Bidirectional Recurrence for Cardiac Motion Tracking with Gaussian Process Latent Coding

TL;DR

The GPTrack is introduced, a novel unsupervised framework crafted to fully explore the temporal and spatial dynamics of cardiac motion that significantly improves the precision of motion tracking in both 3D and 4D medical images while maintaining computational efficiency.

Abstract

Quantitative analysis of cardiac motion is crucial for assessing cardiac function. This analysis typically uses imaging modalities such as MRI and Echocardiograms that capture detailed image sequences throughout the heartbeat cycle. Previous methods predominantly focused on the analysis of image pairs lacking consideration of the motion dynamics and spatial variability. Consequently, these methods often overlook the long-term relationships and regional motion characteristic of cardiac. To overcome these limitations, we introduce the \textbf{GPTrack}, a novel unsupervised framework crafted to fully explore the temporal and spatial dynamics of cardiac motion. The GPTrack enhances motion tracking by employing the sequential Gaussian Process in the latent space and encoding statistics by spatial information at each time stamp, which robustly promotes temporal consistency and spatial variability of cardiac dynamics. Also, we innovatively aggregate sequential information in a bidirectional recursive manner, mimicking the behavior of diffeomorphic registration to better capture consistent long-term relationships of motions across cardiac regions such as the ventricles and atria. Our GPTrack significantly improves the precision of motion tracking in both 3D and 4D medical images while maintaining computational efficiency. The code is available at: https://github.com/xmed-lab/GPTrack

Figures (8)

• Figure 1: Regional Motions in Cardiac: The left sequential MRI frames within a heartbeat cycle illustrate that motion direction and intensity are completely different between the right atrium and myocardium during End-diastole and End-systole. Formulate Cardiac Motion as Prior Knowledge: The right figure depicts the regions of motion trajectory across the heartbeat cycle, alongside the probability distributions of motion trajectory. Curves (Middle) are the motion trajectory changes of different MRI sequences (Left). Highlighting the cardiac motion trajectory that follows a certain pattern can be modelled as prior knowledge via the Gaussian Process (Right).
• Figure 2: Comparsion between our GPTrack (a) and conventional registration framework (b).
• Figure 3: The overview pipeline of GPTrack (one layer). The $x$, $h$, $\dot{h}$ and $z$ denote input, forward hidden states, backward hidden states and latent coordinates. Feature $\vec{f}_t$ with probabilistic prior on the latent space via Gaussian Process then enters the decoder to predict the motion field $\phi$. Subscript $t$ denotes the $t$-th position in total $T$ moments. $elu(\cdot)$ represent the exponential linear units clevert2015fast.
• Figure 4: The visualization in 3D Echocardiogram video of motion tracking error. We visualised the last frame of tracking result and ground truth from 32 consecutive frames in CardiacUDA yang2023graphecho. Colours Red, Blue, Green and Orange denote cardiac structures RA, RV, LV and LA, respectively.
• Figure 5: The visualization in 4D Cardiac MRI of motion tracking error. We visualised the result of the last frame tracking from ED to ES and corresponding ground truth in ACDC yang2023graphecho. Colours Red, Blue, and Green denote cardiac structures MYO, LA, and LV, respectively.