Displacement Error Propagation From Embedded Markers to Brain Strain

A computational pipeline towards large-scale and multiscale modeling of traumatic axonal injury

Contemporary biomechanical modeling of traumatic brain injury (TBI) focuses on either the global brain as an organ or a representative tiny section of a single axon. In addition, while it is common for a global brain model to employ real-world impacts as input, axonal injury models have largely been limited to inputs of either tension or compression with assumed peak strain and strain rate. These major gaps between global and microscale modeling preclude a systematic and mechanistic investigation of how tissue strain from impact leads to downstream axonal damage throughout the white matter. In this study, a unique subject-specific multimodality dataset from a male ice-hockey player sustaining a diagnosed concussion is used to establish an efficient and scalable computational pipeline. It is then employed to derive voxelized brain deformation, maximum principal strains and white matter fiber strains, and finally, to produce diverse fiber strain profiles of various shapes in temporal history necessary for the development and application of a deep learning axonal injury model in the future. The pipeline employs a structured, voxelized representation of brain deformation with adjustable spatial resolution independent of model mesh resolution. The method can be easily extended to other head impacts or individuals. The framework established in this work is critical for enabling large-scale (i.e., across the entire white matter region, head impacts, and individuals) and multiscale (i.e., from organ to cell length scales) modeling for the investigation of traumatic axonal injury (TAI) triggering mechanisms. Ultimately, these efforts could enhance the assessment of concussion risks and design of protective headgear. Therefore, this work contributes to improved strategies for concussion detection, mitigation, and prevention.

Biomechanical Response of Head Surrogate With and Without the Helmet

Measurements of brain deformations under injurious loading scenarios are actively sought. In this work, we report experimentally measured head kinematics and corresponding dynamic, two-dimensional brain simulant deformations in head surrogates under a blunt impact, with and without a helmet. Head surrogates used in this work consisted of skin, skull, dura, falx, tentorium, and brain stimulants. The head surrogate geometry was based on the global human body models consortium's head model. A base head surrogate consisting of skin-skull-brain was considered. In addition, the response of two other head surrogates, skin-skull-dura-brain, and skin-skull-dura-brain-falx-tentorium, was investigated. Head surrogate response was studied for sagittal and coronal plane rotations for impactor velocities of 1 and 3 m/s. Response of head surrogates was compared against strain measurements in PMHS. The strain pattern in the brain simulant was heterogenous, and peak strains were established within ∼30 ms. The choice of head surrogate affect the spatiotemporal evolution of strain. For no helmet case, peak MPS of ∼50-60% and peak MSS of ∼35-50% were seen in brain simulant corresponding to peak rotational accelerations of ∼5000-7000 rad/s2. Peak head kinematics and peak MPS have been reduced by up to 75% and 45%, respectively, with the conventional helmet and by up to 90% and 85%, respectively, with the helmet with antirotational pads. Overall, these results provide important, new data on brain simulant strains under a variety of loading scenarios-with and without the helmets.

Approximating subject-specific brain injury models via scaling based on head-brain morphological relationships

Most human head/brain models represent a generic adult male head/brain. They may suffer in accuracy when investigating traumatic brain injury (TBI) on a subject-specific basis. Subject-specific models can be developed from neuroimages; however, neuroimages are not typically available in practice. In this study, we establish simple and elegant regression models between brain outer surface morphology and head dimensions measured from neuroimages along with age and sex information (N = 191; 141 males and 50 females with age ranging 14-25 years). The regression models are then used to approximate subject-specific brain models by scaling a generic counterpart, without using neuroimages. Model geometrical accuracy is assessed using adjusted [Formula: see text] and absolute percentage error (e.g., 0.720 and 3.09 ± 2.38%, respectively, for brain volume when incorporating tragion-to-top). For a subset of 11 subjects (from smallest to largest in brain volume), impact-induced brain strains are compared with those from "morphed models" derived from neuroimage-based mesh warping. We find that regional peak strains from the scaled subject-specific models are comparable to those of the morphed counterparts but could be considerably different from those of the generic model (e.g., linear regression slope of 1.01-1.03 for gray and white matter regions versus 1.16-1.19, or up to ~ 20% overestimation for the smallest brain studied). These results highlight the importance of incorporating brain morphological variations in impact simulation and demonstrate the feasibility of approximating subject-specific brain models without neuroimages using age, sex, and easily measurable head dimensions. The scaled models may improve subject specificity for future TBI investigations.

Cerebral vascular strains in dynamic head impact using an upgraded model with brain material property heterogeneity

Cerebral vascular injury (CVI) is a frequent consequence of traumatic brain injury but has often been neglected. Substantial experimental work exists on vascular material properties and failure/subfailure thresholds. However, little is known about vascular in vivo loading conditions in dynamic head impact, which is necessary to investigate the risk, severity, and extent of CVI. In this study, we resort to the Worcester Head Injury Model (WHIM) V2.1 for investigation. The model embeds the cerebral vasculature network and is further upgraded to incorporate brain material property heterogeneity based on magnetic resonance elastography. The brain material property is calibrated to match with the previously validated anisotropic V1.0 version in terms of whole-brain strains against six experimental datasets of a wide range of blunt impact conditions. The upgraded WHIM is finally used to simulate five representative real-world head impacts drawn from contact sports and automotive crashes. We find that peak strains in veins are considerably higher than those in arteries and that peak circumferential strains are also higher than peak axial strains. For a typical concussive head impact, cerebral vascular axial strains reach the lowest reported yield strain of ∼7-8%. For severe automotive impacts, axial strains could reach ∼20%, which is on the order of the lowest reported ultimate failure strain of ∼24%. These results suggest in vivo mechanical loading conditions of the cerebral vasculature (excluding bridging veins not assessed here) due to rapid head rotation are at the lower end of failure/subfailure thresholds established from ex vivo experiments. This study provides some first insight into the risk, severity, and extent of CVI in real-world head impacts.

Displacement voxelization to resolve mesh-image mismatch: Application in deriving dense white matter fiber strains

BACKGROUND AND OBJECTIVE

It is common to combine biomechanical modeling and medical images for multimodal analyses. However, mesh-image mismatch may occur that prevents direct information exchange. To eliminate mesh-image mismatch, we develop a simple but elegant displacement voxelization technique based on image voxel corner nodes to achieve voxel-wise strain. We then apply the technique to derive dense white matter fiber strains along whole-brain tractography (∼35 k fiber tracts consisting of ∼3.3 million sampling points) resulting from head impact.

METHODS

Displacements at image voxel corner nodes are first obtained from model simulation via scattered interpolation. Each voxel is then scaled linearly to form a unit hexahedral element. This allows convenient and efficient voxel-wise strain tensor calculation and displacement interpolation at arbitrary fiber sampling points via shape functions. Fiber strains from displacement interpolation are then compared with those from the commonly used strain tensor projection using either voxel- or element-wise strain tensors.

RESULTS

Based on a synthetic displacement field, fiber strains interpolated from voxelized displacement are considerably more accurate than those from strain tensor projection relative to the prescribed ground-truth (determinant of coefficient (R²) of 1.00 and root mean squared error (RMSE) of 0.01 vs. 0.87 and 0.10, respectively). For a set of real-world reconstructed head impacts (N = 53), the strain tensor projection method performs similarly poorly (R² of 0.80-0.90 and RMSE of 0.03-0.07), with overestimation strongly correlated with strain magnitude (Pearson correlation coefficient >0.9). Up to ∼15% of the fiber strains are overestimated by more than the lower bound of a conservative injury threshold of 0.09. The percentage increases to ∼37% when halving the threshold. Voxel interpolation is also significantly more efficient (15 s vs. 40 s for element strain tensor projection, without parallelization).

CONCLUSIONS

Voxelized displacement interpolation is considerably more accurate and efficient in deriving dense white matter fiber strains than strain tensor projection. The latter generally overestimates with overestimation magnitude strongly correlating with fiber strain magnitude. Displacement voxelization is an effective technique to eliminate mesh-image mismatch and generates a convenient image representation of tissue deformation. This technique can be generalized to broadly facilitate a diverse range of image-related biomechanical problems for multimodal analyses. The convenient image format may also promote and facilitate biomechanical data sharing in the future.

MR Imaging of Human Brain Mechanics In Vivo: New Measurements to Facilitate the Development of Computational Models of Brain Injury

Computational models of the brain and its biomechanical response to skull accelerations are important tools for understanding and predicting traumatic brain injuries (TBIs). However, most models have been developed using experimental data collected on animal models and cadaveric specimens, both of which differ from the living human brain. Here we describe efforts to noninvasively measure the biomechanical response of the human brain with MRI-at non-injurious strain levels-and generate data that can be used to develop, calibrate, and evaluate computational brain biomechanics models. Specifically, this paper reports on a project supported by the National Institute of Neurological Disorders and Stroke to comprehensively image brain anatomy and geometry, mechanical properties, and brain deformations that arise from impulsive and harmonic skull loadings. The outcome of this work will be a publicly available dataset ( http://www.nitrc.org/projects/bbir ) that includes measurements on both males and females across an age range from adolescence to older adulthood. This article describes the rationale and approach for this study, the data available, and how these data may be used to develop new computational models and augment existing approaches; it will serve as a reference to researchers interested in using these data.

Intracranial Displacement Measurements Within Targeted Anatomical Regions of a Postmortem Human Surrogate Brain Subjected to Impact

The dynamic response of the human brain subjected to impulsive loading conditions is of fundamental importance to the understanding of traumatic brain injuries. Due to the complexity of such measurements, the existing experimental datasets available to researchers are sparse. However, these measurements are used extensively in the validation of complex finite element models used in the design of protective equipment and the development of injury mitigation strategies. The primary objective of this study was to develop a comprehensive methodology to measure displacement in specific anatomical regions of the brain. A state-of-the-art high-speed cineradiography system was used to capture brain motion in post-mortem human surrogate specimens at a rate of 7500 fps. This paper describes the methodology used to capture these data and presents measurements from these tests. Two-dimensional displacement fields are presented and analyzed based on anatomical regions of the brain. These data demonstrated a multi-modal displacement response in several regions of the brain. The full response of the brain consisted of an elastic superposition of a series of bulk rotations of the brain about its centre of gravity. The displacement field could be linked directly to specific anatomical regions. The methods presented mark an improvement in temporal and spatial resolution of data collection, which has implications for our developing understanding of brain trauma.

Measurement of brain simulant strains in head surrogate under impact loading

Impact-induced traumatic brain injury (TBI) is a major source of disability and mortality. Knowledge of brain strains during impact (accelerative) loading is critical for the overall management of TBI, including the development of injury thresholds, personal protective equipment, and validation of computational models. Despite these needs, the current understanding of brain strains in humans or humanlike surrogates is limited, especially for injury causing loading magnitudes. Toward this end, we measured full-field, in-plane (2D) strains in a brain simulant using the hemispherical head surrogate. The hemispherical head was mounted on the Hybrid-III neck and subjected to impact loading using a linear impactor system. The resulting head kinematics was measured using a triaxial accelerometer and angular rate sensors. Dynamic, 2D strains in a brain simulant were obtained using high-speed imaging and digital image correlation. Concurrent finite element (FE) simulations of the experiment were also performed to gain additional insights. The role of stiff membranes of the head was also studied using experiments. Our results suggest that rotational modes dominate the response of the brain simulant. The wave propagation in the brain simulant as a result of impact has a timescale of ~100 ms. We obtain peak strains of ~20%, ~40%, ~60% for peak rotational accelerations of ~838, ~5170, ~11,860 rad/s², respectively. Further, peak strains in cortical regions are higher than subcortical regions by up to ~70%. The agreement between the experiments and FE simulations is reasonable in terms of spatiotemporal evolution of strain pattern and peak strain magnitudes. Experiments with the addition of falx and tentorium indicate significant strain concentration (up to 115%) in the brain simulant near the interface of falx or tentorium and brain simulant. Overall, this work provides important insights into the biomechanics of strain in the brain simulant during impact loading.