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Segmentation of liver tumors from Computed Tomography (CT) and tumor burden analysis play an important role in the choice of therapeutic strategies for liver diseases and treatment monitoring. In this paper, a new segmentation method for liver tumors from contrast-enhanced CT imaging is proposed. As manual segmentation of tumors for liver treatment planning is both labor intensive and time-consuming, a highly accurate automatic tumor segmentation is desired. The proposed framework is fully automatic requiring no user interaction. The proposed segmentation evaluated on real-world clinical data from patients is based on a hybrid method integrating cuckoo optimization and fuzzy c-means algorithm with random walkers algorithm. The accuracy of the proposed method was validated using a clinical liver dataset containing one of the highest numbers of tumors utilized for liver tumor segmentation containing 127 tumors in total with further validation of the results by a consultant radiologist. The proposed method was able to achieve one of the highest accuracies reported in the literature for liver tumor segmentation compared to other segmentation methods with a mean overlap error of 22.78 % and dice similarity coefficient of 0.75 in 3Dircadb dataset and a mean overlap error of 15.61 % and dice similarity coefficient of 0.81 in MIDAS dataset. The proposed method was able to outperform most other tumor segmentation methods reported in the literature while representing an overlap error improvement of 6 % compared to one of the best performing automatic methods in the literature. The proposed framework was able to provide consistently accurate results considering the number of tumors and the variations in tumor contrast enhancements and tumor appearances while the tumor burden was estimated with a mean error of 0.84 % in 3Dircadb dataset.

In many liver related clinical applications such as computer aided surgery and treatment planning, segmentation of liver and liver tumors is required. The need for a proper segmentation is further emphasized by the fact that liver cancer is amongst top cancers with the most fatalities (Grendell et al., 1996[

Unfortunately, due to the difficulties related to manual tumor segmentation and a compelling lack of publicly accessible datasets. Liver tumor segmentation methods have received less attention from researchers while many accurate liver segmentation methods have been proposed by many researchers (Heimann et al., 2009[

As a result of the LTSC'08, five semi-automatic, four automatic and one interactive segmentations were developed, as expected the interactive method based on a combination of graph-cuts and watershed algorithms proved to be the most accurate (Stawiaski et al., 2008[

Recent publications include interactive tumor segmentation based on intensity distribution combined with hidden Markov fields (Häme and Pollari, 2012[

The LTSC '08 included a CECT dataset containing 20 tumors in total, unfortunately due to lack of maintenance on the LTSC'08 challenge website the dataset has become unavailable. As mentioned before, the lack of a common dataset resulted in publications on the subject being mostly from 2008 to 2010 with some publications afterward while their overall accuracy can be considered lower than desired. Recently, two datasets - one containing 120 tumors (Ircad, 2016[

Percentage of tumor tissue present in the organ (in this case liver) called tumor burden is commonly utilized in both monitoring and assessment of pathological livers and can be used in the development of treatment strategies (Jagannath et al., 1986[

Tumor burden is also utilized for evaluation of the effectiveness of cytotoxic anti-cancer drugs by radiologists (Prasad et al., 2002[

Furthermore, a main constraint for the surgical resection planning is the lesion/liver ratio after surgical resection (Nordlinger et al., 1996[

The main advantage of an automatic segmentation over other segmentation methods is the reproducibility as no human interaction is required and the segmentation can run in the background without the need for any interaction from the user. An accurate Computer-aided detection/diagnosis (CAD) system with accurate segmentation methods for liver and liver tumors can have a great impact in the overall treatment planning of the patient as precise tumor volume and location estimation for all tumors inside the liver can result in the determination of the best course of treatment early on.

In this paper, an automatic liver tumor segmentation is proposed based on contrast-enhanced computed tomography imaging. The proposed method based on a hybrid of fuzzy c-means algorithm with cuckoo optimization (CS-FCM) and random walkers method (RW) with priors was shown to have promising performance. The proposed segmentation is validated on publicly available clinical datasets with varying contrast and enhancements and further evaluated by a consultant radiologist to assess the clinical value of the proposed method. The performance of the proposed method and the low error in tumor burden determination compared to manual segmentation makes the proposed segmentation method a viable alternative to other segmentation methods.

The proposed method is evaluated using 3Dircadb dataset from Research Institute against Digestive Cancer (IRCAD) (Ircad, 2016[

Expert radiologists have manually outlined liver tumor contours for all images on a slice-by-slice basis in order to determine the ground truth. The number of slices in each series, the slice thickness and the pixel spacing varied from 64 to 502, 0.5 to 5.0 mm and 0.54 to 0.87 mm respectively with the image resolution being 512 × 512 in all cases. The 3Dircadb dataset is segmented by a single radiologist while the MIDAS dataset has the segmentation from five different radiologists; radiologist 1 was utilized as the ground truth in this study. However, 3 tumors from the 3Dircadb dataset are excluded from the segmentation as the tumor enhancement and contrast is not sufficient for automatic segmentation. All internal structures of the liver such as vessels and tumors are included in the liver mask during manual segmentations as the tumor segmentation is done inside the liver mask. A vessel is considered as a part of the liver if it is completely surrounded by the liver tissue. If a vessel is partially enclosed by the liver (often the case where large veins such as vena cava and portal vein enter or exit the liver), only the parts surrounded by liver tissue are included in the manual segmentation

It should be noted that the developed framework was run with Matlab 2013a on a personal computer with 8 GB of ram and an Intel i7 CPU. All the images utilized in this study are processed with window level recommendations for Abdominal CT imaging, as illustrated in Figure 2

A 3×3 Median filter is utilized for smoothing the images as shown in Figure 3

Fuzzy set theorem, introduced by (Zadeh, 1965[

In this paper, soft clustering (fuzzy c-means) is used as each pixel can belong to many clusters based on a membership degree resulting in better performance in images with poor contrast, region overlapping and inhomogeneity of region contrasts such as CT images, compared to hard clustering where each pixel can only belong to a single cluster. As traditional fuzzy c-means (FCM) algorithm where clustering is only based on pixel intensities is very sensitive to noise, addition of spatial relations between pixels has been proposed by many researchers to improve the performance (Ahmed et al., 2002[

The main disadvantage of FCM algorithm is its tendency to get trapped in local minima as it is very sensitive to initial solution (initial random cluster centers), metaheuristic approaches such as genetic algorithms (GA), tabu search (TS), simulated annealing (SA), ant colony based optimization (ACO) and their hybrids have been proposed by many researchers to overcome this limitation (Maulik and Bandyopadhyay, 2000[

As a fuzzy clustering method, fuzzy c-means algorithm is based on the representation of clusters by their respective centers. The data space _{1}, _{2}, …, _{N}

Based on following constraints:

Where _{ij}_{C}_{×}_{N}_{j}_{i} is represented by the matric _{j}_{i}

Equation (1) can be solved by converting to an unconstraint problem by Lagrange multiplier. Membership degree and cluster centers are calculated using an alternate calculation cycle as they cannot be calculated simultaneously. Convergence is achieved by alternatively fixing the classes and calculating the membership function, followed by calculating the cluster centers by fixing the membership function. Algorithm 1 represents the pseudo code for FCM.

For image segmentation, the intensity value of the pixel _{i}_{j}_{i} is denoted by ^{2}(_{i}_{j}_{i}_{j}_{ij}

Inspired by reproduction strategies of cuckoo birds, cuckoo search optimization was proposed by (Yang and Deb, 2010[

Choosing a random nest, each bird lays one egg representing a set of solutions for the optimized problem.

With a fixed number of nests, there is a probability that the host might discover and discard the egg.

The nests containing the best solutions (egg) will be carried to the next iteration (new generation).

Levy flight (modeled after bird flight) is used in generating new solutions in cuckoo search, given by:

Where ϑ represents the step size and is determined by the scale of the problem (in this study set as 1), the product

Essentially, the consecutive jumps and steps of a cuckoo search form a random walk process that obeys a heavy tail probability distribution. Algorithm 2 represents the pseudo code for performing the Cuckoo search (CS).

Stopping criterion can be based on the following conditions:

1. If after _{erp}

2. Number of the iterations reaching maximum _{maxiter}

Based on recommendation by (Yang and Deb, 2010[_{a}

Graph-Cut (GC) based segmentation is an alternative to boundary based segmentation methods, being a semi-automatic segmentation the user is required to provide the seeds representing the background and the object to be segmented, GC represents the image pixels as nodes on a graph with weighted edges representing the adjacency between the pixels. By finding the minimum cost function between all possible cuts of the graph, the GC segments the image into background and the object (Boykov et al., 2001[

The principle of random walker segmentation is the construction of an undirected graph _{ij}_{ij}_{i}_{j}

Where _{i}_{j}^{L}

Weight _{ij}

With the help of the circuit theory, Grady (2006[

A Dirichlet problem can be defined as the problem of finding a harmonic function subject to certain boundary values. A Dirichlet integral could be represented as:

Where

Let's denote _{m}_{u}_{u}_{m}_{u}_{m}_{i}_{u}

Where the probabilities of seeds ^{L }

Where combinatorial Laplacian matrix of

Where _{v}_{i}_{ij}_{i}

Where

Eq. 11 can be decomposed as:

Where _{U}_{M}_{U}_{U}

Which represents a system of linear equations where |_{U}

Only

After minimizing

The workflow of the random walker method for image I can be summarized as:

1. Provide a set of marked pixels with L labels corresponding to desired segmentation regions

2. Map the image features such as intensities, texture information or other image features to edge weights and built the Laplacian matrix

3. Perform the random walker and obtain segmentation label for each region.

In some segmentation tasks, the number of objects and their density estimation might be known prior to segmentation or can be generated from training and pre-labeling. In this study we utilize random walkers method with integrated priors (RW_{p}

The segmentation obtained by the CS-FCM is used for labeling of the pixels for the random walker segmentation. Figure 4_{ij}_{P} can be used to greatly enhance the segmentation results compared to regular RW algorithm. Figure 5_{P}, as it can be seen, the use of RW_{P} greatly increases the accuracy of the segmentation. As evident from cropped CT images of tumors shown in Figure 6

Before any discussion on the results a brief introduction of statistical performance measures utilized are given below, these statistics are calculated based on guidelines and the evaluation software by Taha and Hanbury (2015[

Volumetric overlap error (VOE) represents the number of pixels in the intersection of segmented region (A) and the ground truth (B), divided by the number of pixels in the union of A and B. A value of 0 % represents perfect segmentation while any increase in this value correlates to increased discrepancy between segmentation and ground truth. It can be calculated in percent from the following formula:

Relative absolute volume difference (RVD) expressed in percent, whereby the total volume of the segmented region is divided by the total volume of ground truth. It can be calculated by the following formula:

This measure should not be utilized solely to assess the performance of any segmentation method as a value of 0 (perfect segmentation) can also be obtained from an inaccurate segmentation, as long as the segmented region volume is equal to the volume of the ground truth. Please note that negative values represent under segmentation while positive values point to over segmentation.

Dice similarity coefficient (DSC) represents the overall performance of the image segmentation algorithm. It can be calculated by the following formula:

A value of 0 represents no overlap between the segmented region and ground truth while a value of 1 represents perfect segmentation.

It should be noted that while all tumor sizes over 5 mm were included in 3Dircadb dataset segmentation, RECIST standard was the basis for the expert segmentation in MIDAS dataset. Tumors under 5 mm are not included in the segmentation as they are visible in only one or two slices in a CT series acquired with 2-3 mm slice thickness and usually offer no notable value for analysis. Apart from 3Dircadb dataset, almost all other publications are based on datasets with segmentation based on the RECIST standard. Figure 7

Based on the statistical performance, it can be assumed that the proposed method is amongst the most accurate segmentation methods proposed and tested for liver tumor segmentation from CTCE images, achieving a comparable or higher accuracy compared to other methods. In the case of 10 tumors from the MIDAS dataset, the proposed segmentation method was able to achieve an average DSC of 0.81 while the VOE was at 15.61 % and RVD was 4.02 %. Average DSC of 0.75, VOE of 22.78 % and RVD of 8.59 % was the performance of the proposed method on the 3Dircadb dataset containing 117 tumors, considering that the 3Dircadb dataset included many small tumors representing considerable difficulties in automatic segmentation, these results are promising. While preparing the LTSC '08 segmentation challenge (Deng and Du, 2008[

The proposed segmentation method is comparable to other approaches developed with a runtime of around 30 seconds per slice, of which nearly 5 seconds were taken by random walker and the rest were used by CS-FCM for initial clustering. The proposed method is also viable as an alternative approach to manual segmentation by radiologists while being faster than manual segmentation for a CT volume containing many tumors with average manual segmentation time of 4.2 minutes per tumor (Häme and Pollari, 2012[

Lower than expected performance of the segmentation methods for liver tumors can be associated with the vague boundaries of tumors making an accurate segmentation a challenging task. On the other hand, the small size of tumors results in increased statistical errors as a discrepancy of a dozen pixels can lead to a considerably increased error. Furthermore, from the dataset it is evident that many radiologists tend to over segment the tumor boundary and some even consider close tumors as a single tumor. However, there is no gold standard as the segmentation purely subjective and dependent on the radiologist, evident from MIDAS dataset where there is a disagreement of 9.8 % on the boundaries of ten tumors between five professional radiologists.

Due to the availability of a dataset (3Dircadb) containing radiologist segmentation of both liver and liver tumors, the tumor burden error (TBE) calculation (the difference between automatically and manually measured tumor burdens) of the proposed method has also been done. As discussed earlier, one of the most important variables for treatment monitoring and liver surgical planning is the tumor burden. Unfortunately, probably due to a lack of appropriate datasets, aside from (Linguraru et al., 2012[

After the extraction of liver and liver tumors from the CT series, 3D virtualization can be utilized to help the physician in better visualizing the liver and possible tumors inside the liver. This is done as going through a CT series on a slice by slice basis can be both tedious and time-consuming. Figure 8

Proper segmentation of liver and liver tumors is a prerequisite for any accurate CAD system utilized in liver cancer treatment planning and monitoring as accurate volume calculation and location estimation is the key in accurate prognosis. The proposed segmentation method was shown to provide accurate segmentation. One of the largest liver tumor datasets in the literature with varying contrast and enhancements were utilized for validating the results of the proposed method, the proposed method achieved excellent results in all instances with the average overlap error for tumor segmentation improved by almost 6 % compared to some of the best automatic methods in the literature. With a total runtime of about 16 minutes per patient, the proposed method is fast enough to be considered as a viable segmentation method for liver tumors. The proposed method was also able to achieve a tumor burden error of 0.84 %, well under the 10 % error threshold for clinical applications. The accuracy of the proposed method was further verified by a consultant radiologist for ensuring clinical applicability of the proposed method.

The proposed method is based on well-documented algorithms, making the implementation relatively easy for inclusion in any CAD system and can be easily expanded to other tumors and segmentation challenges from a medical perspective. Further development of the proposed framework can be automatic analysis and classification of the segmented tumors for an integrated liver CAD system for use in liver treatment planning as tumor grading is another important part of liver diagnosis and graphic processing unit based acceleration for decreased processing time.

Authors declare that they have no conflict of interest.