Capturing Longitudinal Changes in Brain Morphology Using Temporally Parameterized Neural Displacement Fields

TL;DR

This work addresses the challenge of longitudinal brain morphology analysis by introducing a time-parameterized implicit neural representation (INR) to model voxel-wise deformations across multiple timepoints. An MLP-based deformation field is conditioned on continuous time via a time-embedding subnetwork, enabling interpolation and extrapolation of 4D brain morphometry and the generation of Jacobian maps at unobserved times. A novel monotonic regularization term, derived from analytic temporal derivatives of the INR, enforces consistent, biologically plausible progression of tissue changes, improving robustness to noise. Applied to 4D MRI data from ADNI, the method demonstrates plausible longitudinal trajectories and potential biomarker utility, while acknowledging per-subject optimization and structure-specific challenges as areas for future improvement.

Abstract

Longitudinal image registration enables studying temporal changes in brain morphology which is useful in applications where monitoring the growth or atrophy of specific structures is important. However this task is challenging due to; noise/artifacts in the data and quantifying small anatomical changes between sequential scans. We propose a novel longitudinal registration method that models structural changes using temporally parameterized neural displacement fields. Specifically, we implement an implicit neural representation (INR) using a multi-layer perceptron that serves as a continuous coordinate-based approximation of the deformation field at any time point. In effect, for any N scans of a particular subject, our model takes as input a 3D spatial coordinate location x, y, z and a corresponding temporal representation t and learns to describe the continuous morphology of structures for both observed and unobserved points in time. Furthermore, we leverage the analytic derivatives of the INR to derive a new regularization function that enforces monotonic rate of change in the trajectory of the voxels, which is shown to provide more biologically plausible patterns. We demonstrate the effectiveness of our method on 4D brain MR registration.

Figures (14)

• Figure 1: Given observed scans (pink arrows), our model represents the deformation field $\phi_t$ as a function (yellow circle). At inference, the model predicts time dependent fields, $\phi_t$ as well as $|J|$ maps for both observed and unobserved time points.
• Figure 2: Interpolating and extrapolating Jacobian maps: The residual plot is the difference in $|J|$ maps when the time point is held out versus when it is used to fit the data. We provide examples from other subjects in Figure \ref{['fig:inter-extra2']}.
• Figure 3: Comparing $|J|$ maps generated from NiftyReg with our proposed method. Black circle indicates inconsistent transformation over time. The bright red regions represents folded voxels.
• Figure 4: Voxel-wise rate of change within the Thalamus over a span of 26.5 months with and without the monotonic constraint. The black vertical lines are points where data was observed.
• Figure 5: Effect of Noise; Top:mean $|J|$ plotted over 2 years, Bottom: $\frac{\partial |J|}{\partial{t}}$ for each structure.