Machine learning in cardiovascular flows modeling: Predicting arterial blood pressure from non-invasive 4D flow MRI data using physics-informed neural networks

Abstract

Advances in computational science offer a principled pipeline for predictive modeling of cardiovascular flows and aspire to provide a valuable tool for monitoring, diagnostics and surgical planning. Such models can be nowadays deployed on large patient-specific topologies of systemic arterial networks and return detailed predictions on flow patterns, wall shear stresses, and pulse wave propagation. However, their success heavily relies on tedious pre-processing and calibration procedures that typically induce a significant computational cost, thus hampering their clinical applicability. In this work we put forth a machine learning framework that enables the seamless synthesis of non-invasive in-vivo measurement techniques and computational flow dynamics models derived from first physical principles. We illustrate this new paradigm by showing how one-dimensional models of pulsatile flow can be used to constrain the output of deep neural networks such that their predictions satisfy the conservation of mass and momentum principles. Once trained on noisy and scattered clinical data of flow and wall displacement, these networks can return physically consistent predictions for velocity, pressure and wall displacement pulse wave propagation, all without the need to employ conventional simulators. A simple post-processing of these outputs can also provide a cheap and effective way for estimating Windkessel model parameters that are required for the calibration of traditional computational models. The effectiveness of the proposed techniques is demonstrated through a series of prototype benchmarks, as well as a realistic clinical case involving in-vivo measurements near the aorta/carotid bifurcation of a healthy human subject.

arXiv comment30 pages, 13 figures

References in corpus (12)

• Adam: A Method for Stochastic Optimization
• TensorFlow: A system for large-scale machine learning
• An overview of gradient descent optimization algorithms
• Physics-Constrained Deep Learning for High-dimensional Surrogate Modeling and Uncertainty Quantification without Labeled Data
• Physics Informed Deep Learning (Part I): Data-driven Solutions of Nonlinear Partial Differential Equations
• Bayesian Deep Convolutional Encoder-Decoder Networks for Surrogate Modeling and Uncertainty Quantification
• Machine Learning of Linear Differential Equations using Gaussian Processes
• Adversarial Uncertainty Quantification in Physics-Informed Neural Networks
• Physics Informed Deep Learning (Part II): Data-driven Discovery of Nonlinear Partial Differential Equations
• Deep learning of dynamics and signal-noise decomposition with time-stepping constraints
• Learning Parameters and Constitutive Relationships with Physics Informed Deep Neural Networks
• Physics-informed deep generative models

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