APPRAISAL OF TWO REPORTS ON MATHRMATICAL ANALYSES OF I-IEAD liq:URY 31 January 1972 ----------- APPRAISAL OF TWO RRPO.RTS ON MATI-i-@MATICAT- ANAT-YSI-:S OF IlrAD INJURY Two papv-rs concern(,d with rnathernitical modeling of head injury dy-naml ics ha%,c@, been submitted ror biomedical appraisal. 1, 2Ecth reports define rnathernat2ica-I models of pressure-acceleration dynamics inside the skull during impact @vent@; by assuming that: (I) The skull is a thin, isotropic, ho-nogerious, elastic. spherical shell. (2) The brain is an ideal cornprrssibl-e fluid. (32) All impact loading is axisyn-imetric. Referi-nce I considers the cavitation hypothesis of brain damage for head impact,, and as.5urnes a specific impacting load in addition to appropriate constants to define the primary assumptions noted above. The evolved model uses extensional shell theory and coupled differential oquations solved by 2 finite difference.techniques to define the tirne-variable pressure field inside the shell. The authors feel that their model supports the cavitation hypothesis because the model indicatea trans;.ent zones of negative pressure at the impact pole and the opposite (contrecoup) pole at different times after the start of irnpact. The authors acknowledge th2at their work does not verify the cavita- t.@on hypothesis and does not rule out other mecharisrns of brain damage from non-penetrating impact. Reference 2 considers the pressure effects of various inipacting force wave- forms in zelation to the previously proposed General Motors' Severity index. 2. 3 The Severity Index is an nth power of impact acceleration, or force, integra.- ted with respect to time for the'duration of impact. Brief positive pulses of impact fo'rce in square, triangular, half sine and eccentric waveforms were defined so as to have identical Severity Inde-.$E values, ir.Ld@cating that all the ptilses had roughly sirriilar products of average amplitude times du8ration. Ask MF Tjio fuur. puls(-s were used as inputs to ti-ic niatlici-natic i,.iodcl tic,scribecl ;tbovq, a-icl ttic n-&Odet showt!(l t2hat t[ic pressure dy7tiamics ,)f tll(! physical systen-i would be "nearly the sii-ne" for all pulses tested. From this fiiiding, the alltlior,.A conclucle, "These results inclicate ilia- il-le C,cnzrtl 1-iiitc@rs' SeveriLy ln(lex is a useful means oA' cictcrrninit-ig the sc-verity of vastly diilxt.@nt ptilse.-.% applic(i in linear syrlen-is. " Tlio itit)-torq go on to citiiioi-k. liowc-vcr, that "t2hese results (lo not necessarily indicate thal the Severity ln(lex is a -.,alid means of predicting the hazard or injury potential of Iific-rent pulses. An evaluation such as tIlaL n-iust be accomplished @)y furtiicr experiniciatation and clinical investigations 12. The two papers appear to be ingerkious examples of ana- lytical modeling technique applied to the complex dynamics of fluid filled spherical shells subjectei@ to impact. Z. Reference I shows that, uncler the asgtimcd conditions, transient negative pressures will occur at both the impact and contrt--2 coup poles of tlie impacted shell. 3. Reference 2 shows t]-iat, under the assurned conrlitio-.is, similar impact forces (differing mainly in wavefori-n) selected to have identical General Motors' Severity Indices will cause sim-41ar dynamic pressure patt2erns. 4. It is unfortunate that neither report mentions the det-tilud results of Lindgren who measured the dynamic pressure pitle-rns of fluid filled spheres and human cadaver heads subjecled to irnpacl. Lirclgren recorded negative pressures at both the contrecoup and impact pole.-;, as well as similar press--ire patterns arisin,, from rirnilar ii-npac:t forces. S. With regard to the concussion Lhresholci problem, it would be'extremely interesting to see the powerful analytic echniques of Reference I and 2 used in a retrospective s-2arch for a useful common der-orriinalor in a large number of the published investi-ations on experimental concussion. qp 11 I MOB REFERENCES 1. Bon2dict, J. V. Harris, E. 1-1. and von Rosenberg, D. U. "An An4- lytical lilvestigation of Lhe Calvitation 1-.ypotli--!sis of Braii-i 2 Dan-iage, " Journal of 13.xs,.c=gEjlia2aliaa, September 1970, pp 597-603-. (LJNCL) 2. 'be-iedict, J. V. md Lin, D. J. , "Analytical [nvestination of the 0 General Motors' Severity Index, " ASME Pub2lication 71-WA/ BI-IF-6, American Society of Mechanical Engineers, New York, 1971. (UNCL) 3. Cadd, C. W. "Use of a 'A"ci-hted-Impulse C:-iterion for rstirnating Injury Hazard, " in Proci:edings of the Tenth S',@inp Ca.zl Crash Confer2erice, Society of Automotive Engineers, New York, 1966, pp 95- 100. (UNCL) "Experixnentat Studies of Mecha 4. Lin6gron, S. 0. nical Effects in I-lead Injury, " Acta Chi-rur&ilca Scandinavica Supplement 360, 7 1966, pp I- 100. (UiNCJ@) -3-