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APPRAISAL OF TWO REPORTS ON MATHIMATICAL ANALYSES OF HEAD INJURY

Two papers concerned with mathematical modcling of head injury dynamics have models of pressure-acceleration dynamics inside the skull during impact vvents by assuring that:

(I) The skull is a thin, isotropic, homogenous, elastic. spherical shell.

(2) The brain is an ideal comprcssible fluid.

(3) All irmpact loading is axisymmetric.

Reference I considers the cavitation hypothesis of brain damage for head impact,, and assumes a specific impacting load in addition to appropriate constants to define the primary assumptions noted above. The evolved model uscs extensional shell theory and coupled differential cquations solved by finite difference techniques to define the tirne-variable pressure field inside the shell. The authoxs feel that their model supports the cavitation hypothesis because the model indicates transient zones of negative pressure at the impact pole and the opposite (contrecoup) pole at different times after the start of impact. The authors acknowledge that their work does not verify the cavitation hypothesis and does not rule out other mecharisms of brain damage from non-penetrating impact.

Reference 2 considers the pressuxe effects of various impacting force waveforms in zelation to the previously proposed General Motors' Severity inJex. The Severity Index is an nth power of impact acceleration, or force, integrated with respect to tirne for the duration of impact. Brief positive pulses of impact force in square, triangular, half sine and eccentric waveforms were defined so as to have identical Severity Index values, indicating that all the pulses had roughly similar products of average amplitude times duration.

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The four pulses were used as inputs to the mathematie model deseribed above, and the nodel showed that the pressure dymamics of the pbysical systen would be "nearly the same" [or all pulses tested. From this finding. the authors conclude, "These results indicate tha: the General Monors Severity Index is a uscful mcans of determining the soverity of vasily difforent pulses applicd to linear systems." The authors go on ta caution, however, that "thesc results do not necessarily indicate that the Severity Index is a valid mcans of predicting the hazard or injury potential of Jlifferent pulsus. An evaluation such as that must be accomplishcd Sy furtiier experimentation and clinical investigations. . ."

Comments

1. The two papers appear to be ingenious exarplcs of analytical modeling technique applied to the complex dynarics of fluid filled spherical shells subjectec to impact.

2. Reference 1 shows that, under the assumed condilions. transient negative pressures will occur at both the impact and contrcoup poles of the impacted shell.

3. Rcfexence 2 shows that. under the assurned conditions, similar impact forces (differing mainly in waveformn) selected to have identical General Motors'Severity Indices will cause similar dynamic pressure patterns,

4. It is unfortunate that neitincr report mentions the detailed results of Lindgren who measured the dynamic pressure patterns 4 of fluid filled spheres and human cadaver heads subjected to impaci. Lirdgren recorded negative pressures at both the contrecoup and imnpact poles, as well as similar pressure patterns arising from similar irpact forces.

5. With regard to the concussion threshold problem, it would be extremely interesting to see the powerful analytic 'echniques of Reference 1 and 2 used in a tetrospective scarch for a useful common derominator in a large number of the published investigations on experimental concussion.

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REFERENCES

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