TopoTxR: A topology-guided deep convolutional network for breast parenchyma learning on DCE-MRIs

Abstract

Characterization of breast parenchyma in dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) is a challenging task owing to the complexity of underlying tissue structures. Existing quantitative approaches, like radiomics and deep learning models, lack explicit quantification of intricate and subtle parenchymal structures, including fibroglandular tissue. To address this, we propose a novel topological approach that explicitly extracts multi-scale topological structures to better approximate breast parenchymal structures, and then incorporates these structures into a deep-learning-based prediction model via an attention mechanism. Our topology-informed deep learning model, TopoTxR, leverages topology to provide enhanced insights into tissues critical for disease pathophysiology and treatment response. We empirically validate TopoTxR using the VICTRE phantom breast dataset, showing that the topological structures extracted by our model effectively approximate the breast parenchymal structures. We further demonstrate TopoTxR's efficacy in predicting response to neoadjuvant chemotherapy. Our qualitative and quantitative analyses suggest differential topological behavior of breast tissue in treatment-naïve imaging, in patients who respond favorably to therapy as achieving pathological complete response (pCR) versus those who do not. In a comparative analysis with several baselines on the publicly available I-SPY 1 dataset (N = 161, including 47 patients with pCR and 114 without) and the Rutgers proprietary dataset (N = 120, with 69 patients achieving pCR and 51 not), TopoTxR demonstrates a notable improvement, achieving a 2.6% increase in accuracy and a 4.6% enhancement in AUC compared to the state-of-the-art method.

Keywords: 3D CNN; DCE-MRI; Persistent homology; Spatial attention; Topology; pCR prediction.

Fig. 1:

(a): 3D rendering of a phantom breast with highlighted glandular tissues (white) and topological structures (blue); (b): glandular tissues; (c): topological structures.

Fig. 2:

(a) A example MRI image, and different radiomics features such as (b) 3D shape of a tumor, (c) intratumoral texture (Haralick entropy), and (d) whole breast texture (Haralick energy). In (e), we show topological structures from TopoTxR, capturing the geometry of fibroglandular tissues.

Fig. 3:

Our proposed TopoTxR pipeline. We extract 1D and 2D topological structures from breast MRI based on persistent homology. Rather than using binary masks, we extract topological structures with intensity values from raw MRIs (”soft” topological masks) for mask loss ${ℒ}_{mask}$ supervision. Each 3D CNN branch includes five 3D CNN blocks and a topology-guided spatial attention module (TGSA). The input to TGSA is the feature map from the third convolution layer, $F_i$, while its output to the fourth convolution layer is the generated attention map multiplied by $F_i$. The model features two distinct 3D CNN branches with a fully connected network for pCR prediction.

Fig. 4:

From left to right: a synthetic image $f$, sublevel sets at thresholds $b_1<b_2<d_2<d_1$, and the 1D persistence diagram. The red loop represents a 1D structure born at $b_1$ and killed at $d_1$. The green loop represents a 1D structure born at $b_2$ and killed at $d_2$. They correspond to the red and green dots respectively in the diagram.

Fig. 5:

(a) Example of a cubical complex whose cells are sorted monotonically non-decreasing according to the function values. (b) 2D boundary matrix $\partial$. (c) Reduced boundary matrix. (d) Persistence diagram and resulting topological cycles of $\partial$. (e) 1D boundary matrix.

Fig. 6:

Row 1: 3D renderings of VICTRE phantom breasts of four distinct profiles. Rows 2 and 3: two slices at different positions of the corresponding breast phantoms. Red: 1-voxel width breast outline; blue: extracted topological structures; white: ground truth breast tissues. Each slice’s rendering includes several additional slices around the target cross sections for detailed examination.

Fig. 7:

Qualitative comparison of patients with and without pCR. First column: Slices of breast DCE-MRIs with tumor masked in orange (tumor masks are not used in TopoTxR). Columns 2-4: 3D renderings of topological structures from three different views. 1-D structures (loops) are rendered in blue and 2-D structures (bubbles) in red. Right: cumulative density function of topological structures’ birth times.

Fig. 8:

Attention maps of CNNs when making decisions about pCR predictions. Red: voxels contributing to decisions of CNNs; blue: voxels corresponding to extracted topological structures. Columns 1, 3, 5, and 7 display 3D renderings of the attention maps, while columns 2, 4, 6, and 8 present cross-sections corresponding to the 3D renderings on their left.