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In this study, we propose a computational characterization technique for obtaining the material properties of axons and extracellular matrix (ECM) in human brain white matter. To account for the dynamic behavior of the brain tissue, data from timedependent relaxation tests of human brain white matter in different strain rates are extracted and formulated by a viscohyperelastic constitutive model consisting of the Ogden hyperelastic model and the Prony series expansion. Through micromechanical finite element simulation, a derivative-free optimization framework designed to minimize the difference between the numerical and experimental data is used to identify the material properties of the axons and ECM. The Prony series expansion parameters of axons and ECM are found to be highly affected by the Prony series expansion coefficients of the brain white matter. The optimal parameters of axons and ECM are verified through micromechanical simulation by comparing the averaged numerical response with that of the experimental data. Moreover, the initial shear modulus and the reduced shear modulus of the axons are found for different strain rates of 0.0001, 0.01, and 1 s −1 . Consequently, first-and second-order regressions are used to find relations for the prediction of the shear modulus at the intermediate strain rates.

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Modal analysis is a strong tool of mechanical diagnosis and behavior of bodies and structures. The method can be employed for human head as a body to recognize its natural frequencies. Brain injury can be destructive around the brain’s resonant frequencies with the external applied loading and motion. Vibrations due to an assault on the head are sent throughout the brain under impacts or high motions. These waves propagate and attenuate at different rates within the brain depending on the magnitude and direction of the impact loading or motion. By conducting modal analysis of the brain and identifying its resonant frequencies we can measure the risk of injury and reduce or possibly even eliminate vibrations in these frequency ranges. This paper employs a finite elements method to simulate the impacts for different impact angles on a human head. A numerical technique based on dynamic mode decomposition (DMD) will be used to extract the modal properties for the brain tissue in regions near the corpus callosum and brain stem. The study aims to identify a frequency range in which the brain is more susceptible to vibration with the end goal of better understanding the brain in the frequency domain and preventing future TBIs. Three modal frequencies were identified with frequency ranges of 44–68Hz, 68–155Hz, and 114–299Hz. It is found that the impact angle, displacement direction, and region of the brain have a significant impact on the modal response of brain tissue during any impact. The study also provides insight into the effects of impact angle, displacement direction, and different regions of the brain.

Magnetic resonance elastography (MRE) is commonly used as an image-based alternative for palpation of the internal organs of human body. The presence of tumor or other kind of pathologies in biological tissues can increase its stiffness. Therefore, while MRE technique is capable to provide a quantitative measurement, the qualitative description of the tissue stiffness could be potentially informative as well for physicians. MRE can be divided into several steps including the generation of waves in the tissue, measuring the field displacement of the tissue by magnetic resonance imaging devices, and then applying the constitutive based inversion algorithms to measure the material properties of the tissue. The inversion algorithms are dependent to the constitutive model in use, and moreover, it could be computationally expensive. To overcome this hindrance, in this paper, we propose a machine learning framework for categorizing the tissue stiffness based on the magnetic resonance elastography finite element simulation data. In our finite element simulation, the shear waves are generated in an axisymmetrical model by applying harmonic displacement at the center of the model with the known excitation frequency. To obtain the field displacement of the model, in the first step, the natural frequencies of the system will be calculated through numerical Block-Lanczos eigensolver algorithm. Thereafter, a transient dynamic modal analysis is carried out to find the corresponding displacement response of the tissue in different time steps of the simulation. To obtain the training dataset, ten simulations with the pre-assigned linear elastic modulus in the range of 2 to 6 kPa is conducted and the displacement of the tissue in three points at the end of the first and second cycle will be recorded as the features of the dataset. Each instance of the dataset is labelled as “Low“ or “High”, corresponding to its stiffness quantitative value lying in ranges of 2–4 kPa or 4–6 kPa. A machine learning classifying algorithm, a logistic regression hypothesis will be trained on this dataset. The trained hypothesis will be then tested on six new unseen simulation data with known elastic modulus values. The trained logistic regression was able to classify the tissue stiffness with the perfect accuracy score of 1.0. The findings of this study can be used for qualitative description of the tissue stiffness that can be beneficial for pathology diagnosis and moreover, it eliminates the need on the usage of inversion algorithms which leads to reduction in the computational complexity of tissue characterization.