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.

The effects of clinically‐derived parametric data uncertainty in patient‐specific coronary simulations with deformable walls

“…In this context, popular approaches are the multi-element generalized polynomial chaos, 79 LARS-based approaches 80 and generalized multi-resolution basis (MW). 26,28,30 Finally, we would also like to mention the use of stochastic surrogates based on Gaussian process regression or Kriging 81 are recently applied to the solution of forward and inverse problem in cardiovascular modeling reported, for example, in Kissas et al 82 .…”

Digital Twin: Values, Challenges and Enablers From a Modeling Perspective

“…This is inspired from the deep reinforcement learning with gradient acting as the policy function. Physics-informed ML ideas have been also utilized in various areas including inorganic scintillator discovery [348], fluid dynamics [349]- [351], projectionbased model reduction [352], cardiovascular system modeling [353], and wind farm applications [354]. In [355], the authors have presented a comprehensive review on the taxonomy of explicit integration of knowledge into ML.…”

Multiscale Modeling Meets Machine Learning: What Can We Learn?

“…Recent trends in computational physics suggest that exactly this approach [14]: to create data-efficient physics-informed learning machines [96,97]. Biomedicine has seen the first successful application of these techniques in cardiovascular flows modeling [50] or in cardiac activation mapping [109], where we already have a reasonable physical understanding of the system and can constrain the design space using the known underlying wave propagation dynamics. Another example where machine learning can immediately benefit from multiscale modeling and physics-based simulation is the generation of synthetic data [106], for example, to supplement sparse training sets.…”

“…This technique is particularly powerful when dealing with sparse data from systems that obey known physical principles. Examples in biomedicine include diagnosing cardiovascular disorders non-invasively using four-dimensional magnetic resonance images of blood flow and arterial wall displacements [50], creating computationally efficient surrogates for velocity and pressure fields in intracranial aneurysms [99], and using nonlinear wave propagation dynamics in cardiac activation mapping [109]. Combining deterministic and stochastic models.…”

“…An intriguing implication of such theory-driven machine learning approaches is related to their ability to leverage auxiliary observations to infer quantities of interest that are difficult to measure in practice [100]. An example includes the use of physics-informed neural networks to infer the arterial blood pressure directly and non-invasively from four-dimensional magnetic resonance images of blood velocities and arterial wall displacements by leveraging the known dynamic correlations induced by first principles in fluid and solid mechanics [50]. A commom thread between these approaches is that they rely on conventional neural network architectures, including fully connected or convolutional, and constrain them using physical laws as penalty terms in the loss function that drives the learning process.…”