Traumatic Brain Injury, Waves, Fractals
One of the challenges faced by our brains is to understand their own mechanical responses under impact-type loadings, such as may arise in sports or automotive accidents. Over the past few decades this challenge is being met with an ever more powerful array of methods: analytical, experimental, and computational.
At the Beckman Institute, such methods have jointly led to an MRI-based computational mechanics model of traumatic brain injury and its in vivo validation (in joint work with Prof. Brad Sutton). Various loading cases have been simulated, always indicating that blunt impacts to the skull give rise not only to a fast pressure wave but also to a slow, and potentially much more damaging, shear wave that converges spherically toward the brain center. Fortunately, this wave’s amplification is balanced by the brain tissues’ viscoelasticity and random heterogeneity. One extra aspect of human brain’s random structure is that its surface is fractal – indeed, having the largest fractal dimension of all the mammalian brains. This indicates another challenge: develop methods to study waves in fractal media – brains as well as many other structures present in nature.
One path in that direction is offered by a recently developed calculus on non-integer dimensional domains. We briefly review such techniques, show how they may be applied to mechanics/physics problems, and contrast them with the more established (but less physical) fractional calculus models.
Martin Ostoja-Starzewski did his undergraduate studies (1977) at the Cracow University of Technology, Poland, followed by master’s (1980) and Ph.D. (1983) degrees at McGill University, Canada -- all in mechanical engineering. His research interests are primarily in thermomechanics of random and fractal media, advanced continuum theories, as well as aerospace, bio- and geo-physical applications. He is the co-author of more than 180 journal papers as well as two books, “Microstructural Randomness and Scaling in Mechanics of Materials,” CRC Press (2007); and “Thermoelasticity with Finite Wave Speeds,” Oxford University Press (2009). He also (co-)edited 14 books and journal special issues and has helped co-organize various meetings. He has been on the editorial boards of many journals, including J. Thermal Stresses, Probabilistic Engineering Mechanics, ASME J. Applied Mechanics, Int. J. Damage Mech., Archive of Applied Mechanics, Acta Mechanica, Mathematics and Mechanics of Complex Systems, and Mechanics Research Communications. He is also co-editor of the CRC Modern Mechanics and Mathematics Series and a Fellow of American Society of Mechanical Engineers, American Academy of Mechanics, Society of Engineering Society, World Innovation Foundation, as well as an Associate Fellow of the American Institute of Aeronautics and Astronautics. In the winter of 2012 he was the Timoshenko Distinguished Visitor at Stanford. Presently, he is site co-director of NSF Industry/University Cooperative Research Center for Novel High Voltage/Temperature Materials and Structures.