Discovering 3D Hidden Elasticity in Isotropic and Transversely Isotropic Materials with Physics-informed UNets

Three-dimensional variation in structural components or fiber alignments results in complex mechanical property distribution in tissues and biomaterials. In this paper, we use a physics-informed UNet-based neural network model (El-UNet) to discover the three-dimensional (3D) internal composition and space-dependent material properties of heterogeneous isotropic and transversely isotropic materials without a priori knowledge of the composition. We then show the capabilities of El-UNet by validating against data obtained from finite-element simulations of two soft tissues, namely, brain tissue and articular cartilage, under various loading conditions. We first simulated compressive loading of 3D brain tissue comprising of distinct white matter and gray matter mechanical properties undergoing small strains with isotropic linear elastic behavior, where El-UNet reached mean absolute relative errors under 1.5 % for elastic modulus and Poisson's ratio estimations across the 3D volume. We showed that the 3D solution achieved by El-UNet was superior to relative stiffness mapping by inverse of axial strain and two-dimensional plane stress/plane strain approximations. Additionally, we simulated a transversely isotropic articular cartilage with known fiber orientations undergoing compressive loading, and accurately estimated the spatial distribution of all five material parameters, with mean absolute relative errors under 5 %. Our work demonstrates the application of the computationally efficient physics-informed El-UNet in 3D elasticity imaging and provides methods for translation to experimental 3D characterization of soft tissues and other materials. The proposed El-UNet offers a powerful tool for both in vitro and ex vivo tissue analysis, with potential extensions to in vivo diagnostics. STATEMENT OF SIGNIFICANCE: Elasticity imaging is a technique that reconstructs mechanical properties of tissue using deformation and force measurements. Given the complexity of this reconstruction, most existing methods have mostly focused on 2D problems. Our work is the first implementation of physics-informed UNets to reconstruct three-dimensional material parameter distributions for isotropic and transversely isotropic linear elastic materials by having deformation and force measurements. We comprehensively validate our model using synthetic data generated using finite element models of biological tissues with high bio-fidelity-the brain and articular cartilage. Our method can be implemented in elasticity imaging scenarios for in vitro and ex vivo mechanical characterization of biomaterials and biological tissues, with potential extensions to in vivo diagnostics

Physics-informed UNets for Discovering Hidden Elasticity in Heterogeneous Materials

Soft biological tissues often have complex mechanical properties due to variation in structural components. In this paper, we develop a novel UNet-based neural network model for inversion in elasticity (El-UNet) to infer the spatial distributions of mechanical parameters from strain maps as input images, normal stress boundary conditions, and domain physics information. We show superior performance, both in terms of accuracy and computational cost, by El-UNet compared to fully-connected physics-informed neural networks in estimating unknown parameters and stress distributions for isotropic linear elasticity. We characterize different variations of El-UNet and propose a self-adaptive spatial loss weighting approach. To validate our inversion models, we performed various finite-element simulations of isotropic domains with heterogenous distributions of material parameters to generate synthetic data. El-UNet is faster and more accurate than the fully-connected physics-informed implementation in resolving the distribution of unknown fields. Among the tested models, the self-adaptive spatially weighted models had the most accurate reconstructions in equal computation times. The learned spatial weighting distribution visibly corresponded to regions that the unweighted models were resolving inaccurately. Our work demonstrates a computationally efficient inversion algorithm for elasticity imaging using convolutional neural networks and presents a potential fast framework for three-dimensional inverse elasticity problems that have proven unachievable through previously proposed methods.Comment: 25 pages, 9 figure

Associating Frailty and Dynamic Dysregulation between Motor and Cardiac Autonomic Systems

Frailty is a geriatric syndrome associated with the lack of physiological reserve and consequent adverse outcomes (therapy complications and death) in older adults. Recent research has shown associations between heart rate (HR) dynamics (HR changes during physical activity) with frailty. The goal of the present study was to determine the effect of frailty on the interconnection between motor and cardiac systems during a localized upper-extremity function (UEF) test. Fifty-six older adults aged 65 or older were recruited and performed the UEF task of rapid elbow flexion for 20-seconds with the right arm. Frailty was assessed using the Fried phenotype. Wearable gyroscopes and electrocardiography were used to measure motor function and HR dynamics. Using convergent cross-mapping (CCM) the interconnection between motor (angular displacement) and cardiac (HR) performance was assessed. A significantly weaker interconnection was observed among pre-frail and frail participants compared to non-frail individuals (p<0.01, effect size=0.81$\pm$0.08). Using logistic models pre-frailty and frailty were identified with sensitivity and specificity of 82% to 89%, using motor, HR dynamics, and interconnection parameters. Findings suggested a strong association between cardiac-motor interconnection and frailty. Adding CCM parameters in a multimodal model may provide a promising measure of frailty.Comment: 16 pages, 3 tables, 4 figure

Low-rank representation of head impact kinematics: A data-driven emulator

Head motion induced by impacts has been deemed as one of the most important measures in brain injury prediction, given that the majority of brain injury metrics use head kinematics as input. Recently, researchers have focused on using fast approaches, such as machine learning, to approximate brain deformation in real-time for early brain injury diagnosis. However, those requires large number of kinematic measurements, and therefore data augmentation is required given the limited on-field measured data available. In this study we present a principal component analysis-based method that emulates an empirical low-rank substitution for head impact kinematics, while requiring low computational cost. In characterizing our existing data set of 537 head impacts, consisting of 6 degrees of freedom measurements, we found that only a few modes, e.g. 15 in the case of angular velocity, is sufficient for accurate reconstruction of the entire data set. Furthermore, these modes are predominantly low frequency since over 70% to 90% of the angular velocity response can be captured by modes that have frequencies under 40Hz. We compared our proposed method against existing impact parametrization methods and showed significantly better performance in injury prediction using a range of kinematic-based metrics -- such as head injury criterion and rotational injury criterion (RIC) -- and brain tissue deformation-metrics -- such as brain angle metric, maximum principal strain (MPS) and axonal fiber strains (FS). In all cases, our approach reproduced injury metrics similar to the ground truth measurements with no significant difference, whereas the existing methods obtained significantly different (p<0.01) values as well as poor injury classification sensitivity and specificity. This emulator will enable us to provide the necessary data augmentation to build a head impact kinematic data set of any size.Comment: 20 pages, 13 figures, 4 table

Hyper-acute effects of sub-concussive soccer headers on brain function and hemodynamics

IntroductionSub-concussive head impacts in soccer are drawing increasing research attention regarding their acute and long-term effects as players may experience thousands of headers in a single season. During these impacts, the head experiences rapid acceleration similar to what occurs during a concussion, but without the clinical implications. The physical mechanism and response to repetitive impacts are not completely understood. The objective of this work was to examine the immediate functional outcomes of sub-concussive level impacts from soccer heading in a natural, non-laboratory environment.MethodsTwenty university level soccer athletes were instrumented with sensor-mounted bite bars to record impacts from 10 consecutive soccer headers. Pre- and post-header measurements were collected to determine hyper-acute changes, i.e., within minutes after exposure. This included measuring blood flow velocity using transcranial Doppler (TCD) ultrasound, oxyhemoglobin concentration using functional near infrared spectroscopy imaging (fNIRS), and upper extremity dual-task (UEF) neurocognitive testing.ResultsOn average, the athletes experienced 30.7 ± 8.9 g peak linear acceleration and 7.2 ± 3.1 rad/s peak angular velocity, respectively. Results from fNIRS measurements showed an increase in the brain oxygenation for the left prefrontal cortex (PC) (p = 0.002), and the left motor cortex (MC) (p = 0.007) following the soccer headers. Additional analysis of the fNIRS time series demonstrates increased sample entropy of the signal after the headers in the right PC (p = 0.02), right MC (p = 0.004), and left MC (p = 0.04).DiscussionThese combined results reveal some variations in brain oxygenation immediately detected after repetitive headers. Significant changes in balance and neurocognitive function were not observed in this study, indicating a mild level of head impacts. This is the first study to observe hemodynamic changes immediately after sub-concussive impacts using non-invasive portable imaging technology. In combination with head kinematic measurements, this information can give new insights and a framework for immediate monitoring of sub-concussive impacts on the head

Associating frailty and dynamic dysregulation between motor and cardiac autonomic systems

Frailty is a geriatric syndrome associated with the lack of physiological reserve and consequent adverse outcomes (therapy complications and death) in older adults. Recent research has shown associations between heart rate (HR) dynamics (HR changes during physical activity) with frailty. The goal of the present study was to determine the effect of frailty on the interconnection between motor and cardiac systems during a localized upper-extremity function (UEF) test. Fifty-six individuals aged 65 or above were recruited and performed the previously developed UEF test consisting of 20-s rapid elbow flexion with the right arm. Frailty was assessed using the Fried phenotype. Wearable gyroscopes and electrocardiography were used to measure motor function and HR dynamics. In this study, the interconnection between motor (angular displacement) and cardiac (HR) performance was assessed, using convergent cross-mapping (CCM). A significantly weaker interconnection was observed among pre-frail and frail participants compared to non-frail individuals (p &lt; 0.01, effect size = 0.81 ± 0.08). Using logistic models, pre-frailty and frailty were identified with sensitivity and specificity of 82%–89%, using motor, HR dynamics, and interconnection parameters. Findings suggested a strong association between cardiac-motor interconnection and frailty. Adding CCM parameters in a multimodal model may provide a promising measure of frailty

Multi-directional dynamic model for traumatic brain injury detection

Traumatic brain injury (TBI) is a complex injury that is hard to predict and diagnose, with many studies focused on associating head kinematics to brain injury risk. Recently, there has been a push towards using computationally expensive finite element (FE) models of the brain to create tissue deformation metrics of brain injury. Here, we developed a 3 degree-of-freedom lumped-parameter brain model, built based on the measured natural frequencies of a FE brain model simulated with live human impact data, to be used to rapidly estimate peak brain strains experienced during head rotational accelerations. On our dataset, the simplified model correlates with peak principal FE strain by an R2 of 0.80. Further, coronal and axial model displacement correlated with fiber-oriented peak strain in the corpus callosum with an R2 of 0.77. Using the maximum displacement predicted by our brain model, we propose an injury criteria and compare it against a number of existing rotational and translational kinematic injury metrics on a dataset of head kinematics from 27 clinically diagnosed injuries and 887 non-injuries. We found that our proposed metric performed comparably to peak angular acceleration, linear acceleration, and angular velocity in classifying injury and non-injury events. Metrics which separated time traces into their directional components had improved deviance to those which combined components into a single time trace magnitude. Our brain model can be used in future work as a computationally efficient alternative to FE models for classifying injuries over a wide range of loading conditions.Comment: 10 figures, 3 table

Physics-informed UNets for discovering hidden elasticity in heterogeneous materials

Soft biological tissues often have complex mechanical properties due to variation in structural components. In this paper, we develop a novel UNet-based neural network model for inversion in elasticity (El-UNet) to infer the spatial distributions of mechanical parameters from strain maps as input images, normal stress boundary conditions, and domain physics information. We show superior performance - both in terms of accuracy and computational cost - by El-UNet compared to fully-connected physics-informed neural networks in estimating unknown parameters and stress distributions for isotropic linear elasticity. We characterize different variations of El-UNet and propose a self-adaptive spatial loss weighting approach. To validate our inversion models, we performed various finite-element simulations of isotropic domains with heterogenous distributions of material parameters to generate synthetic data. El-UNet is faster and more accurate than the fully-connected physics-informed implementation in resolving the distribution of unknown fields. Among the tested models, the self-adaptive spatially weighted models had the most accurate reconstructions in equal computation times. The learned spatial weighting distribution visibly corresponded to regions that the unweighted models were resolving inaccurately. Our work demonstrates a computationally efficient inversion algorithm for elasticity imaging using convolutional neural networks and presents a potential fast framework for three-dimensional inverse elasticity problems that have proven unachievable through previously proposed methods

Elasticity imaging using physics-informed neural networks: Spatial discovery of elastic modulus and Poisson's ratio

Elasticity imaging is a technique that discovers the spatial distribution of mechanical properties of tissue using deformation and force measurements under various loading conditions. Given the complexity of this discovery, most existing methods approximate only one material parameter while assuming homogeneous distributions for the others. We employ physics-informed neural networks (PINN) in linear elasticity problems to discover the space-dependent distribution of both elastic modulus (E) and Poisson's ratio (ν) simultaneously, using strain data, normal stress boundary conditions, and the governing physics. We validated our model on three examples. First, we experimentally loaded hydrogel samples with embedded stiff inclusions, representing tumorous tissue, and compared the approximations against ground truth determined through tensile tests. Next, using data from finite element simulation of a rectangular domain containing a stiff circular inclusion, the PINN model accurately localized the inclusion and estimated both E and ν. We observed that in a heterogeneous domain, assuming a homogeneous ν distribution increases estimation error for stiffness as well as the area of the stiff inclusion, which could have clinical importance when determining size and stiffness of tumorous tissue. Finally, our model accurately captured spatial distribution of mechanical properties and the tissue interfaces on data from another computational model, simulating uniaxial loading of a rectangular hydrogel sample containing a human brain slice with distinct gray matter and white matter regions and complex geometrical features. This elasticity imaging implementation has the potential to be used in clinical imaging scenarios to reliably discover the spatial distribution of mechanical parameters and identify material interfaces such as tumors. Statement of significance: Our work is the first implementation of physics-informed neural networks to reconstruct both material parameters – Young's modulus and Poisson's ratio – and stress distributions for isotropic linear elastic materials by having deformation and force measurements. We comprehensively validate our model using experimental measurements and synthetic data generated using finite element modeling. Our method can be implemented in clinical elasticity imaging scenarios to improve diagnosis of tumors and for mechanical characterization of biomaterials and biological tissues in a minimally invasive manner.24 month embargo; available online: 17 November 2022This item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at [email protected]