Microscopy: Science, Technology, Applications and Education
A.
Méndez-Vilas and J. Díaz (Eds.)
______________________________________________
Lacunarity: a complementary research tool on bone biology
G.D. Rabelo1, C.C.G. Moura2, M.E. Beletti1, and P. Dechichi1
1
Area of Morphology, Department of Biomedical Sciences, Federal University of Uberlândia, Pará Avenue 1720,
38400902, Uberlândia, Brazil.
2
Area of Cell Biology, Department of Biomedical Sciences, Federal University of Uberaba, Tutunas Avenue
490, 38061500 Uberaba, Brazil.
Histological analysis of bone samples have been used to evaluate the effect of different therapies on bone diseases, as well
as the influence of dental implant design or orthodontic forces on bone remodeling processes. Several analytical
approaches have been applied as research tools. However, few studies leading into account the relationship between
architectural parameters such as lacunarity and the functionality of several biological systems. Lacunarity is a
mathematical quantitative technique used to evaluate the canal system organization and robustness. This parameter
associated to traditional morphometric analysis such as the percentage of bone matrix is useful to evaluate the alterations
on cortical bone after different experimental treatment models. The aim of the present study was to describe lacunarity
algorithm as complementary tool to image analysis on cortical bone decalcified and histologically processed. Rabbit tibia
subject to radiotherapy was used as experimental model. The animals were divided in control (nonirradiated) and test
group (irradiated with 15 Gy cobalt-60). Seventy five days after irradiation the animals were euthanized and tibia segments
were routinely processed to histological analysis. Pictures of bone sections were taken and had their bone channels
segmented and called regions of interest (ROI). Images were analyzed through developed algorithms using the SCILAB
mathematical environment, getting percentage of bone matrix, ROI areas, ROI perimeters, their standard deviations and
lacunarity. Statistical analysis revealed significant differences (p<0.05) in bone matrix percentage, area and perimeters of
the channels, their respective standard deviations and lacunarity between the groups. The results demonstrated that the
radiotherapy causes reduction of bone matrix and modifies the morphology of bone channels network, which confirm the
relevance of the methodology to appreciate the mechanisms associated to bone turnover. The association of these
histomorphometric parameters shows great promise for improving the comprehension of bone metabolism in further
studies.
Keywords: lacunarity analysis, cortical bone, bone matrix
Introduction
Histological analysis of bone samples have been used to evaluate the effect of different therapies on bone diseases [1,2],
the influence of bone substitutes and technical procedures for bone repair and augmentation [3-5], as well as the
influence of dental implant design [6] or orthodontic forces [7,8] on bone remodeling processes. Several analytical
approaches have been applied for histomorphometric evaluation on decalcified or undecalcified bone sections [1, 7, 910]. Stain techniques for undecalcified sections, such as Von Kossa’s or Goldner’s are used to visualize the osteoid
matrix [11]. Another frequently used technique is tetracycline pulse labeling for epifluorescence, which reflects the rate
of mineralization [7,10]. A large number of histological and immunohistochemical stains can be employed on
decalcified sections in order to evaluate cortical and trabecular bone [11,12], specific matrix proteins related to
biomineralization [11], and cell viability [2]. The current literature shows a variety of parameters able to be assessed by
histomorphometry [9], including total bone volume [1,2,8,9], osteoid and mineralizing surface [1,2], percentage of
mineralized matrix [4,5], resorptive surface [11], osteoclast and osteocyte count [2,3], etc. However, these simple
surface-based histomorphometry methods don’t lead into account the intricate network formed by bone cells and bone
cylinders named osteons or Haversian systems, in which the blood vessels are entrapped, nourishing the cells [13]. The
organization of bone canals systems is crucial to development and maintenance of the cellular framework within whole
bones [13, 14], reflecting on their structure and biomechanical properties [15]. The concepts related to bone
vascularization and its spatial organization, when transformed in mathematical models, might be valuable to medical
treatment and surgical procedures [13-15]. Fractals and lacunarity are architectural parameters to describe the intricate
organization on cortical and trabecular bone [13-14,16-17]. However, little attention has been directed to the
relationship between architectural parameters such as lacunarity and the functionality of several biological systems [18].
Lacunarity is potentially useful to cortical bone measures due its potentiality to describe spatial distribution of real data
sets which demonstrate heterogeneity of structure, as demonstrated by Viana et al (2009)[13] and Rabelo et al.
(2010)[15]. This parameter associated to traditional morphometric analysis such as the percentage of bone matrix could
help to explain the earliest pathophysiological changes on cortical bone after different experimental treatment models,
such as gamma (γ) radiation to head and neck malignances treatment [15].
Irradiated bone shows moderate bone resorption with osteoclastic activity, characterized by the presence of lacunae
of cortical bone reabsorption near the medullary portion [19] and an increase in porosity [20]. These structural changes
promoted by radiotherapy on bone and its lower regeneration capacity [21] might be harmful to bone micro-structure,
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©FORMATEX 2010
Microscopy: Science, Technology, Applications and Education
A. Méndez-Vilas and J. Díaz (Eds.)
______________________________________________
which turn it an interesting model to histomorphometric analysis using lacunarity algorithm. Therefore, the aim of the
present study was to analyze the characteristics of the irradiated bone channels network using lacunarity algorithm as
complementary tool to image analysis on cortical bone decalcified and histologically processed.
Material and Methods
This study is committed to showing the the feasibility of texture measures, specifically lacunarity algorithm, to evaluate
the effects of some therapies under bone architecture and biology, also demonstrating the complementarity of this
method with traditional histomorphometric parameters. For testing purposes, 14 young rabbits (Oryctolagus cuniculus),
with average weight of 3.5 Kg were used. The project was conducted after Institutional Animal Care and Use
Committee at Federal University of Uberlândia approval. The animals were separated in two groups: Irradiated and
non-irradiated (control) and the irradiated group received, in the tibia region, bilaterally, a single acute exposure of 15
Gy (Co60, AECL MEDICAL, Phoenix Model, Kanata, Ontario, Canada) at 80 cm. The euthanasia was performed 75
days after irradiation by anesthesia overdose.
Bone biopsies with 1 cm of diameter were removed from the tibias, fixed with a 10% phosphate buffered (0.1M)
solution, pH 7.2, decalcified in 4% EDTA and embedded in paraffin. For each sample, three nonconsecutive sections
(5µm thick, separated by 100 µm) were cut perpendicular to the long axis of the bone core and stained with hematoxilin
and eosin to histomorphometric analysis. The images were obtained using a microscope (Olympus BX 40) in
conjunction with a digital camera (OLY-200 Olympus) connected to a PC microcomputer through a 3153 data
Translation card. One image with objective lens of 10X and four images with objective lens of 40X were obtained in
each section. The images captured with an objective lens 40X were assessed to osteocyte and empty osteocyte lacunae
counting, which was performed by using the ImageJ software (ImageJ 1.40g, Wayne Rasband, National Institutes of
Health, USA). These parameters were measured twice for each field in a total of 672 captured images. Numeric values
were recorded in tables and a percentage was made from the total of elements.
The images captured with objective lens of 10X were used to implement lacunarity algorithm. The images were
processed to eliminate artifacts (Fig A) and a binary image of the bony component was obtained (Fig B). A total of 168
images were analyzed using a methodology proposed by Oliveira et al. (2006), which consists in a histological analysis
performed by algorithms developed in the SCILAB mathematical environment, considering several morphological
features of bone channels and image texture characterization. Each image was segmented and analyzed separately. The
segmented bone channels were called regions of interest (ROI). The bone matrix and ROI features were analyzed
according to the following variables: percentage of bone matrix by area (the black pixels amount in the image from
which is possible to estimate the density of bone matrix in the material), ROI area (the average of the pixels number
inside the ROI); standard deviation of the ROI area; ROI perimeter (the average of the sum of the distance between
pixels along each ROI border, considering two types of adjacencies: linear and diagonal); standard deviation of the ROI
perimeter and lacunarity.
Fig. A Digitalized histological image.
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Microscopy: Science, Technology, Applications and Education
A.
Méndez-Vilas and J. Díaz (Eds.)
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Fig. B Binary image obtained through algorithms developed in the SCILAB mathematical environment.
Data were initially evaluated using Kolmogorov-Smirnov. The results through bone matrix and ROI features were
analyzed by means of the non-parametric Mann Whitney test (error probability, 5%) and the percentage of osteocytes
empty lacunae were analyzed by means of the parametric unpaired, two-tailed Student´s t test.
Results
Bone sections in irradiated and control groups maintained their histological references, as harvesian channels,
osteocytes and empty lacunae, showing basophilic tidemarks probably related to bone remodeling process in both.
The data showed significant difference in bone matrix area between the control (96.71%) and irradiated (94.25%)
groups, between area and perimeters of the channels and their respective standard deviations (p<0.05). The lacunarity
showed significant difference among the control (16.48) and irradiated (13.80) groups. There was no significant
difference in percentage of empty osteocyte lacunae (Table 1).
Table 1 – Bone matrix area, ROI area and perimeter, standard deviation (SD), Lacunarity and Empty osteocytes lacunae.
Bone Matrix
ROI
ROI area
ROI
ROI
Lacunarity
Empty Osteocyte
Groups
area (%)
area
SD
perimeter
perimeter SD
Irradiated
94.25
535.8
1245
97.74
69.34
13.80
20.60
Control
96.71
310.8
311.4
88.08
43.20
16.48
22.23
p
0.0003*
0.0173*
0.0072*
0.0437*
0.0039*
0.014*
0.3177
Lacunae (%)
Discussion
In the last years, researches enrolling biological aspects of bone behavior have progressively strengthened the
assumption that the bone tissue constituents are organized in intricate fashion [13-17, 22,23], increasing the useful of
computational mathematic methods on histomorphometric analysis [13,14,23,24]. This study used lacunarity as
mathematician tool to evaluate challenges promoted by γ radiation in bone structure.
Lacunarity and fractal are analytical methods proposed to investigate complex systems in a cellular biological
context [18]. Both methods are quantitative techniques and have no observer dependency [16,17]. In current study, just
lacunarity was applied to image measures, as previously demonstrated by Dougherty and Hennebry (2002)[23]. Though
the lacunarity have been originally developed to describe a property of fractals, they not show self-similarity, which
allows to apply lacunarity in images that show a limited fractalness [17,18,23]. In a general sense, lacunatity
characterize the spatial organization of an image that may be manisfest by texture [18], as observed to the intricate
network formed by Haversian and Volkman’s canals [13-15].
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Microscopy: Science, Technology, Applications and Education
A. Méndez-Vilas and J. Díaz (Eds.)
______________________________________________
Previous studies have been successfully used lacunarity analysis to evaluate the trabecular network in cancellous
bone [23,24] and to determine the canals system organization on cortical bone [13-17]. These studies have tried to
estimate the bone texture and spatial organization using lacunarity measures on 2-D images histological sections and
recently, on 2-D images obtained by direct digital radiographs [16,17] and computed tomography [24]. The present
research evaluates lacunarity on decalcified cortical bone sections stained with hematoxilin and eosin, but the same
methodology might be performed in undecalcified thick sections.
The basic principles used here to lacunarity assessment have applicability to cortical sections prepared with
fluorescent dyes as tetracycline or stained for immunohistochemical. The same approach for different histological
methods is possible because the images need to be pre-processed to derive binary images. Additionally, artifacts created
during histotechnological steps might be eliminated by semi-automatic computer procedures to reduce the presence of
noise and blurring within the image system [24]. If used in adequate fashion, these correction procedures don’t change
the lacunarity sensitivity, which allow its application in parallel to conventional histomorphometric techniques to
appreciate other parameters as bone volume, osteoid and mineralizing surface, mineral apposition values, cell count.
In present study the same sections were used to obtain images in 10X and 40X, which were used to evaluate the
percentage of bone matrix and osteocyte/lacunae count, respectively. Images obtained in 10X were used to implement
lacunarity algorithm and to measure some traditional histomorphometric parameters. The former supply information
regarding bone formation rate which indirectly demonstrate the cell activity, while the latter is related to bone channel
system distribution and organization. Structural changes in bone and its healing process after radiation has been
characterized as changes in composition and replacement of its components in many studies [20,26,27], but this
research described a new way to demonstrate such alterations, as cortical bone matrix disorganization.
In irradiated group, the significant difference in bone matrix area and lacunarity probably represents alterations in
micro-structure and morphological characteristics. These features were confirmed by differences in area and perimeter
of bone channels that indicates a response to radiation effects, suggesting an unorganized bone remodeling process. The
mean values calculated to standard deviation ROI area and perimeter were used to evaluate the size and shape variation
on bone channel systems. The data indicate that ɣ radiation affects the general channels organization, which is
evidenced by more expressive standard deviation in irradiated group, reflecting in the sizes and shape of bone channels.
The high values to lacunarity obtained in control group are related to an important characteristic of this mathematic
measure: translational invariance. In a general sense, lacunarity is measure of the lack of rotational or translacional
invariance in an image [18]. Therefore, the lacunarity in control group is related to a spatial homogeneity in the
distribution of ROIs, while in irradiated group, these findings represent alterations on bone micro-structure, indicating
substantial changes in the Havers systems and their respective bone channels. These alterations can suggest important
implications on biomechanical and morphological properties, as demonstrated preciously in studies using conventional
histomorphometric methods [20,26]. This study also counted the osteocytes. It has been suggested that osteocytes
density regulate the morphometric parameters of predicted architecture and the remodeling process [2, 27]. Maeda et al.
(1988) [20] demonstrated a reduction in the number of osteocytes, which is related to immediate effects of radiation.
However, the osteocytes count did not change after radiotherapy, suggesting a recovery of the number of cells, probably
related to the long period between the irradiation and sacrifice. Therefore, the absence of differences on osteocyte
number did not exclude some changes in cells metabolism of irradiated bone, as alterations on growth factor [28]. In
addition, it is important to emphasize that the same sections were used to osteocyte count and to lacunarity analysis,
allowing several analytical opportunities to the better understanding of intricate organization of Harvesian system and
bone behavior.
The results indicate that radiotherapy causes reduction of bone matrix and modifies the micro-structure of bone
channels network, making it more heterogeneous and less organized, suggesting important implications on
morphological and biomechanical cortical bone properties. All in all, this work described how concepts of complex
network theory, used jointly with traditional morphometric parameters, can be effectively applied in order to appreciate
the mechanisms associated to bone turnover, providing a precise representation of the connectivity of bone channels,
improving the comprehension of bone vascularization [13,22]. Once the neovascularization is strictly related to
regenerative properties and bone remodeling, the representation of channels network distribution and organization
allows all the rich concepts regarding bone turnover to be applied [13-15,22]. Though the present study had evaluated
irradiated bone, the mathematical model used could be an interesting methodology to further investigations of structural
changes on cortical bone subject to orthodontic forces or the bone remodeling on implants subjects to early load. Hence,
lacunarity is a complimentary research tool on bone biology and its association with others histomorphometric
parameters shows great promise for improving the comprehension of bone metabolism.
©FORMATEX 2010
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Microscopy: Science, Technology, Applications and Education
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Méndez-Vilas and J. Díaz (Eds.)
______________________________________________
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