Research Article

Fractal-like hierarchical organization of bone begins at the nanoscale

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Science  04 May 2018:
Vol. 360, Issue 6388, eaao2189
DOI: 10.1126/science.aao2189

Curving bones

On larger length scales, bone is known to have a hierarchical structure in which small crystals of calcium phosphates arrange themselves around helices of collagen. These make up larger structures, such as the osteons found in compact bone. However, at smaller lengths, does the hierarchical structure persist? By combining three-dimensional electron tomography with two-dimensional electron microscopy, Reznikov et al. observed structural ordering from the nanoscale upward. At the smallest scale, needle-shaped mineral units form platelets that organize into stacks bridging multiple collagen units.

Science, this issue p. eaao2189

Structured Abstract


The components of bone assemble hierarchically to provide stiffness and toughness. Deciphering the specific organization and relationship between bone’s principal components—mineral and collagen—requires answers to three main questions: whether the association of the mineral phase with collagen follows an intrafibrillar or extrafibrillar pattern, whether the morphology of the mineral building blocks is needle- or platelet-shaped, and how the mineral phase maintains continuity across an extensive network of cross-linked collagen fibrils. To address these questions, a nanoscale level of three-dimensional (3D) structural characterization is essential and has now been performed.


Because bone has multiple levels of 3D structural hierarchy, 2D imaging methods that do not detail the structural context of a sample are prone to interpretation bias. Site-specific focused ion beam preparation of lamellar bone with known orientation of the analyzed sample regions allowed us to obtain imaging data by 2D high-resolution transmission electron microscopy (HRTEM) and to identify individual crystal orientations. We studied higher-level bone mineral organization within the extracellular matrix by means of scanning TEM (STEM) tomography imaging and 3D reconstruction, as well as electron diffraction to determine crystal morphology and orientation patterns. Tomographic data allowed 3D visualization of the mineral phase as individual crystallites and/or aggregates that were correlated with atomic-resolution TEM images and corresponding diffraction patterns. Integration of STEM tomography with HRTEM and crystallographic data resulted in a model of 3D mineral morphology and its association with the organic matrix.


To visualize and characterize the crystallites within the extracellular matrix, we recorded imaging data of the bone mineral in two orthogonal projections with respect to the arrays of mineralized collagen fibrils. Three motifs of mineral organization were observed: “filamentous” (longitudinal or in-plane) and “lacy” (out-of-plane) motifs, which have been reported previously, and a third “rosette” motif comprising hexagonal crystals. Tomographic reconstructions showed that these three motifs were projections of the same 3D assembly. Our data revealed that needle-shaped, curved nanocrystals merge laterally to form platelets, which further organize into stacks of roughly parallel platelets separated by gaps of approximately 2 nanometers. These stacks of platelets, single platelets, and single acicular crystals coalesce into larger polycrystalline aggregates exceeding the lateral dimensions of the collagen fibrils, and the aggregates span adjacent fibrils as continuous, cross-fibrillar mineralization.


Our findings can be described by a model of mineral and collagen assembly in which the mineral organization is hierarchical at the nanoscale. First, the data reveal that mineral particles are neither exclusively needle- nor platelet-shaped, but indeed are a combination of both, because curved acicular elements merge laterally to form slightly twisted plates. This can only be detected when the organic extracellular matrix is preserved in the sample. Second, the mineral particles are neither exclusively intrafibrillar nor extrafibrillar, but rather form a continuous cross-fibrillar phase where curved and merging crystals splay beyond the typical dimensions of a single collagen fibril. Third, in the organization of the mineral phase of bone, a helical pattern can be identified. This 3D observation, integrated with previous studies of bone hierarchy and structure, illustrates that bone (as a material, as a tissue, and as an organ) follows a fractal-like organization that is self-affine. The assembly of bone components into nested, helix-like patterns helps to explain the paradoxical combination of enhanced stiffness and toughness of bone and results in an expansion of the previously known hierarchical structure of bone to at least 12 levels.

Proposed model of crystal organization in bone.

Patterns specified by our model (top) are compared with projections of the STEM tomogram reconstructed from a STEM tilt series, showing the mineral organization in different directions (bottom).


The components of bone assemble hierarchically to provide stiffness and toughness. However, the organization and relationship between bone’s principal components—mineral and collagen—has not been clearly elucidated. Using three-dimensional electron tomography imaging and high-resolution two-dimensional electron microscopy, we demonstrate that bone mineral is hierarchically assembled beginning at the nanoscale: Needle-shaped mineral units merge laterally to form platelets, and these are further organized into stacks of roughly parallel platelets. These stacks coalesce into aggregates that exceed the lateral dimensions of the collagen fibrils and span adjacent fibrils as continuous, cross-fibrillar mineralization. On the basis of these observations, we present a structural model of hierarchy and continuity for the mineral phase, which contributes to the structural integrity of bone.

Bone is a most impressive natural material that combines stiffness (for support and leverage) and toughness (for protection and impact resistance)—properties usually considered mutually exclusive. In bone, stiffness coexists with toughness by virtue of bone’s hierarchical organization: Smaller structural units form larger structural units, which in turn are structured themselves in this manner into higher-order units.

In light of previous studies of bone structure analyzed at different scales, an informative and intriguing picture emerges. At the macroscopic level, most bones incorporate a helical motif in their anatomical shape. This helical motif can be recognized by the twisting of grooves and tuberosities along the shaft of the humerus, by the curvature of the clavicle, or by the course of a rib with respect to the body axis (1). These twisted or helical morphologies are easy to identify on robust bones that are well adapted to loading. In humans, multiple Haversian canals traverse compact bone at the millimeter level. They are roughly aligned with the longitudinal axis of the shaft. Indeed, they form helical arrays where each canal and its associated osteon lie along a screw-shaped trajectory with a roughly constant small pitch; this is presumably an adaptation to loading (2). At the micrometer level, the helical secondary osteons themselves are formed of concentric lamellae of mineralized collagen fibrils. These fibrillar arrays are inclined with respect to the central Haversian canal at an average angle of approximately 30°, thus forming an assembly of nested coils with alternating pitches (3). A single lamella in three dimensions often appears as a layer of bundles, each 2 to 3 μm in diameter, in which mineralized collagen fibrils twist around the bundle axis, just as filaments of a rope twist around its axis with a shallow pitch (4). At the nanometer level, the helical theme continues as quasi-hexagonal packing of triple helices of collagen into a fibril (5). Each collagen triple helix itself is a supercoil of single α-chain helices (6). This abridged overview of independently described helical motifs in bone highlights remarkable self-affinity of structure across 9 or 10 orders of magnitude (in mathematical terms, self-affinity is a less restricted notion than self-similarity). Indeed, in nature it is not uncommon to observe self-affine patterns (also called fractal-like), in which a part of the structure resembles larger entities and/or the whole structure (7). Many natural self-affine patterns are helical or spiral (8).

Existing evidence describing bone structural hierarchy indicates that below the submicrometer level, the helical pattern pertains only to the collagen component. For bone mineral alone, the paradigm of self-affinity is not obvious. Details of the architecture of both the organic and inorganic constituents of bone have become available with the advancement of x-ray diffraction and electron microscopy methodologies. The mineral of bone—carbonate-substituted hydroxyapatite—must occupy a preformed, osmotically crowded, covalently cross-linked organic niche. Before mineralization, the organic phase of bone is already assembled and is capable of the fine regulation of crystal nucleation and growth (9). Bone mineral is nano- and polycrystalline with a substantial degree of disorder and a considerable amount of substitution (1012). These features lead to inherent difficulties in the interpretation of crystallographic data. Furthermore, x-ray–based methods require relatively large sampling volumes where the crystallographic observations are averaged and often isolated from their immediate structural context. Another characterization challenge is that bone apatite is associated with disordered or amorphous phases (13). These mineral phases, such as octacalcium phosphate (14) and amorphous calcium phosphate (15), are stabilized by noncollagenous proteins (16), citrate ions (17), and a rigid hydration shell (18). Therefore, the ripening of the crystals is inhibited especially where they interface with organic moieties (19). As a result, multiple mineral phases are thought to coexist in bone (20, 21), which also complicates the interpretation of crystallographic studies. The complex structure of skeletal mineral often makes it difficult to prepare samples for electron microscopy imaging without causing specimen preparation artifacts such as disintegration, dehydration, and/or destabilization of metastable mineral phases (22). Finally, the three-dimensional (3D) structure of bone mineral, and thus the hierarchical structure, cannot be reconstructed exclusively on the basis of 2D information.

For these reasons, it is not surprising that diverse, sometimes conflicting views have evolved regarding bone mineral morphology and its relationships to the organic extracellular matrix. A number of predominantly electron microscopy–based studies identify the bone mineral building blocks as being acicular (needle-shaped) nanocrystals with diameters between 3 and 10 nm and a length of several hundred nanometers (2325), or as platelets with a variety of dimensions ranging from 5 nm × 20 nm × 40 nm (26) to 100 nm in the largest dimension (27). Furthermore, there is apparent disagreement as to whether the mineral phase is growing in an intra- or extrafibrillar fashion (28)—a matter of great importance for the structural integrity of bone. Hence, there is no consensus on the fine details of bone mineral morphology and organization. Besides explaining its unique mechanical properties, a clearer understanding of the mineral-organic interface in the context of bone hierarchical structure will provide insight into skeletal pathologies, growth and development defects, diagenesis (postmortem modification over time), and the metabolic role of bone as an ion reservoir. The organization and relationships between mineral and the organic extracellular matrix are important in such diverse fields as osteology, endocrinology, forensic medicine, and archeology, and this information may additionally inspire the design of novel composite materials.

Our work aims to evaluate the mineral phase of bone in three dimensions, within its immediate structural framework, in such a way that preparation artifacts are minimized and the hierarchical context of bone structure is taken into consideration. Using advanced preparation methodology and high-resolution electron microscopy, we explain how earlier conflicting models can be reconciled and advanced by the findings presented here.

Two-dimensional projections of the apatite mineral phase

Lamellar bone is the most common type of bone in a mature human skeleton. Mineralized collagen fibrils are ordered and tightly packed within a single lamella (29). On the micrometer scale, mineralized collagen fibrils can be considered to be roughly co-aligned, whereas their orientation changes more or less abruptly at the boundaries between adjacent lamellae.

By aligning a focused ion beam (FIB)–milled, electron-transparent specimen perpendicular to the lamellar boundaries, one can expect to observe the collagen fibrils with respect to the image plane in a wide range of orientations from edge-on views to in-plane views (29). We assumed that, using such specimen geometry, nearly in-plane and nearly edge-on arrays of mineralized collagen fibrils could be observed in the resulting cross sections (fig. S1). Interestingly, three distinct motifs of mineral organization were identified (Fig. 1).

Fig. 1 Three projections of bone structure as observed by TEM and corresponding electron diffraction patterns.

(A) The filamentous pattern shows curved crystals more than 100 nm in length. (B) Diffraction pattern from (A) shows well-defined (002) plane-related reflections, which are oriented in the direction of the elongated crystals. (C) The lacy pattern comprises groups of parallel, slightly bent crystals surrounding electron-transparent voids. (D) The absence of the (002) plane-related reflections indicates that the crystals’ c axes are oriented out of plane. (E) Nested rosettes, a previously unknown pattern, show crystals of about 5 nm in size arranged into left-handed helices. (F) Corresponding diffraction pattern with (002) plane-related reflections being absent, similar to that in (D). (G to I) Higher magnification of the same motifs. (G) The filamentous motif. (H) The lacy motif. (I) The rosette motif. Note a nearly hexagonal outline of the dark crystallite in (I); the inset shows a HRTEM image of the area indicated by the small white square, and the white circles in (A), (C), and (E) indicate the areas from which the SAED patterns in (B), (D), and (F) were recorded.

Of the three revealed motifs of nanoscale bone organization, the first, in-plane motif (Fig. 1A) contains extended quasi-linear elements; we term this the “filamentous” motif. The characteristic banding pattern of type I collagen fibrils (the 67-nm D-periodicity) can be followed in this orientation, confirming that the fibrils are roughly aligned with the image plane. The filamentous mineral particles are roughly co-oriented with the D-periodicity (at an angular range of approximately ±20°) and therefore are aligned with the long axes of the collagen fibrils. However, the length of the mineral particles usually exceeds 67 nm, which suggests that they are not confined to a single period of the collagen fibril. Similar filamentous motifs have been reported previously (3032). The second, “lacy” pattern (Fig. 1C) incorporates groups of concentrically curved, thin mineral particles surrounding irregular voids 30 to 50 nm in diameter. The third pattern of mineral particle arrangement is relatively dense and comprises left-handed “rosettes” with lateral crystal sizes between 5 and 10 nm. These rosettes of edge-on imaged particles are assembled in a quasi–closely packed pattern when the outlines of entire rosettes are considered. Overall, the lateral particle size distribution was found to be lognormal with an average particle diameter of 5.8 nm and a variation of ±1.4 nm.

Selected-area electron diffraction (SAED) patterns obtained from all three motifs are shown in Fig. 1, B, D, and F. All SAED patterns indicate polycrystallinity and are somewhat spotty in nature because of the limited number of refracting crystals in the analyzed volumes (SAED area diameter, 250 nm). The azimuthal intensity distribution is therefore not homogeneous, yet the radial intensity distribution clearly indicates the presence of apatite-related reflections and allows for the extraction of important crystallographic information. The filamentous motif shows a pair of arcs corresponding to the (002) plane-related reflection. The arc axis with respect to the center of the diffraction patterns is aligned with the texture of the filamentous motif, and the angular dispersions of both are in agreement. The systematic absence of (002) plane-related reflections in Fig. 1, D and F indicates that the crystallographic c axes are considerably tilted out of the plane of view, as would be expected if the mineralized collagen fibrils are out-of-plane.

Higher-magnification images of the three motifs are shown in Fig. 1, G to I. The crystallographic planes of mineral particles can be traced to about 5 nm laterally (in thickness, such as in Fig. 1I and to some extent in Fig. 1H) and to more than 100 nm longitudinally (e.g., Fig. 1G). Note that the individual crystals are not exactly straight in Fig. 1, A and G, but rather display bending, with curvature radii varying between 50 and 150 nm.

As shown in Fig. 1, C and E, we found two motifs when the mineralized fibrils are observed in cross section. The observed lacy motif has been reported in (12, 2831, 33, 34), whereas the rosette motif has not previously been described. Each of the rosettes is a chain of hexagonally faceted crystals with clearly visible lattice fringes when imaged by high-resolution transmission electron microscopy (HRTEM) (Fig. 1I). Analysis of the lattice fringes shows that the long c axes of the crystals are approximately parallel to the zone axis (Fig. 1I and fig. S2). As a result, the c-axis orientation could be approximately indicated in the SAED pattern in Fig. 1B as in-plane and in Fig. 1F as out-of-plane, whereas the corresponding a and b axes are randomly distributed, as confirmed by the SAED patterns.

The lateral extension of the rosettes in the motif shown in Fig. 1E is between 100 and 120 nm, which is consistent with the diameter of collagen fibrils in bone. Furthermore, their close-packing arrangement is reminiscent of the quasi-hexagonal packing of bone collagen fibrils (5, 35). These observations raise the question of how the same, presumably edge-on, projection can generate two distinct structural patterns.

Three-dimensional morphology of bone mineral

Tomographic tilt series were acquired from five FIB-milled sections, of which we present the results for two sections that at the 0° tilt angle revealed (i) a domain containing the filamentous and the lacy motifs simultaneously, and (ii) a domain containing exclusively the lacy motif. The lateral resolution of tomographic images exceeds the z-resolution because the z-axis dimension is reconstructed from tilted projections of an electron-transparent specimen. In tilted projections, the electron beam travels through a larger thickness than at the 0° tilt projection. For this reason, it was important to reconstruct 3D images from specimen areas containing in-plane and out-of-plane mineralized collagen fibrils. The resulting reconstructions were rendered and are shown in Figs. 2 and 3. Z-contrast imaging allows for a clear distinction of the mineral phase in the context of the organic matrix. However, the mass density variation attributable to the sequence of gap and overlap regions also makes it possible to observe the collagen D-periodicity simultaneously with the mineral phase, without the need for any staining agent.

Fig. 2 Filamentous and lacy motifs: Reconstructed and rendered STEM tomogram in different projections of a FIB-milled specimen of mature human lamellar bone.

(A) Sample showing mostly the filamentous pattern with a fragment of the lacy pattern in the bottom left corner; these patterns originate from two adjacent lamellae. (B) The same volume slightly tilted around the horizontal axis. (C) The same volume as in (A) tilted approximately 50° to 60° around the horizontal axis. (D) The same volume as in (A) tilted approximately –30° around the horizontal axis. Note the angular offset of approximately 60° between the crystallites of the neighboring motifs apparent in (C). Colored arrows indicate the axes of the reconstructed 3D volume orientation in space.

Fig. 3 Lacy motif: Reconstructed and rendered STEM tomogram in different projections of a FIB-milled specimen of mature human lamellar bone.

(A to C) The same volume viewed vertically (A), tilted approximately 30° around the horizontal axis (B), and tilted approximately 60° around the horizontal axis (C). Note that in the right top corner of (C) the faint D-periodicity of collagen can be detected. (D) A fragment of the same sample in such an orientation that acicular projections of the crystallites appear, resembling the rosette pattern in Fig. 1E. Colored arrows indicate the axes of the reconstructed 3D-volume orientation in space.

We collected tilt series of scanning transmission electron microscopy (STEM) images at tilt-angle increments of 2° through a tilt range of ±70°. The tilt series were reconstructed into 3D stacks (tomograms) with the use of a filtered back-projection algorithm applying the IMOD 4.9.0 software [ (36)]. The volume-rendered tomograms are presented in movies S1 and S2. The 3D reconstructed volumes show the in-plane filamentous motif and/or the out-of-plane lacy motif. In the 3D view, both appear as assemblies of irregularly shaped, opaque, elongated mineral particles. Crystals in the filamentous motif are roughly aligned with the collagen fibrils that are identified by their D-periodicity (Fig. 2A). The lacy motifs display lens-shaped voids 20 to 50 nm in diameter; within the imaged volume, the size and distribution of these voids are far less than those of collagen fibrils observed in 3D studies of demineralized bone (37).

Having found two adjacent motifs (lacy and filamentous) at the boundary of two bone lamellae in the same tomogram, with the same thickness and imaged under identical conditions, we performed virtual reslicing of digitally isolated filamentous and lacy areas. This allowed us to examine whether these two motifs are projections of morphologically identical crystalline assemblies. Two cubic volumes, each of 100 nm × 100 nm × 100 nm size, were cropped from each area and globally labeled by applying a White TopHat algorithm (38)—a function used for en masse extraction of small features in digital image processing (Avizo 9.2, FEI, USA). The resulting binary cubic images were digitally resliced at 90° so that the original in-plane area would be viewed edge-on, and vice versa. Subsequently, all images comprising the resliced stack were overlaid into a single image (a digital projection) using average pixel values, and the brightness was adjusted. The resulting original and reciprocal projections of in-plane and out-of-plane arrays are presented in Fig. 4, demonstrating that essentially the lacy and filamentous motifs are different projections of the same 3D arrangement.

Fig. 4 Labeling algorithm and comparison of the lacy and filamentous patterns in bone in reciprocally oriented projections.

(A) Tomogram slice with superimposed labels of the lacy (blue) and filamentous (pink) patterns. (B) Labeled volumes show extensively aggregated and coalesced elongated entities of variable size and irregular shape. (C) Volumes cropped to an identical size in all three dimensions are transformed in such a way that former XY planes now are XZ planes (i.e., the in-plane labels are viewed in the out-of-plane orientation, and vice versa). (D) Digital manipulation of the filamentous label field (from left to right): Original labels in a cubic stack are averaged in terms of pixel value to form a pseudo-2D image, which is similar to the corresponding area in (A). The resliced label field stack is averaged in terms of pixel value to form a pseudo-2D image in an orthogonal direction. (E) Digital manipulation of the lacy label field follows the same sequence of steps. Note the similarity of the resliced projected filamentous label field to the original lacy motif, and vice versa.

Besides demonstrating that lacy and filamentous motifs are different projections of identical structures, Fig. 4 also shows that the TopHat-labeling algorithm results in a reliable and feature-retaining segmentation of bone mineral. We used 3D rendering of individual mineral particle labels to study their morphology while avoiding the masking effect of the neighboring, coalescing labels. Separate mineral particles and their aggregates showing the least degree of confluence are shown in Fig. 5. Unobscured observation of highly irregular individual particles shows that there exist three hierarchical levels of mineral particle aggregation: lateral, stacked, and wedged, increasing in order of size (Table 1). The smallest entity above the noise level that could be labeled is an acicular particle with a shorter dimension of 5 nm and a longer dimension of at least 30 nm. These acicular particles are consistent with the dimensions of the crystalline domains observed by TEM (Fig. 1, A and G, filamentous motif). The extended needles show bending, with a curvature of approximately 100 to 150 nm, similar to the values observed for the crystals constituting the lacy pattern in Fig. 1H. The angular distribution of the needles is in the range of up to ±20° relative to the main axis of the collagen fibrils in the original image (Fig. 2, filamentous portion in all panels), and thus they are similar to the azimuthal length of the (002) plane-related reflection arcs found in the diffraction patterns of the filamentous motif (Fig. 1B). These filaments aggregate laterally and form larger, platelet-shaped morphologies, and for that reason their maximal length cannot be reliably defined. The platelets often show longitudinal striations corresponding to the filament directions. Mostly, individual filaments are visible only at the fringes of a platelet (resembling the fingers of a hand), and in some cases these can be captured as self-standing entities. The platelet-shaped aggregates of acicular particles have two distinct features: (i) They form stacks of two to four parallel platelets separated by a well-defined uniform gap of about 2 nm, and (ii) the platelet-shaped aggregates often show a gentle twist along their longitudinal axis, resembling the shape of a fan blade. Finally, platelets and their stacks converge into larger aggregates in such a way that the gap between them becomes wedge-shaped. These largest aggregates exceed the dimensions of the D-period and the interfibrillar spaces observed in 3D images of demineralized collagen in bone (29). Note that only the smallest converging aggregates are presented here, and these illustrate the lower limit of their dimensions; it must be kept in mind that most of the aggregates are more extended than those shown in Fig. 5 and fig. S3. Apparently, these larger crystalline structures incorporating nested arrays of simpler acicular and platelet-shaped particles are not associated with only one collagen fibril, but rather they span several collagen fibrils, and can thus form an interlinked mineral network through cross-fibrillar mineralization (being both intrafibrillar and extrafibrillar).

Fig. 5 Evaluation of the tomogram shown in Fig. 2.

Individual labels were selected within the lacy pattern [(A) to (E)] and the filamentous pattern [(F) to (H)]. Only the mineral aggregates that showed the least degree of confluence with each other were selected. (A and B) The same 10 labels in situ, in two different projections. (C to E) Four of these 10 labels in individually adjusted projections to highlight their 3D shape. (F to H) Ten individual labels from the filamentous pattern; (G) and (H) show two of these in adjusted projections. There are three levels of confluence of mineral formations with each other: (i) lateral merging of needle-shaped entities into platelets; (ii) planar merging of platelet-shaped entities into stacks of two to four, with a uniform gap between them; and (iii) merging of adjacent stacks at an angle [like fan blades, especially obvious in (C), (E), and (H)] with a wedge-shaped clearance between them. Almost all labels in three dimensions show a delicate twist, especially visible in (B). The overall ratio of label density to total volume was the same in both samples (approximately 0.45 to 0.5).

Table 1 Description of hierarchically organized bone apatite crystals and their approximate sizes.
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A three-dimensional model of mineral assembly

We applied the information obtained from the 2D projections and the 3D electron tomography to construct a 3D model of the mineral phase, as shown in movie S3. By relating the facts that (i) there are three distinct projection patterns of crystalline assemblies, (ii) the crystals are slightly curved, (iii) the lacy pattern is already clearly visible when the filamentous projection is tilted by just 30° to 50° with respect to the fibrils’ long axes, and (iv) the collagen helices are staggered in a superhelical fashion (5, 6, 39), we suggest that apatite crystals within a continuous collagenous matrix follow an asymmetrical, subtly splaying pattern of organization, as illustrated in Fig. 6. The individual curved acicular mineral particles are partly aligned with the long axes of the collagen fibrils. Because of their curvature and their longitudinal dimensions (≥100 nm), these acicular mineral particles also splay away from the fibril, thus providing space for an adjacent tier of acicular particles along the collagen fibril axis. Thus, an intercalated cross-fibrillar network is formed, in which the acicular units are associated with the collagen fibrils and with the extrafibrillar space, and are likely associated with the neighboring collagen fibrils. Of note, the propensity of fine apatite crystals to splay away from a constraining fibril has been previously reported in vitro (40). For the sake of illustration clarity, the model of curved splaying acicular units does not reflect the fact that they partly coalesce laterally to form thin platelets, but their coalescence can be clearly observed in the tomographic images. Therefore, the model here underestimates the amount of extrafibrillar mineral. The subtle curvature of most acicular units, as noticeable in 2D and 3D images, is slightly accentuated in the model. The model viewed in the direction perpendicular to the collagen fibril axes (i.e., fibrils in-plane) is congruent with the filamentous motif and provides a good explanation for the angular distribution of the crystals of approximately 20° relative to the fibril axis. The same model viewed in the direction almost aligned with the fibril axes (i.e., fibrils roughly out-of-plane) produces a lacy motif with lens-shaped holes surrounded by parallel segments of curved filaments. Finally, the same model viewed exactly edge-on with respect to the collagen fibril axes results in concentric rosettes of cross-sections of the acicular units. To summarize, the same 3D structure—assembled arrays of curved, coarsely aligned acicular elements that splay away from one collagen fibril toward adjacent neighboring fibrils via the confined extrafibrillar space—explains the occurrence of all the motifs observed in 3D projections, as well as the 3D-rendered tomographic images.

Fig. 6 Morphology and organization of crystals within mineralized collagenous matrix of bone, as seen in different orientations.

A proposed model of crystal organization in bone is compared with 2D projections obtained from TEM and STEM (second column of panels) and the tomogram reconstructed from the STEM tilt series (amber-colored, third column of panels). The first column of panels shows the orientation of a thin specimen with respect to the ordered array of mineralized collagen fibrils in lamellar bone. The last column of panels features the same simplified 3D model of bone apatite crystals viewed in three different projections: in-plane, out-of-plane, and edge-on views. For the sake of clarity, the model drawing has fewer concentric tiers of curved filaments than it presumably would accommodate.

The repercussions of this hierarchical mineral/collagen assembly pattern are manifold, affecting the mechanical properties of bone as well as the metabolic role of the carbonated apatite phase as a reservoir for mobilization and sequestration of inorganic ions (41). The uniform gaps between the platelet-shaped formations are known to contain disordered calcium phosphate, structural water (42, 43), and possibly noncollagenous proteins (44) and polysaccharides (19). These unstructured sheaths maintain the uniform high aspect ratio of individual crystallites, which contribute to their flexibility and toughness as well as their reduced sensitivity to stress-induced crack formation—a feature characteristic for the mechanical behavior of high–aspect ratio structures, for example, of nanotubes or nano-whiskers (45). From the mechanical perspective of composite materials theory, a high aspect ratio of staggered filler units within the matrix, together with a high density of the filler units, both contribute to higher material strength and stiffness (46). Notably, in bone the high aspect ratio of the thin elongated crystals is purposefully maintained by the rigid layers of structural water between neighboring mineral particles (42, 43, 47), whereas the loss of structural water from bone tissue is associated with age-related decay of bone mechanical properties (48).

The mechanism by which acicular crystals merge to form platelets remains unclear. In concert with the theory of biomineralization occurring through an amorphous precursor stage (49, 50), the crystallization of biological apatite could be expected to proceed along the path of least interference within a cross-linked collagenous matrix that is rich in mineralization inhibitors that regulate crystal growth. The formation of an ordered crystalline phase throughout the amorphous template can be locally disrupted by the presence of noncollagenous organic entities (51), substantial amounts of bound water and inorganic impurities (14, 17), or prestress of the collagenous matrix (52). It remains unknown whether acicular crystals merge into platelets or whether thin prestressed platelets split into acicular crystals at their periphery. The interfacial role of water is mediated by numerous organic inclusions (9, 19) and inorganic impurities (14), both of which can disrupt the long-range order of bone apatite.

The higher-level coalescence of stacks of platelets into larger wedged aggregates is an illustration of continuity of the mineral phase transversely spanning the dimensions of more than one collagen fibril. The collagenous matrix of bone is extensively cross-linked by intermolecular covalent bonds (53). In bone—as opposed to tendon, for example—it is difficult to discern individual collagen fibrils and their trajectories because they are all aligned in register. To examine the true length of individual collagen fibril segments, we performed manual labeling of demineralized bone collagen fibrils imaged by FIB scanning electron microscopy (FIB-SEM) in a digitally resliced edge-on orientation. Figure 7 and movie S4 show that individual fibrils can only be tracked along a segment length of 200 nm on average before they split or merge with other fibrils, thus effectively forming a continuous 3D network. Because individual fibrils are integrated into a continuous network, both fibril segments and extrafibrillar spaces are of a finite length, rarely exceeding a few hundred nanometers. It could be coincidental that the average segment length of the collagen network and the maximal size of a mineral aggregate are of similar values. However, it is possible that the longitudinal dimension of the extrafibrillar space serves as a limiting factor influencing the extent of mineral aggregation. Such a physical confinement is in accord with the need to keep mineral particles small in order to optimize material toughness. This observation is also consistent with the noticeable crystallite growth in bone observed in the process of diagenesis and postmortem decay of organic matter (54).

Fig. 7 Discernible segment length of collagen fibrils in the extracellular matrix of bone.

(A) Reconstructed volume of demineralized and stained collagen fibrils in bone. (B) Individual fibrils color-labeled where they can be continuously traced in the edge-on view. Each of 100 labels is shown in a different color visualizing the distribution of segment lengths.

Although the mechanisms of collagen cross-linking into a continuous framework and the mechanisms of crystallite aggregation are obviously different, the final results converge to provide for the continuity of bone tissue’s organic and inorganic components. The preservation of bone morphology at multiple scales has been previously demonstrated using specimens treated by deproteinization or demineralization in hydrated conditions (55, 56).

The impact of morphology on effective mineral surface area

The small size of bone crystallites has been reported to contribute to the substantial surface area of mineral in the human skeleton, which is on the order of 0.1 km2/kg (5759) according to gas absorption experiments. The effective mineral surface area reportedly decreases at a temperature exceeding 300°C when the loss of bound water and charring of organic constituents occur, indicating crystal merging (59). To quantitatively compare the impact of the mineral morphology on the total surface area, we calculated the total crystallite specific surface area fromEmbedded Image(1)where Ai and Vi are the area and volume of the crystal morphology, respectively, and ρAP is the density of the apatite phase. For platelet-shaped crystals, we findEmbedded Image(2)with average crystallite dimensions w, d, and t, whereas for the acicular morphology the surface per mass unit can be calculated fromEmbedded Image(3)where d is, in this case, the acicular crystallite cross-sectional diameter.

Using an apatite density of 3190 kg/m3 and a typical mineral content of the skeleton amounting to 32 weight percent (wt %) (60) [not to be confused with 67 wt % in mineralized extracellular matrix of bone (61) usually assumed for a dissected, defatted, dry specimen], these values were used to calculate the specific surface area for a thin platelet of 5 nm × 25 nm × 100 nm to be compared with the value obtained for acicular crystallites with cross-sectional diameter of 5 nm and length of 100 nm. We find that for an average-size human [having a total skeleton mass of roughly 10 kg, of which about 32% is ash (60)], the total surface area of the acicular bone crystallites is approximately 0.9 km2 (for comparison, this is about twice the area of Vatican City and is consistent with the estimates based on gas adsorption measurements). In contrast, if the bone mineral geometry were plate-shaped, with the crystal size being 5 nm × 20 nm × 100 nm, the total surface area would be almost 40% lower, which is incongruent with the gas adsorption experiments. To validate the surface area dependence on imaging resolution, we calculated the surface-to-volume ratio of the 3D-rendered mineral as a function of pixel size. The original pixel size in the 3D tomographic images was 0.98 nm and it was digitally coarsened to 5 nm—a decrease of resolution where the acicular elements could not be clearly visualized but the plate-shaped aggregates could still be well defined. Interestingly, in the tomogram with the pixel size artificially coarsened from <1 nm to 5 to 6 nm, the surface-to-volume ratio was 40% lower relative to the original resolution (i.e., at which the acicular crystals were well resolved; see fig. S4).

Fractal-like hierarchical bone architecture

The hierarchical assembly of the organic and inorganic components of bone is implemented in a bottom-up manner through the interactions between cells and the extracellular matrix during growth, development, and maintenance. However, the paradigm of bone hierarchy was originally elaborated using a top-down approach by the English physician Clopton Havers, who in 1691 first distinguished five nested structural levels spanning from a bone’s anatomy to its basic components: the “earth” (organic matter) and the “fixed salt” (inorganic matter) (62). Major methodological leaps have enriched our concept of bone hierarchy. The key review by Weiner and Wagner in 1998 described seven nested levels of organization (63). With the advent of nanoscale 3D imaging, nine hierarchical levels were defined in 2014 (4). The current understanding of the hierarchical structure of bone is that the organic and inorganic components blend at the submicrometer level to generate mineralized collagen fibrils, as shown in Fig. 8. The hierarchical and self-affine assembly of collagen as the major component of bone’s organic phase has been demonstrated previously and is in accordance with the overall hierarchy of bone at the tissue and organ level, up to the macroscopic scale. The demonstration here of bone mineral as a separate hierarchical phase, although counterintuitive, is not at odds with the bigger picture, nor is the observation of the gentle curvature and cross-fibrillar low-pitch coiling of nanocrystals. We show that a helical motif repeats itself on every scale of bone architecture, and that this pertains to both collagen and mineral. Observations that crystals curve and bend are possible in light of the crystals’ nanoscale-level high aspect ratio, their formation via an amorphous precursor stage, and their location within a prestressed hydrated matrix. The shallow-pitch helical morphology of bone mineral crystals is in accordance with the nested self-affine helical motifs found throughout the hierarchy of bone structure in general and gives rise to the identification of bone as a fractal-like structure.

Fig. 8 A scheme of hierarchical organization in bone.

For levels VII to XII (green), see Reznikov et al. (4, 29, 71). Both ordered and disordered motifs of lamellar bone comprise mineralized collagen fibrils (VI) that are 80 to 120 nm thick and form a continuous network. Collagen fibrils are composed of quasi–hexagonally packed microfibrils (V), each of which incorporates multiple staggered triple helices (IV) that in turn are formed from repetitive chains (III) of amino acids (II). Collagen levels V to II are discussed in detail by Orgel et al. (5, 35, 39, 72, 73). The inorganic component of the mineralized collagen fibrils (VI) itself incorporates several nested structural motifs, listed as follows in decreasing order of complexity: mineral aggregates (V), stacks of platelets (IV), platelets (III), and acicular crystals (II). [(V) copyright 2006, National Academy of Sciences, U.S.A.]

As nature uses and reuses effective strategies (64), and as helical motifs are abundant in shells, horns, cones, and spider webs (8) among other biological structures, we suggest that the fractal-like organization (i.e., the self-affine helical motif occurring across multiple scales) is another way to further optimize bone structure-function relations over millions of years of evolutionary refinement.

Materials and methods

Samples and preparation

Our study focused on compact lamellar bone samples prepared from the proximal femur of two female individuals, 48 and 50 years old. The Imperial College Tissue Bank (application R13004) approved collection and research of excess human tissue from surgeries performed at Charing Cross Hospital, London. The proximal femur samples were collected from elective arthroplasty for osteoarthritis where prior written informed consent was obtained from the patient. The lower femoral necks, also referred to as the “calcar” area (compact bone tissue, generally not affected by the joint degenerative disease), were cut in two planes, along and across the long axis, so that compact bone osteons would be cut in both long and cross sections. The resulting sample sections were polished, and shallow ridges of osteonal lamellae were identified by optical microscopy. The polished bone samples were defatted in acetone and embedded in Epon (Electron Microscopy Sciences, USA) in vacuum; embedding in vacuum was conducted in order to fill bone porosities with a solid medium. The top surface of the embedded samples was exposed with a glass knife and a diamond knife to visualize osteonal lamellae as shallow ridges oriented in concentric circles (transverse osteon section) or as a parallel series (longitudinal osteon section).

Ion beam milling by FIB-SEM provides precise ablation of the mineralized substrate and controlled thinning of the area of interest until electron transparency is obtained. We prepared 100-nm-thick specimens by FIB milling and the lift-out technique, using a Helios Nanolab 600, FEI, USA, following an automated procedure (AutoTEM G2 software, FEI, Netherlands) at 30 keV. The real-time visual control of the milling and thinning processes in the FIB-SEM allows for the preparation of a TEM specimen in the desired orientation (perpendicular to the lamellar planes for both configurations) and sufficiently distanced from the osteocyte lacunae. Specimens were mounted on a semi-grid for thinning to obtain electron transparency (approximating a 100-nm section thickness) using current reduction from 0.46 nA to 28 pA, at 30 keV. Final polishing of the thinned samples was conducted at ion acceleration voltages of 16 keV and then 5 keV, using at the same time electron currents sufficient for visual control in order to gently remove surface unevenness, redeposited debris, and the products of local mineral amorphization. Using an appropriate sequence of decreasing voltage and current values prevents ion beam–related artifacts (65) and allows for the best possible preservation of the structural features of the sample, which is especially important for specimens containing organic-inorganic interfaces (32) and components sensitive to contact with water (22).

The TEM investigation of the ultrastructure of bone followed a two-pronged approach using bright-field and high-resolution TEM in conjunction with SAED to obtain and characterize 2D projections of the crystal structure. STEM tomography was used to identify the 3D assembly pattern particularly of the mineral phase in unmodified air-dried bone embedded in epoxy resin in vacuum.

Transmission electron microscopy

For 2D imaging of cross sections, we used a conventional JEOL 2011 TEM as well as a JEOL 2200 FS TEM operating in the STEM mode with a third-order probe aberration corrector and a high-angle annular dark field imaging detector (inner collection angle, 110 mrad). Both microscopes were operated at a 200-kV acceleration voltage. For diffraction pattern collection and high-resolution imaging, we notably found the use of an LaB6 electron source beneficial compared to a field emission gun source because the lower spatial electron coherence minimizes damage by the electron beam.

The appropriate choice of imaging conditions for observing the details of the mineral/organic organization in bone constitutes a major challenge. For TEM analyses, low electron doses are required to avoid material ablation and redeposition during imaging (66). Generally, STEM allows for better contrast at low beam exposure compared to plane-view TEM, and is thus less prone to producing artifacts of this type (66). In addition, STEM provides directly interpretable contrast, and is therefore also preferable for tomography because plane-view TEM imaging depends strongly on Bragg contrast. Because the local contrast depends on the sample orientation, tomographic imaging is difficult and the achievable spatial resolution is limited. For this reason, STEM methodology is preferable over the TEM methodology for 3D tomographic imaging of polycrystalline samples such as bone.

STEM tomography

We used STEM in conjunction with a high angular annular dark field (HAADF) detector, an imaging approach sensitive to variations in the atomic number Z, thus enabling the simultaneous imaging of collagen and mineral phases in situ. Furthermore, tomographic sample tilting in the STEM mode allows 3D imaging with nanometer-level resolution (67), as required for the small dimensions of the apatite crystals.

Tomography was performed using an FEI Tecnai Osiris STEM (X-FEG Schottky field emitter) operated at 200 kV, 245 μA, using a Fischione 2020 advanced tomography holder with a previous data set obtained using manual tilt at a JEOL 2200 FS (68). The image size acquired at 0.5 nA was 2048 × 2048 pixels, with a total acquisition time of 2.15 s per frame as follows: area search (0.15 s), focus (0.5 s), exposure (1 s), and tracking (0.5 s), automated and equal for each frame. Data were acquired using the FEI Tecnai Osiris using the FEI Xplore3D and Inspect3D acquisition, post-alignment, and reconstruction software. To produce the resulting 3D volumes, the tilt series was then processed using the IMOD software package ( using the filtered back-projection algorithm without applying fiducial markers. We subsequently used the FEI Avizo 9.2 software for 3D rendering and segmentation.

FIB-SEM tomography

The FIB-SEM tomography workflow is described in (29). Briefly, the bone sample was demineralized in parallel with mild fixation (69), conditioned with alcian blue to stabilize noncollagenous organic components, fixed with glutaraldehyde, and stained with osmium tetroxide (OTOTO protocol). The sample was high-pressure frozen and freeze-substituted, which preserves the dimensions and architecture as in the hydrated state. The sample was then embedded in Epon and sectioned, and imaging was performed using a dual-beam FEI Helios 600 Nanolab FIB-SEM operating in the serial-surface view mode with the slice thickness equal to the lateral resolution of the 2D images in the stack, being approximately 10 nm at 30 keV, 86 pA. The stack was aligned using Fiji (NIH, USA) (70). Labeling of individual collagen fibrils was carried out using the local threshold algorithm in Avizo 9.2, FEI, USA. For the current study, the stack of adult human osteonal lamellar bone (originally referred as M77) was used for collagen segment tracing. An area of well-aligned, ordered, nearly horizontal collagen fibrils within one lamella was selected. In the edge-on projection, a cross section of a fibril was labeled based on the local gradient and then traced in both directions until the same cross section could not be identified. In this manner, 100 collagen fibril segments were traced, their length was recorded in nanometers, and the distribution histogram of the segment length values was analyzed.

Specific surface area and crystallite morphologies

Mineral morphology in bone has important implications because of the resulting high surface area and its adsorption capacity, particularly for water molecules. The surface area of a single-crystal platelet having dimensions w, d, and t isEmbedded Image(4)The volume of an individual platelet isEmbedded Image(5)and the platelet mass isEmbedded Image(6)where ρAP is the mass density of the bone apatite. For an acicular crystal with hexagonal symmetry where the crystal length l is much larger than its lateral extension d, we findEmbedded Image(7)The volume of an individual (acicular) needle isEmbedded Image(8)and the needle mass isEmbedded Image(9)To obtain the total surface area resulting from the specific geometries, it is necessary to multiply the surface area of the individual crystals by 0.32 (32 wt % mineral content) and the number of crystals constituting the mineral phase (which is the ratio of the total mineral mass divided by the mass of an individual crystal). Thus,Embedded Image(10)with the index representing either a plate-shaped or acicular geometry. This results in the following expressions for the total specific surface areas for both geometries:Embedded Image(11)Embedded Image(12)The respective specific areas per mass aPL and aAC are given by the total areas divided by the total masses.

Supplementary Materials

References and Notes

Acknowledgments: We thank C. Boig for support with sample preparation; C. Vacar (FEI) for helpful discussions on tomogram segmentations; T. Roncal-Herrero for support with STEM imaging (R.K. and N.R.); J. O. P. Orgel (Illinois Institute of Technology), O. Smirnov (Petersburg Nuclear Physics Institute), S. Weiner (Weizmann Institute of Science), and M. D. McKee (McGill University) for critical reading of this manuscript; the direct-care teams at Charing Cross Hospital for consenting patients and collecting tissue samples; the patients who agreed to donate tissue for research; the Imperial College Healthcare National Health Service (NHS) staff; G. A. Thomas and Imperial College Tissue Bank staff who helped with the collection of the samples; R. L. Abel (Imperial College London) for sharing samples; J. Orgel for collagen panels III and IV in Fig. 8; and Harvey Flower Electron Microscopy Suite, Imperial College London, for using their characterization facilities. Funding: This work was carried out in the framework of the projects SMILEY (FP7-NMP-2012-SMALL-6-310637) and the UK Engineering and Physical Sciences Research Council (EPSRC) (grant EP/I001514/1), funding the Material Interface with Biology (MIB) consortium (R.K. and M.B.). M.B. acknowledges support from the 4D LABS shared research facility, which is supported by the Canada Foundation for Innovation (CFI), British Columbia Knowledge Development Fund (BCKDF), Western Economic Diversification Canada, and Simon Fraser University. M.M.S. acknowledges funding support from a Wellcome Trust Senior Investigator Award (098411/Z/12/Z) N.R. gratefully acknowledges support from the Value-In-People Award from the Wellcome Trust Institutional Strategic Support Fund (097816/Z/11/B). The Imperial College NHS Tissue Bank is funded by the National Institute for Health Research–Biomedical Research Centres (NIHR-BRC), UK. Author contributions: R.K. conceived the idea and planned the experiments. M.B., L.L., N.R., and R.K. carried out the experiments. N.R. and R.K. reconstructed and processed experimental data. R.K. generated the model presented. All authors discussed the results and contributed to the final manuscript. Competing interests: The authors declare no competing interests. Data and materials availability: Data are available online at DOI: 10.5281/zenodo.1196033 All (other) data needed to evaluate the conclusions in the paper are present in the paper or the supplementary materials.

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