Introduction

DCE-MRI is currently the best choice for clinical breast diagnosis. Due to abnormal vascular perfusion within the lesion area, DCE-MRI exhibits significantly high contrast between diseased and normal tissue. This technology provides strong support for accurate diagnosis and early detection of breast tumors^[1]. Segmentation remains a challenging initial step in clinical diagnosis. On the one hand, tumor sizes usually exhibit different shapes. On the other hand, tumor sizes may vary significantly from case to case^[2]. In addition, issues such as noise, artifacts and data imbalance pose significant challenges in the field of medical image segmentation. DCE-MRI segmentation tasks usually utilize self-attention or convolution-based methods to segment enhanced images.Convolution networks struggle with contextual information capture due to limited receptive fields.Self-attention networks exhibit high complexity, with computational demands quadratically increasing with the number of image patches^[3]. Therefore, we have developed a shift local self-attention approach that not only incorporates the advantages of convolution (e.g. local inductive bias and translation equivariance) but also offers the high flexibility of the transformer. The additional shift operations significantly preserve its long-range modeling capability.

Methods

Data: In this experiment,a total of 22,440 2D slices were collected from 130 cases.The tumor annotations were performed by professional radiologists.The data were split into training and testing sets in a 7:3 ratio at the case level.
Model: In this work,we utilized a backbone featuring a local self-attention mechanism,which constrains the keys and values of each query within a specific local range centered around it,as opposed to computing correlations with the entire image.The entire proposed network architecture is shown in Fig.1. Local self-attention offers the advantages of reducing computational complexity while retaining the benefits of traditional convolution,such as local inductive bias and translation equivariance^[4].We efficiently obtained a local receptive field window for each patch through depthwise convolutions with fixed kernels^[5] , thus improving the computational efficiency of local self-attention.Specifically, for feature maps $$$\{\mathcal{F}\}\in\chi^{H^{\prime}*W^{\prime}*\mathcal{C}}$$$ ($$$H^{\prime}$$$ and $$$W^{\prime}$$$ representing the height and width of the feature maps,respectively,and C denoting the dimension),the mappings $$$(q,k,v)\in R^{H^{\prime}*W^{\prime}*C}$$$ were obtained.For $$$(k, v)$$$, a depthwise convolution with $$$(kernel\_size * kernel\_size)$$$ fixed convolution kernels(e.g. if kernel_size=3, $$$\{W_1=\begin{bmatrix}1&0&0\\0&0&0\\0&0&0\end{bmatrix},W_2=\begin{bmatrix}0&1&0\\0&0&0\\0&0&0\end{bmatrix}\ldots,W_9=\begin{bmatrix}0&0&0\\0&0&0\\0&0&1\end{bmatrix}\}$$$was employed for convolution calculations, as indicated in Equation (1,2). The resulting outputs $$$\{(K_i,V_i)\text{,i=1,2,...,kernel_size}^2\}$$$ were flattened into rows and concatenated along the column dimension, yielding a domain matrix with dimensions of $$$(\text{kernel_size}^2,H^{\prime}*W^{\prime})$$$, denoted as $$$\{O^m,m=k,v\}$$$, which is shown in Fig.2. Each column of the matrix represents the pixels within a kernel_size * kernel_size neighborhood of each pixel in (k, v), and each row represents the pixels in different directions within each pixel in (k, v). Subsequently, matrix multiplication was performed between q and $$$O^{k}$$$, the value of which was softmaxed and then multiplied by $$$O^{v}$$$. Additionally, we introduced a shift operation for domain matrices $$$\left\{O_{n}^{m} \epsilon\left.\lambda^{(kernel\_size^2,H^{\prime}\ast W^{\prime})},\left \langle m=k,v \right \rangle,\left \langle n=1,2,...,H^{\prime}\ast W^{\prime} \right \rangle \right\}\right. $$$. As shown in Fig. 3, by shift along the dimension of pixel count, the original domain matrix $$$\{\left ( O_{n}^{k} , O_{n}^{v} \right ) ,k=1,2,...,H^{\prime}*W^{\prime}\}$$$ that performs the attention computation with$$$ q_n $$$will be changed to a domain matrix $$$\left ( O_{n\pm shift\_size}^{k} , O_{n\pm shift\_size}^{v} \right ) $$$ with the same shift distance $$$q_{n\pm shift\_size}$$$ in the same shift direction. This method enhances long-range modeling capabilities that are partially lost due to local computation. The corresponding calculation changes from Equation (3) to Equation (4).
$$K_i=W_i\otimes k~~~~~~~~~~~~~~~~~~~ i=1,2,...,\mathrm{kernel}\_{\mathrm{size}}^2 ~~~~\left ( 1 \right )$$
$$V_i=W_i\otimes v~~~~~~~~~~~~~~~~~~~ i=1,2,...,\mathrm{kernel}\_{\mathrm{size}}^2 ~~~~\left ( 2 \right )$$
$$Attention(Q,K,V)=softmax\left(\frac{q_{n}\cdot {O_{n}^{k}}^{T}}{\sqrt{d_{k}}}\right)O_{n}^{v} ~~~~~~n=1,2,...,H^{\prime}*W^{\prime}~~~~\left ( 3 \right ) $$
$$Attention(Q,K,V)=softmax\left(\frac{q_{n}\cdot {O_{n\pm shift\_size}^{k}}^{T}}{\sqrt{d_{k}}}\right)O_{n\pm shift\_size}^{v}~~~~~~ n=1,2,...,H^{\prime}*W^{\prime}~~~~~~~\left ( 4 \right ) $$

Results

We use Precision, Recall, DICE, and IOU as evaluation metrics and calculate the average and standard deviation of these metrics across all cases. The results of the calculations are presented in Fig. 4. Fig. 5 shows examples obtained from different algorithmic segmentation networks that outperform the majority of networks. Performance evaluations and graphical visualizations indicate that our approach is optimal.

Dicussion

Tregardless of whether the shift operation is used, the local attention method tends to have a higher precision compared to other models and a lower recall, indicating a bias toward predicting false negatives while reducing false positives. This may be due to the 4x upsampling in the final layer. However, in terms of the overall results, our method still achieves a high degree of accurate segmentation,outperforms the majority of networks

Conclusion

In this work, we propose a local attention-based segmentation network for breast tumor DCE-MRI, incorporating a novel shift operation, which performs well in various performance evaluations.