Physics-Informed Learning for Time-Resolved Angiographic Contrast Agent Concentration Reconstruction

TL;DR

This paper tackles the ill-posed problem of time-resolved angiographic contrast-agent reconstruction from rotational 4D-DSA by introducing a physics-informed learning approach. A neural network is trained on CFD-derived CA transport data to implicitly encode hemodynamics, and it predicts spatially averaged CA concentrations along vessel centerlines over time (1D+T). The method uses backprojection- and artifact-based input features, branch-wise processing, and a reduced-order model to achieve fast inference while mitigating vessel overlap and foreshortening artifacts. On a test set of CFD-simulated geometries, it achieves a mean absolute error of about $0.02$ and a mean absolute percentage error around $5\%$, with strong robustness to reconstruction artifacts, highlighting the potential to enhance time-resolved flow reconstructions in clinical contexts.

Abstract

Three-dimensional Digital Subtraction Angiography (3D-DSA) is a well-established X-ray-based technique for visualizing vascular anatomy. Recently, four-dimensional DSA (4D-DSA) reconstruction algorithms have been developed to enable the visualization of volumetric contrast flow dynamics through time-series of volumes. . This reconstruction problem is ill-posed mainly due to vessel overlap in the projection direction and geometric vessel foreshortening, which leads to information loss in the recorded projection images. However, knowledge about the underlying fluid dynamics can be leveraged to constrain the solution space. In our work, we implicitly include this information in a neural network-based model that is trained on a dataset of image-based blood flow simulations. The model predicts the spatially averaged contrast agent concentration for each centerline point of the vasculature over time, lowering the overall computational demand. The trained network enables the reconstruction of relative contrast agent concentrations with a mean absolute error of 0.02 $\pm$ 0.02 and a mean absolute percentage error of 5.31 % $\pm$ 9.25 %. Moreover, the network is robust to varying degrees of vessel overlap and vessel foreshortening. Our approach demonstrates the potential of the integration of machine learning and blood flow simulations in time-resolved angiographic flow reconstruction.

Figures (9)

• Figure 1: Overview of the learning-based method consisting of a simulation and a network part. Simulation Cerebral vessel tree surfaces extracted from segmentations are converted to volumetric polyhedral meshes. A computational fluid dynamics solver is employed to simulate hemodynamics and CA transport for a set of boundary conditions. The simulated CA concentrations are spatially integrated for $P \in \mathbb{N}$ centerline slices and $T \in \mathbb{N}$ timesteps, resulting in $\mathbf{X} \in \mathbb{R}^{P \times T}$. Moreover, the X-ray C-arm acquisition process is simulated by computing the 2D projection image for each timepoint $\mathbf{Y} = (\mathbf{Y}_1, \dots, \mathbf{Y}_T | \, \mathbf{Y}_t \in \mathbb{R}^{H \times W})$. A dataset $\{(\mathbf{X_i}, \mathbf{Y_i})\}$ of 1D+T concentrations and corresponding projection images is generated by simulating different flow and X-ray acquisition scenarios. Network The projections $\mathbf{Y_i}$ and the C-arm geometry are utilized to compute backprojection, vessel overlap, and foreshortening input features for each centerline and time point. The centerline is split into branches that are processed individually by a convolutional neural network (CNN). The final loss is calculated with the ground truth CA concentration values $\mathbf{X_i}$.
• Figure 2: Plot visualizing the CA flow rate $Q_\text{CA}$, physiological blood flow rate $Q_{B}$ (assuming no injection), and the resulting total flow rate $Q_T$ with a mixing factor of $m=0.3$. The cardiac cycle waveform was generated for an elderly patient (secondary systole) with a mean $Q_B$ of 4mLs.
• Figure 3: Visualization of the neural network input features for the ICA of a selected case. Measured intensities on the detector are backprojected to centerline points for each timestep. The vessel's overlap map between centerline points $\mathbf{p}_i$ and $\mathbf{p}_j$ for each timestep is determined by the overlap of the projected maximum inscribed spheres on the detector. The foreshortening map is the angle between the centerline normal vectors and the projection direction at each centerline point. Here, the siphone of the ICA introduces vessel overlap and foreshortening artifacts.
• Figure 4: Visualization of the neural network architecture. It consists of five residual blocks with increasing number of channels $C_i$. A block applies two convolutional layers ($5\times5$ kernels), each followed by instance normalization, and a leaky rectified linear unit (LReLU). Before the output, a $1\times1$ convolution is applied.
• Figure 5: Result of our DSA simulation for an exemplary case. The ground truth concentration curve (CFD) and the detector intensity curve at position $x_1$ is visualized over time. Also, the 3D CFD vascular filling state at timesteps $t_1, t_2$, and $t_3$ in combination with the corresponding simulated projection images is depicted. Starting from approximately 3.25s, the simulations include severe vessel foreshortening and overlap at $x_1$ for the respective projection angles.