Integrating material properties from magnetic resonance elastography into subject-specific computational models for the human brain

Traumatic axonal injury: Clinic, forensic and biomechanics perspectives

Identification of Traumatic axonal injury (TAI) is critical in clinical practice, particularly in terms of long-term prognosis, but also for medico-legal issues, to verify whether the death or the after-effects were attributable to trauma. Multidisciplinary approaches are an undeniable asset when it comes to solving these problems. The aim of this work is therefore to list the different techniques needed to identify axonal lesions and to understand the lesion mechanisms involved in their formation. Imaging can be used to assess the consequences of trauma, to identify indirect signs of TAI, to explain the patient's initial symptoms and even to assess the patient's prognosis. Three-dimensional reconstructions of the skull can highlight fractures suggestive of trauma. Microscopic and immunohistochemical techniques are currently considered as the most reliable tools for the early identification of TAI following trauma. Finite element models use mechanical equations to predict biomechanical parameters, such as tissue stresses and strains in the brain, when subjected to external forces, such as violent impacts to the head. These parameters, which are difficult to measure experimentally, are then used to predict the risk of injury. The integration of imaging data with finite element models allows researchers to create realistic and personalized computational models by incorporating actual geometry and properties obtained from imaging techniques. The personalization of these models makes their forensic approach particularly interesting.

The White Matter Fiber Tract Deforms Most in the Perpendicular Direction During In Vivo Volunteer Impacts

White matter (WM) tract-related strains are increasingly used to quantify brain mechanical responses, but their dynamics in live human brains during in vivo impact conditions remain largely unknown. Existing research primarily looked into the normal strain along the WM fiber tracts (i.e., tract-oriented normal strain), but it is rarely the case that the fiber tract only endures tract-oriented normal strain during impacts. In this study, we aim to extend the in vivo measurement of WM fiber deformation by quantifying the normal strain perpendicular to the fiber tract (i.e., tract-perpendicular normal strain) and the shear strain along and perpendicular to the fiber tract (i.e., tract-oriented shear strain and tract-perpendicular shear strain, respectively). To achieve this, we combine the three-dimensional strain tensor from the tagged magnetic resonance imaging with the diffusion tensor imaging (DTI) from an open-access dataset, including 44 volunteer impacts under two head loading modes, i.e., neck rotations (N = 30) and neck extensions (N = 14). The strain tensor is rotated to the coordinate system with one axis aligned with DTI-revealed fiber orientation, and then four tract-related strain measures are calculated. The results show that tract-perpendicular normal strain peaks are the largest among the four strain types (p < 0.05, Friedman's test). The distribution of tract-related strains is affected by the head loading mode, of which laterally symmetric patterns with respect to the midsagittal plane are noted under neck extensions, but not under neck rotations. Our study presents a comprehensive in vivo strain quantification toward a multifaceted understanding of WM dynamics. We find that the WM fiber tract deforms most in the perpendicular direction, illuminating new fundamentals of brain mechanics. The reported strain images can be used to evaluate the fidelity of computational head models, especially those intended to predict fiber deformation under noninjurious conditions.

Effect of Human Head Shape on the Risk of Traumatic Brain Injury: A Gaussian Process Regression-Based Machine Learning Approach

INTRODUCTION

Computational head injury models are promising tools for understanding and predicting traumatic brain injuries. However, most available head injury models are "average" models that employ a single set of head geometry (e.g., 50th-percentile U.S. male) without considering variability in these parameters across the human population. A significant variability of head shapes exists in U.S. Army soldiers, evident from the Anthropometric Survey of U.S. Army Personnel (ANSUR II). The objective of this study is to elucidate the effects of head shape on the predicted risk of traumatic brain injury from computational head injury models.

MATERIALS AND METHODS

Magnetic resonance imaging scans of 25 human subjects are collected. These images are registered to the standard MNI152 brain atlas, and the resulting transformation matrix components (called head shape parameters) are used to quantify head shapes of the subjects. A generative machine learning model is used to generate 25 additional head shape parameter datasets to augment our database. Head injury models are developed for these head shapes, and a rapid injurious head rotation event is simulated to obtain several brain injury predictor variables (BIPVs): Peak cumulative maximum principal strain (CMPS), average CMPS, and the volume fraction of brain exceeding an injurious CMPS threshold. A Gaussian process regression model is trained between head shape parameters and BIPVs, which is then used to study the relative sensitivity of the various BIPVs on individual head shape parameters. We distinguish head shape parameters into 2 types: Scaling components ${T_{xx}}$, ${T_{yy}}$, and ${T_{zz}}$ that capture the breadth, length, and height of the head, respectively, and shearing components (${T_{xy}},{T_{xz}},{T_{yx}},{T_{yz}},{T_{zx}}$, and ${T_{zy}}$) that capture the relative skewness of the head shape.

RESULTS

An overall positive correlation is evident between scaling components and BIPVs. Notably, a very high, positive correlation is seen between the BIPVs and the head volume. As an example, a 57% increase in peak CMPS was noted between the smallest and the largest investigated head volume parameters. The variation in shearing components ${T_{xy}},{T_{xz}},{T_{yx}},{T_{yz}},{T_{zx}}$, and ${T_{zy}}$ on average does not cause notable changes in the BIPVs. From the Gaussian process regression model, all 3 BIPVs showed an increasing trend with each of the 3 scaling components, but the BIPVs are found to be most sensitive to the height dimension of the head. From the Sobol sensitivity analysis, the ${T_{zz}}$ scaling parameter contributes nearly 60% to the total variance in peak and average CMPS; ${T_{yy}}$ contributes approximately 20%, whereas ${T_{xx}}$ contributes less than 5%. The remaining contribution is from the 6 shearing components. Unlike peak and average CMPS, the VF-CMPS BIPV is associated with relatively evenly distributed Sobol indices across the 3 scaling parameters. Furthermore, the contribution of shearing components on the total variance in this case is negligible.

CONCLUSIONS

Head shape has a considerable influence on the injury predictions of computational head injury models. Available "average" head injury models based on a 50th-percentile U.S. male are likely associated with considerable uncertainty. In general, larger head sizes correspond to greater BIPV magnitudes, which point to potentially a greater injury risk under rapid neck rotation for people with larger heads.

Full-field, frequency-domain comparison of simulated and measured human brain deformation

We propose a robust framework for quantitatively comparing model-predicted and experimentally measured strain fields in the human brain during harmonic skull motion. Traumatic brain injuries (TBIs) are typically caused by skull impact or acceleration, but how skull motion leads to brain deformation and consequent neural injury remains unclear and comparison of model predictions to experimental data remains limited. Magnetic resonance elastography (MRE) provides high-resolution, full-field measurements of dynamic brain deformation induced by harmonic skull motion. In the proposed framework, full-field strain measurements from human brain MRE in vivo are compared to simulated strain fields from models with similar harmonic loading. To enable comparison, the model geometry and subject anatomy, and subsequently, the predicted and measured strain fields are nonlinearly registered to the same standard brain atlas. Strain field correlations (\(\:{C}_{v}\)), both global (over the brain volume) and local (over smaller sub-volumes), are then computed from the inner product of the complex-valued strain tensors from model and experiment at each voxel. To demonstrate our approach, we compare strain fields from MRE in six human subjects to predictions from two previously developed models. Notably, global \(\:{C}_{v}\) values are higher when comparing strain fields from different subjects (\(\:{C}_{v}\)~0.6-0.7) than when comparing strain fields from either of the two models to strain fields in any subject. The proposed framework provides a quantitative method to assess similarity (and to identify discrepancies) between model predictions and experimental measurements of brain deformation, and thus can aid in the development and evaluation of improved models of brain biomechanics.

Strain concentration drives the anatomical distribution of injury in acute and chronic traumatic brain injury

Brain tissue injury caused by mild traumatic brain injury (mTBI) disproportionately concentrates in the midbrain, cerebellum, mesial temporal lobe, and the interface between cortex and white matter at sulcal depths 1-12. The bio-mechanical principles that explain why physical impacts to different parts of the skull translate to common foci of injury concentrated in specific brain structures are unknown. A general and longstanding idea, which has not to date been directly tested in humans, is that different brain regions are differentially susceptible to strain loading11,13-15. We use Magnetic Resonance Elastography (MRE) in healthy participants to develop whole-brain bio-mechanical vulnerability maps that independently define which regions of the brain exhibit disproportionate strain concentration. We then validate those vulnerability maps in a prospective cohort of mTBI patients, using diffusion MRI data collected at three cross-sectional timepoints after injury: acute, sub-acute, chronic. We show that regions that exhibit high strain, measured with MRE, are also the sites of greatest injury, as measured with diffusion MR in mTBI patients. This was the case in acute, subacute, and chronic subgroups of the mTBI cohort. Follow-on analyses decomposed the biomechanical cause of increased strain by showing it is caused jointly by disproportionately higher levels of energy arriving to 'high-strain' structures, as well as the inability of 'high strain' structures to effectively disperse that energy. These findings establish a causal mechanism that explains the anatomy of injury in mTBI based on in vivo rheological properties of the human brain.

A sensor-enabled cloud-based computing platform for computational brain biomechanics

BACKGROUND AND OBJECTIVES

Driven by the risk of repetitive head trauma, sensors have been integrated into mouthguards to measure head impacts in contact sports and military activities. These wearable devices, referred to as "instrumented" or "smart" mouthguards are being actively developed by various research groups and organizations. These instrumented mouthguards provide an opportunity to further study and understand the brain biomechanics due to impact. In this study, we present a brain modeling service that can use information from these sensors to predict brain injury metrics in an automated fashion.

METHODS

We have built a brain modeling platform using several of Amazon's Web Services (AWS) to enable cloud computing and scalability. We use a custom-built cloud-based finite element modeling code to compute the physics-based nonlinear response of the intracranial brain tissue and provide a frontend web application and an application programming interface for groups working on head impact sensor technology to include simulated injury predictions into their research pipeline.

RESULTS

The platform results have been validated against experimental data available in literature for brain-skull relative displacements, brain strains and intracranial pressure. The parallel processing capability of the platform has also been tested and verified. We also studied the accuracy of the custom head surfaces generated by Avatar 3D.

CONCLUSION

We present a validated cloud-based computational brain modeling platform that uses sensor data as input for numerical brain models and outputs a quantitative description of brain tissue strains and injury metrics. The platform is expected to generate transparent, reproducible, and traceable brain computing results.

Design and characterization of 3-D printed hydrogel lattices with anisotropic mechanical properties

The goal of this study was to design, fabricate, and characterize hydrogel lattice structures with consistent, controllable, anisotropic mechanical properties. Lattices, based on three unit-cell types (cubic, diamond, and vintile), were printed using stereolithography (SLA) of polyethylene glycol diacrylate (PEGDA). To create structural anisotropy in the lattices, unit cell design files were scaled by a factor of two in one direction in each layer and then printed. The mechanical properties of the scaled lattices were measured in shear and compression and compared to those of the unscaled lattices. Two apparent shear moduli of each lattice were measured by dynamic shear tests in two planes: (1) parallel and (2) perpendicular to the scaling direction, or cell symmetry axis. Three apparent Young's moduli of each lattice were measured by compression in three different directions: (1) the "build" direction or direction of added layers, (2) the scaling direction, and (3) the unscaled direction perpendicular to both scaling and build directions. For shear deformation in unscaled lattices, the apparent shear moduli were similar in the two perpendicular directions. In contrast, scaled lattices exhibit clear differences in apparent shear moduli. In compression of unscaled lattices, apparent Young's moduli were independent of direction in cubic and vintile lattices; in diamond lattices Young's moduli differed in the build direction, but were similar in the other two directions. Scaled lattices in compression exhibited additional differences in apparent Young's moduli in the scaled and unscaled directions. Notably, the effects of scaling on apparent modulus differed between each lattice type (cubic, diamond, or vintile) and deformation mode (shear or compression). Scaling of 3D-printed, hydrogel lattices may be harnessed to create tunable, structures of desired shape, stiffness, and mechanical anisotropy, in both shear and compression.

Development and validation of subject-specific 3D human head models based on a nonlinear visco-hyperelastic constitutive framework

Computational head models are promising tools for understanding and predicting traumatic brain injuries. Most available head models are developed using inputs (i.e. head geometry, material properties and boundary conditions) from experiments on cadavers or animals and employ hereditary integral-based constitutive models that assume linear viscoelasticity in part of the rate-sensitive material response. This leads to high uncertainty and poor accuracy in capturing the nonlinear brain tissue response. To resolve these issues, a framework for the development of subject-specific three-dimensional head models is proposed, in which all inputs are derived in vivo from the same living human subject: head geometry via magnetic resonance imaging (MRI), brain tissue properties via magnetic resonance elastography (MRE), and full-field strain-response of the brain under rapid head rotation via tagged MRI. A nonlinear, viscous dissipation-based visco-hyperelastic constitutive model is employed to capture brain tissue response. Head models are validated using quantitative metrics that compare spatial strain distribution, temporal strain evolution, and the magnitude of strain maxima, with the corresponding experimental observations from tagged MRI. Results show that our head models accurately capture the strain-response of the brain. Further, employment of the nonlinear visco-hyperelastic constitutive framework provides improvements in the prediction of peak strains and temporal strain evolution over hereditary integral-based models.

Quantifying the Effect of Sex and Neuroanatomical Biomechanical Features on Brain Deformation Response in Finite Element Brain Models

Recent automotive epidemiology studies have concluded that females have significantly higher odds of sustaining a moderate brain injury or concussion than males in a frontal crash after controlling for multiple crash and occupant variables. Differences in neuroanatomical features, such as intracranial volume (ICV), have been shown between male and female subjects, but how these sex-specific neuroanatomical differences affect brain deformation is unknown. This study used subject-specific finite element brain models, generated via registration-based morphing using both male and female magnetic resonance imaging scans, to investigate sex differences of a variety of neuroanatomical features and their effect on brain deformation; additionally, this study aimed to determine the relative importance of these neuroanatomical features and sex on brain deformation metrics for a single automotive loading environment. Based on the Bayesian linear mixed models, sex had a significant effect on ICV, white matter volume and gray matter volume, as well as a section of cortical gray matter regions' thicknesses and volumes; however, after these neuroanatomical features were accounted for in the statistical model, sex was not a significant factor in predicting brain deformation. ICV had the highest relative effect on the brain deformation metrics assessed. Therefore, ICV should be considered when investigating both brain injury biomechanics and injury risk.

Data-driven Uncertainty Quantification in Computational Human Head Models

Computational models of the human head are promising tools for estimating the impact-induced response of the brain, and thus play an important role in the prediction of traumatic brain injury. The basic constituents of these models (i.e., model geometry, material properties, and boundary conditions) are often associated with significant uncertainty and variability. As a result, uncertainty quantification (UQ), which involves quantification of the effect of this uncertainty and variability on the simulated response, becomes critical to ensure reliability of model predictions. Modern biofidelic head model simulations are associated with very high computational cost and high-dimensional inputs and outputs, which limits the applicability of traditional UQ methods on these systems. In this study, a two-stage, data-driven manifold learning-based framework is proposed for UQ of computational head models. This framework is demonstrated on a 2D subject-specific head model, where the goal is to quantify uncertainty in the simulated strain fields (i.e., output), given variability in the material properties of different brain substructures (i.e., input). In the first stage, a data-driven method based on multi-dimensional Gaussian kernel-density estimation and diffusion maps is used to generate realizations of the input random vector directly from the available data. Computational simulations of a small number of realizations provide input-output pairs for training data-driven surrogate models in the second stage. The surrogate models employ nonlinear dimensionality reduction using Grassmannian diffusion maps, Gaussian process regression to create a low-cost mapping between the input random vector and the reduced solution space, and geometric harmonics models for mapping between the reduced space and the Grassmann manifold. It is demonstrated that the surrogate models provide highly accurate approximations of the computational model while significantly reducing the computational cost. Monte Carlo simulations of the surrogate models are used for uncertainty propagation. UQ of the strain fields highlights significant spatial variation in model uncertainty, and reveals key differences in uncertainty among commonly used strain-based brain injury predictor variables.