\section{Introduction}

Prostate cancer (PCa) is the fourth most prevalent cancer worldwide, despite exclusively affecting the male population \cite{bray_global_2024}. Prostate biopsies remain the gold standard for classifying cancer aggressiveness; however, the procedure is associated with health risks \cite{borghesi_complications_2017}. To minimize unnecessary biopsies, magnetic resonance imaging (MRI) is increasingly used alongside prostate-specific antigen (PSA) blood tests as an effective, non-invasive tool for detection of clinically significant PCa (csPCa) using the prostate imaging-reporting and data system (PI-RADS) v2.1 protocol \cite{park_performance_2021}. However, the diagnostic accuracy of MRI assessment can vary significantly depending on the reader's level of expertise \cite{wei_diagnostic_2021}.

A promising solution to mitigate this inter-reader variability in prostate MRI assessment is the application of artificial intelligence (AI) for automatic PCa detection. Training and validating AI models, however, requires large amounts of labeled data. In response to this need, the organizers of the PI-CAI challenge provided a large-scale multi-center dataset comprising 10,207 bi-parametric MRI (bpMRI) cases to advance research in PCa detection \cite{saha_artificial_2024}. While only a small subset of this dataset (N=1,500) is publicly available for training and validation, it still surpasses the size of previously available labeled prostate bpMRI datasets \cite{adams_prostate158_2022, litjens_spie-aapm_2017}.

The top-performing submissions to the PI-CAI challenge utilized either convolutional neural network (CNN)-based architectures \cite{debs_deep_2022, li_prostate_nodate, karagoz_prostate_2023} or hybrid CNN-transformer architectures \cite{yuan_z-ssmnet_2022, kan_implementation_nodate}. The challenge organizers also introduced three strong baseline methods, leveraging three widely used CNN-based architectures. The first, nnU-Net, is a self-configuring network for medical segmentation that optimizes pre- and post-processing as well as architectural parameters based on the dataset and available computing resources \cite{isensee_nnu-net_2021}. The second, nnDetection, is similarly self-configuring but focuses on object detection using the Retina U-Net architecture \cite{baumgartner_nndetection_2021, jaeger_retina_2020}. The final baseline is a standard CNN-based U-Net \cite{ronneberger_u-net_2015}.

While CNN-based architectures dominate the field, they are inherently limited in capturing long-range dependencies due to the localized nature of convolutional filters. Transformer-based architectures, on the other hand, offer greater potential for modeling long-range dependencies but face challenges such as computational complexity, particularly in dense prediction tasks like segmentation, where small patch sizes and windowed self-attention are often required \cite{liu_swin_2021}. These constraints reduce their ability to fully leverage long-range information.

A recent alternative to CNNs and transformers called Mamba \cite{gu_mamba_2023}, claims to excel at leveraging long range dependencies for sequence to sequence tasks while maintaining a linear time complexity. U-Mamba \cite{ma_u-mamba_2024}, is one of the most popular mamba adaptations for medical image segmentation tasks, which is reported to achieve state of the art segmentation performance. However, efficacy on PCa detection in bpMRI remains unknown.

% The prostate consists of two main zones: the transitional zone (TZ) and the peripheral zone (PZ), with the latter accounting for the majority of PCa occurrences. In PCa assessment using the PI-RADS v2.1 protocol, the dominant MRI sequence is determined by the zone in which the PCa is located. Zonal segmentation in MRI using deep learning has been extensively studied in prior research \cite{adams_prostate158_2022, Kou_2024, cuocolo_deep_2021, aldoj_automatic_2020}. However, most deep learning-based PCa detection approaches have largely neglected the integration of anatomical knowledge, such as prostate zones. While some studies have incorporated prostate zones alongside PCa detection \cite{yuan_z-ssmnet_2022, karagoz_prostate_2023}, they use zonal masks as additional inputs rather than as segmentation targets. Notably, \cite{zheng_atpca-net_2024} included zonal information as an output class but relied on multi-parametric MRI (mpMRI). However, bpMRI has been shown to be non-inferior to mpMRI for diagnosing PCa, and is now commonly used as a more cost-effective and less time-consuming alternative. \cite{twilt_evaluating_2024}.

The prostate comprises two main zones: the transitional zone (TZ) and the peripheral zone (PZ), with the PZ accounting for most PCa cases. In PI-RADS v2.1, the dominant MRI sequence is determined by the lesion's zone. While zonal segmentation in MRI using deep learning has been extensively studied \cite{adams_prostate158_2022, Kou_2024, cuocolo_deep_2021, aldoj_automatic_2020}, most PCa detection methods overlook anatomical knowledge like prostate zones. Some PCa detection studies use zonal masks as inputs \cite{yuan_z-ssmnet_2022, karagoz_prostate_2023}, while \cite{zheng_atpca-net_2024} included zones as output classes using mpMRI.
While DCE (included in mpMRI) has been reported to improve PCa detection in certain populations, particularly in men of African descent \cite{racial_dce}, recent studies have demonstrated that bpMRI is non-inferior to mpMRI for general PCa diagnosis and is now commonly used as a more cost-effective and less time-consuming alternative \cite{twilt_evaluating_2024}. The increasing adoption of bpMRI in clinical workflows supports its relevance for deep learning-based PCa detection.

% However, bpMRI has been shown to be non-inferior to mpMRI for diagnosing PCa, and is now commonly used as a more cost-effective and less time-consuming alternative \cite{twilt_evaluating_2024}.

% However, most deep learning-based PCa detection approaches have largely neglected the integration of anatomical knowledge, such as prostate zones, which are crucial for radiologists' assessments based on the PI-RADS v2.1 protocol. 

% \subsection{Contributions}
% This paper advances deep learning-based PCa detection in bpMRI by evaluating the previously unknown efficacy of U-Mamba \cite{ma_u-mamba_2024}, a Mamba-based architecture designed to efficiently model long-range dependencies with linear time complexity. A novel parallel multi-task extension of U-Mamba is proposed, integrating prostate zonal segmentation masks to incorporate anatomical context and enhance performance for PCa detection. The methodology is validated on an out-of-distribution in-house dataset (N=200) and an external dataset (N=100), demonstrating superior detection performance compared to a selection of state-of-the-art models.

We propose a zonal anatomy-guided multi-task learning (MTL) approach using U-Mamba \cite{ma_u-mamba_2024}, marking its first application to PCa detection in bpMRI. While MTL has been explored before, our work is the first to use zonal anatomy as auxiliary segmentation targets, leveraging U-Mamba's long-range dependency modeling and linear time complexity to improve lesion detection in bpMRI. We introduce two MTL strategies (Single-Decoder and Dual-Decoder) to incorporate anatomical priors, significantly improving lesion detection. While achieving zonal segmentation performance on par with inter-reader variability, our results show that integrating zonal masks enhances PCa detection, with U-Mamba MTL-Single ranking 23rd out of 424 on the PI-CAI leaderboard, underscoring its competitiveness. The strong performance on both tasks suggests that U-Mamba MTL could serve as a promising clinical decision support tool for PCa assessment.




