Response of the Brain to Sagittal Angular Acceleration

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Shear deformation of the brain due to head rotation has long been postulated as a major cause of brain injury because of the very low shear stiffness of brain tissue (Holbourn, 1943). Animal, physical, and finite element models have been used to investigate brain response due to rotational impacts. But three-dimensional finite element simulations of rotational impacts are rare, and little information on the distribution of shear stress/strain of the human brain due to rotational impact is available. In this section, the brain injury model — version 95 was exercised to investigate elastic and viscoelastic responses of the brain to an impulsive sagittal plane rotation of the head. An angular acceleration pulse taken from Abel's monkey test data (1978) was scaled to provide input for the human brain. The scaling method used maintained an approximately equal shear strain level in the brain and equal displacement of the head.

FIGURE 7.17 Head acceleration in three different impact speeds for padded impacts.

FIGURE 7.18 Impact force in three different impact speeds for padded impacts.

FIGURE 7.18 Impact force in three different impact speeds for padded impacts.

FIGURE 7.19 Head acceleration in three impact speeds for unpadded impacts.

TIME

FIGURE 7.19 Head acceleration in three impact speeds for unpadded impacts.

FIGURE 7.20 Impact force in three impact speeds for unpadded impacts

FIGURE 7.20 Impact force in three impact speeds for unpadded impacts

^ 5.0 % 4.0

CN VO O

A= G-Test B= G-B700 C= G-B70 D= G-Khali E= G-DiMasi FIGURE 7.21 Shear relaxation functions for the brain.

Responses of the brain to impulsive sagittal rotational accelerations were obtained. The influence of the brain material properties on model response was also investigated.

In Fig. 7.21, curve A is the exponential relaxation function from Shuck and Advani's test data (1972), while curve B is based on our curve fitting for white matter with P = 700 s-1. curve C, used as the upper bound of the relaxation function, is for P = 70 s-1; curve D is taken from Khalil and Viano (1977); and curve E is from DiMasi et al (1991).

The deduced viscoelastic moduli from curve A were used to make a baseline run. In addition, five more runs were performed with different brain material parameters to study the influence of brain material properties on model response. In case B-70 P was changed to 70 s-1 from the baseline value to get results for the upper bound. Case SG50 assumed a 50% higher shear modulus for the white matter than that of the gray matter with P = 700 s-1. Case SG50-B70 was the upper-bounds case for case SG50 with P = 70 s-1. Case E-MAX was the elastic analysis assuming the shear modulus of G0 used for the baseline. Case E-MIN was the elastic analysis assuming the shear modulus of G^ used for the baseline. The material properties used in this study are listed in Table 7.8.

To extrapolate impact test results obtained from animals to humans, a scaling relationship must be established. Ommaya et al. (1967) applied Holbourn's scaling law

where 0 = angular acceleration, M = brain mass, to predict a concussion threshold for man from monkey test data. Margulies et al. (1985) also used this scaling law in their physical model tests. This kind of scaling is not complete. For dynamic problems, scaling of time should also be considered.

TABLE 7.8 Material Properties of the Brain Used for Parametric Study

TABLE 7.8 Material Properties of the Brain Used for Parametric Study

Base

41

34

7.6

6.3

700

B-70

41

34

7.6

6.3

70

SG50

51

34

9.5

6.3

700

SG50-B70

51

34

9.5

6.3

70

E-MAX

G = 41

G = 34

E-MIN

G=7.6

G=6.3

white

gray

white

gray

FIGURE 7.22 Angular acceleration impulse scaled from Abel's data.

If the brain is idealized as a sphere with a radius R, it can be shown that to have the same stress level in two different sizes of the brain, the scaling for rotational acceleration is

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