Traumatic Brain Injury (TBI) is one of the most dreadful human ailments. It can be caused by a rapid head motion during any kind of an accident - car, bicycle, skiing, skating, etc., or even during a roller-coaster ride.

Experimental and medical data link TBI to the creation of elastic (shear) waves within the brain matter. In the past decade, I have been modeling (together with other researchers and NSF/NIH support) traumatic brain dynamics by means of linear and nonlinear variants of a Partial Differential Equation (PDE) system that describes the propagation of such waves in the brain. Due to the mathematical complexity of this system and geometrical complexity of the brain, the solution of these PDEs has required developing sophisticated computational methods.

To present dynamics within the brain, we have developed Curved-Vector-Field (CVF) plots that can readily be converted into MPEG movies. In comparison to typical vector plots, CVF plots allow the representation of fields with highly varying magnitudes. Click here to download MPEG movies visualizing brain dynamics in various traumatic scenarios. 

Our numerical simulations show, in particular, that:   

• high strain values within the brain tissue (sufficient to cause neuronal damage) can be triggered by a simple head translation or rotation;
• repetitive back and forth head rotations can create a resonance effect that amplifies the strain values within the brain;
• physical differences between the gray matter, the white matter, and the cerebral fluid lead to high strain values along the boundaries of brain substructures. 

We have also introduced  a novel universal Brain Injury Criterion (BIC), which generalizes the translational Head Injury Criterion (HIC) to arbitrary planar head motions. The BIC utilizes the maximal power transferred from the skull to the brain along a 2D cross-section as an indicator of the severity of a brain injury. Mathematical calculations and computer simulations conducted by us show that the HIC and the existing rotational brain injury tolerance criteria can be linked together by the BIC.