by equaton At tme t equal to zero the ntal angular poston (gven n Table 3.2) and ntal velocty (zero ntal angular velocty) are known, so for an external acceleraton shown n Fgure 3.4, the angular acceleraton of each of the segments can be found. At ths pont, the segment angular acceleraton and angular velocty vectors can be combned to form the 16 by 1 column vector shown on the left hand sde of equaton Ths column vector s then numercally ntegrated over tme to obtan the segment angular velocty and poston vector shown on the rght hand sde of equaton 3.18, whch s a functon of tme. The Runge-Kutta numercal ntegraton method (ODE45 n Matlab) s used to obtan the response of the rgd lnkage model for a tme varyng nput acceleraton for the models wthout jont dampng. For the numercal ntegraton usng fully-defned vscoelastc parameters, ODE15s (desgned for numercal ntegraton of stff systems n Matlab) was found to produce faster soluton results. M Q V C K 1 (3.17) e ntal 40

58 T 1 Acceleraton (g) d dt (3.18) 10 8 X Y Tme (s) Fgure 3.4: Rgd lnkage 8.5 g whplash acceleraton appled at the T 1 vertebra 3.3 Determnng Vscoelastc Jont Parameters Based on the prevous formulaton, the dynamc response of the rgd lnkage model s determned for a gven stffness and dampng confguraton and acceleraton profle. The goal at ths stage s to determne the lumped parameter stffness and dampng values whch wll provde the most realstc head and neck response durng whplash. Although the tssue propertes of the ntervertebral dscs, facet jonts, lgaments, etc. are generally well understood, ther contrbuton to the lumped parameter stffness and dampng jont values of the rgd lnkage model s not trval. The cadaver test results of Grauer et al. [4] provde the realstc whplash response for both the head and neck under a known collson acceleraton. By applyng the same collson acceleraton to the rgd lnkage model, the model response and expermental response are compared to assess the performance of the rgd lnkage model. A numercal ft quantfyng how closely the model response matches the expermental response s then defned, where an mproved model response corresponds to a lower ft value. At ths pont, an optmzaton routne s mplemented to determne the stffness and dampng values whch wll mnmze the ft value 41

59 and attempt to capture the expermental cadaver whplash response. Ths procedure s llustrated n Fgure 3.5. Fgure 3.5: Inverse method to determne vscoelastc parameters The ft value, mentoned prevously, must capture not only the head response (dsplacement and rotaton) but also the neck response (ntervertebral extensons) for t to accurately assess the whplash moton. As dscussed n secton 2.2, t s beleved that whplash njury depends on both the head movement relatve to the torso [3] and also ntervertebral neck extensons [57], so t s mportant that the model attempt to accurately capture all of these motons. The ft value for head dsplacement headposft s a summaton of the square of the dfference between the expermental head poston x ( t), y ( t) and model head poston x head (t), y head (t) at each exp exp tme step as shown n equaton Poston values are n mllmeters and tsteps corresponds to the total number of tme steps for the response. The expermental results of Grauer et al. [4] were avalable from 0 to s over s ncrements so there were 35 tme steps tsteps for the summaton. headposft tsteps 2 2 x exp t) xhead ( t) yexp ( t) yhead ( t) t 1 ( (3.19) In order to assess the head rotaton ft headrotft the sum of the squares of the dfference between the expermental head rotaton ( t) and the model head rotaton ) are added at each tme step accordng to equaton exp head (t 42

60 tsteps t t exp ( ) head ( ) headrotft 2 (3.20) t 1 By addng the sum of headposft and headrotft, an assessment of the level of the ft for the complete head response s acheved. headft headposft headrotft (3.21) The ntervertebral extenson of the neck s a measure of the rotaton of each vertebra relatve to ts adjacent nferor vertebra as shown n Fgure 3.6. In the case where the T 1 vertebra s fxed, the C 7 -T 1 ntervertebral extenson ( ) s equal to the rotaton of C 7 vertebra ( ) beyond ts 1 t ntal orentaton ( ) as gven by equaton At the hgher vertebral levels, both the 1, ntal t nferor and superor vertebra can rotate. In ths scenaro the ntervertebral extenson (t) s equal to the dfference n the rotaton of the superor and nferor vertebral rotatons relatve to ther ntal confguratons as shown n equaton 3.23 and Fgure 3.6. The rotaton of the superor vertebra s equal to the dfference n the net rotaton (t) from ts ntal orentaton ( ). 1 t, ntal t The rotaton of the nferor vertebra s equal to the dfference n the net rotaton ( ) from ts ntal orentaton ( ). 1, ntal t 1 t (3.22) 1 ( t ) 1( t) 1, ntal ( t ) ( t) 1 ( t), ntal 1, ntal where 1 (3.23) 43

61 Fgure 3.6: Intervertebral extenson of the cervcal spne The ft for the neck ntervertebral extenson extft s equal to the sum of the squares of the dfference between the expermental ntervertebral extenson ( t) and model ntervertebral extenson (t) over the 8 ntervertebral levels and tme. Ths s gven by equaton As mentoned prevously, the value for tsteps s 35, based on the number of expermental data ponts obtaned. exp, extft tsteps 8 exp, t) ( t) t ( (3.24) The total ft ft s equal to the sum of the ft contrbuton from the head moton headft and the neck ntervertebral rotatons extft as shown n equaton Ths ft value gves a measure of how well the model response replcates the expermental whplash moton of cadaver subjects. The lowest ft value s desred, correspondng to best overall approxmaton of the whplash moton. ft headft extft (3.25) 44

62 In order to determne the stffness and dampng parameters to provde the most realstc neck response, a constraned optmzaton routne was performed n Matlab. Four dfferent models of ncreasng complexty were used to determne the parameters whch would provde the best whplash response as shown n Table 3.3. For the unform jont stffness no dampng (UJSND) model, a common stffness value s defned at each of the ntervertebral jonts. For the jont stffness no dampng model (JSND), the stffness values at each of the jonts are assumed to be ndependent of one another. For the jont dampng no stffness model (JDNS), 8 ndependent dampng varables defne the dampng at each of the jonts. In the jont stffness jont dampng model (JSJD), ndependent varables for stffness and dampng are defned at each of the ntervertebral levels. Table 3.3: Rgd lnkage whplash models and nput parameters Model Name Model Parameters UJSND Unform Jont Stffness, No Dampng K unform JSND Jont Stffness, No Dampng K 1-8 JDNS Jont Dampng, No Stffness C 1-8 JSJD Jont Stffness, Jont Dampng K 1-8,C 1-8 The optmzaton crtera for determnng the model parameters and response are shown n Table 3.4. Upper and lower bounds were set wthn the optmzaton to constran the optmzaton varables wthn realstc lmts. The lower bound was set to zero and the upper bound for each of the models s gven n Table 3.4. Many optmzaton routnes were performed over the optmzaton space usng the parameter values shown n Table 3.4 as the startng ponts for the optmzaton routne. For example, wth the JSND model there were 8 stffness parameters wth two dfferent startng values used for each parameter. Ths led to 2 8 optmzatons startng from dfferent ntal condtons. The parameters from the best optmzaton run (lowest overall ft value) were chosen as the most realstc confguraton for that model. 45

63 Table 3.4: Optmzaton crtera for determnng vscoelastc parameters Model Upper Bound Intal Condtons UJSND Nm/rad Entre range JSND Nm/rad 5 Nm/rad, Nm/rad JDNS Nms/rad 5,500 Nm/rad, Nm/rad JSJD Nm/rad Nms/rad 5 Nm/rad 5 Nms/rad, 500 Nms/rad 3.4 Dynamc Response for Rgd Lnkage Model The optmzed parameters for the best ft optmzed models are shown n Table 3.5. For the smplest model the jont stffness s found to be 366 Nm/rad at the 8 ntervertebral jonts of the spne. Ths corresponds to a total neck stffness of 48.5 Nm/rad (0.85 Nm/deg) whch provdes very good agreement wth 0.73 Nm/deg cervcal stffness n extenson gven by Whte et al. [48]. The jont stffness no jont dampng model has hgh stffness n the lower segments and low stffness n the upper segments. Ths restrcts the moton n the lower segments durng whplash whch lmts ts ablty to acheve the realstc S-shaped whplash moton as shown n Fgure 1.1. The jont stffness jont dampng model dsplays a range of stffness values from nearly zero up to 256 Nm/rad. At the jonts where the stffness s very close to zero, the assocated Vogt dampng parameter s seen to be non-zero. As a result, the damper wll resst the moton at these locatons. Ths suggests that the energy n the neck s prmarly stored n the jonts 2, 3, 6, 7, and 8 wth jonts 1, 3, 4, 5, and 6 actng to dsspate the energy of the collson. It should be noted ths analyss has focused on capturng the whplash response early n the collson sequence as t s ths regon that s beleved to be assocated wth njury [2, 34]. For ths reason the ft values and optmzaton parameters are based on the ntal whplash response as shown n Fgures 3.7 to Ths may lead to model and jont parameters may not capture the accurate whplash response beyond ths tme wndow. 46

64 Model Table 3.5: Optmzed rgd lnkage lumped parameter values Jont 1 C 7 -T 1 Jont 2 C 6 -C 7 Jont 3 C 5 -C 6 Rotatonal Stffness (Nm/rad) Jont 4 C 4 -C 5 Jont 5 C 3 -C 4 Jont 6 C 2 -C 3 Jont 7 C 1 -C 2 Jont 8 Skull rot UJSND JSND * * JDNS JSJD Model Rotatonal Dampng (Nms/rad) Jont 1 Jont 2 Jont 3 Jont 4 Jont 5 Jont 6 Jont 7 Jont 8 UJSND JSND JDNS JSJD * upper bound The response for each of the optmzed models s shown n Fgures The relatve dsplacement of the head to the T 1 vertebra n the horzontal drecton s shown n Fgure 3.7. The sold lne n the fgure demonstrates the cadaver head response observed by Grauer et al. [4] durng expermental testng. The other 4 lnes demonstrate the responses for the 4 other rgd lnkage models: unform jont stffness no jont dampng (UJSND), jont stffness no jont dampng (JSND), jont dampng no jont stffness (JDNS), and jont dampng jont stffness (JDJS). Durng whplash, the head s ntally forced backward relatve to the T 1 vertebra before reboundng forward as shown by the negatve relatve dsplacement n Fgure 3.7. Apart from the jont dampng (JDNS) model, all models show a reasonable approxmaton of the head peak x dsplacement, wth the unform jont stffness model (UJSND) slghtly over predctng deflecton and the jont stffness (JSND) and jont stffness jont dampng (JSJD) models slghtly under predctng the response. All 3 of these models dsplay peak relatve head dsplacement at approxmately 130 ms whle the cadaver response reaches a peak at 90 ms after the ntal collson. After reachng the peak deflecton, the vscoelastc jont stffness jont dampng model produces the best response wth a more gradual decrease n deflecton over tme, smlar to that of the cadaver results. the 47

65 Relatve Head X Dsplacement (m) UJSND JSND JDNS JSJD Cadaver Tme (s) Fgure 3.7: Rgd lnkage model comparson of relatve head to T 1 vertebra horzontal dsplacement durng whplash The head dsplacement relatve to the T 1 vertebra for the rgd lnkage models and cadaver response s shown n Fgure 3.8. It should be noted that the scale s greatly reduced from that of the x dsplacement shown n Fgure 3.7. The models show smlar trends to that of the head x dsplacement, wth the UJSND, JSND, and JSJD models reachng a peak value 20 ms after the cadaver. As before, the unform jont stffness model slghtly exceeds the peak y relatve dsplacement from the cadaver testng and the JSND and JSJD models underestmate the peak deflecton. After reachng ts peak value, the jont stffness jont dampng model shows a good ft wth the cadaver response over tme. 48

66 Relatve Head Y Dsplacement (m) UJSND JSND JDNS JSJD Cadaver Tme (s) Fgure 3.8: Rgd lnkage model comparson of relatve head to T 1 vertebra vertcal dsplacement durng whplash The overall model performance for head rotaton over tme s shown n Fgure 3.9. The jont dampng model demonstrates a very poor response compared to the cadaver expermental results. The other 3 models produce a good approxmaton of the peak head rotaton wth the peak head rotaton occurrng at 100 ms, 125 ms, and 135 ms for the cadaver, jont stffness jont dampng, and unform jont stffness models. Beyond ths peak, the jont stffness jont dampng model produces the most realstc response over tme. Although both the model and cadaver responses are smlar, the cadaver head rotaton s seen to ncrease more rapdly than the rgd lnkage models after around 50 ms. The cadaver response also dsplays a concave downward decrease n the rotaton from about 100 to 150 ms. The models, by contrast, exhbt a smooth transton before and after reachng ther peak rotaton levels. 49

67 Head Rotaton (deg) UJSND JSND JDNS JSJD Cadaver Tme (s) Fgure 3.9: Rgd lnkage model comparson of head rotaton durng whplash In addton to the head response of whplash, the moton of the neck durng whplash s also mportant for assessng whplash njury [57]. Fgure 3.10 demonstrates the ntervertebral response durng whplash for the four dfferent rgd lnkage models and cadaver expermental results. Lookng at the cadaver response n Fgure 3.10A, there are two man characterstcs to note. The frst s the flexon of the cervcal spne at the skull to C 1 and C 1 to C 2 levels occurrng around 40 to 80 ms after the collson. At ths tme, the upper spne segments are flexed whle the other segments are extended, correspondng to the S-shaped curvature shown n Fgure 1.1. It s mportant to note that ths does not mply that the segments are actually rotatng forward n global coordnates but only that they have rotated forward relatve to ther adjacent nferor segments. The other characterstc of note s the large extenson of the upper cervcal segments as the head rotates backward durng whplash. The JSND, JDNS and JSJD models all exhbt large ntervertebral extensons at the C 1 to C 2 jont smlar to the cadaver results. Of these models, only the jont stffness jont dampng model exhbts the s-shaped flexon/extenson characterstc of the upper and lower cervcal neck segments durng whplash. The JSJD model also dsplays an ncrease n the C 4 to C 5 jont extenson over tme whch s not seen n the cadaver results. 50

68 Fgure 3.10: Rgd lnkage model comparson of ntervertebral extensons durng whplash 51

69 Fgure 3.10D shows the ntervertebral extensons over tme for the vscoelastc JSJD model. From ths fgure t s evdent that the Skull-C 1, C 1 -C 2, C 4 -C 5, and C 6 -C 7 jonts allow moton whle the other segments are vrtually locked. Referrng to Table 3.5 these flexble locatons correspond to jonts 2, 4, 7, and 8 whch have low rotatonal dampng values of 0 Nms/rad, 11 Nms/rad, 0 Nms/rad, and 0 Nms/rad. By contrast, the rgd jonts 1, 3, 5, and 6 have dampng values of 906 Nms/rad, 569 Nms/rad, 530 Nms/rad, and 645 Nms/rad, wth lttle or no assocated Vogt stffness. Ths demonstrates the ablty of the Vogt damper to resst moton durng the rapd whplash moton. The resultng ft values for each model confguraton s shown n Fgure The jont stffness jont dampng model provdes the best overall ft for head (headft) and neck (extft) moton. Ths s not surprsng consderng the vscoelastc nature of the soft tssue of the neck [45, 48]. Both the unform jont stffness and jont stffness jont dampng models show a good overall ft for the ntervertebral extensons of the neck, but the unform jont stffness does not capture the realstc head moton as well as the JSJD model. Ths s demonstrated n Fgures 3.8 and 3.9 where the UJSND model produces excessve head deflecton relatve to the T 1 vertebra n the horzontal and vertcal drectons. The jont dampng model (JDNS) s seen to produce the worst overall whplash response due to ts nablty to sprng backward and forward durng whplash. Ths demonstrates the mportance of the stffness of the neck to produce the forward moton of the head n the later stages of the whplash moton. The smplest unform jont stffness model has the best (lowest) extft value correspondng to the best approxmaton of the neck moton durng whplash. As dscussed prevously, ths model does not capture the mportant s-shaped curvature of the neck durng whplash, whch s mportant n assessng whplash njury. Wth ths n mnd the jont stffness jont dampng model s seen to provde the most realstc assessment of both the head and neck moton durng whplash. 52

70 Ft x 105 Headft Extft UJSND JSND JDNS JSJD Fgure 3.11: Rgd lnkage model performance summary for cadaver ft results 53

71 Chapter 4 Fnte Element Model of Whplash In ths chapter, we use the fnte element method to develop 2 dynamc models of whplash. The frst makes use of rgd lnkages to smulate the ntervertebral motons and the second treats the problem usng beam elements. The purpose of ths work s threefold: () to enable the verfcaton of the lumped mass model developed n chapter 3, () to nvestgate the applcaton of a contnuous beam structure to model whplash, and () to support the expermental nvestgatons. 4.1 Overvew of Fnte Element Method The fnte element method s a powerful numercal tool for solvng engneerng and bomedcal problems. All fnte element methods nvolve dvdng the physcal system nto small subsectons known as elements. For each element the degrees of freedom and response to external condtons can be appled. Then, by usng large numbers of elements, the features of the overall system can be captured. One of the attractons of the fnte element method s the ease wth whch t can be appled to real bomedcal engneerng problems nvolvng complex geometrcal features. The drawback of usng multple elements comes wth the amount of numercal computatons requred to solve the resultng sets of smultaneous algebrac equatons. In the followng sectons of ths chapter, we ntend to dscuss the fnte element detals of the developed models. The rgd lnkage model defnes rgd lnkage, vscoelastc jonts, and lumped masses n a mult-body dynamcs assessment of the whplash response. The beam model, on the other hand, follows the same profle usng many beam elements to defne the model. Both formulatons use non-lnear transent analyss to capture the moton over tme. The non-lnear approach s requred to take nto account the changes n the mass matrx and appled loadng whch occur durng the large deformatons of the whplash response. Transent analyss s requred to determne the response of the system over each tme step due to the appled loads. It s worth notng that the models were developed n the commercal software ANSYS. A 2-dmensonal analyss of the whplash response n the sagttal plane s performed usng ths software. 54

72 4.2 Rgd Lnkage Model In ths model, the moton of head and ntervertebral dscs s captured usng rgd lnkages and vscoelastc jonts. Fgure 4.1 shows the approxmated geometry of the head and neck usng the dscretzed fnte element rgd lnkage model. Eght rgd beam elements (known n ANSYS as MPC184) and eght vscoelastc revolute jonts (known n ANSYS as MPC184) were used to defne the structure of the neck n the same manner as the rgd lnkage model developed n chapter 3. Jont locatons and mass values were defned accordng to Table 3.2. Jont mass values were defned at each of the locatons shown n Fgure 4.1 wth a 5.5 kg mass and kg m 2 nerta defned at the locaton of the center of gravty of the head, correspondng to that of a 50th percentle male. Each of the vscoelastc jonts n the model were defned wth unque lnear rotatonal stffness and dampng values. These values were defned accordng to the optmzed jont stffness jont dampng values shown n Table 3.5. Fgure 4.1: Rgd lnkage FE model wth revolute jonts and rgd beam elements (R revolute jont, M pont mass, I nerta) Typcal whplash acceleraton s used to load the system at the base of the neck at node 1. As Fgure 4.2 ndcates, the acceleraton profle contans a lnear ncrease n the horzontal acceleraton up to 8.5 g s at s and decreases lnearly back to zero at s. Zero 55

73 T 1 Acceleraton (g) acceleraton s appled n the forward drecton beyond ths tme. Zero acceleraton s appled n the upward (y) drecton throughout as the effects of gravty are gnored X Y Tme (s) Fgure 4.2: Rgd lnkage FE 8.5g whplash acceleraton appled at the T 1 vertebra Full transent analyss wth large deflectons s used n ths analyss. Four load steps are used to defne the nput acceleraton for the system over tme: () zero ntal acceleraton, () ramped acceleraton up to 8.5 g at s, () ramped acceleraton down to zero at s, and (v) zero acceleraton up to s. The ntal condtons for the system were zero ntal poston and velocty at each of the nodes. At ths pont, the response over each load step was solved and a stable and converged soluton was acheved. The results for the whplash head response are shown n Fgure 4.3. The head dsplacement relatve to the T 1 vertebra s shown on the left axs and the head rotaton s shown on the rght axs. The head x dsplacement s approxmately 8 cm relatve to the T 1 vertebra at ts maxmum and the relatve y dsplacement s approxmately 2 cm, also n the negatve drecton. The peak head rotaton s approxmately 45 degrees. Ths supports the earler clam for the mportance of performng non-lnear analyss to capture the effects of large dsplacements. 56

74 Relatve Head Dsplacement (m) Head Rotaton (deg) Rot X Y Tme (s) Fgure 4.3: Rgd lnkage FE tme varaton of head response durng whplash Fgure 4.4 shows the relatve acceleraton between the head and the T 1 vertebra. The left ordnate shows the horzontal (x) and vertcal (y) acceleraton and the rght ordnate shows the angular acceleraton of the head. Ths fgure shows the head ntally accelerates backwards before reboundng and acceleratng forward. At the same tme, the angular acceleraton of the head s ntally postve, causng the head to rotate counterclockwse (when vewed from the rght-hand sde as per Fgure 4.1) before reachng a maxmum velocty and acceleratng n the opposte drecton. 57

75 Rel Head to T 1 Acceleraton (g) Head Angular Accel (Rad/s 2 ) Ang X Y Tme (s) Fgure 4.4: Rgd lnkage FE tme response of head acceleraton durng whplash The ntervertebral extenson of the rgd lnkage fnte element model durng whplash s shown n Fgure 4.5. Smlar to the rgd lnkage response of chapter 3, extensons are observed n the C 6 -C 7, C 4 -C 5, C 1 -C 2, and Skull-C 1 jonts durng the whplash motons. The ntal flexon n the upper segments around 40 to 90 ms s not evdent n the response for the fnte element rgd lnkage model and extensons are lower than those of Grauer et al. [4] and the vscoelastc rgd lnkage model developed n chapter 3. These fndngs are dscussed further n Chapter 6. 58

76 Intervertebral Extenson (deg) Skull-C C 1 -C 2 C -C 2 3 C -C 3 4 C -C 4 5 C -C 5 6 C -C 6 7 C -T Tme (s) Fgure 4.5: Rgd lnkage FE tme varaton of ntervertebral extenson durng whplash 4.3 Beam Model The present work was further extended by modelng the moton of the head and ntervertebral dscs usng beam elements. Beam elements provde 2 useful benefts n addton to those of the rgd lnkage model: () the capture of a contnuous smulated neck deformaton profle resultng from whplash loadng and () ease of applcaton for expermental valdaton of the dynamc whplash response. Fgure 4.6 demonstrates the fnte element beam model used to approxmate the response of the cervcal spne and head durng whplash. The ntal posture of the model s equvalent to that of the rgd lnkage models developed prevously, wth the beam elements formng straght lne segments between the nstantaneous axs of rotaton locatons shown n Table 3.2. Each beam segment s dvded nto 10 elements, leadng to 80 total beam elements (known n ANSYS as Beam3 elements) for the model as shown n Fgure 4.7. These elements are capable of supportng both axal and compresson loads as well as transverse loads and bendng moments. The beam elements of the model are gven a densty of 2.5 kg/m 3 to produce a total neck mass of 0.5 kg. Ths mass s chosen to be roughly equvalent to the mass of the physcal neck samples used n the expermental valdaton. Addtonal mass and nerta values are defned at the center of gravty of the head usng an ANSYS Mass21 element. 59

77 Fgure 4.6: Beam FE model wth contnuous beam mass, head mass, and nerta Fgure 4.7 demonstrates the approach used to determne the bendng stffness to approxmate the stffness of the rgd lnkage model. In the case of the rgd lnkage structure, the rotatons n each segment seg are a functon of the net moment actng on the jont M and the rotatonal jont stffness k accordng to equaton 4.1. M (4.1) seg k For the beam element, the deformaton s contnuous over ts length. A pure moment appled to the end of a beam segment wll lead to a constant nternal moment and curvature along ts length as shown n Fgure 4.7. The bendng moment M bend n the beam s equal to the product of the modulus of elastcty of the materal E, the second moment of area I, and the curvature of the d beam as shown n equaton 4.2. dl M bend d bend EI (4.2) dl 60

78 Rearrangng ths equaton and ntegratng over the segment length gves the beam angle as a functon of the bendng moment equaton 4.3. M bend, bendng stffness EI, and segment length L as per M bend L (4.3) bend EI Equatng equatons 4.1 and 4.3 gves the bendng stffness EI as a functon of the segment length L and rgd lnkage rotatonal jont stffness k for the equvalent beam model. Ths s shown n equaton 4.4. EI k L (4.4) Usng equaton 4.4, the equvalent bendng stffness can be determned for each of the segment lengths shown n Fgure 4.6 and gven n Table 3.2. For the unform jont stffness jont dampng rgd lnkage model, the stffness at each of the jonts was found to be 366 Nm/rad to provde the most realstc response. Wth ths stffness value, the average equvalent bendng stffness s found to be equal to 9.2 Nm 2. Note that ths approach seeks to match the equvalent rotatons at the nodal locatons of nterest but that the deflectons, and therefore nodal dsplacements, wll dffer. The parameters specfed to defne the beam element to acheve ths equvalent bendng stffness value are shown n Table

79 Fgure 4.7: Equvalent beam element Table 4.1: Fnte element beam model parameters Beam Propertes Head Propertes Total mass 0.5kg Mass 5.5kg Densty 2.5kg/m 3 Inerta 0.035kg m 2 Thckness x10-3 m Depth m I zz 4.5x10-11 m 4 E 205GPa EI 9.2Nm 2 Typcal whplash acceleraton was used to load the system at the locaton of the T 1 vertebra. As Fgure 4.8 ndcates, the acceleraton profle contans a snusodal profle, whch decays to a small level correspondng to the approprate components of the gravtatonal acceleraton along the x and y axes. Ths acceleraton profle was used to model the acceleraton profle for an expermental test fxture nclned at 10 degrees (global x axs nclned 10 degrees from the horzontal). In order to determne the ntal posture for the model under the applcaton of gravtatonal loads, a statc analyss was performed to determne the statc deformaton of the 62

80 T 1 Acceleraton (g) neck under gravtatonal forces. These nodal deformatons were then used to defne the ntal confguraton for the model n the transent analyss X Y Tme (s) Fgure 4.8: Beam FE whplash acceleraton appled at the T 1 vertebra In the followng we provde only a sample of the output to demonstrate the response of the beam model durng whplash. Detaled analyss of the results, ncludng the analytcal model and the expermental nvestgatons, wll be dscussed n chapter 6. Fgure 4.9 shows the tme varaton of the dsplacement components of the head relatve to the T 1 vertebra n the x and y drectons. The fgure shows that for the gven 8.5 g acceleraton profle, the relatve head dsplacement n the x drecton ncreases dramatcally and reaches a peak value of m at 130 ms. The relatve head dsplacement n the y drecton also reaches ts much smaller peak value of m at ths tme. The head rotaton reaches ts maxmum value of 57.8 degrees slghtly before ths at 120 ms. 63

81 Relatve Head Dsplacement (m) Head Rotaton (deg) Rot X Y Tme (s) Fgure 4.9: Beam FE tme varaton of head response durng whplash The head acceleraton relatve to the T 1 vertebra s shown n Fgure 4.10 for the x and y rectlnear coordnates. Durng the ntal stage of whplash (0 to 60 ms), the head s accelerated n the negatve x drecton relatve to the T 1 vertebra. After the head has reached ts maxmum relatve velocty n the backward drecton, t sustans a larger forward acceleraton as the neck ressts the posteror moton of the head. The forward horzontal acceleraton of the head reaches a peak of 5.2 g at 145 ms. The vertcal acceleraton of the head dsplays a smaller and delayed ntal negatve acceleraton as the head approaches ts maxmum rotaton. Ths s followed by a strong ncrease n the vertcal acceleraton up to a maxmum value of 4.0 g at a tme of 135 ms. The angular acceleraton of the head ncreases steadly up to a maxmum of 589 rad/s 2 at a tme of 102 ms. The postve angular acceleraton of the head corresponds to the counterclockwse rotaton of the head n the sagttal plane when vewed from the rght-hand sde of the ndvdual (x n forward drecton, y n upward drecton relatve to the seated ndvdual). After the head reaches a maxmum angular velocty n the counterclockwse drecton, the acceleraton decreases to a mnmum value of -6 g at 100 ms as the neck ressts the CCW rotaton of the head. These 64

82 Rel Head to T 1 Acceleraton (g) Head Angular Accel (Rad/s 2 ) large rectlnear acceleratons and veloctes (area under each acceleraton curve) have been lnked to njury due to ther lnk wth damagng pressure effects n the neck durng whplash [3]. 6 4 Ang X Y Tme (s) -600 Fgure 4.10: Beam FE tme varaton of head acceleraton durng whplash Due to the contnuous deformaton of the beam fnte element structure, the ntervertebral extenson of the neck can be defned n two dfferent ways to assess the whplash response. The frst method, shown n Fgure 4.11A, compares the nodal rotatons at each of the nstantaneous axs of rotaton locatons. Ths gves a measure of the relatve extensons at the jonts smlar to that of the rgd lnkage model. Whle ths method s analogous to that of the rgd lnkage model, t s challengng to measure these rotaton values durng physcal testng due to ther small sze. Fgure 4.11B shows the alternatve method for determnng the ntervertebral extenson of the neck by trackng the locatons of the nstantaneous axes of rotaton and assumng lnear segments between these ponts. Once these IAR locatons are determned and the segments defned, the ntervertebral extensons can be determned usng the same approach demonstrated n Fgure 3.6. Fgure 4.11 compares the results for these two methods. The response for both methods are smlar wth a few mnor dfferences. The extenson values for the jont poston method n Fgure 4.11B are reduced compared to the jont rotaton method n Fgure 4.11A. Ths s due to the lnear segment approxmaton for the jont poston extenson calculaton, leadng to the 65

83 underestmaton of the rotatons at the IAR nodal locatons. Ths jont poston approach also affected the relatve magntude of the extenson values observed at each of the jonts, wth the largest changes occurrng at the C 7 -T 1 jont as shown n Fgure Fgure 4.11: Beam FE tme varaton of ntervertebral extenson durng whplash (A) jont rotatons (B) jont postons 66

84 Chapter 5 Expermental Investgatons In ths chapter, we outlne the detals of the fxture desgn and experments performed to test the whplash models developed n ths thess. The desgn contans a lnear sled mounted on a steel frame wth precson rals and gudes as well as a smulated head and neck. The fxture s fully nstrumented wth stran gauges, accelerometers, and reflectors for mage capture and mage analyss. The test rg s desgned to be capable of producng acceleratons up to 8.5 g accordng to that of the dynamc RCAR head restrant standards [29]. 5.1 Test Fxture Desgn The desgn of the nclned sled s characterzed by ts ablty to provde mpact loads to examne the effect of the acceleraton upon the moton of the head relatve to the torso. The exploded vew of the complete whplash test fxture desgn s shown n Fgure 5.2. The end supports act to secure two 2 dameter and two ½ dameter precson steel rals at 10 degrees to the horzontal. The lower end support shown n Fgure 5.2 s bolted to the floor to avod any unwanted moton of the fxture tself. In order to avod bndng ssues, the rals are fxed parallel to one another to wthn 1/1000 of an nch. The parallelsm of the ½ dameter rals are less of an ssue due to ther flexblty over ther 92 span. The other mportant components of the fxture desgn are the test sled to smulate the typcal acceleraton durng whplash, compresson sprngs to provde the desred overall sled acceleraton, and a release latch to ensure repeatablty between whplash test trals. The locaton of the release latch controls how far the test sled travels under the acceleraton due to gravty pror to contactng the fxture sprngs. Ths determnes the mpact velocty of the sled nto the sprngs and the peak acceleraton of the sled. The sprng stffness mass k sprng and sled m sled determne the approxmate collson tme for the experment based on the natural frequency of vbraton for a sprng and mass system accordng to equaton 5.1. Ths equaton 67

85 gnores the effects of head oscllaton, energy losses, and non-lnear sprng stffness on the response. t m sled collson (5.1) k sprng Four sprngs (2 on each ½ ral) are used n order to provde the desred stffness and load capacty for the system. The sprng stffness and sled mass for the fxture s gven n Table 5.1. Usng these values the total collson tme s calculated to be 0.083s whch s slghtly lower than the s collson tme typcally used for whplash testng [29]. In order to reduce hgh frequency vbratons from the fxture to the test sled, dampers were added on both ends of the sprngs. Fgure 5.1: Expermental whplash test fxture 68

86 Sled Table 5.1: Whplash test fxture parameters Descrpton Value (+/-) Unts Mass kg Sprngs Stffness N/m Neck Wde nstrumented mass kg Nomnal nstrumented mass kg Narrow nstrumented mass kg Head Mass kg Instrumented mass kg Center of gravty locaton (measured radally from CAD CoG) 2 5 mm Moment of Inerta kg m 2 The sled desgn wth the smulated head and neck s shown n Fgure 5.2. The sled conssts of an alumnum plate and block to provde a mountng surface for the lnear bearngs and smulated head. Four low-frcton 2 dameter lnear bearngs wth pllow blocks are used to support the sled loads and allow the sled to slde down the 8 precson rals. Two ½ dameter lnear bearngs wth pllow blocks are used to track along the ½ precson rals and transfer the loads from the fxture sprngs to the test sled. Dowel pns are nserted on the back sde of these pllow blocks to provde addtonal support durng loadng. The neck mountng block s frmly secured to the sled base usng four M8 fasteners. The smulated neck s secured to the sled by two fasteners sandwchng the neck between the neck block and neck plate. Ths ensures accurate algnment of the neck sample whle restrctng any undesrable deflecton n the regon below the T 1 vertebra locaton. 69

87 Fgure 5.2: Fxture sled assembly desgn 5.2 Head and Neck Desgn The smulated head and neck desgn used to capture the whplash response are shown n Fgures 5.3 and 5.5. These desgns capture the head propertes of the 50th percentle male and the stffness of the neck. The neck desgn chosen for modelng whplash s based on the beam fnte element model dscussed prevously. A bendng stffness of 9.2 Nm 2 s chosen to be roughly equvalent to the rgd lnkage jont stffness found for the smplest unform jont stffness jont dampng model. As a result, ths expermental testng can serve to valdate both methodologes developed n chapters 3 and 4. The bendng stffness EI s equal to the product of the modulus of elastcty for the materal E and the second moment of area I for a gven beam cross secton. A range of 70

88 materals and cross-secton desgns can be used to acheve ths desred beam flexblty. It s also mportant, however, that the beam wthstand the large deflectons and loads durng whplash wthout yeldng. The stress n a beam subjected to bendng s gven n equaton 5.2, as a functon of the moment about the neutral axs M, the perpendcular dstance from the neutral axs y, and the second moment of area about the neutral axs I. My (5.2) I For a gven materal, a certan second moment of area s requred to acheve the requred 9.2 Nm 2 bendng stffness. In ths case, both the appled moment (based on the whplash loadng) and second moment of area are constraned n equaton 5.2. In order to reduce the peak stress n the sample, the perpendcular dstance from the neutral axs must be lmted by makng the sample as thn as possble. The fnal desgn parameters usng AISI4130 steel to satsfy these requrements are shown n Tables 5.2 and 5.3. Ths materal s selected because of ts low cost and hgh strength and ductlty after heat treatment. Table 5.2: Expermental neck sample mass and heat treatment summary Neck Sample Mass [+/ ] (kg) Mass* [+/ ] (kg) Heat Treatment Narrow HRC (HT-1) Outsourced Nomnal HRC (HT-1) Outsourced Wde HRC (HT-2) In-house * Instrumented wth stran gauge Table 5.3: Expermental neck sample geometry and mechancal propertes Neck Sample Wdth [+/- 0.05] (mm) Thckness [+/- 0.01] (mm) E (GPa) I (x10-11 m 4 ) EI (N m 2 ) Value [+/-] Value [+/-] Value [+/-] Narrow Nomnal Wde

89 The neck samples are formed out of 2 plates of steel by cuttng them to the desred length and bendng them to the profle shown n Fgure 5.3. A template s used to ensure that each sample s made to the profle specfed on the drawng. Each of the bend locatons on the beam sample correspond to the locatons of the nstantaneous axes of rotaton for the 50th percentle male as provded n Table 3.2. Four neck samples and 3 tensle samples are made from the 4130 plate materal for testng and materal valdaton. The heat treatment and mass for each of the neck samples s gven n Table 5.2. The wde sample was heat treated n-house usng a conventonal oven to heat the sample to 855 degrees Celsus followed by a water quench and 480 degree Celsus temper. Ths caused sgnfcant carbon buldup and warpage of the sample so the other two test samples were outsourced to obtan ther heat treatment n a more controlled envronment. Fgure 5.3: Heat treated 4130 steel neck sample desgn The resultng materal propertes for each of the heat treatments and the base 4130 steel materal are shown n Fgure 5.4. For the nomnal wdth sample, ANSYS predcted a peak stress of 898 MPa at the base of the neck for the 8.5 g collson. In order to avod yeldng for ths aggressve loadng, the yeld pont for the materal should be above ths value. From Fgure 5.4, the yeld stress s 222 MPa, 747 MPa, and 1080 MPa for the vrgn (no heat treatment), HT-2, and HT-1 heat treatments. The yeld stress for the nomnal and narrow neck samples s well above the 72

90 Stress (MPa) expected maxmum stress durng whplash, so the materal should behave elastcally durng the response. For the wde neck sample wth HT-2 heat treatment, the maxmum stress s approxmately equal to the maxmum stress expected for the nomnal sample. Ths sample s desgned to be 25 % stffer than the nomnal sample, so lower deformatons and maxmum stress values are expected. Ths s confrmed by the expermental results for head deflectons durng whplash and the absence of observable yeldng n the neck sample after testng. The resultng bendng stffness for each of the neck samples tested s shown n Table HT HT Stran (%) Fgure 5.4: Neck materal propertes. The head s desgned to capture the mass and nerta of the 50th percentle male. In accordance wth the work of Grauer et al. [4] and matchng that of the analyss n chapters 3 and 4, the head s desgned to be 5.5 kg wth a moment of nerta of kg m 2. The head center of gravty s desgned to be located at the center of the slot where the neck attaches to the head. Ths ensures the center of mass of the head s postoned at the locaton correspondng to the tp of the neck sample. A robust attachment, usng 4 set screws, ensures that the head and neck are securely fastened to one another. The measured values for the fnal head specmen are shown n Table 5.1. These values show excellent agreement wth the desgn values n the computer aded desgn software SoldWorks. The moment of nerta of the head about the center of mass s found usng a bflar pendulum to suspend the head sample and observe ts perod of oscllaton [96, 97]. 73

91 Fgure 5.5: Head assembly 5.3 Imagng and Instrumentaton Accelerometers, stran gauges, and hgh speed photography are used to capture the moton of the sled, head, and neck durng whplash. Accelerometers are placed on the sled, along the axs of moton (x axs for analyss) and on the head n the local x and y drectons (algned wth the skull- C 1 neck segment). Durng the whplash moton, the rotaton of the head causes these local axes to rotate relatve to the global x and y coordnates, so the orentaton of the head at a gven tme s used to resolve these acceleratons nto ther components n the global x and y drectons. A stran gauge s placed at the base of the neck to montor the peak stress observed durng the experments. The stran gauge s connected to a Wheatstone brdge and an amplfer crcut to amplfy the output sgnal. A measurement computng analog to dgtal converter (USB-1608FS) s used to transfer the data to the local computer. Two dfferent accelerometers are used for the 74

92 measurements and data acquston: () Kstler 8632C50 and () Measurement Specaltes ACH- 01. Both accelerometers requre dfferent electrcal confguratons wth the Kstler accelerometers requrng a constant current source and the ACH-01 accelerometer requrng a constant voltage source and amplfer for the output sgnal. The crcut dagram for each of the accelerometers s ncluded n appendx B. Fgure 5.6 demonstrates the whplash test fxture setup ncludng the Fastec Imagng TSHRMS hgh-speed camera and Lowel 250 W adjustable lght source. Fgure 5.6: Moton capture nstrumentaton for whplash test fxture Fgure 5.7 demonstrates the reflectve targets appled to the sled, head, and neck to accurately assess the whplash moton. Two reflectve targets on the sled are used to ensure the camera frame s algned wth the drecton of the sled moton. The reflectve targets on the sled (x drecton) and vertcal sled block (y drecton) are spaced apart by 200 mm to provde accurate scalng of the moton capture mages. The dstance from the camera to the x-axs sled ponts, y- axs sled ponts, head and neck are used to scale the motons observed usng the moton capture software. Three ponts on the head are used to defne the locaton of the center of gravty of the head (mddle reflectve target on head) and the rotaton of the head at each tme step. Addtonal 75

93 reflectve targets are placed on the nstantaneous axes of rotaton at the C 7 -T 1 jont up to the Skull-C 1 jont. Fgure 5.7: Expermental reflectve targets for hgh-speed moton capture 5.4 Moton Capture Software Moton capture software, developed by Ben Cornwell-Mott n the Mechancs and Aerospace Desgn Lab, s used to record the locaton of each of the reflectve targets over tme. The software works by analyzng each frame to determne the locaton of each of the reflectve locatons and assgns a number to each locaton. The numerc center of a cluster of pxels above a certan brghtness range s chosen for that locaton. A typcal frame durng the whplash moton s shown n Fgure 5.8. For each successve frame, the software attempts to mantan the numberng structure for the ponts that dd not move beyond a gven range between frames. If the pont moves beyond ths zone between frames, a new unused number s assgned to that locaton. Durng the analyss, multple numbers correspondng to the same reflectve target are sttched together to provde the response of that target over the entre test run. Ths methodology s found to provde a very good overall assessment of the whplash moton over tme. In some cases, ponts are found to dsappear or shft as nterferng reflectve areas nfluence the reflectve center locaton. Frame corrupton s also an occasonal ssue where ndvdual frames are unreadable. These ssues posed no dffculty when analyzng the whplash postons over tme but are an ssue when the veloctes and acceleratons of the assocated moton are consdered. Dgtal smoothng 76

94 of the data s used to overcome ths ssue and ponts assocated wth dscontnutes n the poston data have been removed as requred. Fgure 5.8: Typcal moton trackng frame for head, neck, and sled durng whplash 5.5 Typcal Dynamc Results The typcal dynamc results for the whplash moton are shown for the wde sample n the followng fgures. For both the accelerometer and moton capture data, smoothng s used to dgtally flter out the expermental nose. The smoothng s appled accordng to equaton 5.3, where the smoothed value smoothed 1 s a functon of the smoothng factor, unsmoothed value x 1, and prevous smoothed value smoothed. For the moton capture data, the poston data s smoothed usng a smoothng factor of 0.18 for the wde and nomnal neck samples (usng a camera frame rate of 250 frames per second) and smoothng factor of 0.02 for the narrow neck sample for a camera frame rate of 1000 frames per second. The accelerometer data s smoothed usng a 0.18 smoothng factor. Note that ths s the dgtal equvalent of applyng a low pass flter to the accelerometer output sgnal. smoothed x 1 1 smoothed 1 (5.3) The 8.5 g expermental sled acceleraton s shown n Fgure 5.9. The ntal collson tme s taken as the tme correspondng to the maxmum sled velocty pror to the collson. The collson tme s 170 ms for the collson based on the moton capture data. The peak sled acceleraton s 5 g for the collson. Both accelerometers are not found to provde a good assessment of the collson 77