Quantitative analysis of collagen fiber angle in the submucosa of small intestine

Computers in Biology and Medicine 34 (2004) 539 – 550 www.elsevierhealth.com/locate/compbiomed

Quantitative analysis of collagen %ber angle in the submucosa of small intestine Jidong Yua , Yanjun Zenga;∗ , Jingbo Zhaob , Donghua Liaoa; b , Hans Gregersenb a

b

Biomechanics Lab., Biomedical Engineering Center, Beijing Polytechnic University, Beijing 100022, China Center for Sensory-Motor Interaction, Aalborg University and Department of Surgery, Aalborg Hospital, Denmark Received 4 December 2001; received in revised form 23 June 2003; accepted 23 June 2003

Abstract It is of interest to know how distension changes the angle and content of collagen in the submucosa of small intestine. We describe the application of a two-dimensional quantitative analysis technology to determine the angles between collagen %bers in the submucosa using digital image processing. A polarization microscope was used to obtain a series of animal intestinal slice images. The images were studied by analyzing the relationship between the pixel values of each of the polarized angles to obtain the collagen %ber angle. The statistical distribution of the angle as function of the degree of distension can be analyzed. ? 2003 Elsevier Ltd. All rights reserved. Keywords: Intestinal submucosa; Image processing; Collagen %ber angle; Scleroderma; Intestinal slice

1. Introduction The composition of collagen %bers and their distribution in the tissue may change in di=erent diseases. The directional distribution of collagen %bers plays an important role in function and soft tissue repair [1–9]. Digital image processing technology has o=ered an accurate, simple and rapid method to analyze a large amount of medical images, especially for quantitative analysis of smaller pictures, such as microscopic images. Several techniques have been used to study the quantitative analysis of collagen %ber distribution, such as quantitative polarized light microscopy, small angle scattering image analysis and X-ray di=raction [1–9]. However, these methods are limited in the image size, processing time and to de%ne the orientation angles to 90◦ [9]. Collagen %bers in the small intestine at a pressure-free ∗

Corresponding author. Tel.: +86-10-673-92172; fax: +86-10-673-91738. E-mail address: [email protected] (Y. Zeng).

0010-4825/$ - see front matter ? 2003 Elsevier Ltd. All rights reserved. doi:10.1016/j.compbiomed.2003.06.001

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state are oriented at approximately +30◦ and −30◦ to the longitudinal direction. It is likely that the collagen %ber angle change with the intestinal pressure but this issue has not been studied so far. The purpose of this study is to introduce a method to analyze 2D collagen %ber angles and their distribution in the submucosa of the normal small intestine and to obtain the relationship between collagen %ber angles and the distension pressure. The images were collected in a semiautomatic way and the analysis was processed automatically. This method can also be applied to other soft tissues, such as ligaments, tendons and cardiac muscle. 2. Materials and methods 2.1. Optical principle In polarized light microscopy, polarized light is delivered onto the sample for analyzing and handling after being passed through a second %lter glass. When the angle between the optical axis of two polarizing lenses is 0◦ (i.e. the two optical axes are parallel to the muscle direction), the collagen %bers that are parallel to the optical axis will be the darkest, i.e. the minimum pixel value domain. Therefore, the areas with collagen %bers parallel to muscle direction and the area ratio between the objective domain and the entire analysis area can be obtained. The muscle direction was set to coincide with the optical axis of polarizing objective by maintaining the objective lens stationary. When the polarizing eyepiece is rotated ◦ , all areas with collagen %bers at ◦ or 90 + ◦ with the muscle %ber will be the darkest [10–12]. Using a method similar to the one mentioned above, the areas at ◦ and 90 + ◦ with the muscle %ber and the corresponding area ratio with the entire analysis domain will be obtained. Hence, the relationship between the area ratio at each angle and collagen angle can be calculated. The collagen %ber distributions are uniform and are presented as reticular distribution. Moreover, the angles between the longitudinal and latitudinal collagen %bers and the muscle %bers are +30◦ and −30◦ . Therefore, the area ratio of these two direction’s collagen %bers is the largest, and the collagen %ber angle can be reckoned from the area ratio. In this paper,  was set as 5◦ to test our method.  can also be set as other values, and the smaller the , the more accurate the %ber angle obtained. 2.2. Isolation of small intestine Seven Sprague–Dawley rats (250 –300 g body weight) were used. They had free access to water but were fasted for 24 h before the experiment. The animals were killed by cervical dislocation. The abdomen was opened and the small intestine was separated from adjacent organs. An 18-cm-long segment from the middle part of small intestine (jejunum) was cut and excised within 2 min, and transferred to an organ bath containing oxygenated Krebs solution at pH 7.4 with 6% Dextran and 0.25% EGTA. 2.3. Procedures The 18-cm long intestinal segment was cut into six 3-cm-long segments. One of the six segments served as a control and was %xed in 4% formalin in no-load condition. One end of the remaining %ve segments was ligated while the other end was connected via a tube to a Muid container for application

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Fig. 1. Schematic diagram of the distension system.

of pressures in the range 2–20 cm H2 O to the intestinal segment (Fig. 1) [13]. After applying each pressure for 3 min, a record of the whole intestine segment was obtained by using a video camera (SONY CCD/RGB, JAPAN). The outer diameter on the di=erent segments was measured from the digitized images. The outlet was clamped to maintain the volume, and the segment was placed in 4% formalin for 24 h and used for later preparation of histological slice. Previous studies on collagen orientation have shown that formalin could be used to %x the collagen tissue [14,15]. 2.4. Slice preparation After the specimen was %xed for 24 h, longitudinal and transverse segments were taken from the middle of the specimen. The longitudinal segment was 1:0 cm long and the transversal segment 0:5 cm. Then, the specimens were dehydrated in a series of graded ethanol (70%, 90%, 95% and 100%) and embedded in paraQn. Serial sections (5 m) were longitudinally cut from di=erent layers (adventitia, middle or muscle layer, submucosa and mucosa) and 5 m transversel sections were cut. ParaQn was cleared from the slides with coconut oil (15 min, 40 –60◦ C). The sections were then rehydrated in 99%, 96% and 70% ethanol followed by a 10 min wash in water. The tissue was then stained with picrosirius red and hemotoxylin and eosin. The slides were used for collagen analysis [16–21]. 2.5. Image acquisition A diagram of the data acquisition process is illustrated in Fig. 2. The system can be divided into two major parts: collecting and analyzing. Each part has its own function. The collecting part is made up of the polarized light microscope, a recording system and an image collecting card. The polarized light microscope includes an electronic biology microscope with polarized light lens (polarizer), an analyzer and a %xing platform. The polarizer and analyzer are cross installed and they can be revolved around the microscope optical axis to spin for obtaining polarized images from di=erent angles. The recording system has a low illumination and a high resolution for recording and monitoring images simultaneously by connecting with the time generator to record time and the

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Fig. 2. Diagram of the system for image acquisition.

image collecting card to record the image information into the computer. The image analyzing part is made up of PC digital computer and external equipment. A series of polarized images were acquired by the recorder through the microscope at every ◦ , and stored as TIFF form (RGB system type) via image collecting card on the computer. ◦ is the polarized light angle interval by which the eyepiece is being rotated. 2.6. Image processing Image processing is based on pixel analysis. The processing procedure in this study was executed as follows: (1) normalize the pixel values, (2) %gure out the results using proper algorithms, (3) sum up all the data for curve %tting, and (4) %nally obtain the collagen %bers angles. The image format used in this study is the TIFF format which is a commonly used format of multipurpose character. It is not only suitable for handling the image data produced by an image scanner, but also for storing data in other forms. TIFF %les adopt a 24-bit non-compressed format of high resolution. The most important reason for selecting TIFF format is that the pixel values in the polarized image are suitable for the principles presented previously [20–22]. From the TIFF images an optimum threshold value was decided. Since the polarized intestine section image is stored at every  degree, the number of images and the %le name of each image were input into the system. 2.6.1. Pre-processing image 9ltering The images contained data both from the submucosa and the nearby muscle layers (Fig. 3(1)). It was therefore necessary to de%ne a region of interest. A %lter process on the original image is necessary to reduce the noise before image analysis and to select the intermediate gray level that only has collagen %bers. In this study, a frequency domain strengthening method was selected for reducing the noise. Because both the edge and the noise in the image correspond to the high-frequency section of the image’s Fourier transformation, the way to reduce the noise e=ects to the frequency domain is to weaken the frequency in this area. A Butterworth low-pass wave %lter was used in this study because the low-pass Butterworth special wave %lter provides a smooth transition between the frequencies. The ringing e=ect of the Butterworth wave %lter’s output will not a=ect the results.

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Fig. 3. Original and polarized images obtained from the small intestine: (1) original image; (2) polarized image ( = 0◦ ); (3) polarized image ( = 5◦ ); (4) polarized image ( = 10◦ ).

A Butterworth wave %lter with n steps and D0 as truncated frequency has the transfer function H (u; v) =

1 : 1 + [D(u; v)=D0 ]2n

(1)

Taking the truncated frequency as 50% of the highest value of H for the polarized image shown in Fig. 3(2), a mean-square deviation was selected for optimization before designing an optimum wave %lter due to its complex noise signals. If s(t) was de%ned as image input, h(t) as the wave %lter, and y(t) as the output, then the error e(t) = s(t) − y(t):

(2)

This is the di=erence between the real output and the expected output, and this di=erence is a function of time. The better the h(t) selected, the smaller the error signal. The mean-squared error is de%ned by
∞ 2 e2 (t) d(t) (3) MSE = {e (t)} = −∞

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Fig. 4. Schematic diagram for optimum threshold value selection. P1 (z), and P2 (z) are the pixel value probability density function of the goal area and the background area, E1 (t) and E2 (t) are error the probability for the goal area and the background area.

Spreading out Eq. (3) then, yields MSE = {e2 (t)} = {[s(t) − y(t)]2 } = {s2 (t) − 2s(t)y(t) + y2 (t)} = T1 + T2 + T3 :

(4)

2.6.2. Determination of threshold value The collagen %ber orientation can be completely obtained from the pixel values of the selected area. Therefore, selecting an optimal threshold value becomes the most important step for obtaining an accurate result. In order to acquire the threshold value in the polarized image (Fig. 3(2) – (4)), the threshold selecting method must be repeated many times in the image slices and related to pixel values. For reducing the probability of incorrect isolation, an optimal threshold value selecting method is performed in this study. Fig. 4 is an approximation of the pixel value probability density function p(z). The density function is a sum of the two unimodal density functions that require isolation. With the known density function, then an optimum threshold value can be found for dividing the image into two areas (goal area and background area ) and to obtain the minimized error. The mixed probability density function in Fig. 4 is de%ned by     P2 (z − 1 )2 (z − 2 ) P1 p(z) = P1 p1 (z) + P2 p2 (z) = √ exp − + √ exp − ; (5) 212 222 1 2 2 2 where 1 and 2 are, respectively, the average pixel values of goal area and background area, and 1 and 2 are the corresponding mean square deviations. P1 and P2 are the prior probability of the pixel values of the goal area and of the background. There are %ve unknown parameters that need to be solved in the mixed probability density function in terms of the probability de%nition of P1 + P2 = 1. Assuming 1 ¡ 2 , as shown in Fig. 4, a threshold value T is selected to make pixels whose values are smaller than T as goal area, while larger than T as the background. Then the probabilities of mistaking a goal pixel as a background pixel or mistaking a background pixel as a goal pixel are, respectively,
T
∞ E1 (T ) = p2 (z) d z and E2 (T ) = p1 (z) d z: (6) −∞

T

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The total error probability is E(T ) = P2 E1 (T ) + P1 E2 (T ):

(7)

To acquire the optimum threshold value that has the minimum error, E(T ) is di=erentiated with respect to T and the derivative is set to 0 and hence P1 p1 (T ) = P2 p2 (T ):

(8)

By substitution into Eq. (5), we get X = 12 − 22 ;

(9)

Y = 2(1 1 2 − 2 2 2);

(10)

Z = 1 22 2 − 2 21 2 + 21 22 2 ln(2 P1=1 P2):

(11)

Normally, there are two roots for this quadratic equation. However, if the variances of these two areas are equal, there is only one root, i.e. the threshold value   2 1 +  2 P2 + Toptimal = : (12) ln 2 1 −  2 P1 Furthermore, if the prior probabilities of the two pixel values are equal (or the variance is zero), then the optimum threshold value is the intermediate value of the average pixel values in the two areas. The parameter p(z) of the image’s mix probability density function [22] can be obtained by using the mean square minimum di=erence method. 2.7. Image reading With an open designated polarized image, the pixel values of the selected area can be read into three m × n matrixes a1, a2, a3, respectively, in which m (0 –732) is the number of lateral pixels, and n (0 –549) is the number of longitudinal pixels. The three matrixes are the RGB values of the image (unit8 mode). 2.8. Data processing Only if the unit8 mode pixel values transformed to double mode can they be operated on mathematically. In order to pick up as much information from each pixel as possible, the three matrixes are normalized as a(i) = double(aij);

(13)

F(m; n) = Sa(i):

(14)

The matrix F(m; n) is used for further processing, where the pixel values smaller than the selected threshold value is the collagen %ber in the polarized image. Calculate the pixel number whose value is smaller than the selected threshold value s(j), and de%ne s(j) b(j) = ; (15) m×n

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where b(j) is the area ratio of the collagen %ber area to the focused area in polarized image number j. Then, the ratio sequence of image series can be obtained and saved in array Y (j).

3. Results The analysis results are shown in Table 1. For the same slice, the area ratio changed with di=erent polarized angles, and for di=erent slices with the same polarized angle, the area ratio also changed with pressure. The largest area ratios are determined by both the distension pressure and the polarized angles. For instance, with the distension pressure of 0 cm H2 O, the biggest ratio is 0.7666 at the angle of 30◦ . It means that the collagen %ber angle is mainly 30◦ at the pressure-free state. Fig. 5 shows on the abscissa the polarized angle and on the ordinate the area ratio. The relationship between the distension pressure and the %ber angles are shown in Fig. 6. The %ber angles are obtained

Table 1 Area ratio of the slice images at di=erent polarized angles at various distension pressures Pressure (cm H2 O)

0◦

5◦

10◦

15◦

20◦

25◦

30◦

35◦

40◦

45◦

0 2 5 10 15 20

0.7288 0.7649 0.6817 0.7162 0.7139 0.7548

0.7465 0.7713 0.6874 0.7375 0.7285 0.7700

0.7016 0.7732 0.6959 0.7563 0.7455 0.7885

0.6694 0.7890 0.7118 0.7877a 0.7611 0.8125

0.6238 0.7576 0.7535 0.7730 0.7760 0.8270a

0.5978 0.7399 0.7591 0.7469 0.8337a 0.7807

0.7666a 0.7245 0.7632 0.7272 0.8000 0.7457

0.5290 0.7956a 0.7744 0.6866 0.7693 0.7400

0.4852 0.6730 0.7976a 0.6764 0.7580 0.7372

0.4669 0.6654 0.7664 0.6684 0.6873 0.7320

a

The biggest ratio of this slice image.

Fig. 5. The area ratio distributions as function of the angle at distension pressures from 0 –20 cm H2 O.

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Fig. 6. The relationship between the distention pressure and the collagen %ber angle.

Fig. 7. The relationship of the maximum area ratio and the distension pressure.

from Table 1 where the obtained %ber angles correspond to the largest area ratio in each pressure state. The distension pressure and the biggest area ratio are shown in Fig. 7. 4. Discussion Table 1 shows that the area ratio in the same slices with various polarized angles changed signi%cantly under the same distension pressure. Fig. 7 shows that the biggest area ratios of images changed with the distension pressure. It seems that the collagen %ber angle is not directly proportional to the pressure applied. The possible reason is that the collagen %ber needs stress relaxation during the intestinal distension. We will test this in future studies. Using other methods to change its stress still needs to be tested in future experiments. This method has good reproducibility. Furthermore, the smaller the  used, the more accurate the %ber angle acquired. This method of calculating collagen %ber angle through the pixel value ratios has its feasibility and reliability, and this type of quantitative analysis allows greater area of soft tissue to be analyzed with

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relatively lower cost and simple equipment. The disadvantage of this method is that the selection of the threshold value a=ects the accuracy. However, this disadvantage can be overcome by repetitive computations. In this paper, we proposed a quantitative analytical method to acquire the collagen %ber angle of soft tissue in the intestinal slice. The method was tested and the results show that the method is practical and e=ective for basic research on gastrointestinal disease. 5. Summary Several gastrointestinal diseases change the collagen structure in the gastrointestinal tract. For example, systemic sclerosis (scleroderma) in%ltrates smooth muscle with large amounts of collagen. Gastrointestinal scleroderma is a common clinical disorder with distinct collagen %ber changes. Collagen synthesis is increased and the ratio of %ne collagen %bers increases markedly. The connective tissue between muscle %ber bundles becomes hyperplastic, and changes in the orientation of collagen %bers occur [1–8]. Obstructive diseases also change the collagen structure and content. In normal tissue, the submucosal layer consists almost entirely of collagen (it is called the skeleton of the small intestine) and it is well known that the %bers run in a cross–cross pattern with 30◦ angle to the longitudinal direction. We are interested in determining how distension changes the collagen %ber angle. This paper describes the application of a two-dimensional quantitative analysis technology to determine the angles between collagen %bers in submucosa of normal intestine through computer digital image processing using area changes. A polarization microscope was used to obtain a series of animal intestine slice images being processed under polarized light. The images were studied by analyzing the relationship between the pixel values of each of the polarized angles to obtain the collagen %ber angle. The statistical distribution of the angle as function of the degree of distension can be analyzed. The analysis results are shown in Table 1. For the same slice, the area ratio changed with different polarized angles, and for di=erent slices with the same polarized angle, the area ratio also changed with the pressure. The largest area ratios are determined by both the distension pressure and the polarized angles. For instance, with the distension pressure of 0 cm H2 O, the biggest ratio is 0.7666 at the angle of 30◦ . It means that the collagen %ber angle is mainly 30◦ at the pressure-free state. References [1] M.S. Sacks, D.C. Gloeckner, Quanti%cation of the %ber architecture and biaxial mechanical behavior of porcine intestinal submucosa, J. Biomed. Mater. Res. 46 (1999) 1–10. [2] M. Clarke, Intestine submucosa and polypropylene mesh for abdominal wall repair in dogs, J. Surg. Res. 60 (1996) 107–114. [3] S.F. Badylak, Small intestine submucosa as a large diameter vascular graft in the dog, J. Surg. Res. 47 (1989) 74–80. [4] K. Fackler, L. Klein, A. Hiltner, Polarizing light microscopy of intestine and its relationship to mechanical behaviour, J. Micros. 124 (1981) 305–311.

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[5] L. Klein, H. Eichelberger, M. Mirian, A. Hiltner, Ultrastructural properties of collagen %brils in rat intestine, Connect. Tissue Res. 12 (1983) 71–78. [6] G. Gabella, The cross-ply arrangement of collagen %bers in the submucosa of the mammalian small intestine, Cell Tissue 248 (1987) 491–497. [7] C.W. Doering, J.E. Jail, J.S. Janicki, R. Pick, S. Aghili, C. Abrahams, K.T. Weber, Collagen network remodeling and diastolic sti=ness of the rat left ventricle with pressure overload hypertrophy, Cardiovasc. Res. 218 (1987) 45–55. [8] P. Whittaker, D.R. Boughner, R.A. Kloner, Analysis of healing after myocardial infarct expansion, Circulation 84 (1991) 2123–2134. [9] J.P. Dickey, B.R. Hewlett, G.A. Dumas, D.A. Bednar, Measuring collagen %ber orientation: a two-dimensional quantitative macroscopic technique, J. Biomech. Eng. 120 (1998) 537–540. [10] J.M. Orberg, L. Klein, A. Hiltner, Scanning electron microscopy of collagen %bers in intestine, Connect. Tissue Res. 9 (1981) 187–193. [11] J.M. Orberg, E. Baer, A. Hiltner, Organization of collagen %bers in the intestine, Connect. Tissue Res. 11 (1983) 285–297. [12] T. Komuro, The lattice arrangement of the collagen %bers in the submucosa of the rat small intestine: scanning electron microscopy, Cell Tissue Res. 251 (1988) 117–121. [13] J.B. Zhao, X. Lu, F.Y. Zhuang, H. Gregersen, Biomechanical and morphometric properties of the arterial wall referenced to the zero-stress state in experimental diabetes, Biorheology 37 (2000) 385–400. [14] P.B. Canham, H.M. Finlay, S.Y. Tong, Stereological analysis of the layered collagen of human intracranial aneurysms, J. Microsc. 183 (Pt 2) (1996) 170–180. [15] P.B. Canham, H.M. Finlay, J.G. Dixon, S.E. Ferguson, Layered collagen fabric of cerebral aneurysms quantitatively assessed by the universal stage and polarized light microscopy, Anat. Rec. 231 (4) (1991) 579–592. [16] G. Gabella, The collagen %brils in the collapsed and the chronically stretched intestinal wall, J. Ultrastruct. Res. 85 (1983) 127–138. [17] Y.L. Yao, B. Xu, W.D. Zhang, Y.G. Song, Gastrin, somatostatin, and experimental disturbance of the gastrointestinal tract in rats, World J. Gastroenterol. 7 (2001) 399–400. [18] J.E. Jail, J.S. Janicki, R. Pick, C. Abrahams, K.T. Weber, Fibrosis included reduction of endomyocardium in the rat after isoproterenol treatment, Circ. Res. 65 (1989) 258–264. [19] C.F. Xia, Y. Huo, C.S. Tang, G.Y. Zhu, Interleukin 10 and atherosclerosis, Adv. Cardiovasc. Dis. 22 (2001) 264–266. [20] M. Eghbali, T.F. Robinson, S. Seifter, O.O. Blumenfeld, Collagen accumulation in heart ventricles as a function of growth and aging, Cardiovasc. Res. 23 (1989) 723–729. [21] X.P. Zou, F. Liu F, Y.X. Lei, Z.S. Li, Change and role of "-endorphine in plasma and gastric mucosa during the development of rat gastric stress ulceration, Shanghai Biomed. Eng. 22 (2001) 3–8. [22] J. Pickering, D. Boughner, Quantitative assesment of the age of %brotic lesions using polarized light microscopy and digital image analysis, Am. J. Pathol. 138 (1991) 1225–1231.

Jidong Yu received his M.S. major in computer application in medical image processing from Beijing University of Technology, China in 2002. He now works in Chinese National Information Center as an engineer. Professor Y.J. Zeng graduated from Tsinghua University. He worked in the bioengineering department, UCSD as a visiting professor from 1981 to 1984. Now he is the director of Biomechanics & Medical Information Institute at Beijing University of Technology. He has about 200 papers published in Chinese and overseas journals. Jingbo Zhao received the M.D. degree from the Norman Bethune University of China in 1986. He worked at the China– Japan Friendship Hospital in Beijing and became associate professor in 1994. From 1997 till now, he was a visiting researcher at Aarhus University, later in Aalborg University and the Center of Excellence in Visceral Biomechanics and Pain, Aalborg Hospital, Denmark . He is in charge of the pathology and tissue remodeling team at the Center.

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Donghua Liao graduated and obtained the Ph.D. degree from Xi’an Jiaotong University, China in 1998. From 1998 to 2000, she was a lecturer at the Biomedical Engineering Center, Beijing University of Technology. Since august 2000, she has been a postdoc at the Center of Excellence in Visceral Biomechanics and Pain, Aalborg Hospital, Denmark. She is in charge of the computer modeling and image team at the center. Hans Gregersen received the M.D. degree from Aarhus University in 1988. He has worked in Denmark, England and U.S.A. He is now the chairman of research at Aalborg Hospital in Denmark.