Cortical Bone Mapping: Measurement and Statistical Analysis of Localised Skeletal Changes
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Purpose of Review
Cortical bone mapping (CBM) is a technique for measuring localised skeletal changes from computed tomography (CT) images. It can provide measurements with accuracy surpassing the underlying imaging resolution. CBM can detect changes in several properties of the cortex, with no prior assumptions about the likely location of said changes. This paper summarises the theory behind CBM, discusses its strengths and limitations, and reviews some studies in which it has been applied.
CBM has revealed associations between fracture risk and cortical properties in specific regions of the proximal femur which present feasible therapeutic targets. Analyses of several pharmaceutical and exercise interventions quantify effects that are distinct both in location and in the nature of the micro-architectural changes. CBM has illuminated age-related changes in the proximal femur and has recently been applied to other bones, as well as to the assessment of cartilage.
The CBM processing pipeline is designed primarily for large cohort studies. Its main impact thus far has not been in the realm of clinical practice, but rather to improve our fundamental understanding of localised bone structure and changes.
KeywordsCT Fracture Cortical bone mapping Statistical parametric mapping
Imaging plays an important role in the investigation and understanding of skeletal disease. The most commonly used modality for osteoporosis assessment is dual-energy X-ray absorptiometry (DXA), since it is relatively safe, well understood, and capable of measuring properties that are good predictors of fracture . Nevertheless, there are advantages to be gained through the use of modalities, such as quantitative computed tomography (QCT), that are able to reveal the 3D structure of the bone. QCT is an essentially conventional CT with an additional calibration phantom for converting Hounsfield units to material densities. Although even high-resolution peripheral QCT (HRpQCT) cannot delineate precisely the micro-architecture of cortical and trabecular bone , QCT can capture far more detail than is possible with DXA. A number of emergent techniques have been proposed for the analysis of skeletal QCT data , motivated by the need to further understand the links between bone health, fracture risk, and the specific benefits of pharmaceutical treatments and exercise regimes. Early detection and improved diagnostic accuracy are important goals, since there can be a latency of several years before treatments start to show any benefit .
Traditionally, QCT studies involved specific types of image analysis within predetermined regions of interest, for instance the average bone density within the femoral neck. In contrast, computational anatomy techniques [3, 5] permit the study of each bone as a whole, looking for effects over the entire volume or surface without preconceptions regarding their location or nature. The discipline of computational anatomy encompasses mechanical assessment of bone strength (finite element analysis, FEA), volumetric image analysis (voxel- and tensor-based morphometry, VBM or TBM) and surface-based image analysis (cortical bone mapping, CBM). While CBM is the focus of this review, the statistical approaches required to quantify effects in CBM are similar to those needed for VBM and TBM, and the accurate cortical measurements that underpin CBM may also be used to improve the quality of FEA bone models.
CBM studies have demonstrated links between bone features and ageing, fracture risk, and even radiotherapy, and also the effects of pharmaceutical and exercise regimes. Since CBM is surface-based, results are best displayed as colour maps, revealing where on the bone surface the effects are most prominent. The source data is typically whole-body QCT [3, 6•], though HRpQCT has been used for studies of the distal limbs  and palaeoanthropological specimens . However, neither HRpQCT nor QCT can reveal the porous structure of bone, since the imaging resolution is limited to around 0.3 mm for the former and 1.5 mm for the latter. Much of the CBM pipeline is therefore concerned with making accurate measurements of cortical properties in low-resolution data. Further challenges are posed by the sheer quantity of measurements (thousands per scan, with typically hundreds of scans per study) and their subsequent statistical analysis. It is therefore welcome that free software is available for each stage of the CBM pipeline.1
Surface-Based Bone Measurement
CT imaging systems have finite resolution, and hence each CT sample reflects the X-ray linear attenuation of the imaged material averaged over a small volume. This attenuation is usually expressed in Hounsfield units (HU), where -1000 HU corresponds to air and 0 HU to water. Despite this normalisation, HU values for tissue and bone depend on the energy distribution of the X-rays, which varies between CT scanners. In QCT, a calibration phantom is scanned to facilitate conversion from HU to bone-equivalent material density (BMD, mg/cm3). The finite resolution volumes are generally larger than the voxel size (the spacing between samples in the 3D data set). In whole-body CT, the volumes’ in-slice dimension is typically 1.5 mm, with the between-slice dimension depending on slice spacing, but typically exceeding the in-slice dimension.
For structures that are larger than the finite resolution volume, the effect is to blur their edges a little, with no catastrophic consequences for thickness or density measurement. However, trabecular bone, and cortical bone in many places, is thinner than the finite resolution volume, and consequently QCT measurements may not be what they seem . It is quite possible for an apparent measurement of cortical ‘density’ to be more representative of cortical ‘mass’, and for cortical ‘thickness’ to reflect the imaging resolution above any property of the cortex itself. Much depends on how the measurements are taken, a detail which is frequently lacking in the literature, making inter-study comparisons very difficult.
Thresholding is the most common technique for estimating cortical thickness and density. Cortical bone is detected when the CT data exceeds a predetermined threshold; cortical thickness follows as the distance between points where the CT data crosses the threshold, and cortical density is the average of the CT values between these points. Alternatively, the threshold may be adapted to local properties of the data. If it is set to halfway between the peak and surrounding CT values, we have the full width half-maximum (FWHM) technique , with the density then given by the peak value. In contrast, CBM is a model-based approach. The various model parameters (material densities, cortical edge locations and the CT blur) are initially guessed, the resulting CT data is simulated and compared with the actual CT data, and the model parameters are then optimised until the simulated and real data match. This approach was initially proposed for the measurement of cartilage  and later adapted for cortical bone analysis . CBM was further developed to improve density estimation [6•, 10] and is now widely adopted by the research community [14, 15, 16, 17].
Inspection of the legends in Fig. 2 shows that FWHM and thresholding produce poor estimates of thickness (mm) and ‘density’ (HU), whereas CBM is more reliable, especially when the cortex is thin. There are some subtleties not discussed here, particularly when it comes to density estimation which, for very thin cortices, is inherently less precise than thickness estimation [6•, 10]. However, the broad conclusions remain unchanged, with CBM consistently outperforming the other techniques.
While cortical thickness (CTh, mm) and ‘density’ (in HU) can be measured without a calibration phantom, QCT data is required for true cortical bone mineral density (CBMD, mg/cm3). However, the most reliable measurement that can be made is cortical mass surface density (CMSD, mg/cm2). This is a poorly understood quantity, but of significant value precisely because it can be measured with high accuracy and is a good indicator of cortical bone strength. Unlike the DXA-based quantity ‘areal density’ (aBMD), which has the same units but is not a true measure of density at all, CMSD is a well-defined material property, the cortical mass per unit surface area, calculated by multiplying CBMD × CTh. Since either thicker or denser bone result in increased CMSD, CMSD is a good indicator of bone strength. The legends in Fig. 2 show uncalibrated CMSD in units of HUmm. Note how CBM consistently estimates CMSD with high accuracy, even when the cortex is thin.
Unlike VBM and TBM, CBM is intrinsically a surface-based technique designed to estimate properties of cortical bone. Nevertheless, the model-fitting produces an estimate of the average trabecular density immediately adjacent to the cortex, the endocortical trabecular density (ECTD, mg/cm3). Endocortical trabecular bone supports the cortex and therefore plays an important role in bone strength. In total, then, CBM produces four measurements which can be mapped across the surface and analysed for statistically significant effects: CTh, CBMD, CMSD, and ECTD. These four measurements are shown in Fig. 1a.
Mapping of Measurements
Having established how to measure cortical properties at a single location, the next step is to repeat this process at many locations covering the region of interest on the bone. This requires an approximate representation of the bone surface as a triangle mesh, a set of connected triangles which is the standard way to represent surfaces in computer graphics. Part of the underlying triangle mesh is revealed in Fig. 1b. Cortical measurements are then made at each vertex of the mesh, in the direction of the normal to the mesh at that vertex. The measurements are not particularly sensitive to the form or location of the mesh, provided the vertices are within around 2 mm of the true cortical surface . In most CBM studies, the mesh is generated by a semi-automatic segmentation technique, taking around 10 min per proximal femur [6•]; more automated methods are also possible . An even distribution of triangles, as shown in Fig. 1b, is necessary for regular sampling of the cortical properties on the surface.
CBM measurements may then be displayed as colours on the mesh. Variations in hue are essential for this purpose, since brightness is already exploited to create the 3D impression. The choice of colour scale has a strong impact on perception of the measurements. A good scale should not exhibit mach banding (abrupt, perceived transitions at arbitrary measurement values) and should reveal small variations at all ranges . The ubiquitous ‘rainbow’ colour scale fails on both these counts, while the scale used throughout this paper is sound.
Registration and Statistical Parametric Mapping
In typical studies, cortical maps are produced for hundreds of individuals and then analysed using statistical parametric mapping (SPM), a methodology that has its roots in neuroimaging . A prerequisite, termed spatial normalisation in the SPM lexicon, is that the cortical measurements are transferred onto a template (or canonical) surface. This is achieved by aligning the canonical surface with each individual, and then projecting the measurements from the vertices of the individual mesh onto the nearest vertices on the canonical mesh, as shown in Fig. 1c.
Surface-to-surface alignment (or registration) is a common procedure in medical image analysis. Registration algorithms lie on a spectrum from fully automatic to highly manual, the latter requiring expert labelling of anatomical landmarks. While the automatic methods have obvious appeal, the registrations they produce can be somewhat arbitrary. Thus, individuals with identical cortical properties, but different shapes, may align differently with the canonical surface, and the cortical properties will no longer appear identical on the canonical mesh . Systematic misregistration of this nature is particularly problematic when the study explicitly references shape (e.g. “How does CMSD depend on femoral bone shape?”), in which case registration based on explicit anatomical landmarks is preferred . A by-product of the registration process is a compact representation of each specimen’s shape , which may be of interest in its own right or incorporated as a regressor in the subsequent statistical analysis.
Finally, the cortical measurements, now all expressed on the canonical mesh, are smoothed before a general linear model (GLM) is fitted to the data at each vertex. For example, a case-control study might fit a model in which CMSD is explained by age, weight, shape, and group (case or control). F or t statistics are then calculated at each vertex, to test whether CMSD depends significantly on the regressors, with random field theory furnishing the corresponding p values, corrected for multiple comparisons to control the overall image-wise chance of false positives. The coefficients of the GLM can be masked to highlight those regions where the effect is statistically significant, for example with p < 0.05, as shown in Fig. 1d. Alternatives to SPM include principal component analysis (PCA) of the cortical data, with t tests to detect significant differences in PCA coefficients between groups .
The accuracy of the first stage of CBM has been assessed by comparing measurements from low-resolution, QCT scans of cadaveric femurs with measurements of the same femurs obtained with higher-resolution, HRpQCT imaging at 82 μm. The initial CBM study  assessed 16 specimens from the Melbourne femur collection, of mixed sex and ages 40–83, revealing CTh accuracy of 0.0 ± 0.6 mm for cortices in the range 0.3–4 mm. Follow-on studies, with improved methodology and a larger cohort of 18 female and 17 male specimens of ages 59–96 years from the Medical University of Vienna [6•], demonstrated CTh accuracy of 0.1 ± 0.4 mm (for the range 1–6 mm) and 0.2 ± 0.2 mm (for 0.3–1 mm), CBMD accuracy of − 30 ± 180 mg/cm3 (for 1–6 mm) and 190 ± 330 mg/cm3 (for 0.3–1 mm), CMSD accuracy of 8 ± 25 mg/cm2 (for 1–6 mm) and 1 ± 11 mg/cm3 (for 0.3–1 mm), and ECTD accuracy of − 20 ± 60 mg/cm3 (for 1–6 mm) and 3 ± 30 mg/cm3 (for 0.3–1 mm). Similar validation methods for CBM measurements of the skull assessed CTh accuracy as 0.1 ± 0.6 mm for the range 0–4 mm, despite complications caused by the close proximity of the inner and outer tables .
Since the raison d’etre of CBM is to reveal the location as well as the significance of skeletal changes, CBM results are best summarised pictorially. We therefore provide a number of figures which are collated and normalised to assist in inter-study comparisons. When the sample size is small, it is sometimes necessary to average cortical measurements over the surface to arrive at statistically significant results. Any differences in the CTh, CMSD, ECTD and CBMD effects provide insight into the mechanisms of cortical change.
CBM was used to quantify healthy ageing in a cohort of 619 Caucasian women aged 19–97 . The results provide a standard reference for each of the CBM measurements, and highlight how different areas of the proximal femur are preserved into later life. Figure 3b, c demonstrates that, while ECTD starts to deteriorate at most locations from an early age, CMSD and CTh are preserved in some areas well into the sixth decade .
A further CBM study measured the effects of switching treatment from alendronate (ALN) to TPTD, compared with adding TPTD to ongoing ALN . The results demonstrated more significant increases in CTh and decreases in CBMD when switching from ALN to TPTD, suggesting that ALN moderates the effects of TPTD, particularly in load-bearing regions. In another multi-trial analysis, the effects of TPTD over different treatment periods of 18 and 24 months were compared . Despite difficulties analysing data over multiple trials, the results showed a statistically significant increase in ECTD from 18 to 24 months, confirming continued TPTD effects over the longer treatment period.
Several studies have used CBM to identify links between focal cortical defects and fracture risk. The first such study combined data from the Czech Republic and the UK, looking at 313 female and 30 male subjects, with 158 fractures, 145 controls, and 50 fallers without fracture [33•]. The results revealed distinct patterns of CMSD and ECTD linked to different fracture types, with focal reductions of around 20% CMSD and 50% ECTD in cases compared with controls. It was further demonstrated that CBM predicts fracture type better than aBMD measurements alone.
CBM of the proximal femur has value beyond treatment monitoring and fracture prediction. For example, CBM-based thickness and density measurements have been used to build FEA models that allow sophisticated assessment of bone strength in relation to fracture risk [37, 38]. CBM has also been used to monitor adverse effects of radiotherapy in patients with anal cancer. In , the hips of 22 patients were scanned at baseline and after radiotherapy. The pre-therapy and post-therapy hips were aligned using anatomical landmarks and then compared at several a priori regions of interest. The results showed that a dose exceeding 40 Gy was a significant predictor of clinically significant focal cortical bone thinning, with > 30% reduction in CTh at the femoral neck and a 6% reduction in ECTD as well.
Other Skeletal Sites
CBM has also been used to investigate links between thoracic stereotactic radiotherapy and spontaneous fracture of the ribs . The methodology was similar to the aforementioned femoral radiation study , with a priori regions of interest in lieu of SPM. In a cohort of 28 patients, there was a clear relationship between CTh and dose, with 2% CTh thinning for doses of 0–10 Gy, 7% for 10–20 Gy, 14% for 20–30 Gy, 15% for 30–40 Gy, and 18% for > 40 Gy. Healthy variation in cortical thickness of the ribs has been studied in a similar manner .
CBM has furthered understanding of injury biomechanics by providing more detailed measurements of skull cortices in healthy ageing , though again the statistics were handled differently and not using SPM.
Finally, CBM has found application in the field of palaeoanthropology. Although sample sizes tend to be small, and statistical power is therefore diminished, CBM studies of the hand and foot bones of extant and extinct hominoids have shed light on skeletal loading and function [8, 45].
Conclusions and Future Directions
CBM is a powerful methodology that offers accurate assessment of the skeletal cortex from low-resolution QCT data, with good differentiation between thickness, density, and mass. By transferring the measurements onto a canonical surface, and analysing the resulting distributions using SPM, it is possible to identify regions where the cortical properties depend on regressors of interest (for example age, or case/control, or baseline/post-treatment), with no need for a priori assumptions as to the locations of said regions. Weaknesses of CBM include the need for an approximate segmentation of the outer bone surface, which is typically the most time-consuming stage of the processing pipeline. Unlike the voxel-based alternatives VBM and TBM, CBM provides information only about the cortex and the endocortical trabecular bone.
Two recent developments indicate likely future trends in CBM-type analysis. By extending the cortical model to allow for a finite-width, endocortical region where the bone density decreases linearly from cortical to trabecular levels, it is possible to detect and assess specifically endocortical bone remodelling. It has recently been demonstrated that such measurements are feasible using low-resolution, clinical QCT . Secondly, since CBM is fundamentally concerned with the measurement of thin plate-like structures, it can be applied not just to the skeletal cortex, but to any other thin structure. In this spirit, CBM has been used to assess the space between bones in a joint , which is indicative of cartilage thickness and therefore important in the evaluation of osteoarthritis. Whereas cartilage can only be inferred indirectly from the joint space in CT, CBM has also been successful in assessing cartilage thickness directly, at the knee, using MRI .
Compliance with Ethical Standards
Conflict of Interest
Graham Treece has a patent (Cortical bone mapping, WO 2011/042738) issued. Andrew Gee declares no conflict of interest.
Human and Animal Rights and Informed Consent
This article does not contain any studies with human or animal subjects performed by any of the authors.
Papers of particular interest, published recently, have been highlighted as: • Of importance
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