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.

Mechanical Properties of White Matter Tracts in Aging Assessed via Anisotropic MR Elastography.

Magnetic resonance elastography (MRE) is a promising neuroimaging technique to probe tissue microstructure, which has revealed widespread softening with loss of structural integrity in the aging brain. Traditional MRE approaches assume mechanical isotropy. However, white matter is known to be anisotropic from aligned, myelinated axonal bundles, which can lead to uncertainty in mechanical property estimates in these areas when using isotropic MRE. Recent advances in anisotropic MRE now allow for estimation of shear and tensile anisotropy, along with substrate shear modulus, in white matter tracts. The objective of this study was to investigate age-related differences in anisotropic mechanical properties in human brain white matter tracts for the first time. Anisotropic mechanical properties in all tracts were found to be significantly lower in older adults compared to young adults, with average property differences ranging between 0.028-0.107 for shear anisotropy and between 0.139-0.347 for tensile anisotropy. Stiffness perpendicular to the axonal fiber direction was also significantly lower in older age, but only in certain tracts. When compared with fractional anisotropy measures from diffusion tensor imaging, we found that anisotropic MRE measures provided additional, complementary information in describing differences between the white matter integrity of young and older populations. Anisotropic MRE provides a new tool for studying white matter structural integrity in aging and neurodegeneration.

Shear wave speeds in a nearly incompressible fibrous material with two unequal fiber families.

The mechanical properties of soft biological tissues can be characterized non-invasively by magnetic resonance elastography (MRE). In MRE, shear wave fields are induced by vibration, imaged by magnetic resonance imaging, and inverted to estimate tissue properties in terms of the parameters of an underlying material model. Most MRE studies assume an isotropic material model; however, biological tissue is often anisotropic with a fibrous structure, and some tissues contain two or more families of fibers-each with different orientations and properties. Motivated by the prospect of using MRE to characterize such tissues, this paper describes the propagation of shear waves in soft fibrous material with two unequal fiber families. Shear wave speeds are expressed in terms of material parameters, and the effect of each parameter on the shear wave speeds is investigated. Analytical expressions of wave speeds are confirmed by finite element simulations of shear wave transmission with various polarization directions. This study supports the feasibility of estimating parameters of soft fibrous tissues with two unequal fiber families in vivo from local shear wave speeds and advances the prospects for the mechanical characterization of such biological tissues by MRE.

Preoperative prolapse phenotype is predictive of surgical outcome with minimally invasive sacrocolpopexy.

BACKGROUND: The gold-standard treatment for advanced pelvic organ prolapse is sacrocolpopexy. However, the preoperative features of prolapse that predict optimal outcomes are unknown. OBJECTIVE: This study aimed to develop a clinical prediction model that uses preoperative scores on the Pelvic Organ Prolapse Quantification examination to predict outcomes after minimally invasive sacrocolpopexy for stages 2, 3, and 4 uterovaginal prolapse and vaginal vault prolapse. STUDY DESIGN: A 2-institution database of pre- and postoperative variables from 881 cases of minimally invasive sacrocolpopexy was analyzed. Data from patients were analyzed in the following 4 groups: stage 2 uterovaginal prolapse, stage 3 to 4 uterovaginal prolapse, stage 2 vaginal vault prolapse, and stage 3 to 4 vaginal vault prolapse. Unsupervised machine learning was used to identify clusters and investigate associations between clusters and outcome. The k-means clustering analysis was performed with preoperative Pelvic Organ Prolapse Quantification points and stratified by previous hysterectomy status. The "optimal" surgical outcome was defined as postoperative Pelvic Organ Prolapse Quantification stage <2. Demographic variables were compared by cluster with Student t and chi-square tests. Odds ratios were calculated to determine whether clusters could predict the outcome. Age at surgery, body mass index, and previous prolapse surgery were used for adjusted odds ratios. RESULTS: Five statistically distinct prolapse clusters (phenotypes C, A, A>P, P, and P>A) were found. These phenotypes reflected the predominant region of prolapse (apical, anterior, or posterior) and whether support was preserved in the nonpredominant region. Phenotype A (anterior compartment prolapse predominant, posterior support preserved) was found in all 4 groups of patients and was considered the reference in the analysis. In 111 patients with stage 2 uterovaginal prolapse, phenotypes A and A>P (greater anterior prolapse than posterior prolapse) were found, and patients with phenotype A were more likely than those with phenotype A>P to have an optimal surgical outcome. In 401 patients with stage 3 to 4 uterovaginal prolapse, phenotypes C (apical compartment predominant, prolapse in all compartments), A, and A>P were found, and patients with phenotype A>P were more likely than those with phenotype A to have ideal surgical outcome. In 72 patients with stage 2 vaginal vault prolapse, phenotypes A, A>P, and P (posterior compartment predominant, anterior support preserved) were found, and those with phenotype A>P were less likely to have an ideal outcome than patients with phenotype A. In 297 patients with stage 3 to 4 vaginal vault prolapse, phenotypes C, A, and P>A (prolapse greater in posterior than in anterior compartment) were found, but there were no significant differences in rate of ideal outcome between phenotypes. CONCLUSION: Five anatomic phenotypes based on preoperative Pelvic Organ Prolapse Quantification scores were present in patients with stages 2 and 3 to 4 uterovaginal prolapse and vaginal vault prolapse. These phenotypes are predictive of surgical outcome after minimally invasive sacrocolpopexy. Further work needs to confirm the presence and predictive nature of these phenotypes. In addition, whether the phenotypes represent a progression of prolapse or discrete prolapse presentations resulting from different anatomic and life course risk profiles is unknown. These phenotypes may be useful in surgical counseling and planning.

Theoretical relationships between axoneme distortion and internal forces and torques in ciliary beating.

The axoneme is an intricate nanomachine responsible for generating the propulsive oscillations of cilia and flagella in an astonishing variety of organisms. New imaging techniques based on cryoelectron-tomography (cryo-ET) and subtomogram averaging have revealed the detailed structures of the axoneme and its components with sub-nm resolution, but the mechanical function of each component and how the assembly generates oscillations remains stubbornly unclear. Most explanations of oscillatory behavior rely on the dynamic regulation of dynein by some signal, but this may not be necessary if the system of dynein-driven slender filaments is dynamically unstable. Understanding the possibility of instability-driven oscillations requires a multifilament model of the axoneme that accounts for distortions of the axoneme as it bends. Active bending requires forces and bending moments that will tend to change the spacing and alignment of doublets. We hypothesize that components of the axoneme resist and respond to these loads in ways that are critical to beating. Specifically, we propose (i) that radial spokes provide torsional stiffness by resisting misalignment (as well as spacing) between the central pair and outer doublets, and (ii) that the kinematics of dynein arms affect the relationships between active forces and bending moments on deforming doublets. These proposed relationships enhance the ability of theoretical, multifilament models of axonemal beating to generate propulsive oscillatory waveforms via dynamic mechanical instability.

Multi-scale measurement of stiffness in the developing ferret brain.

Cortical folding is an important process during brain development, and aberrant folding is linked to disorders such as autism and schizophrenia. Changes in cell numbers, size, and morphology have been proposed to exert forces that control the folding process, but these changes may also influence the mechanical properties of developing brain tissue. Currently, the changes in tissue stiffness during brain folding are unknown. Here, we report stiffness in the developing ferret brain across multiple length scales, emphasizing changes in folding cortical tissue. Using rheometry to measure the bulk properties of brain tissue, we found that overall brain stiffness increases with age over the period of cortical folding. Using atomic force microscopy to target the cortical plate, we found that the occipital cortex increases in stiffness as well as stiffness heterogeneity over the course of development and folding. These findings can help to elucidate the mechanics of the cortical folding process by clarifying the concurrent evolution of tissue properties.

Effect of Direction and Frequency of Skull Motion on Mechanical Vulnerability of the Human Brain.

Strain energy and kinetic energy in the human brain were estimated by magnetic resonance elastography (MRE) during harmonic excitation of the head, and compared to characterize the effect of loading direction and frequency on brain deformation. In brain MRE, shear waves are induced by external vibration of the skull and imaged by a modified MR imaging sequence; the resulting harmonic displacement fields are typically "inverted" to estimate mechanical properties, like stiffness or damping. However, measurements of tissue motion from MRE also illuminate key features of the response of the brain to skull loading. In this study, harmonic excitation was applied in two different directions and at five different frequencies from 20 to 90 Hz. Lateral loading induced primarily left-right head motion and rotation in the axial plane; occipital loading induced anterior-posterior head motion and rotation in the sagittal plane. The ratio of strain energy to kinetic energy (SE/KE) depended strongly on both direction and frequency. The ratio of SE/KE was approximately four times larger for lateral excitation than for occipital excitation and was largest at the lowest excitation frequencies studied. These results are consistent with clinical observations that suggest lateral impacts are more likely to cause injury than occipital or frontal impacts, and also with observations that the brain has low-frequency (∼10 Hz) natural modes of oscillation. The SE/KE ratio from brain MRE is potentially a simple and powerful dimensionless metric of brain vulnerability to deformation and injury.

Robust acoustic trapping and perturbation of single-cell microswimmers illuminate three-dimensional swimming and ciliary coordination.

We report a label-free acoustic microfluidic method to confine single, cilia-driven swimming cells in space without limiting their rotational degrees of freedom. Our platform integrates a surface acoustic wave (SAW) actuator and bulk acoustic wave (BAW) trapping array to enable multiplexed analysis with high spatial resolution and trapping forces that are strong enough to hold individual microswimmers. The hybrid BAW/SAW acoustic tweezers employ high-efficiency mode conversion to achieve submicron image resolution while compensating for parasitic system losses to immersion oil in contact with the microfluidic chip. We use the platform to quantify cilia and cell body motion for wildtype biciliate cells, investigating effects of environmental variables like temperature and viscosity on ciliary beating, synchronization, and three-dimensional helical swimming. We confirm and expand upon the existing understanding of these phenomena, for example determining that increasing viscosity promotes asynchronous beating. Motile cilia are subcellular organelles that propel microorganisms or direct fluid and particulate flow. Thus, cilia are critical to cell survival and human health. The unicellular alga Chlamydomonas reinhardtii is widely used to investigate the mechanisms underlying ciliary beating and coordination. However, freely swimming cells are difficult to image with sufficient resolution to capture cilia motion, necessitating that the cell body be held during experiments. Acoustic confinement is a compelling alternative to use of a micropipette, or to magnetic, electrical, and optical trapping that may modify the cells and affect their behavior. Beyond establishing our approach to studying microswimmers, we demonstrate a unique ability to mechanically perturb cells via rapid acoustic positioning.

Measurement of relative motion of the brain and skull in the mini-pig in-vivo.

The mechanical role of the skull-brain interface is critical to the pathology of concussion and traumatic brain injury (TBI) and may evolve with age. Here we characterize the skull-brain interface in juvenile, female Yucatan mini-pigs from 3 to 6 months old using techniques from magnetic resonance elastography (MRE). The displacements of the skull and brain were measured by a motion-sensitive MR imaging sequence during low-amplitude harmonic motion of the head. Each animal was scanned four times at 1-month intervals. Harmonic motion at 100 Hz was excited by three different configurations of a jaw actuator in order to vary the direction of loading. Rigid-body linear motions of the brain and skull were similar, although brain rotations were consistently smaller than corresponding skull rotations. Relative displacements between the brain and skull were estimated for voxels on the surface of the brain. Amplitudes of relative displacements between skull and brain were 1-3 µm, approximately 25-50% of corresponding skull displacements. Maps of relative displacement showed variations by anatomical region, and the normal component of relative displacement was consistently 25-50% of the tangential component. These results illuminate the mechanics of the skull-brain interface in a gyrencephalic animal model relevant to human brain injury and development.

Mechanical stiffness and anisotropy measured by MRE during brain development in the minipig.

The relationship between brain development and mechanical properties of brain tissue is important, but remains incompletely understood, in part due to the challenges in measuring these properties longitudinally over time. In addition, white matter, which is composed of aligned, myelinated, axonal fibers, may be mechanically anisotropic. Here we use data from magnetic resonance elastography (MRE) and diffusion tensor imaging (DTI) to estimate anisotropic mechanical properties in six female Yucatan minipigs at ages from 3 to 6 months. Fiber direction was estimated from the principal axis of the diffusion tensor in each voxel. Harmonic shear waves in the brain were excited by three different configurations of a jaw actuator and measured using a motion-sensitive MR imaging sequence. Anisotropic mechanical properties are estimated from displacement field and fiber direction data with a finite element- based, transversely-isotropic nonlinear inversion (TI-NLI) algorithm. TI-NLI finds spatially resolved TI material properties that minimize the error between measured and simulated displacement fields. Maps of anisotropic mechanical properties in the minipig brain were generated for each animal at all four ages. These maps show that white matter is more dissipative and anisotropic than gray matter, and reveal significant effects of brain development on brain stiffness and structural anisotropy. Changes in brain mechanical properties may be a fundamental biophysical signature of brain development.

Comparison of Deformation Patterns Excited in the Human Brain In Vivo by Harmonic and Impulsive Skull Motion.

Noninvasive measurements of brain deformation in human participants in vivo are needed to develop models of brain biomechanics and understand traumatic brain injury (TBI). Tagged magnetic resonance imaging (tagged MRI) and magnetic resonance elastography (MRE) are two techniques to study human brain deformation; these techniques differ in the type of motion and difficulty of implementation. In this study, oscillatory strain fields in the human brain caused by impulsive head acceleration and measured by tagged MRI were compared quantitatively to strain fields measured by MRE during harmonic head motion at 10 and 50 Hz. Strain fields were compared by registering to a common anatomical template, then computing correlations between the registered strain fields. Correlations were computed between tagged MRI strain fields in six participants and MRE strain fields at 10 Hz and 50 Hz in six different participants. Correlations among strain fields within the same experiment type were compared statistically to correlations from different experiment types. Strain fields from harmonic head motion at 10 Hz imaged by MRE were qualitatively and quantitatively similar to modes excited by impulsive head motion, imaged by tagged MRI. Notably, correlations between strain fields from 10 Hz MRE and tagged MRI did not differ significantly from correlations between strain fields from tagged MRI. These results suggest that low-frequency modes of oscillation dominate the response of the brain during impact. Thus, low-frequency MRE, which is simpler and more widely available than tagged MRI, can be used to illuminate the brain's response to head impact.

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.

Anisotropic mechanical properties in the healthy human brain estimated with multi-excitation transversely isotropic MR elastography.

Magnetic resonance elastography (MRE) is an MRI technique for imaging the mechanical properties of brain in vivo, and has shown differences in properties between neuroanatomical regions and sensitivity to aging, neurological disorders, and normal brain function. Past MRE studies investigating these properties have typically assumed the brain is mechanically isotropic, though the aligned fibers of white matter suggest an anisotropic material model should be considered for more accurate parameter estimation. Here we used a transversely isotropic, nonlinear inversion algorithm (TI-NLI) and multiexcitation MRE to estimate the anisotropic material parameters of individual white matter tracts in healthy young adults. We found significant differences between individual tracts for three recovered anisotropic parameters: substrate shear stiffness, µ (range: 2.57 - 3.02 kPa), shear anisotropy, ϕ (range: -0.026 - 0.164), and tensile anisotropy, ζ (range: 0.559 - 1.049). Additionally, we demonstrated the repeatability of these parameter estimates in terms of lower variability of repeated measures in a single subject relative to variability in our sample population. Further, we observed significant differences in anisotropic mechanical properties between segments of the corpus callosum (genu, body, and splenium), which is expected based on differences in axonal microstructure. This study shows the ability of MRE with TI-NLI to estimate anisotropic mechanical properties of white matter and presents reference properties for tracts throughout the healthy brain.

Basal bodies bend in response to ciliary forces.

Motile cilia beat with an asymmetric waveform consisting of a power stroke that generates a propulsive force and a recovery stroke that returns the cilium back to the start. Cilia are anchored to the cell cortex by basal bodies (BBs) that are directly coupled to the ciliary doublet microtubules (MTs). We find that, consistent with ciliary forces imposing on BBs, bending patterns in BB triplet MTs are responsive to ciliary beating. BB bending varies as environmental conditions change the ciliary waveform. Bending occurs where striated fibers (SFs) attach to BBs and mutants with short SFs that fail to connect to adjacent BBs exhibit abnormal BB bending, supporting a model in which SFs couple ciliary forces between BBs. Finally, loss of the BB stability protein Poc1, which helps interconnect BB triplet MTs, prevents the normal distributed BB and ciliary bending patterns. Collectively, BBs experience ciliary forces and manage mechanical coupling of these forces to their surrounding cellular architecture for normal ciliary beating.

Islet primary cilia motility controls insulin secretion.

Primary cilia are specialized cell-surface organelles that mediate sensory perception and, in contrast to motile cilia and flagella, are thought to lack motility function. Here, we show that primary cilia in human and mouse pancreatic islets exhibit movement that is required for glucose-dependent insulin secretion. Islet primary cilia contain motor proteins conserved from those found in classic motile cilia, and their three-dimensional motion is dynein-driven and dependent on adenosine 5'-triphosphate and glucose metabolism. Inhibition of cilia motion blocks beta cell calcium influx and insulin secretion. Human beta cells have enriched ciliary gene expression, and motile cilia genes are altered in type 2 diabetes. Our findings redefine primary cilia as dynamic structures having both sensory and motile function and establish that pancreatic islet cilia movement plays a regulatory role in insulin secretion.

Generation of ciliary beating by steady dynein activity: the effects of inter-filament coupling in multi-filament models.

The structure of the axoneme in motile cilia and flagella is emerging with increasing detail from high-resolution imaging, but the mechanism by which the axoneme creates oscillatory, propulsive motion remains mysterious. It has recently been proposed that this motion may be caused by a dynamic 'flutter' instability that can occur under steady dynein loading, and not by switching or modulation of dynein motor activity (as commonly assumed). In the current work, we have built an improved multi-filament mathematical model of the axoneme and implemented it as a system of discrete equations using the finite-element method. The eigenvalues and eigenvectors of this model predict the emergence of oscillatory, wave-like solutions in the absence of dynein regulation and specify the associated frequencies and waveforms of beating. Time-domain simulations with this model illustrate the behaviour predicted by the system's eigenvalues. This model and analysis allow us to efficiently explore the potential effects of difficult to measure biophysical parameters, such as elasticity of radial spokes and inter-doublet links, on the ciliary waveform. These results support the idea that dynamic instability without dynamic dynein regulation is a plausible and robust mechanism for generating ciliary beating.

Intracellular connections between basal bodies promote the coordinated behavior of motile cilia.

Hydrodynamic flow produced by multiciliated cells is critical for fluid circulation and cell motility. Hundreds of cilia beat with metachronal synchrony for fluid flow. Cilia-driven fluid flow produces extracellular hydrodynamic forces that cause neighboring cilia to beat in a synchronized manner. However, hydrodynamic coupling between neighboring cilia is not the sole mechanism that drives cilia synchrony. Cilia are nucleated by basal bodies (BBs) that link to each other and to the cell's cortex via BB-associated appendages. The intracellular BB and cortical network is hypothesized to synchronize ciliary beating by transmitting cilia coordination cues. The extent of intracellular ciliary connections and the nature of these stimuli remain unclear. Moreover, how BB connections influence the dynamics of individual cilia has not been established. We show by focused ion beam scanning electron microscopy imaging that cilia are coupled both longitudinally and laterally in the ciliate Tetrahymena thermophila by the underlying BB and cortical cytoskeletal network. To visualize the behavior of individual cilia in live, immobilized Tetrahymena cells, we developed Delivered Iron Particle Ubiety Live Light (DIPULL) microscopy. Quantitative and computer analyses of ciliary dynamics reveal that BB connections control ciliary waveform and coordinate ciliary beating. Loss of BB connections reduces cilia-dependent fluid flow forces.

Quantifying stability of parameter estimates forin vivonearly incompressible transversely-isotropic brain MR elastography.

Easily computable quality metrics for measured medical data at point-of-care are important for imaging technologies involving offline reconstruction. Accordingly, we developed a new data quality metric forin vivotransversely-isotropic (TI) magnetic resonance elastography (MRE) based on a generalization of the widely accepted octahedral shear-strain calculation. The metric uses MRE displacement data and an estimate of the TI property field to yield a 'stability map' which predicts regions of low versus high accuracy in the resulting material property reconstructions. We can also calculate an average TI parameter stability (TIPS) score over all voxels in a region of interest for a given measurement to indicate how reliable the recovered mechanical property estimate for the region is expected to be. The calculation is rapid and places little demand on computing resources compared to the computationally intensive material property reconstruction from non-linear inversion (TI-NLI) of displacement fields, making it ideal for point-of-care evaluation of data quality. We test the predictions of the stability map for both simulated phantoms andin vivohuman brain data. We used a range of different displacement datasets from vibrations applied in the anterior-posterior (AP), left-right (LR) and combined AP + LR directions. The TIPS and variability maps (noise sensitivity or variation from the mean of repeated MRE scans) were consistently anti-correlated. Notably, Spearman correlation coefficients ∣R∣>0.6 were found between variability and TIPS score for individual white matter tracts within vivodata. These observations demonstrate the reliability and promise of this data quality metric to screen data rapidly in realistic clinical MRE applications.

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.

Estimation of the mechanical properties of a transversely isotropic material from shear wave fields via artificial neural networks.

Artificial neural networks (ANN), established tools in machine learning, are applied to the problem of estimating parameters of a transversely isotropic (TI) material model using data from magnetic resonance elastography (MRE) and diffusion tensor imaging (DTI). We use neural networks to estimate parameters from experimental measurements of ultrasound-induced shear waves after training on analogous data from simulations of a computer model with similar loading, geometry, and boundary conditions. Strain ratios and shear-wave speeds (from MRE) and fiber direction (the direction of maximum diffusivity from diffusion tensor imaging (DTI)) are used as inputs to neural networks trained to estimate the parameters of a TI material (baseline shear modulus µ, shear anisotropy φ, and tensile anisotropy ζ). Ensembles of neural networks are applied to obtain distributions of parameter estimates. The robustness of this approach is assessed by quantifying the sensitivity of property estimates to assumptions in modeling (such as assumed loss factor) and choices in fitting (such as the size of the neural network). This study demonstrates the successful application of simulation-trained neural networks to estimate anisotropic material parameters from complementary MRE and DTI imaging data.