Implicit Neural Representations for Registration of Left Ventricle Myocardium During a Cardiac Cycle

TL;DR

This work targets modeling the left ventricle myocardium (LVmyo) motion across the cardiac cycle via deformable image registration (DIR) in cardiac CT. It introduces implicit neural representations (INRs) to parameterize the deformation field $\Phi(\mathbf{x})=\mathbf{x}+u(\mathbf{x})$ and extends them with signed distance fields (SDF) of the LVmyo alongside CT HU values, weighted by $\alpha$ in the loss $(1-\alpha)L_{\text{sim}}(I_S\circ\Phi,I_T) + \alpha L_{\text{sim}}(S_S\circ\Phi,S_T) + \lambda L_{\text{reg}}(\Phi)$. Two registration strategies—sequential and non-sequential—are evaluated on 20-frame cardiac CT cycles, showing that incorporating SDF cues ($\alpha>0$) improves Dice similarity (DSC) and 95th percentile Hausdorff distance (HD95), with $\alpha=1.0$ yielding the best DSC while $\alpha=0.8$ can offer a better target registration error (TRE). The results indicate that INR-based DIR with LVmyo SDF guidance is a memory-efficient, viable alternative to CNN-based DIR for temporal LVmotion analysis, with potential for cycle-consistency regularization across the cardiac cycle.

Abstract

Understanding the movement of the left ventricle myocardium (LVmyo) during the cardiac cycle is essential for assessing cardiac function. One way to model this movement is through a series of deformable image registrations (DIRs) of the LVmyo. Traditional deep learning methods for DIRs, such as those based on convolutional neural networks, often require substantial memory and computational resources. In contrast, implicit neural representations (INRs) offer an efficient approach by operating on any number of continuous points. This study extends the use of INRs for DIR to cardiac computed tomography (CT), focusing on LVmyo registration. To enhance the precision of the registration around the LVmyo, we incorporate the signed distance field of the LVmyo with the Hounsfield Unit values from the CT frames. This guides the registration of the LVmyo, while keeping the tissue information from the CT frames. Our framework demonstrates high registration accuracy and provides a robust method for temporal registration that facilitates further analysis of LVmyo motion.

Figures (5)

• Figure 1: Registration process for a single point. The MLP learns the deformation $u(\mathbf{x})$ by sampling values from the CT frame and the SDF in the source domain at $\mathbf{x}$ and in the target domain at $\mathrm{\Phi}(\mathbf{x})$.
• Figure 2: 3D rendering of the CT frame in the ES-phase. The landmarks 1, 3 and 4 are rendered as lines representing the movement over a cardiac cycle, they are colored blue at 0% with a gradient to red at 95%.
• Figure 3: Axial slices of a registration example with the sequential approach in the top row (a) - (e) and the non-sequential approach in the bottom row (f) - (j). (a) and (b) shows the source and target frames which are before the ES-phase and the ES-phase it self, respectively. (c) - (e) shows the transformed CT scan and LVmyo segmentation after the registration from (a) to (b) using $\alpha=0.0$, $\alpha=0.8$ and $\alpha=1.0$, respectively. (f) and (g) shows the source and target frames which are before the ED-phase and the ES-phase. Again (h) - (j) shows the transformation using using $\alpha=0.0$, $\alpha=0.8$ and $\alpha=1.0$, respectively. The arrows highlights trabeculated area of the LV.
• Figure 4: Evaluation between the LVmyo segmentation and the moved LVmyo segmentation averaged over all patients in DSC. (a) shows the sequential approach, while (b) shows the non-sequential approach. The shaded area marks one standard deviation, and the scan percentage marks registration to this phase of the cardiac cycle.
• Figure 5: Movement of landmark 4 through a cardiac cycle illustrated in the sagittal plane. (a) is the annotated movement, while (b), (c) and (d) shows the movement using the non-sequential approach with $\alpha=0.0$, $\alpha=0.8$ and $\alpha=1.0$, respectively.