From Physics online…
A numerical study suggests that head impacts primarily induce a few low-frequency, damped modes of vibration in brain tissue, a finding that could inform the design of sports helmets.
Strike a bell or a drum and its sound will be dominated by a few vibrational patterns (“modes”), each of which has a characteristic shape, frequency, and damping rate. A new study has found that the mechanical response of the human brain to impact can similarly be described with a small number of dynamic modes. Kaveh Laksari of the University of Arizona in Tucson, Mehmet Kurt of the Stevens Institute of Technology in New Jersey, and colleagues used measurements of head impacts during football games as input to a computer model that simulates the point-by-point displacement of tissue within the brain . Their analysis of the simulated motion shows that this “displacement field” can be described with just a few modes whose characteristic frequencies are around 20 to 40 Hz. Their findings could offer insight into the mechanics of traumatic brain injury (TBI), perhaps leading to new designs for protective equipment.
TBI is a pervasive and serious medical problem. “Mild” TBI, otherwise known as a concussion, is common in sports ; more severe injuries arise from automobile accidents, falls, or military combat . Even impacts that don’t rise to the level of a concussion can, when repeated many times, cause a neurodegenerative condition known as chronic traumatic encephalopathy . This is why researchers have grown increasingly concerned about athletes playing contact sports such as football.
The general mechanical principles behind most TBIs are well understood. During an impact, the skull accelerates rapidly. The brain, which has considerable inertia and is surrounded by cerebrospinal fluid, accelerates slightly less quickly than the skull and deforms under forces from the various membranes, blood vessels, and connective tissue that attach it to the skull. This rapid deformation, or strain, of brain tissue stretches and injures delicate nerve fibers, degrading brain function.
This general picture is not, however, sufficient for predicting the short- and long-term effects of TBI. And, unfortunately, the more detailed mechanics of head impacts remain largely mysterious. That’s partly because brain deformation is challenging to observe: The brain is well hidden and any attempt to expose it could change its behavior or disrupt its structure and functioning. Another issue is the complexity of the brain as a material: It is both heterogeneous (different locations in the brain have different material properties) and anisotropic (it responds differently to forces applied along different directions) . Also, brain tissue’s response to a deforming force isn’t perfectly spring-like but is instead nonlinear and damped . Finally, every head is unique, and each impact differs in location, magnitude, and direction. This combination of features makes it difficult to say precisely how the brain deforms during either mild or severe TBI.
Researchers have set out to gather this missing information in various ways. On the experimental front, some groups have used magnetic resonance imaging (MRI) [7, 8] to measure brain motion in volunteers whose heads were subjected to reasonably mild (not injury-producing) accelerations. Other groups have measured brain motion at injury-level accelerations in the brains of cadavers . An alternative tack is to rely on detailed finite-element computer simulations [10, 11], which simultaneously solve equations that describe small, individual elements of brain tissue. This approach can predict brain motion for a given head acceleration, using different material models to describe the skull, brain, cerebrospinal fluid, and membranes.