Comsol Artificial Kidney Model

1 Nvidia, Santa Clara, Ca, Usa

Abstract. Automated segmentation of kidneys and kidney tumors is an important step in quantifying the tumor’s morphometrical details to monitor the progression of the disease and accurately compare decisions regarding the kidney tumor treatment. Manual delineation techniques are often tedious, error-prone and require expert knowledge for creating unambiguous representation of kidneys and kidney tumors segmentation.

Figure: System Model & Simulation Flow for Comsol Artificial Kidney Model

In this work, we propose an end-to-end boundary aware fully Convolu- tional Neural Networks (CNNs) for reliable kidney and kidney tumor semantic segmentation from arterial phase abdominal 3D CT scans. We propose a segmentation network consisting of an encoder-decoder archi- tecture that specifically accounts for organ and tumor edge information by devising a dedicated boundary branch supervised by edge-aware loss terms. We have evaluated our model on 2019 MICCAI KiTS Kidney Tu- mor Segmentation Challenge dataset and our method has achieved dice scores of 0.9742 and 0.8103 for kidney and tumor repetitively and an overall composite dice score of 0.8923.

Figure: System Model & Simulation Flow for Comsol Artificial Kidney Model

Keywords: Abdominal CT · Kidneys · Tumor · Segmentation Deep

Introduction

Kidney cancer accounted for nearly 175,000 deaths worldwide in 2018 , and it is projected that 14,770 deaths will occur due to the disease in 2019 in the US . Current kidney tumor treatment planning include Radical Nephrectomy (RN) and Partial Nephrectomy (PN). In RN, both the tumor and the affected kidney are removed whereas in PN the tumor is removed but kidneys are saved . Although RNs were historically prevalent as a standard treatment procedure for kidney tumors, new capabilities for earlier detection of the tumors as well as advancements in surgery has made PNs a viable treatment approach .

Figure: System Model & Simulation Flow for Comsol Artificial Kidney Model

Automated segmentation of kidneys and kidney tumors assists physicians to obtain accurate morphometrical details of the tumor in an efficient and reliable manner as the manual delineation process is often tedious and error-prone. The decision for kidney tumor treatment plan can be made by leveraging such impor- tant tumor’s morphometrical information. Recently, deep learning approaches for

A. Myronenko, And A. Hatamizadeh

Fig. 1. Example of an axial slice of 3D CT images of two patients in KiTS dataset. Red color indicates kidneys, green color indicates tumor region. semantic image segmentation have demonstrated prominent results in medical image analysis for various applications . The powerful non-linear fea- ture extraction capabilities of CNNs along with the effectiveness of the encoder- decoder architectures have made it possible to employ CNNs for challenging segmentation tasks.

Figure: System Model & Simulation Flow for Comsol Artificial Kidney Model

In this paper, we propose a boundary-aware fully Convolutional Neural Net- works for end-to-end and reliable semantic segmentation of kidneys and kidney tumor by encoding the information of edges in a dedicated stream that is super- vised by edge-aware losses. We have trained and tested our model on 2019 KiTS Kidney Tumor Segmentation Challenge and results demonstrate the effectiveness of our proposed framework.

Figure: System Model & Simulation Flow for Comsol Artificial Kidney Model

Related Work

Traditionally, various techniques such as deformable models, GrabCuts, region growing and atlas-based methods have been applied to the problem of kidney segmentation. In recent years, researchers have attempted to leverage the power of deep learning and CNNs to build segmentation frameworks that are more au- tomated and less dependant on incorporation of prior shape statistics. Thong et al. proposed a 2D patch-based approach for kidney segmentation in contrast- enhanced CT scans by leveraging a modified ConvNet. Jackson et al. devel- oped a framework for detection and segmentation and of kidneys in non-contrast CT images by utilizing a 3D U-Net. Yang et al. proposed a method for kidney and renal tumor segmentation in CT angiography image by a modified residual FCN that is equipped with a pyramid pooling module. Furthermore, Yin et al.

Figure: System Model & Simulation Flow for Comsol Artificial Kidney Model

employed a cascaded approach for segmentation of kidneys with renal cell carcinoma by training a CNN that predicts a bounding box around kidney and a 3D Kidney Tumor Segmentation using Boundary-Aware Networks

3×176×176×176

Fig. 2. Our proposed CNN architecture. subsequent CNN that segments the kidneys. Recently, Xia et al. proposed a two-stage approach for segmentation of kidney and space-occupying lesion area by using SCNN and ResNet for image retrieval and SIFT-flow and MRF for smoothing and pixel matching.

Figure: System Model & Simulation Flow for Comsol Artificial Kidney Model

Framework Architecture

As illustrated in Figure 2, our network consists of the main segmentation branch and the additional boundary stream that processes the feature maps at the boundary level . The main branch follows an asymmetric encoder-decoder structure. The input to the encoder is a 176x176x176 crop which is initially fed into a 3x3x3 convolution with 16 filters. Feature maps are then extracted at each resolution by feeding them into a residual block followed by a strided 3x3x3 convolution (for downsizing and doubling of feature dimension). The bot- tom of the encoder entails four consecutive residual blocks that are connected to the decoder. The extracted feature maps in the decoder are upsampled us- ing bilinear interpolation and added with feature maps from the encoder. The output of the decoder is concatenated with the output of the boundary and fed into a 1x1x1 convolution with 2 channels where channel-wise sigmoid activation

1

1+exp(−X) determines the probability of each voxel belonging to kidneys and tumor or only tumor classes.

Boundary Stream

The purpose of the boundary stream is to highlight the edge information of the feature maps extracted in the main encoder by leveraging an additional attention-driven decoder. The attention gates in every resolution of the bound- ary stream process the feature maps that are learned in the main encoder as well as the output of the previous attention gates. For the first attention gate, we first concatenate the output of the encoder with its previous resolution and feed it into a residual block. In the attention gates, each input is first fed into a 3x3x3 convolutional layer with matching number of feature maps and then fused together, followed by ReLU. The output of the ReLU is fed into a 1x1x1 convolution layer followed by sigmoid function σ to obtain the attention map.

Figure: System Model & Simulation Flow for Comsol Artificial Kidney Model

Consecutively, an element-wise multiplication between the boundary stream fea- ture maps and the computed attention map results in the output of the attention gates.

Figure: System Model & Simulation Flow for Comsol Artificial Kidney Model

Loss Functions

We use a dice loss function on the predicted outputs of the main stream as well as the boundary stream. The dice loss is as follows :

(1)

Where ypred, ytrue denote the voxel-wise semantic predictions of the main stream and their corresponding labels, ϵ is a small constant to avoid division by zero and summation is carried over the total number of voxels.

Figure: System Model & Simulation Flow for Comsol Artificial Kidney Model

Additionally, we add a weighted Binary Cross Entropy (BCE) loss to the boundary stream loss in order to deal with the imbalanced number of boundary

(2)

Where x, θ, y−and y+ denote the 3D input image, CNN parameters, edge and non-edge voxel sets respectively. β is the ratio of non-edge pixels over the entire number of voxels and P(ypred,j) denotes the probability of the predicated class at voxel j.

Figure: System Model & Simulation Flow for Comsol Artificial Kidney Model

The total loss function that is minimized during training is computed by taking the average of losses for tumor-only and foreground class predictions.

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