Accelerated simulation methodologies for computational vascular flow modelling
Michael MacRaild,
Ali Sarrami-Foroushani,
Toni Lassila
et al.
Abstract: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 method… Show more
Reduced order modelling (ROMs) methods, such as proper orthogonal decomposition (POD), systematically reduce the dimensionality of high‐fidelity computational models and potentially achieve large gains in execution speed. Machine learning (ML) using neural networks has been used to overcome limitations of traditional ROM techniques when applied to nonlinear problems, which has led to the recent development of reduced order models augmented by machine learning (ML‐ROMs). However, the performance of ML‐ROMs is yet to be widely evaluated in realistic applications and questions remain regarding the optimal design of ML‐ROMs. In this study, we investigate the application of a non‐intrusive parametric ML‐ROM to a nonlinear, time‐dependent fluid dynamics problem in a complex 3D geometry. We construct the ML‐ROM using POD for dimensionality reduction and neural networks for interpolation of the ROM coefficients. We compare three different network designs in terms of approximation accuracy and performance. We test our ML‐ROM on a flow problem in intracranial aneurysms, where flow variability effects are important when evaluating rupture risk and simulating treatment outcomes. The best‐performing network design in our comparison used a two‐stage POD reduction, a technique rarely used in previous studies. The best‐performing ROM achieved mean test accuracies of 98.6% and 97.6% in the parent vessel and the aneurysm, respectively, while providing speed‐up factors of the order .
Reduced order modelling (ROMs) methods, such as proper orthogonal decomposition (POD), systematically reduce the dimensionality of high‐fidelity computational models and potentially achieve large gains in execution speed. Machine learning (ML) using neural networks has been used to overcome limitations of traditional ROM techniques when applied to nonlinear problems, which has led to the recent development of reduced order models augmented by machine learning (ML‐ROMs). However, the performance of ML‐ROMs is yet to be widely evaluated in realistic applications and questions remain regarding the optimal design of ML‐ROMs. In this study, we investigate the application of a non‐intrusive parametric ML‐ROM to a nonlinear, time‐dependent fluid dynamics problem in a complex 3D geometry. We construct the ML‐ROM using POD for dimensionality reduction and neural networks for interpolation of the ROM coefficients. We compare three different network designs in terms of approximation accuracy and performance. We test our ML‐ROM on a flow problem in intracranial aneurysms, where flow variability effects are important when evaluating rupture risk and simulating treatment outcomes. The best‐performing network design in our comparison used a two‐stage POD reduction, a technique rarely used in previous studies. The best‐performing ROM achieved mean test accuracies of 98.6% and 97.6% in the parent vessel and the aneurysm, respectively, while providing speed‐up factors of the order .
State-of-the-art biomedical applications such as targeted drug delivery and laparoscopic surgery are extremely challenging because of the small length scales, the requirements of wireless manipulation, operational accuracy, and precise localization. In this regard, miniaturized magnetic soft robotic swimmers (MSRS) are attractive candidates since they offer a contactless mode of operation for precise path maneuvering. Inspired by nature, researchers have designed these small-scale intelligent machines to demonstrate enhanced swimming performance through viscous fluidic media using different modes of propulsion. In this review paper, we identify and classify nature-inspired basic swimming modes that have been optimized over large evolutionary timescales. For example, ciliary swimmers like Paramecium and Coleps are covered with tiny hairlike filaments (cilia) that beat rhythmically using coordinated wave movements for propulsion and to gather food. Undulatory swimmers such as spermatozoa and midge larvae use traveling body waves to push the surrounding fluid for effective propulsion through highly viscous environments. Helical swimmers like bacteria rotate their slender whiskers (flagella) for locomotion through stagnant viscid fluids. Essentially, all the three modes of swimming employ nonreciprocal motion to achieve spatial asymmetry. We provide a mechanistic understanding of magnetic-field-induced spatiotemporal symmetry-breaking principles adopted by MSRS for the effective propulsion at such small length scales. Furthermore, theoretical and computational tools that can precisely predict the magnetically driven large deformation fluid–structure interaction of these MSRS are discussed. Here, we present a holistic descriptive review of the recent developments in these smart material systems covering the wide spectrum of their fabrication techniques, nature-inspired design, biomedical applications, swimming strategies, magnetic actuation, and modeling approaches. Finally, we present the future prospects of these promising material systems. Specifically, synchronous tracking and noninvasive imaging of these external agents during in vivo clinical applications still remains a daunting task. Furthermore, their experimental demonstrations have mostly been limited to in vitro and ex vivo phantom models where the dynamics of the testing conditions are quite different compared the in vivo conditions. Additionally, multi-shape morphing and multi-stimuli-responsive modalities of these active structures demand further advancements in 4D printing avenues. Their multi-state configuration as an active solid-fluid continuum would require the development of multi-scale models. Eventually, adding multiple levels of intelligence would enhance their adaptivity, functionalities, and reliability during critical biomedical applications.
Blood flow reconstruction in the vasculature is important for many clinical applications. However, in clinical settings, the available data are often quite limited. For instance, transcranial Doppler ultrasound is a non-invasive clinical tool that is commonly used in clinical settings to measure blood velocity waveforms at several locations. This amount of data is grossly insufficient for training machine learning surrogate models, such as deep neural networks or Gaussian process regression. In this work, we propose a Gaussian process regression approach based on empirical kernels constructed by data generated from physics-based simulations—enabling near-real-time reconstruction of blood flow in data-poor regimes. We introduce a novel methodology to reconstruct the kernel within the vascular network. The proposed kernel encodes both spatiotemporal and vessel-to-vessel correlations, thus enabling blood flow reconstruction in vessels that lack direct measurements. We demonstrate that any prediction made with the proposed kernel satisfies the conservation of mass principle. The kernel is constructed by running stochastic one-dimensional blood flow simulations, where the stochasticity captures the epistemic uncertainties, such as lack of knowledge about boundary conditions and uncertainties in vasculature geometries. We demonstrate the performance of the model on three test cases, namely, a simple Y-shaped bifurcation, abdominal aorta and the circle of Willis in the brain.
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