Automated Liver Segmentation using a Normalized Probabilistic Atlas Marius George Linguraru, Zhixi Li, Furhawn Shah, See Chin and Ronald M. Summers Radiology and Imaging Sciences, Clinical Center, National Institutes of Health, Bethesda MD, USA ABSTRACT Probabilistic atlases of anatomical organs, especially the brain and the heart, have become popular in medical image analysis. We propose the construction of probabilistic atlases which retain structural variability by using a size-preserving modified affine registration. The organ positions are modeled in the physical space by normalizing the physical organ locations to an anatomical landmark. In this paper, a liver probabilistic atlas is constructed and exploited to automatically segment liver volumes from abdominal CT data. The atlas is aligned with the patient data through a succession of affine and non-linear registrations. The overlap and correlation with manual segmentations are 0.91 (0.93 DICE coefficient) and 0.99 respectively. Little work has taken place on the integration of volumetric measures of liver abnormality to clinical evaluations, which rely on linear estimates of liver height. Our application measures the liver height at the mid-hepatic line (0.94 correlation with manual measurements) and indicates that its combination with volumetric estimates could assist the development of a noninvasive tool to assess hepatomegaly. Keywords: liver, probabilistic atlas, segmentation, volume, height, mid-hepatic line

1. INTRODUCTION We are working toward building a probabilistic atlas of abdominal organs for free use in statistical and structural analysis and as a teaching tool in the medical community. Atlases allow the study of shape and positional variability for segmentation, registration, diagnosis, biomechanical analysis and soft tissue modeling. Soft tissue interventions equally benefit from the analysis of anatomical variability. In this context, we propose the construction and exploitation of a probabilistic atlas of the liver. Recently, much work has taken place on the construction of probabilistic atlases of anatomical organs, especially the brain [15,25] and the heart [13,18] and their application in registration and segmentation. Particularly, the construction of an unbiased atlas was presented in [10], to build the average shape of brain structures. These techniques are leading the way into similar studies of other organs and more comprehensively of groups of organs, such as the abdomen; to date, a four-organ probabilistic abdominal atlas has been constructed [17]. Independently, the analysis of shape variability of anatomical structures is of key importance in a number of clinical disciplines, as abnormality in shape is often related to disorders. Statistical shape analysis techniques have enjoyed a remarkable popularity within the medical image analysis community. Most existing statistical shape analysis methods rely on Principal Component Analysis (PCA) to build a compact model of principal modes of variation from a training set [3,19]. Liver segmentation has also received special attention and a variety of techniques for the automated and interactive segmentation of the liver have been proposed. A technique based on statistical analysis combined with dimensionality reduction from sparse information models is presented in [5]. The method is very fast and achieves satisfactory results. In [9] a shape-guided deformable model is introduced using an evolutionary algorithm with very good overlap with the ground truth, but outliers (unacceptable segmentations) are omitted from the analysis. A group of organs, including the liver, was segmented using contrast enhancement information in the abdomen in [12]; parts of the heart were erroneously labeled as liver. More recently, a method based on active contours using gradient vector flow was developed to address both liver and hepatic tumor segmentation [14] with similar segmentation errors as [12].

Medical Imaging 2009: Biomedical Applications in Molecular, Structural, and Functional Imaging, edited by Xiaoping P. Hu, Anne V. Clough, Proc. of SPIE Vol. 7262, 72622R · © 2009 SPIE · CCC code: 1605-7422/09/$18 · doi: 10.1117/12.810938

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In 2007, a liver segmentation from computed tomography (CT) data was organized [6]. A variety of automated techniques were presented and their performance evaluated through a combination of metrics, including volume overlap and error and root-mean square error. Most notably a method using a combination of shape constrained statistical deformable models based on a heuristic intensity model had the best performance amongst automated methods [11] with slight under-segmentation of the liver. Region growing was used in [21] with good results, but the technique was sensitive to liver abnormalities. A semantic formulation of knowledge and context is presented in [23], but the segmentation overlap is only 84%. Finally, some of the best segmentation results are achieved by interactive and semiautomated methods, such as those described in [2,4]. In clinical practice, cases of hepatomegaly are detected by the visual inspection of liver radiological data and more precisely by manually measuring the liver height at the mid-hepatic line. Studies evaluated liver size especially in ultrasound images [7,16]. However, height measurements do not characterize fully the morphology of liver, such as accounting for an enlarged left lobe. More recently, volumetric liver measurements were performed both in ultrasound [8] and CT [1,22], indicating that volumes are also important in liver disorders. We propose the construction of a liver atlas that retains structural variability by using a size-preserving affine registration, and normalizes the organ locations to an anatomical landmark (xiphoid). The spatial relationship between liver and the rest of abdominal organs is preserved and the liver is modeled in the anatomical space. Restricting the degrees of freedom in the transformation, the bias from the reference data is minimized, in terms of organ shape. Preserving the size of organs and normalizing their position to that of the xiphoid, there is no bias toward the reference size and location. The versatility of the liver atlas is exemplified through its application in automated liver segmentation by organ propagation through registration. The automated quantification of liver size could eventually lead to the development of a noninvasive tool for assessing hepatomegaly.

2. METHODS AND MATERIALS 2.1 Data For the generation of the atlas and analysis of anatomical variability, 10 abdominal non-contrast CT scans of patients with no abnormalities in the liver were used: 5 male and 5 female (mean age of 59.9 years: 60.6 for male and 59.2 for female). Data were collected with a LightSpeed Ultra scanner (GE Healthcare) and image resolution ranged from 0.54 to 0.77 mm with an inter-slice distance of 1 mm. The liver was manually segmented in 20 non-contrast CT scans, 10 for building the atlas and 10 for testing the segmentation algorithm. For additional tests, we used 20 contrast-enhanced CT scans with manual segmentations of the liver dowloadable from www.sliver07.isi.uu.nl. These CT data were acquired in transversal direction with pixel spacing between 0.55 and 0.80 mm and the inter-slice distance between 1 and 3 mm. Contrast-enhanced images corresponded to mainly pathological cases and were acquired on a variety of scanners from different manufacturers. Parameters were trained on CT data not included in the tests. 2.2 Atlas Construction For the construction of the atlas, a random image from the database is set as reference J, and all other subject data, addressed as images I, are registered to the reference. For all subjects, the manual segmentation of livers was performed and masks of the organs were generated. Then each organ was registered individually to its corresponding mask in the reference set. Inter-patient organ variability was retained by using a size-preserving affine registration. Spatial variability was minimized by normalizing the organs to an anatomical landmark (xiphoid). Previously, non-linear registration was used for the generation of an abdominal atlas [17]. In order to retain a higher level of organ variability in the atlas, we restricted the degrees of freedom of the registration algorithm, and did not change the size and physical position of the organs. Organ coordinates in each subject were normalized relative to the position of the xiphoid. Hence, we employed a modified affine registration method based on normalized mutual information M [24], where p(I,J) is the joint probability distribution of images I and J, and p(I) and p(J) their marginal distributions, as in Equation (1). No scaling was permitted during the deformation and the physical coordinates of organs (image independent) were used, normalized by the xiphoid.

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M (I | J ) =

p (I ) + p ( J ) . p (I , J )

(1)

Finally, registered livers were translated in the atlas to the location of the average normalized centroid. The spatial normalization offers a mean model of liver location in the abdomen. The probabilistic model of the liver was generated using the algorithm presented in Figure 1. Liver

Reference Rescale to physical Cartesian coordinates

Normalize location by xiphoid Liver normalized

Reference normalized Affine registration

Liver registered Rescale to original size Liver rescaled Add Liver probabilistic atlas Move to average liver centroid Normalized Probabilistic Atlas Figure 1. A schematic of the construction of the liver atlas.

2.2 Liver Segmentation For the segmentation of liver by volume propagation, a more flexible intra-subject registration is required to compensate for the residual deformation not covered by an affine registration. We employed the non-linear registration algorithm based on B-splines [20]. The deformation of objects is governed by an underlying mesh of control points in a coarse to fine multiresolution approach. B-splines allow to locally control the deformation T and a compromise between the similarity provided by a function F (in this case the mutual information M) and smoothing S is searched, as in Equation (2). For more detail on the B-spline definition of the transformation T, please refer to [20].

arg min[F (I | T (I )) − S (T )] , S (T ) =

∫ (∂ T ) 2

x, y ,z

x, y ,z

(2)

dxdydz

.

A schematic of the segmentation algorithm is presented in Figure 2. For segmentation, the atlas of the liver at various probability thresholds (10% through 90%) was registered to the test cases using a combination of affine and B-spline non-linear transforms. The volume overlap (VO) of the computer-aided diagnosis (CAD) segmented livers with the

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manual segmentations, and dice coefficient (DC) were calculated according to Equation 3. For comparison, the segmentation using the liver atlas and a single liver model was performed.

Vmanaul I VCAD , Vmanaul + VCAD − (Vmanaul I VCAD ) 2(Vmanaul I VCAD ) . DC = Vmanaul + VCAD

VO =

(3)

Reference CT

Patient CT Global affine registration

Liver Atlas registered

Liver Atlas

Affine + non-linear registration Liver segmented Figure 2. A schematic of the automated liver segmentation algorithm.

To correlate with clinical evaluations of liver performed by linear measurements of liver height, the mid-hepatic line (MHL) was approximated at the half-distance between the spine (found interactively by the user) and the liver dome (found automatically by the algorithm). The maximum liver height along the sagittal plane at the location of MHL was computed and compared with manual measurements. The implementation uses Visual C++ 8.0 (Microsoft), OpenGL 2.1 (SGI), QT (Qt Software), and the Insight Segmentation and Registration Toolkit (ITK) 3.4.

3.

RESULTS

A normalized probabilistic atlas of the liver was created using a modified affine transformation. Each atlas voxel contains probabilities associated with the presence of the liver; the liver location is modeled via spatial normalization. Figure 3 exemplifies the registration and two livers used in the construction of the atlas and presents the probabilistic liver model. In the next step of the algorithm a new abdominal CT is registered to the reference using an affine transformation. An example of liver detection using only a global affine registration is shown in Figure 4.a. The improvement of liver segmentation after employing a non-linear registration of the liver atlas is presented in Figure 4.b. We found that registering the new CT to the reference CT by global non-linear transformation was producing unsatisfactory results, due to the high inter-patient abdominal variability. The mean overlap of the segmented livers from non-contrast CT was 0.85, with relative volume error of 4.9%, using a probability threshold of 40% for the liver atlas. For comparison, the overlap using a single liver model was 0.80. Superior results were achieved using the atlas on contrast-enhanced CT data with an overlap of 0.91 and relative volume error of 3.1%. The correlation between manual and automated volume measurements on contrast-enhanced CT was 0.99 (p-value >0.4), with an R2 value of 0.97. Table 1 summarizes the volumetric segmentation results. The root-meansquare (RMS) error between manual and automated segmentations on contrast enhanced CT was 3.98 mm. The Pearson correlation coefficient (PCC) between manual and automated volume measurements was 0.98 (p-value>0.4), with an R2 value of 0.97. Comparative statistical values are presented in Table 2.

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a

c

b

Figure 3. Liver atlas construction: (a) image of two livers before registration (b) and after the modified affine registration; and (c) the probabilistic atlas with lowest probability in blue (cold) and highest in red (hot).

b

a

Figure 4. An example of automated liver segmentation: (a) the probabilistic liver atlas is overlaid on a new CT after affine transformation; and (b) after non-linear registration.

Table 1. Relative volume error (RVE), volume overlap (VO) and dice coefficient (DC) of the automated liver segmentation from non-contrast and contrast-enhanced CT data using a single liver model and a probabilistic atlas of the liver.

RVE (%) Non-contrast CT Contrast-enhanced CT

VO (%)

DC (%)

Atlas

Single Model

Atlas

Single Model

Atlas

Single Model

4.9±4.1

9±6.7

85.1±3.1

79.8±4.4

88.2±3.7

84.2±4.6

3.1±2

6.5±4

90.9±2.2

86.5±3.6

93.2±2.6

88.8±3.8

The correlation between manual and automated measurements of liver height at MHL was 0.94 (p-value>0.07) with an R2 value of 0.88. Figure 5 shows intra-observer and observer-CAD correlations of the measurements of liver height at mid-hepatic line. Given the high variability of liver shapes, the correlation between volumetric and height

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measurements was 0.82, indicating that although they correlate well, volumetric and linear quantifications of liver size may offer complementary information for diagnosis. Table 2. Root mean square (RMS) error, Pearson correlation coefficient (PCC) and R2 correlation of the automated liver segmentation from non-contrast and contrast-enhanced CT data using a single liver model and a probabilistic atlas of the liver.

RMS (mm)

R2

PCC

Atlas

Single Model

Atlas

Single Model

Atlas

Single Model

Non-contrast CT

6.02±4.13

9.87±7.53

0.982

0.952

0.964

0.905

Contrast-enhanced CT

4.16±2.84

6.49±4.71

0.987

0.954

0.974

0.905

Inter-observer MHL 35 30

Observer 2

25 2

R = 0.97

20 15 10 5 0 0

5

10

15

20

25

30

35

Observer 1 Observer 2 - CAD MHL

Observer 1 - CAD MHL 35

35

30

30

25

25

2

2

20

CAD

CAD

R = 0.8853 15

15

10

10

5

5

0

R = 0.8813

20

0

0

5

10

15

20

25

30

35

0

5

Observer 1

10

15

20

25

30

35

Observer 2

Figure 5. Correlations of linear estimations of liver height at the mid-hepatic line (MHL) between observers and CAD.

4. DISCUSSION We propose a probabilistic atlas of the liver, which retains structural variability by using a size-preserving modified affine registration. The liver location is modeled in the physical space and its position normalized to an anatomical landmark (xiphoid). Restricting the degrees of freedom in the transformation, the bias from the reference data is minimized, in terms of organ shape. Preserving the size of organs and normalizing their position, there is no bias toward the reference size and location.

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Tumors

Figure 6. Liver segmentation results presented in 2D slices at axial locations of the 3D data. The segmented liver is shown in blue overlaid on the abdominal CT. Note that the algorithm is robust to the presence of liver abnormalities, as pointed by arrows.

The analysis of the atlas should provide information about abdominal anatomy, inter-subject variability for computeraided diagnosis and the evaluation liver disorders. The modifications in the proposed atlas construction method are new and suited for use in clinical applications. Its use for liver segmentation performs for the first time the automated comparative quantification of volumetric and linear liver measurements, which could eventually help develop a noninvasive tool for assessing liver disorders, such as hepatomegaly. The segmentation of the liver is robust in the proximity of the heart and to the presence of tumors in the liver. The segmentation generally includes part of the vena cava, which is semi-enhanced in the contrast-enhanced abdominal CT data. Parts of the right kidney are occasionally erroneously segmented and they represent the largest source of errors in the computation of the overlap with the manual segmentation. Future work will focus on the potential of the atlas to become a reference and statistical tool for segmentation, registration, and modeling of normal and abnormal soft tissue. More cases will be used to compute probabilities as segmented data will become available. Regarding the segmentation of the liver, we will aim to correct the errors of the current algorithm and investigate the use of volumetric data for the study of hepatomegaly.

5. CONCLUSION An atlas of the liver was built in the process of constructing a probabilistic atlas of abdominal organs. The probabilistic liver enables a 5% improvement in segmentation overlap over a single reference model in accurate liver volume measurements in non-contrast CT data. The application to contrast-enhanced CT images led to an additional 6% improvement to 91% overlap (93% DICE coefficient). The correlation between manual and automated measurements of liver height at MHL was 0.94 (p-value>0.07). Volumetric assessments of the liver show the potential to offer complementary information for the diagnosis of liver disorders.

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Acknowledgement This work was supported by the Intramural Research Program of the National Institutes of Health, Clinical Center.

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