Maximum Principal Strain Rate Research Articles

Brain Deformation Estimation With Transfer Learning for Head Impact Datasets Across Impact Types.

The machine-learning head model (MLHM) to accelerate the calculation of brain strain and strain rate, which are the predictors for traumatic brain injury (TBI), but the model accuracy was found to decrease sharply when the training/test datasets were from different head impacts types (i.e., car crash, college football), which limits the applicability of MLHMs to different types of head impacts and sports. Particularly, small sizes of target dataset for specific impact types with tens of impacts may not be enough to train an accurate impact-type-specific MLHM. To overcome this, we propose data fusion and transfer learning to develop a series of MLHMs to predict the maximum principal strain (MPS) and maximum principal strain rate (MPSR). The strategies were tested on American football (338), mixed martial arts (457), reconstructed car crash (48) and reconstructed American football (36) and we found that the MLHMs developed with transfer learning are significantly more accurate in estimating MPS and MPSR than other models, with a mean absolute error (MAE) smaller than 0.03 in predicting MPS and smaller than [Formula: see text] in predicting MPSR on all target impact datasets. High performance in concussion detection was observed based on the MPS and MPSR estimated by the transfer-learning-based models. The MLHMs can be applied to various head impact types for rapidly and accurately calculating brain strain and strain rate. This study enables developing MLHMs for the head impact type with limited availability of data, and will accelerate the applications of MLHMs.

AI-based denoising of head impact kinematics measurements with convolutional neural network for traumatic brain injury prediction.

Wearable devices are developed to measure head impact kinematics but are intrinsically noisy because of the imperfect interface with human bodies. This study aimed to improve the head impact kinematics measurements obtained from instrumented mouthguards using deep learning to enhance traumatic brain injury (TBI) risk monitoring. We developed one-dimensional convolutional neural network (1D-CNN) models to denoise mouthguard kinematics measurements for tri-axial linear acceleration and tri-axial angular velocity from 163 laboratory dummy head impacts. The performance of the denoising models was evaluated on three levels: kinematics, brain injury criteria, and tissue-level strain and strain rate. Additionally, we performed a blind test on an on-field dataset of 118 college football impacts and a test on 413 post-mortem human subject (PMHS) impacts. On the dummy head impacts, the denoised kinematics showed better correlation with reference kinematics, with relative reductions of 36% for pointwise root mean squared error and 56% for peak absolute error. Absolute errors in six brain injury criteria were reduced by a mean of 82%. For maximum principal strain and maximum principal strain rate, the mean error reduction was 35% and 69%, respectively. On the PMHS impacts, similar denoising effects were observed and the peak kinematics after denoising were more accurate (relative error reduction for 10% noisiest impacts was 75.6%). The 1D-CNN denoising models effectively reduced errors in mouthguard-derived kinematics measurements on dummy and PMHS impacts. This study provides a novel approach for denoising head kinematics measurements in dummy and PMHS impacts, which can be further validated on more real-human kinematics data before real-world applications.

Finding the Spatial Co-Variation of Brain Deformation With Principal Component Analysis.

Strain and strain rate are effective traumatic brain injury metrics. In finite element (FE) head model, thousands of elements were used to represent the spatial distribution of these metrics. Owing that these metrics are resulted from brain inertia, their spatial distribution can be represented in more concise pattern. Since head kinematic features and brain deformation vary largely across head impact types (Zhan et al., 2021), we applied principal component analysis (PCA) to find the spatial co-variation of injury metrics (maximum principal strain (MPS), MPS rate (MPSR) and MPS × MPSR) in four impact types: simulation, football, mixed martial arts and car crashes, and used the PCA to find patterns in these metrics and improve the machine learning head model (MLHM). We applied PCA to decompose the injury metrics for all impacts in each impact type, and investigate the spatial co-variation using the first principal component (PC1). Furthermore, we developed a MLHM to predict PC1 and then inverse-transform to predict for all brain elements. The accuracy, the model complexity and the size of training dataset of PCA-MLHM are compared with previous MLHM (Zhan et al., 2021). PC1 explained variance on the datasets. Based on PC1 coefficients, the corpus callosum and midbrain exhibit high variance on all datasets. Finally, the PCA-MLHM reduced model parameters by 74% with a similar MPS estimation accuracy. The brain injury metric in a dataset can be decomposed into mean components and PC1 with high explained variance. The spatial co-variation analysis enables better interpretation of the patterns in brain injury metrics. It also improves the efficiency of MLHM.

A Machine Learning Approach to Investigate the Uncertainty of Tissue-Level Injury Metrics for Cerebral Contusion.

Controlled cortical impact (CCI) on porcine brain is often utilized to investigate the pathophysiology and functional outcome of focal traumatic brain injury (TBI), such as cerebral contusion (CC). Using a finite element (FE) model of the porcine brain, the localized brain strain and strain rate resulting from CCI can be computed and compared to the experimentally assessed cortical lesion. This way, tissue-level injury metrics and corresponding thresholds specific for CC can be established. However, the variability and uncertainty associated with the CCI experimental parameters contribute to the uncertainty of the provoked cortical lesion and, in turn, of the predicted injury metrics. Uncertainty quantification via probabilistic methods (Monte Carlo simulation, MCS) requires a large number of FE simulations, which results in a time-consuming process. Following the recent success of machine learning (ML) in TBI biomechanical modeling, we developed an artificial neural network as surrogate of the FE porcine brain model to predict the brain strain and the strain rate in a computationally efficient way. We assessed the effect of several experimental and modeling parameters on four FE-derived CC injury metrics (maximum principal strain, maximum principal strain rate, product of maximum principal strain and strain rate, and maximum shear strain). Next, we compared the in silico brain mechanical response with cortical damage data from in vivo CCI experiments on pig brains to evaluate the predictive performance of the CC injury metrics. Our ML surrogate was capable of rapidly predicting the outcome of the FE porcine brain undergoing CCI. The now computationally efficient MCS showed that depth and velocity of indentation were the most influential parameters for the strain and the strain rate-based injury metrics, respectively. The sensitivity analysis and comparison with the cortical damage experimental data indicate a better performance of maximum principal strain and maximum shear strain as tissue-level injury metrics for CC. These results provide guidelines to optimize the design of CCI tests and bring new insights to the understanding of the mechanical response of brain tissue to focal traumatic brain injury. Our findings also highlight the potential of using ML for computationally efficient TBI biomechanics investigations.

Seismic hazard assessment of the central North Anatolian Fault (Turkey) from GPS-derived strain rates and b-values

ABSTRACTThe North Anatolian Fault (NAF) represents one of the most seismically active transform zones on Earth. It is characterized by high rates of crustal deformation that generate destructive earthquakes. These rates are induced by convergence of the northward-migrating Arabian and African plates with respect to the stable Eurasian plate. Therefore, the NAF represents a natural earthquake laboratory with a wide range of earthquake sizes (M ≤ 7.9) to investigate by using interdisciplinary approaches (seismological, magnetism, geological, gravitational, and geodetic studies). In this study, we compare the results of an analysis of b-values from seismicity and GPS (Global Positioning System) measurements of the strain rate to understand their coupling in terms of faulting and earthquake hazard implications. In particular, this comparison allows investigation of the spatial correlation between b-value and strain rate maps and is thus able to locate fault segments that have a high potential of generating large earthquake(s). b-Values range from 0.5 to 1.5 along the central NAF. The maximum principal strain rates are positive (tensile), and the minimum principal strain rates are negative (compressive). The surface strain is positive, showing that tensile strain is predominant in areas with high strain rates, consistent with the trend of the corresponding stresses.

Elastic capsule deformation in general irrotational linear flows

Knowledge of the response of elastic capsules to an imposed fluid flow is necessary for predicting the deformation and motion of biological cells and synthetic capsules in microfluidic devices and in microcirculation. Capsules have been studied in shear, planar extensional and axisymmetric extensional flows. Here, the flow gradient matrix of a general irrotational linear flow is characterized by two parameters, its strain rate, defined as the maximum of the principal strain rates, and a new term, q, the difference of the two lesser principal strain rates, scaled by the maximum principal strain rate; this characterization is valid for ellipsoids in irrotational linear flow, and gives good results for spheres in general linear flows at low capillary numbers. We demonstrate that deformable non-spherical particles align with the principal axes of an imposed irrotational flow. Thus, it is most practical to model deformation of non-spherical particles already aligned with the flow, rather than considering each arbitrary orientation. Capsule deformation was modeled for a sphere, a prolate spheroid and an oblate spheroid, subjected to combinations of uniaxial, biaxial and planar extensional flows; modeling was performed using the immersed boundary method. The time response of each capsule to each flow was found, as were the steady-state deformation factor, mean strain energy and surface area. For a given capillary number, planar flows led to more deformation than uniaxial or biaxial extensional flows. Capsule behavior in all cases was bounded by the response of capsules to uniaxial, biaxial and planar extensional flows.

Horizontal Strain Rate Distribution on an Active Ice Shelf Rift from in-situ GPS Data

Mass loss from the Antarctic ice sheet predominantly occurs at the fringing ice shelves via iceberg calving, which is controlled by the initiation and propagation of large rifts that precede iceberg detachment and can lead to ice shelf break-up. This paper reports on the analysis of Global Positioning System (GPS) data collected at an active rift system on the Amery Ice Shelf, East Antarctica, over two field seasons. Horizontal strain rates are determined for a network of 11 sites observed over three weeks during the 2004/05 Antarctic summer period, and the results are combined with, and compared to, strain rates obtained in the 2002/03 season. Maximum principal strain rates across the network vary between 6 and 32 [x 10-3/yr], while minimum principal strain rates are generally about 1-17 [x 10-3/yr]. Changes evident in the strain distribution can mostly be attributed to existing fractures passing through the GPS network and the episodic movement of the rift tip. It is confirmed that rift propagation in 2005/06 was slowing down. Opening rates are inferred from baselines situated normal to the rift. Analysis of the network using a cumulative sum approach is found to be an effective method to detect small baseline length changes associated with rift propagation.

GPS-Derived Strain Rates on an Active Ice Shelf Rift

Ice shelves are important components of the Antarctic ice sheet due to their ice-ocean-atmosphere interface and vulnerability to global increases (or decreases) in atmospheric and oceanic temperatures. The development of rifts, which are fractures that penetrate through the entire ice shelf thickness, precede large tabular iceberg detachment and can lead to ice shelf break-up. Changes in strain rates on an active propagating rift system on the Amery Ice Shelf, East Antarctica are determined using in-situ Global Positioning System (GPS) measurements. Results for the 2002/03 Antarctic summer period (Dec-Feb) confirm previous observations by [2] that rift propagation occurs in episodic bursts separated by several days. Transverse-to-flow (i.e. parallel-to-rift) strain rates exceed longitudinal-to-flow (i.e. normal-to-rift) rates by up to a factor of 5 and maximum principal strain rates around the rift tip vary from 12 to 21 [x 10-3/yr]. A rotation in the direction of the principal strain is evident around the rift tip, indicating a change in the mechanics of rift fracture. It is demonstrated that cumulative sum analysis [12], obtained by differencing a pair of residual baseline time series situated approximately normal and parallel to the rift, is an effective method to detect small baseline length changes.

Relationship between non-cylindrical fold geometry and the shear direction in monoclinic and triclinic shear zones

We investigate the relationship between non-cylindrical fold geometry and the shear direction of the hosting high-strain zone by numerical modeling, and show that apical axes of non-cylindrical folds may develop into directions highly oblique to the shear direction if the zone has a pure shear component. The common practice of using well-developed sheath folds as indicators for the shear direction is not reliable and the use of immature non-cylindrical or sheath folds appears more reliable. Hinge lines of mature sheath folds approach parallelism with the fabric attractor (to which all material lines rotate), which can have variable angles with respect to the shear direction. In thinning zones, the fabric attractor is the direction of the maximum principal strain rate of the pure shear component and is parallel to the shear zone boundary. In thickening zones, it lies somewhere in the quadrant between the direction of the maximum principal strain rate of the pure shear component (perpendicular to the shear zone boundary) and the simple shear direction, and is generally oblique to the shear zone boundary. The exact location depends on the flow geometry of the shear zone.

Simultaneous measurement of velocity and CH layer distribution in turbulent non-premixed flames

The velocity field and the location of the CH layer are measured simultaneously in diluted ethylene flames by applying particle image velocimetry (PIV) and planar laser-induced fluorescence (PLIF) of CH radicals. CH layer measurements are used to locate the position of the flame front, and accompanying velocity fields provide the instantaneous velocity, strain, and residence time information simultaneously. The location of the CH layer is found to correspond well with the location of the stoichiometric velocity contour and also with high strain rate zones: however, significantly higher values of instantaneous velocity and strain rates, compared to the mean value, are frequently observed. The residence time on the flame surface is estimated by dividing the thickness of the CH layer by the mean value of radial velocity on the CH layer. The flame sheet residence time estimated by this method remains nearly constant with axial distance downstream. The mean value of the maximum principal strain rate on the CH layer is observed to decrease along the axial direction while the change in the value is relatively small except for the region near the nozzle exit. The mean value of the strain rate is found to show a good correlation to a S≈(x/d) −0.7 relation for a wide range of Reynolds number.

Geodetic measurements of horizontal strain near the White Wolf fault, Kern County, California, 1926–1993

The White Wolf fault, located north of the Big Bend segment of the San Andreas fault, is the NE‐SW trending, left lateral‐oblique reverse fault responsible for the Ms=7.8 1952 Kern County earthquake. We combined Global Positioning System (GPS) measurements with historical triangulation and trilateration data to determine changes in the strain rate over 7 decades (1926–1993). We reanalyzed the historical geodetic data and calculated an elevated preseismic (1926–1952) maximum shear strain rate of 0.62±0.16 μstrain/yr across the White Wolf fault. The maximum shear strain rate decreased with distance toward the Garlock fault to 0.09±0.08 μstrain/yr. In the decade following the earthquake (1952–1963), the near fault was high (0.85±0.23μstrain/yr), and decreased to 0.23±0.13 μstrain/yr across the Garlock fault. In 1993, we resurveyed many of the same monuments with GPS receivers to estimate fault‐crossing and off‐fault strain rates for the preceding 30 years. Across the White Wolf fault, the maximum shear strain rate dropped to 0.19±0.07 μstrain/yr. The azimuths of the maximum principal strain rates (ϕ) for the 1963–1993 epoch rotate from a fault normal orientation (−57°±15°) across the White Wolf fault to 11°±3°E across the Garlock fault.

Strain and vorticity patterns in ideally ductile transpression zones

The prevalent model for ductile shear zones assumes that they develop by progressive simple shearing, resulting in a monoclinic fabric in which the vorticity vector is parallel to the shear zone and perpendicular to the lineation. But some ductile shear zones exhibit an amount of coaxial flattening, or a fabric pattern which appear to be incompatible with the assumptions of plane strain and progressive simple shear. In certain sections of the Archean Larder Lake—Cadillac deformation zone (LCDZ), for example, vorticity indicators (asymmetric pressure wings, Z-folds, SC fabrics), best seen on horizontal surfaces, indicate dextral transcurrent motion, whereas stretching lineations have variable but steep plunges. In the Proterozoic Mylonite Zone (MZ) of south-west Sweden, vorticity indicators combined with foliation and lineation data suggest a continuous change from reverse dip-slip motion close to the footwall to sinistral transcurrent motion adjacent to the hangingwall of the zone. Such departures from the ideal progressive simple shear zone pattern may in fact be common. Rather than invoke two stages of deformation, we explore the possibility that these patterns could be the result of ductile transpression. Ductile transpression between relatively rigid walls implies an extrusion of material out of the shear zone. When the material cannot slip freely along the boundaries of the zone, the extrusion strain is by necessity heterogeneous. In order to explore these heterogeneous strain distributions, we have developed a continuum mechanics model in which the ‘transpressed’ rock is a linear viscous material squeezed upward between two parallel, rigid, vertical walls. Transpression is further generalized by modelling oblique (i.e. with a dip-slip component) relative displacements of the walls. Models, which can vary in their obliquity and their ‘press’/‘trans’ ratio, are examined for their distributions of K-values, strain rate intensity, ‘lineation’ (direction of maximum principal strain rate), ‘foliation’ (plane perpendicular to the direction of minimum principal strain rate) and vorticity. To quantify the expected petrographic effect of the vorticity when the strain path has triclinic symmetry, we introduce a sectional kinematic vorticity number, W s k. The model predicts ‘foliations’ and ‘lineations’ which vary in orientation and intensity across the zone. In some model zones, the vorticity vector can be nearly parallel to the ‘foliation’ and perpendicular to the ‘lineation’, as expected in progressive simple shear, but it can also be locally nearly parallel to the ‘lineation’, as in the LCDZ. Commonly, however, the vorticity vector is not parallel to any of the principal directions of instantaneous strain, and the deformation has triclinic symmetry. The pattern of foliations and lineations in the MZ can readily be matched to that in an oblique transpression model zone.