Knowledge-Driven Automated Extraction of the Human Cerebral Ventricular System from MR Images

Yan Xia, QingMao Hu, Aamer Aziz, Wieslaw L. Nowinski

Biomedical Imaging Lab, Institute for Infocomm Research 21 Heng Mui Keng Terrace, Singapore 119613

Email: yanxia@i2r.a-star.edu.sg

Abstract. This work presents an efficient and automated method to extract the human cerebral ventricular system from MRI driven by anatomic knowledge. The ventricular system is divided into six three-dimensional regions; six ROIs are defined based on the anatomy and literature studies regarding variability of the cerebral ventricular system. The distribution histogram of radiological properties is calculated in each ROI, and the intensity thresholds for extracting each region are automatically determined. Intensity inhomogeneities are accounted for by adjusting intensity threshold to match local situation. The extracting method is based on region-growing and anatomical knowledge, and is designed to include all ventricular parts, even if they appear unconnected on the image. The ventricle extraction method was implemented on the Window platform using C++, and was validated qualitatively on 30 MRI studies with variable parameters.

1. Introduction

The human cerebral ventricular system consists of four intercommunicating chambers: left and right lateral, third, and fourth ventricle. The ventricles contain cerebrospinal fluid (CSF). Changes in CSF volume and shape are associated with several neurological diseases, such as congenital anomalies, post-traumatic disorders, tumors, pseudo-tumors, neurodegenerative diseases, inflammatory diseases, headache, cognitive dysfunction / psychiatric diseases, and post-operative changes. Quantification of the degree of dilatation of ventricles is important in diagnosis of various diseases and to measure the response to treatment, and in predicting the prognosis of the disease process. Extraction and quantification of the ventricular system from medical images is therefore of primary importance.

Due to the great importance of the ventricular system, its extraction has attracted a lot of research work. Major representative methods for the extraction of ventricles have been region-growing assisted by morphological operat ions (Schnack et al., 2001 [1]), thresholding (Worth et al., 1998 [2]), template matching (Kaus et al., 2001 [3]), atlas warping (Holden et al, 2001 [4]), level sets (Baillard et al., 2000 [5]), active models (Wang et al., 1998 [6]), fuzzy set and information fusion (Geraud, 1998 [7]), genetic method (GA) optimization (Sonka et al, 1996 [8]), pure region-growing (Hahn et al, 1998 [9]), and knowledge based methods (Fisher, et al, 2002 [10]). Despite

numerous approaches proposed to solve the problem, there is no simple method suitable for clinical use. This is due to the human intervention required, inability to handle pathological and abnormal cases, and/or inability to extract the complete ventricular system. Moreover, the existing methods are too slow to be clinically acceptable. Because of the anatomical complexity of the cerebral ventricular system and the lack of fast and reliable extraction procedures, a fast, automatic, accurate, and robust method is desirable to extract the complete ventricular system.

In this paper, we present an efficient and automated method to extract the human cerebral ventricular system from MRI driven by anatomic knowledge. The method is based on region-growing and anatomical knowledge, and is focused on automatically extracting all ventricular parts, even if they appear unconnected on the image.

2. Materials and Methods

The method is based on the following anatomical principles: (1) Ventricles are surrounded by white and gray matter. (2) All of the ventricles are interconnected to enable circulation of cerebrospinal fluid in nature and could, in principle, be extracted with one region-growing operation. However, owing to the partial volume effect, noise, and spatial and contrast resolutions of the scan, parts of the system may appear not to be connected on the image and additional anatomical knowledge of the shape and position of the ventricular system needs to be inserted in the method to find these unconnected parts and remove those connected to nonventricular regions (cisterns, sulci). To facilitate this, the ventricular system is divided into six 3D sub-regions that could be extracted independently. The sub-regions are the body of the left lateral ventricle (including the anterior and posterior horns, VLL-B), the body of the right lateral ventricle (including the anterior and posterior horns, VLR-B), the inferior (temporal) horn of the left lateral ventricle (VLL-I), inferior (temporal) horn of the right lateral ventricle (VLR-I), third ventricle (V3), and fourth ventricle (V4). Anatomic knowledge of the ventricular system is inserted to guide the metho d in defining the sub-regions, drawing a region of interest (ROI) for each sub -region, calculating statistical characteristics of each ROI and locating a seed point in each ROI, extracting for sub-regions, and connecting them to get the complete ventricular system.

2.1. Preprocessing Steps

The brain MRIs are loaded initially. Next the location of the Midsagital Plane (MSP) is extracted from the volume data [11], and the coordinates of the anterior commissure (AC) and posterior commissure (PC) are identified on the MSP image [12]. A coordinate system (xyz) is defined such that x runs from subject’s right to left, z runs from superior to inferior, and y runs from anterior to posterior. Thus the xz plane is coronal, the yz plane is the sagittal, and the xy plane is axial that is parallel to the AC-PC line. The axial, coronal, and sagittal orientations are thus available. The original volumetric dataset is reformatted into above coordinate system (however, there is not need to use an isotropic volume). The reformatted dataset facilitates using

any orientation for setting the ROI and performing region growing. It also helps in defining the anatomical landmarks accurately.

2.2. Define Multiple Regions of Interest (ROIs)

Six regions of interest (ROIs) are defined corresponding to the respective ventricular sub-regions: VLL-B, VLR -B, VLL-I, VLR-I, V3, and V4. The initial ROIs are defined taking into account the worst -case assumption (the biggest ROI necessary) based on literature studies of variability, [13] [14]. Figure 1 shows the ROI of left lateral ventricle. It is defined on the coronal plane passing through the AC (VAC). T aking AC as base point, ROI is set 25 mm laterally and 35 mm superiorly. Figure 2 shows a ROI of the inferior horn of the right lateral ventricle, which will be set on all the coronal slices between VAC and coronal plane passing through the PC (VPC). The horizontal profile is then drawn at the level of the inferior point of V3; a middle point (a) is marked at half the distance between MSP and the temporal bone marrow fat signal point in the profile as reference. The ROI 20 mm x 20 mm is drawn in reference to this point so that the coordinates are (a, a-10) (a, a+10) laterally and (a, a-20) inferiorly. The initial ROI of V3 on the MSP is antero-posteriorly between AC, and PC and superior-inferiorly between [AC– 35 mm, AC + 10 mm] (Figure 3). For the V4, initially a large ROI with width of 45 mm and height of 55 mm is used on the MSP, Figure 4. The ROI shape is changed to quadrangular so as to exclude the clivus (bone), ambient cistern, quadrigeminal cistern, and cisterna magna.

Figure 1 ROI for the left lateral

ventricle Figure 2 ROI for the inferior horn of

the right lateral ventricle

Figure 3 ROI for the third ventricle Figure 4 ROI for the fourth ventricle

2.3. Calculate Statistics and Adapt Size of each ROI

The thresholds for gray matter (GM), white matter (WM), and CSF in each sub-region have to be determined automatically before extracting the ventricular system. This is done by finding the peaks in the histogram that characterize the distribution of the voxel intensities in the studied region of interest.

Calculate the Histogram of ROI. Each ROI is defined to facilitate analysis that will produce statistically significant findings necessary for each ventricular sub-region’s extraction. The histogram obtained from an ROI containing the lateral ventricle and adjacent structures on T1-wieghted MRI is shown in Figure 5. This produces a multi-modal histogram where the intensity peaks and ranges corresponding to WM, GM, CSF, and other classes can be chosen. The ventricles filled with CSF are defined by those spatially connected pixels with intensity between two thresholds.

Figure 5 Original and smoothed histograms of ROI

Smooth the Histogram. Histograms of real data have substantial local variations that hamper determination of global peaks and valleys. Some initial smoothing methods have to be applied to reduce the local variations. In this work, the Fourier filter based on the frequency components of a signal is applied to the original histogram. It works by taking the Fourier transform of the signal, cutting off all frequencies above a specified limit, and inversely transforming the result. The best cut-off frequency of the Fourier filter is found automatically based on knowledge of anatomy, radiology, and image processing. An initial small cut -off frequency is assigned, the Fourier filter is imposed on the signal and then the inverse transformation is performed. The inverse result is checked using the following constrains:

• The number of peaks in the smoothed histogram is equal to or less than 5 because there are CSF, CSF/GM, GM, GM/WM and WM in the ROI.

• A peak is ignored if its area is smaller than the cumulative area of the histogram (i.e., if its area is less than 1/30th of the total area).

• A peak is ignored if it is between the intensities at 5% and 95% of the cumulative area of the histogram.

Gray scale

0.01

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0.04

0.05

0.06

0.07

0 32 64 96 128

Original histogram

Smoothed histogram

Fre

quen

cy

0

If the result meets the above constrains, the cut -off frequency is the best one for the smoothing. If not, the cut -off frequency will be adaptively reduced/increased and the smoothing be repeated until a new inverse result fulfils these constrains. The original and smoothed histograms are shown in Figure 5. The original histogram contains many noisy peaks. The smoothed histogram has only main peaks after undergoing a Fourier-filter smoothing. The noise is greatly reduced while the main peaks are hardly changed without distorting the signal significantly. Smoothing increases the signal-to-noise ratio and allows the signal characteristics (peak position, height, width, area, etc.) to be measured more accurately.

Identify the Peaks in the Histogram. The histogram is modeled as the sum of five smoothed, modified normal distribution (Gaussian) functions -- one distribution each for CSF, CSF/GM, GM, GM/WM and WM. In Equation (1), µ is the mean, σ is the standard deviation and h is the height of the Gaussian function.

∑=

−−×=

5

12

2

2)(

exp)()(i i

ixihxf

σµ

(1)

Figure 6 shows the smoothed histogram distribution and the result of modeling each separately by a Gaussian function described the intensity distributions. After modeling, the peaks, ranges and intersections of modeled distributions can be taken. Neuroanatomical and radiological knowledge is incorporated to locate the peaks corresponding to CSF, GM, and WM. It is assumed that the highest intensity peak corresponds to WM on T1-weighted/SPGR MRI while the lowest intensity peak corresponds to CSF, and the lowest intensity peak corresponds to WM on T2-weighted MRI while the highest intensity peak corresponds to CSF. After identifying the peaks in the histogram, the upper and lower gray -value thresholds of each peak are computed on both sides of the peak (mean) of the Gaussian, at two standard deviations away so that 95% of the data usually falls wit hin the region, or the cross points with right/left neighborhood Gaussian functions (Figure 6).

Figure 6 The Result of Gaussian Fitting

Reduce ROI Adaptively. As the initial ROIs are defined based on the worst case

0.06

Gray value

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0.03

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0.05

0 32 64 96

Smoothed histogram Modeling function

128

upper threshold

lower threshold

Fre

quen

cy lower

threshold

literature variability studies, the distribution of CSF, GM, and WM in some cases may be unbalanced (some peaks corresponding to either WM, GM or CSF are so small that they are not easily identifiable in the histogram), which may hinder an accurate processing of the histogram. To improve the density distribution balance, the ROI is reduced adaptively. When the ratio of the WM/GM to CSF peak is greater than a given number, the ROI is reduced by a given percentage, and the histogram is recalculated and the new thresholds are gotten. The adaptive reduction of ROI is performed iteratively until the required distribution is achieved.

Adjust the Thresholds for Each Slice. The initial thresholds will be changed adaptively during the growing of the ventricular system to cope with the partial volume effect and intensity inhomogeneity. For the partial volume effect, it based on a two compartment model, and can assume that each voxel near the edge of the ventricular system may contain up to two classes, CSF and GM or WM. Using the class averages for each of these two compartments, the contribution of each class can be calculated from the grown voxel intensity. In Equation (2), I means the measured voxel intersity, µ is the mean, α means the proportion of CSF in the measured voxel.

csfwmgm

wmgm I

µµ

µα

−

−=

/

/ (2)

When α value is greater than 0.5, meaning that the proportion of CSF in the measured voxel is mor e than 50%, the measured voxel may belong to ventricular regions or cisternal regions. This is decided based on anatomy knowledge.

It is important to use local thresholds to extract the ventricle region on the current slice to reduce the influence of intensity inhomogeneities. Since the intensity inhomogeneities are visually obvious on GM or WM for radiologist, the ratio of the means of GM/WM is taken as the multiplicative correction factor for each slice:

)(

)(

/

/

wmgm

wmgmslice local

globalCorrect

µ

µ=

(3)

Where “local” means current slice, “global” means the slice that a ROI is defined on (Figure 1 -- Figure 4), and sliceCorrect means the intensity inhomogeneities

correction factor for current slice (axial, sagittal, or coronal). The result of ( slicecsf Correctlocal ×)(µ ) is the threshold that is used to extract the ventricle

region in the current slice.

2.4. Extract Ventricular Region

The ventricular regions are grown in 3D independently starting from the defined seed points. Each region growing is directional which allows for better control of growing in 3D space. Moreover, the extraction sequence is firstly extracting third ventricle,

next fourth ventricle, and then the left and right ventricles (VLL and VLR) for controlling leakage and connections.

Extract V3. Third ventricle is a small but with complex shape ventricle. The V3 is subdivided into four subregions by the planes passing through the AC and PC points, namely VAC, VPC, AC-PC axial plane, Figure 7. The seed point of V3 is point whose grey scale level is closest to the CSF mean value on the AC-PC line segment. Subregion 2 is grown superiorily direction and subregion 4 is grown inferiorily direction on all subsequence axial slices starting from the seed point. Subregion 1 is grown anteriorly direction on coronal slices starting from any pixel common with subregion 4. Subregion 3 is grown superiorily on axial slices starting from any pixel common with subregion 2.

The following leakages may occur in V3: 1) anteriorly through the lamina terminalis to the chiasmatic cistern, 2) ventrally through the mesencephalic tegmentum to the interpeduncular cistern, 3) posteriorly through the posterior commissure (stalk of the pineal body) to the cisterna ambiens. So, suitable spatial constraints are imposed into method for leakage prevention:

• As the shape of the roof of V3 is oblique, the distance between the superior and inferior points of sub-region 1 decreases, and the width of subregion 1 on a processed coronal slice is not allowed to increase by 50% over that of the previous slice along anterior direction.

• To prevent leakage posteriorly through the PC (stalk of the pineal body) to the cisterna ambiens, two spatial constraints are imposed: 1) The maximum width of the foreground region of subregion 3 on a currently processed axial slice is on PC line (PC line is the intersection between VPC and the current axial slice); 2) The distance between the gravity centre of the foreground region of subregion 3 and the MSP should be small less than 4 mm in sagittal direction [13].

Extract V4. V4 is subdivided into two subregions by the axial plane passing through the seed point located at the middle point of the longest CSF segment on MSP, Figure 7. V4 is grown on axial slices, superiorily in subregion 1 and inferiorily in subregion 2 starting from the axial slice containing the seed point. The aqueduct cannot be extracted directly as its diameter is quite small (about 1.2 mm in average) in most cases, it can be positioned at the lowest intensity in a small search area on T1-weighted MR image (or the highest on T2-weighted images).

Figure 7 Sub-regions of V3 and V4

The following leakages may occur in V4: 1) dorsoposteriorly through the superior medullary velum to the cisterna ambiens, 2) ventroposteriorly through the inferior medullary velum to the cisterna magna.To prevent leakage dorsoposteriorly through the superior medullary velum to the cisterna ambiens, two constraints are imposed:

• The number of the grown pixels of the current axial slice should not increase by 50% over that in the previous slice in inferior direction.

• The distance between the gravity centre of the grown region and the MSP should be less than 2 mm in sagittal direction. The gravity centre of the grown region should not deviate more than 2 mm away from that of the previous slice in sagittal direction [13].

To prevent the leakage ventroposteriorly through the inferior medullary velum to the cisterna magna, the width of the foreground region at the lateral recesses should be less than 2 mm in sagittal direction [13].

Extract VLL-B and VLR-B. Each of VLL-B and VLR -B regions is grown in 3D space on coronal slices, slice by slice. Growing is initiated anteriorly direction from the seed point located at the middle longest CSF segment on VAC. When this sub-region growing is complet ed, it is continued posteriorly direction on all subsequent coronal slices. Eventually it is continued anteriorly when attempting to extract the posterior part of the inferior horn. The VLL-B/VLR -B growing stops when there are no more connected voxels left to add to the result. This extraction result includes at least the main bodies of the lateral ventricles.

Leakage may occur in a posterior ventral part of the body of the lateral ventricles. Moreover, in some cases, a large cystic elongated space between the lateral ventricles may be present representing the cavum septum pellucidum and cavum vergae. A potential leakage has to be checked when the extracting operation has finished at these spaces. On radiological images the cavum is relatively perpendicular and predictable, and the septal wall can be easily detected (it has higher signal intensity as compared to CSF on T1-weighted images). For the leakage into the quadrigeminal cistern, the grown area in current coronal slice is compared with that of the previous slice (y+1). When a sudden appearance of a large connected area of such voxels is possibly a leak into quadrigeminal cistern. If such a region is below the PC in inferior direction, in the area behind the VPC up to the seed point of V4, this region can be considered as leakage. When the leakage occurs, the voxels of this leakage region are set to a value that is outside of CSF range. Also, the CSF range should be narrowed and the last region-growing step is carried out again followed by checking whether the leakage is avoided. This time the “wrong” region cannot be grown. This procedure is repeated until all growing is done.

Extract VLL-I and VLR-I. Connections between VLL-B with VLL-I and VLR-B with VLR -I are too thin to be visible on MRI in most cases with the current resolution. When VLL-B and VLR-B do not include the temporal horns, the seed point for each left and right temporal horn will be located (at the geometric center of the largest CSF region in the ROIs), and VLL-I and VLR-I be extracted.

Each of VLL-I and VLR-I regions is grown in 3D space on coronal slices, slice by slice. Growing is initiated anteriorily from the seed point. Follow the CSF of temporal

horn through anterior slice until no more CSF is seen. At same time, the gray matter wil l begin to extend superior to the hippocampus as slices move anteriorly. When this is completed, growing is followed the CSF of temporal horn through posterior sequent coronal slices. The lateral boundary is defined by the CSF of temporal horn at beginning and then by the white matter adjacent to the gray matter of hippocampus until no more gray matter is seen through posterior slices.

The following leakages may occur in these regions: 1) inferomedially through the hippocampus to the interpeduncular cistern, 2) medially through white matter (optic radiation) and cortex (choroidal fissure) to the subarachnoid space. To prevent potential leakages, the foreground region(s) on a processed coronal slice is (are) not allowed to grow beyond the boundary of ROI for VLL-I or VLR-I.

3. Results

The ventricle extraction method is implemented on the Window platform using C++. First evaluation of the method was done on a T1-weighted MR brain study, with volume size of 256*256*168, voxel size of 1.0*1.0*0.67 mm, of good image quality, with known underlying extraction result of ventricular system. The run time of the extraction method was less than 30 seconds on a Pentium 3 800 MHz PC with 128 MB of RAM. Figure 8 shows the extraction results in some axial slices. The third ventricle, fourth ventricle, lateral ventricle, aqueduct, the temporal horns of the lateral ventricle, and the connection between VL-B and VL-I were extracted clearly. The “raw” automatic extraction result was not edited.

Figure 8 Axial slices showing the ventricular system extracted

4. Discussion

To test the validity and applicability of the method, 30 real clinical MR volume data were collected from different sources. The volume data were acquired using a T 1-weighted spin echo and a Spoiled Gradient Echo Recovery (SPGR) sequence. They include healthy controls and patients with various tumors (Figure 9), age ranging from 12 to 60 years, both females and males. The volume size of the scans range from 192*256*192 to 256*181*256, the voxel size from 0.897 to 1 mm in sagittal, from 0.879 to 2.0 mm in coronal, and 0.67 to 3.5 mm in axial directions. Furthermore, some volume data has significant partial volume effect and inhomogeneity, Figure 10.

Figure 9 Pathological Data Figure 10 partial volume and

inhomogeneity The run time of the extraction method was less than 1 min for all of the data on a

Pentium3 800 MHz, 128 MB RAM PC regardless of the complexity of the ventricular system and the severity of the leakages. The method for automatic determination of intensity model parameters using statistical worked well even for a wide variety of scan data sets obtained at different times from different scanners under different protocols. On one of the 30 datasets the method failed to run correctly because the slice thickness was 3.5 mm at axial direction, the method cannot pass the seed point and grow the lateral ventricles correctly. The roof of third ventricle could not be found in one of the data set, because the V3 was too thin for the case (12-year old subject), the partial volume effect caused the V3 roof to be invisible. On another dataset the connection between VLR-B and VLR -I could be located entirely, also because the hippocampus was too narrow at some places (60-year old subject). These tests show the method gives qualitatively good results (visual check of the extrication) for complete ventricular system; a more thorough validation is being carried out by the radiology experts.

Our method assumes that the main body of the lateral ventricle can be extracted with one region-growing operation. Posterior or anterior parts of the lateral ventricle is (are) not connected to the main body on the image because the connection is too thin. Additional steps should be added the method to automatically find and grow the piece(s) and discard the other nearby loose ends of sulci and cisterns.

Our method assumes that the MSP has been generated and the AC and PC landmarks have been detected. The calculation of MSP and the detection of AC and PC have their own inaccuracies, [11][12]. The inaccuracies propagate in our method,

and may have an influence on the extraction accuracy; AC is particular sensitive to the accuracy of the extraction result.

Our method is based on region -growing and anatomical knowledge. Slice thickness influences more on accuracy than the partial volume effect and inhomogeneity. When the slice thickness especially in coronal and axial directions, is too big, the method can not get a good extraction result and might even fail to run. The tests show that the method fails to run correctly when the slice thickness is greater than 3.5 mm in axial direction and 2.0 mm in coronal direction.

Noise has a more notable effect than partial volume and RF inhomogeneity on the method because the method is driven by anatomic knowledge and statistics. The method was not able to determine the location of the initial peaks (thresholds) when the data is very noisy with large intensity inhomogeneities or in data where there was very little gray -white contrast (i.e. these two peaks merging together). The method should adequately handle the parameter estimation, partial volume, and intensity inhomogeneities although these problems may not fit well into the theoretical formalism.

Our emphasis here was to automate a precise segmentation procedure for ventricular system. The utility of the method to the general image processing is to deal directly with problems by using deep domain specific knowledge. This method provides an example of the application of neuroanatomical and radiological knowledge (expectations about tissue response in MR such as histogram peak sizes and knowing which peak to use in which situation; templates locating ROIs and seed points; specific sequence of successive region extraction and detection of leakages and connection) along with image processing and pattern recognition methods (locating peaks using the Gaussian fitting; excluding edge voxels from influencing threshold determination; and directional region growing from a starting point).

5. Conclusion

We have proposed an efficient and automated method to extract the complete human cerebral ventricular system from MRI driven by anatomic knowledge. The combination of neuroanatomy, radiological properties, variability of the ventricular system, and image processing techniques in the formulation of the method is advantageous as they aid to identify the thresholds of extraction, locate the starting point for the 3D region growing, localize the ventricular system structure and guide the system extraction including handling of the leakages and connection during the system extraction more reliably. The proposed method runs correctly on MR images acquired using different pulse sequences when the slice thickness was less than 3.0 mm at axial direction or is less than 2.0 mm at coronal direction, and yields a good qualitative result of complete ventricular system even in the presence of significant inhomogeneity and partial volume effect. The noise, slice thickness and partial volume effect have significant influence in extraction. We continue to validate the method by quantifying the extraction results. We will also extend this concept to other neuroanatomical structures such as hippocampus and corpus callosum.

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