Aneurysm Growth Time Series Reconstruction Using Physics-informed Autoencoder
Jiacheng Wu
TL;DR
This work addresses predicting aneurysm rupture by reconstructing patient-specific growth histories $X(t)$ from parameter vectors $\theta$ using a physics-informed autoencoder. It combines a latent representation $Z$ of the time series, a parameter-to-latent mapper, and an autoencoder decoder to recover $X$, with temporal dynamics captured via moving-average and convolutional components. Physics knowledge is injected as soft constraints in the autoencoder objective through Crank-Nicolson discretization of the governing equations, including $ m = M [ k_g (\sigma-\sigma_h) + f_h ]$ and $ \sigma = \frac{\rho P r^2}{M R}$. Results show that constraints provide robustness benefits under noisy data, improving reconstruction accuracy when measurement noise and bias are present, and highlighting the approach's potential for data-limited biomedical time-series where physical priors are informative.
Abstract
Arterial aneurysm (Fig.1) is a bulb-shape local expansion of human arteries, the rupture of which is a leading cause of morbidity and mortality in US. Therefore, the prediction of arterial aneurysm rupture is of great significance for aneurysm management and treatment selection. The prediction of aneurysm rupture depends on the analysis of the time series of aneurysm growth history. However, due to the long time scale of aneurysm growth, the time series of aneurysm growth is not always accessible. We here proposed a method to reconstruct the aneurysm growth time series directly from patient parameters. The prediction is based on data pairs of [patient parameters, patient aneurysm growth time history]. To obtain the mapping from patient parameters to patient aneurysm growth time history, we first apply autoencoder to obtain a compact representation of the time series for each patient. Then a mapping is learned from patient parameters to the corresponding compact representation of time series via a five-layer neural network. Moving average and convolutional output layer are implemented to explicitly taking account the time dependency of the time series. Apart from that, we also propose to use prior knowledge about the mechanism of aneurysm growth to improve the time series reconstruction results. The prior physics-based knowledge is incorporated as constraints for the optimization problem associated with autoencoder. The model can handle both algebraic and differential constraints. Our results show that including physical model information about the data will not significantly improve the time series reconstruction results if the training data is error-free. However, in the case of training data with noise and bias error, incorporating physical model constraints can significantly improve the predicted time series.