Structural and functional assessment of trabecular and cortical bone by micro magnetic resonance imaging



Osteoporosis is a multifactorial disorder of bone mineral homeostasis affecting the elderly. It is a major public health issue with significant socioeconomic consequences. Recent findings suggest that bone loss—the key manifestation of the disease—is accompanied by architectural deterioration, both affecting the bone's mechanical competence and susceptibility to fracture. This article reviews the potential of quantitative micro MRI (μ-MRI), including a discussion of the technical requirements for image acquisition, processing, and analysis for assessing the architectural implications of osteoporosis and as a means to monitor the response to treatment. With current technology, the resolution achievable in clinically acceptable scan times and necessary signal-to-noise ratio (SNR) is comparable to trabecular thickness. This limited spatial resolution regime demands processing and analysis algorithms designed to operate under such limiting conditions. It is shown that three different classes of structural parameters can be distinguished, characterizing scale, topology, and orientation. There is considerable evidence that osteoporotic bone loss affects all three classes but that topological changes, resulting from conversion of trabecular plates to rods, with the latter's eventual disconnection, are particularly prominent. Clinical applications discussed can be divided into those dealing with assessment of osteoporotic fracture risk as opposed to the study of the effect of disease progression and regression in response to treatment. Current data suggest that noninvasive assessment of cortical and trabecular bone (TB) architecture by μ-MRI may provide new surrogate endpoints to assess the efficacy of intervention in osteoporosis treatment and prevention. J. Magn. Reson. Imaging 2007. © 2007 Wiley-Liss, Inc.


Bone as a Living Tissue

Bone is a unique mineralized tissue that is the building material of the skeleton of all vertebrates. It has multiple functions, chief among which is locomotion and protection of internal organs while also serving as the body's major calcium store. Bone is a living composite biomaterial composed of an organic substrate consisting largely of type I collagen (∼40% by volume) interspersed with mineral crystals composed of nonstoichiometric calcium hydroxy apatite (∼45%). The remaining volume (∼15%) is occupied by water that is either bound to collagen or resides in the spaces of the lacunocanalicular system. This combination confers to bone its unique mechanical properties in terms of tensile and compressive strength and is responsible for the material's viscoelastic properties (1). Structurally, one distinguishes between cortical bone (CB) and trabecular bone (TB). TB is predominant in the axial skeleton and near the joints of long bones. It consists of a network of interconnected plates and struts fused to and encased by a thin cortex. In the human skeleton trabeculae are typically 100–150 μm thick, whereas the thickness of CB varies between 1 and 5 mm.

In the adult skeleton, bone constantly remodels, a term that implies a dynamic equilibrium between bone formation and bone resorption. At midlife, this process is balanced, i.e., bone resorption, effected by cells called osteoclasts, is exactly compensated by an equal amount of new bone deposited through the action of osteoblasts, the bone-forming cells. The remodeling process is governed by the mechanical demands placed on the skeleton but it is also regulated hormonally. Manifestations of perturbations of these control mechanisms include bone loss that occurs during prolonged exposure to microgravity (2) or inadequate or missing production of gonadal steroids (e.g., see Ref.3). Osteopenia refers to a condition of reduced bone mass, not yet considered pathologic and usually without clinical symptoms. It may, however, be regarded as a precursor of osteoporosis, which is clinically indicated for treatment with antiresorptive (4) or anabolic drugs (5). The most common form of osteoporosis is caused by the rapid loss in estrogen levels in women following menopause, often referred to as postmenopausal osteoporosis. Although generally less extensively studied and understood, there is increasing recognition that osteoporosis in men is prevalent, in particular among the elderly and men with testosterone deficiency (see, for example, Ref.6).

Bone Strength and Density

Bone mineral density (BMD) has been used for over two decades as a surrogate parameter for assessing fracture risk and, by inference, bone strength (7). The use of bone densitometry as a diagnostic quantitative imaging technique rests on the empirical observation that the strength of TB (the type of bone where most fractures occur) scales with bone density. Carter and Hayes (8) measured the compressive strength of TB ex vivo in specimens using material testing techniques, concluding that the strength is proportional to the square of the apparent density while the modulus is proportional to the cube of apparent density. The density should correctly be termed “apparent” since it is not the true density of the bone material that is measured but rather the amount of bone per unit volume of tissue, which comprises both bone and marrow. Quantitative computed tomography (CT) would be suited to measure BMD and a considerable amount of literature exists on quantitative whole-body CT for measuring BMD in the vertebrae and femur (9, 10). However, in the current clinical setting BMD is measured by instruments dedicated for this purpose. The most common among these is dual-energy X-ray absorptiometry (DEXA) (e.g., see Ref.11). DEXA emerged from single- and dual-photon absorptiometry, which use a radionuclide source rather than an X-ray tube as a radiation source. DEXA and its predecessors are projection-imaging techniques that return an apparent areal density expressed as grams per centimeters squared (g/cm2) of mineral. Hence, the technique is unable to distinguish between cortical and TB. Further, DEXA densities are confounded by intersubject variations in bone size (12). During the past 10 years, peripheral quantitative CT (pQCT) has become available as an alternative to DEXA. Like general-purpose CT this is a tomographic technique but one that is confined to peripheral skeletal locations, primarily the forearm and tibia.

The notion of bone strength and clinically, fracture risk, being related to BMD, has become the basis of the current clinical definition of osteoporosis. Accordingly, a subject having BMD measured at either the lumbar spine or proximal femur of less than 2.5 SD (also referred to as the “T-score”) below the mean of the young adult population, is considered osteoporotic (13). Similarly, a T-score of less than −1 but greater than −2.5 places a subject into the osteopenic category (14). In terms of the above definition, 30% of postmenopausal white women in the United States have osteoporosis (15) and the prevalence in Europe and Asia is similar. The prevalence in blacks, however, is generally lower (16).

Bone Quality

There is rapidly growing evidence of the role of descriptors other than apparent density, as determinants of the bone's mechanical properties (17–19). Although low BMD increases fracture risk, not all patients who are osteoporotic will sustain a fracture. Rather, low BMD is a risk factor for fracture just like high cholesterol is a risk factor for heart disease. In fact, BMD is a rather poor predictor of fracture risk. Laboratory data show that, on the average, BMD explains about 60% of bone strength as estimated from a meta-analysis of 38 studies investigating some measure of bone strength (20). It is straightforward to see that the nature of bone loss is essential in determining its impact on bone strength. For example, for the same fractional reduction in bone volume, a mechanism that causes uniform thinning compromises strength less than one that disrupts entire structural elements by inhomogeneous erosion (21). Figure 1 shows an electron micrograph of a single trabecula showing a deep osteoclastic resorption pit, which can lead to substantial magnification of local stresses and eventual rupture and disconnection. Therefore, structural connectivity, which can be assessed by evaluating the topological changes that accompany bone loss and treatment, is critical (22). Similarly, CB undergoes structural alterations with advancing age, and more so in osteoporosis, leading to increased porosity (23) that impairs the bone's breaking strength (24). Last, it is generally assumed that the chemical and nanostructural organization of bone is invariant; i.e., the composition and ultrastructure of bone is the same in osteoporotic and healthy bone. Currey (25) showed almost four decades ago that a few percentage points of change in mineralization can change static strength and modulus of elasticity several-fold.

Figure 1.

Electron micrograph of (650 × magnification) of a single trabecula of vertebral TB with deep Howship lacunae caused by excessive osteoclastic resorption causing stresses that will eventually lead to mechanical failure [Reproduced from Mosekilde L. Consequences of the remodelling process for vertebral bone structure: a scanning electron microscopy study (uncoupling of unloaded structures). Bone Miner 1990;10:13–35, with permission].

The above findings are not surprising in that they merely reflect the fact that bone cannot defy general engineering principles that dictate that volume fraction and intrinsic material properties, along with the geometry and topology of the structural elements, determine the critical load a structure can sustain. The recognition that factors other than BMD determine bone strength has given rise to the concept of “bone quality,” a rather loosely defined term comprising architecture, matrix, and mineral properties. In 1994 the World Health Organization (WHO) therefore redefined osteoporosis as a “disease characterized by low bone mass and microarchitectural deterioration causing increased bone fragility” (13). In 2001 a National Institutes of Health (NIH) Consensus Development Panel concluded that osteoporosis should be defined as a “skeletal disorder characterized by compromised bone strength predisposing a person to an increased risk of fracture” (26). This definition takes into consideration that there are other factors that influence bone quality such as the microarchitecture, remodeling rate (bone turnover), damage accumulation, and mineralization. The problem with this definition is that strength cannot be measured in vivo, thus requiring surrogates that somehow quantify parameters that determine bone quality and therefore strength. Among all measures of bone quality, alterations in architecture have so far received the most attention, last but not least because it is, next to bone volume fraction (BVF), the most prominent manifestation of the disease and one that is relatively amenable to quantification by noninvasive imaging modalities.


Quantification of Architecture and Geometry of Cortical Bone

Besides TB atrophy, age-related and postmenopausal osteoporosis leads to cortical thinning (27–29) and increased porosity (23, 30). This effect is partially compensated by an increase in cortical diameter through periosteal expansion (31, 32), an effect that would at least partly offset the thinning-induced reduction in torsional stiffness and buckling resistance (33).

Recent data suggest that weakened CB may primarily be responsible for intracapsular hip fracture (34), thus emphasizing the importance for quantitatively assessing and monitoring cortical structure. Support for the role of CB architecture as a risk factor for hip fracture is found in several studies of postmenopausal osteoporosis, in which strong associations have been reported between proximal femur geometry and fracture incidence (35, 36). Additionally, BMD supplemented by femoral geometry has been shown to be more predictive of breaking strength than BMD alone (37).

Noninvasive assessment of CB structure in osteoporosis is typically being performed on the basis of X-ray projection radiographs (38) or DEXA (36, 39). However, the projection nature of these images cannot capture the three-dimensional (3D) geometry of cortical architecture. The femoral neck (a site of particular interest because of the high incidence of osteoporotic hip fractures) is angulated relative to the coronal plane, therefore making it difficult to accurately evaluate cross-sectional geometry from such images. Whole-body CT (40) and pQCT (41) are increasingly being used to measure 3D cortical geometry, but these techniques are confined to the more distal locations of the peripheral skeleton, such as the wrist and ankle. Nevertheless, these studies support the importance of 3D cortical structure analysis. MR is well suited for direct acquisition of images at arbitrary orientation to optimally capture 3D structure. CT, on the other hand, requires reformation of axial data, typically resulting in reduced resolution.

Recently, a number of articles have appeared in which quantitative MRI approaches were used for quantifying CB structure and geometry (42–46).

MR-based CB analysis is complicated by bone's signal characteristics and anatomy. In conventional MR images, bone typically appears with background signal intensity (in spite of a 10–15% water content that has T2 < 1 msec (47) and therefore is not detectable with echo times used clinically), while the medullary space contains various proportions of hematopoietic and fatty marrow. The periosteal region consists of various soft tissues including muscle and connective tissues (e.g., tendon), which, similar to bone, appear with background intensity by virtue of their extremely short T2. The detection of the endosteal boundary is further complicated by partial volume effects from the often gradual transition from TB to CB. On the periosteal boundaries, the presence of low-intensity connective tissue such as tendons and ligaments adjacent to CB, unless appropriately dealt with, could mistakenly be assigned to CB. Finally, the chemical shift artifact between fat and water causes a spatial shift in the images along the frequency-encoding direction that must be compensated for.

Gomberg et al (48) designed an algorithm to segment CB from soft tissues for measuring CB structure and geometry with specific applications targeted to the proximal femur. The algorithm requires a minimum of user intervention, starting by the operator defining a region within marrow, roughly following the cortical boundary. From this boundary, outward-directed lines of sufficient length are traced in such a manner that they transect the cortical shell roughly perpendicularly. Plotting the signal along these lines produces a map of consecutive profiles. These are then normalized to the intensity of the marrow signal, which is considered to be the highest intensity among all tissues in the image. The profile maps are subsequently processed with one-dimensional (1D) and two-dimensional (2D) morphologic image operators and binarized to determine the cortical boundaries that are then mapped back onto the spatial image. After removal of erroneous boundary points CB cross-sectional area and thickness can be computed. Figure 2 illustrates the sequence of image acquisition steps required for measuring CB structural parameters of the femoral neck.

Figure 2.

Illustration of the imaging protocol for measuring cortical cross-sectional architecture of the femoral neck (a). GE axial localizer image for prescription of coronal oblique images (b); double-oblique cross-sectional images perpendicular to the neck axis (c). d: same as (c) with cortical boundaries highlighted [Reproduced from Gomberg BR, Saha PK, Wehrli FW. Method for cortical bone structural analysis from magnetic resonance images. Acad Radiol 2005;12:1320–1332, with permission].

Besides developmental, age-related, and osteoporotic changes, primary or secondary hyperparathyroidism are known to affect CB (49). Cortical thinning in the appendicular skeleton is one of the skeletal manifestations of renal osteodystrophy (ROD) (50, 51). In a recent study aimed at examining the potential of quantitative MR for the evaluation of ROD, Wehrli et al (46) measured both CB and TB structural parameters in a small cohort of patients on maintenance hemodialysis. A total of 17 hemodialysis patients (average parathyroid hormone (PTH) level 502 ± 415 μg/liter) were compared with 17 age-, gender-, and body-mass index–matched control subjects. High-resolution 2D spin-echo images were collected at the tibial midshaft for measurement of cortical cross-sectional area (CCA) and mean cortical thickness (MCT) using the methodology described above for CB segmentation (48). The most prominent findings were a reduction in relative CCA expressed as a percentage of total bone area and MCT (61.2 vs. 69.1%, P = 0.008, and 4.53 vs. 5.19 mm, P = 0.01).

In summary, morphologic measurements of CB by high-resolution MR in conjunction with imaging processing techniques may be useful for assessing osteoporosis risk and for studying the implications of metabolic bone disease such as those resulting from end-stage renal disease.

Methods for Quantification of TB Architecture

The classical approach to structural analysis of cancellous bone has been histomorphometry from sections by means of stereology (52), an approach that allows estimation of the third dimension by inference. The technique is fraught with error and uncertainty since trabecular architecture is inherently 3D and highly anisotropic (53, 54). This problem was recognized early and led to the development of serial sectioning techniques from which 3D images could be reconstructed (55). These methods, however, were rapidly superseded by nondestructive imaging techniques, chief among which was micro-CT (μ-CT) (56–59). CT appears to be particularly suited for investigating the structure of calcified tissues because of the very large difference in the attenuation coefficients between bone and the surrounding soft tissues [e.g., see Hildebrand et al (60) and references therein].

In vivo, however, the situation is quite different. Dose limitations and point-spread function (PSF) blurring of X-ray-based tomographic methods limit the achievable resolution even at peripheral anatomic sites. In digital imaging, resolution is often falsely equated with voxel size. Gordon et al (61) used a commercial pQCT system to obtain images at a voxel size of 0.33 × 0.33 × 2.5 mm3 of the distal radius to derive marrow pore size and connectivity information. A higher performance pQCT system was built in the Institute for Biomedical Engineering at the Swiss Federal Institute of Technology in Zurich (62, 63). With this system, images at a voxel size of 165 × 165 × 165μm3 could be obtained although the width of the beam-size limited PSF was about 280 μm (64). More recently, a commercial high-resolution p-QCT scanner has become available (Xtreme™, Scanco Inc.), designed for imaging the distal radius. The system uses cone-beam scanning and reconstruction at a nominal voxel size of (89 μm)3 (65) or even (80 μm)3 (66). The prospect of performing structure analysis in the axial skeleton by multidetector CT has recently also been demonstrated. Ito et al (67) analyzed TB images in the vertebrae at 250 × 250 × 500 μm3 voxel size, showing structural parameters to distinguish fracture from nonfracture subjects. However, the radiation dose at which the studies were performed was as high as 77 mGy, which is more than twice that of the reference level for body CT. By contrast, the effective dose for high-resolution p-QCT for a 2.8 minute scan has been quoted as 3 μSv (66), which is almost negligible.

The high innate contrast between bone (which appears with background intensity) and bone marrow, along with its noninvasiveness, render MRI uniquely suited for imaging TB microarchitecture in vivo. Further, in 3D spin-echo spin-warp imaging, the imaging technique generally used in MR microimaging of TB, the PSF is a sinc function, resulting in only 20% PSF broadening, which is generally less than in p-QCT. Figure 3 compares clinical images obtained with the two modalities. It is noted that the effective resolution in the MRI is superior in spite of the considerably larger voxel size, which highlights the importance of the PSF behavior as a determinant of image resolution.

Figure 3.

Comparison of cross-sectional images of the distal radial metaphysis in vivo acquired with two different imaging modalities. a: High-resolution pQCT, 89 × 89 × 89 μm3 voxel size (65). b: 1.5T MRI, 137 × 137 × 410 μm3 voxel size (93).

It is useful to distinguish between methods that attempt to resolve TB microarchitecture directly vs. those that seek to obtain structural information indirectly without the need to resolve individual trabeculae. In this article we will confine ourselves to a review of the direct methods, which are based on acquisition of high-resolution images and which demand a voxel size of the same order of magnitude or less than TB thickness (at least in two of the three spatial directions—typically those perpendicular to the long eigenvector of the fabric tensor). This requirement is difficult to meet in the axial skeleton (e.g., vertebrae) or the proximal femur, the two locations where the majority of osteoporotic fractures occur. Therefore, high-resolution MRI (subsequently termed micro-MRI [μ-MRI]) is generally performed at peripheral skeletal locations only such as the distal tibia (68, 69), calcaneus (70–72), and wrist (73–76). The feasibility of assessing texture in the proximal femur, albeit at considerably lower resolution, has also been explored (72, 77).

Other methods, not discussed here, seek to extract structural information indirectly, i.e., without the need to resolve individual trabeculae (for a recent review, see Ref.78). Indirect detection exploits a particular property of the material, most typically induced magnetism, based on bone being more diamagnetic than marrow (79). The compartmentation of the two coexisting phases induces local inhomogeneous magnetic fields in the vicinity of the trabeculae (80, 81). These local fields, in turn, lead to a damping of the free induction decay (FID), usually expressed in terms of a shortening of the effective transverse relaxation time, T2*, which has been shown to be a function of the density and orientation of the trabeculae (82). Other approaches have been investigated as well, such as measurement of the TB volume fraction, exploiting the reduction in signal amplitude due to fractional occupancy of the voxel by bone (83, 84). Finally, indirect detection of TB microstructure by exploiting the amplitude modulation of the double quantum signal from remotely coupled protons caused by the structural regularity of the TB network, has also been investigated (85, 86).

Technical Requirements for TB Microimaging

Image Acquisition Strategies

Considering the size of trabeculae (80–150 μm), resolution is perhaps the single most critical parameter. Intuition would tells us that the voxel size ought to be on the order of structure size in order to be able to extract structural information. Recall that SNR scales with voxel volume and as the square root of imaging time. Let us then first consider a voxel size of about 1 mm3 as it is used for clinical imaging of the brain. If, on the other hand, we were to aim for isotropic resolution of 150 μm, this would exact a 300-fold SNR penalty, assuming all other parameters remain unaltered. At a given field strength there is practically only one way to boost SNR, which is to reduce the size of the receive radiofrequency (RF) coil. SNR for a circular surface coil scales inversely with coil radius a (the exact relationship depends on the relative contributions from tissue and coil to overall circuit resistance). Suppose we manage to gain a factor of 10 by constraining coil and imaging object, we are still left with a disparity of a factor of 30. Relaxing the resolution along the direction of the trabeculae's preferred orientation (usually the primary loading direction) by a factor of three and accepting a four-fold increase in scan time, we are still off by a factor of five below that of the brain scan. To deal with the remaining shortfall we will have to content ourselves with lower SNR, say 10:1 instead of perhaps 30:1 in a typical brain scan. We are further aided by the much shorter relaxation time of protons in marrow lipids (which are prevalent in the distal extremities). The shorter T1 (0.3 seconds instead of 1 second for tissue water) translates into another factor of two, and we have thus made up the SNR deficit imposed by the 300 times smaller imaging voxels.

There are several types of pulse sequences that are currently in use for structural imaging of TB. Besides SNR and resolution, the pulse sequence needs to be robust by providing artifact-free images of SNR adequate for the processing algorithms to operate reliably. Ideally, the images should provide a faithful representation of topology (e.g., preserving connectivity) and scale (e.g., TB thickness and BVF). The pulse sequence should further allow scanning of a sufficiently large volume along the z (slice-encoding direction, perpendicular to the bone's long axis, field-of-view with respect to z [field of view along the z-axis (FOVz)]), all while allowing scan time to be maintained within the limits of patient tolerance (10 to 15 minutes). Last, the pulse sequence should provide means for motion sensing (e.g., navigators) allowing for retrospective motion correction (unless autofocusing, as discussed below, is practical).

The demands for short pulse repetition time are best met with gradient-echo (GE) sampling, be it a spoiled fast GE (FGRE) or a fully balanced steady-state free precession (b-SSFP) sequence (87). Most clinical studies from other laboratories are based on 3D spoiled GE imaging (e.g., see Refs.76 and88). More recently, b-SSFP has emerged as a possible substitute (72, 89). All clinical work in these authors' laboratory has been performed with various versions of a 3D spin-echo technique customized for this application [fast large-angle spin echo (FLASE) (90–92)]. Another fast 3D spin-echo pulse sequence specifically designed for structural imaging of TB, called fast low-angle dual echo (FLADE) has recently been reported (93). Both GRE and b-SSFP-type pulse sequence are sensitive to off-resonance effects caused by the locally induced field gradients at the bone–bone marrow interface (albeit for different reasons) in contrast to spin-echo pulse sequences. Therefore, spin-echo techniques provide images with less intensity distortions, notably structural thickness that is closer to the actual values (89). On the other hand, the minimum scan time achievable with GRE and b-SSFP techniques is shorter since they allow for considerably shorter TR. On the other hand, in order to mitigate signal distortions from off-resonant spins, b-SSFP requires combination of the data from multiple phase-cycled acquisitions (72, 94). In terms of SNR efficiency (SNR per unit scan time), GRE is inferior to the other two pulse sequence families. Both b-SSFP and partial flip-angle spin-echo images can provide high-quality TB images (Fig. 4). Image voxel sizes reported in the literature with the various techniques range from 137 × 137 × 350 μm3 in the distal radius (74, 75) to 172 × 172 × 700 μm3 in the calcaneus (76) and 234 × 234 × 1500 μm3 in the proximal femur (77).

Figure 4.

Comparison of TB structural images obtained with two different 3D pulse sequences on the distal radial metaphysis in two different subjects at 1.5T. a: FLASE (scan time: 11.5 minutes, voxel size: 137 × 137 × 410 μm3, SNR ∼12 [Reproduced from Magland J, Vasilic B, Wehrli FW. Fast low angle dual spin-echo (FLADE): a new robust pulse sequence for structural imaging of trabecular bone. Magn Reson Med 2006;55:465–471, with permission of Wiley-Liss, Inc., a subsidiary of John Wiley & Sons, Inc.]. b: b-SSSP (scan time: four minutes, voxels size: 156 × 156 × 500 μm3, SNR ∼5, [Reproduced from Techawiboowong A, Song H, Saha P, Wehrli F. Implications of pulse sequence in structural imaging of trabecular bone. J Magn Reson Imaging 2005;22:647–655, with permission of Wiley-Liss, Inc., a subsidiary of John Wiley & Sons, Inc.]. Note signal loss artifacts in (b) on the medial and ventral side of dense trabeculation, caused by off-resonance effects of local induced gradients at the bone–bone marrow interface.

Motion Prevention and Correction

Another problem that is peculiar to very high-resolution in vivo imaging is subject motion. Clearly, movement during the scan, even on a submillimeter scale, can cause significant artifacts that can prevent correct structural information from being obtained. Even when using restraining techniques, involuntary subject movement cannot completely be prevented and retrospective motion correction techniques are needed. Usually, lower resolution is chosen in the direction of greatest translational symmetry (i.e., along the bone's macroscopic axis). Therefore, through-plane motion is usually not problematic while image corruption from translational and rotational displacements in the transverse plane can be very detrimental. Translational displacements during the scan can effectively be corrected with navigator echoes incorporated into the pulse sequence, for example by alternately measuring the displacements in the two orthogonal in-plane directions (91). Figure 5a and b show a single image slice from a 16-minute scan before and after navigator correction. In a recent study involving nearly 200 clinical scans in the author's laboratory, Vasilic et al (95) found that the average displacement during the scan is highly dependent on anatomic location, with the radius being considerably more susceptible to motion than the distal tibia, as shown from the histograms in Fig. 5c and d. Rotational motion can be equally damaging. It has been shown, for example, that a rotation as small as 1° can cause an error in the derived structural parameters as large as 20% (96).

Figure 5.

Effectiveness of translational navigator motion correction in a 3D FLASE image data set acquired in the distal tibial metaphysis of a subject at a voxel size of 137 × 137 × 410 μm3: uncorrected (a) and corrected (b) histograms of average displacement during the scan in 184 wrist (c) and 188 ankle (d) scans from ongoing clinical studies in the author's laboratory (95).

Alternative methods for translational motion correction have also been investigated. The autofocusing technique (97) allows for retrospective correction of motion occurring during the scan, therefore obviating collection of any additional data. Autofocusing is an iterative process that involves applying trial phase shifts to a small portion of data space (e.g., a few ky lines) to compensate for possible translational motion and comparing the resulting image with the original. A “focus” parameter then provides a criterion to either accept or reject the image resulting from substitution of that particular portion of k-space. Typically, a range of phase shifts is examined and the value that yields the best focus parameter value is retained. This process is then repeated by applying trial shifts to other parts of the data set. Autofocusing has also been effective for translational motion correction of in vivo TB images (98). In principle, this approach allows for correction of both translational and rotational displacements. Lin et al (99) recently showed that substantial improvements are achievable with translational and rotational autofocusing in addition to the use of translational navigator correction.


Registration and isolation of TB region.

Prior to subjecting the images to extraction of the structural parameters, several preprocessing steps are necessary, most of which can be accomplished with little or no user supervision. Input into the processing chain is typically in the form of the motion-corrected raw images. The first step ensures that the location of the analysis volume is held constant between subjects (or within subjects when repeat scans are performed, for example, to evaluate the effect of treatment). This step is important since the density, orientation, and structural characteristics of the bone is highly location dependent. To facilitate longitudinal studies requiring comparison of the baseline data with repeat scans at multiple successive time points, a graphical interface was designed that enables the user to load a baseline image and up to 10 retest scans that can then be registered either automatically or manually (95). Registration is performed by full discrete 3D translations with in-plane rotations (which typically suffice since the limb, e.g., distal forearm or tibia can easily be positioned so that it is parallel to the magnet bore). Registration then is achieved by iteratively rotating and translating the follow-up images until the difference image has reached a predetermined minimum. A screen shot of the interface is given in Fig. 6.

Figure 6.

Screenshot of the segmentation and registration routine used in the authors' laboratory. top left/right: axial and coronal slice of a baseline and follow-up scan. bottom left: difference image; bottom right: enlarged region of either the baseline or follow-up scans (95).

The second task involves the isolation of the TB region, which can be almost completely automated (e.g., see Ref.100). Here, we use a set of morphological opening and closing operators by exploiting the fact that the TB region is enclosed by a low-intensity cortical shell.

TB segmentation.

The most fundamental parameter is BVF (also denoted BV/TV = bone volume/tissue volume in histomorphometric notation). In a high-resolution low-noise image this is a trivial task since the intensity histogram is bimodal, in which case the image can be binarized by setting a threshold at the midpoint of the two modes. In this manner, high-resolution μ-MR or μ-CT images of bone specimens are typically segmented (e.g., see Ref.101). However, once the voxel size becomes comparable to the thickness of the structural elements to be resolved, then, irrespective of SNR, partial volume mixing causes histogram broadening and the two peaks coalesce into a single broad peak (73, 74). At this junction, different approaches have been practiced. Majumdar et al (73) chose an empirical threshold as a means of standardization by inverting the grayscale of the image, and setting a threshold at the intensity corresponding to 50% of histogram peak (toward lower intensity), to result in what they referred to as “apparent trabecular volume fraction,” app TB/TV. An alternative approach seeks to evaluate true TB/TV by computing the BVF maps as grayscale images in which the pixel gray value represents the fractional occupancy of bone (102, 103). One possibility is based on deconvolving the histogram. The idea is to remove the broadening caused by partial volume mixing, spatially variant receiver coil sensitivity, and noise. The desired result of this process is a noiseless image from which the marrow volume fraction (MVF) can be determined by voxel intensity summation providing the BVF as BVF = 1 – MVF. The noiseless histogram, A(I), and the measured histogram, M(I), are related by the convolution of A(I) and N(I), the transfer function of the noise, as M(I) = A(I) ⊗ N(I) where ⊗ represents the convolution operator. Hwang and Wehrli (102) conceived an iterative deconvolution method taking into account the Rician nature of magnitude MR noise. After deconvolution the histogram intensities are assigned to the image pixels on the basis of the probability of a pixel to contain bone, as well as connectivity arguments.

Another algorithm based on edge detection enables fast BVF mapping. The basic idea is to convolve the images with a discrete 2D Laplacian operator (103). The value of the Laplacian is theoretically zero at the edge separating bone from marrow. To decrease noise sensitivity, the local average of the Laplacian for each voxel intensity within a local circular region is computed and the local classification threshold determined as the intensity for which the local average Laplacian is zero. The image is then binarized and connectivity criteria are applied to remove isolated islands of bone.

Resolution enhancement.

Most methods for TB structure determination rely on binary images, whose generation, as pointed out above, is problematic. Whereas segmentation criteria such as those described previously can be used to yield some measure of BVF and binary images from which morphologic parameters are extracted, it is advantageous to first enhance resolution of the acquired images through application of appropriate interpolation algorithms. One possible approach is to make use of prior knowledge in that only two intensities are present in the absence of partial volume mixing, i.e., bone of zero intensity and marrow of given constant intensity (as long as the marrow is all fatty at the measurement site). A method that exploits these fundamentals and that allows improvement of the apparent resolution consists of partitioning the voxel into subvoxels and redistributing the bone among the subvoxels (104). Subvoxel processing is based on two assumptions: 1) smaller voxels are more likely to have high BVF (as they become more completely occupied by bone); and 2) bone is generally in close proximity to more bone. The starting point of the algorithm is the partitioning of each voxel into eight subvoxels while conserving bone mass, i.e., the total BVF in the original voxel is divided among the subvoxels. The amount allotted to a subvoxel is determined by the amount and location of bone outside the voxel but adjacent to the subvoxel. In this manner bone tends to be sequestered in the area of the voxel that is closest to other bone. Therefore, the subvoxel method simulates data acquisition on a finer digital grid. The processing steps involving masking to isolate TB region, followed by BVF mapping and subvoxel processing are illustrated in Fig. 7.

Figure 7.

Preprocessing steps involving masking to select TB region (a); BVF mapped imaging with grayscale representing fractional bone volume in each pixel (b); and subvoxel processing (c). The subvoxel processed image indicates position of virtual core from which the 3D projection image (d) was derived. The virtual core illustrates the plate-like, highly tubular architecture characteristic of the distal tibia in this 51 year-old man who has normal BMD.

Quantitative Characterization of 3D Trabecular Bone Architecture

The methodology for quantifying trabecular networks dates back more than three decades, well before the advent of nondestructive imaging. Whitehouse (53) and Raux et al (105) measured area fraction, thickness, spacing, and orientation of trabeculae in optical images obtained from stained histologic sections using the principles of stereology (106), methods still widely used in bone research. In stereology, 3D information is derived from 2D sections. It is therefore obvious that the reduced dimensionality can have significant implications in that faithful reconstruction of the third dimension hinges on the correctness of certain assumptions, i.e., the method is model based.

Before we proceed further in discussing advanced structure analysis algorithms that are applicable to the characterization of TB networks from 3D in vivo images, it is helpful to divide the different types of structural parameters into those that characterize (1) scale, (2) orientation, and (3) topology. Examples of parameters of scale are TB thickness and volume fraction. Topology is the branch of mathematics concerned with the geometric properties of deformable objects (107). For example, topological criteria allow us to determine the number of loops or nodes in the network. To illustrate the difference between topology and scale, consider a TB network that undergoes slight uniform thickening. Topologically, the network remains unaltered but the scale properties have changed. Conversely, if a connection was broken or a plate perforated, the two networks would differ in topology. The third class of structural parameters relates to network orientation. Consider a deformable isotropic structure that is stretched in a predefined direction. This operation would not alter the object's topology but would increase the spacing between neighboring structural elements along the direction of stretching, i.e., it would cause structural anisotropy. The three classes of parameters are illustrated in Fig. 8.

Figure 8.

Structural parameters used to characterize TB networks can be divided into three classes: scale, orientation, and topology, all of which are relevant in conferring mechanical properties to the bone.

Last, in order to be practical, structural measures have to be robust by being derivable from images acquired in vivo, i.e., in a regime of limited resolution and SNR as well as intensity nonuniformities that are present in surface-coil images. While, as we shall see, it is possible with appropriate algorithms, to obtain accurate estimates of TB thickness and BVF, topological quantities are inherently susceptible to the resolution at which the data have been acquired.

Measurements of Scale

Parfitt et al (108) conceived a simple model of TB consisting of parallel interconnected plates that can be characterized on the basis of images from histologic sections. In spite of their simplicity, these parameters remain the mainstay of structural analysis on the basis of light microscopic images from stained embedded section of TB. Kleerekoper et al (109) showed that these empirical measures of structural competence were useful discriminators of subjects with from those without osteoporotic fractures when densitometric measures failed to discriminate the groups.

We have already addressed the measurement of TB volume fraction. The second scale parameter of interest is TB thickness for which both 2D and 3D algorithms are being practiced. In 2D, thickness is typically measured by treating a trabecula as an elongated structure. Under these circumstances TB thickness (trabecular thickness TB.Th) is obtained as TB area divided by one-half of the perimeter (110), or even simpler, TB area is divided by the length of the skeleton network. Thickness can also be obtained as the mean intercept length (MIL) of parallel test lines across trabeculae, and these quantities can be averaged over all angles of the test lines. Analogous approaches also yield TB separation (TB.Sp, the average distance between adjacent trabeculae) and trabecular number (TB.N, defined as the reciprocal of the distance between the centers of adjacent trabeculae). Chung et al (101) and Majumdar et al (111) later adapted these methods for automated processing of digital images.

While at high resolution where TB.Th ≪ pixel size holds, this approach yields accurate values, at in vivo resolution where TB.Th ∼ pixel size, the resulting parameters are typically denoted “apparent” (112). These 2D methods have since been superseded by 3D approaches. One such method is the distance transform, the principle of which is to inscribe the largest sphere inside the trabecula (113). Mean thickness then is obtained as twice the radius averaged over all points on the midline of the TB network. This method has since been adopted for processing of in vivo TB imaging data to yield model-independent measures of app TB.Th and TB.N (114).

The limitations of the simple distance transform is that it is not amenable to grayscale images such as BVF maps. Saha et al (115) conceived a method denoted fuzzy distance transform (FDT) that obviates the need to binarize the images, which, as we have seen, is fraught with problems in the limited spatial resolution regime of in vivo MRI. Whereas in binary images the shortest path between two points is simply the length of the straight-line segment joining them, in a grayscale image of a fuzzy object the shortest path must be evaluated by considering all paths joining them. The length of a path in a fuzzy object such as a grayscale BVF map is the intensity (i.e., BVF)-weighted line integral along the path, the rationale being that pixels representing reduced BVF (due to partial volume averaging) be assigned weight proportional to voxel BVF. The fuzzy distance between two points is then computed as the minimum length of all paths between the two points. TB.Th is obtained by computing the fuzzy distance to the boundary along the medial axis of the target object (i.e., trabeculae). Details of the algorithm are given in Ref.115 and its application to TB is described in Ref.116. The method was found to be extremely robust to noise and is accurate over a wide range of resolutions and the algorithm was found to be able to retrieve small changes in response to treatment. A case in point is an experimental study in a rabbit model of steroid-induced osteoporosis in which short-term effects of exposure to dexamethasone were examined (117). Although imperceptible to the eye, the serial changes in average TB.Th over a period of eight weeks could unambiguously be determined, in good agreement with ex vivo μ-CT data (20).


As pointed out previously, homogeneous thinning of a trabecular structure, while affecting parameters of scale (TB thickness and volume fraction), does not entail a change in the structure's topology as long as no connections are broken or a trabecular plate is perforated. The mechanism of osteoporosis secondary to gonadal steroid depletion (e.g., postmenopausal osteoporosis) involves gradual deepening of osteoclastic resorption pits that eventually lead to fenestration of plates and disconnection of rods. Thus bone loss is often compounded by disproportionately large topological changes (108, 118–120). Feldkamp et al (57) showed that TB network connectivity can be expressed in terms its topological characteristics. One such measure is the Euler-Poincaré characteristic, χ, given as X = β0 − β1 + β1 to quantify network connectivity. Quantities β0, β1 and β2 are the Betti numbers, representing the number of objects, handles (loops), and cavities that remain invariant under rubber-sheet transformation. Trabecular bone consists of a single object (there are no free-floating trabeculae), nor are there cavities (i.e., marrow spaces completely enclosed by bone, hence β0 = 1 and β2 = 0. A well-connected network has a large negative Euler number, which becomes less negative as connections are broken. Often, connectivity density is expressed as β1 = 1 − X (120). Feldkamp et al (57) presented an algorithm for computing the 3D Euler number from digital images by resorting to voxel connectivity arguments, a method which has been used widely to study the effect of bone loss on architecture (120–122).

It is plausible that at a given BVF a well-connected network is stronger. For example, disruption of a trabecular rod reduces the number of loops by one, thus decreasing connectivity. However, it becomes obvious that connectivity based on the Euler number has inherent flaws. Consider, for example, a TB plate becoming perforated as a result of local thinning. Such a process, characteristic of postmenopausal osteoporosis, would then, in terms of the definition, increase connectivity by creation of an additional loop.

Since the transformation of plate-like to rod-like trabeculae is a hallmark of age-related changes that occur in the skeleton, analysis methods that can capture and quantify this process on the basis of 3D images would be highly desirable. One such approach is the Structure-Model Index (SMI) (60, 123). It is based on the notion that the partial derivative ∂s/∂r, with s and r representing the surface and “radius” of a structural element, is a function of the element's curvature. It is obvious that the relative surface change upon radial expansion is largest for an element of circular cross-section (i.e., a “rod”) and smallest for a plate. This elegant method has been used successfully for the characterization of structures derived from μ-CT images (60). An example of the SMI applied to two visually different specimens of calcaneal TB is shown in Fig. 9. The method, however, is less suited for analysis of in vivo images since it requires an accurate surface representation of the structure, which is difficult to achieve at in vivo resolution. A similar idea applicable to 2D images the TB pattern factor (TBPf), which is a parameter conceived on the basis of the notion that the perimeter of a structure increases upon dilation if it is convex, but decreases if it is concave. The TBPf then is calculated as ∂P/∂A, i.e., the differential change in perimeter, P, relative to the change in bone area, A, as the 2D bone section is dilated (124). An intact, well-connected TB network has predominantly concave elements, whereas heavily eroded structures have more convex elements.

Figure 9.

3D rendition of μ-CT images of cadaver specimens of bone from the calcaneus, illustrating the age-related changes in trabecular architecture, notably, the conversion of plates to rods, which can be expressed in terms of SMI, which was 1.1 (a) and 2.3 (b) [Reproduced from Hildebrand T, Laib A, Muller R, Dequeker J, Ruegsegger P. Direct three-dimensional morphometric analysis of human cancellous bone: microstructural data from spine, femur, iliac crest, and calcaneus. J Bone Miner Res 1999;14:1167–1174, with permission].

Another method, designed for unambiguous determination of the topological classes of digitized structures is digital topological analysis (DTA) (125). DTA has more recently been applied to digital images of TB (126, 127). DTA relies on the three local topological entities described above; i.e., the numbers of objects, handles, and cavities, except that these relationships are examined for each bone voxel in its 3 × 3 × 3 neighborhood consisting of 26 neighboring voxels. The process initially involves conversion of the 3D structure to a skeletonized surface representation, which consists of only 1D and 2D structures (i.e., curves and surfaces). Each voxel is then classified in a three-step approach as belonging to a curve, surface, or junction (or intersections between these three basic classes). The local topology is established for the central bone voxel on the basis of the number of objects, handles, and cavities in the bone structure after this central voxel has been replaced by marrow. The topological classes can be determined from the number of objects, tunnels, and cavities using look-up tables (except for some classes in which a more extended neighborhood has to be examined). The resulting classes are curve interior (C), curve edges (CE), curve–curve junctions (CC), surface interior (S), surface edges (SE), surface–surface junctions (SS), and surface–curve junctions (SC). In addition, a profile class (P) has been defined as a voxel pertaining to a two-voxel ribbon having no neighboring S-type, SC-type, or SS-type voxels. Analogous to curves, there exist profile-interior (PI) and profile-edge (PE) voxel classes.

Next to the simple topological parameters defined above, composite parameters prove to be useful as discriminators of different structural arrangements (126). One is the surface-to-curve ratio (S/C), which is the ratio of the sum of all surface-type voxels (S, SE, SS, and SC) divided by the sum of curve-type voxels (C, CE, and CC). This ratio has been shown to be a sensitive indicator for the conversion of plates to rods. Similarly, the erosion index (EI) is defined as the ratio of the sum of parameters expected to increase upon osteoclastic resorption (e.g., CE- and SE-types), divided by the sum of parameters expected to decrease upon such processes (e.g., S-type). Perforation of plates, for example, decreases the number of surface-interior voxels. Likewise, disruption of rods decreases the number of curve-interior (C-type) while increasing the number of curve-edge (CE-type) voxels. The principle of DTA is illustrated in Fig. 10.

Figure 10.

a: Hypothetical digitized structure of portion of TB after binarization and skeletonization with voxel topological classes indicated. b: 3D rendition of TB core. c: Cubic subregion of (b). d: Skeleton representation and topological assignment using the color coding in (a).

Pothuaud et al (128, 129) conceived a method which is somewhat akin to the DTA approach. Here, the images are processed to yield a 3D skeleton line graph from which topological indices are determined. One limitation of this approach is that no distinction is made in the treatment of plates and rods during the skeletonization process.

Structural Anisotropy

The structural anisotropy, most manifest in the preferred orientation of the trabeculae, is a direct consequence of Wolff's (130) law that conveys that bone models and remodels in response to the stresses to which it is subjected. Hence, it is plausible that the trabeculae preferentially orient along the major stress lines. Odgaard et al (131) provided quantitative evidence by showing that the mechanical principal directions are aligned with those obtained by 3D structure analysis. Whitehouse (53) was perhaps the first to devise a method for quantifying TB structural anisotropy by showing that the MIL between trabeculae varies as a function of test-line direction. When plotted on a polar diagram, MIL was found to map an ellipse. Harrigan and Mann (132) extended this approach to three dimensions, showing that anisotropy can be expressed in terms of eigenvalues and eigenvectors of a second-rank tensor. Toward this goal he mapped MIL on three orthogonal surfaces of a cubic sample of bone, from which eigenvalues and eigenvectors of the structure's fabric (the tensorial representation of structural anisotropy) could be computed.

Structural orientation has since then received a great deal of attention as an independent predictor of the bone's mechanical properties. Turner (133), for example, found that TB density-weighted anisotropy explained 90% of the variance in yield strain. There is also evidence that TB loss in itself is anisotropic. Mosekilde (134) found that the decrease in mechanical competence upon bone loss in the vertebrae is exacerbated by preferential loss of transverse trabeculae, rendering the bone prone to failure by buckling. The preferential loss of transverse trabeculae appears to be a hallmark of osteoporosis occurring at other skeletal locations as well, such as in the proximal femur where subjects with hip fractures were found to have fewer trabeculae perpendicular to the major loading direction (135).

The most common among the methods conceived to quantify fabric is the MIL method. Analogous to the 2D problem, the MIL (across marrow or bone) is computed as a function of polar and azimuthal angle. The data are subsequently transformed to a Cartesian frame and fit to the equation of an ellipsoid. Chung et al (136) first applied this approach to map the fabric tensor of bovine tibia and human trabecular vertebral and radial bone on the basis of 3D μ-MR images from specimens.

Gomberg et al (137) conceived a method that is based on DTA as a means to quantify structural orientation. In an isotropic network of TB plates the surface normals are randomly distributed. However, if the structure is anisotropic, the surface normals have a preferential direction. Since DTA unambiguously identifies voxels belonging to surfaces, a regional surface normal can be determined by fitting a plane through the voxels constituting a local neighborhood. Modeling regional distributions of these vectors then allows assessment of anisotropy measures, such as mean and variance of the orientation distribution. Similarly, straight lines can be fit through curves (resulting from skeletonization of rods) and thus the orientation of rods determined separately from those of TB plates.

The quasiregular nature of the TB network offers yet another approach toward quantification of fabric. It is based upon computing the 3D spatial autocorrelation function (ACF) (138). Further, Autocorrelation (AC) is applicable to grayscale images, thus obviating the need for binarization. The underlying idea is that the trabecular network can be treated as a quasiperiodic lattice (139). For such a lattice, the first peak of the ACF occurs at the lattice spacing whereas the full-width at half-maximum (FWHM) is a measure of structural thickness. Rotter et al (140) proposed AC analysis as a means of characterizing TB. More recently, Wald et al (138) worked out an algorithm for mapping the full anisotropy ellipsoid for TB thickness and spacing from in vivo MRIs.

A perhaps even more promising approach for quantifying trabecular architecture that is able to provide information on scale (e.g., thickness of structural elements), topology (plate- vs. rod-like architecture), and orientation (structural anisotropy), is tensor scale (141, 142). The local scale using a tensor model (an ellipse in 2D and an ellipsoid in 3D) provides a parametric representation of size, orientation, and anisotropy of local structures and is thus well suited to characterize TB networks. Regional structure is represented by a local best-fit ellipsoid (ellipse in 2D) and the structural orientation is determined from the eigenvectors along the semiaxes. The method was found to be remarkably robust over a wide range of resolution regimes and is thus applicable to in vivo imaging of TB structure. A convenient way to display the anisotropic properties of the bone is by means of a hue-saturation-intensity (HSI) color coding scheme of the color vector at any pixel encodes orientation, anisotropy, and thickness, respectively, while regional anisotropy is obtained from rose plots (Fig. 11). The current implementation is in 2D but its extension to 3D should be relatively straightforward. The method is remarkably robust to resolution in that in spite of the four-fold decrease in linear resolution (from 22 to 88 μm) neither the orientation of the principal axes nor the anisotropy was found to change significantly (83.99 vs. 83.62 degrees and 0.8978 vs. 0.8949, respectively).

Figure 11.

Tensor-scale-based TB anisotropy at various resolutions. a: Longitudinal 2D bone volume-fraction map derived from a μCT image of TB (22 μm isotropic resolution) of a cadaver specimen from the distal radius showing significant anisotropy along the radial axis. b: Same data resampled at 88 μm isotropic resolution. c,d: Color-coded tensor-scale images of (a) and (b). e: HSI color coding to represent t-scale images. f: Orientation rose plots (thick lines) and fitted anisotropy ellipses (thin lines) obtained for images corresponding to 22 and 88 μm isotropic voxel size showing the method's immunity to image resolution [Reproduced from Saha PK, Wehrli FW. A robust method for measuring trabecular bone orientation ansiotrophy at in vivo resolution using tensor scale. Pattern Recognit 2004;37:1935–1944, with permission].


Fracture Discrimination

Most high-resolution quantitative MR studies reported so far focus on three issues of pivotal clinical relevance: The first is the association between structure and fracture incidence/risk (70, 74–76, 143). The second is concerned with the structural implications of drug treatment (68, 88, 144–146). The third deals with differential diagnosis in metabolic bone disease, such as ROD, in which different forms of the disease have to be distinguished, such as adynamic bone disease from osteitis fibrosa (147).

There is now clear evidence that the findings from histomorphometry, suggesting that inclusion of structural parameters substantially improves the discrimination of patients with osteoporotic fractures from their unfractured peers, are equally true for measurements obtained in vivo at much lower resolution (71, 74–76, 143, 148, 149). Several of these studies now provide compelling evidence for the independent role of architecture as a predictor of bone strength. A recent study performed on 79 postmenopausal women, of whom 29 had vertebral fractures, topological parameters, derived from high-resolution μ-MRI of the distal radius acquired at 137 × 137 × 350 μm3 voxel size with the previously discussed FLASE 3D spin-echo sequence, showed strong associations with vertebral fracture status (75). Vertebral fractures were determined by measuring the total vertebral deformity load by performing morphometric measurements on midline sagittal images and setting a threshold in order to divide the subjects into fracture and control group. Topological parameter densities were computed as described in the previous sections. Further, DTA parameters were compared with integral BMD in the lumbar spine and femur. DTA structural indices were found to be the strongest discriminators of subjects with fractures from those without fractures. Subjects with fractures had lower topological surface density (P < 0.0005) and surface-to-curve ratio, a measure of the ratio of plate-like to rod-like trabeculae (P < 0.0005), than those without fractures. Similarly, the topological EI was higher in the fracture group (P = 0.001). While the BMD of the lumbar vertebrae was lower in the fracture group, the association was less strong than that of some of the topological parameters.

In an ongoing follow-up study designed to test the hypothesis that TB architecture contributes to fracture susceptibility independently of BMD, 46 postmenopausal women were examined by μ-MRI (150) using a protocol similar to that described above and in Ref.75. However, only patients were included who had DEXA bone density T-scores within the range T = −2.5 ± 1.0 to minimize confounding effects from variations in BMD. The total vertebral deformity load was measured on the basis of spin-echo images of the lumbar and thoracic vertebrae, similar to the prior study, and a spinal deformity index (SDI) computed as a continuous variable (75). High-resolution μ-MRI was conducted at two surrogate sites (distal radius and tibia) and the 3D FLASE images obtained at 137 × 137 × 410 μm3 voxel size were subjected to the usual cascade of processing steps, including BVF mapping, subvoxel processing, and skeletonization. The derived DTA structural indices as well as TB.Th and TB/TV were then correlated with the SDI to examine possible associations of vertebral deformity with structure at one of the surrogate sites (Fig. 12). The data show that many of the structural indices were correlated with SDI, some negatively, as would be expected [e.g., BVF, TB.Th, surface density (S), surface-to-curve ratio (S/C)], some positively [e.g., curve density (C) and EI]. The data are commensurate with the notion that a plate-like network (high topological surface density and S/C) is stronger than a more strut-like network (high EI, low S/C). Lastly, it is interesting that there was no significant correlation between SDI and vertebral BMD.

Figure 12.

Correlation coefficients of associations between structural parameters, determined at the distal radius and tibia, and SDI, as the dependent variable (N = 46). Structural measures of scale are BVF and TB.Th, the other parameters are DTA voxel densities (J = junctions, S = surfaces, C = curves, S/C = surface-to-curve ratio, EI = erosion index, discussed earlier). Bars to the right represent results from two-parameter regression. All associations were significant (P = 0.0001 to 0.05).

Further support for the notion of structure's role in fracture resistance has also been provided by another group (76) in a study involving 50 men (26 patients with osteoporosis and 24 age-matched healthy control subjects). Images were obtained in the calcaneus with a b-SSFP sequence at 172 × 172 × 700 μm3 voxel size in 19 minutes scan time. Besides the more conventional histomorphometric indices (apparent TB/TV, TB.Th, and TB.N), a series of parameters, including apparent node-to-node and node-to-terminus count, were derived after the images had been converted to 2D skeleton graphs. In addition, a topological quantity, the TB pattern factor, described previously, was determined. A total of 13 of the 20 structural parameters, especially connectivity parameters, were significantly different in the two groups. Interestingly, when the data were adjusted for differences in BMD, many of the parameters, in particular those related to skeleton characteristics, remained highly significant differentiators of fracture from nonfracture subjects.

Treatment Response Monitoring

So far, the only metric accepted by the U.S. Food and Drug Administration (FDA) as an endpoint to assess the efficacy of treatment is fracture reduction. Since acute fractures are relatively rare events, such efficacy studies in Phase-III trials demand very large numbers of subjects and are therefore extremely costly. So far, BMD has traditionally been used as a secondary endpoint, with often unsatisfactory results. In fact, several studies indicate that the changes in BMD in response to antiresorptive treatment are disproportionately small relative to the rate of fracture reduction (151, 152). For example, in the MORE trial involving 7700 women, three years of treatment with raloxifene (a selective estrogen receptor modulator) were found to result in a reduction in vertebral fracture risk of 40%. However, the incremental increases in BMD accounted for only 4% of the observed risk reduction (151)! Riggs and Melton (153) conjectured that the effect of antiresorptive treatment, by virtue of reducing bone turnover, prevents perforative osteoclastic resorption, therefore explaining why less potent drugs such as raloxifene or calcitonin, can be effective in substantially reducing vertebral fracture risk in spite of their only marginal effect on BMD. Thus, the availability of surrogate endpoints such as some measure of structure—in particular if it can be achieved without subjecting the patient to repeat bone biopsies—would be highly desirable. At the time of writing of this article, numerous studies are either in preparation or already in progress in various laboratories.

Application of μ-MRI toward the goal of monitoring the effect of treatment is particularly challenging as it puts more stringent demands on measurement reproducibility (96, 100), which determines the number of study subjects needed to achieve a desired statistical power. While the random errors from noise are usually small at a given SNR (<1%), the derived parameters themselves prove to be dependent on absolute SNR (95). Besides interscan variations in SNR, major sources of error result from inadequate registration and uncorrected subject motion (96), both of which have been discussed in previous sections. Increasing SNR with concomitantly reduced resolution improves reproducibility, albeit at the expense of sensitivity to detect an effect. Thus, reproducibility alone, expressed, for example, in terms of the coefficient of variation from repeat measurements may be deceptive. A more appropriate metric may be the concordance correlation coefficient or the intraclass correlation coefficient, both relating the intrasubject to the intersubject variances (154). Newitt et al (100) found coefficients of variation for 2D morphometric parameters ranging from 3.4% to 8.3% as derived in the radius of seven subjects, each scanned three times. In a more recent study aimed at evaluating the precision of structural parameters measured in the distal tibia and radius, Gomberg et al (96) reported average coefficients of variation of 4% to 7% after correction for translational motion via navigators.

Several studies reported during the past four years examine the structural implications of antiresorptive treatment (68, 88, 144, 145). Benito et al (68) studied the effect of testosterone treatment on architecture in the distal tibial metaphysis of 10 severely testosterone-deficient hypogonadal men and their age-matched controls by means of μ-MRI evaluating DTA and measures of scale at baseline, and at six, 12, and 24 months. The data showed significant changes in the topological densities for surface-to-curve ratio (−11.2%, P < 0.005) and EI (+7.5%, P < 0.005) at 24 months but no changes in the control group (Fig. 13a and b). The results suggest that antiresorptive treatment results in improved structural integrity, i.e., an increase in the bone's “platelikeness” (increased S/C) and network connectivity (decreased EI); i.e., an anabolic effect. Such an effect is consistent with the notion that drug-induced bone accretion can either fill a whole in a TB plate or cause sufficient expansion of two adjacent trabeculae sharing nodes (Fig. 13c and d). Hence the relatively small increase in BVF (+5.0%, P < 0.001) can have a much larger effect on network topology.

Figure 13.

Registered virtual cores from one hypogonadal subject at baseline (a) and after 24 months of testosterone treatment (b) in subject with largest changes in topology from baseline. Matching individual structural elements are clearly discernable at both time points (ellipses) as well as remodeling-induced changes, including closure of resorption pits (rectangles) [from Benito M, Vasilic B, Wehrli FW, et al. Effect of testosterone replacement on bone architecture in hypogonadal men. J Bone Miner Res 2005;20:1785, modified]. c,d: Model illustrating possible mechanism causing changes in topology leading to conversion of curves to surfaces (i.e., increase in surface/curve ratio); two adjacent trabeculae forming a loop (c); bone accretion causes merging of the two trabecular elements to form a plate (d). Dashed line represents skeleton.

Another study, currently in progress, involving drug intervention and using similar methodology, seeks to assess the effect of estradiol/progestin in early postmenopausal women, to test the hypothesis that hormone replacement therapy (HRT) preserves the trabecular network (146). In brief, images were collected at baseline and 11–13 months with preliminary results for 29 control and 17 HRT subjects that afforded images of adequate quality. Scale parameters at the tibia were not significant while DTA parameters PE (profile edges, essentially free strut ends), curves, S/C, and EI provided highly significant changes (P < 0.0001 to < 0.005) ranging from 8.0% to 9.5% in control subjects while no changes were observed in the HRT group. Similarly, DEXA BMD in the spine (hip) decreased 2.7% (1.4%) in controls (P < 0.0001–0.001) (though less than DTA parameters) but not in HRT subjects. These findings, not previously observed in vivo, are consistent with the known protective effects of HRT ensuring maintenance of a more plate-like TB architecture.

A larger study, using different methodology, dealt with the structural manifestation of treatment of postmenopausal women with salmon calcitonin (a hormone that reduces bone turnover and osteoclastic resorption) (88). Calcitonin, as pointed out previously, only minimally increases BMD in spite of the relatively large reduction in vertebral fracture risk it entails (152). Thus, it is of particular interest whether the mechanism of action affects bone quality in some other way, such as by positively impacting on architectural integrity. In brief, trabecular microarchitecture was assessed at the distal radius, calcaneus and hip in 91 postmenopausal osteoporotic women receiving nasal spray salmon calcitonin (N = 46) or placebo (45) over two years. BMD was evaluated by DEXA at multiple sites and iliac crest bone biopsies were obtained at baseline and after two years (right and left side, respectively, analyzed by μ-CT or histomorphometry). μ-MRI was performed at 1.5T with a 3D GE sequence at 156 × 156 × 500 μm3 in the radius and 195 × 195 × 500 μm3 in the calcaneus. Interestingly, no structural changes were observed in the bone biopsies. However, several parameters in the placebo group indicated significant deterioration of the TB network, such as decreased apparent BV/TV and trabecular number and increased trabecular separation. Of particular interest are the large regional differences in the observed effects, with the more proximal regions of the distal radial metaphysis being more sensitive than the more distal counterparts. For example, app. TB.N decreased 6.9% (P = 0.005) in the most proximal region while no significant effect was seen in the most distal region. Similarly, for TB.S was found to increase 12.9% in the most proximal but no effect was observed at the most distal analysis region. By and large, no significant changes were observed in the treatment group, essentially indicating that treatment preserved the TB network.

The above studies indicate that in spite of the limited resolution achievable currently, in vivo structure assessment by μ-MRI is feasible and capable of detecting relatively subtle but highly significant changes in the absence of, or in response to, treatment. The detected changes are in agreement with those found in animal studies of osteoporosis, suggesting that bone loss entails topological changes involving fenestration of trabecular plates and their conversion to rod-like trabeculae, which eventually become disconnected. The data further lend support to the independent role of structure in determining TB's fracture susceptibility.


The growing recognition of the role of parameters other than BMD in determining bone strength and fracture susceptibility has spurred the search for metrics associated with bone quality, in particular those that can be obtained noninvasively. Central among these is architecture, relating to both trabecular and CB. High-resolution MRI, in conjunction with advanced image processing and analysis techniques, capable of extracting structural information at the limited spatial resolution achievable in vivo, has demonstrated significant potential for this task. Recent data from various clinical pilot studies show promise for these methods as possible means to predict fracture risk and for evaluating the effect of intervention in patients undergoing treatment for osteoporosis. Current limitations are availability and cost but these are likely to be overcome with the development of dedicated instruments.


The author is indebted to Drs. G. Ladinsky, P.K. Saha, B. Vasilic, Aranee Techawiboonwong, and Michael Wald for their assistance and advice during preparation of the manuscript.