Estimating blood flow distribution using physics-based machine learning for contrast-injected medical image data

Abstract

Estimating blood flow is important for diagnosing cardiovascular disease functionally. Blood flow can be measured non-invasively using medical image data or invasively by inserting medical devices into the arteries of interest. Medical image data often utilizes contrast to enhance the intensity of blood and due to the advection and diffusion of the injected contrast by blood motion, we can estimate blood flow inversely by measuring the motion of the contrast. We estimate blood flow by extracting the agent concentration from patient-specific contrast-based medical image data and solving an inverse problem of advection-diffusion and mass conservation equations using machine learning methods. The measured concentration values from medical image data is insufficient for data-driven machine learning techniques. We develop a data-efficient deep learning method by adding constraints based on the governing equations. We formulate an advection-diffusion equation for agent propagation in idealized one-dimensional flow conditions. The mass conservation is formulated with an outflow function to model flow distribution to bifurcating vessels. The derived system of equations is solved using a physics-informed neural network (PINN) whereby the agent concentration function of a neural network is constrained by extracted agent concentration values. This approach is mesh-free and both forward differentiation required for derivative terms for the governing equation and the backpropagation for optimization are performed by automatic differentiation. Finally, we will construct an end-to-end machine learning pipeline that performs direct concentration extraction from angiography data followed by flow estimation. To evaluate the developed methods, we will perform a validation study by solving three-dimensional advection-diffusion equations on ideal geometries and compare estimated flow values against the assigned ones.