Dual-Res Tandem Mamba-3D: Bilateral Breast Lesion Detection and Classification on Non-contrast Chest CT

W1: concerns about math-heavy sections without sufficient intuition

A: We appreciate the comment regarding the need for more intuition in math-heavy sections.

Generally speaking, our method aligns with the way radiologists interpret breast images: they analyze fine local details to identify subtle lesions, while also considering global appearance and bilateral symmetry to detect abnormalities.

Regarding detailed designs, the intuition can be summarized as:

1. Zoom-in & Zoom-out (Dual-Resolution Paths):
   • Intuition: Radiologists “zoom in” to inspect suspicious regions in detail for subtle lesions, and “zoom out” to evaluate the overall breast structure and context.
   • Our model: We use two parallel paths: a high-resolution “zoom-in” path (small patches) for fine-grained segmentation, and a low-resolution “zoom-out” path (large patches) for broader contextual classification. These paths exchange information via the Mutual Fusion mechanism (see Figure 3(a)), emulating how radiologists integrate local and global cues in clinical reading.
2. Cross-breast Comparison (Bilateral/Tandem Input):
   • Intuition: Radiologists routinely compare the left and right breasts, since subtle asymmetry is often a key sign of disease.
   • Our model: Our “Tandem Input” approach processes both breasts together, enabling the model to directly learn cross-breast differences. The input sequence aligns anatomically symmetric locations between sides (see Figure 3(b)), mirroring how radiologists visually match corresponding regions.
3. Multi-orientation Assessment (3D Patch modeling using Mamba-3D):
   • Intuition: Radiologists interpret scans from multiple anatomical planes to understand tumors’ shape and context in 3D.
   • Our model: Mamba-3D prioritizes scanning along different axes, allowing structural information from multiple directions to be integrated, thus mimicking the multi-orientation analysis and comprehensive assessment performed in real clinical evaluation.

W2: concerns regarding figure complexity

A: Thank you for your suggestion regarding figure clarity. We agree that a simplified, high-level schematic would make our framework and overall workflow easier to understand. In the camera-ready version, we will revise Figure 2 to provide a more streamlined summary of the complete framework, and will further simplify other figures as needed to enhance clarity.

W3: omission of Figure 1 citation in the main text

A: We apologize for the oversight. Figure 1 should have been referenced in the first paragraph of the Introduction section, and we will correct the text to ensure it is properly cited and explained in the revised version. We will also systematically review the manuscript to check for other potential omissions or unclear figure references.

All figures are explained in detail in their captions and the corresponding sections of the main text; however, we are happy to further clarify any figure or section that remains ambiguous. We also welcome any specific questions or requests for clarification during the response phase.

L1: concerns about NCCT not optimized for breast imaging

A: We fully recognize that NCCT is not optimized for breast imaging, and that lesion visibility is inherently limited compared to dedicated modalities or contrast-enhanced CTs. This makes our task particularly challenging and, to our knowledge, relatively under-explored in the literature.

However, we believe this is precisely where the value of our work lies: by leveraging chest CT scans that originally conducted for lung or heart screening, our approach enables opportunistic breast cancer detection without additional radiation exposure or economic burden.

Contrast-enhanced CT can have slightly better performance on our task but it needs contrast injection and generally not common, not appropriate for screening. To further enrich our evaluation, we have included additional experiments on contrast-enhanced CT (see our response to Reviewer oeU9’s W4), where performance is stronger as expected. Nevertheless, our model achieves robust and clinically meaningful results on NCCT scans alone, as demonstrated across multi-institutional cohorts.

Mammography and ultrasound can be seen as a specific examination tool for breasts, not aligned with our opportunistic screening intention. Dynamic contrast-enhanced MRI (DCE-MRI) can be deemed as a diagnostic tool, also not suitalble for oppotunistic screening.

Moreover, we have also conducted a supplemental reader study on newly collected NCCT samples from anthor region (see our response to Reviewer THvZ’s Q1), further supporting the practical value of our method in real-world clinical settings.

Thank you for your time and effort in reviewing our paper. As there have been no further comments during the discussion period so far, we would like to check if there are any remaining questions or concerns we can address. Please feel free to let us know if any additional clarification is needed.

Thank you for your efforts in reviewing our submission and for taking the time to read our rebuttal.

We have noticed, based on the last update time in the system, that a final justification has been provided. However, to fulfill the conference’s discussion requirements, we would greatly appreciate it if you could briefly comment on whether our rebuttal has addressed your concerns, and then complete the mandatory acknowledgement in the reviewing system.

If you have any further questions or concerns, please feel free to let us know. We will do our best to respond before the deadline.

Thank you again for your time and support.

W1 part1 & Q2: concerns regarding the Pre-Stage (breast region cropping) of the pipeline

A: Thank you for this important question. The Pre-Stage segmentation is designed solely to localize the breast region, which is a relatively simple task. In our experiments, the Pre-Stage achieved a high Dice score of 0.9598, demonstrating its accuracy and reliablity.

To further minimize the risk of missing boundary lesions or subtle structures (e.g., in obese patients or cases with blurred borders), we adopted a conservative cropping strategy: the predicted bounding box is expanded by 2 voxels along the D-axis and 16 voxels along the H- and W-axes. This ensures that small lesions near the periphery are retained within the cropped region.

Notably, the goal of the Pre-Stage is not to perform fine-grained segmentation but to exclude irrelevant anatomy (e.g., abdominal areas) and isolate the bilateral breast regions for downstream modeling. Across all training and test cases, we have not observed any missed-lesion failure due to Pre-Stage cropping. In future deployment, rare failure cases can be flagged for manual review or fallback processing.

W1 part2: concerns about using NCCT for breast lesion localization

A: We fully acknowledge that using NCCT for breast lesion detection is not a routine diagnostic process in clinical practice. Our purpose is to achieve breast lesion detection and classification on existing chest CT scans, such as those conducted for lung or heart screening. This approach introduces no additional radiation exposure or economic burden to patients, and can be referred to as opportunistic screening.

With the clinical value ahead, we acknowleged that it is relatively difficult for doctors to do breast lesion detection and classification on NCCT due to the lackness of contrast between the lesion and normal tissues. By collecting a large number of data, we are commited to achieve a clinically practical performance on this task leveraging the power of well-designed models. Our experimental results demonstrate that the proposed approach achieves strong and promising performance on NCCT images.

For medical imaging, we would also like to clarify two important points: First, microcalcifications are generally evident in x-ray based imaging modalities, including CT and digital radiography (DR)—even on non-contrast CT—but are typically not obvious in breast ultrasound images. Second, NCCT provides the same spatial resolution as contrast-enhanced CT; its main limitation lies in the limited contrast.

W2 part1: concerns about using N=1 in Delta visualization

A: Thank you for your insightful comment. We focused our Delta visualizations on the N=1 case primarily for clarity and interpretability: at a depth of N=1, the cross-breast (bilateral) interaction patterns introduced by our Tandem Input mechanism can be most directly and transparently visualized and understood.

For higher N (e.g., N=6 as used in our main experiments), we have observed that cross-breast interactions not only persist but often become even more pronounced and widespread across different layers. However, in deeper models, these effects are distributed across multiple blocks, makes concise visualization in the paper challenging.

As additional support, our quantitative results demonstrate that the benefits observed with the Tandem Input mechanism are effective across models with different depths: as shown in Table 9, even with N=1, our model outperforms the strong baseline, while increasing depth to N=6 yields further improvements, confirming the effectiveness of our design beyond the single-layer setting.

We appreciate your suggestion and, if desired, are happy to provide additional Delta visualizations for multi-layer cases in the supplementary material to further illustrate these cross-breast effects in deeper models.

W2 part2: clarification regarding Delta visualization on the HR path

A: The Delta responses on the HR path mainly reflect the model’s focus on local textures and anatomical details, which aligns with its primary role for the segmentation task. Meanwhile, the LR path is designed to focus on capturing bilateral context with shorter sequence length when Tandem Input mechanism is used (i.e., in DRT-M3D), so the Delta visualization of the LR path shows clear cross-breast clues. Overall, the Delta visualization of the two paths in Figure 11 appropriately reflects the distinct roles of the HR and LR paths for their respective tasks.

Compared to DR-M3D, which lacks the Tandem Input mechanism, DRT-M3D exhibits cross-breast responses in the LR path’s Delta visualization, further highlighting the effectiveness of our proposed design for modeling bilateral interactions, whereas in both models the HR path primarily focuses on local segmentation.

W3: deeper analysis of why applying the Tandem Input concept to ViTs and CNNs is less effective than Mamba

A: Thank you for this excellent question. We agree that the Tandem Input design’s impact varies fundamentally across architectures, and a deeper discussion is warranted.

Why does ViT struggle?

The limited effectiveness of Tandem Input on ViTs is not simply due to memory or computation. As token count increases, self-attention matrices become extremely large, leading to peaked and less expressive attention distributions. Although Transformers are theoretically capable of modeling arbitrary long-range dependencies, in practice—especially for very long sequences and without sufficient scaling of model and data size—the effective capture of such dependencies is often sparse and unreliable (Tay et al., 2021). Furthermore, ViT lacks inherent local inductive bias, making it harder to exploit local spatial structure compared to architectures with stronger locality, such as Mamba or CNNs.

Why does CNN struggle?

CNNs cannot directly model long-range bilateral dependencies, as their local receptive fields require progressively stacking many convolutional layers to cover larger spatial extents. Therefore, simply concatenating left and right views along the W-axis is not effective for explicit bilateral modeling. Although stacking these views as channels may seem like a reasonable alternative, breast symmetry is not strictly voxel-to-voxel; due to natural anatomical differences, positional variations, and imaging variability, this approach may mix features from non-corresponding areas and ultimately introduce negative effects.

Why is Mamba-3D effective?

Mamba-3D, in contrast, uniquely combines strong local bias and efficient selective long-range modeling, along with the support for extremely long sequences. With our Tandem Input mechanism, anatomically symmetrical parts of the left and right breasts always have a roughly fixed distance in the sequence (analogous to corresponding words in an antithetical couplet or rhyming lines), allowing the model to better capture cross-breast relationships.

We appreciate the opportunity to clarify these architectural distinctions and will elaborate on these points further in the camera-ready version.

Q1: preliminary results from diverse cohorts and expansion to cross-regional populations

A: Thank you for raising this important point about the generalizability of our approach. The datasets used in our study were collected through collaborations with professional medical institutions, and we are actively expanding our partnerships to include hospitals from additional regions. Data collection and annotation from new cohorts are ongoing.

To report preliminary results from more diverse cohorts, we have conducted a reader study using newly collected 100 cases from a separate region for the classification task. The table below summarizes the performance of our method (DRT-M3D) compared with two radiologists and a baseline method (nnUNet).

While it is important to note that radiologists typically do not assess for breast cancer on NCCT in routine clinical practice; nevertheless, our method achieves markedly higher performance. This demonstrates the robustness of our model and its potential value for opportunistic breast cancer screening.

Q3: specific metrics to validate detection of tiny abnormalities, which are critical for early diagnosis

A: Thank you for highlighting the importance of detecting tiny abnormalities for early diagnosis. To specifically address this concern, we evaluated our model on a subset (22%) of the test set consisting of cases with lesions less than 20 mm in diameter (corresponding to T1-stage breast cancer).

The table below summarizes the performance of our methods and the baseline (nnUNet) on this subset.

Although some metrics decrease slightly compared with the results on the full test set (which includes larger lesions; see Table 1 and Table 2 in the main paper), our model still achieves high Hit-rate, Sensitivity, and AUC on early-stage lesions. These results confirm the model’s practical value for the detection of tiny abnormalities that are critical for early breast cancer diagnosis.

References

[Tay et al., 2021] Tay, Y., Dehghani, M., Abnar, S., et al. Long Range Arena: A Benchmark for Efficient Transformers. International Conference on Learning Representations (ICLR), 2021.

Thank you for your detailed response, which has resolved most of my concerns. The detailed discussion on the architectural differences between Mamba, ViT, and CNNs is good. It provides a deeper understanding of why the Tandem Input mechanism is uniquely effective in their proposed framework. I strongly recommend that the authors incorporate the discussion on different architectures from W3, as well as the Model Efficacy points raised by other reviewers, into the final version of the paper.

Thank you for your time and effort in reviewing our paper. As there have been no further comments during the discussion period so far, we would like to check if there are any remaining questions or concerns we can address. Please feel free to let us know if any additional clarification is needed.

Thank you very much for your prompt and detailed reply. We appreciate your clarification regarding the originality rating. At this point, we confirm that we have no further concerns on this matter.

We fully agree with your perspective on the broader context of the Mamba architecture community and the field of medical imaging. We especially appreciate your aspiration for breakthrough work and dedication to advancing innovation. Our efforts are motivated by the desire to contribute meaningful progress within this dynamic landscape, and your recognition of our contribution is greatly valued.

Thank you again for your valuable time and constructive feedback throughout the review process.

W1: concerns regarding the slower computing speed compared to better FLOPs

A: Thank you for raising this point. We note that transformer-based models benefit from highly optimized implementations in current deep learning libraries (e.g., Pytorch 2.0+), which can result in surprisingly fast runtimes despite high FLOPs.

While our method does not yet benefit from the same kernel-level optimization available for mainstream Transformer models, it achieves practical inference speeds (~0.1s per CT scan, as shown in Figure 9), making it suitable for near real-time application in clinical practice.

We have also provided a detailed table of model efficiency in our response to Q1.

W2: some more clarification of creating the pseudo-3D volume and then flattening it

A: We are happy to provide detailed clarification for the operation illustrated in Figure 3(b). The actual construction of the 1D sequence from the pseudo-3D volume in our design is indeed consistent with the reviewer's understanding, i.e., it is equivalent to independently flattening the left and right breasts' tokens along the prioritized axis and then concatenating them to form the input sequence.

We chose to represent this process as a pseudo-3D volume (as shown in Figure 3(b)) purely for intuitive visualization and explanation, so as to avoid any potential misunderstanding that the left and right sides are first concatenated along a specific axis before flattening, which will lead to interleaving of tokens from the left and right sides under prioritized scanning along specific axes. To clarify this, we performed additional comparative experiments, as described below.

Variant-1: concatenate along the prioritized axis (i.e., D-, H-, W-axes for HWD, DWH, DHW scanning, respectively) before flattening

Variant-2: always concatenate along the W-axis before flattening

Variant-3: interleave tokens from right and left breasts (i.e., R1, L1, R2, L2, ... ; Rx/Lx means the x-th token in the flattened right/left sequence)

Our strategy not only processes all tokens from one side before those from the other in the Mamba layer, but also maintains a roughly consistent distance between anatomically symmetric locations regardless of scanning order. This facilitates effective learning and comparison of bilateral features, as demonstrated in the results above.

W3: concerns about the idea of feeding multi-view inputs to an attention-style model

A: We appreciate the reviewer’s thoughtful comparison. We acknowledge that this work may appear analogous to multi-view approaches commonly seen in 2D mammography literature from the following two points:

1. Our framework explicitly leverages information from both left and right breasts, and takes them as two parts of the input.
2. The prioritized scanning along multiple axes in Mamba-3D is analogous to observing the input 3D data from multiple views.

However, our method is fundamentally distinct from traditional multi-view settings. In our framework, all inputs (high/low-resolution patches of the left/right breast, as shown in Figure 3 of the main paper) are extracted from a single 3D NCCT image. Thus, our approach does not fuse data from independent acquisitions or views, but rather, analyzes different aspects (dual-resolution, left/right breasts) of the same 3D NCCT scan. The notion of “multi-view” here is therefore not directly comparable to classic multi-projection imaging as in mammography.

We hope this clarifies the novelty of our approach and its difference from existing multi-view transformer methods.

W4: the fairness of the evaluation of main results regarding pre-training

A: Thank you for raising this important concern. However, there is a misunderstanding here.

1. Fairness in pre-training application:

   • For baselines not compatible with MAE pre-training (mainly CNN-based models), we have already implemented a supervised pre-training regime: first, training with the segmentation task alone; followed by joint fine-tuning on segmentation and classification. Empirically, this approach greatly improved the baselines’ performance and outperforms the original implementation.
   • For architectures capable of MAE pre-training (models with standard Transformer or Mamba layers), we conducted MAE pre-training without any extra data, followed by fine-tuning using exactly the same protocol as our proposed method. The only difference among these methods lies in model design.

2. Ablation evidence: To further clarify, we present results for nnUNet without the supervised segmentation pre-training stage in the table below. This comparison demonstrates the benefits of this additional pre-training for methods that do not support MAE pre-training.

   Method	Internal	Dice	H.r.	F.s.	Sens.	AUC	External	Dice	H.r.	F.s.	Sens.	AUC
   nnUNet w/o Seg-Pre	|	0.5872	0.8952	0.7437	0.6606	0.9070	|	0.5243	0.8718	0.7003	0.5524	0.8533
   nnUNet w/ Seg-Pre (as reported in the paper)	|	0.6259	0.9127	0.8548	0.7844	0.9536	|	0.5668	0.8889	0.8173	0.6286	0.8889

Q1: concerns about the training speed of the proposed method comparing with other baselines

A: We provide a detailed comparison of GPU memory consumption, training time, and inference time for our method and all baselines in the table below, with “Training Time” representing the sum of pre-training and fine-tuning.

Notably, our approach does not incur a significant training or inference time burden relative to conventional architectures, making it both effective and practical for large-scale clinical deployment.

I appreciate the effort and explanation in the rebuttal, which helps a lot on addressing my concerns to the paper.

Overall, my major concerns has been solved. The new experiment results shows that the comparison made in the paper is generally fair and the computational speed is also relatively acceptable given no hardware-level optimization for Mamba architecture.

I would still suggest to reframe the section about the multi-view feature concatenation in the final version, I see some other reviewer has also mentioned this issue. Current clarification and experiment can help address this issue.

After reading other reviewer's comments, I still insists this paper is above the acceptance bar. The concerns about motivation of using Mamba is clearly explained and demonstrated via experiment in the paper. New results comparing with SoTA also shows a reasonable performance. Overall, I would suggest acceptance for this paper.

W1 & Q1: comparison with more recent SOTAs

A: We appreciate the reviewer’s suggestion on conducting more comparisons with recent SOTA. We have added the results of 5 recent methods mentioned by the reviewer, using the same metrics and datasets as Table 3 in the main paper.

It should be noted that while some methods above are not designed for 3D data or CT modality, we have made every effort to adapt them to our 3D non-contrast CT setting (e.g., using Conv3D instead of the original Conv2D modules) for a fair comparison. The results show that our method has clear advantage over other methods. The strong performance of our method can be attributed to its Dual-Resolution and Tandem Input design, together with Mamba-3D's ability on local and global modeling, which is particularly beneficial for breast lesion detection and classification on NCCT. These merits are further explained in the answer to W2 & Q2.

W2 & Q2: concerns regarding task-architecture rationale and novelty

A: Thank you for the constructive feedback. We address these concerns from three aspects:

1. Why Mamba (Mamba-3D) is well suited to this task:

   • NCCT images pose unique challenges—lesions often appear subtle, and bilateral asymmetries serve as key diagnostic cues. This calls for a model that can capture long-range context without sacrificing local detail.

   • Mamba fits this need well. Unlike CNNs, which are less effective at capturing global context, and ViTs, which trade local detail for manageable sequence length with large patches, Mamba supports small patch decomposition and long-range modeling. This enables retention of fine spatial resolution (important for segmentation) while also capturing global or even cross-breast patterns (critical for classification).

   • As for Mamba-3D, the cyclically prioritized scanning strategy further enhances local spatial modeling for 3D data. Unlike ViT, which often struggles to capture neighborhood relationships as sequence length increases, Mamba-3D enables more efficient learning and faster convergence on volumetric medical images.

2. Novelty of our multi-task design compared to existing methods:

   • In previous studies, the classification branch was derived from the segmentation branch. This resulted in excessive feature sharing between these two tasks. Even though the tasks were related, it could still cause interference between features, leading to suboptimal performance.
   • Our Dual-Resolution design explicitly balances dense (segmentation) and global (classification) tasks. By decoupling feature spaces while enabling interaction through Mutual Fusion, we reduce task interference and promote complementary learning, overcoming limitations seen in previous multi-task frameworks.
   • The comparison results of the mentioned multi-task papers are provided in the table in W1.

3. Additional novelty:

   • Our “Tandem Input” strategy within the Mamba-3D framework enables effective cross-breast contextual reasoning. This is important in clinical diagnosis but has been rarely explored in 3D settings. This strategy has demonstrated improved classification AUC for NCCT-based breast cancer analysis.
   • To our knowledge, this is the first framework to jointly perform breast cancer detection and classification on non-contrast chest CT scans, demonstrating the clinical potential of NCCT for breast cancer opportunistic screening.

In summary, our work introduces targeted architectural and algorithmic innovations tailored to the unique challenges of breast cancer detection on non-contrast 3D CT. By combining effective sequence modeling for small 3D patches, decoupled multi-task design, and bilateral contextual reasoning, we achieve superior performance in both segmentation and classification.

W3: a better explanation of “Tandem Input”

A: Thank you for pointing out the potential confusion around “Tandem Input”. “Tandem” is a term used to describe two or more things arranged one after another or working together in sequence. For example, tandem bicycle refers to a bicycle with two seats and two sets of pedals, arranged one behind the other.

In the context of our work, “Tandem Input” refers to the concatenation of left and right breast token sequences into a unified input while maintaining anatomical alignment. This not only ensures that Mamba-3D scans all voxels from one breast before moving to the other, but also guarantees a roughly fixed distance between anatomically symmetric locations in the sequence (just like the corresponding words in an antithetical couplet or rhyming lines), allowing the model to better capture cross-breast relationships.

Please refer to Reviewer y5XU’s W2 for additional results of other mechanisms for constructing bilateral input sequences.

W4: comparison with contrast CT

A: Thank you for highlighting the importance of comparison with contrast CT. To address this, we have supplemented our study with results based on contrast CT images which are used for initial tumor boundry delineation as mentioned in the Appendix B.

The table below summarizes the performance of our method on corresponding contrast CT data, using the same metrics as Table 3 in the main paper.

As expected, contrast CT achieves higher performance, serving as a practical upper-bound for this task. Notably, our method on NCCT reaches performance (the last 3 lines of the Table in W1) that is close to that of contrast CT, demonstrating its effectiveness and potential clinical value—especially for large-scale screening workflows where contrast CT may not be feasible.

W5: limited performance improvement and comparison with specially designed breast lesion classification methods

A:

1. On performance improvements:

We respectfully disagree that the improvement is limited. As shown in Table 1 and Table 2 of the main paper, our method achieves notable gains over competing methods on key metrics—even though all baselines were thoroughly optimized under identical protocols (same training set, data augmentation, preprocessing, and postprocessing). The table below provides a summary for Dice and AUC. It is notable that even modest improvements are valuable in clinically challenging tasks where metrics such as AUC are already near the ceiling.

2. On comparison with specially designed breast lesion classification methods:

We have included results for all representative methods mentioned by the reviewer, as detailed in our response to W1. Notably, most “specially designed” breast lesion classification methods are variants of nnUNet or UNet, and are often developed on smaller datasets or with different imaging modalities from ours. In our study, we implemented and thoroughly tuned these methods for a fair comparison. As the results demonstrate, our approach outperforms all published competing methods, including those specifically tailored for breast lesion classification.

W6: concerns regarding unfair comparison

A: Thank you for raising this important concern. We would like to clarify that all competing models were effectively pre-trained under comparable conditions: ViT and Mamba-based models underwent MAE pre-training, while CNN-based methods were pre-trained on dedicated breast and lesion segmentation tasks.

Additionally, our pre-training does not qualify as “large-scale”, since we did not use any extra data.

A similar concern was raised by Reviewer y5XU’s W4; please see our detailed response there for further clarification.

W7: unclear comparison in the visualization

A: We appreciate the reviewer’s suggestion regarding visualization clarity. We acknowledge that the differences may be difficult to appreciate in Figure 4. For the camera-ready version, we will address this by providing zoomed-in views and clear highlights (e.g., arrows) to draw attention to regions with notable differences.

W8: concerns regarding model efficacy

A: Detailed comparisons of training time, inference time, and memory consumption are provided in our response to Reviewer y5XU’s Q1, and are omitted here due to space constraints.

In practical scenarios, all evaluated methods—including ours—can deliver predictions for each scan within tens to hundreds of milliseconds, fully meeting real-world throughput requirements. Our model already demonstrates very high computational efficiency.

Thank you for your time and effort in reviewing our paper. As there have been no further comments during the discussion period so far, we would like to check if there are any remaining questions or concerns we can address. Please feel free to let us know if any additional clarification is needed.