Precise Estimation of Renal Vascular Dominant Regions Using Spatially Aware Fully Convolutional Networks, Tensor-Cut and Voronoi Diagrams

08/05/2019
by   Chenglong Wang, et al.
3

This paper presents a new approach for precisely estimating the renal vascular dominant region using a Voronoi diagram. To provide computer-assisted diagnostics for the pre-surgical simulation of partial nephrectomy surgery, we must obtain information on the renal arteries and the renal vascular dominant regions. We propose a fully automatic segmentation method that combines a neural network and tensor-based graph-cut methods to precisely extract the kidney and renal arteries. First, we use a convolutional neural network to localize the kidney regions and extract tiny renal arteries with a tensor-based graph-cut method. Then we generate a Voronoi diagram to estimate the renal vascular dominant regions based on the segmented kidney and renal arteries. The accuracy of kidney segmentation in 27 cases with 8-fold cross validation reached a Dice score of 95 cases obtained a centerline overlap ratio of 80 corresponds to a renal vascular dominant region. The final dominant-region estimation accuracy achieved a Dice coefficient of 80 showed the potential of our proposed estimation approach in a real clinical surgical environment. Further validation using large-scale database is our future work.

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1 Introduction

Partial nephrectomy (PN), which has recently become one of the most common treatments for kidney cancer, can maintain a high residual renal function during surgery shao2011laparoscopic; shao2012precise; yoshino2015. A critical problem during PN is that blood vessel clamping directly influences the quality of the surgery. However, PN surgery remains unstandardized. Due to the trade-off between residual renal function and surgical difficulty, it is difficult to design a criteria for PN surgery. In this work, we provide a better and more accurate computer-assisted diagnosis for PN by estimating the dominant region of each renal artery that facilitates identifying the blood vessels which feed the tumor. Physicians can easily make a surgical plan using such diagnosis information to determine the blood vessel clamping. The feasibility of computer-aided diagnosis (CAD) for PN has been proven ukimura2012three; komai2014novel; isotani2015feasibility. Ukimura et. al ukimura2012three performed PN on four patients who underwent 3D reconstruction for surgical navigation. The kidney surface was extracted by thresholding, the renal arteries were segmented by a simple region-growing method, and the tumor was manually segmented. Komai et al. komai2014novel and Isotani et al. isotani2015feasibility

used commercial software called “Vincent” to perform the computer analysis for PN clamping. The kidney was extracted by a semi-automatic region-growing method, and the renal arteries were segmented by applying facial detection technology using multi-phase information. Then the vascular dominant regions were estimated by applying a Voronoi diagram. All of the above research focused on the clinical study of CAD’s feasibility and its accuracy for PN surgery rather than engineering studies. Precise estimation of the renal vascular dominant regions will contribute to more precise surgery, especially for PN surgeries. To precisely estimate the renal vascular dominant regions, precise kidney and renal artery segmentation is essential. In this work, we used a deep learning technique to extract the kidney and a tensor-based graph-cut approach to precisely segment the renal arteries. Finally, we used the automatically extracted kidney and renal arteries to estimate the vascular dominant regions using a Voronoi diagram. Many organ segmentation methods have already been presented in the literature over the years. Statistical model methods are commonly used in abdominal organ segmentation problems. Lin et al. presented an elliptic candidate region to localize kidneys

lin2006computer. Zhou et al. constructed a prior shape model from a statistical atlas map for a liver segmentation problem zhou2006constructing. Heimann et al. proposed deformable statistical shape models (SSMs) using atlas information heimann2009statistical. Hybrid methods have also been proposed. Skalski et al. used a level-set method with ellipsoidal shape constraints for kidney segmentation skalski2017kidney. Okada et al. used a combination of SSMs and an intensity model for a multi-organ segmentation problem okada2015abdominal. Graphical models have also been widely used for organ segmentation. In our previous work wang2016precise, we used a graph-cut method to semi-automatically segment the kidney. Freiman et al. combined shape and graphical models to automatically extract the kidney region freiman2010non

. Machine learning techniques have also been applied to organ segmentation problems. Cuingnet et al. proposed a coarse-to-fine kidney segmentation method using random forests

cuingnet2012automatic

. Support vector machines (SVMs) have also benn used for organ segmentation

akbari2012automatic; liu2007learning. Recently, researchers have adapted deep learning techniques to organ segmentation. Many state-of-the-art results have been achieved in the lungs harrison2017progressive, the pancreas roth2018spatial, the liver christ2016automatic, the head and neck zhu2018anatomynet, the mammogram mass zhu2018adversarial, and the kidneys thong2016convolutional; zheng2017deep. The segmentation of renal arteries is another critical step in this work. Unlike other tissues like the liver, renal arteries have lower contrast that complicates the extraction of tiny blood vessels. Even though Hessian-based vesselness enhancement filters have been widely used in tubular structure segmentation sato; frangi, they are unable to extract tiny blood vessels, especially of low contrast. Friman et al. presented novel template model tracking with a multiple hypothesis procedure friman. Multiple hypothesis tracking schemes solved the early termination problem, but specifying a global terminal threshold is difficult. It thus leads to serious over-segmentation, especially for tiny blood vessels of low contrast. Recently, a deep learning technique extracted retinal blood vessels fu2016retinal; liskowski2016segmenting; fu2016deepvessel

, showing its high potential for blood vessel segmentation. Since the deep learning technique is a data-demanding approach, it also requires large-scale annotated data for supervised learning. However, creating pixel-wise ground-truth labels for big-data is very labor-intensive, especially for 3D medical data. The main contributions of this paper include the presentation of a fully automated and precise renal vascular dominant estimation approach using a deep learning method for kidney segmentation and a tensor-based graph-cut method for renal artery segmentation. As a preliminary study on CAD system for PN surgery, this work shows the potential of using medical image-processing techniques in improving precise PN surgeries.

Figure 1: Workflow: Our precise estimation approach can be divided into three parts: kidney segmentation, renal artery segmentation and estimation of vascular dominant regions.

2 Methods

In this section, we describe our proposed methods in detail. The workflow is shown in Fig. 1. First, the kidney regions are extracted using a deep learning approach. Second, a fine renal artery segmentation method is performed to segment the renal arteries inside the bounding-box of the kidney regions. After extracting the kidneys and the renal arteries, we estimate the vascular dominant regions with a Voronoi diagram. The relative statistics of the dominant regions are calculated for further surgical planning.

2.1 Kidney segmentation

In this work, we segment the kidney regions with a 3D U-Net-like fully convolutional network (FCN) architecture. U-Net architecture ronneberger2015u; cciccek20163d, which is an extended version of FCN architecture, consists of a contracting path and a symmetric-expanding path. U-Net can achieve high segmentation accuracy with sparse annotated data cciccek20163d. Recently, many U-Net-like architectures have been proposed for segmentation tasks roth2018application; roth2018towards; milletari2016v; shen2018influence; zhu2018anatomynet; zhu2018deeplung; zhu2018deepem; zhu2018adversarial. Our network is based on previous 3D U-Net-like architecture roth2018towards; shen2018influence. Roth et al. presented a U-Net-like architecture for organ segmentation on 3D medical images and achieved state-of-the-art segmentation results roth2018towards. To tackle the GPU memory limitation problem, they used a sliding-windows strategy for large medical data. However, these cropped sub-volumes were trained independently, i.e., the spatial position information of the sub-volumes was ignored during training. Spatial information is a critical feature for organ segmentation because the relative spatial position of the human organs is generally unchanged between patients. Exploiting spatial information should improve organ segmentation accuracy. Many works have involved spatial information into networks. Brust et al. directly incorporated absolute position information into fully connected layers brust2015convolutional. Akoury et al. presented a “Spatial PixelCNN” to impose spatial prior information to maintain the coherence of generated synthetic images akoury2017spatial. Chen et al. incorporated spatial information into the end of an encoder (a bottom feature map) chen20173d; wolterink2015automatic. Zhu et al. incorporated spatially structured learning in an adversarial FCN for mammographic mass segmentation zhu2018adversarial.

Figure 2: Architecture of our presented FCN.

Inspired by the work of Chen et al. chen20173d, we introduce spatial position information into 3D U-Net-like architecture to impose the spatial information of each cropped sub-volume into our FCN architecture. Our proposed network is illustrated in Fig. 2. The backbone U-Net-like structure, which is based on a previous work rothjamit2018, consists of four resolution levels. At each level, a skip connection links the contracting path and the corresponding symmetric-expanding path to provide higher resolution features to the symmetric-expanding path. Unlike original U-Net architecture, the skip connections in this network are summation instead of concatenation. Summation connections were first incorporated in U-Net by Roth et al. roth2018application

. Their experimental results show that summation connections are slightly better than the original concatenation connections in the pancreas segmentation task. Each resolution level contains two series of convolutional layers, batch normalization and ReLU activation, in both the contracting and symmetric-expanding paths. The kernel sizes of all the convolutional and deconvolutional layers in our network are fixed to

. The kernel size of the max pooling layers is fixed to

. We concatenated a three-channel feature map, including coordinates, to the bottom feature map to introduce the position information to FCN. The input coordinate information is the relative coordinates of the input sub-volume in the entire CT normalized to . Let be the three-channel spatial feature map, thus is defined as , where , , and denote coordinates of voxels in a sub-volume. denote width, height and depth of a CT image. Unlike a previous study chen20173d that only considered the center coordinates of the input sub-volume, we used all of the position information and resized the position volume (containing coordinate information) to a suitable input size.

(a) Original sub-volume
(b) Rigid transformation
(c) Elastic transformation
(d) Hybrid transformation
Figure 7: Examples of data augmentation: (a) original sub-volume extracted from CT data. Red region indicates ground-truth label of kidney. (b) and (c) rigid and elastic transformation results. (d) transformation result containing both rigid and elastic transformations

Training

In this work, the input volume size of our network is fixed to

. At each epoch,

sub-volumes are cropped from the original CT volume and fed to the neural network. Here

denotes the batch size. To achieve the best segmentation performance, we exploit the transfer learning technique and pre-train our model on a multi-organ segmentation dataset

roth2018application; shen2018influence, which doesn’t contain any kidney annotation, and fine-tune the model on our kidney dataset. This multi-organ segmentation dataset contains 377 cases, with 340 cases used for pre-training and 37 cases used for validation. The model with the best validation performance is used for fine-tuning. We used all pre-trained layers except the last classification layer. Fine-tuning was done on all layers. Similar to previous works ronneberger2015u; cciccek20163d; roth2018application; roth2018towards; shen2018influence, we used a data-augmentation technique to increase the data variety and robustness. We performed both rigid and elastic transformations to each cropped sub-volume. Rigid transformation includes a translation with a range of pixels at each dimension and a rotation with range of . A B-spline deformation is employed as an elastic transformation to each sub-volume, like in previous works cciccek20163d; roth2018application; roth2018towards

. For each sub-volume, the deformation fields are randomly sampled from a uniform distribution with a maximum displacement of 3, and the number of B-spline control points in each dimension is set to 3 for all data-augmented experiments. In this work, we performed an in-place deformation operation. In a single iteration, we fed one original sub-volume and

hybrid deformed sub-volumes to the network. A data-augmentation example is shown in Fig. 7. We individually show the rigid transformation, the elastic transformation, and the hybrid transformation, which combines the rigid and elastic transformations. Deformation is computed on-the-fly at each epoch during training. In this work, we use pseudo Dice loss instead of conventional cross-entropy loss. Dice loss was first introduced in 2016 milletari2016v. The definition of multi-class Dice coefficient loss used in this work can be written:

(1)

where and denote voxels from the ground-truth volume and segmentation results for class of total classes. is the total voxel amount of the volume.

Testing

The input volume size for testing is the same as in the training. We used a sliding-window strategy to obtain sub-volumes with size

for testing. After predicting all of the sub-volumes, we restored these predictions to a complete 3D labeling data based on their respective positions. The probabilities of the overlapping regions were computed as average probabilities:

, where denotes the probability of voxel from -th sub-volume, .

2.2 Renal artery segmentation

After extracting the kidney region from a CT volume, we performed a renal artery segmentation inside the VOI of the kidney region. Our previous work presented a tensor-based graph-cut blood vessel method called tensor-cut to segment the renal arteries wang2016tensor. This blood vessel segmentation method can segment tiny vascular structures, primarily designed for renal artery segmentation. Tensor-cut models the tubular structure as a second-order tensor using a Hessian matrix and builds a first-order Markov random field (MRF) using both geometry (tensors) and intensity information. Finally, a graph-cut approach is utilized to find the optimal MRF solution.

Figure 8: Left: VOI of original 3-D CT volume of kidney region . Right: result of vesselness enhancement filter .

Vesselness enhancement filter

Vesselness enhancement filters have been widely used in the image processing field since they were proposed in 1998 by Frangi et al. frangi and Sato et al. sato

. By analyzing the eigenvalues of a Hessian matrix, these filters can obtain high response against contrast changes. The Hessian matrix of a 3-D image

is given by

(2)

where stands for the second-order partial derivatives of image around voxel x. The following is Sato’s quantitative vesselness measure, which is specialized to 3-D images where the vessels are brighter than the background:

(3)

Utilizing a quantitative vesselness measure, we obtain the result of vesselness enhancement filter (Fig. 8). The enhanced vessel radius ranges from 1 to 2 mm. A Hessian matrix can be treated as a second-order tensor. The vesselness enhancement filter transfers the higher dimensional tensor to 1-dimensional Euclidean measurement . This transformation introduces external errors. To tackle this problem, our tensor-cut algorithm models the Hessian matrix as a tensor and uses a Riemannian metric to measure the tensors.

Figure 9: The tensor-cut workflow: Both tensors and voxels are used to create a first-order Markov random field (MRF). Then graph-cut algorithm finds optimal solution of the given MRF that corresponds to the final segmentation result.

Tensor-cut

The main idea of the tensor-cut method is to build a first-order MRF using both the geometry and intensity information and a graph-cut algorithm to extract the vascular structures. A simple tensor-cut workflow of tensor-cut is illustrated in Fig. 9. In this section, we briefly introduce the tensor-cut algorithm. More details are available wang2016tensor. As mentioned above, Hessian matrix can be treated as a second-order tensor . First, a vesselness enhancement filter is applied to the CT volume to obtain tensor field , where denotes the total voxel number. To build a MRF with tensors, such tensor characteristics are needed as distance and mean value. We calculated them with an Euclidean metric wang2016precise. Tensors resemble ellipsoids. The dissimilarity is calculated by the length of three principal axes, the angle, and the distance between center points. However, the Euclidean metric ignores the property by which tensors should lie on a manifold space. The tensor-cut method uses a Riemannian metric to measure the distance between two tensors. We used the affine invariant Riemannian metric presented by Pennec et al. pennec2006riemannian. A detailed mathematical proof is available moakher2005differential; pennec2006riemannian

. Instead of using a conventional histogram probability estimation approach, we used a Gaussian mixture model (GMM)

rother2004grabcut. Two GMMs are required for presenting the distribution of the foreground and background regions. GMM distribution under label is denoted by , and are the foreground and background labels. Thus, MRF’s energy function can be defined:

(4)

where , , and are constant parameters to adjust the weight between the two smoothness terms and the tensor term. Two smoothness terms, and , present the dissimilarity of the intensity and tensor terms. As in previous works rother2004grabcut; boykov06; boykov, we used the Potts model. Obviously, the biggest difference between the conventional graph-cut energy and tensor-cut energy functions is the introduction of the tensor term. By introducing an external tensor term, a more accurate MRF model can be obtained for tubular structure segmentation.

2.3 Estimation of vascular dominant region

We estimated the renal vascular dominant regions with a Voronoi diagram that is widely used for calculating vascular dominant regions ukimura2012three; komai2014novel; isotani2015feasibility. Considering the capillaries along the arteries, each branch of the renal arteries is treated as a set of seed points of a Voronoi diagram instead of using the end points of arteries. Let be a branch of renal arteries, and define Voronoi cell function:

(5)

where image voxels are inside of kidney region extracted by the FCN approach. is the Euclidean distance between two points, and denotes the minimal Euclidean distance from point to vessel branch . This is a simple simulation of a real cell getting nutrition from blood vessels.

Figure 10: Different Voronoi partition results depending on different branch clustering: (a) a simple kidney and renal arteries, where green dots denote entries of renal arteries into the kidney. (b), (c), and (d) Voronoi partition results of three different branch clustering strategies.

As demonstrated in Eq. 5, the main factors affecting the accuracy of a Voronoi diagram are kidney region and renal artery branches . In this work, we also provide different partition levels to help physicians better grasp the relationships among arteries, dominant regions, and tumors. Fig. 10 simply illustrates the Voronoi partition strategy used in this work. Fig. 10(a) shows the kidney region and its renal arteries. Green dots represent the entries of the renal arteries in the kidney. Fig. 10(b) shows the branch cluster result based on the entries of the arteries. All the artery branches downstream of the entries are clustered into the same group. This clustering idea is treated as a basic rule. Based on it, we generate different Voronoi partition levels by moving the bifurcation level of the vascular tree. As shown in Fig. 10(c), by moving the bifurcations of Fig. 10(b) one level upstream, we get new Voronoi partition results that show a coarser partition result. Moving the bifurcations one level downstream leads to a more precise partition result (Fig. 10(d)). To get a quantitative measure for the estimation of the vascular dominant regions, we calculated the volume and the volume ratio of each dominant region denoted by and . If dominant regions are adjacent to a tumor, we also calculated the contact area of each adjacent region.

3 Materials

In this work, we used 27 pieces of abdominal contrast-enhanced CT volume data to evaluate the performance of our proposed method. The pixel spacing ranged from to mm, and slice pitch ranged from to mm. All 27 cases containing 54 kidneys were used to evaluate the accuracy of the kidney segmentation. Eight cases containing 14 kidneys were used for evaluating the dominant-region estimation. The ground truth of the kidneys was created by an engineer with medical knowledge. The ground truth of the renal artery was created by two engineers with medical knowledge. Since we directly used our previous method for blood vessel segmentation, we did not perform a quantitative evaluation for blood vessel segmentation in this work. Detailed experimental results are available in our previous work wang2016tensor.

Figure 11: Illustration of computing centerline overlap. Tubular structure in black is gold standard blood vessel, and its centerline is shown as green dash-dot line. Tube is generated by dilating the centerline of radius 1 voxel shown in blue. Red dashed line represents centerline of segmented vessels . Overlapped centerline . , where represents length.
(a) Pre-trained
(b) Fine-tuned
Figure 14: Pre-training and fine-tuning learning curves: Blue curve denotes training Dice coefficient (), and black curve denotes validation . Maximum validation of pre-training achieved , and maximum validation of kidney segmentation achieved .

4 Experiments and Results

4.1 Kidney segmentation

We used an 8-fold cross-validation scheme to evaluate the accuracy of kidney segmentation. We divided all 27 CT volume data into train/validation/test splits at a ratio of . The model with the best validation performance is to be used for test. For a quantitative evaluation, we used three measures: the Dice Similarity coefficient (), Sensitivity (), and the Hausdorff distance (). is a commonly used measure in image segmentation. It is able to reflect the general segmentation ability. , also known as recall rate, measures the ability of the method to extract correct kidney regions. is introduced to measure the surface distance between segmentation results and ground truth. We use the metric to focus on segmentation accuracy of the kidney itself. Therefore, as post-processing, we extracted the top 2 largest connected components as kidney regions. is used to measure the post-processed segmentation results, to reflect the actual segmentation ability of end-to-end FCN, and are still used to measured the original segmentation results without any post-processing. , , and are defined as follows:

(6)

where True Positive (TP), False Positive (FP), True Negative (TN), and False Negative (FN) were measured in a voxel-wise way. , where denotes the voxel coordinate that belongs to surface . and represent the surfaces of the manually annotated ground-truth label and post-processed segmentation results. Experiments were performed on an NVIDIA Quadro P6000 with 24 GB memory. Training on 21 cases took about hours for 4000 iterations, and the testing phase took about five minutes for a single case. For all experiments in this work, we set the learning rate to , the batch size to 6, the sub-volume size to , and the epoch number to 4000 for fine-tuning and 16000 for pre-training.

Figure 15: Validation of U-Net roth2018towards, V-Net milletari2016v

, and our proposed spatially aware FCN. All three of these networks were pre-trained on a multi-organ dataset. Points on curves denote median values of all 8-fold cross validations. Upper and lower bounds of error bars denote the first and third quartiles.

The FCN model was first pre-trained on a multi-organ dataset of seven organ labels, including the liver, the spleen, the stomach, and the pancreas. This multi-organ dataset did not contain any kidney labels. Its latest segmentation is given in previous work shen2018influence, which achieved an average accuracy of (excluding the background regions). The pre-training curve of our FCN model is plotted in Fig. 14(a). The maximum validation score was . The learning curve of the first fold’s fine-tuning on the kidney dataset is shown in Fig. 14(b). The maximum validation score of this fold was . To demonstrate the improvement made by introducing the spatial unit, we also evaluated the baseline U-Net roth2018towards, i.e. the proposed architecture without the spatial unit. Furthermore, we implemented a variant U-Net architecture, V-Net milletari2016v

, for comparison on our kidney dataset. All comparison experiments have the same hyperparameter settings. Validation results of these three methods are shown in Fig.

15. The quantitative results of unseen test data of all 8-fold cross validations are shown in Table. 1. For reference, we also list several similar works on the kidney segmentation task, even though we used a different dataset and annotations. Two detailed segmentation examples using the proposed approach are shown in Fig. 16. Comparison segmentation results are shown in Fig. 25.

Method Modality Case num (%) (%) (mm)
Left Right Left Right
(1) In-house dataset
Atlas-based random forest cuingnet2012automatic CT
Train: 233
Test: 179
96.0
[93.0-97.0]
96.0
[93.0-97.0]
-
Atlas-based graph-cut chu2013multi
CT
(portal-phase)
100 (LOO) - -
CNN+MSL zheng2017deep
CE-CT
(multi-phase)
Train: 370
Test: 78
90.5 - -
Shape-constrained Level-set skalski2017kidney CE-CT 10 86.2 - 19.6
2D patch-based CNN thong2016convolutional CE-CT
Train: 79
Test: 20
93.6
[92.0-95.0]
92.5
[88.8-94.5]
93.78
[90.7–95.6]
4.8
[2.7-9.5]
7.0
[4.1-17.5]
(2) Our kidney dataset
Baseline U-Net roth2018towards CE-CT 27 (8-fold)
84.6
[79.6-90.3]
91.0
[84.5-92.7]
91.1
[83.1-94.2]
12.0
[7.3-15.4]
5.2
[4.8-8.0]
V-Net milletari2016v CE-CT 27 (8-fold)
84.1
[74.3-95.1]
86.7
[74.6-92.9]
85.6
[81.5-94.5]
13.9
[7.5-20.8]
8.1
[5.2-28.1]
Ours CE-CT 27 (8-fold)
87.3
[83.0-90.8]
94.7
[86.4-95.5]
90.5
[86.3-95.5]
7.1
[5.0-9.8]
4.6
[3.8-6.9]
Table 1: Comparison of kidney segmentation methods. Three measurements, Dice coef., sensitivity, and Hausdorff distance, are shown with median[1st - 3rd quartile] or mean standard values. CE-CT denotes contrast-enhanced CT, LOO denotes leave-one-out cross-validation, and 8-fold denotes 8-fold cross validation. All listed methods used own in-house dataset.
Volume rendering Axial slices Volume rendering Axial slices
Figure 16: Two kidney segmentation examples using proposed FCN. Both 3D volume rendering and 2D segmented kidneys ROIs are shown. Red and green lines indicate contour lines of segmented kidneys. Yellow and blue sections shown in volume rendering correspond to 2D ROIs with same colors.
(a) Ground truth (b) U-Net (c) V-Net (d) Our proposed (a) Ground truth (b) U-Net (c) V-Net (d) Our proposed
Figure 25: Two comparison examples. (a), (b), (c), and (d) denote ground truth and segmentation results of U-Net roth2018towards, V-net milletari2016v, our proposed network.

4.2 Renal artery segmentation

We performed renal artery segmentation on the VOIs of the kidney regions that were extracted using the bounding-boxes of the segmented kidneys. Tumors were segmented manually. Instead of using a Dice coefficient, as in previous work, we presented a centerline overlap () coefficient to evaluate the blood vessel segmentation accuracy. Using a blood vessel centerline to measure the segmentation accuracy was previously proposed metz20083d. The Dice coefficient is sensitive to volume variation. In tiny blood vessel segmentation problems, geometric topology error is more important than volume error. The coef. evaluates the overlapping of centerlines extracted from the ground-truth and segmentation results. Fig. 11 describes how to calculate the overlapping ratio. As demonstrated in previous work, the coef. of the segmentation results exceeded .

4.3 Estimation of dominant regions

Figure 26: Experimental result of Voronoi partition performed on original 3-D CT volume. Left: Abdominal blood vessels segmentation result. Thick blood vessels are segmented by region-grow semi-automatically, and renal arteries are extracted by proposed method. Right: Estimation result of renal vascular dominant regions that utilized Voronoi diagram.

We conducted a quantitative evaluation of the estimation of dominant regions in eight cases involving 14 kidneys. We measured each estimated dominant region’s Dice coef. with the ground truth. Since we cannot get the anatomical ground truth of the renal dominant regions, we used the ground truth of both kidney and renal artery to calculate a simulated ground truth of the dominant regions. The quantitative results are shown in Table 2. One partition example on the original CT volume is shown in Fig. 26.

Case 1 Case 2 Case 3 Case 4 Case 5 Case 6 Case 7 Case 8 Mean
Kidney # 2 2 2 2 1 1 2 2
Regions # 12 22 16 10 12 7 10 14
Dice coef. (%)
81.3
[70.2 - 85.1]
77.2
[66.9 - 87.8]
79.7
[73.3 - 86.0]
82.6
[71.9 - 87.0]
82.2
[78.0 - 87.9]
77.3
[73.0 - 81.2]
80.0
[70.6 - 82.4]
77.5
[70.4 - 87.2]
79.9
[70.4 - 86.2]
Table 2: Quantitative evaluation results of renal dominant regions. Eight cases were tested. Second and third rows present number of kidneys and dominant regions of each case. 4th row shows Dice score, and median values with 1st and 3rd quartiles values are demonstrated for each case.
Figure 27: Left: Segmented renal arteries labelled with different colors for each branch. Right: Estimation result of vascular dominant regions. Colors correspond to their dominated blood vessels. 5-mm margin was taken outside of tumor. Blue, yellow, green, and fuchsia regions are directly adjacent to a tumor.

5 Discussion

In this work, we described a precise estimation approach for PN using a deep learning technique for kidney segmentation and a tensor-based graph-cut method for renal artery segmentation. We used our previously proposed “Tensor-cut” method for renal artery segmentation that can obtain over 80% segmentation accuracy wang2016tensor. For kidney segmentation, we presented an improved U-Net-like FCN architecture. The experimental results also demonstrate that better segmentation results were obtained by introduced the spatial information.

5.1 Kidney segmentation

As shown in Table 2, compared with other U-Net-like architectures, our proposed spatially aware FCN achieved better segmentation results. Figure 25 shows that the introduced spatial information effectively suppressed the FPs. Furthermore, our approach demonstrated competitive segmentation accuracy with related kidney segmentation methods. In this work, our and are directly measured on the segmentation results without any post-processing. A 2D patch-based CNN method thong2016convolutional performed post-processing, including opening, closing and extraction of two largest connected components. Therefore, a comparison of is more useful for demonstrating our segmentation ability. Considering our limited dataset, we believe our proposed spatially aware FCN architecture has potentialis able to achieve competitive results with state-of-the-art kidney-segmentation methods. Furthermore, the spatially aware unit can be easily incorporated in other architectures. Although our network achieved good kidney segmentation results, its performance remains limited on such pathology patterns as kidney cysts and some late stage cancer. Several segmentation results are shown in Fig. 31. Figs. 31(a) and (b) show the under-segmented results of kidney cysts. Although the cyst regions have less effect on PN surgical plans, the segmentation of cysts can provide better diagnosis information. Fig. 31(c) shows a case with late-stage cancer, and the proposed method failed to segment the whole kidney. One reason is that we have only one case that contains this pattern in our dataset; increasing the data with this pattern may improve the segmentation performance. Among all 27 tested cases, two cases failed in segmentation (). This has also happened in other experiments using U-Net and V-Net. The major reason for this is that the slice thickness of these two failed cases is 2.0 mm, while that of all other cases ranges from 0.4 to 0.8 mm.

(a)
(b)
(c)
Figure 31: Limited segmentation performance: Yellow arrows indicate under-segmented regions. (a) and (b): limited segmentation performance on kidney cysts. (c): a case with kidney cancer at late stage.

As shown in Fig. 34(a), the automatic segmentation of kidney regions contains the tumor region. Currently, we still need a manual segmentation process to extract tumors. One manually segmented result is shown in Fig. 34(b). A 5-mm margin was taken outside of the tumor for surgical safety. Much research has already been conducted on tumor segmentation using deep learning techniques kamnitsas2017efficient; havaei2017brain. However, fine automatic segmentation of kidney tumors remains an essential future work.

(a)
(b)
Figure 34: Manual tumor segmentation: yellow arrow indicates tumorous region. (a) automatic segmentation results of proposed methods: contour lines are shown in red and green for left and right kidneys. (b) manually segmented result of tumor: yellow region denotes tumor region with 5-mm margin surrounded shown in blue.

5.2 Renal artery segmentation

As demonstrated in our previous work wang2016tensor, the coef. of renal artery segmentation exceeded 80% and extracted about five generations of dichotomous branching that maximally extended from the abdominal aorta. This performance completely meets physician requirements for PN surgical planning. However, under-segmented renal arteries exist. As mentioned above, a renal artery is a critical step in our system. A variation of the segmented blood vessels will directly affect the result of the Voronoi diagram. We illustrated two examples with poor performance (Cases 2 and 6) in Fig. 39 to show the influence. Yellow arrows indicate the under-segmented renal arteries around the tumors. In our experiments, the under-segmented renal arteries slightly affected the estimation results of the dominant regions around the tumors. For Case 2, the renal arteries dominating the orange and green regions are clamped the same as the ground-truth. However, for Case 6, the blue region is over-estimated. Although the segmentation accuracy still need to be improved, the renal artery segmentation performance for dominant-region estimation is acceptable in this work.

(a) 2D axial slices of Case 6
(b) Volume rendering of dominant regions of Case 6
(c) 2D sagittal slice of Case 2
(d) Volume rendering of Case 2
Figure 39: Estimation results of dominant regions: Four tumors (1 in Case 2 and 3 in Case 6) are circled in green. Red regions in 2D slices indicate segmented renal arteries. Yellow arrows show under-segmented arteries around tumors. Volume rendering of each case is also shown in (b)(d). Contours of tumors are rendered in red with black contour line.
1 2 3 4 5 6 7 8 9 all
Yellow Blue Light-green Orange Light-blue Fuchsia Green Gray Brown
() 49596.7 22567.1 22311.6 14275.1 20234 1603.6 8986.3 460101 16719.3 160895
Ratio (%) 30.8 14.0 13.9 8.9 12.6 1.0 5.6 2.9 10.4 100
() 17.6 761.5 174.9 22.5 976.5
Ratio (%) 1.8 78.0 17.9 2.3 100
Table 3: Estimation result of renal vascular dominant regions: Nine regions were partitioned utilizing Voronoi diagram. Region colors refer to Fig. 27. Regions 1, 5, 6, and 7 are directly adjacent to tumors. Vol denotes volume of dominant region, and Area denotes adjacent area of dominant region and tumor. Ratio of both Vol and Area are given in next row.

5.3 Estimation of dominant regions

Figure 40: Selective artery clamping is performed in nephrectromy surgery. Blood vessel in light blue shown in Fig. 27 is clamped to prevent bleeding. Blood vessel in fuchsia is cut off permanently because it is the main blood vessel supply of nutrition to tumors.

We utilized a Voronoi diagram to estimate the dominant regions of the renal arteries. However, due to the limited size of annotated renal artery data, we could only perform quantitative validation on a small number of data (8 cases). The validation results from these 8 cases demonstrate that our estimation approach to the vascular dominant regions is generally correct. From this early study on the estimation of vascular dominant regions, we believe our proposed approach has the potential to improve estimation accuracy for dominant regions in clinical applications. More quantitative clinical validations of the recovery from ischemic damage to normal kidney function can be found in our previous work yoshino2015. Figure 40 shows the computerized analysis result for PN surgical planning. Since surgeons only compared the computerized analysis result with a PN surgery screen in one case, we show one comparison result in this figure. The segmented renal arteries of the left kidney and the corresponding dominant regions are shown in Fig. 27. 5-mm margin was taken outside of the tumor for surgical safety. Two measures were investigated: the volume of the vascular dominant region () and the area of the dominant region adjacent to tumor (). The quantitative result is shown in Table  3. Nephrectomy surgery was performed using a selective artery clamping scheme shown in Fig. 40. We confirmed that four regions are adjacent to the tumor, and thus at most four blood vessel branches should be clamped based on our simulated results. Surgeons clamped two blood vessel branches that dominate regions 5 and 6. An operation report shows that slight bleeding remains in regions 1 and 7. However, a valuable trade-off is found between surgical quality and residual renal function. From surgeon feedback, our proposed approach helped surgeons build preoperative surgical plans and focus on critical arteries during operations.

6 Conclusion

This work presented a preliminary study on precise estimation approach for PN surgical planning.This work proposed a precise estimation approach for PN surgical planning. Our approach mainly consists of three parts: a spatially aware fully connected convolutional network to extract kidney regions, a tensor-based graph-cut method to segment renal arteries, and a Voronoi diagram to estimate the dominant regions. The automatic kidney and renal artery segmentation methods achieved competitive results with state-of-the-art methods in our in-house data. The vascular dominant region is essential information for selective artery clamping, and its precise estimation will contribute to better ways of recovering residual renal function. As a pilot study on the estimation of renal vascular dominant regions, our experimental results in 8 cases demonstrated that our estimation approach achieved reasonable accuracy. However, more clinical evaluations using large-scale database are needed to prove the feasibility of our approach for clinical PN surgical planning.

References