Machine learning augmented reduced-order models for FFR-prediction

Fredrik E Fossan,Lucas O Müller,Jacob Sturdy,Anders T Bråten,Arve Jørgensen,Rune Wiseth,Leif R Hellevik

doi:10.1016/j.cma.2021.113892

Abstract

Computational predictions in cardiovascular medicine have largely relied on explicit models derived from physical and physiological principles. Recently, the application of artificial intelligence in cardiovascular medicine has grown substantially. However, successful application of purely data-driven methods requires a sufficiently large and rich dataset. An alternative to purely data-driven methods is to incorporate prior physics-based knowledge into the learning process to reduce the amount and quality of data necessary for a performant model. We analyzed the benefit of this alternative for prediction of pressure and flow in pathological coronary arteries. We trained fully-connected feed forward neural networks (NN) to predict pressure losses in coronary arteries. The training and test data were obtained by solving the 3D incompressible Navier–Stokes (3DiNS) equations. The coronary flow and various geometrical data were used as inputs to train a purely data-driven NN. We investigated two methods for incorporation of prior physics-based knowledge from a reduced-order model (ROM) into NNs that predicted pressure losses across stenotic and healthy coronary segments. First, we trained NNs to predict the discrepancy between the ROM and 3DiNS pressure loss. Second, we augmented the data by including the ROM pressure loss prediction as an input feature to a NN that predicted 3DiNS pressure. Both approaches for incorporation of prior knowledge from the ROM significantly improved prediction of pressure losses across healthy and stenotic segments relative to the purely data-driven approach, especially for lower amounts of data. The incorporation of NN predictions of coronary segment pressure losses in a coronary network model resulted in Fractional Flow Reserve (FFR) predictions with error standard deviation of 0.021 with respect to 3DiNS FFR. In comparison, the standard deviation of repeated FFR measurements is 0.018.

Highlights

Physical principles have long been applied to study physiology, and advancements in mathematical and computational models have led to continued growth in related research over the past few decades
In this work we explore various approaches for prediction of pressure losses in coronary arteries based on pure physics, pure machine learning, and combinations that include prior physics-based information in the learning process
We evaluated the performance of FFRsimpl vs. FFRsimpl and corresponding 3D iNS FFR predictions (FFR3D) based on the bias, standard deviation, and mean absolute error based on the quantity FFR3D − FFRsimpl

Summary

Introduction

Physical principles have long been applied to study physiology, and advancements in mathematical and computational models have led to continued growth in related research over the past few decades. This has culminated in the application of physics-based computational models in the clinic, such as for diagnosis of obstructive coronary artery disease (CAD) [1]. Data-driven approaches are, dependent on the quality and representation of the data available for training. Predictions from purely data-driven approaches may violate physical principles as well as regulatory requirements [7]

Methods

Discussion

Conclusion