Brain Motion and Deformation During Closed Head Injury in the Presence of Cerebrospinal Fluid

Abstract

This paper presents a new analysis of the physics of closed head injury following brief, intense acceleration of the head. It focuses upon the buoyancy of the brain in cerebrospinal fluid, which protects against damage, the propagation of strain waves through the brain substance, which causes damage, and the concentration of strain in critical anatomic regions, which magnifies damage. Numerical methods are used to create animations or "movies" of brain motion and deformation. Initially a 1 cm gap filled with cerebrospinal fluid (CSF) separates the brain from the skull. Whole head acceleration induces artificial gravity within the skull. The brain accelerates because its density differs slightly from that of CSF, strikes the inner aspect of the skull, and undergoes viscoelastic deformation. The computed pattern of brain motion correlates well with published high-speed photographic studies. The sites of greatest deformation correlate with sites of greatest pathological damage. This fresh biomechanical analysis allows one to visualize events within the skull during closed head injury and may inspire new approaches to prevention and treatment.

A New Biomechanical Head Injury Criterion

“…A recent paper utilizing two dimensional finite element models of the brain confirms the essential correctness of the Brekhovskikh-Gancharov analysis of short duration blows to ellipsoidal head and brain models 22 . Compressive strain waves propagate through the entire brain, just as outlined in Figure 3.…”

“…Only a few studies, using high-speed photography through a transparent plastic calvarium or high speed fluoroscopy of implanted radiodense pellets 8,[19][20][21] , have examined the actual motion of the brain during closed head injury in animals. Fortunately mathematical analysis and modeling of the skull and brain in response to known pulses of head acceleration allow one to study a wide variety of conditions that are difficult, impossible, or unethical to reproduce in animals or humans 22 . This mathematical approach is ideal for developing an improved head injury criterion.…”

“…In this case the skull is analogous to the walls of the elevator, and the brain is analogous to a passenger in the elevator. However, since the brain is surrounded by and suspended in clear aqueous cerebrospinal fluid (CSF), the acceleration felt by the brain is attenuated by about 95 percent, since the brain weighs only about 5% as much in water as it does in air 22 . Nevertheless, considerable isovolumic deformation of the brain (which is quite soft) can take place, as the whole head is accelerated.…”

“…The nature of brain deformation during closed head injury has been revealed using analytical methods and computer models 22 , coupled with remarkable experiments conducted years ago in animals fitted with transparent skull caps and studied with high speed photography 19,21 . During brief, intense impacts the brain's velocity toward the skull increases almost instantaneously (within 1/50's of a second or less) to a velocity of tens of centimeters per second along the axis of the blow.…”

“…Now let us regard the elastic rod as being composed of parallel spring and damper elements connected in series (a Voight/Maxwell body). Assume that the various dampers in series act as an equivalent damper with viscous loss modulus, D, cross sectional area A, and length L. D is a material property of brain tissue, which is defined analogously to Young's modulus of elasticity, with a value on the order of 200 kg/m/s 22 . The total work required to compress the equivalent damper may be estimated as average force exerted by the equivalent damper, multiplied by the distance moved.…”