Low-Rank Representation of Head Impact Kinematics: A Data-Driven Emulator

Arrue, Patricio; Toosizadeh, Nima; Babaee, Hessam; Laksari, Kaveh

doi:10.3389/fbioe.2020.555493

Cited by 5 publications

(3 citation statements)

References 46 publications

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“…(iii) From the above equations, it is clear to see that f-OTD extracts the low-rank approximation directly from the sensitivity evolution equation. In that sense, it is different from data-driven low-rank approximations such as proper orthogonal decomposition [23][24][25] or dynamic mode decomposition [26,27], in which the low rank subspace is extracted from preexisting data. The need to generate data simply does not exist in the f-OTD workflow.…”

Section: Variational Principle For Reduced Order Modelingmentioning

confidence: 99%

Computing Sensitivities in Evolutionary Systems: A Real-Time Reduced Order Modeling Strategy

Donello¹,

Carpenter²,

Babaee³

2020

Preprint

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We present a new methodology for computing sensitivities in evolutionary systems using a model driven low-rank approximation. To this end, we formulate a variational principle that seeks to minimize the distance between the time derivative of the reduced approximation and sensitivity dynamics. The first order optimality condition of the variational principle leads to a system of closed-form evolution equations for an orthonormal basis and corresponding sensitivity coefficients. This approach allows for the computation of sensitivities with respect to a large number of parameters in an accurate and tractable manner by extracting correlations between different sensitivities on the fly. The presented method requires solving forward evolution equations, sidestepping the restrictions imposed by forward/backward workflow of adjoint sensitivities. For example, the presented method, unlike adjoint equation, does not impose any I/O load and can be used in applications in which real time sensitivities are of interest. We demonstrate the utility of the method for three test cases: (1) computing sensitivity with respect to model parameters in the Rössler system (2) computing sensitivity with respect to an infinite dimensional forcing parameter in the chaotic Kuramoto-Sivashinsky equation and (3) computing sensitivity with respect to reaction parameters for species transport in a turbulent reacting flow.

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Section: Variational Principle For Reduced Order Modelingmentioning

confidence: 99%

Computing Sensitivities in Evolutionary Systems: A Real-Time Reduced Order Modeling Strategy

Donello¹,

Carpenter²,

Babaee³

2020

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…Previously, researchers have put in efforts to find the reduced-order decomposition of kinematics and brain deformation in the biomechanics research of TBI. For example, a data-driven emulator was developed to simulate the kinematics of head impacts with the principal components found by principal component analysis (PCA) (e.g., 15 principal components for angular velocity simulation) [21]. Additionally, the dynamic mode decomposition was adopted to extract the deformation modes [22], and a convolutional-neural-networkbased human head model [23] was combined with a precomputed brain [24] response dataset to find the effective kinematics that yields similar brain deformation for the actual kinematics [25].…”

Section: Introductionmentioning

confidence: 99%

“…Additionally, the dynamic mode decomposition was adopted to extract the deformation modes [22], and a convolutional-neural-networkbased human head model [23] was combined with a precomputed brain [24] response dataset to find the effective kinematics that yields similar brain deformation for the actual kinematics [25]. The previous studies focus on the temporal co-variation in the kinematics [21], the temporal co-variation of brain deformation [22], and the co-variation in the relationship between kinematics and deformation [25]. There has been no study insofar that focuses on the spatial co-variation of the peak values in a group of head impacts and particularly the spatial co-variation across different brain elements for a specific dataset.…”

Section: Introductionmentioning

confidence: 99%

Data-driven decomposition of brain dynamics with principal component analysis in different types of head impacts

Zhan¹,

Liu

Cecchi³

et al. 2021

Preprint

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Strain and strain rate are effective traumatic brain injury predictors. Kinematics-based models estimating these metrics suffer from significant different distributions of both kinematics and the injury metrics across head impact types. To address this, previous studies focus on the kinematics but not the injury metrics. We have previously shown the kinematic features vary largely across head impact types, resulting in different patterns of brain deformation. This study analyzes the spatial distribution of brain deformation and applies principal component analysis (PCA) to extract the representative patterns 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). Methods: We apply PCA to decompose the patterns of the injury metrics for all impacts in each impact type, and investigate the distributions among brain regions using the first principal component (PC1). Furthermore, we developed a deep learning head model (DLHM) to predict PC1 and then inverse-transform to predict for all brain elements. Results: PC1 explained > 80% variance on the datasets. Based on PC1 coefficients, the corpus callosum and midbrain exhibit high variance on all datasets. We found MPS×MPSR the most sensitive metric on which the top 5% of severe impacts further deviates from the mean and there is a higher variance among the severe impacts. Finally, the DLHM reached mean absolute errors of < 0.018 for MPS, < 3.7s −1 for MPSR and < 1.1s −1 for MPS×MPSR, much smaller than the injury thresholds. Conclusion: The brain injury metric in a dataset can be decomposed into mean components and PC1 with high explained variance. Significance: The brain dynamics decomposition enables better interpretation of the patterns in brain injury metrics and the sensitivity of brain injury metrics across impact types. The decomposition also reduces the dimensionality of DLHM.

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Efficient Generation of Pretraining Samples for Developing a Deep Learning Brain Injury Model via Transfer Learning

Lin,

Wu,

et al. 2023

Ann Biomed Eng

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Low-Rank Representation of Head Impact Kinematics: A Data-Driven Emulator

Cited by 5 publications

References 46 publications

Computing Sensitivities in Evolutionary Systems: A Real-Time Reduced Order Modeling Strategy

Computing Sensitivities in Evolutionary Systems: A Real-Time Reduced Order Modeling Strategy

Data-driven decomposition of brain dynamics with principal component analysis in different types of head impacts

Efficient Generation of Pretraining Samples for Developing a Deep Learning Brain Injury Model via Transfer Learning

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