Human cortical bone has a complex and dynamic microstructure that undergoes continual change throughout life. An integral component of this microstructure is the network of porous canals that facilitate the distribution of neurovascular structures throughout the cortex. With the exception of a small minority of studies, the analysis of cortical bone microstructure, including the canal network, has largely been restricted to the two-dimensional (2D) realm. Although 2D histomorphometric techniques have and continue to provide a wealth of information regarding bone tissue dynamics (Frost, 1969; Parfitt, 1983; Ott, 2002), they cannot yield a complete picture of the three-dimensional (3D) microstructure of cortical bone. Cortical microstructure exists and remodels in 3D; therefore, a full understanding of its architecture will require 3D analysis (Stout et al., 1999).
To date, the key factors that have limited 3D investigation are methodological. For example, reconstruction from serial sections is tedious (DeHoff, 1983), whereas ink perfusion and casting techniques provide largely qualitative data regarding 3D structure. Automated, computer-assisted reconstruction of serial sections does offer a more efficient alternative (Odgaard et al., 1990), however, such techniques have largely been replaced, for trabecular bone at least, by micro-computed tomography (μCT). μCT offers several advantages, including the preservation of the specimen for correlative analysis and a digital data format, that facilitates quantitative 3D architectural analysis.
With continuing improvements in μCT scan resolution, increasingly smaller structures have been brought within the reach of this technology, and the ability of μCT to resolve the canals within human cortical bone (Wachter et al., 2001a) and reconstruct them in 3D (Cooper and Hallgrímsson, 2002) has recently been demonstrated. Therefore, μCT represents a new, relatively unexplored, tool for 3D analysis of the cortical canal network that we believe has the potential to provide novel insights into the overall microstructure of cortical bone. Our aim in this article is to briefly review what is known about the 3D microstructure of cortical bone, introduce μCT as an efficient technique for quantitative 3D analysis of the cortical canal network, and to discuss the potential of such analysis in future research.
One of the most important advantages of μCT-based analysis of trabecular bone is that it provides an efficient means by which 3D architecture can be quantified.
One of the earliest descriptions of the network of canals within cortical bone was made in 1691 by Clopton Havers, who noted the existence of longitudinal and transverse pores within compact bone and speculated that these canals form an interconnected network, providing a route for the conduction of medullary oils throughout the cortex (Havers, 1691). Longitudinal canals associated with secondary bone still bear his name (Haversian canals). However, in an earlier study, Antonie van Leeuwenhoek (1677–1678) described the composition of compact bone as a collection of “pipes” and included what are likely the first 3D renderings of cortical bone microstructure (Figure 1). Like Havers' later description, van Leeuwenhoek also noted that the longitudinally and transversely arranged pores form an interconnected network. Notably, the identification of the canals within cortical bone preceded that of other microstructural features. It was not until the mid-19th century that Todd and Bowmann (1845) first described Haversian systems (1845) and Tomes and De Morgan (1853) discerned the nature of their formation within localized Haversian (resorption) spaces.
More than 300 years after their first description, the canals within cortical bone are viewed in very much the same way. The longitudinally oriented canals are now divided into two types, non-Haversian and Haversian, corresponding to primary osteons and secondary osteons, respectively, and transversely oriented canals are known as Volkmann's canals in honor of a 19th century German physiologist. However, evidence from a small number of studies has revealed a greater degree of complexity than was suggested by conventional descriptions. These investigations have primarily used two approaches, direct visualization of canals by staining or casting and reconstruction from serial histological sections, to evaluate the 3D microstructure of cortical bone. Staining techniques range from superficial observation of abraded bone surfaces to determine the general orientation of vascular canals (Hert et al., 1994; Petrtyl et al., 1996) to more involved preparations, which include staining followed by clearing, to permit the visualization of deeper canals (Ruth, 1947). These techniques have been particularly effective at demonstrating general patterns of vascular supply within bones (Dempster and Enlow, 1959; Albu and Georgia, 1984), the distribution of resorptive spaces associated with remodeling (Vasciaveo and Bartoli, 1961), and differences in the canal network in the bones of different species (Georgia et al., 1982; Georgia and Albu, 1988). Although effective at visualization of the canal network, casting and staining techniques do not provide a direct means of quantifying 3D structure; therefore, architectural observations are largely qualitative.
Serial sectioning, while tedious, provides a means of visualizing the vascular canal network in relation to nonporous structures. Cohen and Harris (1958), for example, examined the paths of Haversian systems in 3D, and Tappen (1977) examined the 3D structure of resorption spaces associated with the formation of Haversian systems. Before the availability of computers, reconstruction from serial sections required the resourceful use of materials such as cardboard and wires to create 3D models (Amprino, 1948; Cohen and Harris, 1958; Kragstrup and Melsen, 1983). The use of computers in conjunction with histological serial sections has allowed such innovations as real-time manipulation of semitransparent models, permitting the visualization of the spatial relationship between cells and extracellular matrix in 3D (Schnapper et al., 2002).
Direct analysis of serial sections, or 3D reconstructions derived from them, has provided a means of testing hypotheses that have been inferred from analysis of sections. For example, 3D reconstruction of osteons in the canine femur by Stout et al. (1999) demonstrated a “complex pattern, dominated by branching” and lead to the conclusion that several morphologic types of osteons identified in 2D sections may not actually exist “but rather are artifacts of the relative orientation of the plane of sectioning, or where along the length of the haversian canal the section was made”. A specific example that was provided is that dumbbell-shaped osteons are actually artifacts of sectioning through a bifurcating osteon. Such findings underline the need for further 3D analysis of cortical bone microstructure. Investigation of the vascular canal network by μCT may provide an important stepping stone.
APPLICATION OF μCT IMAGING TO CORTICAL BONE
Computed microtomography imaging has been growing in use since its description as a tool for the direct analysis of 3D trabecular bone structure in 1989 (Feldkamp et al., 1989). The most common application of this technology has been the in vitro quantification of osteoporotic change in trabecular bone architecture (Borah et al., 2001). After its introduction, technical developments have resulted in the progressive improvement of scan resolution from 70 microns to resolutions on the order of a single micron (Jiang et al., 2002). The highest resolutions are generally achieved with synchrotron radiation (SR) sources and provide an extraordinary level of detail. For example, osteocyte lacunae are visible in tomographic images with 1.4 μm spatial resolution (Peyrin et al., 1998). The development of higher spatial resolution is ongoing, and sub-micron tomography (0.6 μm) has recently been achieved through the combination of μCT and x-ray microscopy technology (Takeuchi et al., 2002). For commercially available μCT scanners, resolutions of 30 to 15 μm are typical (Borah et al., 2001), reflecting the range of resolutions commonly used for trabecular bone imaging. However, higher resolutions are increasingly available and we use a scanner that is capable of spatial resolutions ranging from 20 to 5 μm.
Clearly, with the ability to resolve osteocyte lacunae, μCT technology has developed beyond the resolution necessary for the analysis of cortical canals. This finding leads to the question of what resolution is needed for their analysis, and the answer requires some knowledge of the scale of the actual canals. Based on data from 2D histological studies, it is known that the size of pores (canals viewed in cross-section) within cortical bone varies both within and among species (Jowsey, 1966). Additionally, due to the formation by of Haversian systems by the infilling of resorption spaces, Haversian canal diameters can vary greatly within a single bone due to the simultaneous presence of systems at various states in the remodeling process. The size of resorption spaces in human bone have been reported to be on the order of 200 to 300 microns (Dempster and Enlow, 1959; Johnson, 1964; Jaworski et al., 1972); therefore, Haversian canal diameters can be expected to range between these values and their “mature” size. Human cortical pore sizes vary considerably across age, sex, and sampling site (Stein et al., 1999; Bousson et al., 2001), making this “mature” size difficult to define. Pfeiffer (1998) reported that human Haversian canals at the femoral midshaft have larger cross-sectional areas than those in ribs, with (assuming circular canal shape) mean diameters of 33 and 27 μm, respectively. However, considerably smaller Haversian canals were also found with the 5th percentiles for femora and ribs being 17 μm and 12 μm, respectively (Pfeiffer, 1998). Similarly, in the human mandible, mean Haversian canal diameter has been reported to be 45 μm; however, 7% of canals measured were 15 μm or less in diameter (Dempster and Enlow, 1959).
The various factors that influence canal size must be kept in mind when choosing scan resolution. If only percent porosity and bone volume fraction are required, lower resolutions may provide adequate results. For example, Wachter et al. (2001a) reported that a 30 μm scan resolution was effective at predicting cortical porosity (%) when compared with conventional histomorphometry in a sample of older adults. However, as human bones contain many canals with diameters well below 30 μm, analyses of 3D architectural characteristics require considerably higher resolutions.
QUANTITATIVE ASSESSMENT OF THE CORTICAL CANAL NETWORK
One of the most important advantages of μCT-based analysis of trabecular bone is that it provides an efficient means by which 3D architecture can be quantified. A host of quantitative parameters have been developed to measure different aspects of trabecular bone architecture, and the reader is referred to a recent review by Borah et al. (2001) for an excellent summary. In general terms, these parameters can be divided into two groups, (1) those that describe the amount of trabecular bone and average characteristics of individual trabeculae, and (2) those that describe the more complex architecture of the trabeculae collectively. Provided that they are measured directly and not based on a structural model, many parameters from the first group are transferable to the analysis of the cortical canals (see Table 1). For example, cortical porosity (Ca.V/TV) reflects the relative volume of porous canals (Ca.V) within the sample tissue volume (TV). This value is the compliment of bone volume fraction (BV/TV) and is analogous to marrow volume fraction in trabecular bone (Ma.V/TV). Likewise, trabecular thickness (Tb.Th) and separation (Tb.Sp), can be translated into measures of cortical canal diameter (Ca.Dm) and canal separation (Ca.Sp). A particularly attractive aspect of these parameters is that many can be measured using existing software developed for trabecular bone analysis.
Table 1. Analogous morphological parameters for trabecular and cortical bone*
All abbreviations are based upon standard nomenclature (Parfitt et al., 1987).
Tissue Volume (TV)
Tissue Volume (TV)
Bone Volume (BV)
Canal Volume (Ca.V)
Bone Surface (BS)
Canal Surface (Ca.S)
Bone Volume Fraction (BV/TV)
Cortical Porosity (Ca.V/TV)
Bone Surface to Tissue Volume (BS/TV)
Canal Surface to Tissue Volume (Ca.S/TV)
Trabecular Thickness (Tb.Th)
Canal Diameter (Ca.Dm)
Trabecular Separation (Tb.Sp)
Canal Separation (Ca.Sp)
The application of parameters used to describe the architecture of trabecular bone to cortical canal analysis is less straightforward. For example, structural model index (SMI), a measure that describes the relative contributions of plate-like and rod-like structures (Hildebrand and Rüegsegger, 1997b), is likely to be of limited utility. The canals within cortical bone are approximately cylindrical, and in terms of SMI, very rod-like. On the other hand, measurement of the connectivity within the network of canals is of interest, particularly with respect to the investigation of remodeling-related change. Connectivity, as defined for trabecular bone analysis, essentially reflects the number of closed loops (holes) in the structure (Odgaard and Gundersen, 1993). Because trabecular bone may be viewed as a tightly packed mesh of loops formed by holes in the bony tissue, this topological approach is appropriate. On the other hand, the canals within cortical bone vary in 3D structure from rectangular meshes to highly branched, complex networks and, therefore, are not well characterized by their topology alone. Indeed, a tree-like network of cortical pores with a large number of branches but no closed loops would have the same connectivity measure as a single pore! Therefore, we suggest defining cortical canal connectivity (Ca.ConnD) in geometric rather than topological terms, as the number of canal intersections per unit volume.
To measure canal connectivity and other architectural characteristics, we have developed custom image analysis software. There exist several standard pattern recognition approaches for image analysis that relate to such tasks. Many of them, however, are inherently stochastic, and their accuracy is at best approximate (Jain et al., 2000). We have chosen a deterministic skeletonization technique that thins structures until only their framework, called a skeleton, remains (Lam et al., 1992). Skeletonization has several important characteristics, including the preservation of the topological properties and a deterministic nature that is well suited for proof-of-correctness analysis. Both of these factors are essential for meaningful analysis of parameters, such as connectivity. Skeletonization has been used successfully for several practical applications including the analysis of biomedical (Selle et al., 2000), and geological (Lindquist and Venkatarangan, 1999) structures. This approach works particularly well with tube-like image segments whose central axes are easily identifiable and, therefore, is well suited to the 3D structure of the cortical canals.
In terms of their implementation, popular 3D thinning algorithms extract the skeleton of an image by peeling subsequent layers of voxels (a voxel, or volume element, is a 3D analogue of a pixel, or picture element). The process stops when no voxel can be removed without altering the topological properties of the remaining 3D structure. The Euler characteristic, which is commonly used to quantify topology, is used to regulate the voxel peeling process. For a 3D object, it is defined as E = number of Components − number of Holes + number of Cavities., whereComponents refers to the number of distinct disconnected elements, Holes refers to holes that pierce the object, and Cavities are enclosed spaces that are not connected to the outside of the object. The thinning procedure is designed so that the value E remains constant at all times. Several additional rules are developed to protect important geometric features of the structural boundaries, such as the end points of the branches. A peeling skeletonization algorithm must be able to identify boundary points that can be removed without altering the topology of the object or violating the geometrical constraints. In our application, we implement a thinning algorithm developed by Lee et al. (1994), which is based on a parallel voxel peeling schema that is fast, robust, and contains several safeguards to preserve the geometric properties of the image. After this process, architectural parameters such as canal connectivity density (Ca.ConnD) and total canal length (Ca.Le) can be measured from the skeletons.
DEMONSTRATION OF THE TECHNIQUE
Box 1 details the methods and materials used for this 3D μCT analysis of two human femora to quantify specific aspects of the architecture of the canal network. Examples of 2D cross-sectional images, 3D surface renderings, and 3D representations of the skeletonized networks are provided in Figures 2, 3, and 4, respectively. The 2D cross-sectional images of the samples demonstrated marked differences in the cross-sectional size of the canals (pores) and overall porosity. 3D renderings demonstrated qualitative differences in the canal networks of the two samples and reflected the same marked difference in overall cortical porosity and canal size that were evident in the 2D cross-sections. After skeletonization, it was clear that sample A had a simpler canal network with many longitudinal canals and relatively fewer canal intersections. On the other hand, sample B had a more complex appearance with many perpendicular and oblique intersecting branches. Quantitative analysis, presented in Table 2 and Figures 5 and 6, revealed that sample B yielded larger values than sample A for nearly all parameters, despite that the two samples had similar numbers of canals (Ca.N). The exception to this pattern was canal separation (Ca.Sp), which was lower in sample B.
Table 2. Quantitative Results for Samples A and B*
All abbreviations are based upon standard nomenclature (Parfitt et al., 1987).
Tissue Volume (TV)
Canal Volume (Ca.V)
Canal Surface (Ca.S)
Cortical Porosity (Ca.V/TV)
Canal Surface to Tissue Volume (Ca.S/TV)
Canal Number (Ca.N)
Canal Diameter (Ca.Dm)
Canal Separation (Ca.Sp)
Canal Length (Ca.Le)
Canal Length to Tissue Volume (Ca.Le/TV)
Canal Connectivity Density (Ca.ConnD)
Box 1. μCT Analysis: Materials and Methods
To illustrate the use of μCT for analysis of the cortical canal network, we applied the technique to anterior midshaft samples from two human femora (5 mm × 10 mm blocks). The previously macerated bones were acquired from teaching materials and were of unknown age and sex. Despite that chronological age was unknown, histological examination revealed marked differences in tissue age. The cortex of the first sample (A) contained many non-Haversian canals, and remodeling-related change was not extensive throughout the cortex, therefore indicating a relatively young tissue age (Kerley, 1965). Alternatively, the second sample (B) was extensively remodeled, showed little sign of primary bone (osteons or lamellae), and had a highly porous appearance, all signs that indicate more advanced tissue age. The samples were scanned at the University of Calgary 3D Morphometrics Laboratory, using a SkyScan 1072 (Aartselaar, Belgium) scanner. A spatial resolution of 10 μm was used, based on past experience (Cooper and Hallgrímsson, 2002). The scan protocol included rotation through 180 degrees at a rotation step of 0.45 degrees, x-ray settings standardized to 100 kV and 100 μA, and an exposure time of 5.9 s per frame. Four-frame averaging was used to improve the signal to noise ratio. Scan times were approximately 4 hr per sample.
After scanning, a 2D reconstruction stage using a cone–beam algorithm was used to produce serial cross-sectional images. These consisted of matrices of 1,024 × 1,024 pixels, which collectively composed a volume of isotropic 10 μm3 voxels. A 3D median filter (5 × 5 × 5 kernel) was used to further improve the signal to noise ratio in the images. Global thresholding was used to segment the eight-bit grayscale images into binary black and white images to facilitate quantitative analysis and 3D visualization of the cortical canals. After this, a 2.5 mm × 2.5 mm region of interest (ROI) from the midcortical regions of each of the samples was cropped from 500 serial images representing 5 mm along the length of the sample. This strategy produced matching 31.25 mm3 volumes of interest from which all measurements were acquired. Surface renderings and measurement of the parameters analogous to trabecular bone analysis (see Table 1) were performed using SkyScan software (3D Creator, version 2.2d). Canal diameter (Ca.Dm) and spacing (Ca.Sp) were measured directly, using a model-independent 3D method (Hildebrand and Rüegsegger, 1997a). Canal number (Ca.N) was measured two-dimensionally as the average number of distinct canals per mm2 in the serial image stacks using the particle analysis function of ImageJ 1.27z (http://rsb.info.nih.gov/ij/). 3D visualization of the skeletonized canal networks and quantitative analysis of architectural parameters were performed using the high-performance computing environment at the University of Calgary's Sun Center of Excellence for Visual Genomics (http://www.visualgenomics.ca/).
The 3D models of the cortical canals were converted into Java 3D objects. The Java 3D models could then be displayed and manipulated in the CAVE immersive virtual reality environment (Sensen, 2002) with 12 degrees of freedom (6 for the head-tracking system and 6 for the joystick-like wand). The large display size and the high resolution of the CAVE, in combination with the unique human-machine interface, allowed rapid study of the complex 3D canal mesh. Using the Java 3D Configured Universe tool, the same Java code can be used on various display environments, including regular computer screens. A demonstration of the canal model, configured for monographic two-dimensional computer displays, and a screenshot are available at http://www.visualgenomics.ca/cave.
DISCUSSION OF LIMITATIONS
The μCT technique we used (Box 1) offers an efficient means of quantifying 3D parameters related to the canal network within human bone. However, as with its application to trabecular bone architecture, μCT is limited to aspects of porosity and volume fraction. μCT does not provide information related to many facets of bone dynamics that can be assessed by histological analysis. For example, it cannot differentiate between resorbing, forming, or resting surfaces nor can it provide information regarding the orientation of collagen fibers (Uchiyama et al., 1997; Muller et al., 1998). With regard to cortical bone, our 2D μCT images acquired at 10 μm resolution showed no evidence of nonporous microstructural details, such as lamellae and cementing lines. As a consequence, no differentiation between pore types (Haversian or non-Haversian) was possible.
Similar findings were reported by Engelke et al. (1993), who compared microradiographs and μCT image data and found that, at 50 μm resolution, osteons were not discernible in the μCT images. An additional limitation of the 10 μm resolution was evident from the 3D reconstruction of sample A. The “break-up” of the integrity of the smaller canals indicates that the resolution was insufficient to consistently resolve them. This certainly must have negatively affected the accuracy of the quantitative parameters, particularly those related to canal length (Ca.Le) and diameter (Ca.Dm). On the other hand, overall porosity was likely impacted less, because only the smallest branches were lost. The effect on the measurement of canal intersections is unclear but also likely to be minor, as the canals tended to be enlarged around such points and, therefore, well preserved in the 3D renderings and skeletons.
In light of these limitations, we have begun exploring the use of 5 μm spatial resolution (Figure 7). At this higher resolution, we have found that canal continuity in 3D renderings is dramatically improved. Additionally, some differences in mineral density associated with different osteons are discernible, but these differences tend to be diffuse and inconsistent along serial images. μCT images acquired at 1.4 μm using SR do show localized differences in mineral density, although distinct lamellae do not appear to be visible (Peyrin et al., 1998). Therefore, further improvements in scan resolution may allow the identification of additional structural detail. However, it should be noted that, as spatial resolution increases, the field of view decreases (Peyrin et al., 2000); thus, it is not necessarily beneficial to pursue the highest resolution possible. Ultimately, a compromise between scan resolution, the size of the region/volume of interest, and the desired parameters is necessary. Further investigation is required to determine the impact of resolution on quantitative parameters, a relationship known as resolution dependency (Muller et al., 1996).
The availability of the CAVE immersive virtual reality environment at the Sun Center of Excellence for Visual Genomics has greatly facilitated our work on connectivity measurements. In particular, fine-tuning the 3D skeletonization algorithm and testing its correctness may have been rather problematic without the ability to interactively visualize the resulting 3D models (Figure 8). Although general characteristics of the cortical pore network may be assessed by examining its 2D projections, (such as those in Figures 3 and 4), the entangled nature of the canal network makes it difficult to discern finer details. The CAVE environment proved to be an indispensable research tool, allowing the visualization of the 3D structure of the canal network, or its skeleton, in its entirety at any time during the development and testing, thereby ensuring the correctness and the quality of the results.
POTENTIAL APPLICATIONS OF 3D ANALYSIS
Cortical bone microstructure exists and remodels in 3D, and section-based analysis is incapable of providing a complete picture of its 3D structure. The complex skeletonized meshes produced by our analysis illustrate this point. However, an important question to address is how, specifically, can 3D analysis of the cortical canal network contribute novel information relevant to bone biology research? Whereas we believe that a variety of applications will be fruitful, we focus our following discussion on two general areas of research, cortical bone mechanics and cortical remodeling, to illustrate some key potentials.
The mechanical properties of bone are the product of many factors, including porosity, tissue density, mineral content, and the orientation of the collagen fibers within the extracellular matrix. Numerous studies have noted the importance of porosity with respect to cortical bone strength and elasticity (Currey, 1988; Schaffler and Burr, 1988; Martin and Ishida, 1989). McCalden et al. (1993) reported that age-related increase in cortical porosity is a major contributor to the concurrent decrease in mechanical properties, accounting for 76% of the loss of bone strength with age. In addition to overall measures of porosity, the spatial arrangement of microstructural features and size of pores have been implicated in mechanical properties such as fracture toughness (Yeni et al., 1997). Due to its clinical significance, the femoral neck has been the focus of numerous studies, which have examined the relationship between cortical microstructure and strength. Cortical porosity is an important factor influencing the fracture toughness of this structure (Yeni and Norman, 2000). Differences in the distribution of cortical porosity in the femoral neck, with increased porosity concentrated in the anterior region have been associated with increased fracture risk (Bell et al., 1999). In addition to the percentage of porosity overall, the dimensions of the individual canals and their spatial arrangement have also been implicated. Large voids (diameter > 385 μm) termed “giant canals” (Bell et al., 1999) have been associated with spatial clustering of remodeling osteons (Jordan et al., 2000) and have been linked with increased fracture risk.
As has been demonstrated, μCT is well suited to measuring cortical porosity (Ca.V/TV) as well as the number (Ca.N), size (Ca.Dm), and spacing (Ca.Sp) of cortical canals. In addition to these parameters, quantification of canal orientation, by using measurements such as degree of anisotropy (a measure of preference in orientation), may be useful because Haversian systems, and hence their central canals, lie in tracts that are related to loading history (Hert et al., 1994; Peyrin et al., 2000). The ability to acquire such quantitative parameters in 3D, and to do so nondestructively, presents several major advantages. First, the analysis of a larger tissue volume may provide a better picture of regional variation in the size and spatial arrangement of canals. By using the methods outlined above, at 10 μm spatial resolution, a sample up to 1 cm long can be analyzed from a single scan. Second, the sample is preserved so further analysis such as mechanical testing or histological sectioning can be conducted on the same tissue volume (Wachter et al., 2001b).
Recently, it has been proposed that cortical remodeling may have a higher 3D level of organization, termed “super-osteons,” that account for the phenomena of remodeling clusters and, possibly, giant canals (Bell et al., 2001). This model hypothesizes that spatial clustering of canals may be the result of a single remodeling entity that branches, producing the appearance of clustered osteons in section. Similarly, giant canals (>385 μm) may be the product of these clusters merging through excessive resorption. This hypothesis effectively links the mechanically oriented investigation outlined above with the physiological process of bone remodeling.
This link leads to the second area where we believe 3D μCT-based analysis will be particularly useful: quantification of remodeling associated bone dynamics. As has been noted, μCT is limited to volume fraction and porosity; thus, it is unable to assess many aspects of cortical microstructural dynamics that have been investigated histologically. However, because the network of cortical canals is an intrinsic component of the creation of Haversian systems, it follows that the structure of the canal network undergoes continual change throughout life. This raises the possibility that 3D morphologic analysis of the canal network may provide novel insights into bone physiology that are not possible with 2D approaches. To illustrate this point, it is important to understand the canal network in the context of the processes responsible for bone formation and turnover. Before the mid-1960s, the cell populations that carry out bone formation (osteoblasts) and resorption (osteoclasts) were believed to operate independently of one another. Over the past four decades, an alternative picture of highly coordinated cellular activity has emerged with two general processes recognized: modeling and remodeling (reviewed in Frost, 2001). Modeling is the process by which bone surfaces are altered, either by formative or resorptive drifts. It is thus the process by which bone shape, thickness, and position in “tissue space” are regulated. Formative modeling drift produces new bone, referred to as primary bone, which incorporates primary vascular spaces that subsequently form primary osteons with non-Haversian canals. The 3D structure of primary osteons and, thus, their canals is determined by the pattern of the vasculature that they assimilate. Subperiosteal bone formation incorporates the longitudinally oriented rectangular meshes that serve as the template for primary osteon structure and as a framework for subsequent changes associated with remodeling (Marotti and Zallone, 1980). These rectangular meshes correspond well with conventional descriptions of the canal network involving primarily longitudinally and transversely oriented canals.
Remodeling creates secondary osteons, and involves the close coordination of osteoclasts and osteoblasts in what is known as the basic multicellular unit (BMU; Frost, 1966). The porous component of the BMU takes the form of a “cutting cone,” where osteoclasts resorb a roughly cylindrical packet of bone, followed by a “closing cone,” where osteoblasts deposit the concentric lamellae within the resorption space (Johnson, 1964) (Figure 9). The large resorption spaces created by BMU cutting cones are readily identifiable using resolutions of 10 μm and lower (unpublished results) and it is potentially possible to count the number of active BMUs per unit volume in 3D reconstruction. The 3D structure of BMUs is also of interest, as they do not always have a simple configuration. 2D section-based studies have found that BMUs can be double ended (Tappen, 1977), branched, or both (Johnson, 1964). It is the more complex form of BMU that is likely responsible for the production of “super-osteons” that result in clustering of remodeling osteons (Bell et al., 2001). New BMUs are initiated at bone surfaces including the periosteal, endosteal, and endocortical walls of existing canals. Tappen (1977), by using serial sections to examine the courses of resorption spaces, found that these structures are the continuations of developing osteons whose canals are, in turn, always connected to previously existing vascular canals by transversely oriented canals (Figure 10). The transverse canals were identified as the points of origin for new secondary osteons that formed through the creation of “breakout zones” in the lateral walls of existing channels in the bone (Tappen, 1977). Therefore, in a general sense, remodeling produced by BMU activity continually modifies the canal network through the creation of new canals that branch off of existing canals.
We propose that quantification of canal intersections in the canal network (Ca.ConnD) may, in essence, provide a measure of cumulative BMU activity. The increase in the number of canal intersections in sample B relative to sample A is consistent with this hypothesis. However, it was somewhat curious that sample B did not have considerably more canals (Ca.N) when viewed in cross-section. This finding was likely the product of measuring Ca.N in a 2D manner, where pores that are interconnected in the sampling plane are collectively counted as a single pore. Due to this, sample B, which had far more transversely oriented interconnecting branches, much larger canal diameters, and much smaller canal spacing, was biased toward a lower canal count. This phenomenon may help to account for the results of previous 2D studies of femoral cortical porosity, which have found that pore numbers increase early in life, level off in the 5th to 6th decade, and then decrease with advancing age (Stein et al., 1999; Bousson et al., 2001). This finding highlights a limitation of the 2D approach and suggests that 3D analysis may be particularly useful in examining older tissue ages. In cross-section, the accumulation of new Haversian systems reaches an asymptote as the addition of new systems eventually obscures the evidence of former systems (Frost, 1987).
A similar asymptote likely exists with respect to 3D change in the canal network. However, as suggested by our results with samples A and B, this limit may be later in 3D than 2D. Admittedly, with such a small sample size, caution should be exercised before drawing inferences about general characteristics of remodeling. BMUs can have complex, branched morphologies; thus, it should not be expected that a simple one-to-one relationship exists between BMU activation and canal intersections. However, qualitatively and quantitatively, there appears to be a shift in the canal network from a relatively simple rectangular mesh in younger bone, to a more complex, highly branched structure with advancing age. While we have focused upon canal interconnections, other parameters, existing and new, will undoubtedly prove useful in analyzing cortical canals in 3D. For example, the addition of transversely oriented branches to a predominantly longitudinally oriented network should act to decrease the degree of anisotropy.
It has been noted for some time that μCT has the potential for the analysis of cortical bone structures (Feldkamp et al., 1989). Until now, however, this potential has remained relatively unexplored. The inability of μCT to resolve fine details, such as lamellae and cementing lines in cortical bone, means for the time being that μCT is limited to the analysis of the cortical canal network. This limitation, combined with the notion that cortical bone has a regular structure that is well defined by histological analysis (McCreadie et al., 2001), has resulted in the limited exploration of μCT applications for cortical microstructural research.
As demonstrated by our results, the cortical canal network is a complex 3D structure that cannot be fully appreciated with 2D sections. Ultimately, nondestructive 3D histomorphometric analysis, comparable to existing histological techniques, may be possible through further technological developments. For now, 3D analysis of the cortical canal network serves as an important stepping stone that we believe will provide numerous insights into the overall 3D microstructure of cortical bone. Achieving a better understanding of the 3D architecture of cortical canal network will enhance our current understanding of the biomechanical properties of bone and how bone remodels in 3D. This, in turn, may improve our understanding of pathological processes that affect bone. The use of μCT for trabecular bone analysis has proven to be a fast, precise method for quantitative morphologic analysis, while at the same time, providing a less-destructive alternative to conventional histomorphometry. We believe that the same benefits can be extended to the analysis of cortical bone microstructure.
We thank the three anonymous reviewers for their constructive comments. This research was supported by Alberta Innovation and Science, the Canadian Foundation for Innovation (grant 3923), the National Science and Engineering Research Council (grant 238992-01 to B.H.), and the University of Calgary. C.S. is supported by the Alberta Science and Research Authority, Western Economic Diversification, the Alberta Network for Proteomics Innovation, Genome Prairie, and Genome Canada. B.H. received funding from the National Science and Engineering Research Council.
Mr. Cooper is a Ph.D. candidate in the Interdisciplinary Ph.D. program in the Departments of Archaeology and Medical Science at the University of Calgary (U of C). His research interests include biological anthropology and bone biology. His ongoing research involves the use of imaging technology to study bone morphology. Dr. Turinsky is currently a Postdoctoral Research Associate with the Sun Center of Excellence for Visual Genomics at U of C. He holds a Ph.D. in Mathematical Computer Science from the University of Illinois at Chicago. His research areas include applied mathematics, data mining, and bioinformatics. Dr. Sensen is a tenured Full Professor for Bioinformatics at the U of C's Faculty of Medicine. He is the director of the Sun Center of Excellence for Visual Genomics, which features the world's first Java 3D-enabled CAVE immersive virtual environment. Dr. Hallgrímsson is an Associate Professor in the Department of Cell Biology and Anthropology and Assistant Dean (USE) in the Faculty of Medicine at the U of C. He is a biological anthropologist and evolutionary biologist who combines developmental genetics with morphometrics to address the developmental basis as well as evolutionary and biomedical significance of components of phenotypic variability.