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Calibrating a viscoelastic model for gray and white matter brain tissue by nanoindentation

The mammalian brain is composed of an outer layer of gray matter, consisting of cell bodies, dendrites, and unmyelinated axons, and an inner core of white matter, consisting primarily of myelinated axons. Recent evidence suggests that microstructural differences between gray and white matter play an important role during neurodevelopment. While brain tissue as a whole is rheologically well characterized, the individual features of gray and white matter remain poorly understood. Here we quantify the mechanical properties of gray and white matter using a robust, reliable, and repeatable method, flat-punch indentation. To systematically characterize gray and white matter moduli for varying indenter diameters, loading rates, holding times, post-mortem times, and locations we performed a series of static and dynamic indentation tests. We found that indenting thick, intact coronal slices eliminates the common challenges associated with small specimens: it naturally minimizes boundary effects, dehydration, swelling, and structural degradation. Increasing the frequency from 0.1 to 50 Hz increased the storage modulus from 1kPa to 10kPa, whereas the loss modulus decreased. To characterize the viscous behavior of both white and gray matter, we adopted a multi-term Prony series. We found a best fit for a two-term Prony series with characteristic time constants of 4s and 170s for both gray and white matter. This suggests that brain tissue possesses two characteristic time scales. Understanding the rheological features of gray and white matter has direct implications on diagnosing, understanding, and eventually manipulating the mechanical environment in neurological disorders including lissencephaly, polymicrogyria, brachycephaly, plagiocephaly, and hydrocephalus.

Author(s):

Rijk De Rooij    
Department of Mechanical Engineering, Stanford University
United States

Silvia Budday    
Chair of Applied Mechanics, University of Erlangen-Nuremberg
Germany

Richard Nay    
Hysitron, Inc.
United States

Paul Steinmann    
Chair of Applied Mechanics, University of Erlangen-Nuremberg
Germany

Thomas Wyrobek    
Hysitron, Inc.
United States

Timothy Ovaert    
Department of Aerospace and Mechanical Engineering, The University of Notre Dame
United States

Ellen Kuhl    
Department of Mechanical Engineering, Stanford University
United States