Bone 71 (2015) 189–195
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Original Full Length Article
The 3D structure of the collagen fibril network in human trabecular bone: Relation to trabecular organization Natalie Reznikov a,⁎, Hila Chase b, Vlad Brumfeld a, Ron Shahar c, Steve Weiner a a b c
Department of Structural Biology, Weizmann Institute of Science, Rehovot, Israel Hunter College, City University of New York, NY, USA Koret School of Veterinary Medicine, Faculty of Agriculture, Food and Environment, The Hebrew University of Jerusalem, Rehovot, Israel
a r t i c l e
i n f o
Article history: Received 9 August 2014 Revised 18 October 2014 Accepted 23 October 2014 Available online 30 October 2014 Edited by: Robert Recker Keywords: Trabecular bone Lamella Collagen array Inter-trabecular angle FIB-SEM µCT
a b s t r a c t Trabecular bone is morphologically and functionally different from compact bone at the tissue level, but both are composed of lamellae at the micrometer-scale level. We present a three-dimensional study of the collagenous network of human trabecular lamellar bone from the proximal femur using the FIB-SEM serial surface view method. The results are compared to human compact lamellar bone of the femoral shaft, studied by the same method. Both demineralized trabecular and compact lamellar bone display the same overall structural organization, namely the presence of ordered and disordered materials and the confinement of the canalicular network to the disordered material. However, in trabecular bone lamellae a significant proportion of the ordered collagen fibril arrays is aligned with the long axis of the trabecula and, unlike in compact bone, is not related to the anatomical axis of the whole femur. The remaining ordered collagen fibrils are offset from the axis of a trabecula either by about 30° or 70°. Interestingly, at the tissue scale of millimeters, the most abundant angles between any two connected trabeculae — the inter-trabecular angles - center around 30° and 70°. This implies that within a framework of interconnected trabeculae the same lamellar structure will always have a significant component of the fibrils aligned with the long axes of connected trabeculae. This structural complementarity at different hierarchical levels presumably reflects an adaptation of trabecular bone to function. © 2014 Elsevier Inc. All rights reserved.
Introduction Trabecular bone is an intricate three-dimensional framework of struts and plates that is surrounded by a continuous layer of cortical bone [1]. The trabeculae are subject to intensive remodeling, and are particularly susceptible to deteriorating age-related changes [2]. An understanding of the structure–function relations of trabecular bone tissue, either in health or in disease, requires a detailed understanding of its hierarchical structure. Here we present information on the 3-D structure of human trabecular bone, and report an interesting correlation between the orientations of the collagen fibrils in trabecular bone matrix at one hierarchical level and the orientations of the trabeculae themselves at another hierarchical level. We do this by specifying a new parameter to characterize the 3-D fabric of the trabecular bone tissue — the inter-trabecular angle. In the mature skeleton of humans, almost all bone is composed of lamellae [1,3,4]. The lamellae are just one structural feature within a complex hierarchy of structural features. Compact bone comprises two varieties of lamellar bone: circumferential lamellar bone and osteonal lamellar bone. Trabecular bone is also composed of lamellae ⁎ Corresponding author. E-mail address: [email protected] (N. Reznikov).
http://dx.doi.org/10.1016/j.bone.2014.10.017 8756-3282/© 2014 Elsevier Inc. All rights reserved.
[1,3,5]. The lamellae are however organized into so-called “lamellar packets” [3,6]. The lamellae of one packet are all aligned, but the lamellae of different packets have different orientations, with the more recently formed lamellar packets truncating the older ones at a low angle ca. 20 – 30° (Fig. 1). The result is that each trabecula has a patchwork-like texture composed of differently oriented lamellar packets (Fig. 1). All lamellae in one packet originate from one uninterrupted deposition event and are separated from their surroundings by cement lines [6]. As in compact bone, trabecular bone lamellae are about 6 μm thick and incorporate osteocytes in lacunae, regularly positioned a few tens of micrometers apart. The osteocytes are interconnected through canaliculi. Moreover, the transition areas between trabecular and compact bone display continuity of lamellar arrays [5, 7]. Unlike remodeling within compact bone which does not usually change the overall bone morphology, remodeling of trabecular elements gradually sculpts a new trabecular surface and eventually leads to re-orientation and re-shaping of individual trabeculae, and ultimately the whole trabecular network [8–11]. The 3-D organization of circumferential and osteonal compact human bone was investigated using a dual beam microscope and the serial surface view (SSV) method. SSV involves sequentially removing thin layers (around 10 nm) from a sample surface using the focused ion beam (FIB), and then imaging the exposed surfaces using the electron
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Micro-CT Marrow residues were removed using 3% sodium hypochlorite and then the specimens were fixed in 2% paraformaldehyde overnight on a rocking platform at 4 °C. Each proximal femur was dried with blotting paper, mounted on the micro-CT stage (Micro XCT-400, Zeiss X-ray microscopy, California USA) in the anatomical position and scanned at 40 kV and 200 μA with the pixel sixe 46.6 μm so that the metaphysis, the neck and the greater and lesser trochanters were in the field of view. Analysis of the trabecular architecture in 3-D
Fig. 1. Scanning electron microscope image of one dissected trabecula showing a mosaic of lamellar packets. Pairs of parallel lines highlight the orientation of lamellae: white solid — the newest lamellar packets, co-oriented with the trabecular axis; black dashed — truncated older lamellar packets, not aligned with the trabecular axis; black dotted — the most truncated and the oldest lamellar packets, not aligned with the trabecular axis. Scale bar 40 μm.
beam (SEM) [12]. The SSV method generates a 3-D stack of images with isometric nanometer-scale resolution in all directions in a volume of about 10 μm in all three orthogonal axes. An important observation of the 3-D study of compact bone was the identification of two different materials within the lamellar structure [13,14]. The predominant material (about 80% by volume) is composed of ordered arrays of collagen fibrils and the minor disordered material is composed of individual collagen fibrils with little or no orientation and abundant ground mass. Every repeating lamellar unit in the ordered material includes differently oriented ordered arrays of mineralized collagen fibrils. Within ordered arrays collagen fibrils are assembled into parallel bundles (rods) with rounded cross-sections and diameters of 2–3 μm. The disordered material is located between individual bundles and between differently aligned bundle arrays. The disordered material is not only a space-filler between the ordered arrays, but houses the whole lacuno-canalicular network of bone and thus may play an important role in mechano-sensing and mineral homeostasis [13,15]. No substantial difference was found in the 3-D structure of the matrices of circumferential and osteonal lamellae [13]. A significant advantage of the SSV method is that aspects of the structure can be quantified. Due to the isometric resolution of the SSV (a “cubic” voxel as a product of the 2D pixel and the slice thickness) and the repetitive and uniform structures of the collagen fibrils, the organization of the collagen network can be statistically analyzed by applying fast Fourier transform to the whole imaged volume and employing the frequency domain for tracing such structural trends as preferred orientation (direction) and extent of disorder (angular dispersion) [13,14]. Here we use SSV to study the 3D structure of the collagen network in human trabecular bone and address the question of whether or not trabecular lamellar bone architecture differs from the architecture of lamellae in compact bone. We also relate the structure at the lamellar level (micrometer range) to the structure of the trabecular network (millimeter range).
We selected functionally and anatomically distinct areas in each CT-volume: the metaphysis and the neck. The cortical shell was digitally removed around the trabecular interior of each sub-volume. The trabecular interior was skeletonized, which means the replacement of each strut by a vector using Fiji software, plugin Skeletonize (http://fiji.sc/ Skeletonize3D). The vector representation of the trabecular meshwork ignores the curvature of trabeculae and assumes that they are straight lines connected at nodes. The coordinates of the origin and the end of each vector (the nodes) were calculated using Fiji software plugin Analyze Skeleton (http://fiji.sc/AnalyzeSkeleton). The relationship between two vectors can be described by the dot product, which incorporates the cosine of the angle between them. a b ¼ kakkbk cosα cosα ¼ ða1 b1 þ a2 b2 þ a3 b3 Þ=
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2 a1 þ a2 2 þ a3 2 a1 þ a2 2 þ a3 2
Based on the coordinates of the nodes we calculated the angle between the pairs of connected vectors — the inter-trabecular angle. A frequency distribution (histogram) of angles in each sub-volume (metaphysis and neck) was plotted and then separated into a minimal number of individual Gaussian peaks using PeakFit 4 (Jandel Co, USA) software. The quality of peak fitting was considered satisfactory when adjusted r2 of the fit was better than 0.99. Bone preparation for FIB-SEM SSV Sections of 1–2 mm thick were cut from the samples F20 and M63 using a water-cooled rotary diamond saw (South Bay, USA). The sections were oriented parallel to the medial surface of the shaft (longitudinally) through the femoral neck basis. The sections were cleaned and defatted in acetone, and then demineralized by immersing in a solution of 5% ethylenediaminetetraacetic acid (EDTA), 2% paraformaldehyde (PFA) in cacodylate buffer, pH 7 on a rocking table for 72 h at room temperature. After demineralization individual trabeculae were dissected with a surgical blade and their anatomical orientation was recorded. We selected longitudinal trabeculae (oriented within ± 15° with respect to the femoral longitudinal axis). These trabeculae are often the thickest and are most noticeable on sections or radiographs. For comparison of different trabecular orientations we also collected oblique trabeculae — those oriented at the highest angle to the femoral longitudinal axis and, therefore, to the first group of trabeculae. Note that the trabeculae of the proximal femur rarely connect at a 90° angle. Hence, we refrain from calling them “transverse” trabeculae.
Materials and methods
Staining (for details see [13,14])
Materials
The samples were washed of residual EDTA using deionized water and pre-stained with Alcian Blue (5% in cacodylate buffer, pH 7) in order to stabilize bone proteoglycans [16], fixed again with 4% gluteraldehyde in cacodylate buffer, pH 7, and washed with deionized water. The staining was performed using the OTOTO protocol, also known as “conductive staining” [17,18]. This protocol uses a sequential application of osmium tetroxide (O) and thiocarbohydrazide (T). The
We used cadaveric samples of proximal femora from two individuals: 20 year old female (F20, no macroscopic signs of bone pathology) and 63 year old male (M63, no ante-mortem fracture history). The bones were kept at −20 °C prior to analysis. The bones analyzed were obtained with complete ethical clearance.
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substrate is first soaked in osmium tetroxide for 40 min, then washed thoroughly with deionized water in order to remove all unbound stain. This is followed by two iterations of 15 min in thiocarbohydrazide, washing, 15 min in osmium tetroxide and washing again. These two compounds, the “O” and the “T”, bind to the substrate in a chain-like manner and provide deep and even contrast, as well as conductive properties. Embedding (for details see [13,14]) Stained samples were washed in deionized water, high-pressure frozen (HPM 010, Bal-Tec, Lichtenstein), freeze-substituted for 28 h (EMAFS, Leica Micro systems, Germany) and embedded in Epon (EMbed 812, EMS, USA). All trabecular struts were positioned horizontally within Epon blocks. Finally, the blocks were trimmed in order to expose the embedded samples. The trimmed blocks were mounted on clamp-equipped holders, wrapped in carbon tape and sputter-coated with gold for 4 min. Serial surface view A Helios Nanolab 600 (FEI, The Netherlands) dual beam microscope was used for the SSV. Shallow outlines of lamellar packets were identified at low magnification. A 20 × 20 × 0.5 μm protective patch of platinum was deposited on the area of interest using ion beam deposition at 30 keV, 0.28 nA. A U-shaped trench was milled around the area of interest at 21 nA in order to expose the underlying lamellar surface for the electron beam. The exposed lamellar surface was polished with a lower ion beam current (0.9 nA). Then the electron beam was focused on the polished exposed tissue in the high-resolution mode at 2 keV, 86–170 pA, 1024 × 886 pixels per frame, 60–100 μs/pixel dwell time, pixel size 10–12.5 nm. The imaging was performed using a mixed secondary electrons/backscattered electrons (SE/BSE) detector (collector bias between 0 to +60 eV). An automated SSV experiment (Slice&View G2, FEI, The Netherlands) was initiated with a milling current of 0.9 nA and a slice thickness of 10 nm (the volumetric pixel was kept isometric in all experiments). Fourteen SSV volumes were collected: F20 — 9 volumes (4 longitudinal, 5 oblique), M63 — 5 volumes (3 longitudinal, 2 oblique). Z-thicknesses of SSV volumes varied between 5 and 18 μm. In all samples we defined the SSV area of interest in the most superficial lamellar packets, i.e. the lamellae resulting from the most recent remodeling events. Image alignment and processing The resultant three-dimensional stacks were processed using two software packages, Fiji/ImageJ (NIH, USA) and Avizo 7.1.0 (VSG, USA). The first step required image registration, which was automatically performed in the translation mode (Fiji) and manually refined (Avizo). The aligned stack was then cropped and the orientation of the fibrils was analyzed using a Directionality plug-in (Fiji). Numerical values of the fibril direction and angular dispersion were exported to an Excel spreadsheet and graphically plotted. The outline of the canalicular network was surface-rendered using gray value thresholding (Avizo). Results We collected SSV volumes from trabecular bone samples of two individuals: 9 volumes from a 20 year old female (F20) (4 from longitudinally oriented trabeculae, i.e. parallel to the femoral long axis, 5 from obliquely oriented trabeculae) and 5 volumes from a 63 year old male (M63) (3 longitudinal and 2 oblique). All SSV volumes were obtained close to the marrow surface of longitudinally sectioned struts i.e., the volumes originated from the most recently formed lamellar packets.
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The 3-D structure of trabecular bone lamellae The lamellar structure of trabecular bone can be described as alternating layers of ordered and disordered collagen arrays. The ordered collagen fibrils form the bulk of the lamellar structure. In the thicker “ordered” motif (Fig. 2) the majority of collagen fibrils show lateral alignment of their gap and overlap regions and close packing with minimal amounts of extrafibrillar material. The fibrils of the ordered array are roughly parallel to the lamellar boundary plane. These fibrils are organized into bundles (Supplementary Material ). The orientation of the whole ordered array with respect to the trabecula long axis of the young individual (F20) shows two predominant orientations: aligned with the trabecular long axis and oblique to the trabecular long axis. The ordered arrays from the older male individual (M63) also have one component aligned with the trabecular axis, but there are also fibrils aligned in a broader range of directions (Fig. 2). The same structural motifs were observed irrespective of whether the trabecula was aligned with the long axis of the whole femur or oblique to the long axis of the whole femur. The thinner “disordered” motif is located at the interfaces between ordered motifs with different preferred orientations. The thickness of the disordered array varies between 0.25 and 0.5 μm. The disordered collagen fibrils have random orientation and are loosely packed. The space between individual collagen fibrils is filled with ground mass (Fig. S2b). The disordered material comprises about 20% by volume of the trabecular bone. The volume ratio of the ordered and disordered materials was calculated by summing up the number of generally ordered slices (dispersion below 20–25°) and the number of slices with higher dispersion values. The canalicular network is confined to the disordered material (Supplementary material 1 including the Video S1). Based on the presence of the ordered and disordered materials, their proportions and geometry, as well as the localization of the cellular elements within the disordered material (Supplementary material), we conclude that the lamellar structure of the trabecular bone is essentially the same as the lamellar structure in compact bone (reported in [13]). The automated algorithm used for determining the direction and dispersion of the ordered collagen fibrils of both ordered and disordered arrays has been described in [14]. Since collagen fibrils have a high aspect ratio, they form a characteristic signature in the frequency domain. The frequency domain can be generated by application of the fast Fourier transform to each image in the stack. The frequency domain of aligned collagen fibrils contains a streak perpendicular to the orientation of the fibrils in the real image and a pair of arcs indicating the orientation of collagen D-periodicity (see Fig. 2, insets). Thus the FFT pattern can be used for calculating directionality (preferred orientation of fibrils) and dispersion (disorder of fibrils) in every image of an SSV stack. Fig. 3 shows the directionality analysis of the ordered fibrils with respect to the trabecular long axis in five SSV stacks of only the young F20 individual. Note the alternation of low angle (light blue/turquoise) and high angle (yellow/red) fibril orientations. The structure is clearly dominated by alternating low and high angle collagen fibril bundles (see also the Video S1 showing the alternation of orientations). When a series of trabecular lamellae is imaged using the SSV, every second ordered array is co-oriented with the long axis of the trabecula. This co-alignment is within ±20° of the trabecular long axis regardless of whether the trabecula was originally aligned longitudinally with the long axis of the whole femur or was oblique to the femur long axis (Figs. 2 and 3). In contrast, compact bone lamellae display diverse orientations of ordered fibrils [13]. Thus, in the F20 trabecular bone the local axis of the trabecula, but not the anatomical axis of the whole femur, is the frame of reference for the orientation of a significant fraction of collagen fibrils within its lamellar packets. We noted the same alternating orientation of collagen fibrils in the M63 bone (Supplementary Material 2 ), although the distribution of angles is somewhat broader. The general trend of orientation of mineralized collagen fibrils close to the
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Fig. 2. Selected slices from SSV stacks showing alternating low-angle and high-angle arrays of ordered collagen fibrils in trabecular lamellar bone. The images are aligned such that the x-axis of the image is parallel to the long axis of the trabecula. Pairs of low and high-angle images are taken from longitudinal and oblique trabeculae of F20 and M63 proximal femora. The insets are fast Fourier transforms of corresponding panels; the FFT shows the fibril orientation with respect to the local axis of a trabecula. The disordered material separating adjacent bundles of ordered fibrils can be seen well in the M63 stack. Scale bar is 1 μm and is the same for all the panels.
trabecular axis has been reported by Rinnerthaler and co-authors [19] in a small angle X-ray scattering study of trabecular bone. We also noted that the ordered collagen fibrils that are not aligned with the trabecular axis in F20 are offset from the trabecular axis by around 40–60°. In order to confirm this observation statistically we pooled directionality measurements from oblique trabeculae of F20 (about 5000 values), as well as from only longitudinal trabeculae (about 5000 values) (Fig. 4A). These pooled measurements were compared to directionality measurements in osteonal and circumferential lamellar bone of the same individual (F20) from the previous study of compact bone [13] (about 3500 values, Fig. 4B).
The orientation plots in Fig. 4 show that the most prominent orientation of ordered collagen fibrils in trabecular bone is at 10° off the trabecular axis in both longitudinal and oblique trabeculae. In the osteonal bone of F20 there is no obvious preferred orientation, and in the circumferential lamellar bone of F20 the preferred orientation is orthogonal to the long axis of the femur. In the oblique trabeculae the other abundant ordered components are offset from the low-angle ordered fibrils by 40° and 70°. In the longitudinal trabeculae the ordered fibrils, which are not aligned with the axis are offset from the lowangle ordered fibrils by 30° and 60°. The alternation of longitudinal and oblique arrays of collagen fibril bundles observed in the F20
Fig. 3. Directionality plots of 5 SSV volumes, F20. The vertical axes show fibril direction in degrees, and the horizontal axes show slice number in a stack and the stack thickness (scale bar applies to all). Color coding on top of each plot emphasizes the repetitive character of the horizontal orientation (light blue). Plots A and B are from SSV stacks from adjoining struts. Plots C, D and E are from another set of adjoining struts. Struts A and C were oriented longitudinally; plots B, D and E were oriented obliquely regarding the anatomical axis of the femur.
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Fig. 4. Distribution of collagen fibril orientations from all the images in pooled stacks. (A) F20 trabecular bone, where the horizontal axis shows the fibrils' direction, i.e. at 0° value are fibrils aligned with the long axis of the trabecula. The horizontal axis shows only absolute orientation values (i.e., positive and negative orientations with respect to the trabecular axis are pooled). (B) F20 compact bone (values from data reported by Reznikov [13]), where the 0° value are fibrils aligned with the long axis of an osteon (OB, osteonal bone) or the entire femur (CLB, circumferential lamellar bone). Y-axis shows the abundance of given orientations. Schematic insets show the orientations of the local axes in trabeculae and in an osteon that defines the 0° directions.
trabecular bone, raises the intriguing hypothesis that the trabeculae themselves are also on the average offset with respect to each other by a similar range of angles, in which case one set of ordered fibril arrays would always be aligned with a trabecular long axis and the other would be aligned with the connected trabecula. The same analysis of the trabecular fibril orientations in the M63 individual revealed similar trends, but with a larger angular spread (Supplementary material 2 ). Analysis of the angles between connected trabeculae using micro-CT Individual trabeculae connect at various angles forming a continuous fabric. We refer to the local angle between a pair of connected trabeculae as the inter-trabecular angle. We determined the range of such angles in the trabecular bone of the proximal femora using micro-CT 3-D images by applying digital skeletonization of the trabecular lattice followed by skeleton analysis. A 3-D lattice of trabecular bone was represented as a 3-D array of vectors. The inter-trabecular angle was calculated as an angle between a pair of vectors sharing a node using their origin and end coordinates (dot-product). The calculated value of the inter-trabecular angle is independent of the global axes and can be explained as an angle between two connected vectors on an imaginary plane drawn through 3 points: the common origin of the vectors and their extremities. The distribution of inter-trabecular angles was analyzed statistically. We analyzed the distributions of intertrabecular angle values in the proximal metaphyses and the femoral neck of two individuals: F20 (Fig. 5) and M63 (Fig. S1). Fig. 5 shows the distribution of inter-trabecular angles of the F20 trabecular bone. Separation of this broad curve into individual Gaussian distributions indicates the presence of distinct inter-trabecular angle populations centered around 105.6°, 63.6° and 30.5°. These three distributions result in a N99% match between the measured and the fitted distribution curves (adjusted r2 N 0.99).
clearly aligned with the long axis of the trabecula and the other, less well defined in terms of orientation, is oblique to the long axis of the trabecula, either at 60–70° or 30–40°. We examined the possibility that the alternating orientations of collagen fibril bundles in trabecular bone may be related at the millimeter scale to the inter-trabecular angles between connected trabeculae. The inter-trabecular angle is a parameter that is independent of the global (anatomical) axes of the specimen. For the F20 individual, we identified using micro-CT, three prominent inter-trabecular angle distributions that center around 105.6°, 63.6° and 30.5°. Considering that 105.6° is effectively the same angular offset as 74.4° (180–105.6 = 74.4), it follows that the mean inter-trabecular angles cluster around similar values as the mean angular offsets between adjacent layers of ordered collagen fibrils in lamellae, which is about 60–70°. This angular complementarity at two very distinct hierarchical levels of organization implies that the same lamellar structure with its two major fibril orientation components will always have one component of fibrils aligned with the long axis of each trabecula and another component of fibrils aligned with a contiguous trabecula (Fig. 6). Fig. 6 also shows that an idealized angle of 70° is equivalent to an angle of 110° when one trabecula connects to another. Note that this relation holds because we only analyzed the last formed lamellar packet, where the lamellar boundary orientation is aligned with the trabecular surface. Had we analyzed internal lamellar packets, then the fibril orientations
Discussion The 3-D structure of lamellae in human trabecular bone is very similar to the structure of human compact bone at the micrometer scale. One intriguing difference was however identified in the bone analyzed from the young F20 individual. In the previously investigated compact osteonal bone there is a wide variation in the orientations of the collagen fibril bundles and in the circumferential lamellar bone there is a preferred orientation in the direction transverse to the long axis of the femur. In contrast, in the trabecular bone, the collagen fibril orientations are dominated by only two alternating components, one of which is
Fig. 5. Distribution of inter-trabecular angles in the proximal metaphysis, F20.
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would be an engineering truss, in which individual members form triangle-based shapes or tetrahedron-based shapes, rather than orthogonal connections. The same mechanical solution could have evolved in trabecular bone to redistribute multidirectional stresses (as in joints). The global orientation of the trabeculae is not random, but according to “Wolff's law” the thickest trabeculae follow the principal stress lines. However, when the effect of trabecular thickness is eliminated by replacing trabecular struts with axial vectors, the tetrahedral theme can be observed. The orientation of the thickest trabeculae with the stress trajectories and the organization of most trabeculae in accordance with the tetrahedral theme are topologically compatible and, likely, collectively contribute to trabecular bone function. The complementarity of the trabecular bone 3D structure at the micrometer scale and the millimeter scale was very pronounced in the case of the young individual (F20), as opposed to the older individual (M63). Due to the small sample size this observation cannot yet be linked to the age, sex, health status or individual variation. A broader study of the local topological theme in trabecular bone would address this intriguing question. Conclusions
Fig. 6. Schematic drawing of orientations of ordered collagen fibrils in adjoining trabeculae. Complementary orientation of the ordered array is shown by longitudinal and oblique hatching. The contiguous trabeculae are 2-dimensional for the simplicity of illustration. The lamellae are not drawn to scale.
Lamellar structure of human trabecular bone is a composite of ordered and disordered materials and is very similar to the compact bone lamellar structure at a scale of micrometers. For a young individual, a significant proportion of ordered collagen fibrils in trabecular lamellar bone are co-oriented with the trabecular long axis. A second set of ordered collagen fibrils is offset from the low angle fibrils by 30–40° or 60–70°. At a higher hierarchical level, we also show that in this individual the mean angle between connected trabeculae is either 30–40° or 60–70°. This implies that the lamellar structure with its two major sets of differently aligned fibril bundles, will always have a significant component of the fibrils aligned with each of the long axes of connected trabeculae. The mean inter-trabecular angles in the proximal femur are characteristic of an equilateral tetrahedron, which might be important for trabecular bone function. Supplementary data to this article can be found online at http://dx. doi.org/10.1016/j.bone.2014.10.017. Acknowledgments
would reflect an earlier trabecular structure that has since undergone remodeling. We therefore hypothesize that there is indeed an interesting geometrical similarity in the offset angles of alternating ordered arrays of collagen fibrils at the hierarchical level of lamellar packets and the offsets of connecting trabeculae at a much higher hierarchical level. Note that this is well defined only in the young, non-osteoporotic F20 individual. In the older individual (M63, supplementary material 2 ) similar trends are apparent, but less consistent. The alignment of a significant portion of the ordered collagen fibrils within 15° with respect to the strut might bear an important biomechanical function, for example, for the load redistribution among many trabecular elements. The inter-trabecular angles were studied at the tissue level and the number of angles measured exceeds by a few orders of magnitude the number of lamellae analyzed by the SSV method. Therefore, the statistical analysis of the inter-trabecular angle distribution describes the general topological theme and not a specific well-defined locus. Note that the three mean values found in the inter-trabecular angle distribution are very similar to the angles found in an equilateral tetrahedron, namely the tetrahedral angle of 109.5°, the dihedral angle of 70.5° and axis-node-face angle of 35.2°. This in turn raises the intriguing possibility that the underlying geometrical motif in this trabecular bone has in fact a tetrahedral geometry. Indeed, the tetrahedron is known to engineers and architects as the simplest and the most stable 3D polyhedron, in which external loads are redistributed between all members without inducing significant distortions. A widely utilized example
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The 3D structure of the collagen fibril network in human trabecular bone: Relation to trabecular organization Natalie Reznikov a,⁎, Hila Chase b, Vlad Brumfeld a, Ron Shahar c, Steve Weiner a a b c
Department of Structural Biology, Weizmann Institute of Science, Rehovot, Israel Hunter College, City University of New York, NY, USA Koret School of Veterinary Medicine, Faculty of Agriculture, Food and Environment, The Hebrew University of Jerusalem, Rehovot, Israel
a r t i c l e
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Article history: Received 9 August 2014 Revised 18 October 2014 Accepted 23 October 2014 Available online 30 October 2014 Edited by: Robert Recker Keywords: Trabecular bone Lamella Collagen array Inter-trabecular angle FIB-SEM µCT
a b s t r a c t Trabecular bone is morphologically and functionally different from compact bone at the tissue level, but both are composed of lamellae at the micrometer-scale level. We present a three-dimensional study of the collagenous network of human trabecular lamellar bone from the proximal femur using the FIB-SEM serial surface view method. The results are compared to human compact lamellar bone of the femoral shaft, studied by the same method. Both demineralized trabecular and compact lamellar bone display the same overall structural organization, namely the presence of ordered and disordered materials and the confinement of the canalicular network to the disordered material. However, in trabecular bone lamellae a significant proportion of the ordered collagen fibril arrays is aligned with the long axis of the trabecula and, unlike in compact bone, is not related to the anatomical axis of the whole femur. The remaining ordered collagen fibrils are offset from the axis of a trabecula either by about 30° or 70°. Interestingly, at the tissue scale of millimeters, the most abundant angles between any two connected trabeculae — the inter-trabecular angles - center around 30° and 70°. This implies that within a framework of interconnected trabeculae the same lamellar structure will always have a significant component of the fibrils aligned with the long axes of connected trabeculae. This structural complementarity at different hierarchical levels presumably reflects an adaptation of trabecular bone to function. © 2014 Elsevier Inc. All rights reserved.
Introduction Trabecular bone is an intricate three-dimensional framework of struts and plates that is surrounded by a continuous layer of cortical bone [1]. The trabeculae are subject to intensive remodeling, and are particularly susceptible to deteriorating age-related changes [2]. An understanding of the structure–function relations of trabecular bone tissue, either in health or in disease, requires a detailed understanding of its hierarchical structure. Here we present information on the 3-D structure of human trabecular bone, and report an interesting correlation between the orientations of the collagen fibrils in trabecular bone matrix at one hierarchical level and the orientations of the trabeculae themselves at another hierarchical level. We do this by specifying a new parameter to characterize the 3-D fabric of the trabecular bone tissue — the inter-trabecular angle. In the mature skeleton of humans, almost all bone is composed of lamellae [1,3,4]. The lamellae are just one structural feature within a complex hierarchy of structural features. Compact bone comprises two varieties of lamellar bone: circumferential lamellar bone and osteonal lamellar bone. Trabecular bone is also composed of lamellae ⁎ Corresponding author. E-mail address: [email protected] (N. Reznikov).
http://dx.doi.org/10.1016/j.bone.2014.10.017 8756-3282/© 2014 Elsevier Inc. All rights reserved.
[1,3,5]. The lamellae are however organized into so-called “lamellar packets” [3,6]. The lamellae of one packet are all aligned, but the lamellae of different packets have different orientations, with the more recently formed lamellar packets truncating the older ones at a low angle ca. 20 – 30° (Fig. 1). The result is that each trabecula has a patchwork-like texture composed of differently oriented lamellar packets (Fig. 1). All lamellae in one packet originate from one uninterrupted deposition event and are separated from their surroundings by cement lines [6]. As in compact bone, trabecular bone lamellae are about 6 μm thick and incorporate osteocytes in lacunae, regularly positioned a few tens of micrometers apart. The osteocytes are interconnected through canaliculi. Moreover, the transition areas between trabecular and compact bone display continuity of lamellar arrays [5, 7]. Unlike remodeling within compact bone which does not usually change the overall bone morphology, remodeling of trabecular elements gradually sculpts a new trabecular surface and eventually leads to re-orientation and re-shaping of individual trabeculae, and ultimately the whole trabecular network [8–11]. The 3-D organization of circumferential and osteonal compact human bone was investigated using a dual beam microscope and the serial surface view (SSV) method. SSV involves sequentially removing thin layers (around 10 nm) from a sample surface using the focused ion beam (FIB), and then imaging the exposed surfaces using the electron
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Micro-CT Marrow residues were removed using 3% sodium hypochlorite and then the specimens were fixed in 2% paraformaldehyde overnight on a rocking platform at 4 °C. Each proximal femur was dried with blotting paper, mounted on the micro-CT stage (Micro XCT-400, Zeiss X-ray microscopy, California USA) in the anatomical position and scanned at 40 kV and 200 μA with the pixel sixe 46.6 μm so that the metaphysis, the neck and the greater and lesser trochanters were in the field of view. Analysis of the trabecular architecture in 3-D
Fig. 1. Scanning electron microscope image of one dissected trabecula showing a mosaic of lamellar packets. Pairs of parallel lines highlight the orientation of lamellae: white solid — the newest lamellar packets, co-oriented with the trabecular axis; black dashed — truncated older lamellar packets, not aligned with the trabecular axis; black dotted — the most truncated and the oldest lamellar packets, not aligned with the trabecular axis. Scale bar 40 μm.
beam (SEM) [12]. The SSV method generates a 3-D stack of images with isometric nanometer-scale resolution in all directions in a volume of about 10 μm in all three orthogonal axes. An important observation of the 3-D study of compact bone was the identification of two different materials within the lamellar structure [13,14]. The predominant material (about 80% by volume) is composed of ordered arrays of collagen fibrils and the minor disordered material is composed of individual collagen fibrils with little or no orientation and abundant ground mass. Every repeating lamellar unit in the ordered material includes differently oriented ordered arrays of mineralized collagen fibrils. Within ordered arrays collagen fibrils are assembled into parallel bundles (rods) with rounded cross-sections and diameters of 2–3 μm. The disordered material is located between individual bundles and between differently aligned bundle arrays. The disordered material is not only a space-filler between the ordered arrays, but houses the whole lacuno-canalicular network of bone and thus may play an important role in mechano-sensing and mineral homeostasis [13,15]. No substantial difference was found in the 3-D structure of the matrices of circumferential and osteonal lamellae [13]. A significant advantage of the SSV method is that aspects of the structure can be quantified. Due to the isometric resolution of the SSV (a “cubic” voxel as a product of the 2D pixel and the slice thickness) and the repetitive and uniform structures of the collagen fibrils, the organization of the collagen network can be statistically analyzed by applying fast Fourier transform to the whole imaged volume and employing the frequency domain for tracing such structural trends as preferred orientation (direction) and extent of disorder (angular dispersion) [13,14]. Here we use SSV to study the 3D structure of the collagen network in human trabecular bone and address the question of whether or not trabecular lamellar bone architecture differs from the architecture of lamellae in compact bone. We also relate the structure at the lamellar level (micrometer range) to the structure of the trabecular network (millimeter range).
We selected functionally and anatomically distinct areas in each CT-volume: the metaphysis and the neck. The cortical shell was digitally removed around the trabecular interior of each sub-volume. The trabecular interior was skeletonized, which means the replacement of each strut by a vector using Fiji software, plugin Skeletonize (http://fiji.sc/ Skeletonize3D). The vector representation of the trabecular meshwork ignores the curvature of trabeculae and assumes that they are straight lines connected at nodes. The coordinates of the origin and the end of each vector (the nodes) were calculated using Fiji software plugin Analyze Skeleton (http://fiji.sc/AnalyzeSkeleton). The relationship between two vectors can be described by the dot product, which incorporates the cosine of the angle between them. a b ¼ kakkbk cosα cosα ¼ ða1 b1 þ a2 b2 þ a3 b3 Þ=
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2 a1 þ a2 2 þ a3 2 a1 þ a2 2 þ a3 2
Based on the coordinates of the nodes we calculated the angle between the pairs of connected vectors — the inter-trabecular angle. A frequency distribution (histogram) of angles in each sub-volume (metaphysis and neck) was plotted and then separated into a minimal number of individual Gaussian peaks using PeakFit 4 (Jandel Co, USA) software. The quality of peak fitting was considered satisfactory when adjusted r2 of the fit was better than 0.99. Bone preparation for FIB-SEM SSV Sections of 1–2 mm thick were cut from the samples F20 and M63 using a water-cooled rotary diamond saw (South Bay, USA). The sections were oriented parallel to the medial surface of the shaft (longitudinally) through the femoral neck basis. The sections were cleaned and defatted in acetone, and then demineralized by immersing in a solution of 5% ethylenediaminetetraacetic acid (EDTA), 2% paraformaldehyde (PFA) in cacodylate buffer, pH 7 on a rocking table for 72 h at room temperature. After demineralization individual trabeculae were dissected with a surgical blade and their anatomical orientation was recorded. We selected longitudinal trabeculae (oriented within ± 15° with respect to the femoral longitudinal axis). These trabeculae are often the thickest and are most noticeable on sections or radiographs. For comparison of different trabecular orientations we also collected oblique trabeculae — those oriented at the highest angle to the femoral longitudinal axis and, therefore, to the first group of trabeculae. Note that the trabeculae of the proximal femur rarely connect at a 90° angle. Hence, we refrain from calling them “transverse” trabeculae.
Materials and methods
Staining (for details see [13,14])
Materials
The samples were washed of residual EDTA using deionized water and pre-stained with Alcian Blue (5% in cacodylate buffer, pH 7) in order to stabilize bone proteoglycans [16], fixed again with 4% gluteraldehyde in cacodylate buffer, pH 7, and washed with deionized water. The staining was performed using the OTOTO protocol, also known as “conductive staining” [17,18]. This protocol uses a sequential application of osmium tetroxide (O) and thiocarbohydrazide (T). The
We used cadaveric samples of proximal femora from two individuals: 20 year old female (F20, no macroscopic signs of bone pathology) and 63 year old male (M63, no ante-mortem fracture history). The bones were kept at −20 °C prior to analysis. The bones analyzed were obtained with complete ethical clearance.
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substrate is first soaked in osmium tetroxide for 40 min, then washed thoroughly with deionized water in order to remove all unbound stain. This is followed by two iterations of 15 min in thiocarbohydrazide, washing, 15 min in osmium tetroxide and washing again. These two compounds, the “O” and the “T”, bind to the substrate in a chain-like manner and provide deep and even contrast, as well as conductive properties. Embedding (for details see [13,14]) Stained samples were washed in deionized water, high-pressure frozen (HPM 010, Bal-Tec, Lichtenstein), freeze-substituted for 28 h (EMAFS, Leica Micro systems, Germany) and embedded in Epon (EMbed 812, EMS, USA). All trabecular struts were positioned horizontally within Epon blocks. Finally, the blocks were trimmed in order to expose the embedded samples. The trimmed blocks were mounted on clamp-equipped holders, wrapped in carbon tape and sputter-coated with gold for 4 min. Serial surface view A Helios Nanolab 600 (FEI, The Netherlands) dual beam microscope was used for the SSV. Shallow outlines of lamellar packets were identified at low magnification. A 20 × 20 × 0.5 μm protective patch of platinum was deposited on the area of interest using ion beam deposition at 30 keV, 0.28 nA. A U-shaped trench was milled around the area of interest at 21 nA in order to expose the underlying lamellar surface for the electron beam. The exposed lamellar surface was polished with a lower ion beam current (0.9 nA). Then the electron beam was focused on the polished exposed tissue in the high-resolution mode at 2 keV, 86–170 pA, 1024 × 886 pixels per frame, 60–100 μs/pixel dwell time, pixel size 10–12.5 nm. The imaging was performed using a mixed secondary electrons/backscattered electrons (SE/BSE) detector (collector bias between 0 to +60 eV). An automated SSV experiment (Slice&View G2, FEI, The Netherlands) was initiated with a milling current of 0.9 nA and a slice thickness of 10 nm (the volumetric pixel was kept isometric in all experiments). Fourteen SSV volumes were collected: F20 — 9 volumes (4 longitudinal, 5 oblique), M63 — 5 volumes (3 longitudinal, 2 oblique). Z-thicknesses of SSV volumes varied between 5 and 18 μm. In all samples we defined the SSV area of interest in the most superficial lamellar packets, i.e. the lamellae resulting from the most recent remodeling events. Image alignment and processing The resultant three-dimensional stacks were processed using two software packages, Fiji/ImageJ (NIH, USA) and Avizo 7.1.0 (VSG, USA). The first step required image registration, which was automatically performed in the translation mode (Fiji) and manually refined (Avizo). The aligned stack was then cropped and the orientation of the fibrils was analyzed using a Directionality plug-in (Fiji). Numerical values of the fibril direction and angular dispersion were exported to an Excel spreadsheet and graphically plotted. The outline of the canalicular network was surface-rendered using gray value thresholding (Avizo). Results We collected SSV volumes from trabecular bone samples of two individuals: 9 volumes from a 20 year old female (F20) (4 from longitudinally oriented trabeculae, i.e. parallel to the femoral long axis, 5 from obliquely oriented trabeculae) and 5 volumes from a 63 year old male (M63) (3 longitudinal and 2 oblique). All SSV volumes were obtained close to the marrow surface of longitudinally sectioned struts i.e., the volumes originated from the most recently formed lamellar packets.
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The 3-D structure of trabecular bone lamellae The lamellar structure of trabecular bone can be described as alternating layers of ordered and disordered collagen arrays. The ordered collagen fibrils form the bulk of the lamellar structure. In the thicker “ordered” motif (Fig. 2) the majority of collagen fibrils show lateral alignment of their gap and overlap regions and close packing with minimal amounts of extrafibrillar material. The fibrils of the ordered array are roughly parallel to the lamellar boundary plane. These fibrils are organized into bundles (Supplementary Material ). The orientation of the whole ordered array with respect to the trabecula long axis of the young individual (F20) shows two predominant orientations: aligned with the trabecular long axis and oblique to the trabecular long axis. The ordered arrays from the older male individual (M63) also have one component aligned with the trabecular axis, but there are also fibrils aligned in a broader range of directions (Fig. 2). The same structural motifs were observed irrespective of whether the trabecula was aligned with the long axis of the whole femur or oblique to the long axis of the whole femur. The thinner “disordered” motif is located at the interfaces between ordered motifs with different preferred orientations. The thickness of the disordered array varies between 0.25 and 0.5 μm. The disordered collagen fibrils have random orientation and are loosely packed. The space between individual collagen fibrils is filled with ground mass (Fig. S2b). The disordered material comprises about 20% by volume of the trabecular bone. The volume ratio of the ordered and disordered materials was calculated by summing up the number of generally ordered slices (dispersion below 20–25°) and the number of slices with higher dispersion values. The canalicular network is confined to the disordered material (Supplementary material 1 including the Video S1). Based on the presence of the ordered and disordered materials, their proportions and geometry, as well as the localization of the cellular elements within the disordered material (Supplementary material), we conclude that the lamellar structure of the trabecular bone is essentially the same as the lamellar structure in compact bone (reported in [13]). The automated algorithm used for determining the direction and dispersion of the ordered collagen fibrils of both ordered and disordered arrays has been described in [14]. Since collagen fibrils have a high aspect ratio, they form a characteristic signature in the frequency domain. The frequency domain can be generated by application of the fast Fourier transform to each image in the stack. The frequency domain of aligned collagen fibrils contains a streak perpendicular to the orientation of the fibrils in the real image and a pair of arcs indicating the orientation of collagen D-periodicity (see Fig. 2, insets). Thus the FFT pattern can be used for calculating directionality (preferred orientation of fibrils) and dispersion (disorder of fibrils) in every image of an SSV stack. Fig. 3 shows the directionality analysis of the ordered fibrils with respect to the trabecular long axis in five SSV stacks of only the young F20 individual. Note the alternation of low angle (light blue/turquoise) and high angle (yellow/red) fibril orientations. The structure is clearly dominated by alternating low and high angle collagen fibril bundles (see also the Video S1 showing the alternation of orientations). When a series of trabecular lamellae is imaged using the SSV, every second ordered array is co-oriented with the long axis of the trabecula. This co-alignment is within ±20° of the trabecular long axis regardless of whether the trabecula was originally aligned longitudinally with the long axis of the whole femur or was oblique to the femur long axis (Figs. 2 and 3). In contrast, compact bone lamellae display diverse orientations of ordered fibrils [13]. Thus, in the F20 trabecular bone the local axis of the trabecula, but not the anatomical axis of the whole femur, is the frame of reference for the orientation of a significant fraction of collagen fibrils within its lamellar packets. We noted the same alternating orientation of collagen fibrils in the M63 bone (Supplementary Material 2 ), although the distribution of angles is somewhat broader. The general trend of orientation of mineralized collagen fibrils close to the
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Fig. 2. Selected slices from SSV stacks showing alternating low-angle and high-angle arrays of ordered collagen fibrils in trabecular lamellar bone. The images are aligned such that the x-axis of the image is parallel to the long axis of the trabecula. Pairs of low and high-angle images are taken from longitudinal and oblique trabeculae of F20 and M63 proximal femora. The insets are fast Fourier transforms of corresponding panels; the FFT shows the fibril orientation with respect to the local axis of a trabecula. The disordered material separating adjacent bundles of ordered fibrils can be seen well in the M63 stack. Scale bar is 1 μm and is the same for all the panels.
trabecular axis has been reported by Rinnerthaler and co-authors [19] in a small angle X-ray scattering study of trabecular bone. We also noted that the ordered collagen fibrils that are not aligned with the trabecular axis in F20 are offset from the trabecular axis by around 40–60°. In order to confirm this observation statistically we pooled directionality measurements from oblique trabeculae of F20 (about 5000 values), as well as from only longitudinal trabeculae (about 5000 values) (Fig. 4A). These pooled measurements were compared to directionality measurements in osteonal and circumferential lamellar bone of the same individual (F20) from the previous study of compact bone [13] (about 3500 values, Fig. 4B).
The orientation plots in Fig. 4 show that the most prominent orientation of ordered collagen fibrils in trabecular bone is at 10° off the trabecular axis in both longitudinal and oblique trabeculae. In the osteonal bone of F20 there is no obvious preferred orientation, and in the circumferential lamellar bone of F20 the preferred orientation is orthogonal to the long axis of the femur. In the oblique trabeculae the other abundant ordered components are offset from the low-angle ordered fibrils by 40° and 70°. In the longitudinal trabeculae the ordered fibrils, which are not aligned with the axis are offset from the lowangle ordered fibrils by 30° and 60°. The alternation of longitudinal and oblique arrays of collagen fibril bundles observed in the F20
Fig. 3. Directionality plots of 5 SSV volumes, F20. The vertical axes show fibril direction in degrees, and the horizontal axes show slice number in a stack and the stack thickness (scale bar applies to all). Color coding on top of each plot emphasizes the repetitive character of the horizontal orientation (light blue). Plots A and B are from SSV stacks from adjoining struts. Plots C, D and E are from another set of adjoining struts. Struts A and C were oriented longitudinally; plots B, D and E were oriented obliquely regarding the anatomical axis of the femur.
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Fig. 4. Distribution of collagen fibril orientations from all the images in pooled stacks. (A) F20 trabecular bone, where the horizontal axis shows the fibrils' direction, i.e. at 0° value are fibrils aligned with the long axis of the trabecula. The horizontal axis shows only absolute orientation values (i.e., positive and negative orientations with respect to the trabecular axis are pooled). (B) F20 compact bone (values from data reported by Reznikov [13]), where the 0° value are fibrils aligned with the long axis of an osteon (OB, osteonal bone) or the entire femur (CLB, circumferential lamellar bone). Y-axis shows the abundance of given orientations. Schematic insets show the orientations of the local axes in trabeculae and in an osteon that defines the 0° directions.
trabecular bone, raises the intriguing hypothesis that the trabeculae themselves are also on the average offset with respect to each other by a similar range of angles, in which case one set of ordered fibril arrays would always be aligned with a trabecular long axis and the other would be aligned with the connected trabecula. The same analysis of the trabecular fibril orientations in the M63 individual revealed similar trends, but with a larger angular spread (Supplementary material 2 ). Analysis of the angles between connected trabeculae using micro-CT Individual trabeculae connect at various angles forming a continuous fabric. We refer to the local angle between a pair of connected trabeculae as the inter-trabecular angle. We determined the range of such angles in the trabecular bone of the proximal femora using micro-CT 3-D images by applying digital skeletonization of the trabecular lattice followed by skeleton analysis. A 3-D lattice of trabecular bone was represented as a 3-D array of vectors. The inter-trabecular angle was calculated as an angle between a pair of vectors sharing a node using their origin and end coordinates (dot-product). The calculated value of the inter-trabecular angle is independent of the global axes and can be explained as an angle between two connected vectors on an imaginary plane drawn through 3 points: the common origin of the vectors and their extremities. The distribution of inter-trabecular angles was analyzed statistically. We analyzed the distributions of intertrabecular angle values in the proximal metaphyses and the femoral neck of two individuals: F20 (Fig. 5) and M63 (Fig. S1). Fig. 5 shows the distribution of inter-trabecular angles of the F20 trabecular bone. Separation of this broad curve into individual Gaussian distributions indicates the presence of distinct inter-trabecular angle populations centered around 105.6°, 63.6° and 30.5°. These three distributions result in a N99% match between the measured and the fitted distribution curves (adjusted r2 N 0.99).
clearly aligned with the long axis of the trabecula and the other, less well defined in terms of orientation, is oblique to the long axis of the trabecula, either at 60–70° or 30–40°. We examined the possibility that the alternating orientations of collagen fibril bundles in trabecular bone may be related at the millimeter scale to the inter-trabecular angles between connected trabeculae. The inter-trabecular angle is a parameter that is independent of the global (anatomical) axes of the specimen. For the F20 individual, we identified using micro-CT, three prominent inter-trabecular angle distributions that center around 105.6°, 63.6° and 30.5°. Considering that 105.6° is effectively the same angular offset as 74.4° (180–105.6 = 74.4), it follows that the mean inter-trabecular angles cluster around similar values as the mean angular offsets between adjacent layers of ordered collagen fibrils in lamellae, which is about 60–70°. This angular complementarity at two very distinct hierarchical levels of organization implies that the same lamellar structure with its two major fibril orientation components will always have one component of fibrils aligned with the long axis of each trabecula and another component of fibrils aligned with a contiguous trabecula (Fig. 6). Fig. 6 also shows that an idealized angle of 70° is equivalent to an angle of 110° when one trabecula connects to another. Note that this relation holds because we only analyzed the last formed lamellar packet, where the lamellar boundary orientation is aligned with the trabecular surface. Had we analyzed internal lamellar packets, then the fibril orientations
Discussion The 3-D structure of lamellae in human trabecular bone is very similar to the structure of human compact bone at the micrometer scale. One intriguing difference was however identified in the bone analyzed from the young F20 individual. In the previously investigated compact osteonal bone there is a wide variation in the orientations of the collagen fibril bundles and in the circumferential lamellar bone there is a preferred orientation in the direction transverse to the long axis of the femur. In contrast, in the trabecular bone, the collagen fibril orientations are dominated by only two alternating components, one of which is
Fig. 5. Distribution of inter-trabecular angles in the proximal metaphysis, F20.
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would be an engineering truss, in which individual members form triangle-based shapes or tetrahedron-based shapes, rather than orthogonal connections. The same mechanical solution could have evolved in trabecular bone to redistribute multidirectional stresses (as in joints). The global orientation of the trabeculae is not random, but according to “Wolff's law” the thickest trabeculae follow the principal stress lines. However, when the effect of trabecular thickness is eliminated by replacing trabecular struts with axial vectors, the tetrahedral theme can be observed. The orientation of the thickest trabeculae with the stress trajectories and the organization of most trabeculae in accordance with the tetrahedral theme are topologically compatible and, likely, collectively contribute to trabecular bone function. The complementarity of the trabecular bone 3D structure at the micrometer scale and the millimeter scale was very pronounced in the case of the young individual (F20), as opposed to the older individual (M63). Due to the small sample size this observation cannot yet be linked to the age, sex, health status or individual variation. A broader study of the local topological theme in trabecular bone would address this intriguing question. Conclusions
Fig. 6. Schematic drawing of orientations of ordered collagen fibrils in adjoining trabeculae. Complementary orientation of the ordered array is shown by longitudinal and oblique hatching. The contiguous trabeculae are 2-dimensional for the simplicity of illustration. The lamellae are not drawn to scale.
Lamellar structure of human trabecular bone is a composite of ordered and disordered materials and is very similar to the compact bone lamellar structure at a scale of micrometers. For a young individual, a significant proportion of ordered collagen fibrils in trabecular lamellar bone are co-oriented with the trabecular long axis. A second set of ordered collagen fibrils is offset from the low angle fibrils by 30–40° or 60–70°. At a higher hierarchical level, we also show that in this individual the mean angle between connected trabeculae is either 30–40° or 60–70°. This implies that the lamellar structure with its two major sets of differently aligned fibril bundles, will always have a significant component of the fibrils aligned with each of the long axes of connected trabeculae. The mean inter-trabecular angles in the proximal femur are characteristic of an equilateral tetrahedron, which might be important for trabecular bone function. Supplementary data to this article can be found online at http://dx. doi.org/10.1016/j.bone.2014.10.017. Acknowledgments
would reflect an earlier trabecular structure that has since undergone remodeling. We therefore hypothesize that there is indeed an interesting geometrical similarity in the offset angles of alternating ordered arrays of collagen fibrils at the hierarchical level of lamellar packets and the offsets of connecting trabeculae at a much higher hierarchical level. Note that this is well defined only in the young, non-osteoporotic F20 individual. In the older individual (M63, supplementary material 2 ) similar trends are apparent, but less consistent. The alignment of a significant portion of the ordered collagen fibrils within 15° with respect to the strut might bear an important biomechanical function, for example, for the load redistribution among many trabecular elements. The inter-trabecular angles were studied at the tissue level and the number of angles measured exceeds by a few orders of magnitude the number of lamellae analyzed by the SSV method. Therefore, the statistical analysis of the inter-trabecular angle distribution describes the general topological theme and not a specific well-defined locus. Note that the three mean values found in the inter-trabecular angle distribution are very similar to the angles found in an equilateral tetrahedron, namely the tetrahedral angle of 109.5°, the dihedral angle of 70.5° and axis-node-face angle of 35.2°. This in turn raises the intriguing possibility that the underlying geometrical motif in this trabecular bone has in fact a tetrahedral geometry. Indeed, the tetrahedron is known to engineers and architects as the simplest and the most stable 3D polyhedron, in which external loads are redistributed between all members without inducing significant distortions. A widely utilized example
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