A GEHERALIZED ACCELERATION MODEL FOR BRAIN INJURY THRESHOLD (GAMBIT) James A. Newman

Biokinetics and Associates Limited Ottawa , Canada

ABSTRACT

A c r i t e ri o n f o r brain inj ury threshold i s proposed w h i c h , for the f i r s t time, endeavours to take into consideration the combined effects of both t rans l a t ional and rotat ional kinema t i cs. The val i d i t y of the mode l is as s e s s ed by w ay of a review of a l l known head inj u ry data bases in which translational and rotational accelerations have been monitored. Available data appears to support no more than a simple linear proportioning of the two types of motion though a squared weighting, as originally proposed (and which intuitively is more plaus ible) also seems valid.

INTK.ODUCfION

The asses s ment of safety systems , and in particular, those associated with the u s e , and a c c idental c o l l i s ion of automob i le s , r e q u i r e s the u s e of a criterion by which the relative likelihood of brain injury , or protection therefrom, can be evaluated.

The generalized model for brain in]ury threshold (GAMBIT) , first introduced in 1985 ( 1 ) , borrows from class i cal engineering treatment of the design of systems in which combined axial and shear s tresses are both simultaneously generated because of the particular location and direction of the applied load. The premise for such an approach (in inanimate engineering systems ) is that whatever the combination of normal and shear stresses, the material failure can be forecast on the basis of an assumed "equivalent" maximum principal or shear s t ress or s t rain. GAMBIT treats induced translational acceleration and rotational acceleration as if they could be regarded as stresses and considers that "failure" due to such combined loading is, in the case of the brain, brain injury.

The original GAMBIT equation is of the form:

where a ( t ) and a.( t ) are the ins t antaneou s values of t ranslational and r o t a t i onal a c c e l e r a t i on r e s p e c t i ve ly and n, m , and s are e m p i r i c a l c o n s t a n t s s e l e c t e d t o f i t the avai lable data. n = m = s = 1 is a s i mple linear weighting of the translational and rotational components (Gl ). n =

m = s = 2 provides an elliptical function in the two kinds of motion (G2).

The assignment of a failure criterion for brain injury, can be handled in a va r i e t y of w ay s . One cou l d , f o r exa m p l e , s e t some l i m i t ing value o f AIS from 1 to 6. Alternatively, one might specify some particular inJury, such as a mild concussion, as the appropriate limit. To a certain degree, this

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mat ter is largely philosophic. In safety system evaluation, judgement as to what system is acceptable and which is not, requires the definition of an " a c c e p t ab l e " brain inju ry. In the case of brain inj u ry , the GAMBIT ass igns t o both the t rans la t i onal and t h e r o t a t i onal a c c e l e rat i o n a l i m i t i n g or c r i t ical value beyond w h i ch ( i n t h e case o f "pure" inert i a l loading) an "unacceptable" injury would occur. ac and Q'.c are the limiting "criti cal" values. These same limits are presumed to remain valid when the brain is loaded by the combined ef f ects of both f orms of motion.

Regrettably, very litt le "pure motion" limiting data for brain damage has been generated. In most experiments conducted to inves tigate "tolerance" limit s , both forms of motion have usually been present. Critical limits will thus have to await more suitable experiments or must rely, as we shall for the present, on extrapolation.

The one major difference between the classical engineering problem and the one under cons ideration h e r e is that brain inj u ry is a s s o c i a t e d w i t h ine r t i a l loading which i s t i m e variant. Be cause o f t h i s , i t has been cons i d e r ed approp r i a t e t o c o n t i nuously mon i t o r t h e "equivalent l o a d " throughout the duration of the event. I f at some time during the event the value of G exceeds 1 , a " f a i l u r e " is noted. G = 1 thus is a boundary i n t h e a- p lane beyond which t h e s y s t e m f a i l s and w i thin w h i ch the s y s t e m passes. The concept is illustrated s chematically in Figure 1 .

300

Vi 200 L!l

...J a: z 0 ...... a: ...J V1 z 1 00 a: Cl:: ......

0 0

THRESHOLO BOUHORRY

FAil G(t)>1

PA S S G(t)<1

500 000 500 ROTAT l ONAL IRAO/SEC/SECI

Figure 1 : Hypothetical GAMBIT Boundaries Gl - Linear. G2 - Eliptical

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1 0000

MODEL VALIDATION

Data Suitability

Expe r i me n t a l evidence that might be u s e d t o validate any form of injury c r i t e ri on has been charact e r i s t i ca l l y confined t o that gathered f rom cadavers , animals , volunteers and, to a limited degree, accident victims. The maj o r i t y of pu b l i s hed a t t e m p t s to derive t ol erance l i m i t s f rom such s t u d i e s has c o n s i d e r e d i nj u ry m e c h a n i s m s and t h e i r r e l a t i o n to translational or linear phenomena only.

The me r i t s and l i m i t a t ions of each of t h e various surrogates have been reviewed extensively in the literature. I n the present S i tu a t i on, t h e s e limitations are even more res trictive as GAMBIT requires information not only on inj ury and linear kinemat i c s , but a l s o on, or at leas t means t o es tablish, rotational motion.

Whatever data there is , it is res t ricted in its usefulness by virtue of at least the following considerations:

1 . Cadaver experiments can, at bes t , provide insight into brain injuries of AIS 3 or more only. Phy s i ca l d i s rup t i on of brain t i s sue may be o b s e rved in cadaver au t o p s i e s by t h e ext ravasat ion of f lu i d dyes inj ected into the arterial system before impact. However, so-called diffuse axonal injuries (DAI) associated with brain cell damage, which might appear as concussion or generalized diffuse brain injury are not v i s u a lly evident.

2 . Ani mal exp e r i ments do p e r m i t t h e obs e rvat i on o f the e f f e c t s of an impact resulting in minor injuries. Animals will exhibit concussion and/or temp orary brain d i s funct ion. Howeve r , of cou r s e , excep t through dubious methods of s ca l i n g , s u ch data cann o t provide nu meri cal l i m i t s d i r e c t ly appl i cable t o humans. Trends (if t hey exis t ) howeve r , can be d i s cerned and can lend s u p p o r t to ( o r dis credit ) a particular model .

3 . E xp e r i me n t s w i t h volunt e e r s are a lw ay s l i m i t ed t o non-inj u r i ous s i tu a t i ons bu t , as such, can p o s s i b ly p rovide lower bounds on tolerance limi t s .

4 . A c c i dent vi c t i ms can b e s ubj e c t t o t h e e n t i re range of brain injury bu t , except for very special c as e s , are a s s o c i ated w i th too many unknowns to be of much value in a validation exercise.

Data Processing Dif ficulties

Until recently , only passing consideration was given to the effects that digital filtering of raw data has on correlations that might exist between various parameters. lt is now becoming very apparent that processing of data through these means cons titutes a s omewhat subj ective and sensitive f o r m of data man i p u l a t i on. To a g r e a t e x t e n t , the degree to which any correlation may be true, is highly dependent on the choice of filter type, cut-off frequency, etc.

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R o t a t i onal accelerat i ons mu s t be comp u t ed from meas u red t rans l a t i onal acceleration measured at known s ites on a rigid body.

Nusholtz (2) and Burkhard (3) have both examined the ef fects of filtering on the computation of angular accelerations f rom linear data. The ef f ects can be pronounced as i l lu s trated in Figure 2. H e r e , trans lational acceleration has been cross-plotted against rotational acceleration for one of the cadaver tests described by Nusholtz et al (2).

� 200 ..... a: 0:: w _J LU u lf 1 50

_J a: z 0

§ 100 V'\ z a: 0:: ..... ..... � 50 ..... _J :::> V'\ w 0::

,.-·f;;�.-;.-.�.:.:.�.-

-------·--·----------„„„ „„„ ( : ··... ·:::„ ... „„ ... �

. i ... „.�����:_<:�::_::_�;;;;;.;::-------·„ .. „._„„„„„„„„„„·„-„„

···· ....

"„ ··„„.:„„„ ------ .::::;;:��!-----'� 2 3 4 5 6 7

RESULTANT ANGULAR ACCELERAT!ON !krod/s/sl B 9 1 0

Figure 2 : Effects of Data Filtering on GAMBIT Locus (Data from Reference 2 )

The data cannot be used directly for GAMBIT validation for these data are with reference to the origin of the instrument cluster not the anatomical center of the head. The same effects would however be expected at the head centre of gravi ty. Notw i t h s t anding t h e s e e f f e c t s , both au thors s ee m to agree that, for cadaver and Hybrid III ATD heads, f ourth order Butterworth f i l t er s w i th a cu t-off frequency in the 4 00-500 Hz range on the l i near accelerometer data provide a good approxima t i on to the r i g i d body i d e a l i z ation of inert i a l inj u ry c r i t e r i a , ( i. e . , s e cond and third o r d e r vibrational modes are effectively extracted f rom the data).

In addition, however, there are several inherent problems with linear axial accelerometery (3). First , one must have precise knowledge of the centre of gravity ( ma s s ) of the obj e c t , as the motion of t h i s point d i c t a t e s the nature of the computed r o t a t i onal componen t s . S e condly, accelerome t e r cross-talk, which may be as high as 5 % with contemporary instruments , leads to s erious errors in calculation of orthogonal d i re c t ion accelerations. Thirdly, very precise calibration and alignment of the accelerometers is requi red. S light e r r o rs i n ei ther of these can p roduce very large computational errors.

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CADAVER HKAD IMPACT TESTS

In 1 984, Nusholtz et al. (4) , reported on nineteen tests conducted on nine d i f f e rent cadaver s p e c i mens. The reader i s ref erred t o the original publication for a full description of the tes t protocol and methodology.

M o s t s igni f i ca n t ly, a nine a c ce le r o m e t e r c lu s t e r was emp loyed and rotational accelerations were computed. Unfortunately (f rom the present p o i n t of v i e w ) , the t e s t s were n o t i n t ended t o provide kinema t i c-inj u ry correlations. In mos t cases , the specimens were irnpacted more than once before autopsy was perf ormed. One cannot , as a consequence, determine if an injury, if i t is observed, is associated with the first or a subsequent i mp a c t or if indeed i t rep r e s e n t s the cumu l a t ive e f f e c t of mul t i p l e impact s .

A m ongs t t h e da t a , there exi s t s t w o t e s t s ( 8 2 E0 4 1 and 8 2 E0 6 1 ) t h a t are o f i n t e res t t o t h e p r e s e n t s tudy. B o t h t e s t s involved ident i c a l i ni t i a l conditions of padded forehead impact t o a s eated repressurized cadaver. In both cases the specimens were impacted twice at the same level. The data were processed with identical sof tware and filtered at 800 Hz with a s ixth order Butterworth filter (sufficient to exclude most of the spurious skull vi bra t i on response).

T h e 82E04 1 cadaver s u s t ained s u barachnoid h e m a t o m a at t h e right f ront a l lobe and subarachnoid he morrhage i n t h e p a r i e t a l a r e a. S p e c i men 8 2E 0 6 l s u s t ained no i n j u ry. The GAMBIT l o c i i f o r t h e s e two cases is s hown in F i gure 3.

z Cl 200 .... � w ...J w u � 150

...J a: z Cl .... 5 100 Vl ff et: .... .... ff 50 .... 5 Vl w et:

0

0

.... ··/ .„-·-····-···············-·····„ .... „.„.)

l:: >/ . -· /

2 3 4 5 6 7 B 9

RESULTANT ANGULAR ACCELERATION Ckrod/s/sl

Figure 3 : GAMBIT Locii For Two Identical Cadaver Head Impact Tests (Data from Reference 4)

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l t surely can be argued that the differences are not great and that injury t o one speci men and not the other i s a r e f l e c t i on of s o m e inherent d i f f e rences in cadaver brain t o lerances. Neve r t h e l e s s , the subj e c t sustaining the injury does have a locus which at high linear accelerations ( 1 4 0 - 1 90G' s ) has r o t a t i onal a c c e le r a t i on s w h i ch exceed that of the non­injured subject. One might consider further that injury to one specimen and not the other is an ind i c a t i on that the r e spons e s a r e "border l i ne " c a s e s . The e l l i p t i ca l boundary f i r s t s u gg e s t e d in ( 1 ) l i e s r e m a rkably c l o s e to s u ch a border. Of int e re s t t o s ome readers w i l l be the o b s e r v a t i on that in 82E04 1 the HIC was 1 0 6 3 while for t e s t 8 2 E 0 6 1 it w a s 1 0 7 3 .

MONKEY IKPACT TESTS

In 1 9 7 9 , Gennarelli and co-workers (5 ) reported on the results of 30 rhesus monkeys subj ected to an angular acceleration pulse in the saggital plane. The m o t ion of the animal head w a s con s t rained via a linkage a r rangement a t t a ched t o a "he l m e t " f i t t e d t o the animal ' s head ( t hus avoiding d i r e c t skull contact phenomena). The level of rotational acceleration was varied by changing the e f f e c t ive radius through w h i ch the animal's head could r o t a t e . The t angent i a l component of a c c e l e r a t ion w a s measured u s ing a s ingle linear accelerometer.

The purpose of their experiments was to class ify the nature of the observed inj ury ( i.e. no injury, f ro n t a l lobe contu s i o n , t e mp o r a l contu s i o n ) according to the mechanical imput. The injuries were graded according t o an Experimental Trauma Scale (ETS) which is s imilar to AIS but f o r animals. For the present purposes , the data is of certain value.

The controlled nature of the m o t i on cau s e s the locus of t rans l a t i o n a l ve r s u s r o t a t i onal a c c e l e r a t i o n t o s i mply b e a s t raight line (i.e. tangential acceleration is always proport i onal t o r o t a t i onal t h r ough the f ixed radius). As a consequence, peak r o t a t i on a l and p eak t r a n s l a t ional a c c e l e ra t i on a lways occur a t the same ins tant i n t i me. If the d a t a s u p p o r t s the n o t i on of combined loading , a corre l a t i on bas ed s i mply on maximum values should exist.

To mask poss i b l e s i z e d i f f erence e f f e ct s , the d a t a f o r each t e s t w a s normalized to the mass o f the average monkey brain. When treated i n this w a y , and p l o t t e d in a GAMBI T plane, the r e s u l t s take the f o r m shown in Figure 4. Shown there are the recorded values and the average for each ETS level. A l s o shown are lines that s e p a r a t e the various groupings into categories.

l t is significant to note that the groupings of data do i llus t rate a t rend. Furthermore, the t rend i s one which lends s u p p o r t t o the idea that b o t h rotational and trans lational acceleration mus t be considered when trying to correlate a certain injury level. The data suggests this trend s ince, on ave rage, inj u ry s e v e r i t y tends to increase as r o t a t i on increa s e s f o r a f i xed level of t ange n t i a l a c ce l e r a t i on. Add i t i onal d a t a i n the l o w t rans l a t i on-high r o t a t i on f i e l d would be helpful to further subs tantiate this observation. The data further suggests that a series of boundaries , s imi lar to those proposed by GAMBIT, are in evidence.

126

150

.... !SI

X „ ' „ ' ..!! 100

ts 1-a: 0:: w __, w u u a: __, a: z 0

50

1-a: __, Vl z a: 0:: 1-

0

0

. �u . a n 0 .

• 0

��'?ON1�'niT

2 3 4 5 6 7 B 9 1 0 1 1 ANGULAR ACCELERATION (krod/s/s x 10 l

Figure 4 : Rhesus Monkey Head Data (Data from Reference 5 )

PIGLET HEAD IMPACT EXPERIMENTS

1 2 1 3 14 1 5

In 1 9 8 4 , Prasad and Daniels ( 6 ) , reported on a s e r i es of 1 5 head i mp a c t tests on piglets. These tests were intended t o provide insight into child h e a d i n j u r y m e c h an i s m s t h r ou g h t h e u s e o f t h e p i g l e t s u r r o g a t e . Ins t rumentation comprised a triaxial accelerometer attached to the animal's snout and a uniaxial accelerometer further out on the snout. This lat ter inst rument a l lowed the comput a t i on of angular a c c e l e r a t i on in the mid­s a g g i tal plane. F o l low ing i m p a c t , the ani mals w e re sacrif i c e d and au t op s i e s perf ormed. Seven of the f i f teen t e s t s r e s u l t e d in injuries t o the animal's brain.

The relationship between the peak angular and average (calculated over the "HIC" dur a t i o n ) t rans l a t i on a l a c c e l e r a t i ons , and the levels of brain injury, normalized for brain mas s , are displayed graphically in Figure 5. As i n the c a s e of the monkey d a t a , the t rends s e e m to support the bas i c premise of the GAMBIT.

1 2 7

2 1 0

l.!)

z 0 1-a: Cl:: w

1 40

_J w u u a: _J a: z 0 1-a: 70 _J VI z a: Cl:: 1-

w > a:

0

0

DISCUSSION

[ndlce1•• llU

ever-o� volue

• I 0 �mffi��M r�q�T

~ 5 1 0 1 5 20

HRXIHUH RNGULRR RCCELERRT I ON lkrod/s/sl

Figure 5 : Piglet Head Impact Data (Data from Reference 6 )

Simplification of Interpretation

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Analyses of certain rotational/t rans lational acceleration locii, indicates that, in s p i t e of theore t i cal general i t i e s , maximum t rans l a t i onal a c c e l e r a t ion and maximum r o t a t ional a c c e le r a t i on of t e n do not occur a t distinctly different times during the impact event. As a consequence, and cons i d e r ing the accura cy of the actual d a t a , i t i s hard t o j u s t i fy the requirement to constantly monitor the accelerations throughout the entire pulse. In fact, it is probably sufficient to s imply record the maximums of each variable and compute G using those precise values.

The merits of this are that it does not presume a particular ins tant when a " c r i t i ca l " s i tu a t i on o c cu r s and , a t the very l e a s t is a conservative approach to the definition of a combined criteria. That i s , G s o computed would be the value that would apply if in fact, maximum translational and rotational accelerat ions did occur at the same ins tant.

Boundary Uncertainty

No p r e c i s e s e p a r a t ion between a non-injurious and an injurious s i tuation can be def ined. The locat i on of any such boundary mus t be a m a t t e r of probability. That is, a given set of inertial conditions carries with it only a c e r t a i n l ikelihood of inj u ry d epending on a variety of variables.

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Age o f t h e vi c t i m , and other phy s i c a l and morphological varia b le s , w i l l determine whether i n fact a head injury will occur.

One pos s ible way to address this matter is to replace the GAMBIT boundary with a region or band that is ass ociated with such probabi lities.

Directional Sensitivity

l t has been suggested, with s ome justification, that the tolerance of the head to impacts from different directions are different. Such behaviour i$ thought to be o b s e rved by no t in g , for examp le , that f o r the same brain injury s everity, the head accelerates at a lower level f or lateral impacts. Presumably if such behaviour is associated with translational motion, it would a l s o be true f or r o t a t i on. Generally, one m i g h t have " c ri t i ca l " a c ce l e r a t i on s f o r each o f t h e s i x degrees o f f reedom. T o deal w i t h this pos s i bili t y , one c ou l d , w i t h the same engineering j us tif i ca t i on u s e d t o def ine G , d e f ine "equiva l e n t " t r an s lational and rotational accelerations. These would take the form:

where the ac ' s represents the o r t hogona l c r i t i c a l values and ax, ay , az , are the component values in the three principal directions.

In gene r a l , t h i s function c o u l d be compu t e d as a funct i on of t i me. A similar expression can be written for the rotational terms. The left hand s i d e s o f both exp r e s s ions w o u l d r e p lace the c o r r e s p onding t e rms in the current GAMBIT formulation. Though technically appropriate (an "ellipsoid of i n f luence" has been sugges t e d b e f o r e ) , such ref inement is w e l l beyond the range of currently available data.

Time Dependency

N o exp l i ci t t i m e dependence on t rans lat ion o r r o t a t i on has been agreed upon. Howeve r , there is the f requent sugg e s t i on that a l lowable average acceleration decreases with the passage of time. The Wayne State Curve is the classi c example of this thinking. Should such a relation be verified f o r b o t h f o r ms of m o t i o n , the GAM B I T boundary could be cons idered as a 3 d i mens ional s u r f a ce i n s t ead o f a s i mp l e line. Figure 6 i l lus t ra t e s the concept .

Whether this "improvement" could ever be validated is a mat ter f or future speculation.

SUMMARY AND CONCLUSIONS

F o r y e a r s i t h a s been a s s u m e d t h a t there has been a r e l a t i onship between the head i nj u ry that a human being w i ll s u s t a i n and the m o t i on that his head undergoes as a result of s ome mechanical input. The GAMBIT evolved by making fairly well -accepted engineering judgements about the s ignificance

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of certain parameters. lt assume s , in particular, that the onset of brain injury occurs when the combined e f f e c t of t rans l a t i on a l and r o t a t i on a l accelerations exceeds some limiting value.

The p r e s e n t s tudy has a t t e mp t e d t o pu l l t o g e t h e r r e c e n t know l e d g e pertaining to brain injury that is induced i n a generalized inertial field. The obj e ct ive of the work has been to provide a t e chn i c a l ly r e a l i s t i c criterion for use with ATD ' s in a car crash environment .

The s t ate-of-the-art in human brain injury criterion definition continues to n o t make s igni f i cant p r o g r e s s . The exis t ing d a t a base is s i mply insuff i c i ent t o expect maj o r s t ri d e s and l i m i t a t ions of ava i l a b l e e xp e r i me n t a l d a t a cont i nues t o t h w a r t e f f o r t s in t h i s area. As more knowledge in this area is amassed, the greater becomes our understanding of the limits of this knowledge. However, engineers typically do not wait for s cience to c o m p l e t e ly c l a r i f y a l l i s sues bef o r e p r o ceeding w i t h t h e i r designs. Thus in recognition of , and in some cases i n spite o f , the above limit s , the GAMBIT model has been pos tulated. With respect specifically to the shape o f the GAMB IT boundary and o f the values o f i ts i n t e r cep t s , the available data is clearly l i m i ted. lt is l i m i t e d p a r t i cu la r ly in t h o s e regions o f high translation/low rotation and high rotation/low translation; regions which would help def ine both the intercept values and the general shape of the curve. At pres ent , an e l i p t i ca l shape ( c ons i s tent w i t h the maximum shear s t re s s theory) appears no more reas onable than a s i mp l e s t raight line.

A s t raight line intersecting the translational acceleration axis at 250G's forms a triangular region within which injuries to cadavers are typically not f ound when the r o t a t iona l a c c e l e r a t i on i n t e r c e p t is approxi ma t e ly 1 0 , 000 rad /sec/sec. The 250G limit is consis tent with the failure criteria employed in helmet evaluation where headform motion is res tricted to being purely linear. No s i m i lar r a t i on a l i z a t ion can be provided f o r the pure r o t a t i o n a l l i m i t , h o w e v e r , t h e 1 0 , 0 0 0 r a d / s e c / s e c d o e s n o t s e e m inconsistent with the range of values which have been suggested a t various times by others.

The revised GAMBIT thus simply becomes :

G - a m - 250 +

References

am � 1 10,000

1 . Newman, J.A. , "A Gene ral i z e d Accelerat ion M o d e l f o r Brain Inj u ry Tolerance� Presented at the Winterlude Head Injury Workshop, O ttawa, Feburary, 1 985.

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2 . Nusholt z , G.S . , Kaike r , P . S . , Mus cot t , G.J. and Suggi t , B.R. , "UMTRI Experimental . Techniques in Head Injury Research", SAE Paper 11851 244. Presented at the Government /Industry Meeting, Washington , May , 1985.

3 . Burkhard, P.M., "A Two Dimensional Accelerometer Analysis Applicable to Impacts " , General Motors Report GMR-47 6 5 , June 2 8 , 1984.

4 . Nusho l t z , G.S. , Lux, P . , Kaik e r , P. and Jani cki , M.A. , "Head Impact R e s p ons e - Skull Deformat ion and Angu lar Accelerations". SAE paper /184 1 6 5 7 , Proceedings of the 28th Stapp Car Crash Conference, Chicago, November , 1 9 8 4 .

5 . Gennare l l i , T.A. , Abe l , J . M � , Adams , H. , and G raham, D. , "Di f f eren t i a l Tolerance of Frontal and T e m p o r a ! Lobes t o Contusion Induced by Angu lar Accelerat ion". SAE Paper 11 7 9 1 0 2 2 , Proceedings of the 2 3 r d Stapp Car Crash Conference , SAn Diego , October, 1 9 7 9 .

6 . Prasad, P. and Daniels , R. , "Biomechanical Analysis of Head, Neck and Torso Injuries to Child Surrogates Due to Sudden Torso Acceleration". SAE paper 11840656, Proceedings of the 28th Stapp Car Crash Conference, Chicago, November , 1 984.

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