A Fractional Viscoelastic Model Of The Axon In Brain White Matter

Traumatic axonal injury occurs when loads experienced on the tissue-scale are transferred to the individual axons. Mechanical characterization of axon deformation especially under dynamic loads however is extremely difficult owing to their viscoelastic properties. The viscoelastic characterization of axon properties that are based on interpretation of results from in-vivo brain Magnetic Resonance Elastography (MRE) are dependent on the specific frequencies used to generate shear waves with which measurements are made. In this study, we aim to develop a fractional viscoelastic model to characterize the time dependent behavior of the properties of the axons in a composite white matter (WM) model. The viscoelastic powerlaw behavior observed at the tissue level is assumed to exist across scales, from the continuum macroscopic level to that of the microstructural realm of the axons. The material parameters of the axons and glia are fitted to a springpot model. The 3D fractional viscoelastic springpot model is implemented within a finite element framework. The constitutive equations defining the fractional model are coded using a vectorized user defined material (VUMAT) subroutine in ABAQUS finite element software. Using this material characterization, representative volume elements (RVE) of axons embedded in glia with periodic boundary conditions are developed and subjected to a relaxation displacement boundary condition. The homogenized orthotropic fractional material properties of the axon-matrix system as a function of the volume fraction of axons in the ECM are extracted by solving the inverse problem.Comment: Accepted for publication at the 12th International Conference on Mathematical Modeling in Physical Science

A study on Poynting effect in brain white matter: A hyperelastic 3D micromechanical model

A novel 3D micromechanical Finite Element Model (FEM) has been developed to depict the Poynting effect in bi-phasic Representative volume element (RVE) with axons embedded in surrounding extra-cellular matrix (ECM) for simulating the brain white matter response under simple and pure shear. In the proposed 3D FEM, nonlinear Ogden hyper-elastic material model describes axons and ECM materials. The modeled bi-phasic RVEs have axons tied to surrounding matrix. In this proof-of-concept (POC) FEM, three simple shear loading configurations and a pure shear scenario were simulated. Root mean square deviation (RMSD) were computed for stress and deformation response plots to depict role of axon-ECM orientations & loading condition on the Poynting effect. Variations in normal stresses (S11, S22, or S33) perpendicular to the shear plane emphasized role of fiber-matrix interactions. At high strains, the stress-strain% plots also indicated modest strain stiffening effects and bending stresses in purely sheared axons

On the influence of inhomogeneous stiffness and growth on mechanical instabilities in the developing brain

The characteristic surface morphology of the mammalian brain is closely correlated with brain function and dysfunction. During development, the initially smooth surface evolves into an elaborately convoluted pattern. Growing evidence suggests that mechanical instabilities emerging from differential growth between a faster growing outer gray matter and a slower growing inner white matter play a major role in brain morphogenesis. Previous studies assume uniform growth and stiffness; yet, recent experiments indicate that the properties of brain tissue are highly inhomogeneous. Here, we hypothesize that regionally varying developmental pathways across the brain result in nonuniform material properties at the onset of cortical folding. We establish a computational model of brain growth to explore the effects of stiffness and growth variations in gray and white matter tissue to mimic cellular processes and evolving tissue microstructure. We present an effective approach to determine critical growth values from geometrical data and systematically study the effect of inhomogeneous material properties on growth-induced primary and secondary instabilities. Our results reveal that critical growth and wavelength strongly depend on the stiffness distribution in the developing brain. Regional variations in cortical growth affect secondary instabilities and evoke highly irregular folding patterns, but characteristic wavelength and critical growth remain relatively stable. The interplay of different influential factors including cortical thickness, brain geometry, stiffness, and growth explains how primary folds are highly preserved across individuals, whereas secondary and tertiary folds vary significantly. Our findings are directly applicable to imaging data of fetal brains and ultimately enable early diagnostics of cortical malformations to improve treatment of neurodevelopmental disorders including epilepsy, autism, spectrum disorders, and schizophrenia

SIMBIO-M 2014, SIMulation technologies in the fields of BIO-Sciences and Multiphysics: BioMechanics, BioMaterials and BioMedicine, Marseille, France, june 2014

Proceedings de la 3ème édition de la conférence internationale Simbio-M (2014). Organisée conjointement par l'IFSTTAR, Aix-Marseille Université, l'université de Coventry et CADLM, cette conférence se concentre sur les progrès des technologies de simulation dans les domaines des sciences du vivant et multiphysiques: Biomécanique, Biomatériaux et Biomédical. L'objectif de cette conférence est de partager et d'explorer les résultats dans les techniques d'analyse numérique et les outils de modélisation mathématique. Cette approche numérique permet des études prévisionnelles ou exploratoires dans les différents domaines des biosciences

An Investigation Of The Relationship Between Axonal Injury, Biomarker Expression And Mechanical Response In A Rodent Head Impact Acceleration Model

In the United States 1.4 million people sustain traumatic brain injury (TBI) each year, resulting in 235,000 hospitalizations and 50,000 fatalities annually. Traumatic axonal injury (TAI) is a serious outcome of TBI that accounts for 40-50% of hospitalizations due to head injury and one third of the mortality due to TBI, and it is difficult to diagnose and evaluate. The purpose of this dissertation is to determine mechanical injury predictors for TAI and identify potential biomarkers to evaluate TAI. In this dissertation, a modified Marmarou impact acceleration injury model was developed to allow the monitoring of velocity of the impactor and characterization of head kinematics during impact. The rat head sustained linear acceleration and angular velocity of 918±281g and 116±45 rad/sec, respectively in 2.25m impacts, and 609±142g and 98±31 rad/sec, respectively in 1.25m impacts. The variability in head kinematics resulting from the same drop height suggested that monitoring of mechanical parameters are critical factors for illustration of the level of closed head injury with this model. Using this modified impact acceleration model, a series studies were performed to investigate correlation between impact mechanics and TAI, as well as correlation between biomarker levels and TAI. In the first part of this dissertation, thirty-one anesthetized male Sprague-Dawley rats (392 ± 13 grams) were impacted using a modified impact acceleration injury device from 2.25 m and 1.25 m heights. Beta-amyloid precursor protein (β-APP) immunocytochemistry was used to assess and quantify axonal changes in CC and Py. Linear and angular responses of the rat head were monitored and measured in vivo with an attached accelerometer and angular rate sensor, and were correlated to TAI data. Logistic regression analysis suggested that the occurrence of severe TAI in CC was best predicted by average linear acceleration, followed by Power and time to surface righting. The combination of average linear acceleration and time to surface righting showed an improved predictive result. In Py, severe TAI was best predicted by time to surface righting, followed by peak and average angular velocity. When both CC and Py were combined, power was the best predictor, and the combined average linear acceleration and average angular velocity was also found to have good injury predictive ability. In the second part of this dissertation, tweenty-four anesthetized male Sprague-Dawley rats were subjected to a closed head injury from 1.25, 1.75 and 2.25 m drop heights (n=8 for each group). 24 h after impact, cerebrospinal fluid (CSF) and serum were collected. CSF and serum levels of neurofilament H (NF-H), glial fibrillary acidic protein (GFAP), interleukin (IL)-6, and amyloid beta (Aβ) 1-42 were assessed by enzyme-linked immunosorbent assay (ELISA). Compared to controls, significantly higher CSF and serum pNF-H levels were observed in all impact groups, except between 1.25 m and control in serum. Furthermore, CSF and serum pNF-H levels were significantly different between the impact groups. For GFAP, both CSF and serum levels were significantly higher at 2.25 m compared to 1.75 m, 1.25 m and controls. There was no significant difference in CSF and serum GFAP levels between 1.75 m and 1.25 m, although both groups were significantly higher than control. TBI rats also showed significantly higher levels of IL-6 versus control in both CSF and serum, but no significant difference was observed between each impact group. Levels of Aβ were not significantly different between groups. Logistic regression analysis suggested that both pNF-H and GFAP levels in CSF and serum were good predictors for severe TBI. Pearson\u27s correlation analysis showed pNF-H and GFAP levels in CSF and serum had positive correlation with power (rate of impact energy), followed by average linear acceleration and surface righting (p\u3c0.01), which were good predictors for traumatic axonal injury (TAI) according to histologic assessment in first part study, suggesting that they are directly related to the injury mechanism

Investigation of Primary Blast Injury and Protection using Sagittal and Transverse Finite Element Head Models

The prevalence of blast related mild traumatic brain injury (mTBI) in recent military conflicts, attributed in part to an increased exposure to improvised explosive devices (IEDs), requires further understanding to develop methods to mitigate the effects of primary blast exposure. Although general blast injury has been studied extensively since the 1950’s, many aspects of mTBI remain unclear, including specific injury mechanisms and injury criteria. The purpose of this work was to develop finite element models to investigate primary blast injury to the head in the loading regimes relevant to mTBI, to use the models to determine the response of the brain tissue, and ultimately to investigate the effectiveness of helmets on response mitigation. Since blast is inherently a wave dominated phenomena, finite element models require relatively small elements to resolve complex pressure wave transmission and reflections in order to accurately predict tissue response. Furthermore, mesh continuity between the tissue structures is necessary to ensure accurate wave transmission. The computational limitations present in analyzing a full three dimensional blast head model led to the development of sagittal and transverse planar models, which provide a fully coupled analysis with the required mesh resolution while remaining computationally feasible. The models consist of a single layer of solid hexahedral elements, and include all of the relevant tissues in the head including the skin, muscle, skull, cerebrospinal fluid, and brain. The sagittal and transverse models were validated using head kinematics against experimental data on Hybrid III head-forms exposed to free-field blast. The peak head accelerations of the models was in close agreement to the experimental data, and the HIC15 predictions were in reasonable agreement. In addition, the models were validated for intracranial pressure using experimental data from cadaveric heads exposed to shock tube loading. The intracranial pressures predicted by the sagittal and transverse models was in good agreement at the frontal, temporal, and parietal locations, and in fair agreement at the occipital location. A simplified three dimensional ellipsoid study was undertaken to verify that sagittal and transverse planar models are capable of representing a three dimensional shape. This investigation confirmed that the pressures predicted by the planar models are accurate at the frontal, temporal, and parietal locations, although underpredicted at the occipital location due to three dimensional wave superposition that becomes significant at the occipital region. The sagittal and transverse models were run at three representative blast load cases, corresponding to 5 kg of C4 at 3, 3.5, and 4 m standoff distances, and the resulting intracranial strains and pressures were investigated. The sagittal and transverse models report peak principal strains of 0.035 – 0.062 and 0.053 – 0.087 respectively. In comparison to the available threshold values of principal strain in the literature, the strains predicted by the models are generally low. While the strains reported by the models in primary blast are small, the strain rates are significantly greater (ranging from 226 – 571 s-1) than those seen in typical automotive or blunt impact scenarios. Furthermore, the models report that significant levels of intracranial pressure, on the order of several atmospheres, can be generated in the brain tissue during primary blast exposure. The peak pressures in the brain tissue for both models typically exceeded the existing injury thresholds for intracranial that are available in the literature. However, these existing criteria were generally developed for automotive crash scenarios, so may not be suitable for the short durations inherent to blast. The magnitudes of intracranial pressure increased significantly with increasing blast load severity, while changes in principal strain were relatively small, and peak strains were low in all three load cases, suggesting that pressure may be a more appropriate injury response metric for blast injury. The sagittal and transverse models were outfitted with various military helmet configurations and materials to investigate the influence of helmet visors, foam lining presence and density, and Kevlar material stiffness on the protective properties of the helmet. The peak head accelerations and intracranial pressures were compared for low and high intensity blast loads. In general, the presence of a helmet resulted in reduced peak head accelerations, and a greater reduction was reported with the addition of a half-visor and full-visor. The presence of a visor significantly reduced positive intracranial pressures in all cases, although increased the maximum negative pressures in some cases. The effects of the foam lining material was not as significant to the model response as the helmet visor configurations, but in general, a lower density foam provided better load mitigation. In cases where there was no foam lining, pressure wave reflections in the air gap between the helmet and head were found to cause greater intracranial pressures in adjacent brain tissue, although the magnitudes of these increased pressures were generally lower than the incident compressive pressures caused by the initial wave impact

Direction-Dependent Responses To Traumatic Brain Injury In Pediatric Pigs

Traumatic brain injury (TBI) in children is a costly and alarmingly prevalent public health concern. Children (4-11 years of age) in the US have the highest rate of TBI-related emergency department visits. The plane of head rotation significantly affects neurocognitive deficits and pathophysiological responses such as axonal injury, but is largely ignored in TBI literature. In Chapter 1, an outline of existing research is provided, including the lack of attention to diagnosis, treatment, and prevention in children, who exhibit distinct biomechanical and neuropathological responses to TBI. Additionally, we hypothesize that the plane of head rotation in TBI induces a) region-specific changes in axonal injury, which lead to acute and chronic changes in electrophysiological responses; b) changes to event-related potentials and resting state electroencephalography (EEG) and c) tract-oriented strain and strain rate alterations in the white matter. All work in this dissertation is based on a well-established piglet model of TBI. In Chapter 2, we assess a novel rotational head kinematic metric, rotational work (RotWork), which incorporates head rotation rate, direction, and brain shape, as a predictor of acute axonal injury. This metric provides an improvement over existing metrics and could be useful in the development of effective child safety equipment used in recreation or transportation. In Chapter 3, we generate functional networks from auditory event-related potentials and use the patterns of change to distinguish injured brains from non-injured; the resulting algorithm showed an 82% predictive accuracy. In Chapter 4, we find elevations in network nodal strength, modularity and clustering coefficient after TBI across all frequency bands relative to baseline, whereas both metrics were reduced in shams. We report the first study using resting state EEG to create functional networks in relation to pediatric TBI, noting that this work may assist in the development of TBI biomarkers. In Chapter 5, we use a high-resolution finite element model to examine the effects of head rotation plane on the distribution of regional strains and strain rates. Sagittal rapid head rotations induced significantly larger volume fraction of damaged brainstem than axial and coronal rotations. We also found that local tissue deformation and histopathology were head direction- and region- dependent but poorly correlated at a local scale. Finally, in Chapter 6, we conclude that the work presented in this dissertation is novel and contributes valuable knowledge to the study of pediatric TBI, and that consideration of the plane of head rotation is critical to the understanding and accurate prediction of pediatric functional and region-dependent responses to TBI

Head impact effects in Small Remotely Piloted Aircraft System (sRPAS) collisions: Gender specific risks and vulnerable population protection

This study focuses on supporting the development of safety regulations for vulnerable populations during drone to head impacts. First, the small female head and neck model was compared to cadaveric data. Then, combined with lab’s previous work, gender-based disparities in head impact responses were highlighted, with small females experiencing higher injury risk metrics, despite lower skull von Mises stress. Beyond small females, children of various ages and their head responses during impacts were also analyzed. In addition to the previously developed quadcopter drone model, a new Mavic Pro drone model was developed, and this model was integrated with human head models during comparison against cadaveric data. The Mavic Pro, despite its lower weight, demonstrated higher injury risks compared to the previously studied Phantom 3. Overall, in this study head kinematics, head injury criteria (HIC), rotational velocities, and brain strains were analyzed, indicating potential risks for vulnerable populations. These findings underscore the need for tailored safety measures, regulatory guidelines, and comprehensive injury prevention strategies in the field of drone operations