I NTRODUCTI ON

MEASUREMENT OF HEAD I MPACT RESPONSE

N . M. A lem , R. L . Sta l naker , J . W . Mel v i n H i ghway Safety Research Insti tute Ann Arbor , Mi chi gan 481 09 U . S . A .

Of great i mportance to quanti tati ve eval uation o f i nj ury to the human head i s the abi l i ty to descri be the mechani cal response of the head when subjected to d i rect i mpact . I n the past fi fteen years , great s tri des have been taken i n th i s d i recti on . Studi es [ l ] have been made to eval uate the effects of trans­l ational and rotati onal head mot i on on the i njury patterns . Other stud i es [2] stressed the i mportance of bra i n pressuri zation duri ng i mpact to the rea l i sti c reproducti on of brai n i nj uries .

The l ack of defi n i t i ve i mpact- i nj ury correl ati on i s partly due to the fai l ure to measure accurately the ki nemat ics of head moti on and the bra i n pres­sure fl uctuati ons i n a l aboratory envi ronment . Early research succeeded only i n measuri ng pl anar head moti on , ei ther by use of accel erometer pai rs [3] or by photometri c analyses [4] . These methods assumed that the head motion was essenti a l ly p l a na r , and that the accel erometer pa i r or the fi l m pl ane was para l l el to the p l ane of moti on . Unle s s the i mpact i s conducted under h i gh ly contro l l ed envi ronment , these assumpti ons are not val i d . Only recently were researchers i n the fie l d of b iomechani cs abl e to measure compl etely the general 3- D mot i on of the head under i mpact [5 , 6 , 7 ] .

Another i mportant factor i n s uccessful experi mental head i nj ury research i s the abi l i ty to use s ubjects wh i ch represent , as c l ose ly as pos s i bl e , the l i vi ng human head . l t was found [2 ] that the pressuri zed head of unembalmed cadaver provi des the best s urrogate to l i vi ng human head .

The obj ect of th i s paper i s to describe the techni ques used for measure­ment of : a ) the fl uctuation of the bra i n pressure � and b ) the 3-0 ki nematics of head mot i on . These techniques were devel oped over the l as t two years and have been app l i ed s uccessfu l ly to measure head moti ons of anthropometri c dummies and cadavers i n non- i mpact car occupant s imul ati ons [8] , and of fi fteen cadaver head i mpacts [9 ] .

PRESSURI ZAT ION

Brai n vascul ar pressuri zati on was attempted i n the early tes ts of our head i mpact research program wi th varyi ng degrees of s uccess . The techn ique was modi fi ed i n the l ater phases of the program to produce more sati sfactory re­s u l ts . The techni que descri bed be l ow i s based on mod i fi cation of the method devel oped by Fayon et a l . [2] , and was found to produce sati s factory pressuri ­zation of the bra i n .

The catheter used for pumpi ng fl u i d i n the vascu l ar system cons i s ted of a Fol ey bal l oon catheter i n whi ch the center section was rep l aced by sui tab le l engths af polyethyl ene tubi ng . Two tubes were necessary : one connected to the i n l et end of the catheter for pressuri zi ng , and another connected to the tip end of the catheter for bal l oon i nfl ati on . A smal l l ead pel l et was i n­serted at the ti p of the catheter for radi ographi c veri fi cation of i ts l ocati on

duri ng i nsert i on . To a l l ow the fl u i d to f low i nto the occl uded b l ood vessel s , ho l e s were made i n the end of the pressuri zati on tube j u st before the bal l oon .

I n order to measure oressure i n the i n ternal carotid artery a s close as pos s i b l e to the brai n , the bal l oon was i nserted through the carot i d artery and down i nto the descendi nq aorta j us t oast the branch of the l eft subcl avi an ar­tery to provi de for pressuri zation through both the l eft and right caroti d ar­teri es . One end of a s econd secti on of pol yethy l ene tub i ng was i nserted i nto the ascending aorta , whi l e the other end was i nserted i nto the i nterna l caro­t id artery . Fi nal l y , i n order to measure the vascu l ar pressure , a thi rd tube was i nserted i nto the i nternal carot id artery to a l l ow a mi ni ature Kul i te pres­sure transducer to be pl aced near the base of the brai n . Once a l l tubes have been pl aced i n the appropri ate arteri es , the caroti d i nc i s i on was sea l ed . The pressuri zati on fl u i d u sed was a mi xture of water and b l ack i nd i a i n k whi ch can eas i l y be i denti fied duri ng autopsy to mark ruptures due to impact .

Just before the impact test , the catheter bal l oon was i nfl ated to b l ock the descendi ng aorta . Then , u s i ng a 5- l i ter contai ner as the water i nk reser­voi r , th i s fl u i d was forced i nto the pressuri zati on tube by pumpi ng a i r i nto the fl u i d contai ner . The a i r p ressure was i ncreased unti l a s teady 1 20 mm Hg vascu l ar pressure was i ndi cated .

Thi s techni que was app l i ed to the l as t fi ve tests of a series of 1 5 head impact tests , and a l l fi ve oroduced satisfactory pressure readi ngs . The transducer output was recorded on ana l og tape , and l ater was d igi t i zed and fi l tered , then p lotted for exami nati on . Typi ca l press u re transducer outputs are shown i n Fi gure l , a l ong wi th the i mpact force appl i ed to the head .

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Fi gure l . Time h i s tories of i mpact force and resul ti ng vascul ar pressure for two head di rect i mpact tests .

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HEAD MOTION

The method used by HSRI for comp l ete measurement of the general 3-D head motion i s based on a techni que used by Cal span [ 1 0 ] to measure the moti on of vehi cl es under s imul ated crashes .

The HSRI method uses 3 tri axi a l l i near accel erometers ri g id ly attached to the s ku l l at 3 arb itrary conveni ent poi nts . The readi ngs of the 9 i nd i v i dual �ccel erometers are mathemati cal l y man ipu l ated to produce a compl ete descri ption of the rigi d-body head moti on , whi ch cons i sts of time h i s tori es of angu lar ac­cel erati on and ve l oci ty vectors , the Eul er ang les and thei r time deri vati ves ( rates ) , the tran s l ati onal accel era ti on vector of any des i red head poi nt ( usu­a l ly the anatomi ca l center) expressed i n the anatomi cal and the l aboratory in­ert i a l reference frames , and fi na l l y , the trans l ati onal vel o c i ty and pos i ti on vectors of that point w i th respect to the fi xed l aboratory reference frame .

Thi s measurement system i nvol ves 3 reference frames : a ) the instrumentation frame ( e1 , e2 , e3 ) , defined by the l ocati ons and ori entati ons of the 3 tri axi al acce lerometers , wh ich i s embedded i n the movi ng head ; b ) the anatomica l refer­ence frame ( i , j , k ) defined by anatomica l l andmarks ( two i n fraorbi tal notches and two upper edges of the audi tory meati ) , i n whi ch the components of the an­gul ar acce l erat i on and vel oc i ty vectors wi l l be expressed ; and c) the l aborato­ry reference frame ( I ,J , K ) , assumed to be i nerti a l to whi ch the angu l ar ori en­tation of the head as wel l as i ts trans l ati onal accel erati on , ve l oci ty and po­s i t ion wi l l be referred .

Once a cadaver i s se l ected for an i mpact tes t , certai n procedures are fol ­l owed i n order to i n strument the head for 3-D moti on measurement . The total measurement protocol cons i s ts of four phases : a ) attach the accel erometer mounts ri g i dl y to the sku l l and a l i gn the sens i ti ve axes i n 3 orthogonal di rec­ti ons , b ) x- ray the head twi ce to determi ne the l ocati on and ori entation of the i nstrumentation frame ( e1 , e2 , e 3 ) wi th respect to the standard anatomi cal frame ( i , j , k ) , c) I n sta l l 9 accel erometers in thei r mounts , conduct the test , record the s i gna l s then di gi ti ze them for computer analys i s , and fi nal ly d ) perform computer cal cul at ion of 3-D head motion u s i ng the 9 d i gi ti zed s i gnal s together w i th the transformati on obtai ned from x- ray analys i s and the test i ni ti a l condi t i ons . The fol l owi ng secti ons descri be the methods used for phases a , b and d above .

ACCELEROMETER MOUNTING

Three s i tes on the s ku l l are sel ected away from the i n tended impact l oca­ti on , so that they prov ide the maximum separati on between the triaxi a l acce lero­meters . The s ca l p was l oca l ly removed expos ing the skul l whi ch i s then c l eaned and dri ed . For each moun t , 3 pi l o t ho les are dri l l ed i n the s ku l l , maki ng sure the bra i n was untouched , to a l l ow three screws to be attached to the skul l . A steel wi re i s wrapped around the 3 parti a l l y exposed screws formi ng an area where the accel erometer mount i s p l aced . I n order to ensure the orthogona l i ty of the sen s i t i ve axes of the accel erometers , a spec i a l a l umi num j i g , s hown i n fi gure 2 , i s p l aced over the 3 mounts wh i ch are then secured to the wi res and screws wi th dental acry l i c . The acryl i c i s a l l owed to harden for about 30 mi n­utes bef6re removing the j i g and l eavi ng the three mounts r ig id ly attached to the s kul l , as shown i n Fi gure 3 .

Fi gure 2 . Spec i a l a l i gnment j i g used to i ns ure orthogonal i ty of 9 acce l erometers . and to measure d i stances from each tri axi a l mount to the ori g i n of the i nstrumentation reference system .

X- RAY MEASUREMENTS

For the purposes of compari ng resu l ts from vari ous head impact tests at vari ous research l aboratories , a s tandard reference frame must be used . Such frame adopted for the head i s based on the Frankfort p l ane of the s ku l l defi ned by the two i nfraorb i ta l notches and the two upper edges of the audi tory meati . Si nce the i ns trumentation frame does not co i nc i de wi th the s tandard anatomi cal frame , i t is necessary to transform the accel eration readi ngs from the ( e1 , e2 , , e3 ) frame to the ( i , j , k ) frame . Thi s requi res the knowl edge of the orthogonal transformation matri x between them . To th i s end , a 3-d imens i onal x-ray tech­n i que was devel oped to comoute s pace in the ( x ,y , z ) coord i nates of the 4 ana­tom i ca l l andmarks whi ch defi ne the anatomi cal frame , and those of the 3 centers of tri axi a l acce l e rometers , whi ch defi ne the i ns trumentation frame . These poi nts a re i denti fied on the radi ographs by smal l l ead pel l ets wh i ch are p l aced at the seven l ocati ons . The x-ray procedure i s to take two orthogonal radi ographs of the i nstrumented head , p l aced i n a pre-ca l i brated x-ray fi el d . Each x- ray fi l m i s analyzed to obta i n ( x ,y ) or ( x , z ) fi l m coordi nate pa i rs for the seven poi nts , whi ch are then combi ned to produce the true l aboratory ( x ,y , z ) coordi nates of these seven poi nts . Once th i s i s done , the transforma­t i on matri x between the i nstrumentation and anatomi cal frames i s obta i ned . The accuracy of th i s method was found to be sati sfactory wi th errors i n x , y or z not exceedi ng 2 mm , whi ch corresnonds to axi s mi sal i gnment of about l degree .

Fi gure 3 . I nsta l l ation of tri axi a l ac9e] erometer mounts(on

) cadaver

head (A ) s i te preparation , t B ) secur i ng wi re C fi nal confi guration of 3 mounts . The fourth central c i te i s for cable t ie down .

HEAD MOTION KI NEMAT I CS

The three tri axi al accel erometers provi de t ime h i s tories of the 3 accel era­t ion vectors at three l ocations Q1 , Q2 and Q3 • These vectors !_1 , i:.z , and .i_3 are then expressed i n the anatomi cal frame ( i ,j , k ) u s i ng the orthogonal matri x determi ned from radi ographs . Assumi ng that the 3 accel erometers are mounted an a r i g i d body , i t i s poss i b l e to wri te :

r = r + � X D .� + w X w X o _ ; ( n = 1 , 2 , 3 ) -n -0 - "'-fl - - "'-fl ( 1 ) where r i s the accel eration vector of a body reference point Q0 ,

w� w a re angu l ar accel erati on and vel oci ty vectors of the head , and E.n Ts the pos i ti on vector of On ( nth accel erometer center ) re l at i ve to

the reference poi nt Q0 , known from radi ographs . I n equation ( 1 ) above , the io , � and w are unknown , whi l e .in and 2.o ( n = 1 , 2 , 3 ) are known. However , s i nce w i s the time deri vati ve of w the pr1 mary unknowns are fo and �· Thus , when thi s-equation i s expanded , i t resu l ts i n n i ne sca l ar di fferenti a l equati ons i n s i x unknown s . The overdetermined system of equati ons may be reduced and parti a l l y uncoupl ed by tak i ng advantage of the redundancy to mi n i mi ze experimental errors .

For each tri axi a l accel erometer , equati on ( 1 ) i s wri tten as :

(r0} -

[p n ] {� } + [w] { [w ] { p n } } - { rn} = O ; ( n = 1 , 2 ,3 ) ( 2 )

where { } i ndi cates a col umn ( 3 x 1 ) matri x of the anatomi cal components o f a gi ven vector , and [ ] i s a s kew-symmetri c ( 3 x 3 ) square matri x ,

e . g . : and [w ] = [ �3 �w3 _:�]

-w2 w 1 0 i n wh i ch the s ubscri pts 1 , 2 , 3 i nd i cate the anatomi cal i , j and k di recti ons , respecti vely . The 3 matri x equations descri bed i n equation ( 2 ) may be further compressed i nto a s i ng l e matri x equation

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Because o f the errors i nevi tably present i n the 9 accel erat ion readi ngs , i . e . , i n the components of { r1 } , { r2 } and { r3 } , the l eft-hand s i de of equa­tion ( 3 ) i s never exactly zero , but rather a smal l ( 9 x 1 ) error vector { d :

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Th i s error may be mi ni mi zed by search i ng for a s o l u ti on wh i ch nul l i fi es the parti a l deri vati ves of the squared error wi th respect to the unknowns . For the angul ar accel erati on vector , th i s cri terion reduces to :

T a { d { d = 0 a {� }

By sel ecti ng the reference ooi nt Q0 as the centro i d of the 3 tri axi a l acce l e rometer centers Q1 , ·02 and Q3 , two thi ngs occur : one is the immedi ate sol uti on for f rei } , the other i s the s i mp l i fi cation of equati on ( 5 ) .

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{ r0 } = 1 /3 { {r1 l + {r2 l + { r 3 l } {�} = [[R]T [RJ]- l [R]T { V}

( 6 )

( 7 )

Equati on ( 7 ) i s a system of 3 s imul taneous di fferenti a l equati ons wh i ch �an be sol ved by numeri cal techniques , wh ich res ul ts i n 3 components of {w} and {w} . Such techni ques , publ i shed el s ewhere [6] , wi l l not be di scussed i n thi s paper .

I - { I /

VAL I DATION OF THE METHOD

In order to val i date the HSRI 9-accel erometer method , a compl etely known 3-D motion was mathemati ca l ly imposed on a hypotheti cal ri gi d body , to wh i ch three hypotheti ca l tri axia l accel erometers were attached . The n i ne accel era­tion readi ngs were cal cu l ated , then used i n the HSRI 3-0 moti on ana lys i s pack­age to produce a compl ete descri pt ion of the moti on . The cal cu l ated motion was then compared to the exactly known moti o n , by ca lcu l ati ng the devi ation between the exact and cal cul ated outputs . Typi cal resul ts are d i s cussed on the next page .

Exper imental val i dation of the method i s more di ffi cul t s i nce i t i s ex­tremely di ffi cu l t to experimental ly produce a prec i se ly known 3 -D motion . How­ever , one non- impact test was conducted to measure the 3 -D mot i on of an em­balmed cadaver head . I n addi tion to the 9-accelerometer i nstrumentati on , a tri ax i a l accel erometer was mounted at the base öf the s ku l l and i ts l ocation was detenni ned wi th the x-ray techni que descri bed earl ier . Us i ng the 3-D analys i s package , the tran s l ati onal accel erati ons of the center of mass of the tri axi a l acce l erometers were computed and compared to the actua l readi ngs at that poi nt . Fi gure 4 s hows the actual and cal cul ated read i ngs of thi s poi nt, and s hows an excepti onal ly good agreement .

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I n one hypothetical cas e , the exact ( except for truncation errors ) s imu­l ated n i ne accel eration readi ngs were used i n the 3-D analys i s to compute the angu l ar vel oci ty and accel erati o n , whi ch were then compared to thei r known exact val ues . The dev i ations between cal cul a ted and exact moti o n , s hown i n fi gure 5 , are i ns i gn i fi cant . I n real s i tuati ons , however , experimenta l errors are i nevi tab l e i n readi ng the 9 di fferent accel erations�

An i n-depth s tudy of the accuracy of thi s and other methods i s underway at HSRI , and i ts resu l ts wi l l be publ i s hed when comp l eted . Th i s accuracy depends l argely on the experimental errors commi tted i n measuri ng the 9-accel erati ons . The major sources of errors are : a ) mi s l ocation and m i sa l i gnment of the tri ­axi a l mounts , b ) ca l i bra ti on errors due to the sens i ti v i ty l imi tati ons of the accel erometers , c) noi se i n the transducer s i gnal s , e i ther external to the mo­tion or resu l t ing from cross-axi s sens i ti vi ty of the transducers i tsel f , and fi nal l y , d ) zero-bi as of the s i qnal s resu l t i ng from mi s - adj ustment of the equi p­ment. Most of these errors can be reduced , however , errors such as cross-ax i s sens i t ivi ty , cal i brat ion and mi sal i qnment are i nherent i n most accel erometers , and cannot be avoi ded . The use of redundant accel erometers , and thei r analys i s wi th l east squares techni ques reduce thei r effects and produce acceptabl e three­di mens i ona l moti on measurement .

SOME I MPACT RESULTS

Fi fteen cadaver heads , comol etely i nstrumented wi th 9-accel erometer pack­age , were di rectly i mpacted from front , rear and s i de . The transducer outputs were recorded on analog tape , whi ch was subsequently p l ayed back for d i g i ti zi ng , di g i ta l fi l teri ng and 3- D head moti on analyses . Limi ted s pace a l l ows to s how the parti a l res u l ts of only three tests , gi ven i n fi gures 6 , 7 and 8 . Compl ete test resu l ts are bei nq presented e l s ewhere [9 ] .

CONCLUS IONS

1 . A brai n vascu l ar oressuri zation technique wh i ch a l l ows adequate per­fus i on of the brai n , rel i ab l e moni tori ng of dynami c pressures during impact and l ocati ng of i nj ury s i tes has been developed .

2 . Three-d imensi onal accel erometry techni ques us ing n i ne accel erometers i n three tri axi a l c l usters was found to be appl i cabl e i n di rect head i mpacts .

3 . The acce l erometry method of HSRI has the advantages of s impl e mounti ng on the cadaver head and i ncreased accuracy due to l arge separation of the tri ­ax i a 1 c 1 us ters .

4 . The analys i s method resul ts i n the best ( i n the l east squares sense) sol uti on for the angu l ar moti on , a defi ni te advantage when dea l i ng wi th experi ­mental data .

ACKNOWLEDGMENTS

Th i s work was supported i n part by the General Motors Research Labora­tori es , the Motor Veh i c l e Manufacturers Associ ation and the Nati onal Hi ghway Traffi c Safety Admi n i s trati on . The authors woul d l i ke to a l s o recogni ze the s i gni fi cant contri buti ons of J . B . Benson and G . S . Nushol tz to the devel op­ment of the experi mental techni ques .

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REFERENCES

l . T . A . Gennarel l i , L . E . Th i bau l t and A. K . Ommaya , 1 1 Pathophys io logi c Re­s ponses to Rotational and Trans l ati onal Accel erati ons . 1 1 Paper 7 20970 , S i xteenth Stapp Car Crash Conf . , SAE 1 972 .

2 . A . Fayon et al . , 11Thorax of 3-Poi nt Bel t Wearers Duri ng a Crash . " Proc . N i neteenth Stapp Car Crash Conf . , paper 751 1 48 , SAE 1 97 5 .

3 . H . J . Mertz and L . M . Patri ck , " I nvesti gation of the Ki nemati cs and Ki ne­t i cs of Whi p l as h . 1 1 Proc . El eventh Stapp Car Crash Conf . , SAE 1 967 .

4 . R . L . Stal naker , V . L . Roberts and J . H . McE l haney , " Door Crashworthi ness Cri teri a . 1 1 Report DOT HS-800-924 , National Techni cal I nformation Servi ce , 1 973 .

5 . E . Becker and G . Wi l l ems , 11An Experimental ly Val i dated 3-0 I nert ia l Trac k­i ng Package for Appl i cati on i n Bi odynami c Research . " Paper 751 1 73 , Proc . N i neteenth Stapp Car Crash Conf . , SAE 1 97 5 .

6 . R . L . Stal naker , N . M . Al em , J . B . Benson and J . W . Mel v i n , 1 1 Va l i dati on Stud i es for Head Impact Injury Model . " Fi nal Report on Contract DOT-HS-031 -3-749 , H i ghway Safety Research I nsti tute , 1 97 5 .

7 . A . J . Padgaonkar , K . W . Kri eger and A . I . Ki ng , "Measurement o f Angu l ar Acce l erati on of Ri g id Body Us i ng Li near Acce l e rometers . 1 1 ASME paper No . 75- APBM- 3 , 1 97 5 .

8 . N . M . Al em , J . B . Benson and J . W . Mel vi n , 11Who l e Body Response Research Program . 11 Fi nal Report No . UM- HSRI-76- 3 , Hi ghway Safety Research i nsti tute , 1 97 6 .

9 . R . L . Sta 1 naker e t a 1 . , " H e a d Impact Response . 1 1 To be presented a t the Twenty-fi rst Stapp Car Crash Conference i n New Orl eans , Lou i s i ana i n October 1 977 .

1 0 . J . A . Bartz and F . E . Butl er , 1 1Passenger Compartment wi th S i x Degrees of Freedom. 11 Auxi l i ary Program to "Three- Dimensi onal Computer S imu l ati on of a Motor Veh i c l e Crash Vi ctim . 1 1 Fi nal Techn� cal Report on DOT Contract No . FH- 1 1 -759 2 , 1 972 .

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