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

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.

Anatomical Features and Material Properties of Human Surrogate Head Models Affect Spatial and Temporal Brain Motion under Blunt Impact

Traumatic brain injury (TBI) is a biomechanical problem where the initiating event is dynamic loading (blunt, inertial, blast) to the head. To understand the relationship between the mechanical parameters of the injury and the deformation patterns in the brain, we have previously developed a surrogate head (SH) model capable of measuring spatial and temporal deformation in a surrogate brain under blunt impact. The objective of this work was to examine how material properties and anatomical features affect the motion of the brain and the development of injurious deformations. The SH head model was modified to study six variables independently under blunt impact: surrogate brain stiffness, surrogate skull stiffness, inclusion of cerebrospinal fluid (CSF), head/skull size, inclusion of vasculature, and neck stiffness. Each experimental SH was either crown or frontally impacted at 1.3 m/s (3 mph) using a drop tower system. Surrogate brain material, the Hybrid III neck stiffness, and skull stiffness were measured and compared to published properties. Results show that the most significant variables affecting changes in brain deformation are skull stiffness, inclusion of CSF and surrogate brain stiffness. Interestingly, neck stiffness and SH size significantly affected the strain rate only suggesting these parameters are less important in blunt trauma. While the inclusion of vasculature locally created strain concentrations at the interface of the artery and brain, overall deformation was reduced.

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.

The Significance of Cross-Sectional Shape Accuracy and Non-Linear Elasticity on the Numerical Modelling of Cerebral Veins under Tensile Loading

Traumatic brain injury (TBI) is a serious global health issue, leading to serious disabilities. One type of TBI is acute subdural haematoma (ASDH), which occurs when a bridging vein ruptures. Many numerical models of these structures, mainly based on the finite element method, have been developed. However, most rely on linear elasticity (without validation) and others on simplifications at the geometrical level. An example of the latter is the assumption of a regular cylinder with a constant radius, or the geometry of the vein acquired from medical images. Unfortunately, these do not replicate the real conditions of a mechanical tensile test. In this work, the main goal is to evaluate the influence of the vein's geometry in its mechanical behaviour under tensile loading, simulating the real conditions of experimental tests. The second goal is to implement a hyperelastic model of the bridging veins where it would be possible to observe its non-linear elastic behaviour. The results of the developed finite element models were compared to experimental data available in the literature and other models. It was possible to conclude that the geometry of the vein structure influences the tensile stress-strain curve, which means that flattened specimens should be modelled when validating constitutive models for bridging veins. Additionally, the implementation of hyperelastic material models has been verified, highlighting the potential application of the Marlow and reduced polynomial (of fourth and sixth orders) constitutive models.

Inverse identification of region-specific hyperelastic material parameters for human brain tissue

The identification of material parameters accurately describing the region-dependent mechanical behavior of human brain tissue is crucial for computational models used to assist, e.g., the development of safety equipment like helmets or the planning and execution of brain surgery. While the division of the human brain into different anatomical regions is well established, knowledge about regions with distinct mechanical properties remains limited. Here, we establish an inverse parameter identification scheme using a hyperelastic Ogden model and experimental data from multi-modal testing of tissue from 19 anatomical human brain regions to identify mechanically distinct regions and provide the corresponding material parameters. We assign the 19 anatomical regions to nine governing regions based on similar parameters and microstructures. Statistical analyses confirm differences between the regions and indicate that at least the corpus callosum and the corona radiata should be assigned different material parameters in computational models of the human brain. We provide a total of four parameter sets based on the two initial Poisson's ratios of 0.45 and 0.49 as well as the pre- and unconditioned experimental responses, respectively. Our results highlight the close interrelation between the Poisson's ratio and the remaining model parameters. The identified parameters will contribute to more precise computational models enabling spatially resolved predictions of the stress and strain states in human brains under complex mechanical loading conditions.

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.

Use of Brain Biomechanical Models for Monitoring Impact Exposure in Contact Sports

Head acceleration measurement sensors are now widely deployed in the field to monitor head kinematic exposure in contact sports. The wealth of impact kinematics data provides valuable, yet challenging, opportunities to study the biomechanical basis of mild traumatic brain injury (mTBI) and subconcussive kinematic exposure. Head impact kinematics are translated into brain mechanical responses through physics-based computational simulations using validated brain models to study the mechanisms of injury. First, this article reviews representative legacy and contemporary brain biomechanical models primarily used for blunt impact simulation. Then, it summarizes perspectives regarding the development and validation of these models, and discusses how simulation results can be interpreted to facilitate injury risk assessment and head acceleration exposure monitoring in the context of contact sports. Recommendations and consensus statements are presented on the use of validated brain models in conjunction with kinematic sensor data to understand the biomechanics of mTBI and subconcussion. Mainly, there is general consensus that validated brain models have strong potential to improve injury prediction and interpretation of subconcussive kinematic exposure over global head kinematics alone. Nevertheless, a major roadblock to this capability is the lack of sufficient data encompassing different sports, sex, age and other factors. The authors recommend further integration of sensor data and simulations with modern data science techniques to generate large datasets of exposures and predicted brain responses along with associated clinical findings. These efforts are anticipated to help better understand the biomechanical basis of mTBI and improve the effectiveness in monitoring kinematic exposure in contact sports for risk and injury mitigation purposes.

Assessment of brain injury characterization and influence of modeling approaches

In this study, using computational biomechanics models, we investigated influence of the skull-brain interface modeling approach and the material property of cerebrum on the kinetic, kinematic and injury outputs. Live animal head impact tests of different severities were reconstructed in finite element simulations and DAI and ASDH injury results were compared. We used the head/brain models of Total HUman Model for Safety (THUMS) and Global Human Body Models Consortium (GHBMC), which had been validated under several loading conditions. Four modeling approaches of the skull-brain interface in the head/brain models were evaluated. They were the original models from THUMS and GHBMC, the THUMS model with skull-brain interface changed to sliding contact, and the THUMS model with increased shear modulus of cerebrum, respectively. The results have shown that the definition of skull-brain interface would significantly influence the magnitude and distribution of the load transmitted to the brain. With sliding brain-skull interface, the brain had lower maximum principal stress compared to that with strong connected interface, while the maximum principal strain slightly increased. In addition, greater shear modulus resulted in slightly higher the maximum principal stress and significantly lower the maximum principal strain. This study has revealed that using models with different modeling approaches, the same value of injury metric may correspond to different injury severity.

A Finite Element Model of Cerebral Vascular Injury for Predicting Microbleeds Location

Finite Element (FE) models of brain mechanics have improved our understanding of the brain response to rapid mechanical loads that produce traumatic brain injuries. However, these models have rarely incorporated vasculature, which limits their ability to predict the response of vessels to head impacts. To address this shortcoming, here we used high-resolution MRI scans to map the venous system anatomy at a submillimetre resolution. We then used this map to develop an FE model of veins and incorporated it in an anatomically detailed FE model of the brain. The model prediction of brain displacement at different locations was compared to controlled experiments on post-mortem human subject heads, yielding over 3,100 displacement curve comparisons, which showed fair to excellent correlation between them. We then used the model to predict the distribution of axial strains and strain rates in the veins of a rugby player who had small blood deposits in his white matter, known as microbleeds, after sustaining a head collision. We hypothesised that the distribution of axial strain and strain rate in veins can predict the pattern of microbleeds. We reconstructed the head collision using video footage and multi-body dynamics modelling and used the predicted head accelerations to load the FE model of vascular injury. The model predicted large axial strains in veins where microbleeds were detected. A region of interest analysis using white matter tracts showed that the tract group with microbleeds had 95th percentile peak axial strain and strain rate of 0.197 and 64.9 s⁻¹ respectively, which were significantly larger than those of the group of tracts without microbleeds (0.163 and 57.0 s⁻¹). This study does not derive a threshold for the onset of microbleeds as it investigated a single case, but it provides evidence for a link between strain and strain rate applied to veins during head impacts and structural damage and allows for future work to generate threshold values. Moreover, our results suggest that the FE model has the potential to be used to predict intracranial vascular injuries after TBI, providing a more objective tool for TBI assessment and improving protection against it.

A Strain-Rate Dependent Constitutive Model for Göttingen Minipig Cerebral Arteries

Computational simulations of traumatic brain injury (TBI) are commonly used to advance understanding of the injury-pathology relationship, tissue damage thresholds, and design of protective equipment such as helmets. Both human and animal TBI models have developed substantially over recent decades, partially due to the inclusion of more detailed brain geometry and representation of tissues like cerebral blood vessels. Explicit incorporation of vessels dramatically affects local strain and enables researchers to investigate TBI-induced damage to the vasculature. While some studies have indicated that cerebral arteries are rate-dependent, no published experimentally based, rate-sensitive constitutive models of cerebral arteries exist. In the present work, we characterize the mechanical properties of axially failed porcine arteries, both quasi-statically (0.01 s-1) and at high rate (<100 s-1), and propose a rate-sensitive model to fit the data. We find that the quasi-static and high-rate stress-stretch curves become significantly different (p>0.05) above a stretch of 1.23. We additionally find a significant change in both failure stretch and stress as a result of strain rate. The stress-stretch curve is then modeled as a Holzapfel-Gasser-Ogden material, with a Prony series added to capture the effects of viscoelasticity. Ultimately, this paper demonstrates that rate dependence should be considered in the material properties of cerebral arteries undergoing high strain-rate deformations and provides a ready-to-use model for finite element implementation.

Instantaneous Brain Strain Estimation for Automotive Head Impacts via Deep Learning

Efficient brain strain estimation is critical for routine application of a head injury model. Lately, a convolutional neural network (CNN) has been successfully developed to estimate spatially detailed brain strains instantly and accurately in contact sports. Here, we extend its application to automotive head impacts, where impact profiles are typically more complex with longer durations. Head impact kinematics (N=458) from two public databases were used to generate augmented impacts (N=2694). They were simulated using the anisotropic Worcester Head Injury Model (WHIM) V1.0, which provided baseline elementwise peak maximum principal strain (MPS). For each augmented impact, rotational velocity (v_rot) and the corresponding rotational acceleration (a_rot) profiles were concatenated as static images to serve as CNN input. Three training strategies were evaluated: 1) "baseline", using random initial weights; 2) "transfer learning", using weight transfer from a previous CNN model trained on head impacts drawn from contact sports; and 3) "combined training", combining previous training data from contact sports (N=5661) for training. The combined training achieved the best performances. For peak MPS, the CNN achieved a coefficient of determination (R²) of 0.932 and root mean squared error (RMSE) of 0.031 for the real-world testing dataset. It also achieved a success rate of 60.5% and 94.8% for elementwise MPS, where the linear regression slope, k, and correlation coefficient, r, between estimated and simulated MPS did not deviate from 1.0 (when identical) by more than 0.1 and 0.2, respectively. Cumulative strain damage measure (CSDM) from the CNN estimation was also highly accurate compared to those from direct simulation across a range of thresholds (R² of 0.899-0.943 with RMSE of 0.054-0.069). Finally, the CNN achieved an average k and r of 0.98±0.12 and 0.90±0.07, respectively, for six reconstructed car crash impacts drawn from two other sources independent of the training dataset. Importantly, the CNN is able to efficiently estimate elementwise MPS with sufficient accuracy while conventional kinematic injury metrics cannot. Therefore, the CNN has the potential to supersede current kinematic injury metrics that can only approximate a global peak MPS or CSDM. The CNN technique developed here may offer enhanced utility in the design and development of head protective countermeasures, including in the automotive industry. This is the first study aimed at instantly estimating spatially detailed brain strains for automotive head impacts, which employs >8.8 thousand impact simulations generated from ~1.5 years of nonstop computations on a high-performance computing platform.