Combined Analysis of the Mechanical Behavior in the Time and Frequency Domain of a Viscoelastic Brain Phantom Material

ABSTRACT The mechanical characterization of brain tissue in multiple time scales is often limited by inconsistent or contradicting responses when different experiments are used. The main reason for theses discrepancies are variations in the experimental setups, as brain tissue is sensitive to changes in the time and length scale. Yet, for a comprehensive characterization, different experiments are necessary. This study addresses the problem of inconsistent responses when using different experimental techniques, and unifies the results conducted in the time and frequency domain in a continuum‐based model. A viscoelastic brain phantom material was examined in the quasi‐static time domain, at the rheometer and in the frequency domain via a vibration analysis at a custom‐built vibration table. The mechanical parameters were determined in an inverse parameter identification based on the time‐dependent material response conducted at the rheometer. The calibrated model was validated for an application in the frequency domain by predicting the vibration response with the identified material parameters. As a material model, the hyperelastic Ogden model combined with a viscoelastic Prony series was used. Different orders of Prony series were investigated regarding their ability to capture both the time and frequency response of the material. The results indicate that the response in both domains can be predicted by a three‐term‐Prony series with relaxation times addressing exactly the time regimes of the experiments. For the rheometer experiments, two times at and are required and for the vibration analysis an additional time at .