Segmentation of Brain Parenchyma and ... - Semantic Scholar

Segmentation of Brain Parenchyma and Cerebrospinal Fluid in Multispectral Magnetic Resonance Images# 1 Section

Arvid Lundervold1 and Geir Storvik2

for Medical Image Analysis and Pattern Recognition, University of Bergen, Arstadveien 19, N-5009 Bergen, Norway 2 Department of Mathematics, University of Oslo, Blindern, N-0316 Oslo, Norway

#Published in IEEE Transactions on Medical Imaging, Vol. 14, No. 2, June 1995, pp. 339-349.

Abstract This paper presents a new method to segment brain parenchyma and cerebrospinal uid spaces automatically in routine axial spin echo multispectral MR images. The algorithm simultaneously incorporates information about anatomical boundaries (shape) and tissue signature (grey scale) using a priori knowledge. The head and brain are divided into 4 regions and 7 dierent tissue types. Each tissue type c is modeled by a multivariate Gaussian distribution N ( ; ). Each region is associated with a nite mixture density corresponding to its constituent tissue types. Initial estimates of tissue parameters f ; g =1 7 are obtained from k-means clustering of a single slice used for training. The rst algorithmic step uses the EM-algorithm for adjusting the initial tissue parameter estimates to the MR data of new patients. The second step uses a recently developed model of dynamic contours to detect three simply closed, non-intersecting curves in the plane, constituting the arachnoid / dura mater boundary of the brain, the border between the subarachnoid space and brain parenchyma, and the inner border of the parenchyma towards the lateral ventricles. The model, which is formulated by energy functions in a Bayesian framework, incorporates a priori knowledge, smoothness constraints and updated tissue type parameters. Satisfactory maximum a posteriori probability estimates of the closed contour curves de ned by the model were found using simulated annealing. c

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Key words: Brain and CSF segmentation, magnetic resonance imaging, contour detection, stochastic optimization

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Segmentation of Brain and CSF in MRI A. LUNDERVOLD and G. STORVIK

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1 Introduction Many neurological diseases and conditions alter the normal volumes and regional distributions of brain parenchyma (gray- and white matter) and cerebrospinal uid (CSF). Such abnormalities are commonly related to the conditions of hydrocephalus, cystic formations, brain atrophy and tumor growth. There are also age-related dierences in volumes of brain parenchyma and CSF [40]. Magnetic resonance imaging (MRI) is the preferred modality in examining these conditions since its tissue discriminating ability is superior to X-ray CT in most such cases [7]. The basis for reliable measurements of the brain parenchyma, CSF volumes and shapes is segmentation. Accurate quantitative measurements can then be used to obtain objective criteria for conditions such as global or regional cerebral atrophy and hydrocephalus. When an MRI examination is performed, the size and shape of anatomy are reviewed as well as the regional distribution in signal intensity to locate lesions or pathological processes. Since qualitative and purely visual rating of anatomical volumes and shapes is time consuming and hampered by intra- and inter-observer variability, several investigators have developed methods to automate or facilitate these measurements by some type of segmentation (e.g. [1, 5, 6, 9, 13, 17, 21, 23, 27, 30, 32, 33, 34, 35, 39, 43, 46, 48, 51, 52] and the editorial [29]). However, some of these methods do not exploit the multispectral information content of the MR signal [5, 13, 17, 21, 27, 32, 46, 48, 51] or do not include proper prior information about anatomy in the segmentation algorithm [1, 5, 9, 33, 35]. Some methods are dependent on large set of heuristic rules [34], or a huge amount of detailed a priori information (e.g. \anatomical atlas") which do not allow much anatomical variation or abnormality [21, 39] while in other methods, segmentation is heavily dependent on an operator [1, 6, 13, 27] or non-automated preprocessing is needed [21]. The aim of this study is to introduce a new model-based segmentation method which uses the multispectral nature of MRI, prior knowledge of anatomy, and an algorithm which approximates the maximum a posteriori probability (MAP) of the model for the given data. We also demonstrate the performance of this method to a small sample of multispectral MRI examinations from clinical routine. However, our segmentation method is restricted to slice images where the brain parenchyma and CSF spaces form connected regions, and this assumption is incorporated in our contour-based algorithm. Our 2D method does not exploit the 3D possibility of MR acquisitions (cfr. [5, 6, 9, 13]), nor do we do any detailed clinical evaluation such as in [6], [33] and [45]. The paper is organized as follows: In Section 2 we explain the relevance of contour detection to our brain segmentation problem, discuss the active contour model and give reasons for using the Bayesian dynamic contour model instead. The details of this model is given in Section 3, and the automated parameter estimation in the model is described. Patients and the MR measurement protocol used in the experiments are presented in Section 4, and the segmentation results are described. Finally, in Section 5, the performance of the method in normal and pathological slices is commented, and topics for further investigations, needed to achieve clinical feasibility, are discussed.

2 Connected regions and contour-based segmentation In the normal case, the ventricle system and brain parenchyma are each connected, three-dimensional objects. However, even though MRI examines anatomical and pathological structures within threedimensional space, both 2D- and 3D MR imaging yield information that are represented in separate two-dimensional slice images. Because of the complicated geometry of brain structures, connected three-dimensional objects will frequently not remain connected in two-dimensional slice images. This is generally the case for the ventricular system. However, in axial slices transecting the body of the lateral ventricles, this structure as well as the brain parenchyma and the subarachnoid space


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are normally imaged as three distinct connected regions (cfr. Fig. 1 and [47])). Thus, in this case we can take advantage of the presence of three closed contours during segmentation.

2.1 Contour detection

Contour detection has been a eld of large interest in recent years. Kass et al. [31] introduced the active contour model (\snakes") to nd salient image contours. For this approach, the contour is represented as a chain with a xed number of vertices. The modeling of the contour is made through dierentiable energy functions measuring local smoothness. The observed image is introduced through an additional energy function incorporating the pixel intensities or their gradients. Discrete dynamic programming has been used for nding the optimal contour [2]. In this case, the requirement of dierentiability of the energy functions can be relaxed and \hard constraints", such as a minimum adjacent internode distance, can be introduced during the minimization process. In Friedland and Adam [20] a centerpoint inside the contour and a number of angularly equispaced radii were de ned. The contour, assumed to be star-shaped, was then represented by the lengths along the radii from the centerpoint. A set of energy functions were constraining the contour, and the optimization algorithm used was based on simulated annealing [20]. By restricting the number of possible lengths along each radius, this representation also falls into the one used for the active contour model. A parametric model based on elliptic Fourier decomposition of the contour was formulated by Staib and Duncan [48]. They assumed a one-to-one and continuous mapping between contour curves in image space and their parameterization. The parameters of the (truncated) elliptic Fourier series were regarded as random variables and boundary nding was formulated as an optimization problem in a Bayesian framework using the MAP estimate. An other approach to contour detection and segmentation is based on elastically deformable neuroanatomies [21, 39]. Using a manually labeled, reformatted, myelin-stained multisection \anatomical atlas" from a normal brain, and the assumption that the topological structure of the brain is invariant among normal subjects, Gee and coworkers [21] used an iterative coarse-to- ne matching strategy [4] to segment the ventricle system and subcortical structures in T2-weighted MRI examinations. The edges of the ventricles and the surface of the brain were used for matching and the resulting deformations were propagated through the brain atlas volume, deforming the rest of the anatomical structures in the process. The only user input to the elastic matching system was the number of deformation cycles and the value of the elastic constant. Miller et al. [39] have extended the previous method. They introduced a set of homeomorphic maps h : ! on an ideal coordinate system R3 where h : x 7! x , u(x) is de ned by a displacement vector eld u, which allows for dilation and contraction of the atlas coordinates into the anatomy of the observed image. Assuming the homeomorphic displacement function arise from an a priori distribution with potential function determined by the kinematics of elastic solids, they take a Bayesian view on the associated potential H (u) 2 R of the posterior distribution. Using stochastic gradient search, they generate the displacement transformation u which is the mean of the posterior distribution de ned by the sum of the elasticity potential and the squared error distance between the observed data and the deformed atlas. Using manual labeling of a registered T1-, T2and spin-density weighted 3D MR examination as the atlas, the estimated transformation h^ was computed for two dierent multispectral MR examinations. The algorithm performed well when segmentation of gray matter nuclei and the ventricular system were compared to that obtained from manual labeling. However, studies of abnormal anatomy using this approach have not yet been reported [39]. In Storvik [50, 49], a Bayesian approach to dynamic contours (hereafter called BDC) was introduced. The approach may be considered to be within the class of active contour models, but dier from the general use of such models in two aspects: 1. A wider class of models (i.e. energy-functions) could be used. In particular, models for the observed image which incorporate grey level characteristics of regions and not only characteristics


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local to the boundary of interest, which is usually used. 2. The optimization technique used was based on stochastic sampling and simulated annealing. The reason for considering such optimization techniques and not techniques based on dynamic programming or variational methods was that sampling based methods allow more exibility in the choice of energy-functions. For the present brain segmentation problem, the use of region-based models for the observed image was of crucial importance in order to recognize the structures of interest, which was the main reason for our choice of using the BDC method for solving this problem.

3 Segmentation and models In this section, we rst describe main principle for Bayesian contour detection, thereafter the choice of models that have been made and nally speci cation of the parameters involved.

3.1 Boundary detection

The boundary detection consists of four main components. These are described below, using the following notation. We let X denote the contour space, and Y the measurement space where the observed data y are multichannel MR signal intensities on a xed 256 256 grid of pixels. A realization from X consisting of three non-intersecting closed contours is denoted x. As usual, MAP denote the maximum a posteriori probability i.e. mode of p(xjy), and g : A ! R denote a real-valued function with domain A. The central issues of the BDC method are:

Representation Each contour is a linked cyclic list of planar nodes. Modeling We use two submodels, (i) an a priori contour model : X ! R which incorporates properties of x like shape and smoothness, and (ii) an observation model f : X Y ! R accounting for the measured signal intensities y. Inference Inference is based on p(xjy) / (x)f (yjx) (Bayes Theorem). We let x0 denote the three contours representing the mode of the posterior probability distribution p(xjy). Computation A numerical algorithm for nding the optimal contour x0 (i.e. MAP estimate)

is applied. Optimal contours can not be achieved through direct optimization, but can be approximated by iterative algorithms based on simulated annealing.

A rough description of the contour representation and the optimization algorithm is given in the Appendix, and we refer to [50] and [49] for more details.

3.2 Model

Here we describe the particular model that has been used. We start by giving assumptions about the slice regions and the tissue types, thereafter specify the prior model chosen for the contours and nally the model for the observed image.

Assumptions about the slice regions and the tissue types

Firstly, we assume an axial ventricular level region-model divided into four regions (Fig. 1). These regions are outside brain, i.e. arachnoid / dura mater (r=1), subarachnoid space (r=2), brain


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parenchyma (r=3), and the lateral ventricles (r=4). The boundaries between region 1 and 2, region 2 and 3, and region 3 and 4 are assumed to be simply closed non-intersecting curves.

Region 1 Region 2 Region 3 Region 4

Boundary of head

Figure 1: A priori region model for the brain. The normal head mask R contains four disjoint, connected regions R , r = 1; 2; 3; 4, and seven dierent tissue types. Each region is characterized by its constituent tissue types, denoted C . Region 1: outside brain (i.e. arachnoid / dura mater), C1 fair and bone, muscle, fat, connective tissueg; Region 2: arachnoid space, C2 fCSFg; Region 3: brain parenchyma, C3 fwhite matter, gray matterg; Region 4: lateral ventricles, C4 fCSFg. r

r

Secondly, we assume the ventricular level slice image consists of seven main tissue classes, air and bone (c=1), muscle (c=2), fat (c=3), connective tissue (c=4), CSF (c=5), and white (c=6) and gray matter (c=7) making up the brain parenchyma. Normal MRI anatomy constrains region 1 to contain at most air and bone, muscle, fat, and connective tissue; region 2 to contain CSF only; region 3 to contain brain parenchyma; and region 4 to contain CSF only. We let R denote the region of interest (i.e. the head mask for a given slice examination) partitioned by the three closed contours x into four disjoint regions R1 ; : : : ; R4 . The set of possible tissue classes within region r is denoted C , where the members of each C are listed above. x

r

Prior model

x

r

The prior model is speci ed through an energy function [44, 54],


(x) = Z1 e, 1 ( ) ; U

6 (1)

x

where Z is a normalizing constant such that the prior is a proper probability distribution. We have chosen U1 to be related to the \fractal" geometric property of the closed contour by 2

of contour x) U1 (x) = (length area inside contour x

(2)

where 2 R is a smoothing parameter. By construction, U1 attains lowest energy values for smooth and circle-shaped contours x. The choice of this energy function compared to the usual choices of stretching and bending energies was made after experimentation with both choices. The favorable result we obtained by using (2) is however highly related to the speci c choice of representation of the boundary that we have used (see the Appendix) and a dierent conclusion could be obtained by other boundary representations. For the particular problem considered, there are actually three contours x = (x1 ; x2 ; x3 ) that are to be recognized. We therefore generalize model (2) to

U1 (x) =

3 X of contour x )2 (length area inside contour x r

r

r

=1

(3)

r

Data model

Regarding the data, each class c = 1; : : : ; 7 is assumed to have a multivariate Gaussian distribution with expectation vector and covariance matrix . For the four-region model, the conditional distribution function will be c

c

f (yjx) =

4 Y X Y r

=1 2

2

Rx r c

i

N (y ; ; ) c;r

i

c

(4)

c

Cr

where R and C are de ned above, and is the prior probability of class c inside region r using non-informative a priori probabilities = j 1 j , r = 1; : : : ; 4; c 2 C . Also in this case, it is possible to transform the probability distribution f to an energy function, denoted U2 , de ned as the negative log-likelihood x r

r

c;r

c;r

r

Cr

U2 (x; y) = , log(f (yjx) 4 X X X = log( N (y ; ; )): r

=1 2 i

Rx r

2

c

c;r

i

c

c

(5) (6)

Cr

Given the total energy function, E = U1 (x)+ U2 (x; y), we then seek to nd the minimum energy curves x0 , corresponding to the maximum a posteriori (MAP) estimate of the curves. In [50] and [49] an iterative algorithm based on simulated annealing was constructed for solving this optimization problem.


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3.3 Speci cation of parameters

There is a whole set of parameters involved in the models described in the previous section. In order to perform contour detection, these parameters need to be speci ed. We will divide the parameters into two parts: parameters involved in the prior model and parameters involved in the data model (tissue type parameters). For the speci c choice of prior model (Eq. (3)), 1 ; 2 and 3 are the only parameters involved. These parameters were chosen by trial and failure on a single patient with normal MRI ndings. The values 1 =10:0, 2 =0:3 and 3 =0:3 showed to give good results for this patient. The larger value for 1 is for the outer contour (e.g. arachnoid / dura mater) which is expected to be more smooth than the two other contours. These parameter values were then used for all other patients examined. Estimation of all tissue type parameters can be based on initial estimates from a single patient examination. Grey-levels may however vary from one patient to another (or even from one slice to another) These estimates are therefore adjusted automatically, using the EM-algorithm, for each new multispectral slice image. This estimation is performed previous to contour detection and is fully automatic. The model for the observations includes the mean vectors and covariance matrices f( ; )g for each tissue type c = 1; : : : ; 7. Considering an arbitrary pixel i 2 R (the total region of interest) in the slice image, the signal intensities will be distributed according to a mixture of Gaussian distributions when the class memberships are unknown, i.e. c

Y i

7 X =1

N (; ; ) c

c

c

(7)

c

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Estimation of parameters in these models have been studied extensively (e.g. [38] and [55]). We will consider the case where is assumed xed to be the non-informative probability 1=7 for c = 1; : : : ; 7. Explicit equations for the maximum likelihood estimates are in this case impossible to obtain, but iterative methods based on the expectation-maximization (EM) algorithm ([18, 56]) are constructed for solving this problem. The algorithm in our case becomes (see also the Appendix): c

1. Assume given initial parameter values f((0) ; (0) ; (0) )g =1 c

c

c

c

;:::;7

2. For each iteration (s) : (a) Calculate the probabilities p (c; ( ,1) ; ( ,1) ) for c = 1; : : : ; 7; i 2 R, where p (c; ( ,1) ; ( ,1) ) = Pr(C = cjy ; = ( ,1) ; = ( ,1) ) C is the unknown class-membership, and y the observed intensity vector of pixel i. (b) Calculate the maximum likelihood estimates for f( ; ; )g =1 7 conditioned on the probabilities p (c; ( ,1) ; ( ,1) ) giving f( ; ( ) ; ( ) )g =1 7 , s c

i

s c

i

i

s c

s c

i

c

s c

s c

c

i

i

c

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s c

s c

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s c

s c

c

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c

;:::;

;:::;

where the stop criterion for iterations were ful lled if maximum change of a mean component in is less than 10 grey level units and maximum change of a variance component in is less than 1:0 104. Note that not only parameter estimates, but also a pixelwise segmentation is obtained from this algorithm. However, because this segmentation is made pixelwise, the global information available is not taken into account and the segmentation makes no distinction between intraventricular CSF and CSF in the arachnoid space. The likelihood function is guaranteed to increase for each iteration [56]. Since the likelihood function will contain many local maxima, only convergence to one of these is ensured. The resulting local maximum will depend on the initial parameter-values. In our case, supervised estimation is c

c


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performed in one patient examination through manual training. These estimates are used as initial parameter-values for all other patients. Thus, convergence will be to the local maximum nearest to to the parameters obtained from the training. This is preferable since the variation from one patient examination to another is not too large due to a xed MR acquisition protocol (Tab. 1).

Initial training

To obtain the initial parameter estimates f(0); (0) g =1 7 we used k-means clustering [3] (k=7) of a single multispectral slice image from a single patient with normal MRI ndings, following the approach described in [53]. Previous experiments with other slice images acquired with the same imaging parameters had shown that the selected number of clusters was sucient to distinguish the seven tissue types. To do the clustering, the N (0; 1)-normalized feature image g was computed for each channel f , l = 1; : : : ; 3 as g (m; n) = (f (m; n) , )= ; m; n = 1; : : : ; 256. Sample mean, and standard deviation, were calculated within the head mask R. The seven seed-points were selected at random from the multispectral image and we ran the iterative k-means algorithm until convergence (e.g. no more reallocations were made according to the criterion function of minimizing the sum of squared deviations from the observed intensity vectors to their cluster means). The seven cluster regions were manually labeled to seven distinct tissue types using knowledge of anatomy guided by an anatomical MR atlas [47]. From the k-means segmentation we calculated the tissue-speci c parameters f ; g =1 7 which were stored for later use. In addition, a four region a priori con guration representing outside brain, subarachnoid space, brain parenchyma, and the lateral ventricles, respectively, was drawn manually (Fig. 2b). c

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For processing the test patient examinations we made a simple production line. The only manual interaction was to trace a rough outline of the head to avoid unnecessary processing of background.

4 Experimental Results The algorithm was applied to a small, but diverse sample of multispectral MRI slice images from clinical routine.

4.1 Patients and MRI measurements

Ten multispectral cerebral MR images from 10 dierent patients were selected from a series of consecutive patients during a time period of one year. The sample consisted of images with normal and pathological brain structures observed radiologically. The selected slices were axial and transected the body of the lateral ventricles. In the majority of cases the lateral ventricles were imaged as a connected region in the middle of the slice, surrounded by brain parenchyma. The criteria for exclusion were inappropriate acquisition parameters according to the measurement protocol (Tab. 1) and examinations showing obvious movement artifacts or inferior image quality for other reasons. The MRI examinations were performed at the MR-center, University of Trondheim, Norway using a Philips 1.5 T Gyroscan with imaging parameters given in Tab. 1. All processing was done with the originally measured data, which had a discrete signal intensity range of 12 bit/pixel; typical for most MR imaging systems. We did not apply any correction for magnetic eld inhomogeneities ([11, 16, 35]) or noise suppression ([22, 24, 37]) since there were no signi cant low frequency or gradient variation in signal intensity across the investigated slices, and the noise level was acceptable.


Pulse sequence type

Spin echo

Pulse timing parameters

TR / TE [ms]

9

(multislice)

Channel 1:

2200 / 25

\-weighted"

Channel 2:

2200 / 100

\T2-weighted"

Channel 3:

460 / 20

\T1-weighted"

Slice

Thickness: 6:5 [mm]

Field of view (FOV): 230 230 [mm]

Matrix

Acquisition: 204 256

Display: 256 256

Number of excitations (NAC) NAC=1 in channel 1&2 NAC=2 in channel 3&4 Interslice spacing

0.6 [cm]

(16 slices)

Orientation of imaging plane

Axial

(head coil)

Table 1: MRI acquisition parameters on the Philips 1.5 T Gyroscan. The MR diagnoses were decided in the routine diagnostic procedure and reviewed by a radiologist. The clinical diagnosis and any histopathological examinations were done at the referring department and the Department of Pathology at the University Hospital of Trondheim, Norway.

4.2 Initial parameter estimates and region con guration

The result from unsupervised k-means clustering of N (0; 1)-normalized channel images from patient A used for training, is shown in Fig. 2a. There was good agreement between the 7 labeled cluster regions and the underlying anatomy (Fig. 2c,d,e). Thus, the tissue-speci c pixels used for initial parameter estimation could be appropriately selected. In Fig. 2c,d,e we have superimposed on each of the channel images the three simultaneously detected closed contours representing the boundaries between the four regions. The resulting segmentation of brain parenchyma and CSF spaces was quite acceptable visually (Fig. 2f). The initial region con guration, xed for all slice image segmentations, is depicted in Fig. 2b.


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Figure 2: Initial training. An axial slice transecting the body of the lateral ventricles from patient A with normal MRI examination. a) N (0; 1)-normalized k-means clustering (k=7). White: fat; very light gray: white matter; light gray: gray matter; medium gray: CSF; dark gray: connective tissue; very dark gray: muscle; black: air and bone: b) Initial region-con guration drawn manually, representing the starting contour x(0) common to all ten slice examinations. White (background): outside brain; black: subarachnoid space; dark gray: brain parenchyma; light gray: the lateral ventricles; c) Contour detection superimposed on proton spin density weighted channel image (SE 2200/25). Outer contour (white) represents the boundary of the brain, the middle contour represents the border between CSF in the subarachnoid space and brain parenchyma, inner contour represents the boundary of the lateral ventricles towards the brain parenchyma. d) T2-weighted channel (SE 2200/100); e) T1-weighted channel (SE 460/20); f) Brain parenchyma and CSF segmentation (same gray scale as in (b) ).


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4.3 Segmentation results

To give information about detail as well as diversity in the test data, we have reproduced one contour detection result at large magni cation (Fig. 3) and results from six more patients at smaller magni cation. Three were normal slice examinations (Fig. 4) and three were slice examinations exhibiting gross pathology (Fig. 5).

Normal cases Figure 3 shows, in larger magni cation, the proton spin density weighted (a) and

the T2-weighted (b) channel images from patient B used for testing. The outer black zone in this and the following gures is part of the slice image background which has been included in the manually traced head mask. The contour detection part of segmentation in this patient is illustrated in Fig. 3c and d. All three contours follow well their corresponding anatomical boundaries - the outer border of the brain (i.e. arachnoid / dura mater), the border between arachnoid space and brain parenchyma and the boundary of the lateral ventricles. Thus, from adjusting initial estimates of tissue type parameters and subsequent contour detection, brain parenchyma, intraventricular CSF and CSF in the subarachnoid space can be segmented precisely.


a

b

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Figure 3: Contour detection An axial slice without pathology from test patient B . a) Proton spin density-weighted acquisition (i.e. channel 1); b) T2-weighted acquisition (i.e. channel 2); c) Closed contour detection, superimposed on the proton spin density-weighted channel; d) Contour detection, superimposed on the T2-weighted channel. Two additional successful segmentations in normal slice images are shown in Fig. 4a,b,c (patient C ) and Fig. 4d,e,f (patient D). The detected contours follow closely their respective anatomical boundaries. In the nal normal slice image of patient E (Fig. 4g,h,i) proper segmentation of CSF in lateral ventricles was not achieved. Only a part of the third ventricle was detected. This was because the lateral ventricles were imaged as several disjoint regions in this slice, violating the model


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assumptions.

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Figure 4: Segmentation in three slice examinations with normal ndings. Left column: T2-weighted channel image; Middle column: The detected three closed contours superimposed on the proton spin density-weighted channel; Right column: The nal parenchyma/CSF segmentation. Light gray represents CSF of the ventricles, darker gray brain parenchyma (gray- and white matter), and black denotes CSF in the subarachnoid space. a { c) Patient C ; d { f) Patient D; g { i) Patient E.


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Pathological cases Processed slices exhibiting large regions of abnormal tissue or dislocated anatomy are presented in Fig. 5. The slice images of patient F contain multiple deep white matter infarctions and ischemic gliosis. This is seen in Fig. 5a and b as patches within white matter having increased signal intensity. Proper segmentation of the lateral ventricles was not obtained due to tissue parameter estimates close to those of CSF in the large, symmetrically located lesions near the posterior horns of the lateral ventricles. However, the arachnoid / dura mater and the subarachnoid space were found in agreement with the underlying anatomy. Patient G (Fig. 5d,e,f) had a large, partly cystic, subependymal anaplastic astrocytoma. A reasonable segmentation of the lateral ventricles was not achieved in this case because they did not have a single closed boundary due to intraventricular tumor growth. The last pathological slice image was from a patient H with enlargement of left lateral ventricle due to failure of temporal lobe development (agensis). Except for this nding, no other lesions or signal abnormalities were present, and the segmentation was satisfactory (Fig. 5h,i,j).


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Figure 5: Segmentation in three slice examinations with gross pathology. Left column: The T2weighted channel image; Middle column: The detected three closed contours superimposed on the proton spin density-weighted channel; Right column: The nal parenchyma/CSF segmentation (same gray scale coding as in Fig. 4). a { c) Patient F having deep white matter infarctions and ischemic gliosis; d { f) Patient G with intraventricular growth of subependymal anaplastic astrocytoma; g { i) Patient H showing enlargement of left lateral ventricle due to agenesis of temporal lobe. For each slice image segmentation, the typical total time for the two-stage method on a DECsta-


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tion 5000/25 was about 18 minutes. Rough manual tracing of the head mask took about 1 minute, and updating of initial tissue parameter estimates took about 12 minutes. Contour detection and nal segmentation was done in about 5 min.

5 Discussion and conclusion The BDC method [50, 49] is introduced for automated segmentation of parenchyma and CSF spaces of the brain from routine multispectral axial spin echo MR images. The segmentation method takes advantage of both the multispectral nature of MRI and the a priori knowledge of normal brain anatomy within the selected slices. The procedure is based on recognition of closed contours in a Bayesian framework where adaptation of parameters to patient data is performed automatically. In the majority of the 10 tested slice images, satisfactory results were obtained for recognition of the boundary of the brain and of CSF in the lateral ventricles and in subarachnoid space, respectively. Also, in slice images which show gross abnormalities (cfr. Fig. 5) we usually obtained acceptable segmentation results. However, in slices images with extensive signal abnormalities (cfr. Fig. 5a,b,c), tissue parameter estimates in lesions can be misleading and yield unsatisfactory results. Improper segmentation occurs in normal slices (cfr. Fig. 4g,h,i) and pathological slices (cfr. Fig. 5d,e,f) where the assumption of connected regions are violated. However, successful segmentation in these cases cannot be expected using our restricted approach. The contour model demands that the MR images must consist of transverse slices where brain parenchyma and CSF regions form connected regions. This is certainly a limitation of the method. However, in clinical routine examinations using axial 2D multislice techniques, the topological property of connectivity of CSF regions and brain tissue regions is usually observed for several slices. The exact number of axial slices having this property is dependent on slice thickness, interslice spacing, and the size and shape of these structures in the given patient. In daily routine, estimates of brain atrophy or degree of hydrocephalus are qualitative and subject to large inter- and intra-observer variation. Thus, automated measurement of regional CSF volumes and brain tissue volumes in central axial slices of the brain, where most of the total CSF volume is located, can be an important supplement to purely visual judgment. Since we used only a single axial slice, and not a full 3D data acquisition of the head, we did not make any volume calculations of brain parenchyma and CSF in this study. These calculations are fairly simple and could be automated by counting pixels within each segmented region and subsequent scaling by voxel-size. For extensive volumetry, however, one should have contiguous slice images from the whole head. In this respect, 3D MR acquisitions are preferable to 2D because it has better signal-to-noise ratio for thin slices [10]. Rapid scan techniques [12, 15] must be used, since acquisition of 3D dataset from the whole brain with conventional spin echo sequences leads to prohibitive scan time. In order to extend the procedure to slices from any level, either the assumption of simply closed curves has to be relaxed, or 3D techniques for recognizing closed, bounding surfaces of objects should be applied. Violating the assumption of connected regions in 2D axial slices will lead to improper segmentation using the present BDC method (cfr. Fig. 4g,h,i). A modi cation will be to let the user specify number of connected regions in each slice. Another approach could be to introduce multiple CSF regions (e.g. \anterior frontal horn of left lateral ventricle", \atrium of right lateral ventricle", etc.), dependent on slice level in a sequence of axial 2D slices such that the boundary of each of these regions is a simply closed curve. However, this will be a rather ad hoc method in the single case, and hence, dicult to automate. To our knowledge there is no energy-based 3D methods (cfr. [14, 42]) published which incorporate the multispectral nature of MRI. However, the BDC theory can be generalized to 3D, and work on a 3D algorithm is under current investigation. Incorporation of a comprehensive 3D anatomical atlas (cfr. [21] and [39]) for segmentation of


17

brain parenchyma, CSF of the ventricle system and of the subarachnoid space only, seems overre ned and will introduce unnecessary computational cost. To simplify the task for a 3D contour detection and segmentation algorithm, the search for speci c pulse sequences that accentuate signal intensity dierences between CSF, gray matter and white matter should be considered. Three dimensional fast-scan MRI protocols for clinical examination of the brain in about 5 minutes are now available on modern scanners [12, 15, 19]. Hennig et al. [28] have used a T2-weighted 3D RARE (rapid acquisition with relaxation enhancement) technique which highlights the signal from CSF. Other promising pulse sequences are 3D FLASH (fast low-angle shot) [19], 3D MP-RAGE (magnetization-prepared rapid gradient echo) [26] which is T1-weighted, and 3D CE-FAST (contrast enhanced fast acquisition in steady state) [25] which is strongly T2-weighted. Current investigations demonstrate the possibility to obtain a multispectral (T1-, T2- and PD-weighted) 3D dataset, covering the whole brain down to the spinal cord with 1.4 l voxels, within less than 20 minutes [36]. When using several pulse sequences (e.g. multispectral feature images), or if multiple imaging modalities such MRI and X-ray CT (cfr. [41]) are used for brain parenchyma and CSF segmentation, one is usually faced with the problem of image misregistration where the geometry diers between corresponding channel images. In this study, misregistration could occur between channel 3 (SE 460/20) and the two other channels (SE 2200/25,100) since two dierent spin echo sequences was applied. The echoes representing the rows of the rst two channel images were acquired only milliseconds apart, while the T1-weighted pulse sequence was applied some minutes later. After inspecting the channel images for all slice examinations we feel con dent that only minor improvements could be achieved if geometric correction (see f.ex. [8]) were performed previous to parameter estimation and contour detection. In conclusion, a method to segment multispectral MRI images into brain parenchyma and CSF has been presented. It performs well in a sample of normal and abnormal slices for which the structures to be segmented are connected and form closed contour boundaries. However, as expected the segmentation method breaks down when this assumption is violated. To obtain clinical applicability with the possibility for extensive evaluation, re nements and generalization to 3D in combination with more optimal MRI pulse sequences is necessary.

APPENDIX Representation of simply closed curves We assume the normal head mask or pixel-lattice R f1; : : : ; 256gf1; : : :; 256g consists of four, disjoint, connected regions: R1 = outside brain (i.e. outside arachnoid / dura mater), R2 = arachnoid space, R3 = brain parenchyma, and R4 = lateral ventricles, where their mutual locations are depicted in Fig. 1 and Fig. 2b. We denote the set of boundaries between these variable regions by X , where a realization x from X consists of three non-intersecting closed contours, denoted x = (x1 ; x2 ; x3 ). Each of these contours x has a polygon representation de ned by a chain of nodes, x = (x1 ; : : : ; x ), where n is the number of nodes for contour i. In the current implementation of the optimization algorithm, the contours are assumed to follow the pixel-sides. The main reason for such a restriction is the need to handle calculations concerning the model f (yjx) (Eq. (4)) fast. The positions of the nodes are then restricted to be on the corners of the pixels with one node for each corner the contour goes through. The number of nodes on a contour will then be stochastic and each node x has integral, planar coordinate points (x 1 ; x 2 ) in a circular, clockwise manner. In this representation, a given pixel will have to be either inside or outside the boundary. Since we i

i

i

i ni

i j

i

i j

i j


18

have quadratic pixels, the angle between three succeeding nodes will be either 90 or 180 , ignoring orientation, and the number n of nodes will be even. o

o

i

Algorithm for optimization based on simulated annealing Simulated annealing is an iterative method for combinatorial optimization. Assume E (x) is the total energy to be minimized. At each step of the iteration, a new candidate con guration is drawn and a switch to the new con guration is made with a probability depending on the energies of both the previous and the new con guration. Typically, in order for the algorithm to converge fast enough, only local changes on the contours are made at each iteration step. The changes are speci ed through the draw of new con gurations. We will assume that at each iteration a corresponding position de ning where changes can occur is given. The algorithm is then as follows: Algorithm Start with an initial con guration X (0) and a position P (0). For each iteration s, carry out the following steps: 1. Assume that X (s) = x and select state x0 by the distribution given by the xth row of some transition matrix Q with restrictions so that changes from x to x0 are only local around position P (s); 2. Put

X (s + 1) =

0 x with probability p (x; x0 ) x otherwise s

where

p (x; y) = minf1; expf,[E (y) , E (x)]=T (s)gg s

and T (s) is a decreasing function. 3. Draw a new position P (s + 1) according to some transition matrix R. Some (mild) restrictions on the choice of Q and R are necessary in order to make the algorithm converge. For details we refer to Storvik [50, 49]. In the current implementation, changes at each iteration are made by moving a few (up to three) pixels from one side of the boundary to the other. Note that in that case calculation of the change in energies corresponding to models (3) and (4) are easy to calculate.

Acknowledgment

We thank Tor nn Taxt for valuable discussions, the anonymous referees for helpfull criticism and comments, and Gunnar Myhr for providing the MR images. This work was supported by the Research Council of Norway (Grant 340.93/018).

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