Modal Analysis of the Human Brain Using Dynamic Mode Decomposition.

The majority of observations and criteria related to brain injuries predominantly focus on acceleration and forces, leaving the understanding of the brain in the frequency domain relatively limited. The impact of an injury can be more profound when considering the brain's resonant frequencies in conjunction with external applied loading and motion. This paper employs a finite element method to conduct an analysis of a human brain under impacts from various angles on the human head. A numerical technique, specifically dynamic mode decomposition (DMD), is utilized to extract modal properties for brain tissue in regions proximate to the corpus callosum and brain stem. Three distinct modal frequencies have been identified, spanning the ranges of 44-68 Hz, 68-155 Hz, and 114-299 Hz. The findings underscore the significance of impact angle, displacement direction, and the specific region of the brain in influencing the modal response of brain tissue during an impact event.

Visco-hyperelastic characterization of human brain white matter micro-level constituents in different strain rates.

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 time-dependent relaxation tests of human brain white matter in different strain rates are extracted and formulated by a visco-hyperelastic 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. Graphical Abstract The applied procedure for characterization of brain white matter micro-level constituents. The macro-level experimental data in different strain rates are used in the context of simulation-based optimization to obtain the properties of axons and extracellular matrix material.

A poro-hyper-viscoelastic rate-dependent constitutive modeling for the analysis of brain tissues.

In this paper, the dynamic behavior of bovine brain tissue, measured from in-vitro unconfined compression tests, is examined and represented through a viscoelastic biphasic model. The experiments have been carried out under three compression speeds of 10, 100, and 1000 mm/s. The results exhibited significant rate-dependent behavior. The brain tissue is modeled as a biphasic continuum consisting of a compressible solid matrix, fully saturated with an incompressible interstitial fluid. The governing equations based on conservation of mass and momentum are used to describe the solid-fluid interactions. An inverse scheme is employed in which a finite element model runs iteratively to optimize constitutive constants. The obtained material parameters of the proposed biphasic model show relatively good agreement (R2 ≥ 0.96) with the experimental tissue mechanical responses at different rates. The model can successfully capture the key aspects of the rate-dependency for both solid and fluid phases under large strain deformation. This poro-hyper viscoelastic model can effectively estimate the global and local rate-dependent tissue deformations, the spatial variations in pore spaces, hydrostatic pressure as well as fluid diffusion through the tissue.

Rate-dependent constitutive modeling of brain tissue.

In this paper, the dynamic behavior of bovine brain tissue, measured from a set of in vitro experiments, is investigated and represented through a nonlinear viscoelastic constitutive model. The brain samples were tested by employing unconfined compression tests at three different deformation rates of 10, 100, and 1000 mm/s. The tissue exhibited a significant rate-dependent behavior with different compression speeds. Based on the parallel rheological framework approach, a nonlinear viscoelastic model that captures the key aspects of the rate dependency in large-strain behavior was introduced. The proposed model was numerically calibrated to the tissue test data from three different deformation rates. The determined material parameters provided an excellent constitutive representation of tissue response in comparison with the test results. The obtained material parameters were employed in finite element simulations of tissue under compression loadings and successfully verified by the experimental results, thus demonstrating the computational compatibility of the proposed material model. The results of this paper provide groundwork in developing a characterization framework for large-strain and rate-dependent behavior of brain tissue at moderate to high strain rates which is of the highest importance in biomechanical analysis of the traumatic brain injury.

Evaluation of brain tissue responses because of the underwash overpressure of helmet and faceshield under blast loading.

Head protective tools such as helmets and faceshields can induce a localized high pressure region on the skull because of the underwash of the blast waves. Whether this underwash overpressure can affect the brain tissue response is still unknown. Accordingly, a computational approach was taken to confirm the incidence of underwash with regards to blast direction, as well as examine the influence of this effect on the mechanical responses of the brain. The variation of intracranial pressure (ICP) as one of the major injury predictors, as well as the maximum shear stress were mainly addressed in this study. Using a nonlinear finite element (FE) approach, generation and interaction of blast waves with the unprotected, helmeted, and fully protected (helmet and faceshield protected) FE head models were modeled using a multi-material arbitrary Lagrangian-Eulerian (ALE) method and a fluid-structure interaction (FSI) coupling algorithm. The underwash incidence overpressure was found to greatly change with the blast direction. Moreover, while underwash induced ICP (U-ICP) did not exceed the peak ICP of the unprotected head, it was comparable and even more than the peak ICP imposed on the protected heads by the primary shockwaves (Coup-ICP). It was concluded that while both helmet and faceshield protected the head against blast waves, the underwash overpressure affected the brain tissue response and altered the dynamic load experienced by the brain as it led to increased ICP levels at the countercoup site, imparted elevated skull flexure, and induced high negative pressure regions. Copyright © 2016 John Wiley & Sons, Ltd. Copyright © 2016 John Wiley & Sons, Ltd.

CFD modeling of the underwash effect of military helmets as a possible mechanism for blast-induced traumatic brain injury.

Underwash occurs as the incoming shockwaves enter the helmet subspace and develop a high pressure region at the opposite side of the head. The mechanism leading to the underwash is yet not well understood. To investigate this effect, the turbulent, supersonic flow of compressible air approaching the head-helmet assembly from different directions was studied through computational fluid dynamics simulations. The effects of different incident overpressures and helmet gap size on the underwash incidence were further evaluated. The backflow-induced pressure from the air traveling outside of the helmet on the outflow from the helmet, as well as the momentum change in the backside curve of the helmet were postulated as the main reasons for this effect. Side shockwaves predicted the highest underwash overpressures. The increase rate of the underwash reduced with increasing the incident shockwave intensity.

Computational biomechanics of human brain with and without the inclusion of the body under different blast orientation.

Three different human head models in a free space are exposed to blast waves coming from four different directions. The four head-neck-body models composed of model a, with the neck free in space; model b, with neck fixed at the bottom; and model c, with the neck attached to the body. The results show that the effect of the body can be ignored for the first milliseconds of the head-blast wave interactions. Also one can see that although most biomechanical responses of the brain have similar patterns in all models, the shear stresses are heavily increased after a few milliseconds in model b in which the head motion is obstructed by the fixed-neck boundary conditions. The free-floating head model results are closer to the attached-body model.

Examination of the protective roles of helmet/faceshield and directionality for human head under blast waves.

A parametric study was conducted to delineate the efficacy of personal protective equipment (PPE), such as ballistic faceshields and advanced combat helmets, in the case of a blast. The propagations of blast waves and their interactions with an unprotected head, a helmeted one, and a fully protected finite element head model (FEHM) were modeled. The biomechanical parameters of the brain were recorded when the FEHM was exposed to shockwaves from the front, back, top, and bottom. The directional dependent tissue response of the brain and the variable efficiency of PPE with respect to the blast orientation were two major results of this study.

A computational study of influence of helmet padding materials on the human brain under ballistic impacts.

The results of a computational study of a helmeted human head are presented in this paper. The focus of the work is to study the effects of helmet pad materials on the level of acceleration, inflicted pressure and shear stress in a human brain model subjected to a ballistic impact. Four different closed cell foam materials, made of expanded polystyrene and expanded polypropylene, are examined for the padding material. It is assumed that bullets cannot penetrate the helmet shell. Finite element modelling of the helmet, padding system, head and head components is used for this dynamic nonlinear analysis. Appropriate contacts and conditions are applied between the different components of the head, as well as between the head and the pads, and the pads and the helmet. Based on the results of simulations in this work, it is concluded that the stiffness of the foam has a prominent role in reducing the level of the transferred load to the brain. A pad that is less stiff is more efficient in absorbing the impact energy and reducing the sudden acceleration of the head and consequently lowers the brain injury level. Using the pad with the least stiffness, the influence of the angle of impacts as well as the locations of the ballistic strike is studied.

A micromechanical procedure for viscoelastic characterization of the axons and ECM of the brainstem.

In this study, the optimal viscoelastic material parameters of axon and extracellular matrix (ECM) in porcine brain white matter were identified using a genetic algorithm (GA) optimization procedure. The procedure was combined with micromechanical finite element analysis (FEA) of brain tissue and experimental stress relaxation tests on brainstem specimens to find the optimal material coefficients of axon and ECM. The stress relaxation tests were performed in tension on 10 brainstem specimens at 3% strain level. The axonal volume fraction in brainstem was measured from the Scanning Electron Microscopy images of the brain tissue. A square periodic volume element was selected to represent the microscale homogenized brainstem tissue. Periodic boundary conditions were applied on the square volume element to mimics the repetitive nature of the volume element. Linear viscoelastic material properties were assumed for the brain tissue constituents under small deformation. The constitutive behavior was expressed in terms of Prony series. The GA procedure searched for the optimal material parameters by fitting the time-dependent tissue stresses of brain tissue FEA to the stresses of relaxation tests under the same loading conditions. The optimization procedure converged after 60 iterations. The initial elastic modulus of axon was found to be 12.86kPa, three times larger than that of ECM. The long-term elastic modulus of axon was 3.7kPa, while for ECM this value was 1.03kPa. The concordance correlation coefficient between FEA estimated elastic modulus of brainstem tissue using the optimal material properties and the experimental elastic modulus of brainstem specimens was 0.952, showing a strong agreement. The optimal material properties of brain tissue constituents can find applications in micromechanical analysis of brain tissue to gain insight into diffuse axonal injures (DAIs).