Simulating progressive intramural damage leading to aortic dissection using DeepONet: an operator-regression neural network

Accelerated simulation methodologies for computational vascular flow modelling

Vascular flow modelling can improve our understanding of vascular pathologies and aid in developing safe and effective medical devices. Vascular flow models typically involve solving the nonlinear Navier-Stokes equations in complex anatomies and using physiological boundary conditions, often presenting a multi-physics and multi-scale computational problem to be solved. This leads to highly complex and expensive models that require excessive computational time. This review explores accelerated simulation methodologies, specifically focusing on computational vascular flow modelling. We review reduced order modelling (ROM) techniques like zero-/one-dimensional and modal decomposition-based ROMs and machine learning (ML) methods including ML-augmented ROMs, ML-based ROMs and physics-informed ML models. We discuss the applicability of each method to vascular flow acceleration and the effectiveness of the method in addressing domain-specific challenges. When available, we provide statistics on accuracy and speed-up factors for various applications related to vascular flow simulation acceleration. Our findings indicate that each type of model has strengths and limitations depending on the context. To accelerate real-world vascular flow problems, we propose future research on developing multi-scale acceleration methods capable of handling the significant geometric variability inherent to such problems.

MetaNO: How to Transfer Your Knowledge on Learning Hidden Physics

Gradient-based meta-learning methods have primarily been applied to classical machine learning tasks such as image classification. Recently, PDE-solving deep learning methods, such as neural operators, are starting to make an important impact on learning and predicting the response of a complex physical system directly from observational data. Taking the material modeling problems for example, the neural operator approach learns a surrogate mapping from the loading field to the corresponding material response field, which can be seen as learning the solution operator of a hidden PDE. The microstructure and mechanical parameters of each material specimen correspond to the (possibly heterogeneous) parameter field in this hidden PDE. Due to the limitation on experimental measurement techniques, the data acquisition for each material specimen is commonly challenging and costly. This fact calls for the utilization and transfer of existing knowledge to new and unseen material specimens, which corresponds to sampling efficient learning of the solution operator of a hidden PDE with a different parameter field. Herein, we propose a novel meta-learning approach for neural operators, which can be seen as transferring the knowledge of solution operators between governing (unknown) PDEs with varying parameter fields. Our approach is a provably universal solution operator for multiple PDE solving tasks, with a key theoretical observation that underlying parameter fields can be captured in the first layer of neural operator models, in contrast to typical final-layer transfer in existing meta-learning methods. As applications, we demonstrate the efficacy of our proposed approach on PDE-based datasets and a real-world material modeling problem, illustrating that our method can handle complex and nonlinear physical response learning tasks while greatly improving the sampling efficiency in unseen tasks.

Categorization of collagen type I and II blend hydrogel using multipolarization SHG imaging with ResNet regression

Previously, the discrimination of collagen types I and II was successfully achieved using peptide pitch angle and anisotropic parameter methods. However, these methods require fitting polarization second harmonic generation (SHG) pixel-wise information into generic mathematical models, revealing inconsistencies in categorizing collagen type I and II blend hydrogels. In this study, a ResNet approach based on multipolarization SHG imaging is proposed for the categorization and regression of collagen type I and II blend hydrogels at 0%, 25%, 50%, 75%, and 100% type II, without the need for prior time-consuming model fitting. A ResNet model, pretrained on 18 progressive polarization SHG images at 10° intervals for each percentage, categorizes the five blended collagen hydrogels with a mean absolute error (MAE) of 0.021, while the model pretrained on nonpolarization images exhibited 0.083 MAE. Moreover, the pretrained models can also generally regress the blend hydrogels at 20%, 40%, 60%, and 80% type II. In conclusion, the multipolarization SHG image-based ResNet analysis demonstrates the potential for an automated approach using deep learning to extract valuable information from the collagen matrix.

A Physics-Guided Neural Operator Learning Approach to Model Biological Tissues From Digital Image Correlation Measurements

We present a data-driven workflow to biological tissue modeling, which aims to predict the displacement field based on digital image correlation (DIC) measurements under unseen loading scenarios, without postulating a specific constitutive model form nor possessing knowledge of the material microstructure. To this end, a material database is constructed from the DIC displacement tracking measurements of multiple biaxial stretching protocols on a porcine tricuspid valve anterior leaflet, with which we build a neural operator learning model. The material response is modeled as a solution operator from the loading to the resultant displacement field, with the material microstructure properties learned implicitly from the data and naturally embedded in the network parameters. Using various combinations of loading protocols, we compare the predictivity of this framework with finite element analysis based on three conventional constitutive models. From in-distribution tests, the predictivity of our approach presents good generalizability to different loading conditions and outperforms the conventional constitutive modeling at approximately one order of magnitude. When tested on out-of-distribution loading ratios, the neural operator learning approach becomes less effective. To improve the generalizability of our framework, we propose a physics-guided neural operator learning model via imposing partial physics knowledge. This method is shown to improve the model's extrapolative performance in the small-deformation regime. Our results demonstrate that with sufficient data coverage and/or guidance from partial physics constraints, the data-driven approach can be a more effective method for modeling biological materials than the traditional constitutive modeling.

G2Φnet: Relating genotype and biomechanical phenotype of tissues with deep learning

Many genetic mutations adversely affect the structure and function of load-bearing soft tissues, with clinical sequelae often responsible for disability or death. Parallel advances in genetics and histomechanical characterization provide significant insight into these conditions, but there remains a pressing need to integrate such information. We present a novel genotype-to-biomechanical phenotype neural network (G2Φnet) for characterizing and classifying biomechanical properties of soft tissues, which serve as important functional readouts of tissue health or disease. We illustrate the utility of our approach by inferring the nonlinear, genotype-dependent constitutive behavior of the aorta for four mouse models involving defects or deficiencies in extracellular constituents. We show that G2Φnet can infer the biomechanical response while simultaneously ascribing the associated genotype by utilizing limited, noisy, and unstructured experimental data. More broadly, G2Φnet provides a powerful method and a paradigm shift for correlating genotype and biomechanical phenotype quantitatively, promising a better understanding of their interplay in biological tissues.

Neural operator learning of heterogeneous mechanobiological insults contributing to aortic aneurysms

Thoracic aortic aneurysm (TAA) is a localized dilatation of the aorta that can lead to life-threatening dissection or rupture. In vivo assessments of TAA progression are largely limited to measurements of aneurysm size and growth rate. There is promise, however, that computational modelling of the evolving biomechanics of the aorta could predict future geometry and properties from initiating mechanobiological insults. We present an integrated framework to train a deep operator network (DeepONet)-based surrogate model to identify TAA contributing factors using synthetic finite-element-based datasets. For training, we employ a constrained mixture model of aortic growth and remodelling to generate maps of local aortic dilatation and distensibility for multiple TAA risk factors. We evaluate the performance of the surrogate model for insult distributions varying from fusiform (analytically defined) to complex (randomly generated). We propose two frameworks, one trained on sparse information and one on full-field greyscale images, to gain insight into a preferred neural operator-based approach. We show that this continuous learning approach can predict the patient-specific insult profile associated with any given dilatation and distensibility map with high accuracy, particularly when based on full-field images. Our findings demonstrate the feasibility of applying DeepONet to support transfer learning of patient-specific inputs to predict TAA progression.

Model-Based Fluid-Structure Interaction Approach for Evaluation of Thoracic Endovascular Aortic Repair Endograft Length in Type B Aortic Dissection

Thoracic endovascular aortic repair (TEVAR) is a commonly performed operation for patients with type B aortic dissection (TBAD). The goal of TEVAR is to cover the proximal entry tear between the true lumen (TL) and the false lumen (FL) with an endograft to induce FL thrombosis, allow for aortic healing, and decrease the risk of aortic aneurysm and rupture. While TEVAR has shown promising outcomes, it can also result in devastating complications including stroke, spinal cord ischemia resulting in paralysis, as well as long-term heart failure, so treatment remains controversial. Similarly, the biomechanical impact of aortic endograft implantation and the hemodynamic impact of endograft design parameters such as length are not well-understood. In this study, a fluid-structure interaction (FSI) computational fluid dynamics (CFD) approach was used based on the immersed boundary and Lattice–Boltzmann method to investigate the association between the endograft length and hemodynamic variables inside the TL and FL. The physiological accuracy of the model was evaluated by comparing simulation results with the true pressure waveform measurements taken during a live TEVAR operation for TBAD. The results demonstrate a non-linear trend towards increased FL flow reversal as the endograft length increases but also increased left ventricular pulsatile workload. These findings suggest a medium-length endograft may be optimal by achieving FL flow reversal and thus FL thrombosis, while minimizing the extra load on the left ventricle. These results also verify that a reduction in heart rate with medical therapy contributes favorably to FL flow reversal.

Analyses of internal structures and defects in materials using physics-informed neural networks

Characterizing internal structures and defects in materials is a challenging task, often requiring solutions to inverse problems with unknown topology, geometry, material properties, and nonlinear deformation. Here, we present a general framework based on physics-informed neural networks for identifying unknown geometric and material parameters. By using a mesh-free method, we parameterize the geometry of the material using a differentiable and trainable method that can identify multiple structural features. We validate this approach for materials with internal voids/inclusions using constitutive models that encompass the spectrum of linear elasticity, hyperelasticity, and plasticity. We predict the size, shape, and location of the internal void/inclusion as well as the elastic modulus of the inclusion. Our general framework can be applied to other inverse problems in different applications that involve unknown material properties and highly deformable geometries, targeting material characterization, quality assurance, and structural design.