Oriented histogram-based vector field embedding for characterizing 4D CT data sets in radiotherapy

TL;DR

The main focus of this study lies on reducing the dimensionality of deformable registration-based vector fields by employing a voxel-wise spherical coordinate transformation and a low-dimensional 2D oriented histogram representation.

Abstract

In lung radiotherapy, the primary objective is to optimize treatment outcomes by minimizing exposure to healthy tissues while delivering the prescribed dose to the target volume. The challenge lies in accounting for lung tissue motion due to breathing, which impacts precise treatment alignment. To address this, the paper proposes a prospective approach that relies solely on pre-treatment information, such as planning CT scans and derived data like vector fields from deformable image registration. This data is compared to analogous patient data to tailor treatment strategies, i.e., to be able to review treatment parameters and success for similar patients. To allow for such a comparison, an embedding and clustering strategy of prospective patient data is needed. Therefore, the main focus of this study lies on reducing the dimensionality of deformable registration-based vector fields by employing a voxel-wise spherical coordinate transformation and a low-dimensional 2D oriented histogram representation. Afterwards, a fully unsupervised UMAP embedding of the encoded vector fields (i.e., patient-specific motion information) becomes applicable. The functionality of the proposed method is demonstrated with 71 in-house acquired 4D CT data sets and 33 external 4D CT data sets. A comprehensive analysis of the patient clusters is conducted, focusing on the similarity of breathing patterns of clustered patients. The proposed general approach of reducing the dimensionality of registration vector fields by encoding the inherent information into oriented histograms is, however, applicable to other tasks.

Figures (2)

• Figure 1: Proposed workflow for reducing the dimensionality of 4D vector field data of a 4D CT patient data set. Block a) DIR of fixed and moving images yields high-dimensional vector field data. Block b) By applying a spherical coordinate transformation to each vector $\mathbf{v}$ in the field, an oriented histogram can be extracted through $r$-weighted $(\phi, \theta)$ binning. Performing this process for all phases of a 4D CT data set results in 9 oriented histograms. In block c), the data is further encoded by extracting the corresponding latent space representation using a lightweight autoencoder.
• Figure 2: UMAP embedding of the 71 in-house (top) and 33 4D Lung (bottom, mark color coding: patient) encoded vector field sequences after embedding them in a 2D manifold (middle, scatter plots) and illustration of selected data points by corresponding image data and all 9 oriented histograms (subfigures a--d [in-house data] and e--h [4D Lung data], white number: moving phase). Amplitude- and phase-based reconstructed 4D CT datasets are marked with $\bullet$ and $\circ$, respectively. Subplots and show two patients whose vector fields and corresponding oriented histograms remarkably resemble each other, despite different lung volumes. Subplots and illustrate two patients with only the right and left lung, respectively, yet having similar vector fields characteristics. Subplotsand depict repeat 4D CTs of one patient with high similarity. Subplotsand illustrate repeat 4D CTs of one patient that show large deviations in both the motion vector fields and the oriented histograms.