Martin Ostoja-Starzewski, professor of mechanical science and engineering and a member of the Beckman Institute’s Bioimaging Science and Technology Group, presented the Beckman Director’s Seminar on “Traumatic Brain Injury, Waves, Fractals” on Thursday, January 26.
As Ostoja-Starzewski states, “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 collaboration with Associate Professor Brad Sutton in the Department of Bioengineering. 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 the human brain’s random structure is that its surface is fractal – indeed, it has the largest fractal dimension among all mammalian brains. This indicates another challenge: develop methods to study waves in fractal media—brains as well as many other structures present in nature,” he said.
Ostoja-Starzewski presented one path in this direction with a recently developed calculus on non-integer dimensional domains. He demonstrated how they could be applied to mechanics/physics problems, and contrasted them with more established (but less physical) fractional calculus models.
Ostoja-Starzewski’s 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 co-director of the NSF Industry/University Cooperative Research Center for Novel High Voltage/Temperature Materials and Structures.