untitled 278 Folia Neuropathologica 2008; 46/4 The cycloid and skeletonization methods for morphometric analysis of fetal brain vessels Tomasz Stêpieñ1, Boguslaw Obara2,3 1Department of Neuropathology, Institute of Psychiatry and Neurology, Warsaw, Poland; 2Strata Mechanics Research Institute, Polish Academy of Sciences, Krakow, Poland; 3Center for BioImage Informatics, Department of Electrical and Computer Engineering, University of California, Santa Barbara, USA Folia Neuropathol 2008; 46 (4): 278-285 A b s t r a c t In our study, we examined 54 images from 9 fetal brains from the 11th to 22nd gestation week (GW). We measured the length density (LD) of vessels (µm/µm2) in the cortical grey matter (CGM) and in the cortical white matter (CWM). The aim of this work was to fi nd a method which could be applied to measure the length density of vessels on two-dimensional (2D) sections. The fi rst method (cycloid method) was based on cycloid function based on Stereo Investigator Software (MicroBrightField). The length in 2D could be estimated on the basis of a number of intersections between a line-probe and the linear objects of interest. In the study, we used a line-probe with systematically spaced sine-weighted curves (cycloids) of known length. In this case, the cycloids were 53.1 µm long. The counting grid was constructed from sine-weighted lines (cycloids), which were used for estimation of the length density of vessels. The second method (skeletonization) was based on the mathematical functions of morphology and colour system transformation. The “binary airway tree” formed by the image segmentation step was skeletonized to identify two- or three-dimensional centrelines of individual branches, and to determine the branch point locations. The idea was to utilize a skeletonization algorithm which was based on properties of the average outward fl ux of the gradient vector fi eld of a Euclidean distance function from the boundary of the structure. Both of these methods (cycloid and skeletonization) could be applied in measuring the length density of vessels on two-dimensional (2D) sections. These morphometric methods allowed us to measure the length density in fetal development of vessels in the cortical grey matter and the cortical white matter. The cycloid method could be applied to measure an approximate length density of vessels. However, skeletonization should be applied to measure more precisely length density of vessels in the cortical grey matter and the cortical white matter. Key words: image analysis, skeletonization, cycloid method, human fetal brain, vascular length density, CD34. Communicating author: Tomasz Stêpieñ, Department of Neuropathology, Institute of Psychiatry and Neurology, Sobieskiego 9, 02-957 Warsaw, Poland, tel. +48 22 458 27 86, Email: tstepien@ipin.edu.pl, obara@ece.ucsb.edu Introduction What is the objective of generating hundreds of digits resulting from microscopic image analysis? It turned out that the mere terms “large, medium, short” are insuffi cient in scientifi c discourse, which calls for unifi cation of parameter description. The- refore, geometric features began to be used to de- scribe the surface of objects in mathematical terms. This brought modern morphometry to life. Howe- Original article Folia Neuropathologica 2008; 46/4 279 Cycloid and skeletonization methods for analysis of brain vessels ver, it still did not answer the question of relations between objects in space. What was needed was a method of transposing geometric parameters from surface to space. This issue was fi rst addressed by Count Buff on in the late 18th century. He made an experiment on needles scattered on the fl oor, sug- gesting that the number of intersections would be directly proportional to the length of the needle, and inversely proportional to the distance between the lines on the fl oor [5]. Buff on’s problem provided the basis for length estimation in modern morphome- try, allowing for quantitative description of a set of solids with measurements (e.g. of size or length) or counting based on 2D cross-sections of the solids. In our study, we examined the length density of vessels in the fetal brain cortical grey matter (CGM) and the cortical white matter (CWM) in fetal brains between GW 11 and GW 22, using two methods. The fi rst one was skeletonization, consisting in measuring objects on the surface, and the second one was the cycloid method, based on Buff on’s experiment. The objects of our interest were blood vessels and their development. Normal vascular development in the brain plays an important role in the appropriate pro- liferation, migration and maturation of neurons, glial cells, in synaptogenesis and in building connections of various structures [9,11,19]. The development of the primitive vascular network in the brain involves two diff erent mechanisms: vasculogenesis and angioge- nesis. Vasculogenesis forms blood vessels from diff e- rentiating endothelial cells (ECs) from mesenchymal precursors (angioblasts/haemangioblasts). Angioge- nesis is a process where vessels sprout and branch from pre-existing ECs and vessels [3,21,24,25]. Patho- logical vasculogenesis and/or angiogenesis during early prenatal development underlie the pathophysio- logy of many neurodevelopmental disorders [14,15,18]. The alteration of capillary length density in the fetal brain may tell us more about factors activated during development. In our study, we tried to establish which method proves useful to measure the length density of vessels on two-dimensional (2D) sections. Material and Methods Brain specimens The cortical grey matter (CGM) and the cortical white matter (CWM) of frontal lobe from a group of 9 fetuses without neuropathological abnormalities were studied. Fetal brains ranging from gestation week (GW) 11 to 22 were fi xed in 4% paraformaldehy- de in 0.1 M phosphate buff er saline (PBS), pH 7.4. The fi xed samples were then embedded in paraffi n, and cut serially at 8 μm in frontal sections, which was fol- lowed by routine staining of brain tissue slices with haematoxylin-eosin (H&E) and immunohistochemi- cal reaction with antibody CD34 (Novocastra 1:25). The gestational age in each case was calculated from the date of the last menstrual period. Image analysis Image analysis and processing techniques are suc- cessfully used in medical image analysis [6,7]. One of the most important parts of image analysis is skeleto- nization. The binary airway tree formed by the image segmentation step is skeletonized to identify the two- or three-dimensional centrelines of individual bran- ches and to determine the branch point locations. Skeletonization of three-dimensional tubular structures is reported by Palágyi et al. [17]. Palágyi’s method specifi cally targets skeletonization of vascu- lar- and airway tree structures in medical images. Bouix et al. [4] presented a fast, robust and automa- tic method for computing centreline paths through tubular structures, to be applied in virtual endoscopy. Bouix’s idea is to utilize a skeletonization algorithm based on the properties of the average outward fl ux of the gradient vector fi eld of a Euclidean distance function from the boundary of the structure. Solta- nian-Zadeh et al. [20] proposed an image processing approach for information extraction from images of the vascular structure. Soltanian-Zadeh’s method allows extraction of information such as skeleton length and diameter from real confocal microscopic images of the vessels in rat brains. Quantitative in- formation revealed in angiograms, for example ves- sel length, diameter, course, and curvature, is essen- tial and can be accessible by computer with image analysis methods, particularly skeletonization [16]. The thinning process is based on the Hit or Miss transform, which is a combination of erosion and di- lation operators that allows a foreground pixel to be matched according to a predefi ned structuring ele- ment. Removing branches of the skeleton tree can be computed by iteratively detecting and removing the end points of the tree, until there are only two of them left. This method successfully removes short spurs from the skeleton but it can also discard end po- 280 Folia Neuropathologica 2008; 46/4 Tomasz Stêpieñ, Boguslaw Obara ints of the skeleton main path, especially when bran- ches are long. The main path is required to maintain its full length, i.e. to connect two pixel positions on the boundary of the original shape. To compute it, an algorithm based on the Euclidean distance between the end points of the skeleton and its nodes is used (Fig. 10). For each node (white colour), the distance between the node and each end point (black colo- ur) is calculated. The end point with the minimum distance is then removed. With this technique, only the longest of all the branches starting from a given node are kept. This process is done iteratively until there is no more node, i.e. only two end points are left. The result of the whole process (Fig. 10D). The dilation of a set I by a structuring element B is denoted as δ B (I) and is defi ned as a locus of points z such that B hits I when its origin coincides with z. δ B (I)={z : B z ∩ I ≠ ∅} (1) Erosion is defi ned as: ε B (I)={z : B z ⊂ I} (2) Based on erosion and dilation, we defi ne opening and closing, which form the basis of morphological fi ltering. The opening of an image I by a structuring element B is defi ned as erosion of I followed by di- lation with B. γ B (I)=δ B (I) ε BT (I) (3) Closing is defi ned as: φ B (I)=ε B (I) δ BT (I) (4) Opening by reconstruction is defi ned as: γ B rec(I)=ρ (I,G) ε B (I) (5) where: G=ε B (I). I image is reconstructed by the marker function G, by an infi nite number of recursive iterations (iterations until stability) of the dilation of G conditioned by I. Closing by reconstruction is defi ned as: φ B rec=(γ B rec(IC))C (6) where: IC – complement of I. Top-hat is defi ned as: T(I)=I – γ(I) (7) Fig. 1. Surface density of vessels. A. Cortical grey matter, B. cortical white matter. Immunohistochemical reaction with antibody CD34, ×200 A B Fig. 2. Representation of input colour image (A) in YIQ colour space, B) Y, C) I, and D) Q components A B C D Folia Neuropathologica 2008; 46/4 281 Cycloid and skeletonization methods for analysis of brain vessels Fig. 3. Segmentation of I image (Fig. 2): A) top-hat, B) thresholding and C) result A B C Fig. 4. Results of length estimation of fi gure 2A image: A) skeleton and B) overlay on fi gure 3C A B Fig. 5. A. Section with immunohistochemical reac- tion with antibody CD34 with haematoxylin con- trast stain, B. surface with cycloid grid (×200) Fig. 6. Sine-weighted curves, cycloids 2π 2 Length Width 1 282 Folia Neuropathologica 2008; 46/4 Tomasz Stêpieñ, Boguslaw Obara In the paper, the author recapitulates the results of research of development and application of an image analysis tool for automatic segmentation and length estimation of 54 microscopic images of fetal brain vessels. The image analysis and processing algorithms were applied to estimate the length of vessels of 54 microscopic images of fetal brain vessels. A sample of input image was used to present the main idea of the procedure. The RGB to YIQ colour system trans- formation was used as a pre-processing procedure for analysed images, where the YIQ representation of the image from Figure 2A is presented on Figures 2B, 2C and 2D. Fig. 9. Test square Fig. 7. Length density of vessels by cycloid me- thod age (GW) 0,020 0,018 0,016 0,014 0,012 0,010 0,008 0,006 0,004 0,002 0 le n gh t d en si ty ( μ /μ m 2 ) 11 12 14 16 17 18 19 21 22 cortical grey matter cortical white matter Fig. 8. Length density of vessels by skeletoniza- tion method age (GW) 0,020 0,018 0,016 0,014 0,012 0,010 0,008 0,006 0,004 0,002 0 le n gh t d en si ty ( μ /μ m 2 ) 11 12 14 16 17 18 19 21 22 cortical grey matter cortical white matter Fig. 10. Pruning method iterations: A) input ske- leton, B) detected end points and nodes, C) fi rst step of pruning, D) fi nal step of pruning (...) A) B) C) D) The main steps of image segmentation procedure are shown in Figure 3. The image segmentation pro- cedure was based on mathematical morphology. At fi rst, the analyzed image was fi ltered by a morpholo- gical top-hat fi lter (Fig. 3A), then the image was thre- sholded and the result is shown in Figure 3B, 3C. Segmented images of fetal brain vessels were used in the length estimation. The length analy- sis algorithm was based on a technique proposed by Fuller et al. [10]. They presented the techniques developed for automatic detection of fi laments on Meudon Hα spectroheliograms, and, by extension, on any full-disk Hα Sun observations. The fi laments were then segmented with a region growing method, which effi ciently refl ects the full extent of these dark areas. The fi laments were fi nally described by means of their pruned skeleton. The length estimation of fetal brain vessels from Figure 2A, based on Fuller’s method (Fig. 4). Colour system transformation (C++ – author’s im- plementation) and image analysis algorithms (Aphe- lion TM – C++ library) [1] were developed in Aphelion ADCIS software and used for the segmentation of the microscopic images of fetal brain vessels. Folia Neuropathologica 2008; 46/4 283 Cycloid and skeletonization methods for analysis of brain vessels Cycloid method Morphometry is a body of mathematical methods relating “geometrical parameters” (such as volume and surface area) of spatial objects to lower dimen- sional measurements obtainable on a section of the structure [2,23]. Morphometric methods enable one to estimate some parameters of anisotropic objects on a section. The length in 2D could be estimated on the basis of various intersections between a line-probe and the linear objects of interest [5]. In our study, we used the stereological method with systematically spaced sine-weighted curves (cycloids) of known length, in our case being 53.1 μm. The counting grid constructed of sine-weighted lines (cycloids) can be used with the vertical section for estimation of lengths and surface areas (Fig. 6). The cycloid test system lines on vertical sections have an isotropic orientation distribution within the three- dimensional structure [2]. The curve has parametric coordinates (θ – sin θ, 1 – cos θ) where θ is the angle between a test line segment and vertical axis. All sections were collected using a 20x- magnify- ing objective. The surface density of vessels (Fig. 5B) is estimated on the basis of intersections between the cycloids and the brain surface and the number of test points (crosses at each end of cycloid arcs). To avoid bias, all cycloids must be positioned equ- ally randomly with respect to the section and their minor principal axis must be parallel to the selected vertical axis [22]. The fi nal calculation of length den- sity of vessels was a result of multiplying two times the sum of total intercepts and area per unit cycloid length through the section sampling fraction and the area sampling fraction. (1) i i (2) (3) (4) p/l – test points per unit length of cycloid, n – num- ber of probes, I i – intercepts, P i – test [I L C]ρη – mean intercepts of projected images per unit length of cycloid, Δ – section thickness, points. (5) (6) where estL = total length of capillaries (μm), al – – area per unit cycloid length, Σl – total intercepts, ssf – sec- tion sampling fraction, asf – area sampling fraction, t – section thickness, h – height of counting frame Photography Photos shown in Figure 1 were produced by a digi- tal photography workstation. Photomicrographs (Fig. 5A-B) were produced by digital photography using an Olympus U-CMAD-2 digital camera attached to an Olympus AX 70 microscope. The fi nal fi gures were constructed using Photoshop v.7. Adjustments of contrast and brightness were made to facilitate re- cognition of the immunohistochemical signal at low high magnifi cation, without altering the appearance of the original materials. The images were registered in RGB (red, green, blue) colour system with standard resolution of 10 000×10 000 pixels. Results We analyzed 54 images of 9 fetal brains aged 11 to 22 GW. The morphometric measurements were per- formed on 2D pictures of samples marked with CD34. In our research, we used two morphometric image analysis methods. Only CD34 marked blood vessels were included in counting. In the cases studied with the cycloid method, there were major fl uctuations ob- served between 11 GW (CGM – 0.01095 μ/μm2; CWM – 0.01034 μ/μm2) and 22 GW (CGM – 0.009361 μ/μm2; CWM – 0.00900 μ/μm2) (Fig. 7). A remarkable drop in length of blood vessel network density was observed in GW 17 and 18. Changes in the length of blood vessel network density in GW 11 to 16 (CGM – 0.01020 μ/μm2; 284 Folia Neuropathologica 2008; 46/4 Tomasz Stêpieñ, Boguslaw Obara CWM – 0.00672 μ/μm2), both in the cortical grey matter and in the cortical white matter, did not pro- ve statistically signifi cant. However, the reduction of the length of blood vessel network density in GW 17 (CGM – 0.00466 μ/μm2; CWM – 0.00577 μ/μm2) and in GW 18 (CGM – 0.00367 μ/μm2; CWM – 0.00407 μ/μm2), both in the cortical grey matter and in the cortical white matter, proved signifi cant. We found statistically signifi cant changes between GW 11 and GW 17 (CGM – p<0.039; CWM – p<0.01), as well as between GW 11 and 18, in the length of blood vessel network density (CGM – p<0.0087; CWM – p<0.001). We also established statistically signifi cant diff eren- ces in the length of blood vessel network density be- tween GW 17 and 21, both in the cortical grey matter and in the cortical white matter (CGM – p<0.01; CWM – p<0.002), as well as between GW 17 and 22 (CGM – p<0.019; CWM – p<0.03). We got similar results when comparing the length of vascular network den- sity between GW 18 and 21 (CGM – p<0.004; CWM – p<0.001). Also, between GW 18 and 22, the diff e- rence in the length of vascular network density sho- wed statistical signifi cance (CGM – p<0.004; CWM – p<0.003), whereas it did not between GW 14 (CGM – 0.00660 μ/μm2) and GW 18 (CGM – 0.00367 μ/μm2) as regards the cortical grey matter. Next, we analy- zed the test sample using skeletonization (Fig. 8). The results did not show as high fl uctuations as in the cycloid method analysis. The length of vascular network density between GW 11 (CGM – 0.00434 μ/μm2; CWM – 0.00419 μ/μm2) and GW 16 (CGM – 0.00273 μ/μm2; CWM – 0.00405 μ/μm2), both in the cortical grey matter and in the cortical white matter, is similar. What is remarkable, however, is the drop in length density of the vascular network in GW 18 (0.001189 μ/μm2), both in the cortical grey matter and in the cortical white matter. The increase in the vascular network length density in the cortical grey matter is similar between GW 19 (CGM – 0.00426 μ/μm2) and GW 22 (CGM – 0.00385 μ/μm2), whereas in the cortical white matter it is sinusoidal, reaching an extreme in GW 21 (0.00452 μ/μm2) and dropping in GW 22 (CWM – 0.00266 μ/μm2). Discussion Skeletonization and cycloid methods could be suc- cessfully applied in 2D image analysis. In our study in the cortical grey matter with the cycloid method were on average 45% higher than those from skeletoniza- tion and as much as 57% higher in the cortical white matter (Table I). Such diff erent results made us use both methods in analyzing objects of known length. Thus, we measured the circumference of a square of 250 μm side by skeletonization (1000 μm) and by cyc- loid method (1319 μ m) (Fig. 9). The outcome confi r- med the diff erences in the study results, which stem from the algorithms used. Skeletonization, consisting in selecting axial points (skeletons) of fi gures, allows for measurement of absolute length of objects on the surface (Fig. 10) [16], whereas the cycloid method, in- cluded in Stereo Investigator Software (MicroBright- Field), is a method of estimation which consists of a known-length cycloid grid and counting intersection points (Fig. 5B). This procedure has a high error bur- den and should be used only very cautiously in 2D Table I. Comparison lenght density of vessels network by cycloid and skeletonization method Age (GW) Lenght density of vessels (µ/µm2) cycloid method skeletonization method cortical gray matter cortical white matter cortical gray matter cortical white matter 11 0.01095 0.01034 0.00434 0.00419 12 0.00766 0.00968 0.00275 0.00365 14 0.00660 0.01192 0.00318 0.00432 16 0.01020 0.00672 0.00273 0.00405 17 0.00466 0.00577 0.00301 0.01139 18 0.00367 0.00407 0.00119 0.00115 19 0.00664 0.00743 0.00426 0.00352 21 0.008198 0.01139 0.00410 0.00452 22 0.009361 0.00900 0.00385 0.00266 Folia Neuropathologica 2008; 46/4 285 Cycloid and skeletonization methods for analysis of brain vessels image morphometric analysis. A good solution seems to be skeletonization, which enables absolute length densities of studied blood vessels to be specifi ed in 2D images. In both methods, we observed a remar- kable drop in length density of vascular network in GW 18. This may be explained by intensive migration of neurons and glial cells and delayed angiogenesis, which changes the relation between blood vessels and the surface of the section, and which might re- sult in reduced vascular length density. The reduction of vascular length density might result from develop- mental atrophy of blood vessels, combined with their diff erentiation [8]. In such a case, the vascular atro- phy might consist of vascular endothelial cells (VECs) in apoptosis [13], which results from reduced vascular fl ow and macrophage function [12]. Morphometric studies may be a good tool for analyzing vasculoge- nesis and angiogenesis in the brain development pro- cess. The cycloid method could be applied to measure approximate length density of vessels. However, ske- letonization should preferably be applied to measure the precise length density of vessels in the cortical grey matter and the cortical white matter. 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