Application of trilateration and Kalman filtering algorithms to track dynamic brain deformation using sonomicrometry

Brain Material Properties and Integration of Arachnoid Complex for Biofidelic Impact Response for Human Head Finite Element Model

Finite element head models offer great potential to study brain-related injuries; however, at present may be limited by geometric and material property simplifications required for continuum-level human body models. Specifically, the mechanical properties of the brain tissues are often represented with simplified linear viscoelastic models, or the material properties have been optimized to specific impact cases. In addition, anatomical structures such as the arachnoid complex have been omitted or implemented in a simple lumped manner. Recent material test data for four brain regions at three strain rates in three modes of loading (tension, compression, and shear) was used to fit material parameters for a hyper-viscoelastic constitutive model. The material model was implemented in a contemporary detailed head finite element model. A detailed representation of the arachnoid trabeculae was implemented with mechanical properties based on experimental data. The enhanced head model was assessed by re-creating 11 ex vivo head impact scenarios and comparing the simulation results with experimental data. The hyper-viscoelastic model faithfully captured mechanical properties of the brain tissue in three modes of loading and multiple strain rates. The enhanced head model showed a high level of biofidelity in all re-created impacts in part due to the improved brain-skull interface associated with implementation of the arachnoid trabeculae. The enhanced head model provides an improved predictive capability with material properties based on tissue level data and is positioned to investigate head injury and tissue damage in the future.

Characterization of material properties and deformation in the ANGUS phantom during mild head impacts using MRI

Traumatic brain injury (TBI) is a major health concern affecting both military and civilian populations. Despite notable advances in TBI research in recent years, there remains a significant gap in linking the impulsive loadings from a blast or a blunt impact to the clinical injury patterns observed in TBI. Synthetic head models or phantoms can be used to establish this link as they can be constructed with geometry, anatomy, and material properties that match the human brain, and can be used as an alternative to animal models. This study presents one such phantom called the Anthropomorphic Neurologic Gyrencephalic Unified Standard (ANGUS) phantom, which is an idealized gyrencephalic brain phantom composed of polyacrylamide gel. Here we mechanically characterized the ANGUS phantom using tagged magnetic resonance imaging (MRI) and magnetic resonance elastography (MRE), and then compared the outcomes to data obtained in healthy volunteers. The direct comparison between the phantom's response and the data from a cohort of in vivo human subjects demonstrate that the ANGUS phantom may be an appropriate model for bulk tissue response and gyral dynamics of the human brain under small amplitude linear impulses. However, the phantom's response differs from that of the in vivo human brain under rotational impacts, suggesting avenues for future improvements to the phantom.

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.

Integrating Human and Non-Human Primate Data to Estimate Human Tolerances for Traumatic Brain Injury

Traumatic brain injury (TBI) contributes to a significant portion of the injuries resulting from motor vehicle crashes, falls, and sports collisions. The development of advanced countermeasures to mitigate these injuries requires a complete understanding of the tolerance of the human brain to injury. In this study, we developed a new method to establish human injury tolerance levels using an integrated database of reconstructed football impacts, sub-injurious human volunteer data, and non-human primate data. The human tolerance levels were analyzed using tissue-level metrics determined using harmonized species-specific finite element brain models. Kinematics-based metrics involving complete characterization of angular motion (e.g., DAMAGE) showed better power of predicting tissue-level deformation in a variety of impact conditions and were subsequently used to characterize injury tolerance. The proposed human brain tolerances for mild and severe TBI were estimated and presented in the form of injury risk curves based on selected tissue-level and kinematics-based injury metrics. The application of the estimated injury tolerances was finally demonstrated using real-world automotive crash data.

Displacement Error Propagation From Embedded Markers to Brain Strain

Head injury model validation has evolved from against pressure to relative brain-skull displacement, and more recently, against marker-based strain. However, there are concerns on strain data quality. In this study, we parametrically investigate how displacement random errors and synchronization errors propagate into strain. Embedded markers from four representative configurations are used to form unique and nonoverlapping tetrahedrons, triangles, and linear elements. Marker displacements are then separately subjected to up to ±10% random displacement errors and up to ±2 ms synchronization errors. Based on 100 random trials in each perturbation test, we find that smaller strain errors relative to the baseline peak strains are significantly associated with larger element sizes (volume, area, or length; p < 0.05). When displacement errors are capped at the two extreme levels, the earlier "column" and "cluster" configurations provide few usable elements with relative strain error under an empirical threshold of 20%, while about 30-80% of elements in recent "repeatable" and "uniform" configurations are considered otherwise usable. Overall, denser markers are desired to provide exhaustive pairwise linear elements with a range of sizes to balance the need for larger elements to minimize strain error but smaller elements to increase the spatial resolution in strain sampling. Their signed strains also provide unique and unambiguous information on tissue tension and compression. This study may provide useful insights into the scrutinization of existing experimental data for head injury model strain validation and to inform how best to design new experiments in the future.

Toward subject-specific evaluation: methods of evaluating finite element brain models using experimental high-rate rotational brain motion

Computational models of the brain have become the gold standard in biomechanics to understand, predict, and mitigate traumatic brain injuries. Many models have been created and evaluated with limited experimental data and without accounting for subject-specific morphometry of the specimens in the dataset. Recent advancements in the measurement of brain motion using sonomicrometry allow for a comprehensive evaluation of brain model biofidelity using a high-rate, rotational brain motion dataset. In this study, four methods were used to determine the best technique to compare nodal displacement to experimental brain motion, including a new morphing method to match subject-specific inner skull geometry. Three finite element brain models were evaluated in this study: the isotropic GHBMC and SIMon models, as well as an anisotropic model with explicitly embedded axons (UVA-EAM). Using a weighted cross-correlation score (between 0 and 1), the anisotropic model yielded the highest average scores across specimens and loading conditions ranging from 0.53 to 0.63, followed by the isotropic GHBMC with average scores ranging from 0.46 to 0.58, and then the SIMon model with average scores ranging from 0.36 to 0.51. The choice of comparison method did not significantly affect the cross-correlation score, and differences of global strain up to 0.1 were found for the morphed geometry relative to baseline models. The morphed or scaled geometry is recommended when evaluating computational brain models to capture the subject-specific skull geometry of the experimental specimens.

Lung Respiratory Motion Estimation Based on Fast Kalman Filtering and 4D CT Image Registration

Respiratory motion estimation is an important part in image-guided radiation therapy and clinical diagnosis. However, most of the respiratory motion estimation methods rely on indirect measurements of external breathing indicators, which will not only introduce great estimation errors, but also bring invasive injury for patients. In this paper, we propose a method of lung respiratory motion estimation based on fast Kalman filtering and 4D CT image registration (LRME-4DCT). In order to perform dynamic motion estimation for continuous phases, a motion estimation model is constructed by combining two kinds of GPU-accelerated 4D CT image registration methods with fast Kalman filtering method. To address the high computational requirements of 4D CT image sequences, a multi-level processing strategy is adopted in the 4D CT image registration methods, and respiratory motion states are predicted from three independent directions. In the DIR-lab dataset and POPI dataset with 4D CT images, the average target registration error (TRE) of the LRME-4DCT method can reach 0.91 mm and 0.85 mm respectively. Compared with traditional estimation methods based on pair-wise image registration, the proposed LRME-4DCT method can estimate the physiological respiratory motion more accurately and quickly. Our proposed LRME-4DCT method fully meets the practical clinical requirements for rapid dynamic estimation of lung respiratory motion.

Calibration of a Heterogeneous Brain Model Using a Subject-Specific Inverse Finite Element Approach

Central to the investigation of the biomechanics of traumatic brain injury (TBI) and the assessment of injury risk from head impact are finite element (FE) models of the human brain. However, many existing FE human brain models have been developed with simplified representations of the parenchyma, which may limit their applicability as an injury prediction tool. Recent advances in neuroimaging techniques and brain biomechanics provide new and necessary experimental data that can improve the biofidelity of FE brain models. In this study, the CAB-20MSym template model was developed, calibrated, and extensively verified. To implement material heterogeneity, a magnetic resonance elastography (MRE) template image was leveraged to define the relative stiffness gradient of the brain model. A multi-stage inverse FE (iFE) approach was used to calibrate the material parameters that defined the underlying non-linear deviatoric response by minimizing the error between model-predicted brain displacements and experimental displacement data. This process involved calibrating the infinitesimal shear modulus of the material using low-severity, low-deformation impact cases and the material non-linearity using high-severity, high-deformation cases from a dataset of in situ brain displacements obtained from cadaveric specimens. To minimize the geometric discrepancy between the FE models used in the iFE calibration and the cadaveric specimens from which the experimental data were obtained, subject-specific models of these cadaveric brain specimens were developed and used in the calibration process. Finally, the calibrated material parameters were extensively verified using independent brain displacement data from 33 rotational head impacts, spanning multiple loading directions (sagittal, coronal, axial), magnitudes (20–40 rad/s), durations (30–60 ms), and severity. Overall, the heterogeneous CAB-20MSym template model demonstrated good biofidelity with a mean overall CORA score of 0.63 ± 0.06 when compared to in situ brain displacement data. Strains predicted by the calibrated model under non-injurious rotational impacts in human volunteers (N = 6) also demonstrated similar biofidelity compared to in vivo measurements obtained from tagged magnetic resonance imaging studies. In addition to serving as an anatomically accurate model for further investigations of TBI biomechanics, the MRE-based framework for implementing material heterogeneity could serve as a foundation for incorporating subject-specific material properties in future models.

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

Advances in brain imaging and computational methods have facilitated the creation of subject-specific computational brain models that aid researchers in investigating brain trauma using simulated impacts. The emergence of magnetic resonance elastography (MRE) as a non-invasive mechanical neuroimaging tool has enabled in vivo estimation of material properties at low-strain, harmonic loading. An open question in the field has been how this data can be integrated into computational models. The goals of this study were to use a novel MRI dataset acquired in human volunteers to generate models with subject-specific anatomy and material properties, and then to compare simulated brain deformations to subject-specific brain deformation data under non-injurious loading. Models of five subjects were simulated with linear viscoelastic (LVE) material properties estimated directly from MRE data. Model predictions were compared to experimental brain deformation acquired in the same subjects using tagged MRI. Outcomes from the models matched the spatial distribution and magnitude of the measured peak strain components as well as the 95^th percentile in-plane peak strains within 0.005 mm/mm and maximum principal strain within 0.012 mm/mm. Sensitivity to material heterogeneity was also investigated. Simulated brain deformations from a model with homogenous brain properties and a model with brain properties discretized with up to ten regions were very similar (a mean absolute difference less than 0.0015 mm/mm in peak strains). Incorporating material properties directly from MRE into a biofidelic subject-specific model is an important step toward future investigations of higher-order model features and simulations under more severe loading conditions.

Statistical Study of the Performance of Recursive Bayesian Filters with Abnormal Observations from Range Sensors

Range sensors are currently present in countless applications related to perception of the environment. In mobile robots, these devices constitute a key part of the sensory apparatus and enable essential operations, that are often addressed by applying methods grounded on probabilistic frameworks such as Bayesian filters. Unfortunately, modern mobile robots have to navigate within challenging environments from the perspective of their sensory devices, getting abnormal observations (e.g., biased, missing, etc.) that may compromise these operations. Although there exist previous contributions that either address filtering performance or identification of abnormal sensory observations, they do not provide a complete treatment of both problems at once. In this work we present a statistical approach that allows us to study and quantify the impact of abnormal observations from range sensors on the performance of Bayesian filters. For that, we formulate the estimation problem from a generic perspective (abstracting from concrete implementations), analyse the main limitations of common robotics range sensors, and define the factors that potentially affect the filtering performance. Rigorous statistical methods are then applied to a set of simulated experiments devised to reproduce a diversity of situations. The obtained results, which we also validate in a real environment, provide novel and relevant conclusions on the effect of abnormal range observations in these filters.

A Machine Learning Enabled Wireless Intracranial Brain Deformation Sensing System

A leading cause of traumatic brain injury (TBI) is intracranial brain deformation due to mechanical impact. This deformation is viscoelastic and differs from a traditional rigid transformation. In this paper, we describe a machine learning enabled wireless sensing system that predicts the trajectory of intracranial brain deformation. The sensing system consists of an implantable soft magnet and an external magnetic sensor array with a sensing volume of 12 × 12 × 4 mm³. Machine learning algorithm predicts the brain deformation by interpreting the magnetic sensor outputs created by the change in position of the implanted soft magnet. Three different machine learning models were trained on calibration data: (1) random forests, (2) k-nearest neighbors, and (3) a multi-layer perceptron-based neural network. These models were validated using both in vitro (a needle inserted into PVC gel) and in vivo (blast exposure to live and dead rat brains) experiments. The in vitro gel deformation predicted by these machine learning models showed excellent agreement with the camera measurements and had absolute error = 138 μm, Fréchet distance = 372 μm with normalized Procrustes disparity = 0.034. The in vivo brain deformation predicted by these models had absolute error = 50 μm, Fréchet distance = 95 μm with normalized Procrustes disparity = 0.055 for dead animal and absolute error = 125 μm, Fréchet distance = 289 μm with normalized Procrustes disparity = 0.2 for live animal respectively. These results suggest that the proposed machine learning enabled sensor system can be an effective tool for measuring in situ brain deformation.

Biomechanics of the Human Brain during Dynamic Rotation of the Head

Traumatic brain injuries (TBI) are a substantial societal burden. The development of better technologies and systems to prevent and/or mitigate the severity of brain injury requires an improved understanding of the mechanisms of brain injury, and more specifically, how head impact exposure relates to brain deformation. Biomechanical investigations have used computational models to identify these relations, but more experimental brain deformation data are needed to validate these models and support their conclusions. The objective of this study was to generate a dataset describing in situ human brain motion under rotational loading at impact conditions considered injurious. Six head-neck human post-mortem specimens, unembalmed and never frozen, were instrumented with 24 sonomicrometry crystals embedded throughout the parenchyma that can directly measure dynamic brain motion. Dynamic brain displacement, relative to the skull, was measured for each specimen with four loading severities in the three directions of controlled rotation, for a total of 12 tests per specimen. All testing was completed 42-72 h post-mortem for each specimen. The final dataset contains approximately 5,000 individual point displacement time-histories that can be used to validate computational brain models. Brain motion was direction-dependent, with axial rotation resulting in the largest magnitude of displacement. Displacements were largest in the mid-cerebrum, and the inferior regions of the brain-the cerebellum and brainstem-experienced relatively lower peak displacements. Brain motion was also found to be positively correlated to peak angular velocity, and negatively correlated with angular velocity duration, a finding that has implications related to brain injury risk-assessment methods. This dataset of dynamic human brain motion will form the foundation for the continued development and refinement of computational models of the human brain for predicting TBI.