COLLAGEN ORIENTATION AND WAVINESS WITHIN THE VEIN WALL

Transcription

1 XI International Conference on Computational Platicity. Fundamental and Application COMPLAS XI E. Oñate, D.R.J. Owen, D. Peric and B. Suárez (Ed) COLLAGEN ORIENTATION AND WAVINESS WITHIN THE VEIN WALL JAN VESELY *, LUKAS HORNY *, HYNEK CHLUP * AND RUDOLF ZITNY * * Faculty of Mechanical Engineering Czech Technical Univerity in Prague Technicka 4, Prague, Czech Republic Jan.Veely1@f.cvut.cz, Key word: Vena cava, Blood veel architecture, Collagen, Fiber orientation ditribution, Aniotropy Summary. Thi paper preent the analyi of the internal tructure and organization of component within the vein wall. Dominant direction and tatitical ditribution of collagen fiber undulation were invetigated in digitalized hitological ection from media and adventitia layer of human vena cava inferior. Orientation of collagen fiber were analyzed by the in-houe developed oftware Binary Direction. Digital image were converted to binary pixel map with collagen fiber enhanced. The oftware employ an algorithm of the Rotation Line Segment to determine ignificant direction in digital image. It wa found that collagen fiber are aligned in circumferential direction in media layer. Contrary to that in adventitia fiber are arranged in longitudinal direction. In contrat to elatic artery, no evidence of helically reinforced compoite tructure wa found. Second goal wa to find out which tatitical ditribution, uually uing in tructural model (Gamma, Beta or Weibull), fit to the undulation ditribution of collagen fiber. Collagen wavine wa characterized by a probability denity function for the train neceary to traighten a crimped fiber. Computer analyi of the end-to-end and contour length wa performed uing Ni-Element oftware. The tatitical analyi ugget that the wavine of collagen fiber i identical in media and adventitia It wa found that the average train neceary for traightening collagen fiber i 0.24±0.11 (±SD) and that all three probability ditribution fit traightening train very well and can be ued in tructural model. 1 INTRODUCTION In recent year a big increae in interet in contitutive model of biological tiue baed on their microtructure wa noticed. Biological tiue comprie a large number of different cell, matrix protein and bonding element. For effective development of tructural contitutive model, good undertanding of internal tructure and organization of the material i neceary. According to [3], the gro mechanical repone of oft tiue i attributed to the mechanical propertie and geometrical arrangement of the tiue component: fiber familie (collagen and elatin) and ground ubtance. The fiber are oriented in different direction and

2 have different undulation (wavine) in the tiue. Upon loading, the fiber loe their wavine and tart to carry a load [1]. It i aumed that gradual recruitment of collagen fiber under a deformation lead to a typical non-linear behavior of oft tiue. A number of invetigator have analyzed the fiber orientation and crimp ditribution to implement them into tructural mechanical model [1, 3, 6, 9]. Thi paper deal with hitomorfometrical analyi of internal tructure of the vein wall. Dominant direction and ditribution of undulation of collagen fiber were invetigated in hitological ection from media and adventitia layer of human vena cava. 2 METHODS COLLAGEN FIBERS ORIENTATION Hitological ection were obtained from abdominal vena cava inferior. The orientation of ection and the definition of collagen fiber angle are hown in Fig. 1. Specimen were routinely fixed in 10% buffered formaldehyde, embedded in paraffin, cut, and tained with orcein. Digitalized image were evaluated by in houe developed oftware BinaryDirection with implemented algorithm of the Rotating Line Segment (RoLS). Figure 1: Definition of the angle. Digital image were converted to binary pixel map by treholding of RGB filter which tranform tained collagen to white (logical unity) pixel and non-collagen component to black (logical zero) pixel. Binary converion wa realized by oftware NIS-Element (NIKON INSTRUMENTS INC., USA, New York). Final orientation were obtained by averaging reult from 5 hitological ection from each layer (media and adventitia). 2.1 ROLS Algorithm Exact mathematical formulation of the Rotating Line Segment (RoLS) wa decribed in detail in [2]. Hitological ection converted to binary pixel map canbe viewed a the matrix with element uniquely correponding to pixel. Element are equal to either zero or unity depending on the pixel color. The algorithm explore neighborhood of each non-zero pixel 2

3 (called target pixel) in the image uing the rotating line egment. The neighborhood of the target pixel i a quare repreented by NxN ubmatrix M, where N i an odd integer. Now, imaginary line egment i rotated tep by tep around the midpoint of the neighborhood. Each rotating tep,, of the line egment i repreented via additional NxN matrix, ay L. L ha only non-zero element in poition correponding to the rotated line egment. The aim of RoLS i to find dominant direction in an image. Thi procedure i baed on ocalled matching coefficient, C(). The matching coefficient i normalized number of non-zero pixel hared with the line egment and neighborhood of target pixel at given rotating tep : C N N i1 j1 M Nl ij L ij (1) l N N L ij i1 j1 Normalization procedure i related to length of quare neighborhood N and number of pixel creating the line egment, l. There are two way how to obtain relevant information about directional frequency of nonzero (collagen) pixel in the neighborhood of target pixel. Firt, one can reduce information from pixel neighborhood to the mot frequent angle (rotation tep with the greatet C()) and create hitogram over the entire image (all target pixel). The econd way i to conider C() a a function of in each pixel and averaged thee function through all target pixel. Obtained reult may depend on N, therefore analye hould be repeated with different value of N and the N hould be choen with repect to characteritic dimenion of tructure oberved in image (eye of expert are the bet optimization tool, a uually). Image-baed determination of tiue architecture may employ many kind of algorithm and mathematical method. Preented algorithm, RoLS, i imilar to the o-called volume orientation (VO) method which operate with point grid and eek for the longet intercept in target volume. VO wa firt decribed in Odgaard et al. [4]. It wa found to be uitable within an analyi of bone architecture. Intereted reader can track detail in [5] or recent review [7]. 2.2 Tet image Tet binary image were evaluated by BinaryDirection before proceing hitological ection to verify that thi oftware i a uitable intrument for fiber orientation analyi. Selected teted image and reult are hown in Fig. 2. Evaluating of teting image howed that oftware BinaryDirection i convenient for determining dominant direction in binary image. (2) 3

4 Figure 2: Teted binary image and empirical probability denity for evaluated image. 3 METHODS COLLAGEN FIBERS UNDULATION The fiber wavine wa characterized tatitically by a probability denity function for the train neceary to traighten a crimped fiber, Fig. 3. Figure 3: Axial fiber train S. Strain S i defined: L 1, L (3) where L o i end-to-end length of the fiber, and L i the contour length of the fiber. o 4

5 Computer analyi of the end-to-end and contour length wa performed manually uing NIS- Element (NIKON INSTRUMENTS INC., USA, New York), Fig. 4. Figure 4: Digital image from media. Meauring of length Lo and L by Ni-Element. Statitical computation were performed in Maple 13 (Mapleoft, Canada, Waterloo). The aim wa to find out uitable tatitical model for probability ditribution. Following ditribution were conidered: Weibull ditribution k-1 k f ( ;, k) e k -, (4) where k > 0 i the hape parameter and λ > 0 i the cale parameter of the ditribution. Beta ditribution f ;, where B i Beta function and, >0 are hape parameter. Gamma ditribution f 1 1 1, (5) B, k 1 e ; k, k k, (6) where i Gamma function, k>0 i the hape parameter and >0 i the cale parameter. In all ditribution 0. 4 RESULTS 4.1 Collagen fiber orientation Fig. 5 Left panel how an example of digital image from media and definition of angle. The ame image converted to a binary pixel map i in Fig. 5 (Right panel). The enitivity 5

6 Jan Veely, Luka Horny, Hynek Chlup and Rudolf Zitny. of the reult to the length of rotating line egment i hown in Fig. 6. It wa found that the uage of different length of the rotating egment N {61 pix, 121 pix, 181 pix, 201 pix} have not ignificant effect on the ditribution of angle. Final reult for image proceed in BinaryDirection from media and adventitia are hown in Fig. 7. Figure 5: Left: Hitological ection from media layer tained with orcein. Collagen fiber are tained in blue. Right: Binary pixel map created from hitological image in left panel. White color repreent collagen fiber. Figure 6: Left: Empirical probability denity function for elected ection from media for 4 length of line egment. Right: Empirical probability denity function for elected ection from adventitia for 4 length of line egment. 6

7 Jan Veely, Luka Horny, Hynek Chlup and Rudolf Zitny. Figure 7: Reulting averaged empirical probability denity function for axial cut from media (red) and adventitia (blue). It wa found that collagen fiber in media are aligned in circumferential direction. Contrary to that fiber in adventitia are oriented in longitudinal direction. 4.2 Collagen fiber undulation Strain were evaluated for media and adventitia eparately. The Chi-Square Goodneof-fit tet wa performed to decide if the data may be conidered a drawn from one tatitical ample. The tet uggeted that it i poible to merge the data from media and adventitia together (P-value = 0.74). The hitogram of obtained train neceary for the traightening and the fit of experimental data by the Weibull, Beta and Gamma probability ditribution, Fig. 9. The average value of traightening train i =0.24 ± 0.1 (±SD). It wa found that all three probability ditribution fit experimental train very well. The bet fit wa achieved with the Beta ditribution (α = 4.20, β = 12.58). 7

8 Figure 8: Fitting of obtained train (from media and adventitia) by Weibull, Beta and Gamma probability ditribution. 5 DISCUSSION The analyi of the hitological image from human abdominal vena cava howed that collagen fiber are in media oriented in the circumferential direction with very compact organization of the collagen. Converely, in adventitia collagen i aligned with the longitudinal direction with pare arrangement of fiber. Thi arrangement of component within the vein wall differ from arrangement for example in aorta. Thi may be a conequence of another type of loading, where keletal mucle are helping venou return mechanim. There i alo lower blood preure in vein than in arterie. Our reult ugget that collagen fiber form unidirectional tructure in each layer of the vein. The ditribution of undulation of collagen fiber in human vena cava can be fitted by all three conidered tatitical ditribution. The Beta ditribution fit the bet. The tatitical analyi ugget that the wavine of collagen fiber i identical in media and adventitia. It wa found that the average train neceary for traightening collagen fiber i Thee reult differ from finding by Sokoli [8], who invetigated the wavine of medial collagen in vena cava inferior in New Zealand rabbit (averaged =0.57). It uggeted peciedependent wavine. 8

9 ACKNOWLEDGEMENTS Thi work ha been upported by the Czech Minitry of Education project MSM ; Czech Science Foundation GA106/08/0557; and Grant Agency of the Czech Technical Univerity in Prague SGS10/247/OHK2/3T/12. REFERENCES [11] De Vita, R. Structural contitutive model for knee ligament. Diertation thei, Univerity of Pittburgh (2005) [2] Horny, L., Hulan, M.; Zitny, R.; Chlup, H.; Konvickova, S.; Adamek, T. Computer-Aided Analyi of Arterial Wall Architecture. IFMBE Proceeding, vol. 25/4, World Congre on Med. Phy. & Biomed. Eng., Munich, Germany (2009) [3] Lanir, Y. Contitutive equation for fibrou connective tiue. Journal of Biomechanic (1983) 16:1 12 [4] Odgaard, A.; Jenen, E.B.; Gunderen, H.J.G. Etimation of tructural aniotropy baed on volume orientation. A new concept. Journal of Microcopy (1990) 157: [5] Odgaard, A. Three-dimenional method for quantification of cancellou bone architecture. Bone (1997) 20: [6] Sach, M.; Sun, W. Multiaxial Mechanical Behavior of Biological Material. Annual Review of Biomedical Engineering (2003) 5: [7] Sander, E.A.; Baroca, V.H. Comparion of 2D fiber network orientation meaurement method. Journal of biomedical material reearch. Part A (2009) 88A: [8] Sokoli, P. D. Paive mechanical propertie and contitutive modeling of blood veel in relation to microtructure. Med Biol Eng Comput (2008) 46: [9] Zullinger, M.; Fridez, P.; Hayahi, K.; Stergiopulo, N. A train energy function for arterie accounting for wall compoition and tructure. Journal of Biomechanic (2003) 37: