Traumatic Brain Injury is one of the most dreadful human ailments. It can be caused by a rapid head acceleration during any kind (car, bicycle, skiing, skating, hiking, etc.) of accident, even when the skull remains intact. TBI affects football and hockey players, boxers, and other athletes as well as people who simply fall onto hard surfaces or ride roller coasters.

Experimental and medical data link TBI to the creation of shear waves in the brain matter. Over the past decade, we have been modeling traumatic brain dynamics by means of linear and nonlinear Partial Differential Equations (PDEs) that describe the propagation of such waves in the brain. Due to the mathematical complexity of the PDE systems used and the complexity of the brain geometry, solving these PDEs has required the development of sophisticated computational methods.

Our new dually-nonlinear computer TBI model extends in two ways the well-established, viscoelastic, linear Kelvin-Voigt model that treats the brain as a solid with no dependence of stress on strain. First, we treat the brain as a nonlinear, viscoelastic fluid. Second, we introduce a nonlinear stress-strain relation derived from experimental data.

Our numerical simulations of planar head motions conducted thus far show that:

• A simple head translation or rotation can trigger complicated oscillations of the brain matter with sufficiently large strain values to cause neuronal damage or hematoma.
• The introduction of nonlinearities enables us to explain the point-wise character and the scattered localization of Diffuse Axonal Injuries (DAI).
• Repetitive back and forth head motions can create a resonance effect that amplifies the strain values within the brain. This effect may explain the Shaken Baby Syndrome.
• The physical differences between the gray matter, the white matter, and the cerebral fluid lead to high strain values along the boundaries between brain substructures, which explain the predominant localization of DAI along these boundaries.

We have also developed 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 some brain regions as an indicator of the severity of a brain injury. Mathematical calculations and computer simulations conducted by us show that the BIC smoothly links the translational HIC with existing rotational brain injury tolerance criteria.

To visualize the dynamics within the brain, we have developed Curved-Vector-Field (CVF) plots and animations. CVF plots utilize curved instead of straight line segments to more clearly visualize the trajectories of the brain parcels. The vector directions are indicated by a dark to light shading. Compared to typical vector plots, CVF plots better represent vector fields with highly varying magnitudes, as are characteristic for the solutions of the nonlinear PDE systems that describe traumatic brain dynamics.

Our approach enables studying vital aspects of TBI mechanisms, diagnosis, and prevention by taking into account the complex brain geometry, the physical differences between brain substructures, and the head motion characteristics. The full implementation of our computer TBI model and the BIC will help in:

• Training medical personnel on many aspects of Traumatic Brain Injuries.
• Studying the way TBI is created during car, sport, roller-coaster, and other accidents.
• Designing better preventive measures such as vehicle interiors, helmets, and regulations.

Szczyrba I., Burtscher M., Szczyrba R., Validating Critical Limits of the Universal Brain Injury Criterion, Proceedings of the International Conference on Bioinformatics and Computational Biology at the 2012 World Congress in Computer Science, Computer Engineering, and Applied Computing, Las Vegas NV, CSREA Press 2012, 199-205. [pdf]

Szczyrba I., Burtscher M., Szczyrba R., Computer Modeling of Diffuse Axonal Injury Mechanisms, Proceedings of the International Conference on Bioinformatics and Computational Biology at the 2011 World Congress in Computer Science, Computer Engineering, and Applied Computing, Las Vegas NV, CSREA Press 2011, 401-407. [pdf]

Szczyrba I., Burtscher M., Szczyrba R., On the Role of a Nonlinear Stress-Strain Relation in Brain Trauma, Proceedings of the International Conference on Bioinformatics and Computational Biology at the World Congress in Computer Science, Computer Engineering, and Applied Computing, Las Vegas NV, July 2008, CSREA Press 2008, Vol. 1, 265-267. [pdf]

Szczyrba I., Burtscher M., Szczyrba R., Computational Modeling of Brain Dynamics During Abrupt Repetitive Head Motions, Proceedings of the International Conference on Modeling, Simulation and Visualization Methods at the World Congress in Computer Science, Computer Engineering, and Applied Computing, Las Vegas NV, June 2007, CSREA Press 2007, 143-149. [pdf]

Szczyrba I., Burtscher M., Szczyrba R., A Proposed New Brain Injury Tolerance Criterion Based on the Exchange of Energy Between the Skull and the Brain, Proceedings of the International Bioengineering Conference of the American Society of Mechanical Engineers, Keystone CO, June 2007, SBC2007-171967. [pdf]

Burtscher M., Szczyrba I., Computational Simulation and Visualization of Traumatic Brain Injuries, Proceedings of the International Conference on Modeling, Simulation and Visualization Methods at the World Congress in Computer Science, Computer Engineering, and Applied Computing, Las Vegas NV, June 2006, CSREA Press 2006, 101-107. [pdf]

Burtscher M., Szczyrba I., On the Role of the Brain's Geometry in Closed Head Injuries, Proceedings of the International Bioengineering Conference of the American Society of Mechanical Engineers, Vail CO, June 2005, b0010704. [pdf]

Burtscher M., Szczyrba I., Numerical Modeling of Brain Dynamics in Traumatic Situations - Impulsive Translations, Proceedings of the International Conference on Mathematics and Engineering Techniques in Medicine and Biological Sciences, Las Vegas NV, June 2005, CSREA Press 2005, 205-211. [pdf]

Szczyrba I., Burtscher M., On the Role of Ventricles in Diffuse Axonal Injuries, Proceedings of the International Bioengineering Conference of the American Society of Mechanical Engineers, Key Biscayne FL, June 2003, 147-148. [pdf]

Szczyrba I., Smolarkiewicz P., Cotter C., Numerical Simulations of Closed Head Injuries, Proceeding of the International Conference on Mathematics and Engineering Techniques in Medicine and Biological Sciences, Las Vegas NV, June 2002, CSREA Press 2002, Vol. 2, 486-492. [pdf]

Cotter C., Smolarkiewicz P., Szczyrba I., A Viscoelastic Fluid Model for Brain Injuries, International Journal for Numerical Methods in Fluids, 2002, Vol. 40, 303-311. [pdf]

Cotter C., Smolarkiewicz P., Szczyrba I., A Viscoelastic Model for Brain Injuries, Proceedings of the International Conference on Fluid Dynamics, Oxford University, UK, March 2001, ICFD, Oxford, 281-288.[pdf]

Cotter C., Smolarkiewicz P., Szczyrba I., On Mechanisms of Diffuse Axonal Injuries, Proceedings of the International Bioengineering Conference of the American Society of Mechanical Engineers, Snowbird UT, June/July 2001, ASME, BED - 50, 315-316. [pdf]

Cotter C., Smolarkiewicz P., Szczyrba I., A Nonlinear Model for Brain Injuries, Proceeding of the International Conference on Mathematics and Engineering Techniques in Medicine and Biological Sciences, Las Vegas NV, June 2000, CSREA Press 2000, Vol. 2, 443-449. [pdf]

   

 

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Igor Szczyrba, University of Northern Colorado

Martin Burtscher, Texas State University-San Marcos

Funiosoft, LLC is a software development company that designs, develops, and hosts the TBI website.

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